Design method of concrete-filled steel tubular composite column-concealed ring beam joint based on force method

Abstract

The application discloses a design method of a steel pipe concrete composite column-hidden ring beam joint based on a force method, and belongs to the technical field of building structure engineering. According to the connecting form of the frame beam and the steel pipe concrete composite column, the method divides the joint into a single-axis arranged beam joint and a double-axis arranged beam joint; by determining parameters such as the geometric size of the joint, material performance and frame beam tension, the hidden ring beam reinforcement framework is equivalent to a circular curved rod with equal cross sections embedded in the pipe outer concrete, an internal force analysis model is established, the section axial force, shear force and bending moment are calculated; the stirrup participation coefficient is introduced, and the adjustment coefficient of the beneficial role of the floor and the constraint strengthening coefficient of the pipe outer concrete are combined to establish a ring reinforcement formula and a simplified design formula suitable for the symmetric equal reinforcement condition of the inner and outer ring-shaped reinforcements. The method can be used for the reinforcement design and bearing capacity checking of the hidden ring beam joint, and has good engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of structural engineering technology, specifically relating to a design method for steel-concrete composite column-hidden ring beam joint based on the force method. Background Technology

[0002] Steel-concrete composite columns (ST-RC), a composite structural form combining a steel-concrete core column with an outer reinforced concrete casing, possess characteristics of high load-bearing capacity, good ductility, and excellent fire and corrosion resistance. They have been successfully applied in important projects in my country. In frame structures, beam-column joints are crucial for ensuring the overall structural performance and seismic safety; the rationality of their construction directly affects construction efficiency, structural reliability, and economy.

[0003] Currently, the connection between ST-RC columns and RC beams mainly follows the "Technical Specification for Steel-Concrete Composite Column Structures" (T / CECS188-2019). Common practices include drilling holes in the steel pipes to allow the longitudinal reinforcement of the frame beams to pass through, or welding steel components to the outside of the pipes to connect with the longitudinal reinforcement of the frame beams. Although these traditional methods can achieve force transmission at the joints, they have problems such as large on-site welding workload, weakening the integrity of the core concrete by drilling holes in the steel pipes, and complex construction procedures, which restrict the promotion and application of ST-RC structural systems and the improvement of their economic efficiency.

[0004] To overcome the aforementioned shortcomings, the academic and engineering communities have successively proposed various improved structures such as externally reinforced joints, ring beam joints, and sleeve connections, which have improved the seismic performance of the joints to some extent. However, these joint structures still suffer from problems such as large on-site welding volume, complex construction, and limited applicability, restricting the promotion and application of the ST-RC structural system in a wider range of engineering fields. Therefore, there is an urgent need to develop a new type of beam-column joint that is simple in construction, convenient to build, does not affect the integrity of the steel pipe, and can effectively transfer the bending moment and shear force at the beam ends of the frame beam, in order to meet the higher requirements of modern building structures for safety, economy, and construction efficiency. Against this background, the concealed ring beam joint, by setting a concealed ring beam composed of inner and outer ring reinforcements and concealed ring beam stirrups in the steel-concrete composite column, and anchoring it to the longitudinal reinforcement of the frame beam with a snap-fit ​​method, significantly enhances the integrity, stiffness, and anchorage reliability of the joint, achieving a strong joint effect with uniform stress, reasonable structure, and convenient construction.

[0005] This invention relates to a design method for this type of steel-concrete composite column-concealed ring beam joint. It should be noted that the concealed ring beam joint itself, as an innovative structural form, has its specific structural features, arrangement, and construction process protected by utility model patent application number 2024200987775. However, how to provide a matching, quantitative design method that can be directly used in engineering design remains a technical problem that needs to be solved by those in the industry. Summary of the Invention

[0006] To address the problems of complex construction, weakened integrity due to openings in the steel tubes, large on-site welding workload, and difficulty in ensuring joint stiffness in existing steel-concrete composite column-reinforced concrete beam connection methods, this invention provides a force-based design method for steel-concrete composite column-concealed ring beam joints. This method, based on the force transmission mechanism of the embedded concealed ring beam reinforcement skeleton, establishes practical design formulas applicable to both uniaxial and biaxial beam joints through theoretical derivation and experimental verification. This achieves the seismic design goal of "strong joints, weak components" and significantly improves construction efficiency and economy. To achieve the above objectives, this invention adopts the following technical solution:

[0007] Determine the node design parameters: including the steel pipe radius. , cross-sectional width of steel-concrete composite column Frame beam section height Area of ​​ring reinforcement in concealed ring beam Yield strength of ring reinforcement in concealed ring beam Area of ​​stirrups in concealed ring beam Spacing Longitudinal reinforcement area of ​​frame beams Yield strength of longitudinal reinforcement in frame beams Elastic modulus of steel bars ;

[0008] Based on the structural mechanics force method, a force analysis model of the steel reinforcement cage of the hidden ring beam is established. The hidden ring beam is equivalent to a circular curved bar with a uniform cross section. Due to its symmetry, a formula for calculating the internal force of the hidden ring beam cross section is established to calculate the internal force of the hidden ring beam cross section.

[0009] Based on the determined node design parameters, a collaborative model of the stirrups in the concealed ring beam is established to quantify the enhancing effect of the stirrups on the overall stiffness of the concealed ring beam's steel reinforcement cage, and a participation factor for the stirrups in the concealed ring beam is introduced. ;

[0010] Based on node design parameters and the participation factor of stirrups in the concealed ring beam Calculate the section moment of the steel reinforcement cage of the concealed ring beam. ;

[0011] Based on the material mechanics strength conditions and the section moment of the steel reinforcement cage of the hidden ring beam Internal forces in the cross section, and establish the maximum circumferential tensile normal stress of the ring reinforcement in the hidden ring beam. Verification formula;

[0012] Based on the maximum circumferential tensile normal stress of the ring reinforcement of the hidden ring beam The verification formula is combined with the internal forces of the section and the participation factor of the stirrups in the hidden ring beam. Introducing a floor slab beneficial effect adjustment coefficient With the external concrete confinement strengthening coefficient Under the condition that the inner and outer ring reinforcements are symmetrically and equally reinforced, establish the area of ​​the ring reinforcement of the hidden ring beam. Calculation formula.

[0013] The area of ​​the ring-shaped reinforcing steel in the hidden ring beam The calculation formula is simplified to the area of ​​the ring reinforcement in the concealed ring beam. Total area of ​​longitudinal reinforcement in frame beams The direct proportional relationship leads to a practical and simplified design formula applicable to the condition that the strength grades of the ring reinforcement in the concealed ring beam and the longitudinal reinforcement in the frame beam are the same.

[0014] Furthermore, the design method of the steel-concrete composite column-hidden ring beam joint is based on the following assumptions: 1) The hidden ring beam is equivalent to a circular curved rod with a uniform cross-section embedded in the concrete outside the steel-concrete composite column tube; 2) The upper half of the hidden ring beam joint is under tension and the lower half is under compression; 3) The material is isotropic and satisfies the plane section assumption.

[0015] Furthermore, the confinement strengthening coefficient of the concrete outside the steel-concrete composite column. The value is 1.1.

[0016] Furthermore, the internal forces of the concealed ring beam section are calculated using the following formula:

[0017] ;

[0018] ;

[0019] ;

[0020] In the formula, The axial force at the section of the hidden ring beam; Shear force at the section of the concealed ring beam; The bending moment of the hidden ring beam section; , is the tensile force value when the longitudinal reinforcement of the frame beam yields; This represents the radial reaction force of the steel pipe wall on the hidden ring beam. The position angle of the hidden ring beam section, with a value range of [value missing]. Based on the arrangement of the frame beams relative to the steel-concrete composite columns in the nodes, the node types are classified, including at least single-axis beam nodes with frame beams connected on one side and double-axis beam nodes with frame beams connected on both sides along the same axial direction, and double-axis beam nodes with frame beams connected to the steel-concrete composite columns along two mutually orthogonal axial directions. The determination is based on the node type: for single-axis beam nodes, F = 0.75P; for double-axis beam nodes, F = P. Calculate the radius of the hidden ring beam b r =0.85*(b c / 2-r), which is the effective width of the hidden ring beam.

[0021] Furthermore, a stirrup participation factor for the concealed ring beam is introduced. The approach involves using a shear lag model and partial shear interaction theory to treat the stirrups of the concealed ring beam as equivalent to radial elastic constraints distributed along the circumferential direction of the concealed ring beam, and establishing the stirrup participation factor of the concealed ring beam. To characterize the degree to which the stirrups of the concealed ring beam enhance the synergistic effect of the inner and outer ring reinforcements:

[0022] ;

[0023] in:

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] In the formula, The equivalent tangential stiffness of the stirrups in the concealed ring beam; The characteristic length; This represents the equivalent area of ​​the ring reinforcement in the concealed ring beam. These are the cross-sectional areas of the outer and inner ring reinforcement bars of the concealed ring beam, respectively. The radial length of the stirrups in the concealed ring beam can be taken as the effective width of the concealed ring beam. ; The Poisson's ratio for steel reinforcement.

[0029] Furthermore, the section moment of the hidden ring beam reinforcement cage Calculate using the following formula:

[0030] ;

[0031] In the formula, and These are the moments of inertia of the outer and inner ring reinforcement bars of the concealed ring beam, respectively. It represents the farthest distance between the inner and outer ring reinforcement bars and the neutral axis of the hidden ring beam section.

[0032] Furthermore, the maximum circumferential tensile normal stress of the ring reinforcement in the concealed ring beam... The verification formula is:

[0033] ;

[0034] Furthermore, the area of ​​the ring reinforcement in the concealed ring beam... The calculation formula is explicitly expressed as relating to the tensile force at the end of the frame beam. The calculation formula introduces the external concrete confinement strengthening coefficient of steel-concrete composite columns. Adjustment coefficient for beneficial effects of floor slabs For the side with a floor slab, take 1.24; for the side without a floor slab, take 1.0.

[0035] When the node is a beam node arranged along a single axis:

[0036] ;

[0037] When the node is a biaxial beam node:

[0038] ;

[0039] In the formula: The effective height of the frame beam section. This refers to the span of the frame beam.

[0040] Furthermore, based on the condition that the strength grades of the ring reinforcement in the concealed ring beam and the longitudinal reinforcement in the frame beam are the same, the practical simplified design formula is as follows:

[0041] (1) Without considering the beneficial effects of the floor slab

[0042] When the node is a beam node arranged along a single axis:

[0043] ;

[0044] When the node is a biaxial beam node:

[0045] ;

[0046] (2) Consider the beneficial effects of the floor slab

[0047] When the node is a beam node arranged along a single axis:

[0048] ;

[0049] When the node is a biaxial beam node:

[0050] .

[0051] Furthermore, the stirrup ratio of the concealed ring beam Controlled by the following formula:

[0052] ;

[0053] In the formula, This is the design value for the tensile strength of concrete. This represents the design value for the tensile strength of the stirrups in the concealed ring beam.

[0054] In summary, the present invention has the following advantages:

[0055] 1) Logically rigorous and highly systematic: The design process progresses step by step from parameter input to construction output, with clear basis for each step, forming a complete technical chain from theoretical analysis to practical design;

[0056] 2) The model has high accuracy and good applicability: By distinguishing the node type and introducing the stirrup participation factor and the floor slab action factor, the model fully reflects the real stress state of the hidden ring beam. The calculation results are in good agreement with the test and finite element analysis. It is applicable to various cross-sectional forms such as circular and square.

[0057] 3) Significantly improved design efficiency: The final practical reinforcement formula is concise and easy to use, which greatly simplifies the calculation workload of designers and facilitates its rapid application and promotion in engineering practice;

[0058] 4) Ensuring seismic performance: This method adheres to the principle of "strong nodes, weak components." Through reasonable parameter control and construction measures, test results show that nodes designed according to this method exhibit the ideal failure mode of beam-end bending failure with the node core area remaining intact, achieving the seismic goal of "nodes being stronger than components." This ensures that the nodes have sufficient load-bearing capacity, stiffness, and energy dissipation capacity, thereby improving the overall seismic performance of the structure.

[0059] 5) Outstanding construction and economic advantages: The designed nodes do not require drilling holes in the steel pipes or welding a large number of steel components on site, which simplifies the construction process and greatly reduces the amount of on-site welding work, improving project quality and construction efficiency. The simplification of the construction process not only significantly improves construction efficiency and shortens the construction period, but also reduces labor and material costs and reduces potential quality hazards caused by complex welding, thus achieving good technical and economic benefits while ensuring structural performance. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of the hidden ring beam node structure.

[0061] Figure 2 This is a structural schematic diagram of the hidden ring beam node from another perspective.

[0062] Figure 3 The diagram shows the node configurations, where (a) is a single-axis beam node—edge node, (b) is a single-axis beam node—middle node, (c) is a double-axis beam node—L-shaped node, (d) is a double-axis beam node—T-shaped node, and (e) is a double-axis beam node—cross-shaped node.

[0063] Figure 4 The diagrams are simplified for calculation, where (a) represents the load on the hidden ring beam, (b) is a symmetrical simplified diagram, (c) is the force method system, and (d) is the static system.

[0064] Figure 5 This is a flowchart of the design method of the present invention.

[0065] In the picture:

[0066] 1-Steel pipe, 2-Outer ring reinforcement, 3-Inner ring reinforcement, 4-Hidden ring beam stirrups, 5-Frame beam longitudinal reinforcement, 6-Steel pipe concrete composite column, 7-Frame beam. Detailed Implementation

[0067] The present invention will be further described in detail below with reference to embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto:

[0068] 1. This invention provides a design method for concealed ring beam joints in steel-concrete composite columns. Given the required calculation parameters, the internal forces of the concealed ring beam section are first calculated using structural mechanics force methods. Then, the allowable circumferential stress of the concealed ring beam reinforcement is checked to ensure it meets the requirements. Furthermore, the participation factor of the concealed ring beam stirrups (4), the confinement strengthening factor of the concrete outside the steel-concrete composite column, and the adjustment factor for the beneficial effects of the floor slab are introduced, ultimately forming a practical and simplified design formula for concealed ring beam joints in steel-concrete composite columns. The derivation process of this method has clear physical meaning, proceeds step-by-step, and is interconnected, with a clear technical route, and can be applied to common engineering designs. Figure 1 , Figure 2 Taking the schematic diagram of the concealed ring beam node shown as an example, the steel-concrete composite column 6 is equipped with a concealed ring beam reinforcement cage: outer ring reinforcement 2, inner ring reinforcement 3, and radially distributed concealed ring beam stirrups 4. The radius of the built-in steel pipe 1 is... The frame beam 7 is equipped with longitudinal reinforcement 5.

[0069] The detailed derivation process is as follows:

[0070] (1) Obtain the parameters required for calculating the hidden ring beam joint of the steel-concrete composite column, including the cross-sectional dimensions of the steel-concrete composite column. , built-in steel pipe radius 1 Frame beam section height h c Area of ​​ring reinforcement in concealed ring beam Area of ​​stirrups in concealed ring beam Spacing Longitudinal reinforcement area of ​​frame beams Yield strength of longitudinal reinforcement in frame beams Yield strength of hidden ring beam reinforcement Elastic modulus of steel bars The material strength is based on the material property test results. The strength of the stirrups 4 of the hidden ring beam is consistent with the yield grade of the ring reinforcement of the hidden ring beam. The outer ring reinforcement 2 and the inner ring reinforcement 3 of the hidden ring beam are arranged at the same height and center. The stirrups 4 of the hidden ring beam are radially distributed at equal intervals within 360 degrees around the central axis of the steel pipe 1.

[0071] (2) Determine the node type and calculate the model: Classify the nodes according to the planar arrangement of beams and columns, including at least: single-axis beam nodes, that is, the nodes where the frame beam 7 is connected to the steel-concrete composite column 6 only along the same axis direction, including single-sided connected beams and double-sided connected beams along the same axis direction, the node types are as follows: Figure 3 As shown in (a) and (b); and the biaxial beam joints, i.e., the joints where the frame beam 7 connects to the steel-concrete composite column 6 along two mutually orthogonal axial directions, including but not limited to L-shaped joints, T-shaped joints, and cross-shaped joints, the joint forms are as follows: Figure 3 As shown in (c), (d), and (e).

[0072] (3) Based on the following assumptions: 1) The hidden ring beam is equivalent to a circular curved bar with equal cross section, which is embedded in the concrete outside the steel tube concrete composite column; 2) The upper half of the hidden ring beam node is under tension and the lower half is under compression; 3) The material is isotropic and satisfies the plane section assumption.

[0073] (4) Take the upper half of the tension part of the hidden ring beam node to establish the stress model, and the calculation diagram is as follows. Figure 4 As shown in the figure. = The tensile force value of the longitudinal reinforcement 5 of the frame beam when it yields; The radial reaction force of the steel pipe wall on the concealed ring beam; for a uniaxial beam node, take... =0.75 For beam nodes with biaxial arrangement, take = The cross-sectional properties can be obtained from the geometric relationship of the hidden ring beam cross-section as follows:

[0074]

[0075]

[0076]

[0077]

[0078] In the formula, E is the elastic modulus of concrete; and They are respectively Moment of inertia and cross-sectional area of ​​the concealed ring beam; and They are respectively Moment of inertia and cross-sectional area of ​​the concealed ring beam; =h c -50mm is the height of the hidden ring beam section.

[0079] in accordance with Figure 4 The force method system of (c) lists the equations:

[0080]

[0081]

[0082]

[0083] In the formula, Let be the calculated radius of the hidden ring beam. b r Define the effective width of the concealed ring beam and define the effective width b of the concealed ring beam. r b is the spacing between the inner and outer ring reinforcement bars of the concealed ring beam. r =0.85*(b c / 2-r); The bending moment of the hidden ring beam under the unit bending moment at point 2; for Bending moment of the hidden ring beam under / 2 action The result of the force method equation, .

[0084] Finally, the formula for calculating the internal forces of the hidden ring beam section can be obtained:

[0085]

[0086]

[0087]

[0088] In the formula, The axial force at the section of the hidden ring beam; Shear force at the section of the concealed ring beam; The bending moment of the hidden ring beam section; Calculate the radius of the hidden ring beam b r =0.85*(b c / 2-r), effective width of the hidden ring beam; The position angle of the hidden ring beam section, with a value range of [value missing]. .

[0089] (5) In order to reasonably consider the restraining and enhancing effect of the stirrups 4 of the hidden ring beam on the overall stiffness of the reinforcing cage of the hidden ring beam, a collaborative action model of the stirrups 4 of the hidden ring beam is established: based on the shear lag model and the partial shear force interaction theory, the stirrups 4 of the hidden ring beam are equivalent to a continuously distributed radial spring, and the participation coefficient characterizing the contribution of the stirrups 4 of the hidden ring beam to the collaborative work of the ring reinforcement is derived. Participation factor of stirrups in concealed ring beams Calculate using the following formula:

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] In the formula, The equivalent tangential stiffness of the stirrups in the concealed ring beam; Characteristic length; equivalent area of ​​the ring reinforcement in the hidden ring beam. ; , These are the cross-sectional areas of the outer ring reinforcement 2 and the inner ring reinforcement 3 of the concealed ring beam, respectively. The elastic modulus of the steel reinforcement; The radial length of the stirrups in the concealed ring beam can be taken as the effective width of the concealed ring beam. ; The Poisson's ratio for the steel reinforcement is taken as 0.3.

[0096] (6) According to the parallel axis theorem in mechanics of materials, the equivalent moment of inertia of the ring reinforcement of the hidden ring beam is... The expression is:

[0097]

[0098]

[0099] In the formula, , The moments of inertia, R1, are the outer ring reinforcement 2 and inner ring reinforcement 3 of the concealed ring beam, respectively. The radii of the outer ring reinforcement 2 and the inner ring reinforcement 3 of the concealed ring beam are respectively. The circumferential radius of the equivalent circular curved rod;

[0100] (7) Participation coefficient based on the stirrups of the concealed ring beam Equivalent area of ​​ring reinforcement in concealed ring beam Radial length of stirrups in concealed ring beam Equivalent moment of inertia of the ring reinforcement of the hidden ring beam To describe the section modulus of the reinforcement cage of the concealed ring beam The expression is:

[0101]

[0102] In the formula, It represents the farthest distance between the inner and outer ring reinforcement bars and the neutral axis of the hidden ring beam section.

[0103] (8) Based on the cross-sectional internal force formulas of equations (8)-(10) and the section modulus formula of the hidden ring beam reinforcement cage of equation (18), the maximum circumferential tensile normal stress of the ring reinforcement of the hidden ring beam is checked according to the material mechanical strength condition. :

[0104]

[0105] Joint test studies and finite element numerical analysis results show that the involvement of the floor slab and the confinement effect of the external concrete significantly affect the bearing capacity of the hidden ring beam joint. An external concrete confinement strengthening factor is introduced. Under the condition of symmetrical reinforcement with the same area for outer ring reinforcement 2 and inner ring reinforcement 3, the area of ​​the ring reinforcement of the hidden ring beam is thus obtained. for:

[0106]

[0107] Based on the research results, the confinement strengthening coefficient of external concrete is... Take 1.1.

[0108] (9) Axial force With bending moment Detailed calculation formula and adjustment coefficient for the beneficial effect of floor slabs Used to describe the area of ​​the ring reinforcement in a concealed ring beam The calculation formula is expressed as follows:

[0109] Ⅰ) When the node is a beam node arranged on a single axis, such as Figure 3 As shown in (a) and (b):

[0110]

[0111] II) When the node is a biaxial beam node, such as Figure 3 As shown in (c), (d), and (e):

[0112]

[0113] In the formula: The effective height of the frame beam section. Let be the span of the beam. Based on the research results, the adjustment coefficient for the beneficial effects of the floor slab is... For the side with a floor slab, take 1.24; for the side without a floor slab, take 1.0.

[0114] (10) Based on the simplified design method of the hidden ring beam node, ignoring the influence of the dimensions of the hidden ring beam, steel pipe 1, concrete composite column 6 and frame beam 7, and assuming that the strength grade of the ring reinforcement of the hidden ring beam is the same as that of the longitudinal reinforcement of the frame beam 5, considering the seismic design principle of "strong node, weak member", the strong node coefficient is taken as 1.15, and a simplified design method of the hidden ring beam node is established:

[0115] I) Without considering the beneficial effects of the floor slab

[0116] When the node is a beam node arranged along a single axis:

[0117]

[0118] When the node is a biaxial beam node:

[0119]

[0120] II) Considering the beneficial effects of the floor slab

[0121] When the node is a beam node arranged along a single axis:

[0122]

[0123] When the node is a biaxial beam node:

[0124]

[0125] (11) The stirrups of the concealed ring beam 4 shall be configured according to the structural requirements of concrete beam stirrups in the "Code for Design of Concrete Structures", that is, to meet the minimum stirrup ratio. Stirrup ratio of the concealed ring beam It can be controlled by the following formula:

[0126]

[0127] In the formula, This is the design value for the tensile strength of concrete. This represents the design value for the tensile strength of the stirrups in the concealed ring beam.

[0128] 2. This invention will provide an engineering example, according to... Figure 5 The technical route details the implementation process of this design method. To ensure the clarity of the formulas and facilitate engineering design, in this embodiment, the outer ring reinforcement 2 and the inner ring reinforcement 3 of the hidden ring beam reinforcement skeleton are arranged symmetrically with equal reinforcement. The subsequent ring reinforcement area design formula and practical simplified design formula are all established under this condition:

[0129] (1) Take a cross-shaped steel-concrete composite column-hidden ring beam node in the frame structure of an office building as an example. The known conditions are as follows: the cross section of frame beam 7 is 400mm×800mm, and the total area of ​​the longitudinal reinforcement 5 of the frame beam is... =2945mm 2The steel-concrete composite column 6 has a cross-section of 1000mm × 1000mm, with an internal steel tube 1 having a radius r = 300mm; the concrete strength grade is C40, and the strength grade of the ring reinforcement in the concealed ring beam and the longitudinal reinforcement 5 in the frame beam are both HRB400; the floor slab thickness is 120mm, and it is integrally cast with the frame beam 7. Design requirements: Determine the configuration of the outer ring reinforcement 2, the inner ring reinforcement 3, and the stirrups 4 of the concealed ring beam.

[0130] Determine the parameters required for the calculation of the hidden ring beam node: steel pipe 1 radius r = 300mm, steel pipe concrete composite column 6 section width b. c =1000mm, effective width b of the concealed ring beam r =0.85*(b c / 2-r)=170mm; Height of the hidden ring beam h r= h c -50 = 750 mm; Calculation radius R0 = r + 0.5b r =385mm, longitudinal reinforcement of frame beam with yield strength f y,s =360N / mm 2 The node is a biaxial beam node, and a floor slab is present. Therefore, in subsequent calculations, F=P is used, and the favorable factor of the floor slab is considered. =1.24.

[0131] (2) The calculation assumptions followed are: 1) The hidden ring beam is equivalent to a circular curved bar with equal cross section, which is embedded in the concrete outside the composite column tube; 2) The upper half of the hidden ring beam node is under tension and the lower half is under compression; 3) The material is isotropic and satisfies the plane section assumption.

[0132] (3) The hidden ring beam nodes are simplified according to the principle of orthogonal symmetry as follows: Figure 4 The simplified calculation diagram is shown. The internal force calculation formulas are obtained using the force method. For a biaxial beam node—a cross-shaped node—the internal forces at its section are:

[0133] Axial force calculation formula: ;

[0134] Shear force calculation formula: ;

[0135] Bending moment calculation formula: ;

[0136] Among them, the design value of the tensile force at the beam end P= =360×2945=1060KN.

[0137] (4) Take the area of ​​the ring reinforcement at the hidden ring beam node with cross-shaped floor slab. The areas of the outer ring steel bar 2 and the inner ring steel bar 3 are respectively The preliminary configuration of the stirrups 4 in the concealed ring beam is as follows: 10@100 (radial arrangement), cross-sectional area of ​​stirrups 4 in the concealed ring beam The spacing of the stirrups 4 in the concealed ring beam is s=100mm, and the radial length of the stirrups 4 in the concealed ring beam is... .

[0138] Equivalent area of ​​ring reinforcement in concealed ring beam :

[0139]

[0140] Equivalent tangential stiffness of stirrups :

[0141]

[0142] Feature length :

[0143]

[0144] Calculation parameters :

[0145]

[0146] Stirrup participation factor :

[0147]

[0148] (5) Assume that the spacing between the inner and outer ring reinforcement bars is approximately equal to the effective width of the hidden ring beam. Then the distance between the outermost fibers of the cross section c = / 2=85mm.

[0149] Furthermore, the skeleton moments of inertia of the outer ring reinforcement 2 and the inner ring reinforcement 3 of the concealed ring beam are calculated. Define the radius of the outer ring reinforcement 2 as R1 and the cross-sectional area as A1; and the radius of the inner ring reinforcement 3 as R2 and the cross-sectional area as A2. According to the construction, the distances from the center of the outer ring reinforcement 2 and the center of the inner ring reinforcement 3 to the center of the steel pipe 1 can be taken as follows: The radius of the inner ring reinforcement 3, R2 ≈ =300mm, the radius of the outer ring reinforcement 2 is R1=r+b r =300+170=470mm; the outer ring steel bar 2 and the inner ring steel bar 3 have the same area.

[0150] The equivalent circular crank's circumferential centroid radius R g The following can be calculated:

[0151]

[0152] Equivalent moment of inertia I of equivalent circular curved rod ring (Right now )for:

[0153]

[0154] Substitute into the formula:

[0155]

[0156] Based on the material mechanics strength conditions, the maximum circumferential tensile normal stress of the ring reinforcement in the concealed ring beam is checked. :

[0157]

[0158] Introducing the beneficial effect adjustment factor β of the floor slab and the confined strengthening factor η of concrete. r Substituting the area of ​​the ring reinforcement at the hidden ring beam node, the circumferential stress of the ring reinforcement in the hidden ring beam is... The calculation formula is:

[0159]

[0160] It is evident that the ring reinforcement of the concealed ring beam meets the strength requirements.

[0161] (6) According to the formula The stirrup ratio of the concealed ring beam was checked and calculated. The configuration of stirrups 4 in the concealed ring beam with 10@100 clearly meets the minimum stirrup ratio requirement.

[0162] 3. The inventors conducted experimental studies on six concealed ring beam specimens. A comparison of calculated and experimental values ​​is shown in Table 1. The obtained concealed ring beam design method agrees well with the experimental and finite element results, which are approximately 1.10 times the calculated results. This verifies that the calculation method of this invention is conservative and possesses excellent computational stability and accuracy. This formula combines theoretical rigor with engineering practicality, providing a reliable basis for the refined design and safety assessment of concealed ring beams.

[0163] Table 1: Comparison of Calculation Results with Experimental / Finite Element Results

[0164]

[0165] Note: The yielding of the annular reinforcement in the concealed ring beam of the specimen is used as the criterion. The beam end load corresponding to the actual reinforcement is calculated and defined. That is, the beam end load obtained by experiment or finite element method. The calculation results obtained by the given formula The ratio, in kN.

[0166] 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 design method of a concrete-filled steel tubular composite column-encased beam joint based on force method, characterized in that, Includes the following steps: Determine the node design parameters: including the steel pipe radius. , cross-sectional width of steel-concrete composite column Frame beam section height Area of ​​ring reinforcement in concealed ring beam Yield strength of ring reinforcement in concealed ring beam Area of ​​stirrups in concealed ring beam Spacing Longitudinal reinforcement area of ​​frame beams Yield strength of longitudinal reinforcement in frame beams Elastic modulus of steel bars ; Based on the structural mechanics force method, a force analysis model of the steel reinforcement cage of the hidden ring beam is established. The hidden ring beam is equivalent to a circular curved bar with a uniform cross section. Due to its symmetry, a formula for calculating the internal force of the hidden ring beam cross section is established to calculate the internal force of the hidden ring beam cross section. Based on the determined node design parameters, a collaborative model of the stirrups in the concealed ring beam is established to quantify the enhancing effect of the stirrups on the overall stiffness of the concealed ring beam's steel reinforcement cage, and a participation factor for the stirrups in the concealed ring beam is introduced. ; Based on node design parameters and the participation factor of stirrups in the concealed ring beam Calculate the section moment of the steel reinforcement cage of the concealed ring beam. ; Based on the material mechanics strength conditions and the section moment of the steel reinforcement cage of the hidden ring beam Internal forces in the cross section, and establish the maximum circumferential tensile normal stress of the ring reinforcement in the hidden ring beam. Verification formula; Based on the maximum circumferential tensile normal stress of the ring reinforcement of the hidden ring beam The verification formula is combined with the internal forces of the section and the participation factor of the stirrups in the hidden ring beam. Introducing a floor slab beneficial effect adjustment coefficient With the external concrete confinement strengthening coefficient Under the condition that the inner and outer ring reinforcements are symmetrically and equally reinforced, establish the area of ​​the ring reinforcement of the hidden ring beam. Calculation formula; The area of ​​the ring-shaped reinforcing steel in the hidden ring beam The calculation formula is simplified to the area of ​​the ring reinforcement in the concealed ring beam. Total area of ​​longitudinal reinforcement in frame beams The direct proportional relationship forms a practical and simplified design formula applicable to the condition that the strength grades of the ring reinforcement of the concealed ring beam and the longitudinal reinforcement of the frame beam are the same. The internal forces of the concealed ring beam section are calculated using the following formula: ； ； ； In the formula, The axial force at the section of the hidden ring beam; Shear force at the section of the concealed ring beam; The bending moment of the hidden ring beam section; , is the tensile force value when the longitudinal reinforcement of the frame beam yields; This represents the radial reaction force of the steel pipe wall on the hidden ring beam. The position angle of the hidden ring beam section, with a value range of [value missing]. Based on the arrangement of the frame beams relative to the steel-concrete composite columns in the nodes, the node types are classified, including at least single-axis beam nodes with frame beams connected on one side and double-axis beam nodes with frame beams connected on both sides along the same axial direction, and double-axis beam nodes with frame beams connected to the steel-concrete composite columns along two mutually orthogonal axial directions; the node type is determined as follows: for single-axis beam nodes, F=0.75P; for double-axis beam nodes, F=P. Calculate the radius of the hidden ring beam b r =0.85*(b c / 2-r), is the effective width of the hidden ring beam; The area of ​​the ring-shaped reinforcing steel in the hidden ring beam The calculation formula is explicitly expressed as relating to the tensile force at the end of the frame beam. The calculation formula introduces the external concrete confinement strengthening coefficient of steel-concrete composite columns. Adjustment coefficient for beneficial effects of floor slabs For the side with a floor slab, take 1.24; for the side without a floor slab, take 1.

0. When the node is a beam node arranged along a single axis: ； When the node is a biaxial beam node: ； In the formula: The effective height of the frame beam section. This refers to the span of the frame beam.

2. The design method according to claim 1, characterized in that, The design method of the steel-concrete composite column-hidden ring beam joint is based on the following assumptions: 1) The hidden ring beam is equivalent to a circular curved rod with a uniform cross section embedded in the concrete outside the steel-concrete composite column tube; 2) The upper half of the hidden ring beam joint is under tension and the lower half is under compression; 3) The material is isotropic and satisfies the plane section assumption.

3. The design method according to claim 1, characterized in that, Concrete-concrete composite steel tube column external concrete confinement strengthening factor The value is 1.

1.

4. The design method according to claim 1, characterized in that, Introducing the stirrup participation factor for concealed ring beams The approach involves using a shear lag model and partial shear interaction theory to treat the stirrups of the concealed ring beam as equivalent to radial elastic constraints distributed along the circumferential direction of the concealed ring beam, and establishing the stirrup participation factor of the concealed ring beam. To characterize the degree to which the stirrups of the concealed ring beam enhance the synergistic effect of the inner and outer ring reinforcements: ； in: ； ； ； ； In the formula, The equivalent tangential stiffness of the stirrups in the concealed ring beam; The characteristic length; This represents the equivalent area of ​​the ring reinforcement in the concealed ring beam. These are the cross-sectional areas of the outer and inner ring reinforcement bars of the concealed ring beam, respectively. The radial length of the stirrups in the concealed ring beam is taken as the effective width of the concealed ring beam. ; The Poisson's ratio for steel reinforcement.

5. The design method according to claim 4, characterized in that, The section moment of the reinforced concrete cage of the concealed ring beam Calculate using the following formula: ； In the formula, and These are the moments of inertia of the outer and inner ring reinforcement bars of the concealed ring beam, respectively. It represents the farthest distance between the inner and outer ring reinforcement bars and the neutral axis of the hidden ring beam section.

6. The design method according to claim 5, characterized in that, Maximum circumferential tensile normal stress of the ring reinforcement in the concealed ring beam The verification formula is: 。 7. The design method according to claim 6, characterized in that, Under the condition that the strength grades of the ring reinforcement of the concealed ring beam and the longitudinal reinforcement of the frame beam are the same, the practical simplified design formula is: (1) Without considering the beneficial effects of the floor slab When the node is a beam node arranged along a single axis: ； When the node is a biaxial beam node: ； (2) Consider the beneficial effects of the floor slab When the node is a beam node arranged along a single axis: ； When the node is a biaxial beam node: 。 8. The design method according to claim 5, characterized in that, Stirrup ratio of concealed ring beam Controlled by the following formula: ； In the formula, This is the design value for the tensile strength of concrete. This represents the design value for the tensile strength of the stirrups in the concealed ring beam.

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