Calculation method of shear bearing capacity of composite concrete-filled steel tube column-steel beam joints with floor slab

Abstract

The present invention discloses a method for calculating the shear bearing capacity of a composite steel tube concrete column-steel beam node with a floor, and belongs to the technical field of building connection nodes. The present invention includes respectively obtaining the yield shear bearing capacity and the ultimate shear bearing capacity of the steel tube web in the core area; obtaining the yield shear bearing capacity and the ultimate shear bearing capacity of the vertical ribs and the anchor webs; taking the sum of the shear bearing capacity of the compression truss and the shear bearing capacity of the constraint truss as the ultimate shear bearing capacity of the concrete; the yield shear bearing capacity of the composite floor-compound column-steel beam node is the sum of the yield shear bearing capacity of the steel tube web in the core area, the yield shear bearing capacity of the vertical ribs, the yield shear bearing capacity of the anchor webs and the ultimate shear bearing capacity of the concrete; the sum of the ultimate shear bearing capacity of each part of the ultimate shear bearing capacity, the node designed and calculated according to the present invention has a large shear capacity reserve, the shear capacity and stiffness of the node domain are large, and the shearing requirements of the node can be met.

Description

Technical Field

[0001] The invention relates to the technical field of building connection nodes, and in particular to a method for calculating the shear bearing capacity of a composite steel tube concrete column-steel beam node with a floor slab. Background Art

[0002] In the field of modern architecture, with the continuous emergence of high-rise and super-high-rise buildings and the deep development and utilization of underground space, structural safety and seismic performance have become key factors that cannot be ignored in design. Among them, the node is the link connecting various components in the structural system, and its shear bearing capacity directly affects the stability and safety of the entire structure. Especially in the composite steel tube concrete column-steel beam node, the accurate evaluation of the shear bearing capacity is particularly complex, which is mainly due to its unique combined structural characteristics and complex force mechanism. Traditional calculation methods often find it difficult to fully consider the significant impact of the floor on the force performance of the node, resulting in certain safety hazards in the design. Although the current specifications provide basic design principles, there are still limitations in the estimation of shear bearing capacity under complex working conditions, especially the failure to fully consider the synergy between the floor and the node, which may lead to the risk of underestimating or overestimating the shear bearing capacity in actual engineering applications.

[0003] In recent years, researchers at home and abroad have conducted some experimental research and theoretical analysis on the shear performance of steel tube concrete column nodes. For example, Fukumoto T et al. proposed a nonlinear shear-shear deformation relationship model for the connection node of square steel tube concrete column and steel beam based on the superposition calculation of the trilinear shear-shear deformation relationship model of steel tube and inner concrete, and within the shear deformation range of +0.04 arc, the theoretical model is basically consistent with the experimental results. Nie Jianguo et al. established a shear stress model for square steel tube concrete column nodes, proposed a restoring force model for the shear-shear deformation curve of square steel tube concrete column nodes, and on this basis proposed a calculation formula for the yield shear bearing capacity and ultimate shear bearing capacity of square steel tube concrete column nodes.

[0004] However, there is a relative lack of research on compound steel tube concrete column-steel beam nodes with floor slabs, especially on accurate calculation methods for their shear bearing capacity. Most existing studies focus on node models without floor slabs, ignoring the strengthening effect of floor slabs on the overall stress behavior of nodes. However, multiple earthquake disasters have shown that concrete floor slabs cause structural asymmetry, and the strong columns and weak beams in seismic design are not realized. In addition, the interaction between reinforced concrete floor slabs and steel beams affects the internal force and deformation distribution of steel tube concrete column-steel beam nodes under reciprocating loads, causing changes in their failure morphology, hysteresis curves, bearing capacity, ductility and energy dissipation capacity. In view of this, the present invention proposes a method for calculating the shear bearing capacity of compound steel tube concrete column-steel beam nodes with floor slabs. Summary of the invention

[0005] The purpose of the present invention is to overcome the problems in the prior art and provide a method for calculating the shear bearing capacity of a composite steel tube concrete column-steel beam node with a floor slab.

[0006] The present invention provides a method for calculating the shear bearing capacity of a composite steel tube concrete column-steel beam node with a floor, comprising: determining the shear bearing capacity of the core steel tube web, vertical ribs, anchor webs and concrete that contribute to the shear bearing capacity of the composite steel tube concrete column-steel beam node with a floor, wherein the shear bearing capacity of the concrete includes the contribution of the shear bearing capacity of the floor;

[0007] After determining the part that contributes to the shear bearing capacity in the composite steel tube concrete column-steel beam node with floor slab, the yield shear bearing capacity and ultimate shear bearing capacity of each part are obtained respectively, where:

[0008] When obtaining the shear bearing capacity of concrete, it is confirmed that the ultimate shear bearing capacity of concrete includes the shear bearing capacity of the compression truss and the shear bearing capacity of the restrained truss according to the diagonal strut mechanism. When calculating the shear bearing capacity of the compression truss, it is necessary to consider the contribution of the concrete floor slab to the shear bearing capacity of the compression truss, and then calculate the shear bearing capacity of the compression truss and the shear bearing capacity of the restrained truss respectively, and take the sum of the shear bearing capacity of the compression truss and the shear bearing capacity of the restrained truss as the ultimate shear bearing capacity of concrete;

[0009] The sum of the yield shear bearing capacity of the steel tube web in the core area, the yield shear bearing capacity of the vertical ribs, the yield shear bearing capacity of the anchor web and the ultimate shear bearing capacity of concrete is taken as the yield shear bearing capacity of the duplex steel tube concrete column-steel beam node with floor slab; the sum of the ultimate shear bearing capacity of the steel tube web in the core area, the ultimate shear bearing capacity of the vertical ribs, the ultimate shear bearing capacity of the anchor web and the ultimate shear bearing capacity of concrete is taken as the ultimate shear bearing capacity of the duplex steel tube concrete column-steel beam node with floor slab.

[0010] As a preferred method, the ultimate shear bearing capacity of concrete is:

[0011] ;

[0012] Shear bearing capacity of concrete main compression trusses for:

[0013] ;

[0014] in, is the concrete width; is the ultimate compressive strength of the concrete diagonal strut; is the angle between the diagonal strut and the vertical plane;

[0015] Ultimate shear capacity of restrained trusses for: ;

[0016] in, is the horizontal pressure; is the length of the A zone of the steel pipe flange; is the flange plastic hinge bending moment.

[0017] As a preferred method, the shear bearing capacity of the main compression truss of concrete When calculating,

[0018] ;

[0019] In the formula, is the core area height, ;in is the thickness of the concrete slab, is the height of steel beam 5, is the thickness of the flange of steel beam 5.

[0020] As a preferred embodiment, the yield shear bearing capacity and ultimate shear bearing capacity of the core area steel tube web are obtained according to the shear tri-fold model of the core area steel tube web. The core area steel tube web includes an inner circular steel tube web and an outer square steel tube web;

[0021] The yield shear bearing capacity of the outer square steel tube web for: ;in, is the cross-sectional area of ​​the web of the outer square steel tube; is the maximum shear stress of the web of the external square steel tube under axial compression; is the yield strength of the web of the outer square steel tube; The web of the outer square steel tube bears the axial compressive stress;

[0022] The ultimate shear bearing capacity of the outer square steel tube web is for: ;in, is the ultimate strength of the outer square steel tube web;

[0023] The yield shear bearing capacity of the inner circular steel tube web for: ;in, is the cross-sectional area of ​​the inner circular steel pipe; is the maximum shear stress of the web of the inner circular steel tube under axial compression; is the yield strength of the web of the inner circular steel tube; The inner tube web bears axial compressive stress.

[0024] The ultimate shear bearing capacity of the inner circular steel tube web is for: ;in, is the ultimate strength of the web of the inner circular steel tube.

[0025] As a preferred method, when obtaining the yield shear bearing capacity and the ultimate shear bearing capacity of the anchor web, first obtain the shear stress cloud diagram of the vertical ribs and the anchor web, and then obtain the shear stress when the vertical ribs and the anchor web yield according to the Mises yield criterion, and calculate the yield shear bearing capacity and the ultimate shear bearing capacity of the vertical ribs based on the obtained shear stress when the vertical ribs yield; calculate the yield shear bearing capacity and the ultimate shear bearing capacity of the anchor web based on the obtained shear stress when the anchor web yields.

[0026] As a preferred embodiment, the yield shear bearing capacity of the vertical ribs is and ultimate shear capacity They are:

[0027] ;in, is the shear cross-sectional area of ​​the vertical rib; is the yield strength of the vertical rib; is the maximum shear stress of the vertical rib under axial compression;

[0028] ;in, is the ultimate strength of the vertical ribs.

[0029] As a preferred embodiment, the yield shear bearing capacity of the anchor web is V sy4 and ultimate shear capacity V su4 They are: ;in, is the shear cross-sectional area of ​​the anchor web; is the maximum shear stress of the anchor web under axial compression; is the anchor web yield strength;

[0030] ,in, is the ultimate strength of the anchor web.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows: the shear bearing capacity calculation method of the duplex steel tube concrete column-steel beam node with floor slab of the present invention accurately locks the part that contributes to the shear bearing capacity in the duplex steel tube concrete column-steel beam node with floor slab, and calculates the shear yield bearing capacity and the shear ultimate bearing capacity of each part respectively, and considers the contribution of the concrete floor slab to the shear bearing capacity of the compression truss when calculating the shear bearing capacity of the compression truss, and finally takes the sum of the calculated yield shear bearing capacity of the core area steel tube web, the yield shear bearing capacity of the vertical ribs, the yield shear bearing capacity of the anchor web and the ultimate shear bearing capacity of concrete as the yield shear bearing capacity of the duplex steel tube concrete column-steel beam node with floor slab; takes the sum of the ultimate shear bearing capacity of the core area steel tube web, the ultimate shear bearing capacity of the vertical ribs, the ultimate shear bearing capacity of the anchor web and the ultimate shear bearing capacity of concrete as the ultimate shear bearing capacity of the duplex steel tube concrete column-steel beam node with floor slab. The above calculation method of the present invention fully considers the effect of the floor slab on the overall node structure under complex working conditions, so that the shear reserve capacity of the duplex steel tube concrete column-steel beam node with floor slab is sufficient when it is destroyed, and the node design complies with the seismic design principle of strong shear and weak bending, avoiding shear brittle failure due to unreasonable node design, resulting in safety hazards in high-rise and super-high-rise buildings.

[0032] The average value of the ratio of the theoretical value of the shear yield bearing capacity of the node calculated by the above-mentioned calculation method of the present invention to the test value is 1.88, and the average value of the ratio of the theoretical value of the shear ultimate bearing capacity to the test value is 1.97. The calculation results of the yield shear bearing capacity and the ultimate shear bearing capacity are significantly greater than the average results in the node test. The present invention also introduces the concept of node shear capacity reserve, that is, the ratio of the theoretical shear capacity of the node to the actual shear force it bears. It can be seen that the node calculated by the above-mentioned calculation method of the present invention has a large shear capacity reserve, and the shear capacity and stiffness of the node domain are large, which can meet the shear resistance requirements of the node. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a three-dimensional structural diagram of a composite steel tube concrete column-steel beam node with floor slab in the prior art.

[0034] Figure 2 This is a force analysis diagram of the web of the outer square steel tube according to an embodiment of the present invention.

[0035] Figure 3 This is a shear-resistant three-fold line model of the steel tube web according to an embodiment of the present invention.

[0036] Figure 4 4 is a shear stress cloud diagram of the vertical ribs in an embodiment of the present invention (unit: MPa).

[0037] Figure 5 This is a cloud diagram of shear stress of the anchor web of an embodiment of the present invention (unit: MPa).

[0038] Figure 6 This is the concrete shear model of the core area of ​​the steel tube concrete column node in the embodiment of the present invention.

[0039] Explanation of the reference numerals: 1. External square steel pipe, 2. Internal round steel pipe, 3. Anchor web, 4. Vertical rib, 5. Steel beam, 6. Connection plate, 7. High-strength bolt, 8. Column horizontal end plate. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solution and advantages of the embodiments of the present disclosure clearer, the technical solution of the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings of the embodiments of the present disclosure. Obviously, the described embodiments are part of the embodiments of the present disclosure, not all of the embodiments. Based on the described embodiments of the present disclosure, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present disclosure.

[0041] Unless otherwise defined, the technical terms or scientific terms used herein should be understood by people with ordinary skills in the field to which the present disclosure belongs. "First", "second" and similar words used in the present disclosure do not indicate any order, quantity or importance, but are only used to distinguish different components. "Including" or "comprising" and similar words mean that the elements or objects appearing in front of "including" or "comprising" cover the elements or objects listed after "including" or "comprising" and their equivalents, and do not exclude other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0042] Please refer to Figure 1 , Figure 1 It is a three-dimensional diagram of the connection structure of the duplex steel tube concrete column-steel beam node with floor in the prior art. The specific structure is that the steel pipe in the core area includes an outer square steel pipe 1 and an inner circular steel pipe 2 located inside the outer square steel pipe 1, holes are opened on the column walls on both sides of the outer square steel pipe 1 connecting the steel beam 5, the anchor web 3 is welded to the inner circular steel pipe 2 and the outer square steel pipe 1, and then the cover plate of the same steel material is welded to the column wall of the outer square steel pipe 1; the steel beam web and the anchor web 3 are connected by a connecting plate 6 and a high-strength bolt 7, the steel beam 5 in the core area of ​​the node is connected to the horizontal end plate 8 of the column by a fillet weld, and a double row of shear bolts are welded on the flange of the steel beam 5 to connect the concrete floor, according to the complete shear connection design, the concrete in this embodiment refers to the core area concrete, that is, the concrete poured in the outer square steel pipe 1 and the inner circular steel pipe 2.

[0043] Figure 1 The core area of ​​the node in the duplex steel tube concrete column-steel beam node structure with floor refers to the part where the beam and column intersect in the node. It can be seen from the force mechanism of the node that the shear bearing capacity of the core area of ​​the duplex steel tube concrete column-steel beam node with floor is mainly borne by the following parts, namely the steel tube web in the core area, the vertical ribs 4 and the anchor web 3 of the main connecting parts of the node, the floor and the concrete diagonal compression rod. Among them, the steel tube web in the core area is divided into two parts, the outer square steel tube web and the inner circular steel tube web, which contribute to the shear bearing capacity. Therefore, the shear bearing capacity of the core area of ​​the duplex steel tube concrete column-steel beam node with floor of the present invention is provided by the outer square steel tube web, the inner circular steel tube web, the vertical ribs 4, the anchor web 3, the floor and the core area concrete.

[0044] The present embodiment provides a method for calculating the shear bearing capacity of a composite steel tube concrete column-steel beam node with a floor, comprising determining the shear bearing capacity of the core steel tube web, the vertical rib 4, the anchor web 3 and the concrete as the part that contributes to the shear bearing capacity in the composite steel tube concrete column-steel beam node with a floor, wherein the shear bearing capacity of the concrete includes the contribution of the shear bearing capacity of the floor;

[0045] After determining the part that contributes to the shear bearing capacity in the composite steel tube concrete column-steel beam node with floor slab, the yield shear bearing capacity and ultimate shear bearing capacity of each part are obtained respectively, where:

[0046] When obtaining the shear bearing capacity of concrete, the ultimate shear bearing capacity of the core area concrete is confirmed to include the shear bearing capacity of the compression truss and the shear bearing capacity of the restrained truss according to the diagonal strut mechanism. When calculating the shear bearing capacity of the compression truss, the contribution of the concrete floor to the shear bearing capacity of the compression truss must be considered. Then, the shear bearing capacity of the compression truss and the shear bearing capacity of the restrained truss are calculated separately, and the sum of the shear bearing capacity of the compression truss and the shear bearing capacity of the restrained truss is taken as the ultimate shear bearing capacity of the concrete.

[0047] The sum of the yield shear bearing capacity of the steel tube web in the core area, the yield shear bearing capacity of the vertical ribs 4, the yield shear bearing capacity of the anchor web 3 and the ultimate shear bearing capacity of concrete is taken as the yield shear bearing capacity of the duplex steel tube concrete column-steel beam node with floor slab; the sum of the ultimate shear bearing capacity of the steel tube web in the core area, the ultimate shear bearing capacity of the vertical ribs 4, the ultimate shear bearing capacity of the anchor web 3 and the ultimate shear bearing capacity of concrete is taken as the ultimate shear bearing capacity of the duplex steel tube concrete column-steel beam node with floor slab.

[0048] In this embodiment, the stress state of the concrete in the core area of ​​the node changes from unidirectional stress to triaxial stress state under the constraint of the steel tube. As the load increases, the concrete in the core area of ​​the steel tube concrete node appears a diagonal compressive stress zone, and then gradually appears diagonal cracks. Several parallel diagonal cracks divide the core area concrete into diagonal compression bars. At the same time, due to the constraint of the outer steel tube 1 on the core concrete, a constrained diagonal compression bar is formed, so the concrete in the core area of ​​the node is divided into two parts: the main diagonal compression bar and the constrained diagonal compression bar. When the node is under the action of low-cycle reciprocating load, the direction of the shear force on the node domain will change with the load, and the direction of the diagonal compression bar will also change alternately. As the load increases further, the concrete reaches the ultimate compressive strength, and the diagonal compression bar at this time is also damaged, indicating that the node domain has reached the ultimate shear bearing capacity.

[0049] In this embodiment, the shear-shear skeleton curve of the concrete in the core area of ​​the composite steel tube concrete column-steel beam node with floor slab adopts a trilinear model. According to the failure mode of typical beam-column nodes and the results of finite element analysis (Overview of shear mechanism and bearing capacity calculation method of beam-column nodes; Experimental study on seismic performance of assembled composite steel tube concrete nodes), it can be known that before the concrete in the core area of ​​the node cracks, the smaller value of the third principal stress is mainly distributed in the inclined strip area along the diagonal direction in the node. Along the diagonal direction of the node, the compressive strain is roughly shuttle-shaped on the cross section; when the node is subjected to shear force, the horizontal end plate 8 of the column and the anchor web 3 are transmitted from the compression area of ​​the beam end and the column end to the edge of the node under the combined action of the tension and pressure at the beam end or the column end, and a part of the force forms an oblique pressure in the core area of ​​the node, and this part of the force is borne by the concrete in the core area of ​​the node with a certain width along the oblique main diagonal direction, which is Figure 6 The "oblique strut mechanism".

[0050] The ultimate shear bearing capacity of concrete in the core area is mainly determined by the shear bearing capacity of the compression truss. and the shear capacity of the restrained trusses The mechanical mechanism of the compression truss includes the main compression truss and the extended compression truss formed by the flange constraint of the steel tube column wall. The main compression truss is evolved from the arch mechanism under the ultimate shear strength of reinforced concrete beams or beams and columns. The shear bearing capacity of the concrete main compression truss V cu1 Calculated by the following formula:

[0051] ;

[0052] in, ;

[0053] is the core area height. For composite beam nodes with floor slabs, ; h c , hb are the thickness of the concrete slab and the height of the steel beam 5, respectively, and is the thickness of the flange of the steel beam 5; is the width of the core area concrete; B c , t cf are the width and thickness of the outer square steel pipe 1, is the ultimate compressive strength of concrete struts.

[0054] like Figure 6 As shown, the length of the steel pipe flange A zone is The plastic hinges at both ends are formed by the reverse horizontal pressure exerted by the confined concrete on the flange. Assume that the turning angle of area A is , then according to the principle of virtual work:

[0055] ;

[0056] In the formula, is the reaction force in area A; M fp is the flange plastic hinge bending moment; the left and right parts are the reaction forces respectively External work done and flange plastic hinge bending moment M fp The internal work done.

[0057] ;

[0058] ;

[0059] In the formula, is the width of the steel pipe, is the thickness of the steel pipe; is the yield strength of the steel pipe.

[0060] but Calculate as follows:

[0061] ;

[0062] The ultimate shear strength of the restrained truss is:

[0063] ;

[0064] The ultimate shear bearing capacity and ultimate shear strain of core concrete are:

[0065] ;

[0066] ;

[0067] Where: is the shear coefficient of concrete, which is 1.2 for the core concrete of square steel tube concrete column;

[0068] is the shear modulus of concrete;

[0069] =0.2 is the Poisson's ratio of concrete;

[0070] is the stiffness degradation coefficient, which is related to the aspect ratio of the core area and the compressive strength of concrete. The calculation formula is:

[0071] .

[0072] Therefore, the ultimate shear bearing capacity of the concrete described in this embodiment is: ;

[0073] Shear bearing capacity of concrete main compression trusses for: ;

[0074] in, is the width of the core area concrete; is the ultimate compressive strength of the concrete diagonal strut; is the angle between the diagonal strut and the vertical plane;

[0075] Ultimate shear capacity of restrained trusses for: ;

[0076] in, is the horizontal pressure; is the length of the A zone of the steel pipe flange; is the flange plastic hinge bending moment.

[0077] As a preferred embodiment, the shear bearing capacity of the concrete main compression truss is When calculating,

[0078] ;

[0079] In the formula, h is the core area height, ;

[0080] in, h c is the thickness of the concrete slab, h b is the height of steel beam 5, t bf is the thickness of the flange of steel beam 5.

[0081] As a preferred embodiment, the yield shear bearing capacity and the ultimate shear bearing capacity of the steel tube web in the core area are obtained according to the shear tri-fold line model of the steel tube web in the core area.

[0082] As a preferred embodiment, the core area steel pipe web includes an inner round steel pipe web and an outer square steel pipe web;

[0083] When the composite steel tube concrete column-steel beam node with floor is subjected to vertical load, the stress on the outer steel tube web is as follows: Figure 2 As shown. s is the compressive stress on the outer steel tube web caused by the vertical axial force, τ s is the shear stress on the outer steel tube web. In order to make the formula derivation process more detailed and clear, the compressive stress and shear stress generated by the vertical axial force on the outer steel tube web are represented by σ s1 and τ s1 The compressive stress and shear stress generated by the vertical axial force on the web of the inner circular steel tube are represented by σ s2 and τ s2 express. Figure 3 is the shear three-fold line model of the steel tube web, where A is the shear yield point of the steel material, corresponding to the yield shear force V of the outer steel tube web sy and yield shear deformation γ sy , B is the shear limit point of the steel material, corresponding to the ultimate shear force V of the web of the external steel tube su and the limiting shear deformation γ su Compared with the geometric dimensions of the steel pipe column web in the length and height directions, the thickness of the steel pipe column web is very small, and the stress in the thickness direction of the steel pipe column web is very small. Therefore, the force analysis of the steel pipe column web can be reasonably simplified and analyzed from the plane stress-strain state. The compressive stress generated by the vertical axial force on the external steel pipe web is obtained as follows:

[0084] ;

[0085] In the formula, is the compressive stress on the steel tube web caused by the vertical axial force; represents the axial pressure on the concrete-filled steel tube column. , Respectively represent the yield strength of the outer square steel tube 1 and the inner round steel tube 2, is the compressive strength of concrete, , Respectively represent the cross-sectional areas of the outer square steel tube 1 and the inner round steel tube 2, Represents the cross-sectional area of ​​concrete.

[0086] The stress state of the web of the external square steel tube can be expressed as: , , , it can be seen that the principal stresses at a point on the web of the external steel tube are:

[0087] ;

[0088] In the formula, is the vertical axial force on the web of the outer steel tube; is the horizontal shear force on the web of the outer steel tube; is the vertical shear force on the web of the outer steel tube; is the compressive stress on the web of the outer steel tube caused by the vertical axial force; is the shear stress generated by the vertical axial force on the web of the outer steel tube; , and are the first principal stress, the second principal stress and the third principal stress respectively.

[0089] When the node reaches the yield state, the steel is in the shear rheological state. According to the VonMises yield criterion, the Mises yield criterion is:

[0090] ;

[0091] in: is the yield strength of the web of the external steel tube. Substituting the above principal stress values ​​into the above formula, we can get:

[0092] ;

[0093] Therefore, the maximum shear stress that the outer square steel tube 1 can withstand under axial pressure is:

[0094] ;

[0095] The yield shear force of the outer square steel tube web is V sy1 and shear deformation sy1 for:

[0096] ;

[0097] ;

[0098] in: is the web area of ​​the outer steel pipe; is the shear modulus of steel; V sy1 represents the yield shear force of the web of the external steel tube, is the yield strength of the web of the outer square steel tube.

[0099] The ultimate shear force of the outer square steel tube web is V su1 and shear deformation su1 for:

[0100] ;

[0101] ;

[0102] Therefore, the yield shear bearing capacity of the outer square steel tube web in this embodiment is for: ;in, is the cross-sectional area of ​​the web of the outer square steel tube; is the maximum shear stress of the web of the external square steel tube under axial compression; is the yield strength of the web of the outer square steel tube; The web of the outer square steel tube bears the axial compressive stress;

[0103] The ultimate shear bearing capacity of the outer square steel tube web is for: ;in, It is the ultimate strength of the outer square steel tube web.

[0104] In this embodiment, the shear stress analysis of the inner circular steel tube web is the same as that of the outer square steel tube 1, and its stress state is the same as that of the outer square steel tube web. The shear area of ​​the inner circular steel tube web is , is the cross-sectional area of ​​the inner circular steel tube 2. Then the yield shear force of the web of the inner circular steel tube is V sy2 and shear deformation sy2 They are:

[0105] ;

[0106] ;

[0107] Ultimate shear force of the web of inner circular steel tube V su2 and shear deformation su2 They are:

[0108] ;

[0109] ;

[0110] Therefore, in this embodiment, the yield shear bearing capacity of the web of the inner round steel tube is for: ;in, is the cross-sectional area of ​​the inner round steel pipe 2; is the maximum shear stress of the web of the inner circular steel tube under axial compression; is the yield strength of the web of the inner circular steel tube; The inner tube web is subjected to axial compressive stress. G S Shear modulus of the web of inner circular steel tube.

[0111] The ultimate shear bearing capacity of the inner circular steel tube web is for: ;in, is the ultimate strength of the web of the inner circular steel tube.

[0112] As a preferred embodiment, when obtaining the yield shear bearing capacity and the ultimate shear bearing capacity of the anchor web 3, the shear stress cloud diagram of the vertical ribs 4 and the anchor webs 3 is first obtained, and then the shear stress when the vertical ribs 4 and the anchor webs 3 yield is obtained according to the Mises yield criterion, and the yield shear bearing capacity and the ultimate shear bearing capacity of the vertical ribs 4 are calculated based on the obtained shear stress when the vertical ribs 4 yield; the yield shear bearing capacity and the ultimate shear bearing capacity of the anchor webs 3 are calculated based on the obtained shear stress when the anchor webs 3 yield.

[0113] As a preferred embodiment, through theoretical analysis and finite element numerical analysis, the vertical ribs 4 and the anchor webs 3 are both in a pure shear stress state. Figure 4 and Figure 5 is the shear stress cloud diagram of the vertical rib 4 and the anchor web 3, where , so the principal stresses are: .

[0114] According to the Mises yield criterion, the shear stress of the vertical rib 4 when it yields is: , is the yield strength of the vertical rib 4. Assuming that the shear stress is uniformly distributed along the vertical rib 4, the yield shear stress of the vertical rib 4 is V sy3 , yield shear deformation , Ultimate Shear Force V su3 and the limiting shear deformation su3 They are:

[0115] ;

[0116] ;

[0117] ;

[0118] ;

[0119] Therefore, in this embodiment, the yield shear bearing capacity of the vertical rib 4 is and ultimate shear capacity They are:

[0120] ;in, is the shear cross-sectional area of ​​the vertical rib 4; is the yield strength of vertical rib 4; is the maximum shear stress of vertical rib 4 under axial compression, A w The cross-sectional area of ​​vertical rib 4;

[0121] ;in, is the ultimate strength of vertical rib 4.

[0122] In this embodiment, the anchor web 3 is used as a connecting structural plate between the web of the steel beam and the flange of the steel tube column, mainly to transfer the shear force at the end of the beam to the composite steel tube concrete column. Therefore, the contribution of the vertical ribs 4 and the anchor web 3 to the shear bearing capacity of the core area of ​​the node is considered according to the pure shear stress condition. The shear stress of the anchor web 3 when it yields is , is the yield strength of the anchor web 3, and the shear area of ​​the anchor web 3 is the horizontal cross-sectional area of ​​the anchor web 3 in the core area of ​​the node. V sy4 , yield shear deformation sy4 , Ultimate Shear Force V su4 and the limiting shear deformation su4 They are:

[0123] ;

[0124] ;

[0125] ;

[0126] ;

[0127] As a preferred embodiment, the yield shear bearing capacity of the anchor web 3 is V sy4 and ultimate shear capacity V su4 They are: ;in, is the shear cross-sectional area of ​​the anchor web 3; is the maximum shear stress of the anchor web 3 under axial compression; is the yield strength of anchor web 3;

[0128] ,in, is the ultimate strength of the anchor web 3.

[0129] Shear bearing capacity design is one of the main contents of compound steel tube concrete column node design. For compound steel tube concrete column-steel beam nodes with floor slabs, the shear bearing capacity contribution is mainly composed of three parts: the shear bearing capacity of the steel tube web in the core area, the shear bearing capacity of the vertical ribs 4 and the anchor web 3, and the shear bearing capacity of the floor slab and concrete diagonal struts.

[0130] In this embodiment, the yield shear bearing capacity of the outer square steel tube web is V sy1 , Yield shear bearing capacity of inner circular steel tube web , the yield shear bearing capacity of vertical rib 4 , Anchor web 3 yield shear bearing capacity V sy4 and the ultimate shear bearing capacity of concrete V cu The sum of the yield shear bearing capacity of the composite steel tube concrete column-steel beam node with floor slab is taken as the yield shear bearing capacity of the composite steel tube concrete column-steel beam node with floor slab; the ultimate shear bearing capacity of the external steel tube web is taken as , Ultimate shear bearing capacity of inner circular steel tube web , Vertical rib 4 Ultimate shear bearing capacity , Ultimate shear bearing capacity of anchor web 3 V su4 and the ultimate shear bearing capacity of concrete V cu The sum of the yield shear bearing capacity of the composite steel tube concrete column-steel beam node with floor slab is V ye and ultimate shear capacity V ue Calculate using the following formula.

[0131] ;

[0132] ;

[0133] The test value calculated according to the above formula , With theoretical value , The comparison results are shown in Table 1.

[0134] Table 1 Comparison between the test value and calculated value of the shear bearing capacity of the nodes

[0135]

[0136] The calculation results obtained by theoretical derivation, i.e., the theoretical values, are compared with the shear force values ​​measured by the test, i.e., the test values, to verify the correctness of the theoretical derivation results. It can be seen from the above table that the external square steel tube web and vertical ribs 4 obtained in the calculation contribute greatly to the shear bearing capacity of the compound steel tube concrete external rib ring plate node, and the remaining contributions are relatively small. Whether the circular steel tube is filled with concrete has a significant impact on its shear bearing capacity. The average value of the ratio of the theoretical value of the shear yield bearing capacity to the test value is 1.88, and the average value of the ratio of the theoretical value of the shear ultimate bearing capacity to the test value is 1.97. The calculation results of the yield shear bearing capacity and the ultimate shear bearing capacity are significantly greater than the average results in the node test. The concept of node shear capacity reserve is also introduced in this embodiment, i.e., the ratio of the theoretical shear capacity of the node to the actual shear force. It can be seen that this type of node has a large shear capacity reserve, and the shear capacity and stiffness of the node domain are large, which can meet the shear requirements of the node.

[0137] The experimental research shows that the failure mode of the composite steel tube concrete column-steel beam node specimen without considering the combined effect of the floor slab is the failure of the beam end, and the failure mode of the node specimen considering the combined effect of the floor slab changes from the failure of the beam end to the failure of the column end. The anchor web 3 has a certain contribution to the shear bearing capacity of the core area of ​​the node. The effect of the floor slab inhibits the development of the shear deformation of the core area of ​​the node. With the increase of the thickness of the floor slab, the shear bearing capacity of the node is improved to a certain extent, while the shear deformation of the node decreases slightly.

[0138] This embodiment adopts a shear tri-fold model for the node domain steel, and a diagonal strut mechanism for the node core area concrete. The calculation formulas for the yield shear bearing capacity and the ultimate shear bearing capacity of the composite steel tube concrete column-steel beam node with floor slab are derived, providing a bearing capacity calculation method for the engineering design of the node. The node calculated and designed according to the above calculation method of this embodiment has sufficient shear reserve capacity when destroyed, indicating that the node design complies with the seismic design principle of strong shear and weak bending.

[0139] In the combined node with floor slab in this embodiment, the floor slab and the steel beam 5 form a combined beam node, which significantly improves the stiffness of the beam end, thereby improving the bending and shear bearing capacity of the beam end; compared with the bearing capacity of the beam end, the column end bearing capacity does not change when the cross-sectional size of the composite steel tube concrete column is constant. If the node design is unreasonable, it is possible that the bearing capacity of the beam end is greater than the bearing capacity of the column end, resulting in column end damage at the node, thereby violating the seismic design principle of "strong column and weak beam". Therefore, the study of the seismic performance of the node must take the role of the floor slab into consideration. At the same time, a reasonably designed node should also meet the failure principle of "strong shear and weak bending, strong node and weak component", so the reasonable failure mode of the node should be bending failure of the beam end, not shear failure of the core area of ​​the node.

[0140] The node specimens used in the test were subjected to a quasi-static test study. The results showed that the composite node eventually suffered bending failure at the beam end or column end, and no shear failure was found in the core area of ​​the node. However, the shear performance of the node should be quantified in order to comprehensively evaluate the stress performance of such nodes. Therefore, this embodiment studies the calculation method of the shear bearing capacity of the composite node with floor slabs, and derives the calculation formula of the shear bearing capacity of the node. The ratio of the theoretical results to the test results is between 1.88 and 1.97, indicating that the composite node considering the floor slab studied in this embodiment has sufficient shear reserve and can meet the seismic design principle of "strong shear and weak bending".

[0141] In the test, all specimens suffered bending failure at the beam ends or column ends. The shear bearing capacity of the combined node obtained from the test results in this embodiment is: the shear bearing capacity of the node corresponding to the bending failure of the combined node; and the shear bearing capacity of the combined node considering the effect of the floor slab obtained by theoretical derivation is the shear bearing capacity that the node can withstand when shear failure occurs, theoretical calculation / test result = 1.88~1.97, which further illustrates that the shear reserve of such combined nodes considering the effect of the floor slab is sufficient, and shear brittle failure will not occur under the action of an earthquake, and can be promoted and applied in combined structures in strong earthquake areas.

[0142] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the shear bearing capacity of a composite steel tube concrete column-steel beam node with a floor slab, characterized in that: include: Determine the shear bearing capacity of the steel tube web, vertical ribs, anchor web and concrete in the core area of ​​the composite steel tube concrete column-steel beam node with floor slab, wherein the shear bearing capacity of the concrete includes the contribution of the shear bearing capacity of the floor slab; After determining the part that contributes to the shear bearing capacity in the composite steel tube concrete column-steel beam node with floor slab, the yield shear bearing capacity and ultimate shear bearing capacity of each part are obtained respectively, where: When obtaining the shear bearing capacity of concrete, it is confirmed that the ultimate shear bearing capacity of concrete includes the shear bearing capacity of the compression truss and the shear bearing capacity of the restrained truss according to the diagonal strut mechanism. When calculating the shear bearing capacity of the compression truss, it is necessary to consider the contribution of the concrete floor slab to the shear bearing capacity of the compression truss, and then calculate the shear bearing capacity of the compression truss and the shear bearing capacity of the restrained truss respectively, and take the sum of the shear bearing capacity of the compression truss and the shear bearing capacity of the restrained truss as the ultimate shear bearing capacity of concrete; The sum of the yield shear bearing capacity of the steel tube web in the core area, the yield shear bearing capacity of the vertical ribs, the yield shear bearing capacity of the anchor web and the ultimate shear bearing capacity of concrete is taken as the yield shear bearing capacity of the composite steel tube concrete column-steel beam node with floor slab; the sum of the ultimate shear bearing capacity of the steel tube web in the core area, the ultimate shear bearing capacity of the vertical ribs, the ultimate shear bearing capacity of the anchor web and the ultimate shear bearing capacity of concrete is taken as the ultimate shear bearing capacity of the composite steel tube concrete column-steel beam node with floor slab; The ultimate shear bearing capacity of the concrete is: V cu =V cu1 +V cu2 ; Shear capacity of concrete compression trusses V cu1 for: Among them, d c is the concrete width; σ cB is the ultimate compressive strength of the concrete diagonal strut; θ is the angle between the diagonal strut and the vertical plane; Ultimate shear capacity V of restrained trusses cu2 for: Where p is the horizontal pressure; l a M is the length of the steel pipe flange A area; fp is the flange plastic hinge bending moment; The shear bearing capacity V of the concrete compression truss cu1 When calculating, Where h is the core area height, h = 0.5h c +h b -t bf ; Among them, h c is the thickness of the concrete slab, h b is the height of the steel beam, t bf is the thickness of the steel beam flange.

2. The method for calculating the shear bearing capacity of a composite concrete-filled steel tube column-steel beam node with a floor slab as claimed in claim 1, characterized in that: The yield shear bearing capacity and the ultimate shear bearing capacity of the steel tube web are obtained according to the shear tri-fold model of the steel tube web in the core area.

3. The method for calculating the shear bearing capacity of a composite concrete-filled steel tube column-steel beam node with a floor slab as claimed in claim 2, characterized in that: The steel tube webs include inner round steel tube webs and outer square steel tube webs; The yield shear bearing capacity V sy1 for: Among them, A w1 is the cross-sectional area of ​​the web of the outer steel tube; τ sy1 is the maximum shear stress of the web of the external square steel tube under axial compression; f sy1 is the yield strength of the web of the outer square steel tube; σ s1 The web of the outer square steel tube bears the axial compressive stress; The ultimate shear bearing capacity V su1 for: Among them, f su1 is the ultimate strength of the outer square steel tube web; The yield shear bearing capacity V sy2 for: Among them, A s2 is the cross-sectional area of ​​the inner circular steel pipe; τ sy2 is the maximum shear stress of the web of the inner circular steel tube under axial compression; f sy2 is the yield strength of the web of the inner circular steel tube; σ s2 The web of the inner tube bears the axial compressive stress; The ultimate shear bearing capacity V su2 for: Among them, f su2 is the ultimate strength of the web of the inner circular steel tube.

4. The method for calculating the shear bearing capacity of a composite concrete-filled steel tube column-steel beam node with a floor slab according to claim 1, characterized in that: When obtaining the yield shear bearing capacity and the ultimate shear bearing capacity of the anchor web, first obtain the shear stress cloud diagram of the vertical ribs and the anchor web, then obtain the shear stress when the vertical ribs and the anchor web yield according to the Mises yield criterion, and calculate the yield shear bearing capacity and the ultimate shear bearing capacity of the vertical ribs according to the obtained shear stress when the vertical ribs yield; calculate the yield shear bearing capacity and the ultimate shear bearing capacity of the anchor web according to the obtained shear stress when the anchor web yields.

5. The method for calculating the shear bearing capacity of a composite concrete-filled steel tube column-steel beam node with a floor slab as claimed in claim 4 is characterized in that: The yield shear bearing capacity V of the vertical ribs sy3 and the ultimate shear bearing capacity V su3 They are: Among them, A lτ is the shear cross-sectional area of ​​the vertical rib; f sy3 is the yield strength of the vertical rib; τ sy3 is the maximum shear stress of the vertical rib under axial compression; Among them, f su3 is the ultimate strength of the vertical ribs.

6. The method for calculating the shear bearing capacity of a composite concrete-filled steel tube column-steel beam node with a floor slab as claimed in claim 4, characterized in that: The yield shear bearing capacity V of the anchor web sy4 and the ultimate shear bearing capacity V su4 They are: Among them, A mτ is the shear cross-sectional area of ​​the anchor web; τ sy4 is the maximum shear stress of the anchor web under axial compression; f sy4 is the anchor web yield strength; Among them, f su4 is the ultimate strength of the anchor web.

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