Method for calculating flexural capacity of assembled integral UHPC-HSC beam-slab-column joint

Abstract

The invention discloses a method for calculating the flexural capacity of an assembled integral UHPC-HSC beam plate column joint. The method comprises the following steps: prefabricating an HSC column, a U-shaped UHPC beam template, a UHPC laminated plate, a post-cast joint, a laminated T-shaped beam plate area and a column bolt connecting piece, and assembling to obtain an integral UHPC-HSC laminated beam plate; according to the structural characteristics of the assembled integral UHPC-HSC beam-slab-column joint, a target beam-slab-column joint playing a key role in beam hinge damage is determined; and assuming a flat section, simplifying a concrete stress graph of a pressed area into an equivalent rectangular stress graph according to the concrete constitutive model and the steel bar constitutive model, and calculating to obtain the bending moment of the beam-column joint according to a balance equation of the force and moment of the beam-column joint area. According to the method, the accuracy of a calculation result is ensured by simplifying the UHPC stress graph of the tensile region and considering the material characteristics.

Description

Technical Field

[0001] The present invention belongs to the field of concrete structure design, and particularly relates to a method for calculating the flexural bearing capacity of assembled monolithic UHPC-HSC beam-column joints. Background Art

[0002] The UHPC composite beam slab is a new type of beam-slab combination formed by using UHPC to make precast U-shaped permanent beam forms and UHPC composite floor slabs, and then pouring post-cast UHPC concrete T-shaped beam cores. UHPC is a new type of material composed of a cement matrix and fibers, and has the advantages of high strength, high toughness, high energy dissipation capacity, high durability, etc. UHPC is mainly composed of cement, active powders (such as silica fume, fly ash, quartz powder, etc.), quartz sand, steel fibers, admixtures and water. The UHPC composite beam slab gives full play to the characteristics of UHPC materials with ultra-high strength and high durability, not only can reduce the self-weight of components, but also can significantly improve the service life of the structure; the precast permanent beam form replaces the traditional formwork, eliminating the need for support during the construction process, reducing the formwork turnover and construction costs, and improving the construction efficiency. Compared with ordinary composite beams, the U-shaped composite beam has better integrity.

[0003] The precast column is made of HSC, which can reduce the self-weight of the component and facilitate the transportation and on-site hoisting of the component. The precast slab is made of UHPC to improve the bearing capacity of the building. The post-cast UHPC is used at the connection position of the beam-column joint. On the one hand, it improves the bearing capacity of the joint and enhances the reliability of the connection; on the other hand, it enhances the integrity of the structure and improves the seismic performance of the structure. In summary, compared with traditional assembled joints, the assembled monolithic UHPC-HSC beam-column joint makes up for the disadvantages of poor connection performance and weak integrity, and has stronger seismic performance.

[0004] The beam-column joint is of great importance in the seismic design of reinforced concrete frame structures. In the Code for Design of Concrete Structures (GB50010-2010) and the Code for Seismic Design of Buildings (GB50011-2010), it is required to design according to the principle of "strong joints and weak members, strong shear and weak flexure". Therefore, proposing an effective method for calculating the flexural bearing capacity of the beam end is an important theoretical basis for the design of new assembled frame structures. However, there is little research on the method for calculating the flexural bearing capacity of assembled monolithic UHPC-HSC beam-column joints, which restricts its further promotion and application. So far, there has been no literature report and practical application on the method for calculating the flexural bearing capacity of assembled monolithic UHPC-HSC beam-column joints. In the prior art, it is common to calculate the flexural bearing capacity of ordinary concrete joints. This calculation method does not take into account the excellent tensile strength of UHPC materials, and the load sharing form of its post-cast UHPC also needs further research. Summary of the Invention

[0005] To solve the above technical problems, a scientific and reasonable calculation method for the flexural bearing capacity of assembled integral UHPC-HSC beam-column joints is provided, which has a simple, accurate, highly applicable and effective calculation method. The present invention provides a calculation method for the flexural bearing capacity of assembled integral UHPC-HSC beam-slab-column joints, including:

[0006] Prefabricated HSC columns, U-shaped UHPC beam forms, UHPC composite slabs, post-cast joints and composite T-shaped beam-slab areas, and column bolt connectors are assembled to obtain an integral UHPC-HSC composite beam-slab-column;

[0007] According to the structural characteristics of the assembled integral UHPC-HSC beam-slab-column joints, beam-slab-column joints with beam hinge failure are determined;

[0008] Assume a plane section. According to the concrete constitutive model and the steel bar constitutive model, the concrete stress diagram in the compression zone is simplified into an equivalent rectangular stress diagram. Based on the force and moment equilibrium equations in the beam-column joint area, the moment of the beam-column joint is calculated.

[0009] Preferably, the manufacturing process of the prefabricated HSC column includes: steel bar binding, column formwork erection, concrete pouring, and rough surfaces are set on the upper and lower bottom surfaces of the precast column, and the bottom of the upper column is poured at 45°.

[0010] Preferably, during the process of erecting the column formwork, it also includes: additionally erecting a cylindrical formwork at the bottom of the upper column and the top of the lower column, and embedding bolt embedded parts;

[0011] Before pouring the bottom of the upper column at 45°, it also includes: first connecting the precast columns with bolts.

[0012] Preferably, the manufacturing process of the prefabricated U-shaped UHPC beam form includes:

[0013] First, steel bar binding and mold assembly are carried out; then pouring is carried out from the bottom form, and the construction is carried out in an inverted pouring manner; finally, after high-temperature steam curing, the formwork is removed after curing, and grooves are opened on three sides of the prefabricated U-shaped UHPC beam form.

[0014] Preferably, the manufacturing process of the prefabricated UHPC composite slab includes:

[0015] Steel bar binding, formwork erection, concrete pouring, high-temperature steam curing, and formwork removal, and a rough surface is set on the upper surface of the prefabricated UHPC composite slab.

[0016] Preferably, the process of simplifying the concrete stress diagram in the compression zone into an equivalent rectangular stress diagram includes:

[0017] According to the equivalent conditions that the resultant force of the concrete compressive stress is equal in magnitude and the acting point of the resultant force of the figure before and after equivalence remains unchanged, determine the reduction coefficient of the stress value in the equivalent rectangular stress diagram and the coefficient of the height of the equivalent rectangular stress diagram to the height of the neutral axis;

[0018] Considering the tensile strength of UHPC, simplify the stress diagram of the tensile zone of UHPC into an equivalent rectangular stress diagram, and determine the reduction coefficient of the stress value and the coefficient of the height of the equivalent rectangular stress diagram to the height of the neutral axis.

[0019] Preferably, the reduction coefficient of the stress value in the equivalent rectangular stress diagram and the coefficient of the height of the equivalent rectangular stress diagram to the height of the neutral axis are determined according to the concrete constitutive model.

[0020] Preferably, when simplifying the stress diagram of the tensile zone of the UHPC into an equivalent rectangular stress diagram, the reduction coefficient of the stress value is determined according to the tensile constitutive model of the UHPC material.

[0021] Preferably, the process of calculating the bending moment of the beam-column joint includes:

[0022] Taking the target beam-column joint of the assembled monolithic UHPC-HSC beam-slab-column joint as the object, establish a calculation sketch of the beam-column joint; wherein, the bottom of the column is a fixed hinge support, the right beam end is a movable hinge support, the top of the column is a free end, and axial force and reciprocating horizontal load are applied;

[0023] According to the moment balance equation of the beam-column joint area, obtain the horizontal shear force at the top of the column;

[0024] Considering the influence of the cast-in-place UHPC and HSC, calculate the bending moment values generated at the beam end of the beam section at the positions of the cast-in-place UHPC and the cast-in-place HSC respectively, and consider different situations of whether the UHPC beam formwork and the cast-in-place UHPC are on the tensile side or the compressive side, and perform bending moment calculations respectively;

[0025] Taking the ultimate compressive strain of the concrete edge in the compression zone of the composite beam section as the peak value for bending moment design, calculate the bending moment values when the lower steel bars are in tension and the upper steel bars are in tension respectively, and determine the bending moment of the section neutral axis at the peak point through the force balance equation and taking moments about the section neutral axis.

[0026] Compared with the prior art, the present invention has the following advantages and technical effects:

[0027] Based on the structure of the assembled monolithic UHPC-HSC beam-column joint, the present invention obtains the beam-end moment of the beam-column joint, considers and analyzes the UHPC beam formwork and the stressed side of the cast-in-place UHPC, and calculates the neutral axis moment of the section under the peak point. Its calculation method is more in line with the requirements of the actual structure, has better safety performance, provides a scientific basis for the beam-end flexural design of the assembled monolithic UHPC-HSC beam-column joint, and its calculation method is simple, accurate, has strong applicability and good effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The drawings forming a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0029] Figure 1 is a schematic overall side view structure diagram of an embodiment of the present invention;

[0030] Figure 2 is a simplified calculation diagram of the joint of an embodiment of the present invention;

[0031] Figure 3 is a geometric dimension and reinforcement drawing of the beam-column joint specimen of an embodiment of the present invention;

[0032] Figure 4 is a strain and stress distribution diagram of the composite beam section when calculating the peak point of the cast-in-place UHPC at the beam-end joint of an embodiment of the present invention; wherein, (a) is the strain and stress distribution diagram when the lower steel bar is in tension and x bp ≤h bc ; (b) is the strain and stress distribution diagram when the lower steel bar is in tension and x bp >h bc ; (c) is the strain and stress distribution diagram when the upper steel bar is in tension and x bp ≤h bc ; (d) is the strain and stress distribution diagram when the upper steel bar is in tension and x bp >h bc ;

[0033] Figure 5 is a strain and stress distribution diagram of the composite beam section when calculating the peak point of the cast-in-place HSC at the beam-end joint of an embodiment of the present invention; wherein, (a) is the strain and stress distribution diagram when the lower steel bar is in tension and x bp ≤h bc ; (b) is the strain and stress distribution diagram when the lower steel bar is in tension and x bp >h bc ; (c) is the strain and stress distribution diagram when the upper steel bar is in tension and x bp ≤h bc ; (d) is the strain and stress distribution diagram when the upper steel bar is in tension and x bp >h bc ;

[0034] Figure 6 Schematic side view structure diagram of the precast column bolt connector according to an embodiment of the present invention;

[0035] Wherein, 1. HSC column; 2. U-shaped UHPC beam formwork; 3. UHPC composite slab; 4. Post-cast joint and composite T-shaped beam and slab area; 5. Column bolt connector. Detailed implementation manners

[0036] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the drawings and in conjunction with the embodiments.

[0037] It should be noted that the steps shown in the flowchart of the drawings may be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than here.

[0038] As Figures 1-6 shown, in this embodiment, a method for calculating the flexural bearing capacity of an assembled monolithic UHPC-HSC beam, slab and column joint is provided, including:

[0039] Precast HSC columns, U-shaped UHPC beam formworks, UHPC composite slabs, post-cast joints and composite T-shaped beam and slab areas, and column bolt connectors are assembled to obtain an assembled monolithic UHPC-HSC composite beam, slab and column;

[0040] According to the structural characteristics of the assembled monolithic UHPC-HSC beam, slab and column joint, determine the beam, slab and column joint with the failure mode of beam hinge failure;

[0041] Assume a plane section. According to the concrete constitutive model and the steel bar constitutive model, simplify the concrete stress diagram in the compression zone into an equivalent rectangular stress diagram, and calculate the bending moment of the beam-column joint according to the force and moment balance equations in the beam-column joint area.

[0042] Furthermore, in this embodiment, according to the structural characteristics of the assembled monolithic UHPC-HSC beam, slab and column joint, determine the beam, slab and column joint with the "beam hinge failure mechanism", and its flexural bearing capacity is determined by the beam end bending moment. According to the plane section assumption, the strain of the beam section changes linearly. When the concrete edge in the compression zone of the beam section reaches the ultimate compressive strain, for the sake of simplified calculation, usually simplify the concrete stress diagram in the compression zone into an equivalent rectangular stress diagram. Calculate the bending moment according to the concrete constitutive model and the steel bar constitutive model. This calculation method has the characteristics of simplicity, accuracy and strong applicability on the one hand; on the other hand, it has good safety and better meets the requirements of actual projects, providing a scientific basis for the flexural design of the assembled monolithic UHPC-HSC beam, slab and column joint.

[0043] According to the tensile stress-strain curves of UHPC and HSC, considering the influence of the tensile strength of UHPC and HSC, the reinforcement of the composite beam, and the post-cast UHPC on the flexural bearing capacity of the beam end, this embodiment proposes a calculation method for the flexural bearing capacity of the beam end of an assembled monolithic UHPC-HSC beam-slab-column joint. The objects of the calculation method include precast HSC columns 1, precast U-shaped UHPC beam forms 2, precast UHPC composite slabs 3, post-cast joints and composite T-shaped beam-slab areas 4, and precast column bolt connectors 5.

[0044] Furthermore, the manufacturing process of the precast U-shaped UHPC beam form 2 includes: first, binding the steel bars and assembling the molds; then, pouring from the bottom form and constructing in an inverted pouring manner; finally, curing by high-temperature steam; after curing, removing the form. In order to enhance the bonding performance between the precast UHPC and the post-cast concrete, the three sides of the precast U-shaped UHPC beam form 2 are grooved.

[0045] Furthermore, the manufacturing process of the precast HSC column 1 includes: binding steel bars, erecting forms, and pouring concrete. To ensure the bonding performance between the precast concrete and the post-cast concrete, rough surfaces are set on the upper and lower bottom surfaces of the precast column; to facilitate the construction of the post-cast concrete in the joint core area, the bottom of the upper column is poured at a 45° angle.

[0046] Furthermore, during the process of erecting the column form, a cylindrical form is additionally erected at the bottom of the upper column and the top of the lower column; bolt embedded parts are pre-buried.

[0047] Furthermore, the manufacturing process of the precast UHPC composite slab 3 includes: binding steel bars, erecting forms, pouring concrete, and finally curing by high-temperature steam. After curing, removing the form. In order to enhance the bonding performance between the precast UHPC and the post-cast concrete, a rough surface is set on the upper surface of the precast slab.

[0048] Furthermore, before pouring the post-cast concrete in the joint core area, first connect the precast columns with bolts.

[0049] To enhance the integrity of the joint core area of the assembled monolithic UHPC-HSC beam-slab-column joint, this embodiment uses a method of prefabricating and embedding a steel plate and bolt holes in the central UHPC small column, and then connecting the upper and lower precast HSC columns 1 with bolts, pouring post-cast UHPC at the joint, and connecting the steel bars by extrusion sleeves.

[0050] Meanwhile, for the connection nodes of the prefabricated structure in this embodiment, bolt connection and post-cast integral connection are combined. Specifically, for the post-cast integral connection, after the beam and column are installed in place, the steel bars in the precast beam and column are connected, and then concrete is post-cast at the connection of the beam and column to make the connection. For the bolt connection, steel plates and bolt holes are embedded in the precast beam and column, and then the beam and column are connected with bolts. In this way, the prefabricated frame can quickly reach a certain strength. And the bolt connection has the advantages of strong adaptability, less affected by the environment, convenient and fast construction, etc. This embodiment combines the bolt connection and the post-cast integral connection, with the advantages of strong integrity and simplified construction.

[0051] This embodiment combines the bolt connection and the post-cast integral connection, with the advantages of strong integrity and simplified construction.

[0052] Further, in the construction process of component assembly and cast-in-place concrete, after the precast components are cured, assembly is carried out, including hoisting the precast HSC column 1 and the precast U-shaped UHPC beam formwork 2; then tying the upper longitudinal bars of the beam and the stirrup bars in the joint core area, and finally erecting the wooden formwork and pouring concrete. The UHPC in the core area is poured from one side at a 45° angle, using a chute for pouring, and after pouring, it is sealed with a wooden formwork.

[0053] To simplify the calculation of the flexural bearing capacity of the beam end of the assembled integral UHPC-HSC beam-column joint, the concrete stress diagram in the compression zone is simplified to an equivalent rectangular stress diagram. According to the two equivalent conditions that the resultant force of the concrete compressive stress is equal in magnitude and the action point of the resultant force of the graph before and after equivalence remains unchanged, the reduction coefficient α1 of the stress value in the equivalent rectangular stress diagram and the coefficient β1 of the height of the equivalent rectangular stress diagram to the neutral axis height can be obtained. According to the Specification for Technical Code of Reactive Powder Concrete Structures DBJ43 / T325 - 2017, the stress diagram in the tension zone of UHPC is simplified to an equivalent rectangular stress diagram. The height remains unchanged, and the reduction coefficient of the stress value is k, taking k = 0.25. The calculation sketch of the beam-column joint is as Figures 2-3 shown. The bottom of the column is a fixed hinge support, the right beam end is a movable hinge support, the top of the column is a free end, and an axial force N c and a reciprocating horizontal load F c are applied. According to the moment balance equation of the beam-column joint area, the horizontal shear force F c at the top of the column is obtained.

[0054] ∑M c =∑M b

[0055] vM c =F c (H1 + H2)

[0056]

[0057] Among them, ∑M c is the sum of the column-end bending moments; ∑M b is the sum of the beam-end bending moments (the bending moments at the beam-end sections in the corresponding state); F c is the horizontal shear force at the column top; H1 is the height of the upper column; H2 is the height of the lower column.

[0058] Therefore, the bending moment of the beam-column joint:

[0059] Furthermore, the bending moment value M I ' generated by the beam section at the post-cast HSC position at the beam end:

[0060]

[0061] Among them, M I is the bending moment of the beam section; L b is the shear-span length of the beam; l is the length of the post-cast UHPC at the beam end.

[0062] For composite beam-slab, considering the tensile strength of UHPC, whether the UHPC beam formwork and the post-cast UHPC are located on the tensile side or the compressive side, the calculation process is different, so they are considered and analyzed separately.

[0063] Furthermore, taking the ultimate compressive strain at the edge of the compressive zone of the composite beam section as the peak value for moment design, as Figure 4 shown by the strain and stress distributions of the composite beam-slab section at the beam end near the column when reaching the peak point.

[0064] When the lower steel bars are in tension, x bp ≤h bc ;

[0065]

[0066] Among them, φ bp is the yield curvature of the beam section; ε nucu is the ultimate compressive strain at the edge of the post-cast UHPC compressive zone; x bp is the height of the compressive zone of the beam section when the beam section yields; ε' s is the strain of the compressive steel bars; a' s is the distance from the resultant force point of the compressive steel bars to the compressive edge of the beam section; ε s is the yield strain of the tensile steel bars; h b0 is the effective height of the beam section, h b is the height of the beam section, a s is the distance from the resultant force point of the tensile steel bars to the tensile edge of the beam section.

[0067] f y A bs +B s Es (ε s -ε y )A bs +2kf sut (h bu3 +h bc -x bp )(b f +b bu1 )+2kf sut (h bu1 +h bu2 )(b bu1 +b bu2 )+kf sut h bul (b b -2b bu1 -2b bu2 )+kf nut h bu2 b bc +kf nut (h bu3 +h bc -x bp )(b bc +2b bu2 )=E s ε s ′A bs′ +2α su1 β su1 f suc (x bp h bc )(b f +b bu1 )+α nu1 β nu1 f nuc h bc (2b f +b b )+α nu1 β nu1 f nuc (x bp -h bc )(b bc +2b bu2 )

[0068] Among them, T s is the resultant force of the tension steel bars; C s ′ is the resultant force of the compression steel bars; f y is the yield strength of the steel bars; A bs is the area of the tension steel bars; E s is the elastic modulus of the steel bars; ε s ′ is the strain of the compression steel bars; A′ bs is the area of the compression steel bars; T su1The tensile force on the side wall of the U-shaped UHPC precast beam formwork; T su2 The tensile force on the bottom wall of the U-shaped UHPC precast beam formwork, C nu1 +C nu2 is the pressure of the post-cast UHPC, and k is the reduction coefficient of the stress value in the equivalent rectangular stress diagram of the UHPC in the tension zone; T nu1 is the tensile force on the upper part of the post-cast UHPC; T nu2 is the tensile force on the lower part of the post-cast UHPC. α su1 is the reduction coefficient of the stress value in the equivalent rectangular stress diagram of the precast UHPC in the compression zone; β su1 is the coefficient of the height of the equivalent rectangular stress diagram of the precast UHPC in the compression zone to the height of the neutral axis; α nu1 is the reduction coefficient of the stress value in the equivalent rectangular stress diagram of the cast-in-situ UHPC in the compression zone; β nu1 is the coefficient of the height of the equivalent rectangular stress diagram of the cast-in-situ UHPC in the compression zone to the height of the neutral axis; f sut Axial compressive strength of precast UHPC in the tension zone; f nut Axial compressive strength of cast-in-situ UHPC in the tension zone; f suc Axial compressive strength of precast UHPC in the compression zone; f nuc Axial compressive strength of cast-in-situ UHPC in the compression zone.

[0069] Taking moments about the section neutral axis:

[0070]

[0071] Preferably, x bp > h bc ;

[0072]

[0073] where ε nucu is the ultimate compressive strain at the edge of the compression zone of the post-cast UHPC;

[0074] From the force balance equation:

[0075] f y A bs +B s E s (ε s -ε y )A bs +2kf sut (h b -x bp )(b bu1 +b bu2 )+kf sut h bul b bc +kf nut (hb -h bul -x bp )b bc = E s ε′ s A′ bs + 2α sul β sul f suc h bu3 (b bu1 + b f ) + 2α sul β sul f suc (x bp - h bu3 - h bc )(b bu1 + b bu2 ) + α nul β nul f nuc h bc (b b + 2b f ) + α nul β nul f nuc h bu3 (b b - 2b bu1 ) + α nul β nul f nuc (x bp - h bu3 - h bc )b bc

[0076] Among them, T su1 is the tensile force of the side wall of the U-shaped UHPC precast beam formwork, T su2 is the tensile force of the bottom wall of the U-shaped UHPC precast beam formwork, T nu is the tensile force of the post-cast UHPC, C su is the pressure of the side wall of the U-shaped UHPC precast beam formwork, C nu1 + C nu2 + C nu3 is the pressure of the post-cast UHPC, α nu1 is the reduction coefficient of the stress value in the equivalent rectangular stress diagram of the post-cast UHPC, β nu1 is the coefficient of the height of the equivalent rectangular stress diagram of the post-cast UHPC to the height of the neutral axis

[0077] Taking moments about the neutral axis of the cross-section:

[0078]

[0079] Preferably, the upper steel bars are in tension, x bp≤h bu1 ;

[0080]

[0081] wherein, E sucu is the ultimate compressive strain at the edge of the bottom wall of the U-shaped UHPC precast beam formwork in the compression zone;

[0082] From the force balance equation:

[0083] f y A bs +B s E s (ε s -ε y )A bs +kf sut (h bul -x bp )b bc +2kf sut (h b -h bc -h bu3 -x bp )(b bu1 +b bu2 )+2kf sut h bu3 (b f +b bu1 )+kf nut h bu2 b bc +kf nut h bu3 (b bc +2b bu2 )+2kf nut h bc (2b f +b b ) = E s ε′ s A′ bs +α sul β sul f suc x bp b b

[0084] wherein, T su1 is the tensile force of the bottom wall of the U-shaped UHPC precast beam formwork, T su2 is the tensile force of the side wall of the U-shaped UHPC precast beam formwork, T nu1 +T nu2 is the tensile force of the post-cast UHPC, C su is the compressive force of the bottom wall of the U-shaped UHPC precast beam formwork, α su1β is the reduction coefficient of the stress value in the equivalent rectangular stress diagram of precast UHPC in the compression zone. su1 f is the coefficient of the height of the equivalent rectangular stress diagram of precast UHPC in the compression zone to the height of the neutral axis. suc Axial compressive strength of precast UHPC in the compression zone;

[0085] Taking moments about the neutral axis of the section:

[0086]

[0087] Preferably, x bp > h bu1 ;

[0088]

[0089] Where, E uc is the compressive strain at the edge of the cast-in-place UHPC;

[0090] From the force equilibrium equation:

[0091] f y A bs + B s E s (ε s - ε y )A bs + 2kf sut (h b - h bc - h bu3 - x bp )(b bu1 + b bu2 ) + 2kf sut h bu3 (b f + b bu1 ) + kf nut (h bu2 + b bu1 - x bp )b bc + kf nut h bu3 (b bc + 2b bu2 ) + kf nut h bc (b b + 2b f ) = E s ε s ′A bs ′ + α su1 β sul f suc h bu1 b bc + 2α sul βsul f suc x bp (b bu1 +b bu2 )+α nul β nul f nuc (x bp -h bul )b bc

[0092] Among them, T su is the tensile force of the side wall of the U-shaped UHPC precast beam formwork, T nu1 +T nu2 +T nu3 is the tensile force of the post-cast UHPC, C su1 +C su2 is the pressure of the bottom wall and side wall of the U-shaped UHPC precast beam formwork, C nu is the pressure of the post-cast UHPC;

[0093] Taking moments about the neutral axis of the cross-section:

[0094]

[0095] Furthermore, as Figure 5 shown, calculate the peak point of the beam cross-section moment at the interface position between the post-cast UHPC and the post-cast HSC for comparison with the flexural bearing capacity of the joint.

[0096] When the lower steel bars are in tension, x bp ≤h bc ;

[0097]

[0098] Among them, φ bp is the yield curvature of the beam cross-section; ε ccu is the ultimate compressive strain at the edge of the compression zone of the post-cast HPC; x bp is the height of the compression zone of the cross-section when the beam cross-section yields; ε′ s is the strain of the compression steel bars; a′ s is the distance from the resultant force point of the compression steel bars to the compression edge of the beam cross-section; ε s is the yield strain of the tensile steel bars; h b0 is the effective height of the beam cross-section, h b is the height of the beam cross-section, a s is the distance from the resultant force point of the tensile steel bars to the tensile edge of the beam cross-section.

[0099] Equilibrium equation of forces:

[0100] f y A bs +B s Es (ε s -ε y )A bs +2kf sut (h bu3 +h bc -x bp )(b f +b bu1 )+2kf sut (h bu1 +h bu2 )(b bu1 +b bu2 )+kf sut h bu1 b b =E s ε s ′A bs ′+2α su1 β su1 f suc (x bp -h bc )(b f +b bu1 )+2α cc β cc f cc h bc (2b f +b bc )+α cc β cc f cc (x bp -h bc )(b bc +2b bu2 )

[0101] Among them, T s is the resultant force of the tension steel bars; C s ′ is the resultant force of the compression steel bars; f y is the yield strength of the steel bars; A bs is the area of the tension steel bars; E s is the elastic modulus of the steel bars; ε s ′ is the strain of the compression steel bars; A′ bs is the area of the compression steel bars; T su1 is the tension force on the side wall of the formwork of the U-shaped UHPC precast beam; T su2 is the tension force on the bottom wall of the formwork of the U-shaped UHPC precast beam, k is the reduction coefficient of the stress value in the equivalent rectangular stress diagram of UHPC in the tension zone; α su1 is the reduction coefficient of the stress value in the equivalent rectangular stress diagram of precast UHPC in the compression zone; β su1 is the coefficient of the height of the equivalent rectangular stress diagram of precast UHPC in the compression zone to the height of the neutral axis; α ccis the reduction coefficient of the stress value in the equivalent rectangular stress diagram of the cast-in-place HSC in the compression zone; β cc is the coefficient of the height of the equivalent rectangular stress diagram of the cast-in-place HSC in the compression zone to the height of the neutral axis; f sut Axial compressive strength of the precast UHPC in the tension zone; f suc Axial compressive strength of the precast UHPC in the compression zone; f cc Axial compressive strength of the cast-in-place HSC in the compression zone.

[0102] Taking moments about the neutral axis of the cross-section:

[0103]

[0104] Preferably, x bp >h bc ;

[0105]

[0106] where ε ccu is the ultimate compressive strain at the edge of the compression zone of the cast-in-place HSC;

[0107] From the force equilibrium equation:

[0108] f y A bs +B s E s (ε s -ε y )A bs +2kf sut (h b -x bp )(b bu1 +b bu2 )+kf sut h bul b bc =E s ε′ s A′ bs +2α sul β sul f suc h bu3 (b bu1 +b f )+2α sul β sul f suc (x bp -h bu3 -h bc )(b bu1 +b bu2 )+2α cc β cc f cc h bc (bb +2b f ) + α cc β cc f cc h bu3 (b bc +2b bu2 ) + α cc β cc f cc (x bp -h bu3 -h bc )b bc

[0109] Take moments about the neutral axis of the cross-section:

[0110]

[0111] Preferably, the upper steel bars are in tension, x bp ≤h bu1 ;

[0112]

[0113] where, E sucu is the ultimate compressive strain at the edge of the bottom wall of the formwork of the U-shaped UHPC precast beam in the compression zone;

[0114] From the force equilibrium equation:

[0115] f y A bs + B s E s (ε s - ε y )A bs + kf sut (h bul - x bp )b bc + 2kf sut (h b - h bc - h bu3 - x bp )(b bu1 + b bu2 ) + 2kf sut h bu3 (b f + b bu1 ) = E s ε′ s A′ bs + α sul β sul f suc x bp b b

[0116] Among them, T su1 is the tensile force of the bottom wall of the U-shaped UHPC precast beam formwork, and T su2 is the tensile force of the side wall of the U-shaped UHPC precast beam formwork, and C su is the pressure of the bottom wall of the U-shaped UHPC precast beam formwork, and α su1 is the reduction coefficient of the stress value in the equivalent rectangular stress diagram of the precast UHPC in the compression zone, and β su1 is the coefficient of the height of the equivalent rectangular stress diagram of the precast UHPC in the compression zone to the height of the neutral axis, and f suc Axial compressive strength of precast UHPC in the compression zone.

[0117] Taking moments about the neutral axis of the cross-section:

[0118]

[0119] Preferably, x bp > h bu1 ,

[0120]

[0121] Among them, E uc is the compressive strain at the edge of the post-cast UHPC;

[0122] From the force equilibrium equation:

[0123] f y A bs + B s E s (ε s - ε y ) A bs + 2kf sut (h b - h bc - h bu3 - x bp )(b bu1 + b bu2 )

[0124] + 2kf sut h bu3 (b f + b bu1 )

[0125] = E s ε s ′ A bs ′+ α su1 β sul f suc h bu1 b bc

[0126] + 2α sul βsul f suc x bp (b bu1 +b bu2 )+α cc β cc f cc (x bp -h bul )b bc

[0127] Among them, T su is the tensile force of the side wall of the U-shaped UHPC precast beam formwork, and C su1 +C su2 is the pressure on the bottom wall and side wall of the U-shaped UHPC precast beam formwork, and C nu is the pressure of the post-poured HSC.

[0128] Taking moments about the neutral axis of the cross-section:

[0129]

[0130] The above is only a preferred specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A calculation method for the flexural bearing capacity of an assembled monolithic UHPC-HSC beam-slab-column joint, characterized in that, Including: Prefabricated HSC columns, U-shaped UHPC beam forms, UHPC composite slabs, post-cast joints and composite T-shaped beam and slab areas, and column bolt connectors, which are assembled to obtain an integral UHPC-HSC composite beam, slab and column; According to the structural characteristics of the assembled integral UHPC-HSC beam, slab and column joints, determine the beam-sway failure mode of the beam, slab and column joints; Assume a plane section. According to the concrete constitutive model and the steel bar constitutive model, simplify the concrete stress diagram in the compression zone into an equivalent rectangular stress diagram. According to the force and moment equilibrium equations in the beam-column joint area, calculate and obtain the bending moment of the beam-column joint.

2. The method according to claim 1, wherein The manufacturing process of the prefabricated HSC column includes: steel bar binding, column formwork erection, concrete pouring, and rough surfaces are provided on the upper and lower bottom surfaces of the prefabricated column, and the bottom surface of the upper column is poured at 45°.

3. The method according to claim 2, wherein During the process of erecting the column formwork, it also includes: additionally erecting a cylindrical formwork at the bottom of the upper column and the top of the lower column, and pre-burying bolt embedded parts; Before pouring the bottom surface of the upper column at 45°, it also includes: first connecting the prefabricated columns with bolts.

4. The method according to claim 1, wherein The manufacturing process of the prefabricated U-shaped UHPC beam form includes: First, carry out steel bar binding and mold assembly; then pour from the bottom formwork and construct in an inverted pouring manner; finally, after high-temperature steam curing, remove the formwork after curing, and groove on three sides of the prefabricated U-shaped UHPC beam form.

5. The method according to claim 1, wherein The manufacturing process of the prefabricated UHPC composite slab includes: Steel bar binding, formwork erection, concrete pouring, high-temperature steam curing, and formwork removal, and a rough surface is provided on the upper surface of the prefabricated UHPC composite slab.

6. The method according to claim 1, wherein The process of simplifying the concrete stress diagram in the compression zone into an equivalent rectangular stress diagram includes: According to the equivalent conditions that the resultant force of the concrete compressive stress is equal in magnitude and the acting point of the resultant force of the diagram before and after equivalence remains unchanged, determine the reduction coefficient of the stress value in the equivalent rectangular stress diagram and the coefficient of the height of the equivalent rectangular stress diagram to the neutral axis height; Considering the tensile strength of UHPC, simplify the stress diagram in the tensile zone of UHPC into an equivalent rectangular stress diagram, and determine the reduction coefficient of the stress value and the coefficient of the height of the equivalent rectangular stress diagram to the neutral axis height.

7. The method according to claim 6, wherein The reduction coefficient of the stress value in the equivalent rectangular stress diagram and the coefficient of the height of the equivalent rectangular stress diagram to the neutral axis height are determined according to the concrete constitutive model.

8. The method according to claim 1, wherein When simplifying the stress diagram in the tensile zone of UHPC into an equivalent rectangular stress diagram, the reduction coefficient of the stress value is determined according to the tensile constitutive model of UHPC material.

9. The method according to claim 1, wherein The process of calculating and obtaining the bending moment of the beam-column joint includes: Taking the target beam-column joint of the assembled integral UHPC-HSC beam-column joint as the object, a calculation sketch of the beam-column joint is established; among them, the bottom of the column is a fixed hinge support, the right end of the beam is a movable hinge support, the top of the column is a free end, and axial force and reciprocating horizontal loads are applied. According to the moment balance equation of the beam-column joint area, the horizontal shear force at the top of the column is obtained. Considering the influence of the cast-in-place UHPC and HSC, the bending moment values generated at the beam end of the beam section at the positions of the cast-in-place UHPC and the cast-in-place HSC are calculated respectively. Considering different situations where the UHPC beam formwork and the cast-in-place UHPC are on the tensile side or the compressive side, the bending moment calculations are carried out respectively. Taking the ultimate compressive strain reached by the concrete edge in the compression zone of the composite beam section as the peak value for bending moment design, the bending moment values when the lower steel bars are in tension and the upper steel bars are in tension are calculated respectively. Through the force balance equation and taking moments about the section neutral axis, the section neutral axis bending moment at the peak point is determined.

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