Method for calculating flexural capacity characteristic value of steel and UHPC (Ultra High Performance Concrete) composite structural beam

Abstract

The invention provides a method for calculating a flexural capacity characteristic value of a steel and UHPC (Ultra High Performance Concrete) composite structural beam. Different constitutive models are adopted according to performance characteristics of UHPC, a T-shaped steel beam and a steel bar in the composite structural beam, and the contribution of material strain hardening performance to the flexural capacity is fully considered; compared with an ideal elastic-plastic model, the real performance of the structure can be better obtained; meanwhile, the cross section curvature, the curvature iterative calculation increment and the neutral axis position iterative calculation increment are given for initial values of conventional bridge calculation, and the neutral axis position and the cross section curvature are searched by adopting an influence coefficient method, so that the search speed is increased, and the problem that convergence cannot be realized due to manual setting of the iterative increment is solved; and finally, the condition that the UHPC top strain reaches the UHPC compression limit strain or the T-shaped steel beam bottom strain reaches the steel limit strain is taken as a judgment condition, and two damage modes of UHPC crushing and the condition that the steel reaches the tensile ultimate strength can be considered at the same time.

Description

Technical Field

[0001] The invention relates to the technical field of bridge engineering, and in particular to a method for calculating a characteristic value of the bending bearing capacity of a composite structural beam of steel and UHPC. Background Art

[0002] Traditional prefabricated bridges are characterized by large quantity and wide application, and their main structural forms are prestressed hollow slab bridges, prestressed T-beam bridges, and prestressed small box girder bridges. The above bridges generally have the following characteristics: (1) Ordinary concrete (NC) is used as the main structural material, which is heavy and easy to crack; (2) The steel bars and prestressed bars are arranged in the concrete body, and their distribution and material consumption are limited by the concrete structure size and casting quality requirements, resulting in the internal force arm being less than the concrete section height when subjected to bending, and low efficiency.

[0003] With the popularity of ultra-high performance concrete (UHPC), existing bridge technologies in recent years have attempted to use UHPC to replace NC as the main building material to achieve the requirements of reducing deadweight and improving performance, such as steel beam-UHPC bridge deck composite beams, but there are also defects such as the material properties cannot be fully utilized, the amount of steel used and the welding workload are large. In order to make full use of the excellent performance of steel and UHPC materials and further improve the economy and applicability of steel-UHPC composite beams, some new composite beam structures have been proposed. Among the currently disclosed technologies, Chinese patent applications with publication numbers CN112391932A and CN112342889A both proposed a UHPC-T-beam using steel sections as external reinforcement. The idea is to use UHPC to bear the high pressure stress of the upper flange and the low tensile stress of the composite web, and use steel sections to bear the high tensile stress of the lower part, making full use of the material properties. Different from traditional concrete beams with internal steel bars and prestressed tendons, or pure steel web composite beam bridges, the mechanical characteristics of externally reinforced UHPC-T beams are very different, showing multiple stress states, namely: horizontal shear resistance of composite shear members, vertical shear resistance of composite webs, and bending resistance of composite beams. The existing technology lacks a calculation method for the characteristic value of the bending bearing capacity of steel-UHPC composite beams, which greatly limits its application and also faces structural safety risks.

[0004] In summary, there is an urgent need for a method for calculating the eigenvalue of the flexural bearing capacity of a composite structural beam of steel and UHPC to solve the problems existing in the prior art. Summary of the invention

[0005] The purpose of the present invention is to provide a method for calculating the characteristic value of the bending bearing capacity of a composite structural beam of steel and UHPC, aiming to solve the problem that there is a lack of a method for calculating the characteristic value of the bending bearing capacity of a steel-UHPC composite beam in the prior art, which greatly limits its application and also faces structural safety risks. The specific technical solution is as follows:

[0006] A method for calculating the characteristic value of the bending bearing capacity of a composite structural beam of steel and UHPC comprises the following steps:

[0007] A1. Set constant parameters, including the calculation error convergence value θ and the curvature iteration calculation increment and the neutral axis position iteratively calculate the increment Δx n ;

[0008] A2. Input the cross-sectional dimensions of the composite structural beam, the properties of each material in the composite structural beam and the nonlinear constitutive model;

[0009] A3. Divide the cross section of the composite structural beam into unit layers, specifically:

[0010] The cross section of the UHPC concrete of the composite structural beam and the cross section of the T-shaped steel beam outside the UHPC concrete are divided into unit layers respectively. At the same time, the cross section of all the longitudinal steel bars in the uppermost layer of the composite structural beam and the cross section of all the longitudinal steel bars in the lowermost layer of the composite structural beam are respectively regarded as a unit layer;

[0011] A4. Assuming the initial cross-sectional curvature of the composite structural beam in

[0012] A5. Assume that the neutral axis position of the composite structural beam is x n , where x n =x n,0 ;

[0013] A6. Calculate the strain of each unit layer based on the plane section assumption;

[0014] A7. Calculate the stress of each unit layer according to the strain of each unit layer and the nonlinear constitutive model corresponding to the unit layer;

[0015] A8. Calculate the resultant force F in the cross section of the composite structure beam based on the stress and area of ​​each unit layer;

[0016] A9. If |F| is not greater than θ, proceed to step A10; if |F| is not greater than θ, then n Repeat A6-A9 after correction;

[0017] A10. Determine whether there is an upper edge compressive strain ε of UHPC concrete top Less than its compressive limit strain, or the tensile strain ε at the lower edge of the T-beam bottom is greater than its ultimate tensile strain; if it exists, let Δx n =0.1Δx nThen repeat steps A4 to A10, if it does not exist, go to step A11;

[0018] A11. Determine whether the upper edge compressive strain ε of UHPC concrete is satisfied. top minus its ultimate compressive strain less than or equal to 0.1·θ, or, the ultimate tensile strain of the T-beam minus the tensile strain at its lower edge ε bottom Less than or equal to 0.1·θ; if satisfied, proceed to step A12; if not satisfied, correct φ and repeat steps A5-A11;

[0019] A12. Calculate the eigenvalue M of the bending bearing capacity of the composite structure beam based on the moment of each unit layer r .

[0020] Preferably, in the above technical solution, the nonlinear constitutive model of each material in step A2 is specifically:

[0021] The nonlinear constitutive model of UHPC concrete is:

[0022]

[0023] Among them, ε u is the strain of UHPC concrete, σ u is the stress of UHPC concrete, E u is the elastic modulus of UHPC concrete; ε cu is the ultimate compressive strain of UHPC concrete; ε te is the tensile elastic limit strain of UHPC concrete; ε tu is the ultimate tensile strain of UHPC concrete; ε tr is the fracture strain of UHPC concrete; f te is the tensile elastic limit stress of UHPC concrete; f tu is the ultimate tensile stress of UHPC concrete;

[0024] The nonlinear constitutive models of T-beam and steel bars in the composite structural beam are:

[0025]

[0026] Among them, ε s is the strain of the T-beam or steel bar, σ s is the stress of the T-beam or steel bar, E s is the elastic modulus of the T-beam or steel bar; ε' y is the ultimate compressive strain of the T-beam or steel bar; ε y is the tensile yield strain of the T-beam or steel bar; ε st is the strain hardening starting strain of the T-beam or steel bar; ε' uis the ultimate tensile strain of the T-beam or steel bar; if there is no yield platform, then ε y =ε st ;f y is the yield stress of the T-beam or steel bar; f u It is the ultimate tensile stress of T-beam or steel bar.

[0027] In the above technical solution, preferably, the calculation method of the strain of each unit layer in step A6 is:

[0028] Strain of the i-th unit layer in UHPC concrete Positive values ​​are tensile strains, negative values ​​are compressive strains; the strain of the kth unit layer in the T-beam is Positive values ​​are tensile strains, and negative values ​​are compressive strains;

[0029] The strain of all longitudinal reinforcements in the bottom layer of the composite structure beam corresponding to the unit layer The strain of all longitudinal reinforcements in the uppermost layer of the composite structural beam corresponding to the unit layer

[0030] Among them, y i is the vertical distance from the center of the i-th unit layer in UHPC concrete to the upper surface of the composite structural beam, y k is the vertical distance from the center of the kth unit layer in the T-shaped steel beam to the upper surface of the composite structure beam, y″ s is the vertical distance from the center of the unit layer corresponding to all the longitudinal reinforcements at the bottom layer of the composite structural beam to the upper surface of the composite structural beam, y' s It is the vertical distance from the center of the unit layer corresponding to all the longitudinal reinforcements in the uppermost layer of the composite structural beam to the upper surface of the composite structural beam.

[0031] In the above technical solution, preferably, the stress calculation method of each unit layer in step A7 is:

[0032] According to formula (8), the stress σ of the unit layer in UHPC concrete is obtained u,i =σ u (ε u,i ), positive values ​​are tensile stress, and negative values ​​are compressive stress; According to formula (9), the stress σ of the unit layer in the T-beam is obtained h,k =σ s (ε h,k ), positive value is tensile stress, negative value is compressive stress; according to formula (9), the stress σ″ of all longitudinal reinforcements in the bottom layer of the composite structure beam is obtained: s =σ s (ε″ s ); According to formula (9), the stress σ' of all longitudinal reinforcements corresponding to the unit layer of the top layer of the composite structure beam is obtained s =σ s (ε's ).

[0033] In the above technical solution, preferably, the resultant force F in the cross section of the composite structural beam in step A8 is specifically:

[0034] F=∑A i σ u,i +∑A k σ h,k +A″ s σ″ s +A′sσ′ s (11)

[0035] Among them, A i is the area of ​​the i-th unit layer in UHPC concrete, A k is the area of ​​the kth unit layer in the T-beam, A″ s A is the area of ​​the unit layer corresponding to all longitudinal reinforcements at the bottom layer of the composite structural beam. s ' is the area of ​​the unit layer corresponding to all the longitudinal reinforcements in the uppermost layer of the composite structural beam.

[0036] In the above technical solution, preferably, in step A12, the characteristic value M of the bending bearing capacity of the composite structure beam is calculated. r , specifically:

[0037]

[0038] In the above technical solution, preferably, in step A9, the influence coefficient method is used to iteratively correct x n , specifically:

[0039] A9.1. Assume that the new neutral axis position of the composite structural beam is x' n , where x' n =x n +Δx n ;

[0040] A9.2. Repeat steps A6-A8 to calculate x' n The resultant force F' in the cross section of the corresponding composite structural beam;

[0041] A9.3. Calculate the change in the resultant force in the cross section of the composite structural beam, ΔF, where ΔF = F'-F;

[0042] A9.4. Correction of the neutral axis position x of the composite structural beam n ,in

[0043] In the above technical solution, preferably, in step A11, the influence coefficient method is used to iteratively correct Specifically:

[0044] A11.1. Assuming the new cross-sectional curvature of the composite structural beam Where φ'=φ+Δφ;

[0045] A11.2. Repeat steps A5-A10 to calculate The corresponding UHPC concrete upper edge compressive strain ε' top and the tensile strain ε' at the lower edge of the T-beam bottom ;

[0046] A11.3. Calculation of the change in compressive strain at the upper edge of UHPC concrete Δε top and the tensile strain change value Δε at the lower edge of the T-beam bottom ; where Δε top =ε' top -ε top , Δε bottom =ε' bottom -ε bottom ;

[0047] A11.4. Correction of the cross-sectional curvature of composite structural beams

[0048] in ε cu is the ultimate compressive strain of UHPC concrete, ε' u1 is the ultimate tensile strain of the T-beam.

[0049] Preferably, in the above technical solution, step A3 further includes: obtaining the vertical distance between the center of each unit layer and the upper surface of the composite structure beam and the area of ​​each unit layer.

[0050] In the above technical solution, the minimum compressive strain is selected from each unit layer of UHPC concrete, which is the upper edge compressive strain ε of UHPC concrete. top , the maximum tensile strain is selected from each unit layer of the T-beam, which is the tensile strain of the lower edge of the T-beam ε bottom .

[0051] The application of the technical solution of the present invention has the following beneficial effects:

[0052] The method for calculating the characteristic value of bending bearing capacity proposed in the present invention is helpful for engineering and technical personnel to judge the key mechanical properties of the structure. The calculation method is scientific and efficient, which helps to promote the engineering application of the innovative structure and create social and economic value.

[0053] The method for calculating the bending bearing capacity proposed in the present invention adopts different constitutive models according to the performance characteristics of UHPC, T-shaped steel beams and steel bars, and fully considers the contribution of the material strain hardening performance to the bending bearing capacity. Compared with the ideal elastic-plastic model, it can better obtain the true performance of the structure and reduce waste.

[0054] The method for calculating the bending bearing capacity proposed in the present invention provides the initial values ​​of the cross-sectional curvature, the curvature iterative calculation increment, and the neutral axis position iterative calculation increment for conventional bridge calculations, and uses the influence coefficient method to search for the neutral axis position and the cross-sectional curvature, which helps to speed up the search and solves the problem of non-convergence caused by artificially set iterative increments.

[0055] The bending bearing capacity calculation method proposed in the present invention takes the top strain of UHPC concrete reaching the compressive limit strain of UHPC or the bottom strain of T-shaped steel beam reaching the limit strain of steel as the judgment condition, which can take into account the two failure modes of UHPC crushing and steel reaching the tensile limit strength at the same time, which is more convenient and faster than the traditional algorithm to make separate judgments.

[0056] In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0058] Figure 1 It is an axonometric view of the composite structural beam of steel and UHPC;

[0059] Figure 2 yes Figure 1 Structural diagram of the middle vertical stirrup group;

[0060] Figure 3 yes Figure 1 Schematic diagram of the structure of the steel tenon and mortise;

[0061] Figure 4 is a flow chart of the design method of the composite structural beam of steel and UHPC of the present invention;

[0062] Figure 5 is a flow chart for calculating the characteristic value of the bending bearing capacity in the design method of the present invention;

[0063] Figure 6 It is a schematic diagram of the nonlinear constitutive model of UHPC concrete;

[0064] Figure 7 It is a schematic diagram of the nonlinear constitutive model of a T-beam or steel bar;

[0065] Figure 8 is a schematic diagram of the cross section of a composite structural beam;

[0066] Fig. 9It is a schematic diagram of strain distribution in the cross section of the composite structure beam;

[0067] Fig.10 It is a schematic diagram of stress distribution in the cross section of the composite structure beam;

[0068] Among them, 100, composite structure beam, 110, UHPC bridge deck, 111, bridge deck transverse reinforcement, 112, bridge deck longitudinal reinforcement, 120, UHPC rib, 121, lower open stirrups, 122, upper open stirrups, 123, the bottom layer of longitudinal reinforcement, 124, the second bottom layer of longitudinal reinforcement, 125, longitudinal distribution reinforcement, 126, transverse short reinforcement, 130, T-shaped steel beam, 131, steel bottom plate, 132, steel web, 133, steel tenon, 134, mortise. DETAILED DESCRIPTION

[0069] In order to facilitate the understanding of the present invention, the present invention will be described more fully below, and preferred embodiments of the present invention are provided. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present invention more thorough and comprehensive.

[0070] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0071] Example:

[0072] Figure 1-Figure 3 A composite structural beam of steel and UHPC is illustrated, the composite structural beam 100 comprises a UHPC bridge deck 110 and a composite rib (not shown) located on the bottom surface of the UHPC bridge deck 110, the composite rib comprises a UHPC rib 120 and a T-shaped steel beam 130, the UHPC rib 120 is located between the UHPC bridge deck 110 and the T-shaped steel beam 130, that is, the UHPC rib 120 and the UHPC bridge deck 110 are cast together to form a T-shaped structure, and the upper edge of the T-shaped steel beam 130 is buried inside the lower end of the UHPC rib 120.

[0073] Furthermore, the T-shaped steel beam 130 includes a steel bottom plate 131 and a steel web 132 disposed on the steel bottom plate 131, the two forming a T-shaped structure, and the upper edge of the steel web 132 (i.e., the side close to the UHPC rib 120) is alternately provided with steel tenons 133 and mortises 134 along the longitudinal bridge direction. Figure 3 As shown, Figure 3 The gray area in the figure is the mortise 134, and the distance between two adjacent tenons 133 is e.x The height of the steel tenon (i.e. the depth of the mortise) is h D The steel tenon 133 and the mortise 134 are buried in the concrete at the lower end of the UHPC rib 120, and the distance between the lower edge of the UHPC rib 120 and the bottom edge of the mortise 134 is C D .

[0074] Furthermore, the UHPC rib 120 includes a rib concrete layer and a rib reinforcement skeleton located in the rib concrete layer, wherein the rib reinforcement skeleton includes a bottom layer of longitudinal reinforcement 123, a second bottom layer of longitudinal reinforcement 124, a longitudinal distribution reinforcement 125, a transverse short reinforcement 126 and a vertical stirrup group (not shown in the figure); the vertical stirrup group includes lower open stirrups 121 and upper open stirrups 122 alternately arranged along the longitudinal bridge direction, such as Figure 1 and Figure 2 As shown, the lower open stirrup 121 and the steel tenon 133 are arranged in a one-to-one correspondence, the upper open stirrup 122 and the mortise 134 are arranged in a one-to-one correspondence, the steel tenon 133 is inserted into the opening at the lower end of the lower open stirrup 121, the lower end of the upper open stirrup 122 is placed in the mortise 134, and transverse short steel bars 126 are provided on both sides of the lower end of the upper open stirrup 122, and the transverse short steel bars 126 are spaced from the lower end of the upper open stirrup 122 (that is, the two are not overlapped); the position of the lower end of the lower open stirrup 121 is lower than that of the upper open stirrup 122 At the lower end, the bottom layer of longitudinal steel bars 123 is used to connect the lower ends of the lower open stirrups 121 along the longitudinal direction, and the second bottom layer of longitudinal steel bars 124 is used to connect the lower ends of the upper open stirrups 122 along the longitudinal direction. Specifically, in this embodiment, the number of the bottom layer of longitudinal steel bars 123 and the second bottom layer of longitudinal steel bars 124 are both two, and they are symmetrically arranged on both sides of the steel web 132; a plurality of longitudinal distribution steel bars 125 are arranged inside the vertical stirrup group along the vertical direction, and specifically, a single longitudinal distribution steel bar 125 passes through the alternately arranged upper open stirrups 122 and lower open stirrups 121 along the longitudinal direction.

[0075] Furthermore, the UHPC bridge deck 110 includes a bridge deck concrete layer and a bridge deck steel bar skeleton located in the bridge deck concrete layer, the bridge deck steel bar skeleton includes an upper transverse steel bar group, a lower transverse steel bar group and a bridge deck longitudinal steel bar 112; a plurality of bridge deck longitudinal steel bars 112 are arranged at intervals along the transverse direction of the bridge, the upper transverse steel bar group is located on the upper side of the bridge deck longitudinal steel bars 112, the upper transverse steel bar group includes a plurality of bridge deck transverse steel bars 111 arranged at intervals along the longitudinal direction of the bridge, the bridge deck longitudinal steel bars 112 are overlapped with the bridge deck transverse steel bars 111 in the upper transverse steel bar group; the lower transverse steel bar group is located on the lower side of the bridge deck longitudinal steel bars 112, the lower transverse steel bar group includes a plurality of bridge deck transverse steel bars 111 arranged at intervals along the longitudinal direction of the bridge, and the bridge deck transverse steel bars 111 in the lower transverse steel bar group are not overlapped with the bridge deck longitudinal steel bars 112.

[0076] Furthermore, the upper end of the lower open stirrup 121 is connected to the bridge deck reinforcement skeleton, specifically, overlapped with the bridge deck longitudinal reinforcement 112 .

[0077] Preferably, the bridge deck concrete layer and the rib concrete layer are both cast using UHPC concrete, and the UHPC concrete is an ultra-high performance concrete having ultra-high durability and ultra-high mechanical properties.

[0078] In order to ensure the safe application of UHPC and steel composite structural beams in small and medium span prefabricated bridges, this embodiment provides a design method for steel and UHPC composite structural beams, such as Figure 4 As shown, the design method includes the following steps:

[0079] S1. Determine the permanent action of the composite structural beam according to the structural dimensions of the proposed composite structural beam, and determine the variable action according to the use requirements and environmental conditions of the composite structural beam;

[0080] Specifically, the determination method of the permanent effect and the variable effect can be referred to the prior art, and no further detailed description is given in this embodiment.

[0081] S2. Obtain the effect design value of the basic combination of actions based on the effect design value of the permanent action and the effect design value of the variable action;

[0082] Preferably, the effect design values ​​of the composite structural beam under permanent action and the effect design values ​​under variable action are determined according to a general bridge internal force calculation method, and the effect design values ​​of the permanent action and the effect design values ​​of the variable action in the "General Specification for Design of Highway Bridges and Culverts" (JTG D60-2015) are combined to obtain the effect design value of the basic combination of actions.

[0083] S3. According to the structural dimensions of the composite structural beam and the design value of the effect of the basic combination of actions, respectively verify whether the characteristic value of the interlayer horizontal shear bearing capacity, the characteristic value of the vertical shear bearing capacity and the characteristic value of the bending bearing capacity of the composite structural beam meet the requirements;

[0084] Specifically, the interlayer horizontal shear bearing capacity characteristic value P of the composite structural beam is determined according to the structural dimensions of the proposed composite structural beam. r , characteristic value of vertical shear bearing capacity V r and the characteristic value of bending capacity M r ;

[0085] The interlayer horizontal shear bearing capacity characteristic value P r The design value of the horizontal shear force between layers in the design value of the effect of the basic combination of actions P d For comparison, if it meets This means that the characteristic value of the interlayer horizontal shear bearing capacity of the composite structure beam is qualified;

[0086] The vertical shear bearing capacity characteristic value V r The vertical shear design value V in the effect design value of the basic combination of actions d For comparison, if it meets This means that the characteristic value of the vertical shear bearing capacity of the composite structural beam has passed the verification;

[0087] The characteristic value of bending bearing capacity M r The design value of the bending moment M in the design value of the effect of the basic combination of actions d For comparison, if it meets This means that the characteristic value of the bending bearing capacity of the composite structural beam is qualified;

[0088] Among them, γ 0 is the importance coefficient of the composite structure beam, which is 0.9, 1.0, and 1.1 respectively according to the importance of the bridge; γ M is the material partial factor, which is used to convert the calculated bearing capacity characteristic value into the corresponding bearing capacity design value and is taken as 1.25.

[0089] Furthermore, the interlayer horizontal shear bearing capacity characteristic value P of the composite structure beam is r The calculation process is as follows:

[0090] The horizontal shear failure modes of composite structural beams can be divided into tenon shear failure and mortise shear failure. Therefore, the characteristic value of the horizontal shear bearing capacity between layers is P r The calculation process is:

[0091] Calculate the horizontal shear bearing capacity characteristic value P corresponding to the shear failure of the steel tenon pl,k , unit N:

[0092] Ppl,k =0.25·e x ·t s ·f y (1)

[0093] Calculate the horizontal shear bearing capacity characteristic value P corresponding to the shear failure of the mortise sh,k , unit N:

[0094]

[0095] Calculation of the interlayer horizontal shear bearing capacity characteristic value P of the composite structure beam r , unit N:

[0096] P r =min(P pl,k ,P sh,k ) (3),

[0097] Among them, e x is the longitudinal spacing of the steel tenons, in mm; t s is the thickness of the steel web, in mm; f y is the yield strength of the steel web, in MPa; η D is the shape coefficient of the mortise, which is related to the shape of the steel tenon. For example, the MCL type key is f cu,k is the standard value of cubic compressive strength of UHPC concrete, in MPa; ρ D is the strengthening coefficient of horizontal reinforcement in the mortise, wherein the horizontal reinforcement in the mortise includes the horizontal section of the transverse short steel bars and the upper opening stirrups, A b It is the sum of the cross-sectional areas of the horizontal reinforcement in the mortise, including the horizontal sections of the short transverse reinforcement and the upper opening stirrups; A D is the area of ​​the mortise, such as MCL type key A D =0.2e x 2 ; E s is the elastic modulus of the steel tenon (i.e. steel web), in MPa; E u is the elastic modulus of UHPC concrete, in MPa.

[0098] Among them, the sum of the cross-sectional areas of the horizontal steel bars in the mortise is A b Should not be less than A b,min , where A b,min The calculation method is:

[0099] A b,min =0.5·P d / f s1 (4)

[0100] Among them, P dIt is the design value of the horizontal shear force between layers in the design value of the effect of the basic combination of actions, in N; f s1 It is the design value of the transverse short reinforcement strength, in MPa.

[0101] Obtain the interlayer horizontal shear bearing capacity characteristic value P of the composite structure beam r Then, add it to the interlayer horizontal shear design value P in the effect design value of the basic combination of actions d Compare and determine whether The characteristic value verification of the horizontal shear bearing capacity of the composite structure beam can be completed.

[0102] Furthermore, the vertical shear bearing capacity characteristic value V of the composite structural beam is r The calculation process is as follows:

[0103] The vertical shear bearing capacity characteristic value of the composite structure beam is provided by the steel web, UHPC ribs and UHPC bridge deck. Since the UHPC bridge deck is usually thin, only the contribution of the steel web and UHPC ribs is considered conservatively, so the vertical shear bearing capacity characteristic value V r The calculation process is:

[0104] Calculate the characteristic value V of the vertical shear capacity of the steel web s , unit N:

[0105]

[0106] Calculation of the vertical shear bearing capacity characteristic value V of UHPC ribbed slab u , in N, consists of the contribution of the UHPC matrix and the vertical stirrup group:

[0107]

[0108] Calculate the vertical shear bearing capacity characteristic value V of the composite structural beam (i.e. composite rib plate) r , unit N:

[0109] V r =V s +V u (7)

[0110] Among them, f y is the yield strength of the steel web, in MPa; t s is the thickness of the steel web, in mm; h s is the height of the steel web, in mm; t u is the thickness of the UHPC rib plate, in mm; h u is the height of the UHPC rib, in mm; f te is the tensile elastic limit strength of UHPC concrete, in MPa; ftu is the tensile strength of UHPC concrete, in MPa; A sv It is the sum of the cross-sectional areas of all vertical segments of a single stirrup in the UHPC rib (the stirrup here refers to the upper open stirrup or the lower open stirrup. The upper open stirrup and the lower open stirrup are generally of the same specification, so the cross-sectional areas of the upper open stirrup and the lower open stirrup are the same; the upper open stirrup and the lower open stirrup in this embodiment are both double-limbed, that is, they have two vertical segments, but in some embodiments, the stirrup may be set to a single limb, that is, only one vertical segment), the unit is mm 2 ; s is the spacing of stirrups in the UHPC rib plate, in mm; f s2 It is the yield strength of stirrups in UHPC ribs, in MPa.

[0111] Obtain the vertical shear bearing capacity characteristic value V of the composite structure beam r Then, add it to the vertical shear design value V in the effect design value of the basic combination of actions. d Compare and determine whether The vertical shear bearing capacity characteristic value verification of the composite structure beam can be completed.

[0112] Further, such as Figure 5 As shown in the figure, the characteristic value of the bending bearing capacity of the composite structure beam is M r The calculation process is as follows:

[0113] Eigenvalue M of the bending bearing capacity of composite structural beams r The calculation adopts the method of considering material plasticity, based on the assumption of a flat section, and obtains the bending bearing capacity of the section through the analysis of the internal force equilibrium condition of the cross section. The specific steps include:

[0114] A1. Set constant parameters, including the calculation error convergence value θ and the curvature iteration calculation increment and the neutral axis position iteratively calculate the increment Δx n ;

[0115] Preferably, The value is usually less than or equal to 10 -7 (m -1 );The value of the calculation error convergence value θ is generally 10 -5 ; Iterative calculation increment Δx of neutral axis position n The value is generally 0.1mm;

[0116] A2. Input the cross-sectional dimensions of the composite structural beam, the properties of each material and the nonlinear constitutive model;

[0117] Different from ordinary concrete, UHPC concrete has the characteristics of strain hardening, and its strength after cracking still contributes to the bending bearing capacity (strain softening). In order to fully consider its influence, UHPC tensile resistance adopts a three-fold line model, UHPC compression resistance adopts a linear elastic model, and T-shaped steel beams and steel bars in the composite structure beams are tensile. The three-fold line model considering the yield platform and strain hardening is used. Because the project focuses on the maximum bearing capacity, except for UHPC tensile resistance, the material constitutive model does not consider the descending section.

[0118] Preferably, Figure 6 As shown in Figure 2, the nonlinear constitutive model of UHPC concrete is:

[0119]

[0120] Among them, ε u is the strain of UHPC concrete, σ u is the stress of UHPC concrete, E u is the elastic modulus of UHPC concrete; ε cu is the ultimate compressive strain of UHPC concrete; ε te is the tensile elastic limit strain of UHPC concrete; ε tu is the ultimate tensile strain of UHPC concrete; ε tr is the fracture strain of UHPC concrete; when ε u =ε cu When u =f cu , reaches the ultimate compressive stress, f cu is the compressive ultimate stress of UHPC concrete; f te is the tensile elastic limit stress of UHPC concrete, f te =E u ·ε te ;f tu is the tensile ultimate stress of UHPC concrete, and the corresponding strain is ε tu .

[0121] like Figure 6 As shown in the figure, the second section of the first quadrant in the nonlinear constitutive model of UHPC considers the contribution of UHPC tensile strain hardening to the bending bearing capacity, and the third section considers the contribution of UHPC to the bending bearing capacity after cracking.

[0122] Preferably, Figure 7 As shown in the figure, the nonlinear constitutive models of the T-beam and steel bars in the composite structural beam are:

[0123]

[0124] Among them, ε sis the strain of the T-beam or steel bar, σ s is the stress of the T-beam or steel bar, E s is the elastic modulus of the T-beam or steel bar; ε' y is the ultimate compressive strain of the T-beam or steel bar; ε y is the tensile yield strain of the T-beam or steel bar; ε st is the strain hardening starting strain of the T-beam or steel bar; ε' u is the ultimate tensile strain of the T-beam or steel bar; for the case of no yield platform, such as some specifications of steel bars, ε y =ε st ;

[0125] When ε s =ε' y When s =f' y , reaching the compressive limit stress, f y ' is the compressive limit stress of the T-beam or steel bar; f y is the yield stress of the T-beam or steel bar, f y =E s ·ε y ;f u is the ultimate tensile stress of the T-beam or steel bar, and the corresponding strain is ε u .

[0126] like Figure 7 As shown in the figure, the second section of the first quadrant in the nonlinear constitutive model is the yield platform considering the stress-strain relationship of the T-shaped steel beam or steel bar, and the third section is the contribution of the strain hardening of the T-shaped steel beam or steel bar to the bending bearing capacity.

[0127] Considering that the ultimate tensile strain of the T-beam will be used in subsequent calculations, in order to distinguish the ultimate tensile strain of the T-beam and the steel bar, ε' u1 The ultimate tensile strain of the T-beam is expressed by ε' u2 Represents the ultimate tensile strain of the steel bar.

[0128] A3. Figure 8 As shown in the figure, the cross section of the UHPC concrete of the composite structural beam is divided into unit layers, and the vertical distance y from the center of each unit layer to the upper surface of the composite structural beam is obtained. i And the area A of each unit layer i ; Divide the cross section of the T-shaped steel beam outside the UHPC concrete into unit layers, and obtain the vertical distance y between the center of each unit layer and the upper surface of the composite structure beam k And the area A of each unit layer k ; Take the cross section of all longitudinal reinforcements at the bottom layer of the composite structural beam as a unit layer and obtain its area A″s And the vertical distance y″ from the upper surface of the composite structural beam s ; Take the cross section of all longitudinal reinforcements in the top layer of the composite structural beam as a unit layer and record its area A s ' and the vertical distance y from the upper surface of the composite structural beam s ;

[0129] Preferably, i represents the i-th unit layer in the UHPC concrete, and k represents the k-th unit layer in the T-shaped steel beam.

[0130] Specifically, the upper surface of the composite structure beam is the upper surface of the UHPC bridge deck, that is, the bridge deck; the bottom layer of longitudinal steel bars of the composite structure beam refers to the bottom layer of longitudinal steel bars 123 in the UHPC rib plate, and the top layer of longitudinal steel bars of the composite structure beam refers to the bridge deck longitudinal steel bars 112 in the UHPC bridge deck.

[0131] Preferably, all unit layers should be on the same cross section of the composite structural beam. When dividing the cross section of the UHPC concrete and the cross section of the T-shaped steel beam outside the UHPC concrete into unit layers, layered forced dividing lines are arranged at all locations where the cross-sectional width and material change, so as to facilitate the calculation of the area of ​​each unit layer and subsequent internal forces. According to the above unit layer division rules, it can be seen that except for the longitudinal steel bars at the bottom and top layers of the composite structural beam, the rest of the steel structure embedded in the UHPC concrete (referring to the steel bars embedded in the UHPC concrete and part of the steel web) is not considered for calculation, which can facilitate the calculation.

[0132] Preferably, the area of ​​a single unit layer in UHPC concrete and T-shaped steel beam is calculated as follows:

[0133] A=b·h' (10),

[0134] Where: b is the width of the unit layer, which is determined by the cross-sectional shape; h' is the height of the unit layer. To ensure the accuracy of the calculation and analysis, the height h' of each unit layer shall not exceed 1 / 50h; h is the total height of the cross section.

[0135] A4. Assuming the initial cross-sectional curvature of the composite structural beam in Preferably, for most bridges, The possible value is 10 -5 (m -1 );

[0136] A5. Assume that the neutral axis position of the composite structural beam is x n , where x n =x n,0 ; Preferably, x n,0 The general value is h / 2.

[0137] A6. Calculate the strain ε of the unit layer in UHPC concrete based on the plane section assumption u,i , the strain of the unit layer in the T-beam ε h,k , the strain of all longitudinal reinforcements in the bottom layer of the composite structure beam corresponding to the unit layer ε″ s and the strain ε' of all longitudinal reinforcements corresponding to the unit layer in the top layer of the composite structure beam s ,like Fig. 9 As shown;

[0138] Specifically, the strain of the i-th unit layer in UHPC concrete is Positive values ​​are tensile strains, negative values ​​are compressive strains; the strain of the kth unit layer in the T-beam is Positive values ​​are tensile strains, negative values ​​are compressive strains; the strains of all longitudinal reinforcements in the bottom layer of the composite structural beam corresponding to the unit layer The strain of all longitudinal reinforcements in the uppermost layer of the composite structural beam corresponding to the unit layer

[0139] A7. Calculate the stress σ of each unit layer in UHPC concrete according to the nonlinear constitutive model of the material. u,i , the stress σ of each unit layer in the T-beam h,k , the stress σ″ of all longitudinal reinforcements in the bottom layer of the composite structure beam s and the stress σ' of the corresponding unit layer of all longitudinal reinforcements in the top layer of the composite structure beam s ,like Fig.10 As shown;

[0140] Specifically, according to formula (8), the stress σ of the unit layer in UHPC concrete is obtained: u,i =σ u (ε u,i ), positive values ​​are tensile stress, and negative values ​​are compressive stress; According to formula (9), the stress σ of the unit layer in the T-beam is obtained h,k =σ s (ε h,k ), positive value is tensile stress, negative value is compressive stress; according to formula (9), the stress σ″ of all longitudinal reinforcements in the bottom layer of the composite structure beam is obtained: s =σ s (ε″ s ); According to formula (9), the stress σ' of all longitudinal reinforcements corresponding to the unit layer of the top layer of the composite structure beam is obtained s =σ s (ε' s ).

[0141] A8. Calculate the resultant force F in the cross section of the composite structure beam based on the stress and area of ​​each unit layer;

[0142] Preferably, the resultant force F in the cross section of the composite structural beam is:

[0143] F=∑A i σ u,i +∑A k σ h,k +A″ s σ″ s +A′ s σ′ s (11).

[0144] A9. If |F| is not greater than (i.e., less than or equal to) θ, then proceed to step A10; if |F| is not greater than θ, then use the influence coefficient method to iteratively correct x. n Then repeat A6-A9;

[0145] Preferably, the influence coefficient method is used to iteratively correct x n Specifically:

[0146] A9.1. Assume that the new neutral axis position of the composite structural beam is x' n , where x' n =x n +Δx n ;

[0147] A9.2. Repeat steps A6-A8 to calculate x' n The resultant force F' in the cross section of the corresponding composite structural beam;

[0148] A9.3. Calculate the change in the resultant force in the cross section of the composite structural beam, ΔF, where ΔF = F'-F;

[0149] A9.4. Correction of the neutral axis position x of the composite structural beam n ,in

[0150] Follow steps A9.1-A9.4 to complete x n The iterative correction and influence coefficient method can speed up the search and solve the problem of non-convergence caused by artificially set iterative increments.

[0151] A10. Determine whether there is an upper edge compressive strain ε of UHPC concrete top Less than its compressive limit strain ε cu , or, the tensile strain ε at the lower edge of the T-beam bottm Greater than its ultimate tensile strain ε' u1 If it exists, then Δx n =0.1Δx nThen repeat steps A4 to A10, if it does not exist, go to step A11;

[0152] Specifically, if there is a compressive strain ε at the upper edge of UHPC concrete top Less than its compressive limit strain ε cu , or, the tensile strain ε at the lower edge of the T-beam bottom Greater than its ultimate tensile strain ε' u1 , it means that during the calculation process, the compressive strain on the upper edge of the UHPC exceeds its compressive limit strain, or the tensile strain on the lower edge of the T-shaped steel beam exceeds its ultimate tensile strain, indicating that the step size taken in the calculation is too large.

[0153] Preferably, the upper edge compressive strain ε of UHPC concrete is top and the tensile strain ε at the lower edge of the T-beam bottom All are obtained from step A6. The minimum compressive strain is selected from each unit layer of UHPC concrete as ε top , the maximum tensile strain is selected from each unit layer of the T-beam as ε bottom .

[0154] A11. Determine whether the upper edge compressive strain ε of UHPC concrete is satisfied. top Subtract its compressive limit strain ε cu Less than or equal to 0.1·θ, or, the ultimate tensile strain ε' of the T-beam u1 Subtract the tensile strain ε at the lower edge bottom Less than or equal to 0.1·θ; if satisfied, proceed to step A12; if not satisfied, use the influence coefficient method to iteratively correct φ and then repeat steps A5 to A11;

[0155] Preferably, the influence coefficient method is used in this embodiment to iteratively correct Specifically:

[0156] A11.1. Assuming the new cross-sectional curvature of the composite structural beam Where φ'=φ+Δφ;

[0157] A11.2. Repeat steps A5-A10 to calculate The corresponding UHPC concrete upper edge compressive strain ε' top and the tensile strain ε' at the lower edge of the T-beam bottom ;

[0158] A11.3. Calculation of the change in compressive strain at the upper edge of UHPC concrete Δε top and the tensile strain change value Δε at the lower edge of the T-beam bottom ; where Δε top =ε' top -ε top , Δε bottom =ε'bottom -ε bottom ;

[0159] A11.4. Correction of the cross-sectional curvature of composite structural beams in

[0160] According to steps A11.1-A11.4, the iterative correction of φ can be completed. The influence coefficient method can speed up the search and solve the problem of non-convergence caused by artificially setting the iteration increment. Search for the cross-sectional curvature corresponding to the maximum bending bearing capacity When the strain at the top of the UHPC concrete reaches the UHPC compressive limit strain or the strain at the bottom of the T-shaped steel beam reaches the steel limit strain as the judgment condition, the two failure modes of UHPC crushing and steel reaching the tensile limit strength can be taken into account at the same time. In order to take into account both the calculation efficiency and the reliability of convergence, the judgment limit is 0.1·θ, which can ensure that the stress error is within 0.1MPa, which is sufficient in engineering accuracy.

[0161] A12. Calculate the flexural bearing capacity characteristic value M of the composite structure beam according to the moment of each unit layer in the UHPC concrete, the moment of each unit layer in the T-shaped steel beam, the moment of all longitudinal steel bars corresponding to the unit layer in the bottom layer of the composite structure beam, and the moment of all longitudinal steel bars corresponding to the unit layer in the top layer of the composite structure beam. r ;

[0162] Preferably, the eigenvalue M of the bending bearing capacity of the composite structural beam is r for:

[0163]

[0164] Specifically, according to steps A1-A12, the bending bearing capacity characteristic value M of the composite structural beam can be calculated. r , M r and the design value of bending moment M d Compare and determine whether The bending bearing capacity verification of the composite structure beam can be completed.

[0165] S4. If all verifications meet the requirements, it means that the composite structural beam meets the technical requirements; if there are items that do not meet the requirements, adjust the structural dimensions of the composite structural beam and repeat steps S1-S4.

[0166] Specifically, only when the characteristic values ​​of the interlayer horizontal shear bearing capacity, vertical shear bearing capacity and bending bearing capacity of the composite structural beam are all verified to be qualified, the composite structural beam is considered to meet the technical requirements. If any one of them fails to pass the verification, it means that the structural design of the composite structural beam is unqualified, and it is necessary to adjust the structural dimensions of the composite structural beam before continuing the verification.

[0167] Through steps S1-S4 in this embodiment, the structural design of the composite structural beam can be verified, providing theoretical guidance for the structural design of the composite structural beam and helping technicians to reasonably design the structural dimensions of the composite structural beam.

[0168] Application examples:

[0169] In this case, based on the specific structural dimensions of a composite structural beam, the above design method is used to verify the structural rationality of the composite structural beam, as follows:

[0170] First, calculate the interlayer horizontal shear bearing capacity characteristic value P of the composite structure beam r for:

[0171] Get the longitudinal arrangement spacing e of the steel tenons x =150mm, steel web thickness t s =19mm, yield strength of steel web (Q355 material) f y =355MPa, and the horizontal shear bearing capacity characteristic value P corresponding to the shear failure of the steel tenon is calculated according to formula (1): pl,k =252.9kN;

[0172] according to Get the shape coefficient η of the mortise D =2.17, standard value of cubic compressive strength of UHPC concrete f cu,k =140MPa, the diameter of the upper opening stirrup is 10mm, the diameter of the transverse short steel bar in the mortise is 12mm, and the sum of the cross-sectional areas of the horizontal steel bars in the mortise is A b =π(5 2 +2×6 2 )=304.6mm 2 , according to A D =0.2e x 2 Get the area A of the mortise D =4500mm 2 , elastic modulus E of steel tenon (i.e. steel web) s =206GPa, elastic modulus E of UHPC concrete u =45.7GPa, according to Calculate the reinforcement ratio ρ in the mortise D= 0.305, and the horizontal shear bearing capacity characteristic value P corresponding to the shear failure of the mortise is calculated according to formula (2): sh,k =633.3kN;

[0173] According to formula (3), the characteristic value P of the interlayer horizontal shear bearing capacity of the composite structure beam is calculated r =252.9kN.

[0174] Secondly, calculate the vertical shear bearing capacity characteristic value V of the composite structure beam r for:

[0175] Obtain the yield strength f of the steel web y =355MPa, steel web height h s =430mm, and the characteristic value of the vertical shear bearing capacity of the steel web V is calculated according to formula (5): s =1674.5kN;

[0176] Get the thickness t of the UHPC rib u =120mm, height of UHPC rib h u =770mm, the sum of the cross-sectional areas of all vertical sections of a single stirrup in the UHPC rib plate A sv =157mm 2 , the spacing of stirrups in UHPC ribs is s = 75 mm, and the yield strength of stirrups in UHPC ribs is f s2 =400MPa, UHPC tensile elastic limit strength f te and ultimate tensile strength f tu f te =10.87MPa, f tu =11.66MPa, and the characteristic value of vertical shear bearing capacity V of UHPC rib plate is calculated according to formula (6): C =1686kN.

[0177] According to formula (7), the vertical shear bearing capacity characteristic value V of the composite structure beam is calculated r =3360.5KN.

[0178] Finally, the eigenvalue M of the bending bearing capacity of the composite structure beam is calculated r for:

[0179] Step 01, set constant parameters: calculate error convergence value θ = 10 -5 , curvature iteration calculation increment Δφ=10 -7 (m -1 ), iterative calculation increment Δx of the neutral axis position n =0.1mm.

[0180] Step 02: Obtain the cross-sectional dimensions of the composite structural beam, the properties of each material, and the nonlinear constitutive model;

[0181] Among them, the nonlinear constitutive model of UHPC is as shown in formula (8), and the nonlinear constitutive model of T-beam and steel bar is as shown in formula (9).

[0182] Elastic modulus E of UHPC concrete u =45.7Gpa, compressive limit strain ε cu =0.0029, ultimate compressive stress f cu =145Mpa; tensile elastic limit stress f of UHPC concrete te =10.87MPa, ultimate tensile stress f tu =11.66MPa, tensile elastic limit strain ε te =0.0002174, ultimate tensile strain ε tu =0.00293, fracture strain ε tr =0.01.

[0183] Elastic modulus E of steel bar (HRB400) s =200GPa, compressive limit strain ε′ y =0.002, ultimate compressive stress f′ y =400MPa; yield stress of steel bar f y =400Mpa, ultimate stress f u =565MPa, yield strain ε y = 0.002, strain hardening starting strain ε without yield platform st =ε y , ultimate tensile strain ε' u2 =0.016.

[0184] Elastic modulus E of T-beam (Q355) s =206GPa, yield stress f y =355Mpa, ultimate tensile stress f u =512MPa, yield strain ε y =0.001723, strain hardening starting strain ε st =0.0198, ultimate tensile strain ε' u1 =0.035;

[0185] Step 03, dividing the cross section of the composite structural beam into unit layers according to step A3;

[0186] Among them, the total height of the cross section h = 1200mm, the distance y″ between the unit layer corresponding to all longitudinal reinforcements at the bottom layer of the composite structural beam and the upper edge of the cross section s=728mm, the sum of the cross-sectional areas of all longitudinal reinforcements at the bottom layer of the composite structural beam (i.e. the area of ​​the corresponding unit layer) is A″ s =402.1mm 2 , the distance y′ between the unit layer corresponding to all longitudinal reinforcements in the top layer of the composite structure beam and the upper edge of the section s =39mm, the sum of the cross-sectional areas of all longitudinal reinforcements in the top layer of the composite structural beam (i.e. the area of ​​the corresponding unit layer) is A′ s =3217.6mm 2 .

[0187] Step 04: Assume that the initial cross-sectional curvature of the composite structural beam is φ = φ 0 =10 -5 (m -1 ).

[0188] Step 05: Assume that the neutral axis position of the composite structural beam is x n =x n,0 =600mm;

[0189] Step 06: Calculate the strain ε of the unit layer in UHPC concrete according to step A6 u,i , the strain of the unit layer in the T-beam ε h,k , the strain of all longitudinal reinforcements in the bottom layer of the composite structure beam corresponding to the unit layer ε″ s and the strain ε' of all longitudinal reinforcements corresponding to the unit layer in the top layer of the composite structure beam s ;

[0190] Step 07: Calculate the stress σ of each unit layer in UHPC concrete according to the nonlinear constitutive model of each material. u,i , the stress σ of each unit layer in the T-beam h,k , the stress σ″ of all longitudinal reinforcements in the bottom layer of the composite structure beam s and the stress σ' of the corresponding unit layer of all longitudinal reinforcements in the top layer of the composite structure beam s ;

[0191] Step 08: Execute the processing of steps A8-A12 to finally obtain the bending bearing capacity characteristic value M of the composite structure beam. r =5338.3kN·m.

[0192] The horizontal shear bearing capacity design value obtained by Design value of vertical shear bearing capacity Design value of moment shear bearing capacity The effect design value is obtained by establishing a finite element analysis model of the composite structure beam. The horizontal shear design value, vertical shear design value, and bending moment design value with structural importance coefficient are: γ 0 Pd =94.5kN,γ 0 V d =716.8kN, γ 0 M d =4167.1 kN·m, where γ 0 =1.0. By comparison, it can be seen that the design values ​​of bearing capacity are all greater than the corresponding design values ​​of effect, indicating that the technical requirements are met.

[0193] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the characteristic value of the bending bearing capacity of a composite structural beam of steel and UHPC, characterized in that: The following steps are involved: A1. Set constant parameters, including the calculation error convergence value θ and the curvature iteration calculation increment and the neutral axis position iteratively calculate the increment Δx n ; A2. Input the cross-sectional dimensions of the composite structural beam, the properties of each material in the composite structural beam and the nonlinear constitutive model; A3. Divide the cross section of the composite structural beam into unit layers, specifically: The cross section of the UHPC concrete of the composite structural beam and the cross section of the T-shaped steel beam outside the UHPC concrete are divided into unit layers respectively. At the same time, the cross section of all the longitudinal steel bars in the uppermost layer of the composite structural beam and the cross section of all the longitudinal steel bars in the lowermost layer of the composite structural beam are respectively regarded as a unit layer; A4. Assuming the initial cross-sectional curvature of the composite structural beam in A5. Assume that the neutral axis position of the composite structural beam is x n , where x n =x n,0 ; A6. Calculate the strain of each unit layer based on the plane section assumption; A7. Calculate the stress of each unit layer according to the strain of each unit layer and the nonlinear constitutive model corresponding to the unit layer; A8. Calculate the resultant force F in the cross section of the composite structure beam based on the stress and area of ​​each unit layer; A9. If |F| is not greater than θ, proceed to step A10; if |F| is not greater than θ, then n Repeat A6-A9 after correction; A10. Determine whether there is an upper edge compressive strain ε of UHPC concrete top Less than its compressive limit strain, or the tensile strain ε at the lower edge of the T-beam bottom is greater than its ultimate tensile strain; if it exists, let Δx n =0.1Δx n Then repeat steps A4 to A10, if it does not exist, go to step A11; A11. Determine whether the upper edge compressive strain ε of UHPC concrete is satisfied. top minus its ultimate compressive strain less than or equal to 0.1·θ, or, the ultimate tensile strain of the T-beam minus the tensile strain at its lower edge ε bottom Less than or equal to 0.1·θ; if satisfied, proceed to step A12; if not satisfied, correct φ and repeat steps A5 to A11; A12. Calculate the eigenvalue M of the bending bearing capacity of the composite structure beam based on the moment of each unit layer r .

2. The method for calculating the characteristic value of the bending bearing capacity of a composite structural beam of steel and UHPC according to claim 1 is characterized in that: The nonlinear constitutive model of each material in step A2 is specifically: The nonlinear constitutive model of UHPC concrete is: Among them, ε u is the strain of UHPC concrete, σ u is the stress of UHPC concrete, E u is the elastic modulus of UHPC concrete; ε cu is the ultimate compressive strain of UHPC concrete; ε te is the tensile elastic limit strain of UHPC concrete; ε tu is the ultimate tensile strain of UHPC concrete; ε tr is the fracture strain of UHPC concrete; f te is the tensile elastic limit stress of UHPC concrete; f tu is the ultimate tensile stress of UHPC concrete; The nonlinear constitutive models of T-beam and steel bars in the composite structural beam are: Among them, ε s is the strain of the T-beam or steel bar, σ s is the stress of the T-beam or steel bar, E s is the elastic modulus of the T-beam or steel bar; ε' y is the ultimate compressive strain of the T-beam or steel bar; ε y is the tensile yield strain of the T-beam or steel bar; ε st is the strain hardening starting strain of the T-beam or steel bar; ε' u is the ultimate tensile strain of the T-beam or steel bar; if there is no yield platform, then ε y =ε st ;f y is the yield stress of the T-beam or steel bar; f u It is the ultimate tensile stress of T-beam or steel bar.

3. The method for calculating the characteristic value of the bending bearing capacity of the composite structural beam of steel and UHPC according to claim 2 is characterized in that: The calculation method of the strain of each unit layer in step A6 is: Strain of the i-th unit layer in UHPC concrete Positive values ​​are tensile strains, negative values ​​are compressive strains; the strain of the kth unit layer in the T-beam is Positive values ​​are tensile strains, and negative values ​​are compressive strains; The strain of all longitudinal reinforcements in the bottom layer of the composite structure beam corresponding to the unit layer The strain of all longitudinal reinforcements in the uppermost layer of the composite structural beam corresponding to the unit layer Among them, y i is the vertical distance from the center of the i-th unit layer in UHPC concrete to the upper surface of the composite structural beam, y k is the vertical distance from the center of the kth unit layer in the T-shaped steel beam to the upper surface of the composite structure beam, y' s ' is the vertical distance from the center of the unit layer corresponding to all longitudinal reinforcements at the bottom layer of the composite structural beam to the upper surface of the composite structural beam, y' s It is the vertical distance from the center of the unit layer corresponding to all the longitudinal reinforcements in the uppermost layer of the composite structural beam to the upper surface of the composite structural beam.

4. The method for calculating the characteristic value of the bending bearing capacity of the composite structural beam of steel and UHPC according to claim 3 is characterized in that: The stress calculation method of each unit layer in step A7 is: According to formula (8), the stress σ of the unit layer in UHPC concrete is obtained u,i =σ u (ε u,i ), positive values ​​are tensile stress, and negative values ​​are compressive stress; According to formula (9), the stress σ of the unit layer in the T-beam is obtained h,k =σ s (ε h,k ), positive values ​​are tensile stress, and negative values ​​are compressive stress; According to formula (9), the stress σ of all longitudinal reinforcements corresponding to the unit layer at the bottom layer of the composite structure beam is obtained: s ”=σ s (ε s ”); According to formula (9), the stress σ' of all longitudinal reinforcements in the uppermost layer of the composite structure beam is obtained. s =σ s (ε' s ).

5. The method for calculating the characteristic value of the bending bearing capacity of the composite structural beam of steel and UHPC according to claim 4 is characterized in that: The resultant force F in the cross section of the composite structural beam in step A8 is specifically: F=∑A i s u,i +∑A k s h,k +A″ s in s +A′ s in s (11), Among them, A i is the area of ​​the i-th unit layer in UHPC concrete, A k is the area of ​​the kth unit layer in the T-beam, A s " is the area of ​​the unit layer corresponding to all longitudinal reinforcements at the bottom layer of the composite structural beam, A s ' is the area of ​​the unit layer corresponding to all the longitudinal reinforcements in the uppermost layer of the composite structural beam.

6. The method for calculating the characteristic value of the bending bearing capacity of the composite structural beam of steel and UHPC according to claim 5 is characterized in that: Step A12 calculates the characteristic value M of the bending bearing capacity of the composite structural beam r , specifically:

7. The method for calculating the characteristic value of the bending bearing capacity of a composite structural beam of steel and UHPC according to any one of claims 1 to 6, characterized in that: In step A9, the influence coefficient method is used to iteratively correct x n , specifically: A9.

1. Assume that the new neutral axis position of the composite structural beam is x' n , where x' n =x n +Δx n ; A9.

2. Repeat steps A6-A8 to calculate x' n The resultant force F' in the cross section of the corresponding composite structural beam; A9.

3. Calculate the change in the resultant force in the cross section of the composite structural beam, ΔF, where ΔF = F'-F; A9.

4. Correction of the neutral axis position x of the composite structural beam n ,in 8. The method for calculating the characteristic value of the bending bearing capacity of a composite structural beam of steel and UHPC according to any one of claims 1 to 6, characterized in that: In step A11, the influence coefficient method is used to iteratively correct Specifically: A11.

1. Assuming the new cross-sectional curvature of the composite structural beam Where φ'=φ+Δφ; A11.

2. Repeat steps A5-A10 to calculate The corresponding UHPC concrete upper edge compressive strain ε' top and the tensile strain ε' at the lower edge of the T-beam bottom ; A11.

3. Calculation of the change in compressive strain at the upper edge of UHPC concrete Δε top and the tensile strain change value Δε at the lower edge of the T-beam bottom ; where Δε top =ε' top -ε top , Δε bottom =ε' bottom -ε bottom ; A11.

4. Correction of the cross-sectional curvature of composite structural beams in ε cu is the ultimate compressive strain of UHPC concrete, ε' u1 is the ultimate tensile strain of the T-beam.

9. The method for calculating the characteristic value of the bending bearing capacity of a composite structural beam of steel and UHPC according to any one of claims 1 to 6, characterized in that: Step A3 also includes: obtaining the vertical distance between the center of each unit layer and the upper surface of the composite structure beam and the area of ​​each unit layer.

10. The method for calculating the characteristic value of the bending bearing capacity of a composite structural beam of steel and UHPC according to any one of claims 1 to 6, characterized in that: The minimum compressive strain selected from each unit layer of UHPC concrete is the upper edge compressive strain ε of UHPC concrete. top , the maximum tensile strain is selected from each unit layer of the T-beam, which is the tensile strain of the lower edge of the T-beam ε bottom .

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