UHPC composite beam bending moment-curvature calculation and feature state recognition method and system and storage medium

Abstract

The invention relates to a bending moment-curvature calculation and characteristic state recognition method and system for a UHPC composite beam and a storage medium, and the method comprises the steps: obtaining geometric parameters and material parameters of the UHPC composite beam, and building a nonlinear constitutive model of each material; unit layer division is carried out on the cross section of the UHPC composite beam, and an initial value of the curvature of the cross section is given; acquiring an approximate solution of the neutral axis by using a dichotomy, and acquiring an accurate solution of the neutral axis by using a Newton method based on the approximate solution of the neutral axis; calculating strain and stress of each unit layer based on plane section assumption, and judging whether the UHPC composite beam is damaged or not; if the UHPC composite beam is not damaged, calculating the bending moment value of the UHPC composite beam, identifying the current characteristic state and recording the curvature and the bending moment value, then updating the curvature of the cross section and recalculating the accurate solution of the neutral axis; and if the damage occurs, outputting a curve of the curvature-bending moment value of the cross section. According to the method, the requirements of calculation and analysis of the composite beam under the sagging moment and the hogging moment can be met.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge engineering, and in particular to a method, system and storage medium for calculating the bending moment-curvature and identifying characteristic states of a UHPC composite beam. Background Art

[0002] Ultra-high performance concrete (UHPC) is widely used in bridge engineering due to its excellent mechanical properties, such as high strength, high toughness and good durability. The composite beam structure formed by combining UHPC with steel beams fully utilizes the compressive properties of UHPC and the tensile properties of steel, and has the characteristics of high bearing capacity and strong spanning capacity. In actual bridge engineering, due to the complexity of load conditions, composite beams are often subjected to positive and negative bending moments at the same time. Positive bending moment causes the UHPC bridge deck to be compressed and the bottom of the steel beam to be tensile, while negative bending moment leads to the opposite stress state. There are significant differences in the stress performance and failure mode of the structure under the two conditions.

[0003] The existing technology for stress analysis of composite beams has the following deficiencies:

[0004] 1) Dispersion of calculation models: Calculation models for positive and negative bending moment conditions need to be established separately, which increases the calculation complexity and makes it difficult to ensure the consistency of the calculation results for the two conditions;

[0005] 2) Inadequate material constitutive treatment: UHPC materials have significant nonlinear characteristics in the tensile zone, especially exhibiting strain hardening behavior in the tensile zone. Existing methods often use simplified models, which makes it difficult to accurately simulate their actual stress state;

[0006] 3) Incomplete determination of characteristic states: There is a lack of unified criteria for determining key characteristic states such as UHPC cracking, steel bar yielding, and steel beam yielding. In particular, the state transition under alternating positive and negative bending moments has not been fully considered.

[0007] 4) Fuzzy control of design bearing capacity: Existing methods focus more on the calculation of ultimate bearing capacity, but the determination of the design bearing capacity status is not clear enough, which is not conducive to engineering designers to conduct preliminary design and safety reserve assessment;

[0008] 5) Single expression method: Calculation results are mostly output in numerical form, lacking intuitive graphical expression, which is not easy for engineering and technical personnel to understand and apply.

[0009] In summary, there is an urgent need for a method, system and storage medium for moment-curvature calculation and characteristic state identification of UHPC composite beams to solve the problems existing in the existing technology. Summary of the Invention

[0010] The present invention aims to provide a method for calculating the bending moment and curvature and identifying characteristic states of UHPC composite beams, aiming to address the deficiencies of the existing technology. The specific technical solutions are as follows:

[0011] A method for calculating the bending moment and curvature and identifying characteristic states of a UHPC composite beam comprises the following steps:

[0012] S1. Obtain the geometric parameters and material parameters of the UHPC composite beam and establish the nonlinear constitutive model of each material;

[0013] S2. Divide the cross section of the UHPC composite beam into unit layers and give the cross section curvature of the UHPC composite beam The initial value of

[0014] S3. Use the bisection method to obtain the approximate solution c0 of the neutral axis. Based on the approximate solution c0 of the neutral axis, use Newton's method to obtain the exact solution x of the neutral axis. n ;

[0015] S4. Calculate the strain and stress of each unit layer based on the plane section assumption;

[0016] S5, judging whether the UHPC composite beam is damaged, if damaged, proceeding to S9, if not damaged, proceeding to S6;

[0017] S6. Calculate the bending moment M of the UHPC composite beam based on the moment of each unit layer. r ;

[0018] S7, identifying the current characteristic state and recording the curvature and bending moment values;

[0019] S8. Update the cross-sectional curvature of UHPC composite beams And re-enter step S3;

[0020] S9, output cross-sectional curvature Bending moment value M r curve.

[0021] Preferably, the approximate solution c0 of the neutral axis is obtained by using the bisection method:

[0022] A1. Set the initial search interval to [a, b] = [0, h], where h is the total cross-sectional height of the UHPC composite beam;

[0023] A2. Take the initial position of the neutral axis as c, where c∈[a,b];

[0024] A3. Calculate the total axial force F(c) of the cross section when the neutral axis is at c. If |F(c)| < ε1 or |ba| < δ, output c as the approximate solution c0 for the neutral axis. Otherwise, proceed to step A4. ε1 is the convergence tolerance set in the bisection method, and δ is the interval length convergence threshold.

[0025] A4. Calculate the total axial force F(a) of the cross section when the neutral axis is at position a and the total axial force F(b) of the cross section when the neutral axis is at position b. If F(a)·F(c)≤0, set b=c to update the search interval. If F(a)·F(c)>0, set a=c to update the search interval.

[0026] A5. Update the value of c to the midpoint of the current search interval and re-enter step A3.

[0027] Preferably, the approximate solution c0 of the neutral axis is obtained by using the bisection method:

[0028] C1. Set the initial search interval to [a, b] = [0, h], where h is the total cross-sectional height of the UHPC composite beam;

[0029] C2. Calculate the total axial force F(a) of the cross section when the neutral axis is at position a and the total axial force F(b) of the cross section when the neutral axis is at position b.

[0030] C3. If F(a)·F(b)>0, it means there is no solution in the current search interval and the calculation ends; if F(a)·F(b)≤0, go to step C4;

[0031] C4. Calculate the midpoint of the current search interval, c = (a + b) / 2, and calculate the total axial force F(c) of the cross section when the neutral axis is at c.

[0032] C5. If |F(c)| < ε1 or |ba| < δ, the midpoint c of the current search interval is output as the approximate solution c0 of the neutral axis. Otherwise, the search interval is updated and steps C2-C5 are repeated.

[0033] Wherein, ε1 is the convergence tolerance set in the bisection method, and δ is the interval length convergence threshold; the specific method of updating the search interval in step C5 is: if F(a)·F(c)≤0, then set b=c to update the search interval; if F(a)·F(c)>0, then set a=c to update the search interval.

[0034] Preferably, the Newton method is used to obtain the exact solution x of the neutral axis based on the approximate solution c0 of the neutral axis. n Specifically:

[0035] B1. Take n = 1, let x n =c0;

[0036] B2. Calculate the neutral axis at xn The total axial force F(x n );

[0037] B3、If |F(x n )|<ε2, then output the current x n is the accurate solution for the neutral axis position; if not, determine whether the current n is less than N. If so, proceed to step B4; if not, terminate the calculation; where N is the maximum number of iterations, ε2 is the convergence tolerance set in the Newton method, and ε2 < ε1;

[0038] B4. Calculate the total axial force F(x n )'s derivative F'(x n );

[0039] B5. Update the neutral axis position to And set n = n + 1 and repeat step B2; where α (n) is the relaxation factor at the nth iteration.

[0040] Preferably, the relaxation factor is dynamically adjusted according to the iterative axial force error, and is expressed as:

[0041] α (n+1) =α (n) β (3),

[0042] Among them, the axial force error ΔF(x n ) is expressed as:

[0043] ΔF(x n )=F(x n )-F(x n-1 ) (4),

[0044] Where: F(x n ) is the total axial force of the section obtained in the nth iteration; α (n+1) represents the relaxation factor at the n+1th iteration; β is the adjustment coefficient. If the axial force errors between two adjacent values show a decreasing trend, β is greater than 1; if the axial force errors between two adjacent values show an increasing trend, β is less than 1; if the axial force errors between two adjacent values are equal, β is equal to 1.

[0045] Preferably, the calculation method of the total axial force of the section is as follows:

[0046] According to the curvature and the set neutral axis position, the strain of each unit layer in the cross section is obtained based on the plane section assumption;

[0047] According to the nonlinear constitutive model of the material and the strain of each unit layer, the stress of each unit layer is calculated;

[0048] The total axial force in the cross section of the UHPC composite beam is calculated based on the stress and area of each unit layer.

[0049] Preferably, the specific method of determining whether the UHPC composite beam is damaged in S5 is:

[0050] In the case of positive curvature, if the strain at the upper edge of the UHPC bridge deck exceeds its ultimate compressive strain, the strain at the lower edge of the steel bottom plate of the T-beam exceeds its ultimate tensile strain, or the strain at the bottom longitudinal reinforcement exceeds its ultimate tensile strain, it indicates that the UHPC composite beam has failed.

[0051] In the case of negative curvature, if the strain at the lower edge of the UHPC rib exceeds its ultimate compressive strain, the strain at the lower edge of the steel bottom plate of the T-shaped steel beam exceeds its ultimate compressive strain, or the strain of the topmost longitudinal reinforcement exceeds its ultimate tensile strain, it indicates that the UHPC composite beam has failed.

[0052] Preferably, when When , the UHPC bridge deck is compressed and the bottom of the T-shaped steel beam is tensile; when When , the UHPC bridge deck is in tension and the bottom of the T-shaped steel beam is in compression.

[0053] The present invention also provides a system for calculating the bending moment and curvature and identifying characteristic states of a UHPC composite beam, the method described in the system comprising:

[0054] Parameter input module, used to input geometric parameters, material parameters, calculation control parameters and initial values of cross-sectional curvature; the calculation control parameters include convergence tolerances ε1 and ε2, interval length convergence threshold δ, maximum number of iterations N, curvature increment, initial relaxation factor and initial adjustment coefficient β;

[0055] Meshing module, used to divide the cross section of UHPC composite beam into unit layers;

[0056] Iterative calculation module uses the bisection method to obtain the approximate solution of the neutral axis, and uses Newton's method based on the approximate solution of the neutral axis to obtain the exact solution of the neutral axis;

[0057] Calculation module, used to calculate the strain and stress of each unit layer and the bending moment value of UHPC composite beam;

[0058] Result processing module for generating cross-sectional curvature Bending moment value M r curve.

[0059] The present invention also provides a storage medium, wherein the storage medium stores a computer program, and the method described is executed when the computer program is run.

[0060] The application of the technical solution of the present invention has the following beneficial effects:

[0061] The method of the present invention can be applied to both positive and negative bending moment working conditions. By establishing a unified calculation framework, integrated processing under positive and negative bending moment working conditions is achieved, a complete material nonlinear constitutive model is established, and the curvature sign is used to distinguish the working conditions and select the corresponding constitutive model for calculation, thereby ensuring the accuracy of stress calculation and providing an accurate data basis for analyzing structural performance.

[0062] The method of the present invention can obtain the stress distribution of UHPC composite beams under various typical conditions by continuously updating the curvature, obtain the stress characteristic points such as steel yielding, steel bar yielding, UHPC cracking, and UHPC crushing during the stress process, and output the cross-sectional curvature in a graphical manner. Bending moment value M r The curve makes it easier for designers to intuitively understand the order in which the composite section reaches these characteristic points during the stress process, thereby guiding the structural stress calculation and cross-sectional layout optimization of the UHPC composite beam and ensuring the safe design of the UHPC composite beam.

[0063] The method of the present invention first obtains an approximate solution to the neutral axis position through the bisection method, and then obtains the accurate solution to the neutral axis position through the Newton method. The accurate neutral axis position can be quickly calculated to provide an accurate data basis for subsequent stress and strain calculations, and solves the problems of oscillation divergence and poor convergence in conventional iterative algorithms.

[0064] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0066] Figure 1 is an axonometric view of the composite structural beam of steel and UHPC (i.e., UHPC composite beam) in Example 1;

[0067] Figure 2 yes Figure 1 Schematic diagram of the structure of the middle vertical stirrup group;

[0068] Figure 3 yes Figure 1 Schematic diagram of the structure of the steel tenon and mortise;

[0069] Figure 4 is a flow chart of the method for calculating the moment-curvature and identifying the characteristic state of the UHPC composite beam in Example 1;

[0070] Figure 5 is a schematic diagram of the nonlinear constitutive model of UHPC concrete in Example 1;

[0071] Figure 6 is a schematic diagram of the nonlinear constitutive model of the T-shaped steel beam or steel bar in Example 1;

[0072] Figure 7 is a schematic cross-sectional view of the composite structural beam in Example 1 under positive curvature;

[0073] Figure 8 This is a diagram of the bending moment-curvature output under the positive bending moment condition in the application case;

[0074] Figure 9 This is a schematic diagram of the output moment-curvature under negative bending moment conditions in the application case;

[0075] Among them, 100, composite structural 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, bottom layer longitudinal reinforcement, 124, second bottom layer 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

[0076] To facilitate understanding of the present invention, the present invention will be described more fully below, along with preferred embodiments thereof. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and comprehensive understanding of the disclosure of the present invention.

[0077] 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 this specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0078] Example 1:

[0079] Figure 1-Figure 3The figure shows a composite structural beam of steel and UHPC (i.e., a UHPC composite beam). The composite structural beam 100 includes 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 includes 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. The upper edge of the T-shaped steel beam 130 is embedded in the lower end of the UHPC rib 120.

[0080] 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, which together form a T-shaped structure. 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 (ie the depth of the mortise) is h D The steel tenon 133 and the mortise 134 are embedded in the concrete at the lower end of the UHPC rib 120. The distance between the lower edge of the UHPC rib 120 and the bottom edge of the mortise 134 is C D .

[0081] Furthermore, the UHPC rib 120 includes a rib concrete layer and a rib reinforcement skeleton located in the rib concrete layer. The rib reinforcement skeleton includes the bottom layer of longitudinal reinforcement 123, the second bottom layer of longitudinal reinforcement 124, longitudinal distribution reinforcement 125, 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 arranged alternately along the longitudinal bridge direction, as shown in FIG. Figure 1 and Figure 2As shown, the lower open stirrup 121 and the steel tenon 133 are arranged in a one-to-one correspondence, and 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, and the lower end of the upper open stirrup 122 is placed in the mortise 134. Both sides of the lower end of the upper open stirrup 122 are provided with transverse short steel bars 126, 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. 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.

[0082] 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.

[0083] Furthermore, the upper end of the lower open stirrup 121 is connected to the bridge deck steel frame, specifically, overlapped with the bridge deck longitudinal steel bars 112.

[0084] Preferably, the bridge deck concrete layer and the rib concrete layer are both cast using UHPC concrete, and the UHPC concrete is ultra-high performance concrete with ultra-high durability and ultra-high mechanical properties.

[0085] Furthermore, the lower end of the UHPC rib 120 is thickened at the embedded steel tenon 133 and mortise 134 (i.e., a reinforced horseshoe is provided) to ensure that the transverse distance from the steel tenon to the edge of the UHPC rib 120 is not less than 5 times the height of the steel tenon, thereby improving the fault tolerance of the centering error between the steel web 132 and the UHPC rib 120. At the same time, it provides bending space for the upper and lower open stirrups and reserves sufficient protective layer thickness for the stirrups, thereby improving the bonding ability between the steel web and the UHPC rib 120.

[0086] In order to accurately evaluate the mechanical performance of composite structural beams at various stages and provide a reliable basis for engineering design and analysis, this embodiment provides a method for moment-curvature calculation and characteristic state identification of UHPC composite beams. Figure 4 As shown, the following steps are included:

[0087] S1. Obtain the geometric parameters and material parameters of the UHPC composite beam and establish the nonlinear constitutive model of each material;

[0088] Unlike conventional concrete, UHPC concrete exhibits strain hardening properties, and its post-crack strength still contributes to flexural capacity. To fully account for these effects, a three-fold line model was used for UHPC tensile strength, a linear elastic model for UHPC compression, and a three-fold line model that considers the yield plateau and strain hardening for the T-beams and rebar in the UHPC composite beams. Because the project focused on maximum load-bearing capacity, the material constitutive models, with the exception of the UHPC tensile model, did not include a descending section.

[0089] Preferably, Figure 5 As shown in Figure 2, the nonlinear constitutive model of UHPC concrete is:

[0090]

[0091] 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 ultimate elastic strain of UHPC concrete under tension; 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 σ u =f cu , reaching the ultimate compressive stress, f cu is the ultimate compressive stress of UHPC concrete; f te is the tensile elastic limit stress of UHPC concrete, fte =E u ·ε te ;f tu is the ultimate tensile stress of UHPC concrete, and the corresponding strain is ε tu .

[0092] like Figure 5 As shown in Figure 2, 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 cracking to the bending bearing capacity.

[0093] Preferably, Figure 6 As shown in Figure 2, the nonlinear constitutive models of the T-steel beam and reinforcement in the UHPC composite beam are:

[0094]

[0095] 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; for the case of no yield plateau, such as some specifications of steel bars, ε y =ε st ;

[0096] When ε s =ε′ y When σ s =f′ y , reaching the compressive limit stress, f y ' is the ultimate compressive 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 .

[0097] like Figure 6 As shown in Figure 2, 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.

[0098] S2. Divide the cross section of the UHPC composite beam into unit layers and give the cross section curvature of the UHPC composite beam The initial value of

[0099] Preferably, the cross section of the UHPC composite beam is divided into unit layers as follows:

[0100] The cross section of the UHPC concrete of the UHPC composite beam and the cross section of the T-shaped steel beam outside the UHPC concrete are divided into unit layers. At the same time, the cross section of all longitudinal steel bars in the top layer of the UHPC composite beam and the cross section of all longitudinal steel bars in the bottom layer of the UHPC composite beam are taken as a unit layer, such as Figure 7 As shown;

[0101] Optimally, all unit layers should be on the same cross-section of the UHPC composite 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, mandatory layer splitting lines are placed at all locations where the cross-section width and material change to facilitate the calculation of each unit layer area and subsequent internal forces. Based on the above unit layer division rules, it can be seen that, with the exception of the longitudinal reinforcement at the bottom and top layers of the UHPC composite beam, the remaining steel structure embedded in the UHPC concrete (referring to the embedded reinforcement and part of the steel web) is not considered in the calculation, which can simplify the calculation.

[0102] Preferably, the cross-sectional curvature here The initial value of can be positive or negative, so that the method of this embodiment can be compatible with the requirements for the analysis of positive and negative bending moment conditions of UHPC composite beams; under the positive bending moment condition, The UHPC bridge deck is in compression, and the bottom of the T-shaped steel beam is in tension. The initial value is usually taken as 5×10 -6 / m; Under negative bending moment conditions, The UHPC bridge deck is in tension, and the bottom of the T-shaped steel beam is in compression. The initial value is usually taken as -5×10 -6 / m.

[0103] S3. Use the bisection method to obtain the approximate solution c0 of the neutral axis. Based on the approximate solution of the neutral axis, use Newton's method to obtain the exact solution x of the neutral axis. n ;

[0104] In this embodiment, a bisection method is used to obtain an approximate solution for the neutral axis, specifically:

[0105] A1. Set the initial search interval to [a, b] = [0, h], where h is the total cross-sectional height of the UHPC composite beam;

[0106] A2. Take the initial position of the neutral axis as c, where c∈[a,b];

[0107] Preferably, in this embodiment, when the curvature is a positive value, the initial position of the neutral axis is 0.5h, that is, the distance between the initial position of the neutral axis and the upper surface of the UHPC bridge deck is 0.5h; when the curvature is a negative value, the initial position of the neutral axis is 0.2h, that is, the distance between the initial position of the neutral axis and the upper surface of the UHPC bridge deck is 0.2h. By giving a suitable initial position, the iterative convergence speed of the bisection method is accelerated.

[0108] A3. Calculate the total axial force F(c) of the section when the neutral axis is at c. If |F(c)| < ε1 or |ba| < δ, output c as the approximate solution c0 of the neutral axis. Otherwise, proceed to step A4. ε1 is the convergence tolerance set in the bisection method, and δ is the interval length convergence threshold, which can be 0.1h.

[0109] A4. Calculate the total axial force F(a) of the cross section when the neutral axis is at position a and the total axial force F(b) of the cross section when the neutral axis is at position b. If F(a)·F(c)≤0, set b=c to update the search interval. If F(a)·F(c)>0, set a=c to update the search interval.

[0110] A5. Update the value of c to the midpoint of the current search interval, that is, c = (a + b) / 2, and re-enter step A3 until the approximate solution c0 is output.

[0111] The above steps A1-A5 provide a method for obtaining an approximate solution to the neutral axis using the bisection method under the premise of a given initial position of the neutral axis. This embodiment also provides a method for obtaining an approximate solution to the neutral axis using the bisection method when the initial position of the neutral axis is not given, as follows:

[0112] C1. Set the initial search interval to [a, b] = [0, h], where h is the total cross-sectional height of the UHPC composite beam;

[0113] C2. Calculate the total axial force F(a) of the cross section when the neutral axis is at position a and the total axial force F(b) of the cross section when the neutral axis is at position b.

[0114] C3. If F(a)·F(b)>0, it means there is no solution in the current search interval and the calculation ends; if F(a)·F(b)≤0, go to step C4;

[0115] C4. Calculate the midpoint of the current search interval, c = (a + b) / 2, and calculate the total axial force F(c) of the cross section when the neutral axis is at c.

[0116] C5. If |F(c)| < ε1 or |ba| < δ, then output the midpoint c of the current search interval as the approximate solution c0 of the neutral axis. Otherwise, update the search interval and repeat steps C2-C5. ε1 is the convergence tolerance set in the bisection method, and δ is the interval length convergence threshold, which can be 0.1h.

[0117] Furthermore, in step C5, the search interval is updated in the following manner: if F(a)·F(c)≤0, then b=c is set to update the search interval; if F(a)·F(c)>0, then a=c is set to update the search interval;

[0118] The approximate solution of the neutral axis position obtained by the bisection method can generally be used for the subsequent stress and strain calculations of each unit layer. However, in this embodiment, in order to obtain a more accurate neutral axis position, the Newton method is used on the basis of the approximate solution to further obtain an accurate solution. The specific steps are as follows:

[0119] B1. Take n = 1, let x n =c0;

[0120] B2. Calculate the neutral axis at x n The total axial force F(x n );

[0121] B3、If |F(x n )|<ε2, then output the current x n is the accurate solution for the neutral axis position; if not, determine whether the current n is less than N. If so, proceed to step B4; if not, terminate the calculation; where N is the maximum number of iterations, ε2 is the convergence tolerance set in the Newton method, and ε2 < ε1;

[0122] B4. Calculate the total axial force F(x n )'s derivative F'(x n );

[0123] B5. Update the neutral axis position to And set n = n + 1 and repeat step B2; where α (n) is the relaxation factor at the nth iteration.

[0124] Preferably, the relaxation factor is dynamically adjusted according to the iterative axial force error (usually limited to 0.1≤α≤0.5) to achieve a balance between computational efficiency and stability. The relaxation factor is adjusted as follows:

[0125] α (n+1) =α (n) β (3),

[0126] Among them, α (n+1)represents the relaxation factor at the n+1th iteration; β is the adjustment coefficient. If the axial force errors between two adjacent iterations show a decreasing trend, β is set to be greater than 1 (such as β = 1.1) to appropriately increase the relaxation factor and accelerate the convergence speed. If the axial force errors between two adjacent iterations show an increasing trend, β is set to be less than 1 (such as β = 0.5) to reduce the relaxation factor and ensure the stability of the calculation. If the axial force errors between two adjacent iterations are equal, β is set to be equal to 1, that is, the relaxation factor is not adjusted.

[0127] Furthermore, the axial force error ΔF(x n ) is expressed as:

[0128] ΔF(x n )=F(x n )-F(x n-1 ) (4),

[0129] Among them, F(x n ) is the total axial force of the section obtained in the nth iteration.

[0130] The calculation method of the total axial force of the cross section in this embodiment will be described in detail below. Specifically:

[0131] See also Figure 7 According to the curvature and the set neutral axis position, the strain of each unit layer in the cross section is obtained based on the plane section assumption:

[0132] 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, negative values are compressive strains; the strains of all longitudinal reinforcements in the bottom layer of the UHPC composite beam correspond to the unit layer. The strain of all longitudinal reinforcement corresponding to the unit layer in the uppermost layer of UHPC composite beam

[0133] Where x is the position of the neutral axis. The positions of the neutral axis assumed by the bisection method and the Newton method are different, and the values of x are also different; y i is the vertical distance from the center of the i-th unit layer in UHPC concrete to the upper surface of the UHPC composite 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 UHPC composite beam, y s ” is the vertical distance from the center of the unit layer corresponding to all longitudinal reinforcements in the bottom layer of the UHPC composite beam to the upper surface of the UHPC composite beam, y s ' is the vertical distance from the center of the unit layer corresponding to all longitudinal reinforcements in the uppermost layer of the UHPC composite beam to the upper surface of the UHPC composite beam.

[0134] Calculate the stress σ of each unit layer in UHPC concrete based on 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 reinforcement corresponding to the unit layer at the bottom layer of UHPC composite beam s ” and the stress σ′ of all longitudinal reinforcements in the uppermost layer of the UHPC composite beam s ,

[0135] Specifically, according to formula (1), 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 (2), the stress σ of the unit layer in the T-shaped steel beam is obtained h,k =σ s (ε h,k ), positive values are tensile stress, and negative values are compressive stress; According to formula (2), the stress σ of all longitudinal reinforcement corresponding to the unit layer in the bottom layer of UHPC composite beam is obtained: s ”=σ s (ε s ”); According to formula (2), the stress σ′ of all longitudinal reinforcement corresponding to the unit layer of the top layer of UHPC composite beam is obtained s =σ s (ε′ s ).

[0136] The total axial force F(x) in the cross section of the UHPC composite beam is calculated based on the stress and area of each unit layer;

[0137] Preferably, the total axial force F(x) in the cross section of the UHPC composite beam is:

[0138] F(x)=∑A i σ u,i +∑A k σ h,k +A″ s σ″ s +A′ s σ′ s (5).

[0139] S4. Calculate the strain and stress of each unit layer based on the plane section assumption;

[0140] After obtaining the position of the neutral axis in step S3, the strain and stress of each unit layer can be accurately calculated. The calculation method is consistent with the strain and stress calculation method when calculating the total axial force of the section in step S3, so it will not be repeated.

[0141] S5, judging whether the UHPC composite beam is damaged, if damaged, proceeding to S9, if not damaged, proceeding to S6;

[0142] Specifically, in the case of positive curvature, if the strain at the upper edge of the UHPC bridge deck exceeds its compressive limit strain, the strain at the lower edge of the steel bottom plate of the T-shaped steel beam exceeds its ultimate tensile strain, or the strain at the bottom layer of longitudinal reinforcement exceeds its ultimate tensile strain, it indicates that the UHPC composite beam has been damaged. In the case of negative curvature, if the strain at the lower edge of the UHPC rib exceeds its compressive limit strain, the strain at the lower edge of the steel bottom plate of the T-shaped steel beam exceeds its ultimate compressive strain, or the strain at the top layer of longitudinal reinforcement exceeds its ultimate tensile strain, it indicates that the UHPC composite beam has been damaged.

[0143] S6. Calculate the bending moment M of the UHPC composite beam based on the moment of each unit layer. r ;

[0144] Specifically, the bending moment M of the UHPC composite beam is calculated based on 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 UHPC composite beam, and the moment of all longitudinal steel bars corresponding to the unit layer in the top layer of the UHPC composite beam. r , the bending moment M of UHPC composite beam r for:

[0145]

[0146] Among them, x in formula (6) n is the exact solution of the neutral axis obtained by Newton’s method, A i represents the area of the i-th unit layer in UHPC concrete, A k represents the area of the kth unit layer in the T-beam, A s " represents the area of the unit layer corresponding to all longitudinal reinforcements in the bottom layer of the UHPC composite beam, A s ' represents the area of the unit layer corresponding to all longitudinal reinforcements in the top layer of the UHPC composite beam.

[0147] S7, identifying the current characteristic state and recording the corresponding curvature and bending moment values;

[0148] The characteristic states of UHPC composite beams are identified based on the strain and stress of each unit layer. The judgment method of each characteristic state under positive bending moment condition is as follows:

[0149] Design bearing capacity state: The stress at the lower edge of the steel bottom plate of the T-shaped steel beam reaches the tensile design strength;

[0150] Characteristic state of the first cracking (hardening onset) of UHPC concrete: the strain at the lower edge of the UHPC rib plate reaches the tensile elastic limit strain;

[0151] Characteristic state of UHPC concrete hardening completion (softening start): the strain at the lower edge of the UHPC rib plate reaches the ultimate tensile strain;

[0152] The characteristic state of the yielding of the bottom longitudinal reinforcement: the strain of the bottom longitudinal reinforcement reaches the tensile yield strain;

[0153] The characteristic state of the initial yield of the T-beam: the strain at the lower edge of the steel bottom plate of the T-beam reaches the tensile yield strain;

[0154] The initial characteristic state of strengthening of T-beam: the strain at the lower edge of the steel bottom plate of the T-beam reaches the strain hardening starting strain;

[0155] Characteristic state of UHPC concrete compressive design strength: The stress on the upper edge of the UHPC bridge deck reaches the design compressive stress;

[0156] Ultimate bearing state: The strain on the upper edge of the UHPC bridge deck reaches the ultimate compressive strain, the strain on the lower edge of the steel bottom plate of the T-shaped steel beam reaches the ultimate tensile strain, or the strain on the bottom longitudinal reinforcement reaches the ultimate tensile strain;

[0157] Preferably, the method for determining each characteristic state under negative bending moment conditions is:

[0158] Design bearing capacity state: the stress of the uppermost longitudinal reinforcement reaches the tensile design strength;

[0159] Characteristic state of the first cracking (hardening onset) of UHPC concrete: the strain at the upper edge of the UHPC bridge deck reaches the tensile elastic limit strain;

[0160] Characteristic state of the end of hardening (beginning of softening) of UHPC concrete: the strain on the upper edge of the UHPC bridge deck reaches the ultimate tensile strain;

[0161] Characteristic state of the end of softening (fracture) of UHPC concrete: the strain on the upper edge of the UHPC bridge deck reaches the fracture strain;

[0162] The characteristic state of the yielding onset of the top longitudinal reinforcement: the strain of the top longitudinal reinforcement reaches the tensile yield strain;

[0163] Characteristic state of compression design strength of T-beam: The stress at the lower edge of the steel bottom plate of the T-beam reaches the compression design strength;

[0164] Characteristic state of compression yield of T-beam: The stress at the lower edge of the steel bottom plate of the T-beam reaches the compression yield strength;

[0165] Ultimate bearing state: The strain at the lower edge of the UHPC rib plate reaches the ultimate compressive strain, the strain at the lower edge of the steel bottom plate of the T-beam exceeds its ultimate compressive strain, or the strain of the topmost longitudinal reinforcement reaches the ultimate tensile strain;

[0166] Based on the stress and strain of unit layers at different positions, the characteristic state of the UHPC composite beam under the current curvature and bending moment can be clarified, helping designers to accurately evaluate the stress performance of the structure at each stage.

[0167] S8. Update the cross-sectional curvature of UHPC composite beams And re-enter S3;

[0168] Preferably, in this embodiment, the cross-sectional curvature The update method is expressed as:

[0169]

[0170] in, is the curvature increment, generally taken

[0171] Of course, in some embodiments, other methods may be used to adjust the cross-sectional curvature. Updates such as cross-sectional curvature The initial value of At this time, N is set to 1; after an update, take N = N + 1 and recalculate And so on.

[0172] By continuously updating the curvature value, the entire stress-bearing process of the UHPC composite beam can be analyzed, helping designers to clarify the performance of the UHPC composite beam at each stage.

[0173] S9, output cross-sectional curvature Bending moment value M r The calculation ends.

[0174] Specifically, The value is the x coordinate, M r The value is the y coordinate to establish a coordinate system, and all the records Data by The values are arranged in ascending order, and all the records are Data according to The order of arrangement of the values is plotted as a curvature-resistance bending moment curve in the coordinate system, and each characteristic state is marked on the curve to intuitively understand the stress performance under each characteristic state.

[0175] Application Cases:

[0176] Taking a UHPC composite beam as an example, the feasibility of the method of this embodiment is verified.

[0177] 1) Parameter input:

[0178] UHPC bridge deck: width 1200mm, thickness 120mm;

[0179] UHPC web: width 120mm, height 480mm;

[0180] Steel web: thickness 16mm, height 575mm;

[0181] Steel base plate: width 400mm, thickness 25mm;

[0182] The top layer of longitudinal steel bars: 12 bars with a diameter of Φ12mm, 20mm from the upper surface of the UHPC bridge deck;

[0183] The bottom layer of longitudinal steel bars: 2 with a diameter of Φ16mm, 20mm away from the lower edge of the UHPC rib.

[0184] 2) Establishment of material constitutive model:

[0185] UHPC material parameters: The mechanical properties of UHPC materials are determined through standard tests: the tensile and compressive elastic modulus is 45.7GPa, which characterizes the stiffness characteristics of the material; the elastic ultimate tensile strength is 10.87MPa, indicating that the material enters the hardening stage from the elastic stage; the ultimate tensile strength is 11.66MPa, representing the maximum tensile stress that the material can withstand; the ultimate compressive strength is 145MPa, which characterizes the compressive bearing capacity of the material; the corresponding strain parameters include: the elastic ultimate strain is 0.000238, corresponding to the elastic ultimate tensile strength; the ultimate strain is 0.00293, corresponding to the ultimate tensile strength; the cracking strain is 0.01, indicating the strain value when the material is completely cracked; the ultimate compressive strain is 0.0032, corresponding to the ultimate compressive strength.

[0186] T-beam parameters: The steel material is Q355 grade steel, and its main mechanical parameters are: elastic modulus is 206GPa, which characterizes the elastic deformation capacity of the material; yield strength is 355MPa, indicating that the material enters the plastic stage; yield strain is 0.00172, corresponding to the yield strength; strengthening starting strain is 0.0198, indicating that the material begins to strengthen; ultimate strain is 0.035, representing the maximum deformation capacity of the material; strengthening section slope is 10329MPa, reflecting the strength growth rate of the material in the strengthening stage; ultimate compressive strain is 0.00172, corresponding to the ultimate compressive strength.

[0187] Rebar parameters: HRB400 grade rebar is used, and its mechanical properties include: elastic modulus of 200GPa, which characterizes the elastic deformation characteristics of the rebar; yield strength of 400MPa, indicating that the rebar enters the plastic stage; yield strain of 0.002, corresponding to the yield strength; strengthening starting strain of 0.002, indicating that the rebar begins to strengthen; ultimate strain of 0.016, representing the maximum deformation capacity of the rebar; strengthening section slope of 11786MPa, reflecting the strength growth rate of the rebar in the strengthening stage; ultimate compressive strain of 0.002, corresponding to the ultimate compressive strength.

[0188] 3) Calculation process:

[0189] (1) Calculation configuration for positive bending moment conditions:

[0190] Set the initial curvature to 5×10 -6 / m,

[0191] The initial neutral axis position is 0.5h=600mm,

[0192] The convergence tolerance ε1 set in the bisection method is 1N.

[0193] The interval length convergence threshold δ is 120 mm.

[0194] The convergence tolerance ε2 set in Newton's method is 0.1N.

[0195] Curvature increment 5×10 -6 / m,

[0196] The calculation ends when the ultimate load state is exceeded.

[0197] (2) Calculation configuration for negative bending moment conditions:

[0198] Set the initial curvature to -5×10 -6 / m,

[0199] The initial neutral axis position is 0.2h=240mm,

[0200] The convergence tolerance ε1 set in the bisection method is 1N.

[0201] The interval length convergence threshold δ is 120 mm.

[0202] The convergence tolerance ε2 set in Newton's method is 0.1N.

[0203] Curvature increment -5×10 -6 / m,

[0204] The calculation ends when the ultimate load state is exceeded.

[0205] 4) Feature state recognition results:

[0206] (1) The output results under positive bending moment conditions are as follows Figure 8 As shown, the curvature and bending moment corresponding to each characteristic point are as follows:

[0207] The lower edge of the UHPC rib reaches the elastic limit strain point (i.e. the first cracking of UHPC): M r =4380.5kN·m

[0208] The lower edge of the steel bottom plate of the T-beam reaches the design strength: M r =5147.4kN·m

[0209] The lower edge of the steel bottom plate of the T-beam reaches the yield strength: M r =6331.0kN·m

[0210] The upper edge of the UHPC bridge deck reaches the designed compressive stress: M r =8088.5kN·m

[0211] The lower edge of the UHPC rib plate reaches the ultimate tensile strength: M r =9031.0kN·m

[0212] The lower edge of the steel bottom plate of the T-beam reaches the strengthening strain: M r =9126.8kN·m

[0213] The upper edge of the UHPC bridge deck reaches the ultimate compressive strain: M r =9418.3kN·m

[0214] (2) The output results under negative bending moment conditions are as follows Figure 9 As shown, the curvature and bending moment corresponding to each characteristic point are as follows:

[0215] The upper edge of the UHPC bridge deck reaches the ultimate tensile elastic strain (i.e., the first cracking of the UHPC): M r =1492.7kN·m

[0216] The top layer of longitudinal reinforcement reaches the designed tensile strength: M r =2697.4kN·m

[0217] The top longitudinal reinforcement reaches yield strength: M r=2878.7kN·m

[0218] The lower edge of the steel bottom plate of the T-shaped steel beam reaches the compressive design strength: M r =3255.1kN·m

[0219] The strain on the upper edge of the UHPC bridge deck reaches the tensile limit strain: M r =3321.6kN·m

[0220] The lower edge of the steel bottom plate of the T-beam reaches compressive yield: M r =3595.9kN·m

[0221] The upper edge of the UHPC bridge deck reaches fracture: M r =2882.1kN·m

[0222] The strain of the top longitudinal reinforcement reaches the ultimate tensile strain: M r =2625.7kN·m

[0223] 5) Analysis of calculation results:

[0224] (1) Ratio of design bearing capacity to ultimate bearing capacity:

[0225] Positive bending moment condition: 1.83 (83% safety reserve, controlled by the compression on the upper edge of the UHPC bridge deck)

[0226] Negative bending moment condition: 1.33 (33% safety reserve, controlled by the tension of the top longitudinal reinforcement)

[0227] (2) Computational efficiency:

[0228] Average number of iterations for positive bending moment condition: 15 times

[0229] Average number of iterations for negative bending moment conditions: 18 times

[0230] Calculation time for a single working condition: <2 seconds

[0231] The convergence is good and there is no divergence.

[0232] Example 2:

[0233] This embodiment provides a system for calculating the bending moment and curvature and identifying characteristic states of a UHPC composite beam. The system in this embodiment adopts the method in Example 1. The system includes:

[0234] Parameter input module, used to input geometric parameters, material parameters, calculation control parameters and initial values of cross-sectional curvature; the calculation control parameters include convergence tolerances ε1 and ε2, interval length convergence threshold δ, maximum number of iterations N, curvature increment, initial relaxation factor and initial adjustment coefficient β;

[0235] Meshing module, used to divide the cross section of UHPC composite beam into unit layers;

[0236] Iterative calculation module uses the bisection method to obtain the approximate solution of the neutral axis, and uses Newton's method based on the approximate solution of the neutral axis to obtain the exact solution of the neutral axis;

[0237] Calculation module, used to calculate the strain and stress of each unit layer and the bending moment value of UHPC composite beam;

[0238] Result processing module for generating cross-sectional curvature Bending moment value M r curve.

[0239] Example 3:

[0240] This embodiment provides a storage medium, in which a computer program is stored. When the computer program is run, the method in embodiment 1 is executed.

[0241] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for calculating the moment-curvature and identifying characteristic states of UHPC composite beams, characterized in that: The following steps are involved: S1. Obtain the geometric parameters and material parameters of the UHPC composite beam and establish the nonlinear constitutive model of each material; S2. Divide the cross section of the UHPC composite beam into unit layers and give the cross section curvature of the UHPC composite beam The initial value of S3. Use the bisection method to obtain the approximate solution c0 of the neutral axis. Based on the approximate solution c0 of the neutral axis, use Newton's method to obtain the exact solution x of the neutral axis. n ; S4. Calculate the strain and stress of each unit layer based on the plane section assumption; S5, judging whether the UHPC composite beam is damaged, if damaged, proceeding to S9, if not damaged, proceeding to S6; S6. Calculate the bending moment M of the UHPC composite beam based on the moment of each unit layer. r ; S7, identifying the current characteristic state and recording the curvature and bending moment values; S8. Update the cross-sectional curvature of UHPC composite beams And re-enter step S3; S9, output cross-sectional curvature -Bending moment value M r curve.

2. The method for calculating the bending moment-curvature and identifying the characteristic state of a UHPC composite beam according to claim 1 is characterized in that: The approximate solution c0 for the neutral axis using the bisection method is: A1. Set the initial search interval to [a, b] = [0, h], where h is the total cross-sectional height of the UHPC composite beam; A2. Take the initial position of the neutral axis as c, where c∈[a,b]; A3. Calculate the total axial force F(c) of the cross section when the neutral axis is at c. If |F(c)| < ε1 or |ba| < δ, output c as the approximate solution c0 for the neutral axis. Otherwise, proceed to step A4. ε1 is the convergence tolerance set in the bisection method, and δ is the interval length convergence threshold. A4. Calculate the total axial force F(a) of the cross section when the neutral axis is at position a and the total axial force F(b) of the cross section when the neutral axis is at position b. If F(a)·F(c)≤0, set b=c to update the search interval. If F(a)·F(c)>0, set a=c to update the search interval. A5. Update the value of c to the midpoint of the current search interval and re-enter step A3.

3. The method for calculating the bending moment-curvature and identifying the characteristic state of a UHPC composite beam according to claim 1, wherein: The approximate solution c0 for the neutral axis using the bisection method is: C1. Set the initial search interval to [a, b] = [0, h], where h is the total cross-sectional height of the UHPC composite beam; C2. Calculate the total axial force F(a) of the cross section when the neutral axis is at position a and the total axial force F(b) of the cross section when the neutral axis is at position b. C3. If F(a)·F(b)>0, it means there is no solution in the current search interval and the calculation ends; if F(a)·F(b)≤0, go to step C4; C4. Calculate the midpoint of the current search interval, c = (a + b) / 2, and calculate the total axial force F(c) of the cross section when the neutral axis is at c. C5. If |F(c)| < ε1 or |ba| < δ, the midpoint c of the current search interval is output as the approximate solution c0 of the neutral axis. Otherwise, the search interval is updated and steps C2-C5 are repeated. Wherein, ε1 is the convergence tolerance set in the bisection method, and δ is the interval length convergence threshold; the specific method of updating the search interval in step C5 is: if F(a)·F(c)≤0, then set b=c to update the search interval; if F(a)·F(c)>0, then set a=c to update the search interval.

4. The method for calculating the moment-curvature and identifying characteristic states of a UHPC composite beam according to claim 2 or 3, characterized in that: Based on the approximate solution c0 of the neutral axis, use Newton's method to obtain the exact solution x of the neutral axis. n Specifically: B1. Take n = 1, let x n =c0; B2. Calculate the neutral axis at x n The total axial force F(x n ); B3、If |F(x n )|<ε2, then output the current x n is the accurate solution for the neutral axis position; if not, determine whether the current n is less than N. If so, proceed to step B4; if not, terminate the calculation; where N is the maximum number of iterations, ε2 is the convergence tolerance set in the Newton method, and ε2 < ε1; B4. Calculate the total axial force F(x n )'s derivative F'(x n ); B5. Update the neutral axis position to And set n = n + 1 and repeat step B2; where α (n) is the relaxation factor at the nth iteration.

5. The method for calculating the bending moment-curvature and identifying the characteristic state of a UHPC composite beam according to claim 4, characterized in that: The relaxation factor is dynamically adjusted according to the iterative axial force error and is expressed as: α (n+1) ＝α (n) ·β (3)， Among them, the axial force error ΔF(x n ) is expressed as: ΔF(x n )=F(x n )-F(x n-1 ) (4), Where: F(x n ) is the total axial force of the section obtained in the nth iteration; α (n+1) represents the relaxation factor at the n+1th iteration; β is the adjustment coefficient. If the axial force errors between two adjacent values show a decreasing trend, β is greater than 1; if the axial force errors between two adjacent values show an increasing trend, β is less than 1; if the axial force errors between two adjacent values are equal, β is equal to 1.

6. The method for calculating the bending moment-curvature and identifying the characteristic state of a UHPC composite beam according to claim 4, characterized in that: The calculation method of the total axial force of the section is as follows: According to the curvature and the set neutral axis position, the strain of each unit layer in the cross section is obtained based on the plane section assumption; According to the nonlinear constitutive model of the material and the strain of each unit layer, the stress of each unit layer is calculated; The total axial force in the cross section of the UHPC composite beam is calculated based on the stress and area of each unit layer.

7. The method for calculating the bending moment-curvature and identifying the characteristic state of a UHPC composite beam according to claim 1, wherein: The specific method for judging whether the UHPC composite beam is damaged in S5 is: In the case of positive curvature, if the strain at the upper edge of the UHPC bridge deck exceeds its ultimate compressive strain, the strain at the lower edge of the steel bottom plate of the T-beam exceeds its ultimate tensile strain, or the strain at the bottom longitudinal reinforcement exceeds its ultimate tensile strain, it indicates that the UHPC composite beam has failed. In the case of negative curvature, if the strain at the lower edge of the UHPC rib exceeds its ultimate compressive strain, the strain at the lower edge of the steel bottom plate of the T-shaped steel beam exceeds its ultimate compressive strain, or the strain of the topmost longitudinal reinforcement exceeds its ultimate tensile strain, it indicates that the UHPC composite beam has failed.

8. The method for calculating the bending moment-curvature and identifying characteristic states of a UHPC composite beam according to claim 1, wherein: when When , the UHPC bridge deck is compressed and the bottom of the T-shaped steel beam is tensile; when When , the UHPC bridge deck is in tension and the bottom of the T-shaped steel beam is in compression.

9. A UHPC composite beam moment-curvature calculation and characteristic state identification system, characterized in that: The system adopts the method according to any one of claims 1 to 8, and the system includes: Parameter input module, used to input geometric parameters, material parameters, calculation control parameters and initial values of cross-sectional curvature; the calculation control parameters include convergence tolerances ε1 and ε2, interval length convergence threshold δ, maximum number of iterations N, curvature increment, initial relaxation factor and initial adjustment coefficient β; Meshing module, used to divide the cross section of UHPC composite beam into unit layers; Iterative calculation module uses the bisection method to obtain the approximate solution of the neutral axis, and uses Newton's method based on the approximate solution of the neutral axis to obtain the exact solution of the neutral axis; Calculation module, used to calculate the strain and stress of each unit layer and the bending moment value of UHPC composite beam; Result processing module for generating cross-sectional curvature -Bending moment value M r curve.

10. A storage medium, characterized in that: The storage medium stores a computer program, which executes the method according to any one of claims 1 to 8 when running.

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