Design method for flexural ultimate strength and fracture toughness of reinforced concrete structures

Abstract

The present application belongs to the technical field of civil engineering, bridge and hydraulic engineering, and particularly relates to a design method for flexural ultimate strength and fracture toughness of reinforced concrete structure. A reinforced concrete structure model, a concrete model and a steel bar model are established, which are respectively referred to as reinforced concrete, concrete and steel bar. The flexural ultimate strength of the reinforced concrete structure is equivalent to the superposition of the tensile strength of the concrete and the tensile strength increment caused by the yield strength of the steel bar. The flexural fracture toughness of the reinforced concrete structure is equivalent to the superposition of the fracture toughness of the concrete and the fracture toughness increment caused by the yield strength of the steel bar. The present application is based on the nonlinear mesoscopic fracture theory, effectively avoids the influence of the size effect on the design of the flexural ultimate strength and fracture toughness of the reinforced concrete structure, greatly improves the design precision, and reasonably evaluates the maximum load that the reinforced concrete structure can bear and the ability to resist further crack expansion in the flexural process by combining with the finite element software.

Description

Technical Field

[0001] This invention belongs to the technical field of civil engineering, bridge and water conservancy engineering, and specifically relates to a design method for the flexural ultimate strength and fracture toughness of reinforced concrete structures. Background Technology

[0002] Reinforced concrete structures are widely used in civil engineering, bridges, and water conservancy projects, and their cracking failure has always been a focus of attention in the engineering community. The appearance of cracks not only affects the aesthetics of the structure but also reduces its durability and load-bearing capacity, and can even lead to safety hazards. Traditional reinforced concrete design methods are usually based on linear elasticity theory, empirical formulas, and construction measures, which inevitably suffer from problems such as size effects, low prediction accuracy, and narrow applicability, making it difficult to meet the high-precision requirements for structural safety in modern civil engineering, bridges, and water conservancy projects. Furthermore, most domestic and international standards only use ultimate strength (such as flexural capacity) as the failure control parameter for reinforced concrete structures, neglecting the influence of fracture toughness (including crack propagation capacity and energy dissipation capacity) on structural toughness and failure modes. Therefore, designing reinforced concrete structures based on flexural ultimate strength and fracture toughness can effectively prevent catastrophic failure of civil engineering, bridges, and water conservancy structures due to brittle fracture under extreme loads (earthquakes, explosions, impacts).

[0003] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the present invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a design method for the flexural ultimate strength and fracture toughness of reinforced concrete structures.

[0005] The technical solution adopted by this invention to solve its technical problem is as follows: A design method for the flexural ultimate strength and fracture toughness of reinforced concrete structures, wherein the flexural ultimate strength f of the reinforced concrete structure is... tult-str Equivalent to the tensile strength f of concrete t-c and the yield strength F of the steel reinforcement sult The resulting increase in tensile strength Δf tult The superposition of the ... ICult-str Equivalent to the fracture toughness K of concrete IC-c With the yield strength F of the steel reinforcement sult Caused fracture toughness increment ΔK ICult The superposition includes the following steps:

[0006] S1. Modeling: Create a reinforced concrete structure model, a concrete model, and a steel reinforcement model, which are abbreviated as reinforced concrete, concrete, and steel reinforcement, respectively.

[0007] S2. Calculate the macroscopic crack length a in reinforced concrete. w0 The nominal strength at the crack tip is calculated based on the design load and reinforced concrete dimensional parameters, and then combined with the tensile strength of the concrete to construct a. w0 Solving the univariate nonlinear equation yields a. w0 ;

[0008] S3, Calculate the tensile strength f of concrete t-c and fracture toughness K IC-c For the precast initial crack length a 0c Three-point bending tests were conducted on the concrete specimens, and the maximum breaking force was measured to be F. max Calculate the f of concrete t-c and K IC-c ;

[0009] S4. The yield strength of the reinforcing steel is used as the closing force F when calculating the yield strength. sult The resulting increase in tensile strength Δf tult and fracture toughness increment ΔK ICult ,

[0010] The closing force at the yield of the steel reinforcement is simplified as a pair of concentrated forces acting on the concrete crack surface. It is assumed that the cohesion on the virtual crack surface is constant and equal to the nominal strength increment Δσ. ns-ult The equilibrium condition of forces in the critical cross section is derived as follows:

[0011] ;

[0012] From Δσ ns-ult With tensile strength increment Δf tult Relationship We can obtain,

[0013] ;

[0014] The increment of ultimate fracture toughness is ;

[0015] In the formula, h is the height of the reinforced concrete specimen; b is the width of the reinforced concrete specimen; c is the thickness of the protective layer plus the radius of the reinforcing bar, i.e., the distance from the center of the reinforcing bar to the bottom of the beam; β is the dispersion coefficient representing the discontinuity of the concrete; d avg The average coarse aggregate particle size; a esu The equivalent crack length is the same as the macroscopic crack length a. w0 There is a correlation;

[0016] S5. The ultimate flexural strength of reinforced concrete is... and fracture toughness .

[0017] Preferably, in step S3, the f of the concrete t-c and K IC-c The calculation formula is as follows:

[0018] ;

[0019] Wherein, the shape function of concrete is L c / h c =2.5;

[0020] ;

[0021] In the formula, W is the self-weight of the concrete specimen; b c h is the width of the concrete specimen. c The height of the concrete specimen; L c The span of the concrete specimen; α = a 0c / h c The joint height ratio of the concrete specimen.

[0022] Preferably, in step S2, the length a of the macroscopic crack in the reinforced concrete is calculated. w0 ,

[0023] For a beam with a distance of c from the center of the reinforcing bar to the bottom, a width of b, a height of h, a span of L, and an average coarse aggregate size of d... avg The macroscopic crack length is a w0 And the closing force when the steel bar yields is F sult Reinforced concrete structure, when a w0 When long enough, its tip approaches the rear boundary of the specimen, reaching the design load F. d Nominal strength σ at the crack tip nult for:

[0024] ;

[0025] In the formula, βˊ is the dispersion coefficient representing the discontinuity of reinforced concrete;

[0026] At this point, the cohesive stress in the virtual crack remains constant at σ. nult ,Depend on The relation can be obtained about a w0 Solving the univariate nonlinear equation yields a. w0 In the formula, f t-c It refers to the tensile strength of concrete; regarding a w0 One-variable nonlinear equations:

[0027] ;

[0028] Among them, the equivalent crack length of reinforced concrete is ;

[0029] The shape function of reinforced concrete is L / h = 4;

[0030] The joint height ratio of reinforced concrete is .

[0031] Preferably, the equivalent crack length caused by the closing force when the steel bar yields is:

[0032] ;

[0033] The corresponding shape function at this time is: .

[0034] Preferably, the reinforced concrete in this method contains at least two or more phases of medium, namely, steel reinforcement and concrete.

[0035] Preferably, the reinforcing steel in the reinforced concrete in this method includes plain round steel bars and deformed steel bars of all strengths.

[0036] Preferably, the concrete in the reinforced concrete of this method includes ordinary concrete, lightweight aggregate concrete, recycled concrete, alkali-activated concrete, and fiber-reinforced concrete.

[0037] Preferably, this method is applicable to reinforced concrete members of medium, small and large sizes.

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0039] 1. Based on the nonlinear microscopic fracture theory, reinforced concrete is discretized into its tensile strength (f) as the ultimate tensile strength of concrete. t-c ) and fracture toughness (K IC-c The increase in tensile ultimate strength (Δf) caused by the closure force of the reinforcing bars tult ) and fracture toughness increment (ΔK) ICult The synergistic superposition of these factors effectively avoids the influence of size effects on reinforced concrete structures and reasonably evaluates the maximum load that reinforced concrete structures can withstand during bending and their ability to resist further crack propagation.

[0040] 2. It effectively solves the problem of quantitative correlation between strength and toughness in the design stage of reinforced concrete structures, and uniformly quantifies the flexural ultimate strength and fracture toughness of reinforced concrete structures, making it suitable for complex load environments and easy to apply in engineering.

[0041] 3. This invention is applicable to reinforced concrete structures of any size and has no size effect. It is applicable to concrete prepared with ordinary sand and gravel aggregates, recycled aggregates, fibers, etc.

[0042] 4. This design method can be combined with finite element software to perform numerical simulation of reinforced concrete structures using the calculation method of this invention. Through multi-scale modeling, parameter coupling optimization, and performance prediction in civil engineering, bridges, and water conservancy projects, it significantly improves the safety and economy of reinforced concrete structures. Attached Figure Description

[0043] Figure 1 A schematic diagram of the limit state for flexural design of reinforced concrete.

[0044] Figure 2 This is a diagram showing the stress distribution of a reinforced concrete beam section under ultimate design conditions.

[0045] Figure 3 This is a stress distribution diagram of the critical section of a plain concrete beam subjected to three-point bending.

[0046] Figure 4 For the crack surface to be subjected to a concentrated force F sult Stress distribution diagram at critical cross section.

[0047] Figure 5 The stress cloud diagram for simulated crack propagation in a reinforced concrete beam is shown, where red indicates cracks. Detailed Implementation

[0048] To facilitate understanding of the present invention, it will be described in more detail below with reference to the accompanying drawings and specific embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described in this specification. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of the present invention.

[0049] A design method for the ultimate flexural strength and fracture toughness of reinforced concrete structures includes the following steps:

[0050] S1. Modeling: Establish a reinforced concrete structure model (referred to as reinforced concrete). Create separate concrete models (referred to as concrete) and steel reinforcement models (referred to as steel reinforcement) for each of its internal components. Regardless of whether it's reinforced concrete or concrete, the type of coarse aggregate is the same, and the average coarse aggregate particle size is represented as d. avg In addition, reinforced concrete includes a protective layer. This protective layer is a layer of concrete covering the area from the outer edge of the reinforcing bars to the surface of the concrete structure, protecting the bars. Its thickness is calculated from the outermost edge of the outermost reinforcing bar. This protective layer prevents corrosion of the reinforcing bars, improves fire resistance, and ensures that the reinforcing bars and concrete work together.

[0051] S2. Calculate the length a of macroscopic cracks in reinforced concrete. w0 a w0 The dimension is mm;

[0052] Let c be the distance from the center of the reinforcing bar to the bottom of the beam, where c equals the thickness of the protective layer plus the radius of the reinforcing bar. Let b be the width, h be the height, L be the span, and d be the average coarse aggregate size. avg All dimensions are in mm, and the macroscopic crack length is a. w0 And the closing force when the steel bar yields is F sult A reinforced concrete structure (dimension N). When a w0 When long enough, its tip approaches the rear boundary of the specimen. Figure 2 As shown, upon reaching F d The nominal strength σ at the crack tip (dimension N) nult (Dimensions in MPa) are:

[0053] ;

[0054] In the formula, βˊ is the dimensionless coefficient representing the discontinuity of reinforced concrete;

[0055] At this point, the cohesive stress in the virtual crack remains constant at σ. nult ,Depend on The relation can be obtained about a w0 A univariate nonlinear equation,

[0056] ;

[0057] Among them, the equivalent crack length of reinforced concrete is The dimension is mm;

[0058] In reinforced concrete, the shape function is Dimensionless, (L / h=4);

[0059] The joint height ratio of reinforced concrete is Dimensionless;

[0060] S3. Calculate the tensile strength of concrete (f) t-c ) and fracture toughness (K IC-c The dimensions are MPa and MPa·m, respectively. 1 / 2 ;

[0061] For the initial crack length of the precast concrete, a 0c A concrete specimen (dimensions in mm) was subjected to a three-point bending test, and the maximum breaking force was measured to be F. max And use the following formula to calculate the f of the concrete. t-c and K IC-c ,

[0062] ;

[0063] Wherein, the shape function of concrete is , dimensionless; (Lc / h c =2.5);

[0064] ;

[0065] In the formula, W is the self-weight of the concrete specimen, with dimensions in N; b c h represents the width of the concrete specimen, in mm. c L represents the height of the concrete specimen, in mm. c α represents the span of the concrete specimen, with dimensions in mm; β is the dimensionless coefficient representing the discontinuity of the concrete; α = a 0c / h c The joint height ratio of the concrete specimen is dimensionless.

[0066] S4. Calculate the closing force F when the steel reinforcement yields. sult The resulting increase in tensile strength Δf tult and fracture toughness increment ΔK ICult The dimensions are MPa and MPa·m, respectively. 1 / 2 ;

[0067] The closing force at the yield of the steel reinforcement is simplified as a pair of concentrated forces acting on the concrete crack surface. It is assumed that the cohesion on the virtual crack surface is constant and equal to the nominal strength increment Δσ. ns-ult (Dimensions are MPa); derived from the force equilibrium condition in the critical cross-section:

[0068] ;

[0069] From Δσ ns-ult With tensile strength increment Δf tult Relationship We can obtain,

[0070] ;

[0071] Among them, the equivalent crack length caused by the closing force when the steel bar yields is The dimension is mm;

[0072] The corresponding shape function at this time is Dimensionless;

[0073] The increment of ultimate fracture toughness is ;

[0074] In the formula, h is the height of the reinforced concrete specimen, in mm; b is the width of the reinforced concrete specimen, in mm; c is the distance from the center of the reinforcing bar to the bottom of the beam, in mm; β is the dispersion coefficient representing the discontinuity of the concrete, dimensionless; d avg a is the average coarse aggregate particle size, in mm.esu The equivalent crack length, in mm, is the same as the macroscopic crack length a. w0 There is a correlation.

[0075] S5. The ultimate flexural strength of reinforced concrete is... and fracture toughness The dimensions are MPa and MPa·m, respectively. 1 / 2 .

[0076] Ultimate flexural strength f of reinforced concrete structure tult-str With the tensile strength f of concrete t-c and the yield strength F of the steel reinforcement sult The resulting increase in tensile strength Δf tult With consistent dimensions, theoretically the former can be obtained by superimposing the latter two; the flexural fracture toughness K of reinforced concrete structures ICult-str The principle of superposition is the same as above.

[0077] This invention is applicable to calculating the ultimate strength and fracture toughness of reinforced concrete structures (beams, columns, or slabs) under bending conditions.

[0078] The "reinforced concrete" mentioned in this invention must contain at least two or more phases of medium, namely, steel bars and concrete.

[0079] The steel bars in "reinforced concrete" as described in this invention include plain round steel bars and deformed steel bars of all strengths.

[0080] The concrete referred to in this invention as "reinforced concrete" includes ordinary concrete, lightweight aggregate concrete, recycled concrete, alkali-activated concrete, and fiber-reinforced concrete.

[0081] This invention is applicable to reinforced concrete components of medium, small, and large sizes, avoiding the influence of size effects.

[0082] The main concept of this invention is to take the bending state of reinforced concrete when the steel bars reach yield as the design limit, at which point the macroscopic crack length is a. w0 The flexural capacity of reinforced concrete mainly depends on the strengthening effect of the steel reinforcement on the concrete. Based on the nonlinear microfracture theory, the ultimate flexural strength f of reinforced concrete structures... tult-str With fracture toughness K ICult-str This can be further equivalent to the tensile strength f of concrete. t-c and fracture toughness K IC-c With the yield strength F of the steel reinforcement sult The resulting increase in tensile strength Δf tult and fracture toughness increment ΔK ICult The superposition of.

[0083] In the embodiment, taking a reinforced concrete beam as an example, the macroscopic crack length 'a' of the reinforced concrete is first calculated using the design method of this application. w0 Then calculate the tensile strength f of the concrete. t-c and fracture toughness K IC-c And calculate the yield strength F of the steel reinforcement. sult The resulting increase in tensile strength Δf tult and fracture toughness increment ΔK ICult Finally, the flexural ultimate strength f of reinforced concrete without size effects is calculated. tult-str With fracture toughness K ICult-str As verified by Examples 1-4 below, the f-values ​​of reinforced concrete with different structural member cross-sectional dimensions corresponding to different types of reinforcing bars obtained by this design method are... tult-str and K ICult-str The near-identical results indicate that the size effect has been effectively eliminated, significantly improving design accuracy in practical engineering. Combining this with finite element method (FEM) simulations of crack propagation paths in reinforced concrete beams under bending conditions ensures safety and reliability in practical engineering applications. Figure 1-5 The method shown is used for crack-resistant design.

[0084] The present invention will be further described in detail below through specific embodiments.

[0085] Example 1: The method for fabricating a reinforced concrete beam is as follows: the cross-sectional dimensions (width b × height h) are 100mm × 100mm, the span L is 400mm, the concrete strength grade is C45, the longitudinal tensile reinforcement consists of two 6mm diameter HRB400 steel bars, the distance c from the center of the steel bars to the bottom of the beam is 30mm, and the average aggregate size d... avg It is 7mm, F sult =9083N, F d =12129N, β ˊ =2.0.

[0086] Design methods for ultimate flexural strength and fracture toughness of reinforced concrete beam structures:

[0087] 1. Calculate the length 'a' of macroscopic cracks in reinforced concrete. w0

[0088] Will , , Substitute a w0 Univariate nonlinear equations ;

[0089] Solving for a w0 =63.6mm.

[0090] 2. Calculate the tensile strength f of concrete. t-c and fracture toughness KIC-c ,

[0091] Take h c =100mm, b c =100mm, L c =250mm, W=114N, F max =7822N, d avg The tensile strength (f) of the concrete was determined with a diameter of 7 mm, α = 0.3, and β = 1.5. t-c ) and fracture toughness (K IC-c The calculation process is illustrated in the example below:

[0092] (1) ;

[0093] (2) ;

[0094] (3) ;

[0095] In the formula, W is the self-weight of the concrete specimen; b c h is the width of the concrete specimen. c The height of the concrete specimen; L c α represents the span of the concrete specimen; β is the dispersion coefficient representing the discontinuity of the concrete; α = a 0c / h c The joint height ratio of the concrete specimen;

[0096] 3. Calculate the yield strength F of the steel reinforcement. sult The resulting increase in tensile strength Δf tult and fracture toughness increment ΔK ICult ,

[0097] (1) The equivalent crack length is ;

[0098] (2) =2.9531;

[0099] (3) ;

[0100] (4) ;

[0101] 5. Ultimate flexural strength of reinforced concrete =5.18 + 21.74 = 26.92 MPa, fracture toughness is =1.5 + 6.3 = 7.8 MPa·m 1 / 2 .

[0102] After testing, the ultimate flexural strength f of the reinforced concrete beam in this embodiment was found to be [value missing]. tult-str =26.92MPa, fracture toughness KICult-str =7.8 MPa·m 1 / 2 .

[0103] Example 2:

[0104] The fabrication method for reinforced concrete beams is as follows: the cross-sectional dimensions (width b × height h) are 140mm × 200mm, the span is 800mm, the concrete strength grade is C45, the longitudinal tensile reinforcement consists of two 10mm diameter HRB400 steel bars, the distance (c) from the center of the steel bar to the bottom of the beam is 60mm, and the average aggregate size (d) is... avg It is 7mm, F sult =24530N, F d =31183N, β ˊ =4.5.

[0105] The design and testing methods for the ultimate flexural strength and fracture toughness of reinforced concrete beams are the same as in Example 1; the f of concrete t-c and K IC-c The same as in Example 1. Testing showed that the ultimate flexural strength f of the reinforced concrete beam in this example... tult-str =25.05MPa, fracture toughness K ICult-str =7.26 MPa·m 1 / 2 .

[0106] Example 3:

[0107] The reinforced concrete beam fabrication method is as follows: the cross-sectional dimensions are 100mm x 100mm (width b x height h), the span is 400mm, the concrete strength grade is C45, the longitudinal tensile reinforcement consists of two 6mm diameter HPB300 plain round steel bars, the distance c from the center of the steel bar to the bottom of the beam is 30mm, and the average aggregate size d... avg It is 7mm, F sult =7502N, F d =9757.8N, β ˊ =1.5.

[0108] The design and testing methods for the ultimate flexural strength and fracture toughness of reinforced concrete structures are the same as in Example 1; the f of concrete t-c and K IC-c The same as in Example 1. Testing showed that the ultimate flexural strength f of the reinforced concrete beam in this example... tult-str =19.95MPa, fracture toughness K ICult-str =5.78 MPa·m 1 / 2 .

[0109] Example 4:

[0110] The reinforced concrete beam is fabricated as follows: the cross-sectional dimensions are 140mm (width b) × 200mm (height h), the span is 800mm, the concrete strength grade is C45, the longitudinal tensile reinforcement consists of two 10mm diameter HPB300 plain round steel bars, the distance c from the center of the steel bar to the bottom of the beam is 60mm, and the average aggregate size d... avg It is 7mm, F sult =21097N, F d =27620N, β ˊ =2.5.

[0111] The design and testing methods for the ultimate flexural strength and fracture toughness of reinforced concrete structures are the same as in Example 1; the f of concrete t-c and K IC-c The same as in Example 1. Testing showed that the ultimate flexural strength f of the reinforced concrete beam in this example... tult-str =19.47MPa, fracture toughness K ICult-str =5.64 MPa·m 1 / 2 .

[0112] The predicted values ​​for Examples 1-4 are shown in Table 1. Examples 1 and 2 involve deformed reinforcing bars in models with different dimensions. A comparison reveals that the flexural ultimate strength and fracture toughness of the reinforced concrete beams in both examples are similar, indicating that the size effect is effectively eliminated. The same applies to Examples 3 and 4, the difference being that plain round reinforcing bars are used. This demonstrates that this design method is applicable to the design of reinforced concrete beams with different dimensions corresponding to different types of reinforcing bars, and can effectively eliminate the size effect.

[0113] Table 1 Summary of Predicted Values ​​for Examples 1-4

[0114]

[0115] Those skilled in the art should recognize that the above embodiments are only used to illustrate this application and are not intended to limit this application. Any appropriate changes and variations made to the above embodiments within the essential spirit and scope of this application fall within the scope of protection claimed in this application.

Claims

1. A design method for the ultimate flexural strength and fracture toughness of reinforced concrete structures, characterized in that, Ultimate flexural strength f of reinforced concrete structure tult-str Equivalent to the tensile strength f of concrete t-c and the yield strength F of the steel reinforcement sult The resulting increase in tensile strength Δf tult The superposition of the ... ICult-str Equivalent to the fracture toughness K of concrete IC-c With the yield strength F of the steel reinforcement sult Caused fracture toughness increment ΔK ICult The superposition includes the following steps: S1. Modeling: Create a reinforced concrete structure model, a concrete model, and a steel reinforcement model, which are abbreviated as reinforced concrete, concrete, and steel reinforcement, respectively. S2. Calculate the macroscopic crack length a in reinforced concrete. w0 The nominal strength at the crack tip is calculated based on the design load and reinforced concrete dimensional parameters, and then combined with the tensile strength of the concrete to construct a. w0 Solving the univariate nonlinear equation yields a. w0 ; S3, Calculate the tensile strength f of concrete t-c and fracture toughness K IC-c For the precast initial crack length a 0c Three-point bending tests were conducted on the concrete specimens, and the maximum breaking force was measured to be F. max Calculate the f of concrete t-c and K IC-c ; S4. The yield strength of the reinforcing steel is used as the closing force F when calculating the yield strength. sult The resulting increase in tensile strength Δf tult and fracture toughness increment ΔK ICult , The closing force at the yield of the steel reinforcement is simplified as a pair of concentrated forces acting on the concrete crack surface. It is assumed that the cohesion on the virtual crack surface is constant and equal to the nominal strength increment Δσ. ns-ult The equilibrium condition of forces in the critical cross section is derived as follows: ； From Δσ ns-ult With tensile strength increment Δf tult Relationship We can obtain, ； The increment of ultimate fracture toughness is ; In the formula, h is the height of the reinforced concrete specimen; b is the width of the reinforced concrete specimen; c is the thickness of the protective layer plus the radius of the reinforcing bar, i.e., the distance from the center of the reinforcing bar to the bottom of the beam; β is the dispersion coefficient representing the discontinuity of the concrete; d avg The average coarse aggregate particle size; a esu The equivalent crack length is the same as the macroscopic crack length a. w0 There is a correlation; S5. The ultimate flexural strength of reinforced concrete is... and fracture toughness .

2. The design method for the ultimate flexural strength and fracture toughness of reinforced concrete structures according to claim 1, characterized in that, In step S3, the f of the concrete t-c and K IC-c The calculation formula is as follows: ； Wherein, the shape function of concrete is L c / h c =2.5; ； In the formula, W is the self-weight of the concrete specimen; b c h is the width of the concrete specimen. c The height of the concrete specimen; L c The span of the concrete specimen; α = a 0c / h c The joint height ratio of the concrete specimen.

3. The design method for the ultimate flexural strength and fracture toughness of reinforced concrete structures according to claim 2, characterized in that, In step S2, the length a of the macroscopic crack in the reinforced concrete is calculated. w0 , For a beam with a distance of c from the center of the reinforcing bar to the bottom, a width of b, a height of h, a span of L, and an average coarse aggregate size of d... avg The macroscopic crack length is a w0 And the closing force when the steel bar yields is F sult Reinforced concrete structure, when a w0 When long enough, its tip approaches the rear boundary of the specimen, reaching the design load F. d Nominal strength σ at the crack tip nult for: ； In the formula, βˊ is the dispersion coefficient representing the discontinuity of reinforced concrete; At this point, the cohesive stress in the virtual crack remains constant at σ. nult ,Depend on The relation can be obtained about a w0 Solving the univariate nonlinear equation yields a. w0 In the formula, f t-c It refers to the tensile strength of concrete; regarding a w0 One-variable nonlinear equations: ； Among them, the equivalent crack length of reinforced concrete is ; The shape function of reinforced concrete is L / h = 4; The joint height ratio of reinforced concrete is .

4. The design method for the ultimate flexural strength and fracture toughness of reinforced concrete structures according to claim 3, characterized in that, The equivalent crack length caused by the closing force when the steel bar yields is: ； The corresponding shape function at this time is: .

5. The design method for the ultimate flexural strength and fracture toughness of reinforced concrete structures according to claim 1, characterized in that, In this method, the reinforced concrete contains at least two or more phases of medium, namely, steel reinforcement and concrete.

6. The design method for the ultimate flexural strength and fracture toughness of reinforced concrete structures according to claim 1, characterized in that, The steel reinforcement in reinforced concrete in this method includes plain round steel bars and deformed steel bars of all strengths.

7. The design method for the ultimate flexural strength and fracture toughness of reinforced concrete structures according to claim 1, characterized in that, The concrete in this method includes ordinary concrete, lightweight aggregate concrete, recycled concrete, alkali-activated concrete, and fiber-reinforced concrete.

8. The design method for the ultimate flexural strength and fracture toughness of reinforced concrete structures according to claim 1, characterized in that, This method is applicable to reinforced concrete members of medium, small, and large sizes.

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