A calculation method for equivalent strength of reinforced concrete

Abstract

The present invention provides a method for calculating the equivalent strength of reinforced concrete, which includes establishing an equivalent compressive model of reinforced concrete material; calculating the elastic limit stress and strain of reinforced concrete and the peak strength and strain of reinforced concrete; calculating the fracture failure strength and strain of reinforced concrete; an equivalent tensile model of reinforced concrete material; calculating the peak strength and strain of reinforced concrete and the yield strength and strain of reinforced concrete. In the established equivalent compressive model of reinforced concrete material, the compressive model determined by three key points can accurately and efficiently express the compressive mechanical properties of reinforced concrete material. In the established equivalent tensile model of reinforced concrete material, the compressive tensile model determined by two key points can accurately and efficiently express the tensile mechanical properties of reinforced concrete material. The established equivalent constitutive model of reinforced concrete has few parameters, is simple to calculate, and can quickly calculate the strength of reinforced concrete material.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering, and in particular to a method for calculating the equivalent strength of reinforced concrete. Background Art

[0002] Material strength testing is a prerequisite for its application in engineering construction. A good reinforced concrete strength calculation method can help engineers quickly and accurately predict the mechanical properties of reinforced concrete materials, and then continuously optimize the materials.

[0003] Currently, engineering calculations for reinforced concrete strength often use a separate approach. This involves calculating the contributions of both the steel and concrete materials to the mechanical properties of the entire component, and then determining the overall strength by considering the bond-slip properties between the steel and concrete materials. This method is computationally intensive, cumbersome, and inefficient, failing to meet the accuracy and efficiency requirements of practical engineering. Therefore, we propose an improved method for calculating the equivalent strength of reinforced concrete. Summary of the Invention

[0004] The purpose of the present invention is to address the problems raised by the existing background technology. In order to achieve the above-mentioned invention purpose, the present invention provides the following technical solutions: a method for calculating the equivalent strength of reinforced concrete, comprising the following steps: S1, establishing an equivalent compression model of reinforced concrete material; the equivalent compression model of reinforced concrete material includes S11, calculating the elastic limit stress and strain of reinforced concrete; S12, calculating the peak strength and strain of reinforced concrete; S13, calculating the fracture failure strength and strain of reinforced concrete;

[0005] S2, reinforced concrete material equivalent tensile model; the reinforced concrete material equivalent tensile model includes S21, peak strength and strain calculation of reinforced concrete and S22, yield strength and strain calculation of reinforced concrete.

[0006] As a preferred technical solution of the present invention, when S11, the elastic limit stress of reinforced concrete and the strain calculation including S111, the strain of steel bars and concrete materials are consistent, the stress of the reinforced concrete section can be expressed as:

[0007] σ=(1-ρ)σ c +ρσ s (1)

[0008] where σ c is the elastic limit stress of concrete; σ s is the elastic limit stress of the steel bar; ρ represents the longitudinal reinforcement ratio.

[0009] As a preferred technical solution of the present invention, S11, calculation of elastic limit stress and strain of reinforced concrete includes S112, in the mechanical property analysis of reinforced concrete material, the steel bar adopts elastic strengthening model. Currently, the research on it is very mature, and its mechanical properties are:

[0010]

[0011] Among them E s is the elastic modulus of the steel bar; E T is the shear modulus of the steel bar; ε s is the strain of the steel bar; ε y is the elastic limit strain of the steel bar.

[0012] As a preferred technical solution of the present invention, S11, calculation of elastic limit stress and strain of reinforced concrete also includes S113, when both the steel bar and the concrete are in the elastic deformation stage, the mechanical properties of the material can be expressed as:

[0013] σ c,1 =E eq ·ε c,1 (3)

[0014] Where: σ c,1 is the elastic limit stress of reinforced concrete; E eq is the equivalent elastic modulus of reinforced concrete material; ε c,1 is the elastic compressive strain of concrete confined by stirrups.

[0015] As a preferred technical solution of the present invention, S12, calculation of peak strength and strain of reinforced concrete includes S121, when the confined concrete material begins to undergo plastic deformation, the stress increase rate of the concrete gradually decreases, the steel bars are still in the elastic stage, and the proportion of pressure borne by the steel bars gradually increases. To simplify the calculation, when the confined concrete reaches the peak strain, it is considered that the steel bars also enter the yield state. At this time, the stress of the reinforced concrete column can be expressed as:

[0016] σ c,2 =(1-ρ)σ sc,2 +ρσ s,2 (4)

[0017] Where: σ sc,2 is the peak strength of confined concrete; σ s,2 is the yield strength of the longitudinal reinforcement; ρ is the longitudinal reinforcement ratio.

[0018] As a preferred technical solution of the present invention, S122, the strain of the reinforced concrete material is the peak strain of the confined concrete, which can be expressed as:

[0019]

[0020] where σ c is the elastic limit stress of concrete; ε c,2 is the ultimate strain of the constrained stirrups.

[0021] As a preferred technical solution of the present invention, after the longitudinal reinforcement yields, its stress remains unchanged. S12, peak strength and strain calculation of reinforced concrete including S122 are significantly enhanced due to the restraining and strengthening effect of stirrups. When stirrups break, it is considered as compressive failure of concrete material. At this time, the mechanical properties of reinforced concrete material can be expressed as:

[0022] σ c,3 =(1-ρ)σ sc,3 +ρf y (6)

[0023]

[0024] Where: ε su is the ultimate strain of the constrained stirrups; ρ is the volume reinforcement ratio of the stirrups; σ y is the yield strength of the stirrup; σ sc,3 It is the stress in the confined concrete when stirrup rupture occurs.

[0025] As a preferred technical solution of the present invention, S21, the peak strength and strain calculation of reinforced concrete includes S211, under axial tension, the effect of stirrups can be ignored. Before reaching the peak strength of concrete, the deformation of both the steel and concrete is small. It can be considered that both the steel and concrete materials are in the elastic stage and the strains of the two are equal. The peak stress of the material can be expressed as:

[0026] σ t,1 =E eq ·ε t,1 (8)

[0027] Where: σ t,1 is the peak stress of reinforced concrete material; ε t,1 is the peak strain of the concrete material.

[0028] As a preferred technical solution of the present invention, S22, the calculation of the yield strength and strain of reinforced concrete includes S221, after exceeding the peak strain, the material enters the softening stage, the concrete material fails under tension, the axial tension is completely borne by the longitudinal reinforcement, and the longitudinal reinforcement enters the yield state. At this time, the mechanical properties of the reinforced concrete material can be expressed as:

[0029] σ t,2 =σ s,2 ·ρ (9)

[0030] ε t,2 =εy (10)

[0031] Where: σ s,2 is the yield stress of the steel bar; ε y is the yield strain.

[0032] As the preferred technical solution of the present invention, the yield strength and strain calculation of S22 and reinforced concrete includes the following: after the S222 steel bar enters the yield stage, necking phenomenon begins to occur. In order to simplify the calculation, it is assumed that tensile fracture occurs when the steel bar material reaches the yield strength, and the tensile stress of the reinforced concrete material is cut off.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] In the solution of the present invention:

[0035] 1. In the established equivalent compression model of reinforced concrete material, the compression model determined by three key points can accurately and efficiently express the compressive mechanical properties of reinforced concrete material.

[0036] 2. In the established equivalent tensile model of reinforced concrete material, the compression-tension model determined by two key points can accurately and efficiently express the tensile mechanical properties of reinforced concrete material.

[0037] 3. The established equivalent constitutive model of reinforced concrete has few parameters and is easy to calculate, and can quickly calculate the strength of reinforced concrete materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A simplified mechanical model diagram of a reinforced concrete column under axial compression provided by the present invention;

[0039] Figure 2 This is a simplified mechanical model diagram of the reinforced concrete column under axial tension provided by the present invention. DETAILED DESCRIPTION

[0040] To make the purpose, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them.

[0041] Therefore, the following detailed description of the embodiments of the present invention is not intended to limit the scope of the invention claimed for protection, but merely represents some embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features and technical solutions in the embodiments can be combined with each other. It should be noted that similar numbers and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0042] Example 1: Please refer to Figure 1-2 A method for calculating the equivalent strength of reinforced concrete comprises the following steps: S1, establishing an equivalent compression model of reinforced concrete material; the equivalent compression model of reinforced concrete material comprises S11, calculating the elastic limit stress and strain of reinforced concrete; S12, calculating the peak strength and strain of reinforced concrete; S13, calculating the fracture strength and strain of reinforced concrete;

[0043] S2, reinforced concrete material equivalent tensile model; the reinforced concrete material equivalent tensile model includes S21, peak strength and strain calculation of reinforced concrete and S22, yield strength and strain calculation of reinforced concrete.

[0044] S11. Calculation of elastic limit stress and strain of reinforced concrete. S111. When the strains of the steel and concrete materials are consistent, the stress in the reinforced concrete section can be expressed as:

[0045] σ=(1-ρ)σ c +ρσ s (1)

[0046] where σ c is the elastic limit stress of concrete; σ s is the elastic limit stress of the steel bar; ρ represents the longitudinal reinforcement ratio.

[0047] S11. Calculation of elastic limit stress and strain of reinforced concrete includes S112. In the analysis of mechanical properties of reinforced concrete materials, the elastic strengthening model is used for steel bars. Currently, the research on this model is very mature, and its mechanical properties are:

[0048]

[0049] Among them E s is the elastic modulus of the steel bar; E T is the shear modulus of the steel bar; ε s is the strain of the steel bar; ε y is the elastic limit strain of the steel bar.

[0050] S11. The calculation of elastic limit stress and strain of reinforced concrete also includes S113. When both the steel bar and concrete are in the elastic deformation stage, the mechanical properties of the material can be expressed as:

[0051] σ c,1 =E eq ·ε c,1 (3)

[0052] Where: σ c,1 is the elastic limit stress of reinforced concrete; E eq is the equivalent elastic modulus of reinforced concrete material; ε c,1 is the elastic compressive strain of concrete confined by stirrups.

[0053] S12. Calculation of peak strength and strain of reinforced concrete includes S121. When the confined concrete material begins to deform plastically, the rate of stress increase in the concrete gradually decreases, while the steel bars remain in the elastic stage, and the proportion of pressure borne by the steel bars gradually increases. To simplify the calculation, when the confined concrete reaches peak strain, the steel bars are assumed to have also entered the yield state. At this time, the stress of the reinforced concrete column can be expressed as:

[0054] σ c,2 =(1-ρ)σ sc,2 +ρσ s,2 (4)

[0055] Where: σ sc,2 is the peak strength of confined concrete; σ s,2 is the yield strength of the longitudinal reinforcement; ρ is the longitudinal reinforcement ratio. S122. The strain of reinforced concrete material is the peak strain of the confined concrete and can be expressed as:

[0056]

[0057] where σ c is the elastic limit stress of concrete; ε c,2 is the ultimate strain of the constrained stirrups.

[0058] After the longitudinal reinforcement yields, its stress remains unchanged. S12, peak strength and strain calculation of reinforced concrete including S122. Due to the restraining and strengthening effect of stirrups, the post-peak ductility characteristics of concrete are significantly enhanced. When stirrups break, it is considered as compressive failure of concrete material. At this time, the mechanical properties of reinforced concrete material can be expressed as:

[0059] σ c,3 =(1-ρ)σ sc,3 +ρf y (6)

[0060]

[0061] Where: ε su is the ultimate strain of the constrained stirrups; ρ is the volume reinforcement ratio of the stirrups; σ y is the yield strength of the stirrup; σ sc,3 It is the stress in the confined concrete when stirrup rupture occurs.

[0062] S21. Peak strength and strain calculations for reinforced concrete include S211. Under axial tension, the effect of stirrups can be ignored. Before reaching the peak strength of concrete, the deformation of both the steel and concrete is small. It can be assumed that both the steel and concrete materials are in the elastic stage, and the strains of the two are equal. The peak stress of the material can be expressed as:

[0063] σ t,1 =E eq ·ε t,1 (8)

[0064] Where: σ t,1 is the peak stress of reinforced concrete material; ε t,1 is the peak strain of the concrete material.

[0065] S22. Calculation of yield strength and strain of reinforced concrete includes S221. After exceeding the peak strain, the material enters the softening stage, the concrete material fails under tension, and the axial tension is completely borne by the longitudinal reinforcement, and the longitudinal reinforcement enters the yield state. At this time, the mechanical properties of reinforced concrete material can be expressed as:

[0066] σ t,2 =σ s,2 ·ρ (9)

[0067] ε t,2 =ε y (10)

[0068] Where: σ s,2 is the yield stress of the steel bar; ε y is the yield strain.

[0069] S22. The yield strength and strain calculation of reinforced concrete includes S222. After the steel bar enters the yield stage, necking phenomenon begins to occur. In order to simplify the calculation, it is assumed that tensile fracture occurs when the steel bar material reaches the yield strength, and the tensile stress of the reinforced concrete material is cut off.

[0070] Example 2: Calculation of σ of reinforced concrete compression model in the present invention sc,2 is the peak strength of confined concrete, ε sc,2 The peak strain of confined concrete can be determined by the Mander model. The research on the Mander model is very mature. According to relevant literature, the approximate simplified calculation formula of Mander can be obtained, which is specifically expressed as follows:

[0071] ① Peak stress calculation:

[0072] For circular and square cross-sections:

[0073]

[0074] For rectangular cross-sections:

[0075]

[0076] Where: Where: σ sc,2 is the peak stress of concrete confined by stirrups, MPa; f c0 is the peak stress of plain concrete (can be determined by reinforced concrete specifications), MPa; V is the stirrup ratio; b / a is the aspect ratio of the rectangular section.

[0077] ② Peak strain calculation:

[0078] For circular cross-sections

[0079]

[0080] For square cross-sections

[0081] ε sc,2 =ε c0 (1-3.5λ V )

[0082] For rectangular cross-sections

[0083]

[0084] Where: ε sc,2 is the peak stress of concrete confined by stirrups, MPa; ε c0 is the peak stress of plain concrete (can be determined by reinforced concrete specifications), MPa; V is the stirrup ratio; b / a is the aspect ratio of the rectangular section.

[0085] (1) Parameter E is required eq (Equivalent elastic modulus of reinforced concrete) can be calculated by the following formula:

[0086] E eq =E s ·ρ+E c (1-ρ)

[0087] Where: Eeq is the equivalent elastic modulus of reinforced concrete; Es is the elastic modulus of steel bars; Ec is the elastic modulus of concrete; ρ is the longitudinal reinforcement ratio.

[0088] (3) The Mander stirrup-confined concrete model adopted is applicable to circular, rectangular and square section stirrup confinement forms.

[0089] (4) The stirrups in the reinforced concrete tension model calculated in the present invention have no restraining effect on the core area concrete.

[0090] During use of the present invention, an equivalent compression model of reinforced concrete material is established:

[0091] Calculation of elastic limit stress and strain of reinforced concrete:

[0092] When the strains of the steel and concrete materials are consistent, the stress in the reinforced concrete section can be expressed as:

[0093] σ=(1-ρ)σ c +ρσ s (1)

[0094] Where: σ c is the elastic limit stress of concrete; σ s is the elastic limit stress of the steel bar; ρ represents the longitudinal reinforcement ratio.

[0095] In the mechanical properties analysis of reinforced concrete materials, the elastic strengthening model is used for steel bars. Currently, the research on this model is very mature, and its mechanical properties are shown in formula (2).

[0096]

[0097] Where: E s is the elastic modulus of the steel bar; E T is the shear modulus of the steel bar; ε s is the strain of the steel bar; ε y is the elastic limit strain of the steel bar.

[0098] When both steel bars and concrete are in the elastic deformation stage, the mechanical properties of the materials can be expressed as:

[0099] σ c,1 =E eq ·ε c,1 (3)

[0100] Where: σ c,1 is the elastic limit stress of reinforced concrete; E eq is the equivalent elastic modulus of reinforced concrete material; ε c,1 is the elastic compressive strain of concrete confined by stirrups.

[0101] Calculation of peak strength and strain of reinforced concrete:

[0102] When the confined concrete material begins to plastically deform, the rate of stress increase in the concrete gradually decreases, while the steel remains in the elastic phase, and the proportion of pressure borne by the steel gradually increases. To simplify the calculation, when the confined concrete reaches peak strain, the steel is assumed to have also entered the yield state. At this point, the stress in the reinforced concrete column can be expressed as:

[0103] σ c,2 =(1-ρ)σ sc,2 +ρσ s,2 (4)

[0104] Where: σ sc,2 is the peak strength of confined concrete; σ s,2 is the yield strength of the longitudinal reinforcement; ρ is the longitudinal reinforcement ratio.

[0105] At this time, the strain of the reinforced concrete material is the peak strain of the confined concrete, which can be expressed as:

[0106]

[0107] Calculation of fracture strength and strain of reinforced concrete:

[0108] After the longitudinal reinforcement yields, its stress remains unchanged. Due to the restraining and strengthening effect of the stirrups, the post-peak ductility characteristics of the concrete are significantly enhanced. When the stirrups break, it is considered that the concrete material has failed under compression. At this time, the mechanical properties of the reinforced concrete material can be expressed as:

[0109] σ c,3 =(1-ρ)σ sc,3 +ρf y (6)

[0110]

[0111] Where: ε su is the ultimate strain of the constrained stirrups; ρ is the volume reinforcement ratio of the stirrups; σ y is the yield strength of the stirrup; σ sc,3 It is the stress in the confined concrete when stirrup rupture occurs.

[0112] Establish an equivalent tensile model of reinforced concrete material:

[0113] Calculation of peak strength and strain of reinforced concrete:

[0114] Under axial tension, the effect of stirrups can be ignored. Before reaching the peak strength of concrete, the deformation of both the steel and concrete is small. It can be considered that both the steel and concrete materials are in the elastic stage, and the strains of the two are equal. The peak stress of the material can be expressed as:

[0115] σ t,1 =Eeq ·ε t,1 (8)

[0116] Where: σ t,1 is the peak stress of reinforced concrete material; ε t,1 is the peak strain of the concrete material.

[0117] Calculation of yield strength and strain of reinforced concrete:

[0118] After exceeding the peak strain, the material enters the softening stage, the concrete material fails under tension, the axial tension is completely borne by the longitudinal reinforcement, and the longitudinal reinforcement enters the yield state. The mechanical properties of reinforced concrete material at this time can be expressed as:

[0119] σ t,2 =σ s,2 ·ρ (9)

[0120] ε t,2 =ε y (10)

[0121] Where: σ s,2 is the yield stress of the steel bar; ε y is the yield strain.

[0122] After the steel bar enters the yield stage, necking phenomenon begins to occur. In order to simplify the calculation, it is assumed that tensile fracture occurs when the steel bar material reaches the yield strength. At this time, the tensile stress of the reinforced concrete material can be cut off.

[0123] The above embodiments are only used to illustrate the present invention and are not intended to limit the technical solutions described in the present invention. Although this specification has described the present invention in detail with reference to the above embodiments, the present invention is not limited to the above specific implementation methods. Therefore, any modification or equivalent replacement of the present invention; and all technical solutions and improvements thereof that do not depart from the spirit and scope of the invention are included in the scope of the claims of the present invention.

Claims

1. A method for calculating the equivalent strength of reinforced concrete, characterized in that: The following steps are involved: S1. Establishing an equivalent compression model of reinforced concrete material; the equivalent compression model of reinforced concrete material includes S11. Calculation of elastic limit stress and strain of reinforced concrete; S12. Calculation of peak strength and strain of reinforced concrete; S13. Calculation of fracture strength and strain of reinforced concrete; S2, reinforced concrete material equivalent tensile model; the reinforced concrete material equivalent tensile model includes S21, peak strength and strain calculation of reinforced concrete and S22, yield strength and strain calculation of reinforced concrete; S11. Calculation of elastic limit stress and strain of reinforced concrete includes S111. When the strains of the steel and concrete materials are consistent, the stress in the reinforced concrete section is expressed as: σ=(1-ρ)σ c +rs s where σ c is the elastic limit stress of concrete; σ s is the elastic limit stress of the steel bar; ρ represents the longitudinal reinforcement ratio; S11. Calculation of elastic limit stress and strain of reinforced concrete includes S112. In the analysis of the mechanical properties of reinforced concrete materials, the elastic strengthening model is used for the steel bars. Its mechanical properties are: Among them E s is the elastic modulus of the steel bar; E T is the shear modulus of the steel bar; ε s is the strain of the steel bar; ε y is the elastic limit strain of the steel bar; S11. The calculation of elastic limit stress and strain of reinforced concrete also includes S113. When both the steel bar and concrete are in the elastic deformation stage, the mechanical properties of the material are expressed as: s c,1 =E eq ·e c,1 Where: σ c,1 is the elastic limit stress of reinforced concrete; E eq is the equivalent elastic modulus of reinforced concrete material; ε c,1 is the elastic compressive strain of concrete confined by stirrups; S12. Calculation of peak strength and strain of reinforced concrete includes S121. When the confined concrete material begins to deform plastically, the rate of stress increase in the concrete gradually decreases, while the steel bars remain in the elastic stage, and the proportion of pressure borne by the steel bars gradually increases. To simplify the calculation, when the confined concrete reaches peak strain, the steel bars are assumed to have also entered the yield state. At this time, the stress of the reinforced concrete column is expressed as: s c,2 =(1-ρ)σ sc,2 +rs s,2 Where: σ sc,2 is the peak strength of confined concrete; σ s,2 is the yield strength of the longitudinal reinforcement; ρ is the longitudinal reinforcement ratio; S122. The strain of reinforced concrete material is the peak strain of the confined concrete and is expressed as: where σ c is the elastic limit stress of concrete; ε c,2 To constrain the ultimate strain of stirrups; After the longitudinal reinforcement yields, its stress remains unchanged. S12, peak strength and strain calculation of reinforced concrete include S122. Due to the restraining and strengthening effect of stirrups, the post-peak ductility characteristics of concrete are significantly enhanced. When stirrups break and fail, it is considered as compressive failure of concrete material. At this time, the mechanical properties of reinforced concrete material are expressed as: s c,3 =(1-ρ)σ sc,3 +ρf y Where: ε su is the ultimate strain of the constrained stirrups; ρ is the volume reinforcement ratio of the stirrups; σ y is the yield strength of the stirrup; σ sc,3 It is the stress in the confined concrete when stirrup rupture occurs.

2. A reinforced concrete equivalent strength calculation method according to claim 1, characterized in that: S21. Calculation of peak strength and strain of reinforced concrete includes S211. Under axial tension, without considering the effect of stirrups, before reaching the peak strength of concrete, the deformation of both the steel and concrete is small. It is assumed that both the steel and concrete materials are in the elastic stage and the strains of the two are equal. The peak stress of the material is expressed as: s t,1 =E eq ·e t,1 Where: σ t,1 is the peak stress of reinforced concrete material; ε t,1 is the peak strain of the concrete material.

3. A reinforced concrete equivalent strength calculation method according to claim 2, characterized in that: S22. Calculation of yield strength and strain of reinforced concrete includes S221. After exceeding the peak strain, the material enters the softening stage, the concrete material fails under tension, and the axial tension is completely borne by the longitudinal reinforcement, which then enters the yield state. The mechanical properties of reinforced concrete are expressed as: s t,2 =s s,2 ·r e t,2 =e y Where: σ s,2 is the yield stress of the steel bar; ε y is the yield strain.

4. A reinforced concrete equivalent strength calculation method according to claim 3, characterized in that: S22. The yield strength and strain calculation of reinforced concrete includes the following: After the S222 steel bar enters the yield stage, necking phenomenon begins to occur. When the steel bar material reaches the yield strength, tensile fracture occurs, and the tensile stress of the reinforced concrete material is cut off.

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