A connection design method for reinforcing structures using ultra-high performance concrete

Abstract

The application discloses a connecting design method of a structure reinforced by using ultra-high performance concrete, and comprises the following steps: (1) determining material parameters; (2) confirming the shear demand of the reinforced structure and the shear stress demand of the connecting interface; (3) determining the planting bar arrangement interval in the shear direction, so that the planting bar arrangement interval meets the demand that the shear stress generated by the planting bar connecting piece is greater than or equal to the shear stress demand of the connecting interface; and (4) calculating the minimum planting bar depth of the planting bar connecting piece. The application studies the bearing mechanism of the connecting interface when the RC structure is reinforced by using UHPC, and gives the specific process of the planting bar design connection, the calculation and design basis of various parameters and performances and the specific bearing capacity calculation method. The design method has clear physical meaning and clear theoretical concept, can be widely applied to the combined interface of the ultra-high performance concrete and the ordinary reinforced concrete structure, has simple and clear design process and good technical and economic effects.

Description

Technical Field

[0001] This invention relates to the field of structural reinforcement engineering, and specifically to a connection design method for a reinforced structure using ultra-high performance concrete based on rebar anchoring. Background Technology

[0002] Ultra-high performance concrete (UHPC) possesses ultra-high strength, ultra-high toughness, and ultra-high durability. Problems that were difficult to solve with traditional concrete materials in bridge applications have been effectively addressed by the introduction of UHPC. When UHPC is applied to the main beams of bridge structures, it can significantly improve the bending, shear, and fatigue resistance of the bridge structure. In recent years, using UHPC to repair damaged bridges has become a promising new application. By coating parts exposed to harsh environments, such as bridge decks, guardrail surfaces, and column surfaces, the durability of the repaired concrete structure can be significantly improved. Furthermore, due to the excellent mechanical and durability properties of UHPC, the repaired structure also achieves superior performance.

[0003] The material properties of UHPC and ordinary reinforced concrete (RC) are significantly different. In order to fully utilize the material properties of this composite structure, a reliable connection is needed between the two to ensure coordinated operation. Common connection types in the past include: (1) interface treatment type (roughening, grooving, etc. of the interface); (2) adhesive bonding type (bonding interface with epoxy resin, etc.); (3) shear key type (the interface is set with interlocking key teeth, etc.); (4) ductile connection connector (metal connectors such as steel bars and studs are set on the interface).

[0004] According to the UHPC-RC rollout tests, rebar anchoring exhibits better ductility compared to interface treatments such as roughening, drilling, and grooving. Furthermore, as the number of anchors increases, the failure mode of the specimen gradually shifts from interface failure to a mixed failure mode of the interface and the RC substrate. Compared to other methods that rely on roughening the interface, adjusting the rebar anchoring design allows for precise control of the failure mode. All of this demonstrates that rebar anchoring clearly offers better ductility, a more defined load-bearing mechanism, and less dispersion. Therefore, in conditions requiring large deformations (such as seismic loads, ship impacts, vehicle impacts, and rockfalls), rebar anchoring is particularly suitable for use as a connection type in UHPC-reinforced components due to its advantages of robustness, good ductility, defined stress distribution, and quantifiable design.

[0005] Although the use of anchored rebar connections in UHPC-strengthened RC components has been adopted in numerous experiments and projects, there is a lack of clear research and standards regarding the calculation and design of the interface bearing capacity of these connections. These anchored rebar connections, designed solely based on experience, pose significant safety risks to subsequent engineering structures. Furthermore, they hinder the promotion and widespread adoption of anchored rebar connections. Summary of the Invention

[0006] This invention provides a connection design method for strengthening structures using ultra-high performance concrete (UHPC), which solves the technical problems of safety and construction issues caused by relying solely on experience in the design of connection methods when using UHPC for rebar connection reinforcement of the strengthened structure.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A connection design method for a reinforced structure using ultra-high performance concrete, wherein the high-performance concrete is connected to the reinforced structure via rebar connectors, the connection design method comprising the following steps:

[0009] (1) Determine the material parameters of the ultra-high performance concrete to be used based on the parameters of the structure being reinforced.

[0010] (2) Confirm the shear requirements of the reinforced structure and calculate the shear stress requirements at the connection interface between the ultra-high performance concrete and the reinforced structure based on the shear requirements of the reinforced structure.

[0011] (3) Calculate the shear bearing capacity of a single rebar connector, and determine the rebar spacing in the shear direction based on the shear bearing capacity of a single rebar connector and the shear stress requirement of the connection interface, so that the rebar spacing satisfies that the shear stress generated by the rebar connector is greater than or equal to the shear stress requirement of the connection interface.

[0012] (4) Calculate the minimum anchoring depth of the rebar connector, so that the implantation depth of the rebar connector in the reinforced structure and in the ultra-high performance concrete is greater than the minimum anchoring depth, thus completing the connection design of the reinforced structure using ultra-high performance concrete.

[0013] As a further preferred embodiment of the above technical solution, in step (2), the shear resistance requirement of the reinforced structure is the design load of the reinforced structure, or the shear resistance requirement of the reinforced structure is the shear bearing capacity calculated based on the material and geometric parameters of the reinforced structure.

[0014] In the above scheme, when the design load is unknown or the shear force requirement cannot be determined based on the design data, the shear capacity of the reinforced structure is used as the shear force requirement, based on the material and geometric parameters of the structure being reinforced. Specifically, this can be calculated using the following formula:

[0015] In the formula, V csα1 represents the shear capacity of the reinforced structure; α2 is the influence coefficient of opposite-sign bending moments (α1 = 1.0 when calculating the shear capacity of simply supported beams and continuous beams near the edge support; α1 = 0.9 when calculating the shear capacity of continuous beams and cantilever beams near the middle support); α2 is the prestress enhancement coefficient (α2 = 1.0 for reinforced concrete flexural members; α2 = 1.25 for prestressed concrete flexural members, but α2 is not increased when the sectional bending moment caused by the resultant force of the reinforcement is in the same direction as the external bending moment, or when cracking is allowed in prestressed concrete flexural members). For the structural member, α2 = 1.0); α3 is the influence coefficient of the compression flange (α3 = 1.0 for rectangular sections; α3 = 1.1 for T-shaped and I-shaped sections); b is the width (mm) of the rectangular section or the web width (mm) of the T-shaped and I-shaped sections at the corresponding normal section of the shear-compression zone; h0 is the effective height (mm) of the section, taken as the distance from the resultant point of the longitudinal tensile reinforcement to the compression edge at the corresponding normal section of the shear-compression zone; P is the reinforcement percentage of the longitudinal tensile reinforcement in the shear section, P = 100ρ, ρ = (A p +A s ) / (bh0), when P>2.5, take P=2.5; A s A is the cross-sectional area of ​​the longitudinal tensile reinforcement; p f is the cross-sectional area of ​​the longitudinal prestressed steel bars; cu,k The standard value (MPa) of compressive strength for a concrete cube with a side length of 150 mm; ρ sv ρ is the reinforcement ratio of stirrups in the inclined section. sv =A sv / (s v b); A sv The total cross-sectional area (mm²) of stirrups arranged in the same section within the inclined section. 2 );s v f represents the spacing (m) of the stirrups within the inclined section; sv This represents the design value of the tensile strength (MPa) of the stirrup.

[0016] As a further preferred embodiment of the above technical solution, in step (2), the shear stress requirement at the connection interface between the ultra-high performance concrete and the reinforced structure is calculated by the following formula:

[0017] In the formula, ≥ d V is the shear stress requirement at the connection interface. cs To meet the shear resistance requirements of the reinforced structure, S * I is the area moment above the interface. z The moment of inertia of the composite section is flexural inertia.

[0018] The shear stress requirement at the connection interface was calculated using the elastic design method in the composite structure.

[0019] As a further preferred embodiment of the above technical solution, in step (3), the shear bearing capacity of a single rebar connector is calculated by the following formula:

[0020] V s =0.72A r f s In the formula, V s For the shear bearing capacity of a single rebar connector, A r f is the cross-sectional area of ​​a single rebar connector. s This represents the tensile strength of a single rebar connector.

[0021] The interfacial bearing capacity of rebar connections can be divided into three stages based on the stress stage: the bond stage, the rebar bearing stage, and the friction stage. The bond stage relies on the bond between the UHPC and the reinforced structure; however, the bond effect is extremely sensitive to environmental factors, making it difficult to precisely control the bond strength at the interface during practical use and design. The friction stage exhibits significant randomness and low friction strength, making it unsuitable as an interface design capacity. Therefore, this invention adopts the rebar bearing stage, where the bearing capacity can be precisely controlled, as the design bearing capacity.

[0022] As a further preferred embodiment of the above technical solution, in step (4), the shear stress generated by the rebar connector is calculated by the following formula:

[0023] In the formula, τ s V represents the shear stress generated by the rebar connector. s For the shear bearing capacity of a single rebar connector, s1 is the rebar spacing in the shear direction; b is the width of the interface between the reinforced structure and the ultra-high performance concrete.

[0024] Adjust s1 so that τ s ≥τ d .

[0025] Determining the rebar spacing s1 is equivalent to determining the number of rebars. If the excellent mechanical properties of the reinforcement material UHPC are to be utilized, it is necessary to ensure that the interface between the two does not fail before the reinforcement layer and the raw materials. Therefore, the rebar spacing must ensure that the shear stress generated by the rebar connector is greater than or equal to the shear stress requirement of the connection interface.

[0026] As a further preferred embodiment of the above technical solution, the spacing of the rebar arrangement is greater than or equal to five times the diameter of a single rebar connector, i.e., s1 ≥ 5d, where s1 is the rebar arrangement spacing in the shear direction and d is the diameter of the rebar connector. The proposed rebar arrangement spacing s1 must also meet the structural requirements to ensure that the structure does not suffer damage such as concrete splitting during drilling.

[0027] As a further preferred embodiment of the above technical solution, the minimum anchoring depth of the rebar connector is calculated by the following formula:

[0028] In the formula, L c,min L represents the minimum anchoring depth for rebar connectors in the reinforced structure. u,min The minimum anchoring depth for rebar connectors in ultra-high performance concrete; f c ′ represents the compressive strength of the cylinder in the reinforced structure, f u ′ represents the compressive strength of ultra-high performance concrete, f s This refers to the tensile strength of the rebar connector.

[0029] After determining the diameter of the rebar connectors and the spacing of the rebars, it is also necessary to determine the minimum rebar embedment depth. Insufficient embedment depth will cause the rebar connectors to be pulled out or result in concrete splitting failure during loading. Therefore, the embedment depth of the rebar connectors in the reinforced structure and UHPC as specified in the design should be greater than L, respectively. c,min and L u,min .

[0030] Compared with the prior art, the advantages of the present invention are as follows:

[0031] This invention establishes, on the one hand, the shear capacity of the rebar used as the design bearing capacity. Compared to other literature and materials that use interfacial bonding as the design bearing capacity, the bearing capacity of rebar used in this invention has superior deformation capacity, more controllable calculation basis, and reliable connection strength. On the other hand, this invention also establishes a calculation method for the shear bearing capacity of rebar connectors. This calculation method and design method have clear physical meaning, enabling industry designers to quickly calculate the required number of rebars. At the same time, this invention clarifies the calculation methods for the minimum rebar spacing and minimum rebar depth, ensuring that the rebar connection will not split due to failure to meet structural requirements, and enabling industry personnel to quickly obtain the rebar insertion depth.

[0032] In summary, this invention studies the load-bearing mechanism of the connection interface when UHPC is used to strengthen RC structures. It also provides a specific process for rebar installation design and connection, as well as the calculation and design basis for various parameters and performance through a specific load-bearing capacity calculation method. The physical meaning of the design method is clear, and the theoretical concepts are well-defined. It can be widely applied to the combined interface of ultra-high performance concrete and ordinary reinforced concrete structures. The overall process is convenient for technical personnel in related fields to carry out calculation and design analysis. Attached Figure Description

[0033] Figure 1 This is a three-dimensional schematic diagram of the connection between ultra-high performance concrete and the reinforced structure in Example 1;

[0034] Figure 2This is a schematic diagram of the connection between the ultra-high performance concrete and the reinforced structure in Example 1, viewed from the front.

[0035] Figure 3 This is a side view of the connection between the ultra-high performance concrete and the reinforced structure in Example 1. Detailed Implementation

[0036] The present invention will be further described in detail below with reference to specific embodiments.

[0037] Example 1:

[0038] This embodiment uses ultra-high performance concrete to reinforce a reinforced concrete beam, and the two are connected by rebar anchoring, as shown in the following diagram. Figure 1-3 As shown in the figure (1 is the RC beam, 2 is the UHPC, and 3 is the rebar connector), Figure 1 A perspective method was used to better illustrate the relationships between the components. The RC beam has a concrete cube strength of 25.6 MPa, internal steel reinforcement strength of 556 MPa, stirrup diameter of 8 mm, tensile longitudinal reinforcement diameter of 12 mm, compressive reinforcement diameter of 10 mm, and a concrete cover thickness of 25 mm at the bottom of the beam. The beam's clear span is 3000 mm, the spacing between loading points is 300 mm, and the RC beam's cross-section is 250 mm high and 150 mm wide. According to the original design requirements, a 50 mm thick UHPC plate with a compressive strength of 204 MPa is needed to reinforce the bottom of the beam. This embodiment uses a connection design method for a reinforced structure with ultra-high performance concrete, including the following steps:

[0039] (1) HRB400 steel bars are proposed to be used as rebar connectors, with a design tensile strength of 400MPa and a diameter of 10mm.

[0040] (2) Calculate the shear requirement V of the reinforced RC beam according to the following formula. cs :

[0041]

[0042] The meanings and values ​​of each parameter in the formula are shown in Table 1.

[0043] Table 1: Meaning and Values ​​of Parameters in the Shear Resistance Calculation Formula for RC Beams

[0044] parameter meaning Value unit <![CDATA[α1]]> Influence coefficient of opposite bending moment 1.00 / <![CDATA[α2]]> Prestress enhancement factor 1.00 / <![CDATA[α3]]> Influence coefficient of the compression flange 1.00 / b Cross-section width 150.00 mm <![CDATA[h0]]> Effective height of cross section 225.00 mm <![CDATA[A s ]]> cross-sectional area of ​​tensile reinforcement 339.29 <![CDATA[mm 2 ]]> P Longitudinal tensile reinforcement ratio 1.01 ％ <![CDATA[f cu ,k]]> Concrete cube compressive strength 25.60 MPa <![CDATA[s v ]]> Stirrup spacing 125.00 mm d stirrup diameter 8.00 mm <![CDATA[f sv ]]> Stirrup strength 574.00 MPa <![CDATA[A sv ]]> Area of ​​stirrups in inclined section 100.53 <![CDATA[mm 2 <!-- 4 -->]]> <![CDATA[ρ sv ]]> The stirrup reinforcement ratio of the inclined section 0.54％ / <![CDATA[V cs ]]> Shear capacity of the inclined section of a concrete beam 96.70 kN

[0045] (3) Calculate the shear stress requirement τd at the connection interface between UHPC and RC according to the following formula:

[0046] In the formula, τ d V is the shear stress requirement at the connection interface. csTo meet the shear resistance requirements of the reinforced structure, S * I is the area moment above the interface. z The moment of inertia of the composite section is flexural inertia.

[0047] τ can be calculated d =0.50MPa.

[0048] (4) Calculate the shear capacity V of a single rebar connector according to the following formula. s :

[0049] V s =0.72A r f s In the formula, V s For the shear bearing capacity of a single rebar connector, A r f is the cross-sectional area of ​​a single rebar connector. s This represents the tensile strength of a single rebar connector.

[0050] V can be calculated s =22.62kN.

[0051] (5) The proposed spacing s1 for the rebar installation is 250mm. The shear stress τ generated by the rebar connector is calculated according to the following formula. s : In the formula, τ s V represents the shear stress generated by the rebar connector. s For the shear bearing capacity of a single rebar connector, s1 is the rebar spacing in the shear direction; b is the width of the connection interface between the reinforced structure and the ultra-high performance concrete.

[0052] τ was calculated s =0.6MPa, at this time τ s Greater than τ d Therefore, the number of rebars at this time meets the requirements. If the rebar spacing s1 planned in this step does not meet the shear stress requirements, the planned rebar spacing value needs to be adjusted.

[0053] (6) Calculate the minimum anchoring depth L of the rebar connector in the UHPC according to the following formula. u,min and the minimum anchoring depth L of the rebar connector in the RC beam c,min :

[0054] In the formula, L c,min L represents the minimum anchoring depth for rebar connectors in the reinforced structure. u,min f′ represents the minimum anchoring depth for rebar connectors in ultra-high performance concrete. c f′ represents the compressive strength of the cylinder in the reinforced structure. u For the compressive strength of ultra-high performance concrete, fs This refers to the tensile strength of the rebar connector.

[0055] The minimum anchoring depth for rebar connectors in RC beams is calculated to be L. c,min = 60.93mm; the minimum anchoring depth for rebar connectors in UHPC is L u,min =13.89mm; therefore, considering the convenience of design and construction, the rebar depth in the RC beam and UHPC can be designed as 90mm and 50mm respectively.

[0056] (7) Check the spacing of the rebar arrangement. As calculated in step (5), the spacing of the rebar arrangement s1 ensures that the shear stress generated by the rebar connector meets the shear stress requirement of the connection interface. At the same time, the spacing of the rebar arrangement is 250mm, which is much greater than the minimum rebar spacing requirement of five times the diameter of the rebar connector 50mm (i.e. 5d). If the requirements are not met, the proposed rebar arrangement spacing needs to be adjusted to meet all requirements. The designed rebar depth also meets the minimum rebar depth requirement. Therefore, the design parameters meet the design requirements.

[0057] The above description is merely a preferred embodiment of the present invention, and the scope of protection of the present invention is not limited to the above embodiments. For those skilled in the art, improvements and modifications obtained without departing from the inventive concept should also be considered within the scope of protection of the present invention.

Claims

1. A connection design method for reinforcing a structure using ultra-high performance concrete, characterized by, The high-performance concrete is connected to the reinforced structure via rebar connectors, and the connection design method includes the following steps: (1) Determine the material parameters of the ultra-high performance concrete to be used based on the parameters of the structure being reinforced; (2) Confirm the shear requirements of the reinforced structure, and calculate the shear stress requirement at the interface between the ultra-high performance concrete and the reinforced structure based on the shear requirements of the reinforced structure; the shear stress requirement at the interface between the ultra-high performance concrete and the reinforced structure is calculated by the following formula: ; wherein is the shear stress demand of the connection interface, is the shear demand of the reinforced structure, S is the area moment above the interface, I z is the combined section flexural moment of inertia; (3) Calculate the shear bearing capacity of a single rebar connector. Based on the shear bearing capacity of a single rebar connector and the shear stress requirement at the connection interface, determine the rebar spacing in the shear direction, ensuring that the rebar spacing satisfies the requirement that the shear stress generated by the rebar connector is greater than or equal to the shear stress requirement at the connection interface. The shear bearing capacity of a single rebar connector is calculated using the following formula: ; wherein is the shear capacity of the individual dowel connector, is the cross-sectional area of the individual dowel connector, f s is the tensile strength of the individual dowel connector; (4) Calculate the minimum anchoring depth of the rebar connector, ensuring that the embedding depth of the rebar connector in the reinforced structure and in the ultra-high performance concrete is greater than the minimum anchoring depth, thus completing the connection design for the ultra-high performance concrete-reinforced structure; the shear stress generated by the rebar connector is calculated by the following formula: In the formula, The shear stress generated by the rebar connector, The shear bearing capacity of a single rebar connector. s 1 represents the spacing of the rebar installation in the shear direction; b It is the width of the interface between the reinforced structure and the ultra-high performance concrete; adjust s 1 makes .

2. The connection design method for using ultra-high performance concrete reinforced structures according to claim 1, characterized in that, In step (2), the shear requirement of the reinforced structure is the design load of the reinforced structure, or the shear requirement of the reinforced structure is the shear bearing capacity calculated based on the material and geometric parameters of the reinforced structure.

3. The connection design method for using ultra-high performance concrete reinforced structures according to claim 1, characterized in that, The spacing between the rebars is greater than or equal to five times the diameter of a single rebar connector, i.e. ,in, s 1 represents the spacing of the rebar installation in the shear direction. d This refers to the diameter of the rebar connector.

4. The connection design method for ultra-high performance concrete reinforced structures according to any one of claims 1-3, characterized in that, The minimum anchoring depth of the rebar connector is calculated by the following formula: In the formula, The minimum anchoring depth for the rebar connectors in the reinforced structure; The minimum anchoring depth for rebar connectors in ultra-high performance concrete; The compressive strength of the cylinder in the reinforced structure. The compressive strength of ultra-high performance concrete. This refers to the tensile strength of the rebar connector.

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