A fiber-reinforced reinforced concrete beam and its bearing capacity calculation method

Abstract

This invention discloses a fiber-reinforced reinforced concrete beam and its bearing capacity calculation method. The fiber-reinforced reinforced concrete beam includes: a concrete body with a loading plate having a concentrated force loading point; the side of the concrete body opposite the concentrated force loading point is the bottom of the concrete beam; and a reinforcing cage within the concrete body, comprising longitudinal bars and several stirrups that enclose and restrain the longitudinal bars. The longitudinal bars are arranged along the length of the concrete body and are parallel and symmetrical about the beam axis. Several CFRP strips are provided in the reinforced area on the surface of the concrete body. The CFRP strips are symmetrically arranged about the central cross-section, with the lower edges of the CFRP strips on the same side of the central cross-section aligned on the same diagonal line, passing through the edge of the loading plate where the concentrated force loading point is located on the same side of the central cross-section, and the upper edges extending to the top surface of the beam. This invention can effectively improve the ultimate bearing capacity and deformation capacity of the beam, change the beam's failure mode, and make beam failure predictable.

Description

Technical Field

[0001] This invention relates to a fiber-reinforced reinforced concrete beam and a method for calculating its load-bearing capacity, belonging to the field of building structure technology. Background Technology

[0002] Reinforced concrete structures are one of the most widely used structural forms, mainly composed of load-bearing components such as beams, columns, slabs, walls, and foundations. Reinforced concrete beams (RC beams) are core load-bearing components in buildings and bridges, and their stress performance directly affects the safety and serviceability of the overall structure. Under various loads, reinforced concrete beams not only bear bending moments but also face complex shear stress problems.

[0003] The shear performance of reinforced concrete beams is essentially a highly complex problem involving multiple coupled factors. Its stress mechanism involves the synergistic action of various mechanisms, including the nonlinear characteristics of concrete, aggregate interlocking force, the effect of longitudinal reinforcement dowels, and the constraint effect of web reinforcement. This makes it extremely difficult to accurately describe the entire stress process theoretically. In practical engineering, shear failure of reinforced concrete beams typically manifests as brittle failure without significant plastic deformation, and the failure mode exhibits significant uncertainty. When the shear span ratio is greater than 2.0, reinforced concrete beams mainly experience two brittle failure modes: diagonal tension failure and shear-compression failure. These two modes differ fundamentally in their failure modes and bearing capacity levels: diagonal tension failure is sudden, with diagonal cracks rapidly penetrating the cross-section once they appear, resulting in a sharp loss of bearing capacity; while shear-compression failure involves crack development, the formation of critical diagonal cracks, and the gradual shrinkage of the shear-compression zone until concrete collapse. Further complicating matters, even within the category of shear-compression failure, the shear bearing capacity of reinforced concrete beams still exhibits significant dispersion. Numerous experimental studies have shown that, within the commonly used range of shear span ratios between 2.0 and 4.0, approximately 50% of the measured shear capacity values ​​for reinforced concrete beams can reach 2 to 3 times the lower limit. This significant variability fully reflects the randomness and unpredictability of the shear failure process, making it difficult to provide accurate and reliable quantitative estimates of the actual shear capacity of reinforced concrete beams, even with sophisticated theoretical models and numerical analysis methods.

[0004] The aforementioned problems have two serious impacts: First, because the accurate value of the shear capacity of reinforced concrete beams is difficult to determine in advance, current design methods can only rely on the lower envelope value of a large amount of experimental data, i.e., using the most unfavorable situation as the design basis. This conservative approach results in the failure to fully utilize the strength of reinforced concrete beams in most actual projects, causing significant waste of steel and concrete resources, which contradicts the current green development concept of carbon reduction and environmental protection. Second, the large fluctuations in shear capacity bring great difficulties to the seismic design of reinforced concrete beams. Under seismic loading, the deviation between the actual bearing capacity of the component and the expected design value may lead to an inaccurate assessment of the structural safety reserve. This could result in either overestimating the bearing capacity and failing to meet the seismic requirements under major earthquakes, or underestimating it and causing unnecessary economic investment. This uncertainty directly affects the reliable control of the seismic performance of the structure.

[0005] The root cause of these problems lies in the significant uncertainty and randomness of the critical diagonal crack angle during the shear failure of reinforced concrete beams. Currently, mainstream design codes both domestically and internationally generally adopt simplified assumptions when constructing formulas for calculating shear capacity, pre-setting the inclination angle of the diagonal crack to a fixed value. Taking the classic truss model as an example, it analogizes the stress mechanism of the beam to a truss system and fixes the inclination angle of the concrete diagonal compression members at 45°. However, in actual engineering, the diagonal crack angle of reinforced concrete beams is affected by a combination of factors such as shear span ratio, stirrup ratio, and concrete strength, often deviating from this idealized assumption. This makes it difficult for empirical formulas based on this assumption to accurately predict the actual bearing capacity.

[0006] To address this issue, the academic community has conducted extensive research attempting to reveal the influence of crack angle. For example, some scholars have employed pressure field theory and its improved models to solve for crack inclination angle by satisfying equilibrium, compatibility, and constitutive relations. However, these models are inherently deterministic and cannot fully reflect the inherent discreteness and randomness of crack initiation and propagation. Other scholars have introduced statistical analysis methods, proposing probability distribution models of crack angle based on experimental data, attempting to describe its variation range statistically. However, these methods still rely on empirical induction and fail to achieve a precise mapping between crack angle and bearing capacity from a mechanistic perspective; therefore, they also cannot provide a definitive and precise value for the shear bearing capacity of a single reinforced concrete beam.

[0007] It is evident that existing theories and methods have not yet effectively addressed the prediction challenges arising from the uncertainty of critical diagonal cracks. To overcome this bottleneck, it is urgent to explore an effective crack control method for the entire failure process of reinforced concrete beams, and on this basis, establish a bearing capacity calculation theory that can accurately reflect the actual stress mechanism, thereby improving the scientific rigor and reliability of shear design for reinforced concrete beams. Summary of the Invention

[0008] To address the aforementioned problems, this invention provides a fiber-reinforced reinforced concrete beam and its load-bearing capacity calculation method, which enables proactive control of the angle of diagonal cracks. This significantly improves and stabilizes the shear bearing capacity and deformation capacity of the reinforced concrete beam at a high level, altering the beam's failure mode and making beam failure predictable.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides a fiber-reinforced reinforced concrete beam, comprising: A concrete body is provided with a loading plate, and the loading plate is provided with a concentrated force loading point. The side of the concrete body opposite to the concentrated force loading point is the bottom of the concrete beam. The longitudinal section of the concrete body where the concentrated force loading point is located is the central longitudinal section. The center line of the length direction of the central longitudinal section is the beam axis. The cross section of the concrete body where the center point of symmetry of the concentrated force loading point is located is the central cross section. A steel reinforcement cage is provided in the concrete body, which includes longitudinal bars and a number of stirrups that wrap and constrain the longitudinal bars. The longitudinal bars are arranged along the length of the concrete body and are arranged parallel and symmetrical about the beam axis. The reinforced area on the concrete surface is provided with several CFRP strips. The CFRP strips are symmetrically arranged about the central cross section. The lower edges of the CFRP strips on the same side of the central cross section are on the same diagonal line, and the diagonal line passes through the edge of the loading plate where the concentrated force loading point is located on the same side of the central cross section. The upper edge extends to the top surface of the beam.

[0010] In one embodiment of the present invention, the angle between the oblique line and the beam axis is 30° to 60°.

[0011] In one embodiment of the invention, the CFRP strips of the same shear span are symmetrical about the central longitudinal section.

[0012] In one embodiment of the present invention, the CFRP strip is bonded in at least two layers, the lower edge of the CFRP strip closest to the concentrated force loading point is higher than the beam axis, the width of the CFRP strip is not less than 3cm, and the spacing between the CFRP strips does not exceed the width of the CFRP strip.

[0013] In one embodiment of the present invention, CFRP strips are also pasted on the concrete surface between the center of the support on the bottom of the beam and the intersection of the oblique line and the bottom of the beam, and the pasting area is not less than 1 / 4 of the beam height.

[0014] In one embodiment of the present invention, CFRP strips are also pasted on the concrete surface between the center of the support on the bottom of the beam and the intersection of the diagonal line and the bottom of the beam. The width of the CFRP strips is the same as the width of the beam.

[0015] In one embodiment of the present invention, the CFRP strip is pasted horizontally or vertically from the bottom of the beam to the top of the beam, and the edges of the CFRP strip below the beam axis are on the same oblique line, and the oblique line passes through the edge of the loading plate where the concentrated force loading point is located.

[0016] In one embodiment of the present invention, the longitudinal reinforcement has at least two layers, the first layer of longitudinal reinforcement and the second layer of longitudinal reinforcement are symmetrical about the beam axis, the first layer of longitudinal reinforcement is set near the concentrated force loading point, and the second layer of longitudinal reinforcement is set near the bottom of the concrete beam; the stirrups are symmetrical about the central cross section and are equidistantly distributed, and the spacing between two adjacent stirrups is 80-350mm.

[0017] Secondly, the present invention provides a construction method for a fiber-reinforced reinforced concrete beam according to the above-mentioned method, the construction method comprising: After the concrete formwork is erected, the longitudinal bars and several stirrups are tied together to obtain the steel reinforcement cage; the steel reinforcement cage is placed in the predetermined position in the concrete formwork. Pour concrete into the reinforced concrete formwork, vibrate it evenly, and smooth the surface; after the concrete reaches the strength for demolding, remove the formwork and cure it. After curing, CFRP strips are pasted at predetermined positions on the concrete surface to obtain a shear-reinforced reinforced concrete beam.

[0018] Thirdly, the present invention provides a method for calculating the bearing capacity of a fiber-reinforced reinforced concrete beam according to the aforementioned method, the method comprising: According to the formula V=V c +V s Calculate the shear capacity of the fiber-reinforced reinforced concrete beam; Where Vc represents the shear force borne by the concrete, and Vs represents the shear force provided by the stirrups. The formula for calculating Vc is as follows:

[0019] in, This is a correction factor for concrete density; it is taken as 1.0 for ordinary concrete and 0.75 for lightweight concrete. For concrete compressive strength, The tensile reinforcement ratio, For the width of the beam, The effective height of the beam; The influence coefficient of the shear span ratio. The crack angle influence coefficient is... The corrected size effect factor is calculated using the following formula:

[0020]

[0021]

[0022] Where 2.0 ≤ a / d ≤ 3.5; when a / d > 3.0, k takes 0.6; when 2.0 ≤ a / d ≤ 3.0, ; The crack control angle is H, where H is the beam height. This is the distance from the point where the concentrated force is applied to the center of the support at the bottom of the beam; The formula for calculating Vs is as follows:

[0023] in, Let be the area of ​​the stirrups. The yield strength of the stirrup. denoted as θ, where θ is the angle between the stirrup and the axis of the member, and s is the distance between the stirrups.

[0024] The beneficial effects of this invention are: The CFRP strips in the shear-reinforced reinforced concrete beams with bonded CFRP strips provided by this invention can effectively control the path and direction of critical diagonal cracks, achieve active control of crack angle, greatly enhance the shear bearing capacity and deformation capacity of reinforced concrete beams, and transform the failure mode of the beams into flexural-shear failure. Meanwhile, the bearing capacity calculation method provided by this invention can effectively predict the shear bearing capacity of reinforced concrete beams with actively controlled angles. This calculation method proposes a shear span ratio influence coefficient and an angle influence coefficient, supplementing existing technologies and reflecting the differences in shear bearing capacity of reinforced concrete beams under different crack angles and different shear span ratios. Furthermore, the size effect coefficient has been corrected, enabling the calculation method to more accurately predict shear bearing capacity, thereby improving the scientific rigor and reliability of shear design for reinforced concrete beams. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of the reinforced concrete beam reinforcement area of ​​the present invention; Figure 2 This is a schematic diagram of a CFRP strip bonding method for reinforced concrete beams according to the present invention; Figure 3 A schematic diagram of the reinforcement details of the reinforced concrete beam of this invention; Figure 4This is a schematic diagram of another CFRP strip bonding method for reinforced concrete beams according to the present invention; Figure 5 This is a schematic diagram of another CFRP strip bonding method for reinforced concrete beams according to the present invention; Figure 6 This is a schematic diagram of the model for predicting the shear behavior of fiber-reinforced reinforced concrete beams according to the present invention; Figure 7 This is a load-deflection curve diagram of an embodiment of the present invention. Detailed Implementation

[0027] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0028] Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains; the terminology used in this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention; the terms “comprising” and “having”, and any variations thereof, in the specification, claims and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0029] In the description of the embodiments of this invention, technical terms such as "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary and secondary relationship of the indicated technical features. In the description of the embodiments of this invention, "multiple" means two or more, unless otherwise explicitly defined.

[0030] In this invention, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least some embodiments of the invention. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this invention can be combined with other embodiments.

[0031] In the description of the embodiments of this invention, the term "and / or" is merely a description of the relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, in this invention, the character " / " generally indicates that the preceding and following associated objects have an "or" relationship.

[0032] The detection methods involved in the following embodiments are as follows: Methods for testing shear load and shear bearing capacity: A shear capacity test was conducted on a simply supported reinforced concrete beam using a three-point symmetrical loading method. A 100t hydraulic jack was used for loading, with a force sensor (maximum range 50t) installed at the jack to measure the applied load. The experiment employed a displacement loading control method with graded loading, increasing the load by 0.5mm per grade at a loading rate of 0.5mm / min. As the load increased, flexural cracks first appeared in the cross-section of the reinforced concrete beam web directly below the loading point, followed by diagonal cracks within the shear span. The critical diagonal cracks extended through pre-set holes, pointing towards the loading point and the support at both ends. These critical diagonal cracks continued to extend towards both ends, increasing in width, until the reinforced concrete beam ultimately failed due to the crushing of the concrete near the loading point. The peak load is the shear capacity of the reinforced concrete beam.

[0033] Methods for testing the deflection and deformation capacity of reinforced concrete beams: Vertical displacement gauges are placed at the center of the bottom surface at mid-span and the center of the top surface directly above the support of the reinforced concrete beam to measure the mid-span deflection value. The deflection value when the load drops to 85% of the peak value is recorded, which is the ultimate deformation capacity of the reinforced concrete beam. The shear span deformation process is recorded by using DIC (Digital Image Correlation) technology.

[0034] Example 1 like Figure 1 , Figure 2 and Figure 3 As shown, this embodiment of the invention provides a fiber cloth reinforced reinforced concrete beam, including a concrete body 1, a plurality of CFRP (carbon fiber reinforced plastic) strips 2 on the surface of the concrete body 1, and a steel reinforcement skeleton 3 inside the concrete body 1; the plurality of CFRP strips 2 are all pasted in the reinforcement area on the surface of the concrete body 1, there are at least 4 CFRP strips 2, and each CFRP strip 2 is pasted with at least 2 layers of CFRP cloth; the steel reinforcement skeleton 3 includes longitudinal bars 8 and a plurality of stirrups 9; the longitudinal bars 8 have at least two layers, from top to bottom, the first layer of longitudinal bars 10 and the second layer of longitudinal bars 11.

[0035] Among them, the pasted CFRP strips 2 are symmetrical about two planes. The cross-section of CFRP strips 2 with different shear spans is symmetrical about the center point of the concentrated force loading point 15 of the reinforced concrete beam, which is the central cross-section 12. The longitudinal section of CFRP strips 2 with the same shear span is symmetrical about the longitudinal section of the concentrated force loading point 15 of the reinforced concrete beam, which is the central longitudinal section 14. The lower edges of the first CFRP strip 4, the second CFRP strip 5, the third CFRP strip 6, and the fourth CFRP strip 7 are on the same oblique line, and this oblique line passes through the edge of the loading plate where the concentrated force loading point 15 is located; the angle between this oblique line and the beam axis 13 is 30° to 60°.

[0036] Furthermore, CFRP strips 16 are also pasted on the concrete surface between the center of the support on the bottom of the beam and the intersection of the diagonal line and the bottom of the beam, with the pasting area being no less than 1 / 4 of the beam height.

[0037] Furthermore, the width of the CFRP strip is not less than 3cm, and the spacing between strips does not exceed the strip width.

[0038] Furthermore, the spacing between two adjacent stirrups 8 is 80–350 mm.

[0039] Example 2 like Figure 1 , Figure 3 and Figure 4 As shown, this embodiment of the invention provides a fiber cloth reinforced reinforced concrete beam. The difference between this embodiment and Embodiment 1 is that the CFRP strips are pasted horizontally from the bottom to the top of the beam. The edges of the CFRP strips below the beam axis 13 are on the same oblique line, and this oblique line passes through the edge of the loading plate where the concentrated force loading point 15 is located.

[0040] Furthermore, CFRP strips are also pasted on the concrete surface between the center of the support on the bottom of the beam and the intersection of the diagonal line and the bottom of the beam. The width of the strips is the same as the width of the beam.

[0041] Example 3 like Figure 1 , Figure 3 and Figure 5 As shown, this embodiment of the invention provides a fiber cloth reinforced reinforced concrete beam. The difference between this embodiment and Embodiment 1 is that the CFRP strips are pasted horizontally or vertically from the bottom of the beam to the top of the beam. The edges of the CFRP strips below the beam axis 13 are on the same oblique line, and this oblique line passes through the edge of the loading plate where the concentrated force loading point 15 is located.

[0042] Furthermore, the width of the CFRP strips is no less than 3cm, and there are no gaps between the strips.

[0043] Furthermore, CFRP strips are also pasted on the concrete surface between the center of the support on the bottom of the beam and the intersection of the diagonal line and the bottom of the beam. The width of the strips is the same as the width of the beam.

[0044] Example 4 This invention provides a construction method for fiber-reinforced reinforced concrete beams, the specific steps of which are as follows: (1) After the concrete formwork is erected, the longitudinal bars 7 and several stirrups 8 are tied together to obtain the steel reinforcement cage 3; the steel reinforcement cage 3 is placed in the predetermined position in the concrete formwork.

[0045] (2) Pour concrete into the reinforced concrete formwork and vibrate it evenly and smooth the surface; after the concrete reaches the strength for demolding, remove the formwork and carry out curing.

[0046] (3) After curing, CFRP strips are pasted at preset positions on the concrete surface to obtain shear-reinforced reinforced concrete beams.

[0047] This invention provides a shear-reinforced reinforced concrete beam with bonded CFRP strips: the total length of the shear-reinforced reinforced concrete beam with bonded CFRP strips is 2000mm, the cross-sectional dimensions are 100mm (width) × 240mm (height), the shear span length is 750mm, and the shear span ratio is 3.56; the concrete material used for casting the reinforced concrete beam is ordinary C30 grade concrete, and the straight longitudinal bars in the reinforcement cage have two layers. From top to bottom, the two compression longitudinal bars are the first layer of longitudinal bars 9, with a strength grade of HRB300 and a nominal diameter of 6mm; the two tension longitudinal bars are the second layer of longitudinal bars 10, with a strength grade of HRB500 and a nominal diameter of 16mm (the reinforcement ratio of the second layer of longitudinal bars 10 is 1.90%); the concrete cover thickness of the straight longitudinal bars 7 is 20mm; the stirrups 8 outside the concentrated force loading point 15 have a strength grade of HRB300 and a diameter of 6mm; no stirrups are configured in the shear span; the mechanical properties of the steel reinforcement and concrete materials are shown in Table 1.

[0048] Table 1: Mechanical Properties of Reinforcing Steel and Concrete Materials

[0049] CFRP strips were used to reinforce concrete, with crack control angles of 30°, 35°, and 40°. The shear capacity and deformation capacity of the reinforced concrete beams were determined using the aforementioned testing methods. The results were as follows: the beam with a crack angle of 30° had a shear capacity of 60.30 mm and a deformation capacity of 4.33 mm; the beam with a crack angle of 35° had a shear capacity of 60.98 mm and a deformation capacity of 3.54 mm; and the beam with a crack angle of 40° had a shear capacity of 67.52 mm and a deformation capacity of 5.13 mm. Comparative Example 1: Comparative Example 1 is a traditional reinforced concrete beam, without CFRP strips pasted on the concrete surface.

[0050] The shear capacity and ultimate deformation capacity of the reinforced concrete beam were determined using the above testing method. The test results showed that the shear capacity reached 47.90 kN and the deformation capacity reached 2.50 mm.

[0051] Example 5 This invention provides a model for predicting the shear behavior of fiber-reinforced reinforced concrete beams, using the 3DRBSM model to numerically simulate the beams.

[0052] In the 3D RBSM model, concrete is modeled as a combination of polyhedral rigid elements, which are randomly generated by the Voronoi method. Each concrete element has three translational degrees of freedom and three rotational degrees of freedom at its center of gravity. The interface between adjacent elements is connected by a triangular mesh of the centroid and vertex members, with the centroid of the mesh set as the integration point. Two tangential springs and one normal spring are configured to transmit bending and torsional forces.

[0053] like Figure 6 As shown, the FRP fabric elements are regular hexahedral elements, formed by arranging regular element points. Similar to concrete elements in RBSM, the FRP fabric elements have six degrees of freedom at their centroids. The interface between adjacent elements is divided into several triangles by their centroids and vertices, with integration points at the centroids of the triangles. Each integration point has one normal spring and two tangential springs for internal force transfer. The compressive and shear strengths of the FRP fabric are not considered in the design. Since failure is mainly caused by delamination due to cracking of the concrete beneath the interface, a large value is taken for the interfacial bond force, assuming no delamination failure occurs between the interfaces. The interface spring stiffness values ​​are as follows:

[0054]

[0055] in, and These represent the elastic moduli of the concrete element and the FRP element, respectively. and These represent the shear modulus of the concrete element and the FRP element, respectively. This represents the length of the perpendicular line from the centroid of the concrete element to its interface. This represents the length of the perpendicular line from the centroid of the FRP element to its interface.

[0056] For the reinforcing steel, regular beam elements are used for modeling. This modeling method allows beam elements to be flexibly placed at any position in the structure, without being limited by the concrete element mesh. Each beam node is defined with two translational degrees of freedom and one rotational degree of freedom using spring elements. Stress transfer between the reinforcing steel and the concrete is achieved through a geometry-less connection element that connects the beam node to the calculation point of the concrete particles. Each linkage element consists of a tangential spring, a normal spring, and a rotational spring: the tangential spring, based on a nonlinear bond stress-slip relationship, is responsible for transferring the shear stress between the beam and the concrete particles; the normal spring is given high stiffness to constrain the relative displacement of the reinforcing steel in the normal direction.

[0057] A reinforced concrete beam model was established using this numerical simulation method, and a large number of simulations were conducted by changing the structural parameters. The simulation results are shown in Table 2 below.

[0058] Table 2 Shear bearing capacity results of fiber-reinforced reinforced concrete beams

[0059] Taking a model with a shear span ratio of 3.56, concrete strength of C60, and an angle of 50° as an example, Figure 7 Show its load-deflection curve. From Figure 7 As can be seen from the data, its shear bearing capacity is significantly enhanced, the deflection corresponding to the maximum load is significantly increased, and its load-deflection curve shows a yield plateau, proving that its failure mode has changed. The fiber cloth reinforcement has changed the failure mode of the beam from shear-compression failure to bending-shear failure.

[0060] This invention provides a model for predicting the shear behavior of fiber-reinforced reinforced concrete beams. The beam is numerically simulated using 3DRBSM. A reinforced concrete beam model is established using this numerical simulation method, and a large number of simulations are conducted by changing the structural parameters. Formulas are proposed based on the experimental and simulation results.

[0061] Example 6 This invention provides a method for testing fiber-reinforced reinforced concrete beams, used to test the shear load and shear bearing capacity of such beams, comprising the following steps: A three-point symmetrical loading method is adopted, and a 100t-level hydraulic jack is used to apply load at the concentrated force loading point. A force sensor with a maximum range of 50t is installed at the jack to measure the load applied to the reinforced concrete beam. The displacement loading control method was adopted, and the load was applied in stages, with each stage increasing the load by 0.5 mm and the loading rate being 0.5 mm / min. As the load increases, the peak load at which the concrete near the concentrated loading point of the reinforced concrete beam is crushed and fails is the shear bearing capacity of the reinforced concrete beam.

[0062] Example 7 This invention provides a method for testing fiber-reinforced reinforced concrete beams, used to test the deflection and deformation capacity of such beams, comprising the following steps: Vertical displacement gauges are placed at the center of the bottom surface at mid-span and at the center of the top surface directly above the support of the reinforced concrete beam to measure the mid-span deflection value. Record the deflection value when the load drops to 90% of the peak value, and plot the load-deflection curve; Among them, DIC technology was used to capture and record the shear deformation process.

[0063] Example 8 This invention provides a method for calculating the bearing capacity of a fiber-reinforced reinforced concrete beam, used to calculate the bearing capacity of such a beam. The method includes: According to the formula V=V c +V s Calculate the shear capacity of the fiber-reinforced reinforced concrete beam; Where Vc represents the shear force borne by concrete 1, and Vs represents the shear force provided by the stirrups. The formula for calculating Vc is as follows:

[0064] in, This is a correction factor for concrete density; it is taken as 1.0 for ordinary concrete and 0.75 for lightweight concrete. For concrete compressive strength, The tensile reinforcement ratio, For the width of the beam, The effective height of the beam; The influence coefficient of the shear span ratio. The crack angle influence coefficient is... The corrected size effect factor is calculated using the following formula:

[0065]

[0066]

[0067] Where 2.0 ≤ a / d ≤ 3.5; when a / d > 3.0, k takes 0.6; when 2.0 ≤ a / d ≤ 3.0, ; The crack control angle is H, where H is the beam height. This is the distance from the concentrated force loading point 15 to the center of the support at the bottom of the beam; The formula for calculating Vs is as follows:

[0068] in, Let be the area of ​​the stirrups. The yield strength of the stirrup. denoted as θ, where θ is the angle between the stirrup and the axis of the member, and s is the distance between the stirrups.

[0069] In this embodiment of the invention, parameters influencing the angle and shear span ratio are introduced. and , The influence coefficient of the shear span ratio. The crack angle influence coefficient is given, and the size effect coefficient is also given. The present invention has been modified to enable the shear capacity calculation method to effectively predict the shear capacity of reinforced concrete beams with actively controlled crack angles. The proposed shear span ratio influence coefficient and angle influence coefficient supplement existing technologies, reflecting the differences in shear capacity of reinforced concrete beams under different crack angles and shear span ratios. Simultaneously, the size effect coefficient has been modified, allowing the calculation method to more accurately predict shear capacity, thereby improving the scientific rigor and reliability of shear design for reinforced concrete beams. The calculated shear capacity of a fiber-reinforced reinforced concrete beam provided in this embodiment is shown in Table 3 below.

[0070] Table 3 Calculated values ​​of shear bearing capacity of fiber-reinforced reinforced concrete beams

[0071] As shown in Table 3, the calculation results of the shear bearing capacity calculation method provided by the present invention are in good agreement. The bearing capacity calculation formula can reflect the influence of parameters such as concrete grade, reinforcement ratio, and effective height on shear bearing capacity. At the same time, the introduced parameters can also reflect the influence of factors such as shear span ratio and angle change on shear bearing capacity. It can better predict the shear bearing capacity of RC beams under different fiber cloth reinforcement schemes.

[0072] In summary, this invention discloses a fiber-reinforced reinforced concrete beam and its load-bearing capacity calculation method. The CFRP strips in the shear-reinforced reinforced concrete beam with bonded CFRP strips effectively control the path and direction of critical diagonal cracks, achieving active control of the crack angle. This significantly enhances the shear capacity and deformation capacity of the reinforced concrete beam, shifting the beam's failure mode towards flexural-shear failure. Simultaneously, the load-bearing capacity calculation method provided by this invention can effectively predict the shear capacity of the reinforced concrete beam with actively controlled crack angles. This calculation method proposes shear span ratio influence coefficients and angle influence coefficients, supplementing existing technologies and reflecting the differences in shear capacity of reinforced concrete beams under different crack angles and shear span ratios. Furthermore, the size effect coefficient has been corrected, enabling the calculation method to more accurately predict shear capacity, thereby improving the scientific rigor and reliability of shear design for reinforced concrete beams. Therefore, this invention can achieve active control of diagonal crack angles, significantly improving and stabilizing the shear capacity and deformation capacity of reinforced concrete beams at a high level, changing the beam's failure mode, and making beam failure predictable.

[0073] Although the invention has been described with reference to preferred embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, the technical features mentioned in the various embodiments can be combined in any manner as long as there is no structural conflict. The invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A fiber-reinforced reinforced concrete beam, characterized in that, include: A concrete body is provided with a loading plate, and the loading plate is provided with a concentrated force loading point. The side of the concrete body opposite to the concentrated force loading point is the bottom of the concrete beam. The longitudinal section of the concrete body where the concentrated force loading point is located is the central longitudinal section. The center line of the length direction of the central longitudinal section is the beam axis. The cross section of the concrete body where the center point of symmetry of the concentrated force loading point is located is the central cross section. A steel reinforcement cage is provided in the concrete body, which includes longitudinal bars and a number of stirrups that wrap and constrain the longitudinal bars. The longitudinal bars are arranged along the length of the concrete body and are arranged parallel and symmetrical about the beam axis. The reinforced area on the concrete surface is provided with several CFRP strips. The CFRP strips are symmetrically arranged about the central cross section. The lower edges of the CFRP strips on the same side of the central cross section are on the same diagonal line, and the diagonal line passes through the edge of the loading plate where the concentrated force loading point is located on the same side of the central cross section. The upper edge extends to the top surface of the beam.

2. The fiber-reinforced reinforced concrete beam according to claim 1, characterized in that, The angle between the oblique line and the beam axis is 30° to 60°.

3. The fiber-reinforced reinforced concrete beam according to claim 1, characterized in that, The CFRP strips of the same shear span are symmetrical about the central longitudinal section.

4. A fiber-reinforced reinforced concrete beam according to claim 1, characterized in that, The CFRP strip is bonded in at least two layers. The lower edge of the CFRP strip closest to the concentrated force loading point is higher than the beam axis. The width of the CFRP strip is not less than 3cm, and the spacing between the CFRP strips does not exceed the width of the CFRP strip.

5. A fiber-reinforced reinforced concrete beam according to claim 1, characterized in that, CFRP strips are also pasted on the concrete surface between the center of the support on the bottom of the beam and the intersection of the diagonal line and the bottom of the beam, with the pasting area being no less than 1 / 4 of the beam height.

6. A fiber-reinforced reinforced concrete beam according to claim 1, characterized in that, CFRP strips are also pasted on the concrete surface between the center of the support on the bottom of the beam and the intersection of the diagonal line and the bottom of the beam. The width of the CFRP strips is the same as the width of the beam.

7. A fiber-reinforced reinforced concrete beam according to claim 1, characterized in that, The CFRP strips are attached horizontally or vertically from the bottom of the beam to the top of the beam. The edges of the CFRP strips below the beam axis are on the same diagonal line, and this diagonal line passes through the edge of the loading plate where the concentrated force loading point is located.

8. A fiber-reinforced reinforced concrete beam according to claim 1, characterized in that, The longitudinal reinforcement has at least two layers. The first layer and the second layer of longitudinal reinforcement are symmetrical about the beam axis. The first layer of longitudinal reinforcement is set near the concentrated force loading point, and the second layer of longitudinal reinforcement is set near the bottom of the concrete beam. The stirrups are symmetrical about the central cross section and are equidistantly distributed. The spacing between two adjacent stirrups is 80-350mm.

9. A construction method for a fiber-reinforced reinforced concrete beam according to any one of claims 1-8, characterized in that, The construction method includes: After the concrete formwork is erected, the longitudinal bars and several stirrups are tied together to obtain the steel reinforcement cage; the steel reinforcement cage is placed in the predetermined position in the concrete formwork. Pour concrete into the reinforced concrete formwork, vibrate it evenly, and smooth the surface; after the concrete reaches the strength for demolding, remove the formwork and cure it. After curing, CFRP strips are pasted at predetermined positions on the concrete surface to obtain a shear-reinforced reinforced concrete beam.

10. A method for calculating the bearing capacity of a fiber-reinforced reinforced concrete beam according to any one of claims 1-8, characterized in that, The method for calculating the bearing capacity includes: According to the formula V=V c +V s Calculate the shear capacity of the fiber-reinforced reinforced concrete beam; Where Vc represents the shear force borne by the concrete, and Vs represents the shear force provided by the stirrups. The formula for calculating Vc is as follows: in, This is the concrete density correction factor. For concrete compressive strength, The tensile reinforcement ratio, For the width of the beam, The effective height of the beam; The influence coefficient of the shear span ratio. The crack angle influence coefficient is... The corrected size effect factor is calculated using the following formula: Where 2.0 ≤ a / d ≤ 3.5; when a / d > 3.0, k takes 0.6; when 2.0 ≤ a / d ≤ 3.0, ; The crack control angle is H, where H is the beam height. This is the distance from the point where the concentrated force is applied to the center of the support at the bottom of the beam; The formula for calculating Vs is as follows: in, Let be the area of ​​the stirrups. The yield strength of the stirrup. denoted as θ, where θ is the angle between the stirrup and the axis of the member, and s is the distance between the stirrups.

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