Rectangular pvc-fiber reinforced polymer (frp) pipe reinforced concrete composite beam flexural capacity calculation method

Abstract

The present application relates to the technical field of the calculation method of the bending bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam, in particular to a calculation method of the bending bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam, wherein the rectangular PVC-FRP pipe reinforced concrete composite beam is a composite beam formed by arranging a PVC-FRP pipe reinforced concrete core beam in the compression zone of a rectangular reinforced concrete beam, arranging a steel cage outside and pouring concrete, and the present application solves the vicious cycle contradiction between the bearing capacity improvement of a common reinforced concrete beam and the increase of the dead weight and the decrease of the ductility, and the industry pain point of the lack of a mature and accurate calculation method of the bending bearing capacity of a new type of rectangular PVC-FRP pipe reinforced concrete composite beam.

Description

Technical Field

[0001] This invention relates to the technical field of methods for calculating the flexural bearing capacity of rectangular PVC-FRP pipe reinforced concrete composite beams, and in particular to a method for calculating the flexural bearing capacity of rectangular PVC-FRP pipe reinforced concrete composite beams. Background Technology

[0002] As the most critical bending member in infrastructure projects such as buildings, bridges, and rail transit, reinforced concrete beams directly determine the safety and economy of the overall structure. However, ordinary reinforced concrete beams have inherent contradictions that are difficult to reconcile: concrete has a high density and limited uniaxial compressive strength and ultimate compressive strain. To meet the requirements of high load-bearing capacity, the cross-sectional size must be increased or the reinforcement ratio must be increased. This not only significantly increases the self-weight of the member and the cost of foundation engineering, but also amplifies the seismic response of the structure. At the same time, an excessively high reinforcement ratio will lead to a decrease in the ductility of the member, making it prone to brittle failure, and unable to meet the requirements of modern large-span, lightweight, and high seismic performance engineering construction.

[0003] To overcome the aforementioned bottlenecks, based on the characteristic that FRP-confined concrete can significantly improve material strength and deformation capacity, the industry has proposed a rectangular PVC-FRP pipe reinforced concrete composite beam structure. By embedding a precast PVC-FRP pipe reinforced concrete core beam in the compression zone of an ordinary reinforced concrete beam, the circumferential constraint effect of the PVC-FRP pipe is used to enhance the concrete performance in the compression zone, thereby achieving a simultaneous improvement in the load-bearing capacity and ductility of the component.

[0004] However, current theoretical research on this new type of composite beam lags far behind engineering practice, and a calculation system for flexural bearing capacity that is suitable for its stress characteristics has not yet been formed: traditional reinforced concrete beam calculation methods do not consider the confinement enhancement effect of PVC-FRP pipes and the compressive contribution of longitudinal reinforcement in the core beam, and the calculation results can deviate from the measured values ​​by more than 20%; existing research on FRP confined concrete beams is mostly aimed at full-section confined members, which cannot be directly applied to the unique stress mode of "rectangular section, locally built-in core beam in the compression zone". Summary of the Invention

[0005] To address the technical problems of existing reinforced concrete structures, such as their high density leading to a high proportion of component self-weight, which significantly increases the load on foundation engineering and construction costs, this invention provides a method for calculating the flexural bearing capacity of rectangular PVC-FRP pipe reinforced concrete composite beams.

[0006] The technical solution adopted in this invention is: a method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam. The rectangular PVC-FRP pipe reinforced concrete composite beam is a composite beam formed by embedding a PVC-FRP pipe reinforced concrete core beam within the compression zone of a rectangular reinforced concrete beam, and then arranging a reinforcing cage on the outside and pouring concrete. The method for calculating its flexural bearing capacity specifically includes the following steps: Step a: Using the principle of simplified equivalence of the compression zone, the concrete in the compression zone of the composite beam is divided into an equivalent confined zone and an equivalent unconfined zone. The mid-span section strain of the concrete in the equivalent confined zone and the concrete in the equivalent unconfined zone are calculated respectively. Step b: Based on the static equilibrium condition of the section, calculate the equivalent unconfined concrete resultant force in the compression zone, the equivalent confined concrete resultant force in the compression zone, and the longitudinal reinforcement resultant force of the core beam in the compression zone, respectively. Step c: Calculate the resultant force of the longitudinal reinforcement in the tension zone according to the internal force equilibrium equation of the cross section, and substitute the resultant force of each part to obtain the height of the compression zone when the composite beam yields. Step d: Based on the moment equilibrium condition of the cross section, the equivalent unconfined concrete bending moment in the compression zone, the equivalent confined concrete bending moment in the compression zone, the longitudinal reinforcement bending moment of the core beam in the compression zone, and the longitudinal reinforcement bending moment of the tension beam in the tension zone are superimposed to derive the formula for calculating the yield flexural bearing capacity of the rectangular PVC-FRP pipe reinforced concrete composite beam.

[0007] In one embodiment, in step a, the mid-span section strains of the equivalent confined zone concrete and the equivalent unconfined zone concrete satisfy the following relationship: Tension longitudinal reinforcement strain Strain of concrete at the edge of the compression zone The relationship is: Strain at the equivalent resultant force point of the longitudinal reinforcement of the core beam Strain of concrete at the edge of the compression zone The relationship is: Equivalent confined concrete strain in compression zone Strain of concrete at the edge of the compression zone The relationship is: in, This represents the distance from the neutral axis to the upper surface of the composite beam when it yields. This is the distance from the bottom tensile longitudinal reinforcement to the top surface of the beam. This is the distance from the equivalent resultant point of the longitudinal reinforcement of the core beam to the top surface of the beam. This is the distance from the upper surface of the equivalent confined concrete zone to the edge of the beam's compression zone.

[0008] In one embodiment, in step b, the static equilibrium condition at the mid-span section of the composite beam when it yields is satisfied as follows: in, This represents the total resultant force in the compression zone when the composite beam yields. This represents the total resultant force in the tension zone when the composite beam yields.

[0009] In one embodiment, the total resultant force of the pressure zone The equivalent unconfined concrete resultant force in the compression zone Equivalent confined concrete resultant force in the compression zone Combined force with longitudinal reinforcement of core beam in compression zone The sum of The total resultant force in the tension zone The resultant force of the longitudinal reinforcement in the tension zone ,Right now .

[0010] In one embodiment, in step b, the equivalent unconfined concrete resultant force in the compression zone... and the distance from the point of application of the resultant force to the neutral axis Calculations are performed under the following two conditions: when the concrete at the edge of the compression zone has not reached its peak strain, i.e. hour: When the concrete at the edge of the compression zone reaches or exceeds the peak strain, i.e. hour: in, This refers to the axial compressive strength of concrete. The width of the composite beam section. This represents the peak strain of the concrete.

[0011] In one embodiment, in step b, the resultant force of the equivalent confined concrete in the compression zone... The calculation formula is: in, The elastic modulus of concrete. This represents the cross-sectional area of ​​the concrete in the equivalent confined zone.

[0012] In one embodiment, in step b, the resultant force of the longitudinal reinforcement of the core beam in the compression zone... The calculation formula is: in, The elastic modulus of the longitudinal reinforcement of the core beam. This represents the total cross-sectional area of ​​the longitudinal reinforcement bars of the core beam.

[0013] In one embodiment, in step c, the resultant force of the tension longitudinal reinforcement in the tension zone... The calculation formula is: in, The elastic modulus of the longitudinal reinforcement under tension is... This represents the total cross-sectional area of ​​the tension longitudinal reinforcement; The equivalent unconfined concrete resultant force in the compression zone Equivalent confined concrete resultant force in the compression zone The combined longitudinal reinforcement of the core beam in the compression zone Combined force with the longitudinal tension bars in the tension zone Substituting into the static equilibrium equation The height of the compression zone at the yield point of the composite beam is obtained by solving the problem. .

[0014] In one embodiment, In step d, the bending moment of each part about the neutral axis of the cross section is calculated using the following formula: equivalent unconfined concrete bending moment in the compression zone. Equivalent confined concrete bending moment in the compression zone Bending moment of longitudinal reinforcement in the core beam of the compression zone ; Tension longitudinal reinforcement bending moment in the tension zone ;in, Let be the distance from the point of application of the resultant force of the equivalent confined concrete in the compression zone to the neutral axis. The distance from the point of application of the resultant force of the longitudinal reinforcement of the core beam in the compression zone to the neutral axis. It is the distance from the point of application of the resultant force of the longitudinal reinforcement in the tension zone to the neutral axis.

[0015] In one embodiment, In step d, the yield flexural bearing capacity of the composite beam is... The sum of the bending moments of each part is: After substituting the calculation formulas for the bending moments of each part, the final calculation model for the yield flexural bearing capacity of the rectangular PVC-FRP pipe reinforced concrete composite beam is obtained.

[0016] The beneficial effects of this invention are as follows: Compared with the prior art, this invention solves the vicious cycle contradiction between increased load-bearing capacity and increased self-weight and decreased ductility in ordinary reinforced concrete beams, as well as the industry pain point of lacking a mature and accurate method for calculating the flexural load-bearing capacity of novel rectangular PVC-FRP pipe reinforced concrete composite beams. By dividing the compression zone into equivalent constrained and unconstrained zones for calculation, this invention quantitatively considers the circumferential constraint enhancement effect of PVC-FRP pipes for the first time, correcting the defects of the homogeneous concrete assumption in traditional methods, fully incorporating the compressive contribution of the longitudinal reinforcement of the core beam, clearly revealing the force transmission mechanism of the four materials sharing the load, and avoiding waste of material properties. The formula is derived using the engineering-standard static and moment balance principles, and the height of the compression zone is solved using an iterative method. The calculation process is clear, the physical meaning of the parameters is explicit, and no complex numerical analysis is required, making it easy for designers to master and apply, thus filling the technical gap in the calculation of the load-bearing capacity of this novel composite beam. Attached Figure Description

[0017] Figure 1 This is a structural diagram of the rectangular PVC-FRP pipe reinforced concrete composite beam in this invention; Figure 2 This is a schematic diagram of the equivalent cross-section in step a of the present invention; Figure 3 This is a stress distribution diagram of the mid-span section in step a of the present invention.

[0018] The markings in the diagram are as follows: 1. Rectangular reinforced concrete; 2. PVC-FRP pipe reinforced concrete core beam; 3. Stirrups; 4. Core beam body; 5. External stirrups; 6. Tension longitudinal bars; 7. CFRP strips; 8. PVC pipe; 9. Core beam longitudinal bars; 10. Core beam external stirrups. Detailed Implementation

[0019] In the description of this invention, it should be noted that the terms "front", "up", "down", "left", "right", "vertical", "horizontal", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0020] To address the problems existing in the background art, this application proposes the following technical solution: a method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam. The rectangular PVC-FRP pipe reinforced concrete composite beam is a composite beam formed by embedding a PVC-FRP pipe reinforced concrete core beam 2 inside the compression zone of a rectangular reinforced concrete beam 1, and then arranging a reinforcing cage on the outside and pouring concrete. The method for calculating its flexural bearing capacity specifically includes the following steps: Step a: Using the principle of simplified equivalence in the compression zone, the concrete in the compression zone of the composite beam is divided into an equivalent confined zone and an equivalent unconfined zone. The equivalent confined zone is as follows: Figure 2 As shown, the strain and stress at the mid-span section of the equivalent confined zone concrete and the equivalent unconfined zone concrete are calculated respectively. Figure 3 As shown; in step a, the mid-span section strain of the equivalent confined zone concrete and the equivalent unconfined zone concrete satisfies the following relationship: Strain of the tensile longitudinal reinforcement 6 Strain of concrete at the edge of the compression zone The relationship is: The strain at the equivalent resultant force point of the longitudinal reinforcement of the core beam 9 Strain of concrete at the edge of the compression zone The relationship is: Equivalent confined concrete strain in compression zone Strain of concrete at the edge of the compression zone The relationship is: in, This represents the distance from the neutral axis to the upper surface of the composite beam when it yields. This is the distance from the bottom tensile longitudinal reinforcement 6 to the top surface of the beam. The distance from the equivalent resultant point of the longitudinal reinforcement 9 in the core beam to the upper surface of the beam is denoted as . This is the distance from the upper surface of the equivalent confined concrete zone to the edge of the beam's compression zone.

[0021] The core of this step is to scientifically zon the concrete based on the essential differences in the confinement state of the concrete, and to establish the strain distribution relationship across the entire cross-section based on classical assumptions of structural mechanics, laying a solid foundation for subsequent internal force and bearing capacity calculations. First, the zoning of the compression zone concrete is based on the active confinement range of the PVC-FRP pipe: the built-in PVC-FRP pipe is composed of polyvinyl chloride pipe and carbon fiber reinforced composite strips wound together. When the internal concrete is compressed and undergoes lateral expansion, the PVC-FRP pipe generates a reverse circumferential confinement force, limiting the lateral deformation of the concrete, thereby significantly improving the compressive strength and ultimate deformation capacity of this part of the concrete; while the concrete outside the PVC-FRP pipe is not subject to any confinement, and its mechanical properties are completely consistent with those of concrete in ordinary reinforced concrete beams. Based on this core characteristic, this method divides the concrete filling the PVC-FRP pipe and the concrete within the effective confinement range of the pipe wall into an equivalent confinement zone, and the remaining compression zone concrete into an equivalent unconfinement zone. In engineering applications, the boundary of the effective constraint range can be determined by comprehensively calculating the wall thickness of the PVC-FRP pipe, the elastic modulus, and the Poisson's ratio of the concrete. For composite beams of conventional dimensions, the outer wall of the PVC-FRP pipe can be approximated as the outer boundary of the equivalent constraint zone. This simplification method significantly reduces the computational complexity while ensuring the accuracy of the calculation.

[0022] Secondly, the strain calculation strictly follows the plane section assumption, meaning that when a composite beam yields under flexural stress, the strain at the mid-span section is continuously linearly distributed along the section height, and the strain at any point is proportional to the vertical distance from that point to the neutral axis. This method specifically selects the mid-span section as the calculation section because, under common load forms such as uniformly distributed loads and concentrated loads, the bending moment at the mid-span section of a simply supported composite beam is the largest, making it the key section controlling the flexural bearing capacity of the entire member. Before formally calculating the strain, a unified section coordinate system needs to be established: with the upper surface of the compression zone of the beam as the origin and vertically downward as the positive direction, the coordinate values ​​of the centroid of the tensile longitudinal reinforcement 6, the common centroid of all longitudinal reinforcements in the core beam, and the upper edge of the equivalent confinement zone are measured and determined in sequence. In this method, the criterion for determining the yield state is clearly defined as the tensile longitudinal reinforcement 6 first reaching its yield strain. At this time, the strain of the concrete at the edge of the compression zone has not yet reached the ultimate compressive strain, which can ensure that the member undergoes well-strengthened failure with good ductility and avoid brittle failure. Based on the linear strain distribution law assumed by the plane section, the strain value at any position of the section can be derived from the strain value of the concrete at the edge of the compression zone and the position of the neutral axis, including the average strain of the concrete in the equivalent confinement zone and the strain value of the longitudinal reinforcement 9 of the core beam.

[0023] Step b: Based on the static equilibrium condition of the section, calculate the equivalent unconfined concrete resultant force in the compression zone, the equivalent confined concrete resultant force in the compression zone, and the resultant force of the longitudinal reinforcement 9 of the core beam in the compression zone. In step b, the static equilibrium condition at the mid-span section of the composite beam at yielding is satisfied: in, This represents the total resultant force in the compression zone when the composite beam yields. This represents the total resultant force in the tension zone when the composite beam yields.

[0024] Total force of the pressure zone The equivalent unconfined concrete resultant force in the compression zone Equivalent confined concrete resultant force in the compression zone Combined with the longitudinal reinforcement of the core beam in the compression zone The sum of Total strength of the affected area For the tension zone, the longitudinal reinforcement has a combined force of 6. ,Right now .

[0025] In step b, the equivalent unconfined concrete resultant force in the compression zone and the distance from the point of application of the resultant force to the neutral axis Calculations are performed under the following two conditions: when the concrete at the edge of the compression zone has not reached its peak strain, i.e. hour: When the concrete at the edge of the compression zone reaches or exceeds the peak strain, i.e. hour: in, This refers to the axial compressive strength of concrete. The width of the composite beam section. This represents the peak strain of the concrete.

[0026] In step b, the equivalent confined concrete resultant force in the compression zone The calculation formula is: in, The elastic modulus of concrete. This represents the cross-sectional area of ​​the concrete in the equivalent confined zone.

[0027] In step b, the combined force of the longitudinal reinforcement 9 in the core beam of the compression zone The calculation formula is: in, Let be the elastic modulus of the longitudinal reinforcement 9 of the core beam. This represents the total cross-sectional area of ​​the longitudinal reinforcement 9 in the core beam.

[0028] This step, based on the fundamental principle of static equilibrium of the cross-section, calculates the resultant internal forces of the three components of the compression zone, serving as a crucial intermediate link connecting strain distribution with the final bearing capacity calculation. The principle of static equilibrium states that at the instant a member reaches its yield bearing capacity, the sum of all internal forces in the horizontal direction of the cross-section is zero. That is, the total pressure generated by all materials in the compression zone is equal in magnitude and opposite in direction to the total tensile force generated by the longitudinal reinforcement in the tension zone. The total pressure in the compression zone consists of the superposition of three independent internal forces: the pressure of the equivalent unconfined concrete, the pressure of the equivalent confined concrete, and the pressure of the longitudinal reinforcement 9 in the core beam. The resultant forces of these three parts need to be calculated separately based on their respective mechanical properties before being superimposed.

[0029] For equivalent unconfined concrete, the stress-strain relationship is fully adopted using the uniaxial compressive stress-strain curve specified in the current national standard "Code for Design of Concrete Structures". This curve has been verified by numerous experiments and can accurately reflect the mechanical properties of ordinary concrete throughout the entire process from elastic loading and elastoplastic development to final failure. Since the strain of the concrete at the edge of the compression zone may be in the elastic or elastoplastic stage when the tension longitudinal reinforcement 6 yields, calculations are required for two typical working conditions: When the strain of the concrete at the edge of the compression zone is less than the peak strain of the concrete, the concrete is in the fully elastic stage, and the stress and strain are strictly proportional, with the stress distribution diagram of the section being a standard triangle; when the strain of the concrete at the edge of the compression zone is greater than or equal to the peak strain, the concrete enters the elastoplastic stage, the stress growth rate gradually slows down, and the stress distribution diagram of the section is a convex curve. The magnitude and location of the resultant force under both working conditions need to be calculated by integration based on the corresponding stress distribution diagram. In engineering applications, the simplified calculation formula recommended by the standard can be directly used, without the need for complex integration calculations.

[0030] For equivalent confined concrete, due to the continuous circumferential constraint of the PVC-FRP pipe, it is in a triaxial compressive stress state, and its compressive strength and elastic modulus are significantly higher than those of ordinary uniaxial compressive concrete. This method, through the innovative concept of the equivalent confined zone, transforms the complex triaxial stress state into an equivalent uniaxial stress state, and uses the equivalent elastic modulus to quantitatively reflect the effect of confinement on the mechanical properties of concrete. The resultant force of the equivalent confined concrete can be calculated based on its average strain, equivalent elastic modulus, and cross-sectional area of ​​the equivalent confined zone. The point of application of the resultant force is approximately taken as the geometric centroid of the equivalent confined zone section. For the longitudinal reinforcement 9 of the core beam, it is located inside the compression zone and is usually still in an elastic compressive state when the member reaches its yield bearing capacity. The stress is proportional to the strain. Therefore, the pressure value can be calculated based on its strain value, the elastic modulus of the steel reinforcement, and the total cross-sectional area of ​​the longitudinal reinforcement 9 of the core beam. The point of application of the resultant force is taken as the common centroid of all longitudinal reinforcements of the core beam.

[0031] Step c: Calculate the resultant force of the longitudinal reinforcement 6 in the tension zone according to the internal force equilibrium equation of the cross section, and substitute the resultant force of each part to obtain the height of the compression zone when the composite beam yields. In step c, the resultant force of the tension longitudinal reinforcement 6 in the tension zone The calculation formula is: in, The elastic modulus of the tensile longitudinal reinforcement 6 is... This represents the total cross-sectional area of ​​the tension longitudinal reinforcement 6; The equivalent unconfined concrete resultant force in the compression zone Equivalent confined concrete resultant force in the compression zone 9 longitudinal reinforcement bars in the core beam of the compression zone Combined force of the longitudinal tension bars in the tension zone Substituting into the static equilibrium equation The height of the compression zone at the yield point of the composite beam is obtained by solving the problem. .

[0032] The core of this step is to accurately determine the height of the compression zone at yield in the composite beam by establishing and solving the static equilibrium equation of the cross-section. This is a key parameter for calculating the final flexural bearing capacity. First, the resultant force calculation of the tension longitudinal reinforcement 6 is based on its defined yield state: when the member reaches its yield bearing capacity, the tension longitudinal reinforcement 6 just reaches its yield strain. At this point, the stress in the tension longitudinal reinforcement 6 is equal to its standard yield strength, and the magnitude of the resultant force is equal to the yield strength multiplied by the total cross-sectional area of ​​the tension longitudinal reinforcement 6. The yield strength of the tension longitudinal reinforcement 6 can be obtained through standard material tensile tests, or it can be determined according to the grade and type of steel reinforcement as specified in current national standards.

[0033] Next, the resultant force of the three parts of the compression zone calculated in step b, along with the resultant force of the tension longitudinal reinforcement 6, is substituted into the static equilibrium equation to obtain an equation regarding the height of the compression zone. Since the resultant force of the equivalent unconfined concrete has a nonlinear relationship with the height of the compression zone (especially when the concrete at the edge of the compression zone reaches its peak strain and enters the elastoplastic stage), this equation is nonlinear and cannot be solved directly analytically; therefore, iterative numerical calculation is required. The specific implementation steps of the iterative method are as follows: First, based on the calculation formula for the compression zone height of ordinary reinforced concrete beams, and combined with the cross-sectional dimensions and reinforcement of this composite beam, assume a reasonable initial compression zone height value; Second, based on this initial compression zone height value, calculate the strain values ​​at each key location of the cross-section according to the method in step a; Third, calculate the resultant force of the three parts of the compression zone according to the method in step b, and superimpose them to obtain the total pressure, while simultaneously calculating the total tensile force in the tension zone; Fourth, compare the magnitudes of the total pressure in the compression zone and the total tensile force in the tension zone. If the total pressure is greater than the total tensile force, it indicates that the assumed compression zone height is too large and needs to be appropriately reduced; if the total pressure is less than the total tensile force, it indicates that the assumed compression zone height is too small and needs to be appropriately increased; Fifth, repeat the calculation process from step two to step four until the difference between the total pressure in the compression zone and the total tensile force in the tension zone is within the pre-set allowable error range. At this point, the compression zone height is the actual compression zone height when the composite beam yields.

[0034] The selection of the error range needs to be comprehensively determined based on the importance and accuracy requirements of the project, and is usually taken as 1% to 5%. For important building structures or bridge projects with high accuracy requirements, an error range of less than 1% can be used. Throughout the iterative calculation process, special attention should be paid to the reasonable range of the compression zone height. If the final calculated compression zone height exceeds the maximum compression zone height specified in the code, it indicates that the beam is an over-reinforced beam, which will experience brittle failure without warning and does not meet the applicable conditions of this method. The cross-sectional dimensions or reinforcement ratio need to be readjusted.

[0035] Step d: Based on the moment equilibrium condition of the cross section, the equivalent unconfined concrete bending moment in the compression zone, the equivalent confined concrete bending moment in the compression zone, the bending moment of the longitudinal reinforcement 9 in the core beam of the compression zone, and the bending moment of the tensile longitudinal reinforcement 6 in the tension zone are superimposed to derive the formula for calculating the yield flexural bearing capacity of the rectangular PVC-FRP pipe reinforced concrete composite beam.

[0036] In step d, the bending moments of each part about the neutral axis of the cross section are calculated using the following formula: Equivalent unconfined concrete bending moment in the compression zone. Equivalent confined concrete bending moment in the compression zone ; Bending moment of longitudinal reinforcement of core beam in compression zone 9 Tension zone longitudinal reinforcement 6 bending moment ;in, Let be the distance from the point of application of the resultant force of the equivalent confined concrete in the compression zone to the neutral axis. The distance from the point of application of the resultant force of the 9 longitudinal reinforcement bars in the compression zone core beam to the neutral axis. This is the distance from the point of application of the resultant force of the 6 longitudinal reinforcement bars in the tension zone to the neutral axis.

[0037] In step d, the yield flexural bearing capacity of the composite beam The sum of the bending moments of each part is: After substituting the calculation formulas for the bending moments of each part, the final calculation model for the yield flexural bearing capacity of the rectangular PVC-FRP pipe reinforced concrete composite beam is obtained.

[0038] This step is based on the fundamental principle of moment equilibrium in a cross-section. By superimposing the bending moments generated by the internal forces of each component about the neutral axis, the yield bending capacity of the composite beam is finally obtained. The principle of moment equilibrium states that at the instant the member reaches its yield capacity, the sum of the moments of all internal forces about any point in the cross-section is zero. This method specifically chooses to take the moments about the neutral axis, which completely avoids calculating the internal forces at the neutral axis, greatly simplifying the calculation process. The bending moment of each internal force about the neutral axis is equal to the magnitude of that internal force multiplied by the perpendicular distance from its point of application to the neutral axis; the total bending moment of the cross-section is the algebraic sum of the bending moments of each component.

[0039] First, the distance from the point of application of the resultant force to the neutral axis needs to be accurately determined: For equivalent unconfined concrete, the location of the point of application of the resultant force is determined by the centroid of the stress distribution diagram. In the elastic stage, the stress distribution is triangular, and the distance from the centroid to the edge of the compression zone is one-third of the height of the compression zone; therefore, the distance to the neutral axis is this value. In the elastoplastic stage, the stress distribution is curved, and the centroid location needs to be calculated by integration. In engineering applications, a simplified formula can be used directly for calculation. For equivalent confined concrete, the point of application of the resultant force is taken as the geometric centroid of the equivalent confined zone section, and the distance to the neutral axis is the absolute difference between the centroid coordinates and the neutral axis coordinates. For the longitudinal reinforcement 9 of the core beam, the point of application of the resultant force is the common centroid of all longitudinal reinforcements of the core beam, and the distance to the neutral axis is the absolute difference between the centroid coordinates and the neutral axis coordinates. For the tension longitudinal reinforcement 6, the point of application of the resultant force is the common centroid of the tension longitudinal reinforcement 6, and the distance to the neutral axis is the absolute difference between the neutral axis coordinates and the centroid coordinates of the tension longitudinal reinforcement 6.

[0040] Then, the bending moments about the neutral axis of each part of the internal forces are calculated separately. The bending moments generated by each part of the compression zone and the bending moments generated by the tension longitudinal reinforcement 6 are all positive bending moments, because both cause the lower part of the beam to be under tension and the upper part to be under compression, which is consistent with the stress characteristics of a bending member. The yield bending capacity of the composite beam is obtained by adding the bending moments of the four parts. The bearing capacity calculation formula obtained by this method fully considers the restraint and reinforcement effect of the PVC-FRP pipe on the concrete and the compressive contribution of the core beam longitudinal reinforcement 9. Compared with the traditional method of calculating the bearing capacity of reinforced concrete beams, the calculation results are more accurate, and the error can be controlled within 5%. It can provide a reliable theoretical basis for the engineering design of this new type of composite beam. This method is applicable to appropriately reinforced composite beams with PVC-FRP pipe reinforced concrete core beams 2 built into the compression zone of rectangular reinforced concrete beam 1, and can be directly applied to the structural design of industrial and civil buildings, urban bridges, rail transit and other fields.

[0041] In summary, this invention, through step a, utilizes the simplified equivalence principle of the compression zone to divide the concrete in the compression zone into an equivalent constrained zone and an equivalent unconstrained zone, and calculates the mid-span section strain separately. For the first time, it establishes a zonal calculation model based on the essential differences in the constrained state of concrete, quantitatively considering the effect of the circumferential constraint of the PVC-FRP pipe on the improvement of the mechanical properties of concrete, and solving the problem of low calculated values ​​caused by the traditional method treating the concrete in the compression zone as a homogeneous uniaxially stressed material. Through step b, based on the static equilibrium condition of the section, it calculates the resultant force of the equivalent unconstrained concrete in the compression zone, the resultant force of the equivalent constrained concrete, and the resultant force of the longitudinal reinforcement 9 of the core beam, correcting the deficiency of the traditional calculation method that ignores the contribution of the longitudinal reinforcement 9 of the core beam in the compression zone. Through step c, it establishes the internal force equilibrium equation of the section and... The iterative method is used to solve for the height of the compression zone at yield in composite beams. The calculation process is derived using the static equilibrium principle familiar to the engineering community, with clear physical meanings of the parameters, eliminating the need for complex finite element numerical analysis. Furthermore, the yield strain reached for the first time by the tensile longitudinal reinforcement 6 is explicitly used as the criterion for determining the yield bearing capacity. During the calculation process, the height of the compression zone is strictly controlled within the range of appropriately reinforced beams allowed by the code, effectively avoiding over-reinforced brittle failure and ensuring structural ductility and service safety. The final formula for calculating the yield flexural bearing capacity is derived by superimposing the bending moments of each part based on the moment equilibrium condition of the cross section in step d. This transforms the complex triaxial compressive stress state of PVC-FRP pipe-confined concrete into an equivalent uniaxial stress state, significantly simplifying the calculation process and making it easier for engineering designers to understand and apply.

[0042] Although embodiments of the invention have been shown and described, the scope of the invention will be defined by the appended claims and their equivalents by those skilled in the art.

Claims

1. A method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam, characterized in that, The rectangular PVC-FRP pipe reinforced concrete composite beam is a composite beam formed by embedding a PVC-FRP pipe reinforced concrete core beam (2) in the compression zone of a rectangular reinforced concrete (1) beam, and then arranging a reinforcing cage on the outside and pouring concrete. The calculation method for its flexural bearing capacity specifically includes the following steps: Step a: Using the principle of simplified equivalence of the compression zone, the concrete in the compression zone of the composite beam is divided into an equivalent confined zone and an equivalent unconfined zone. The mid-span section strain of the concrete in the equivalent confined zone and the concrete in the equivalent unconfined zone are calculated respectively. Step b: Based on the static equilibrium condition of the section, calculate the resultant force of the equivalent unconfined concrete in the compression zone, the resultant force of the equivalent confined concrete in the compression zone, and the resultant force of the longitudinal reinforcement (9) of the core beam in the compression zone. Step c: Calculate the resultant force of the tension longitudinal reinforcement (6) in the tension zone according to the internal force equilibrium equation of the cross section, and substitute the resultant force of each part to obtain the height of the compression zone when the composite beam yields; Step d: Based on the moment balance condition of the cross section, the equivalent unconfined concrete bending moment in the compression zone, the equivalent confined concrete bending moment in the compression zone, the bending moment of the longitudinal reinforcement (9) of the core beam in the compression zone, and the bending moment of the tensile longitudinal reinforcement (6) in the tension zone are superimposed to derive the formula for calculating the yield bending capacity of the rectangular PVC-FRP pipe reinforced concrete composite beam.

2. The method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam according to claim 1, characterized in that, The PVC-FRP pipe reinforced concrete core beam (2) includes a core beam body (4), core beam outer stirrups (10) wrapped around the core beam body (4), and tensile longitudinal bars (6) fixedly connected in the core beam outer stirrups (10). The core beam body (4) includes a PVC pipe (8), CFPR strips wrapped around the PVC pipe (8), and core beam longitudinal bars (9) and core beam stirrups arranged in the PVC pipe (8). In step a, the mid-span section strains of the equivalent confined zone concrete and the equivalent unconfined zone concrete satisfy the following relationship: Strain of tension longitudinal reinforcement (6) Strain of concrete at the edge of the compression zone The relationship is: The strain at the equivalent resultant point of the longitudinal reinforcement of the core beam (9) Strain of concrete at the edge of the compression zone The relationship is: Equivalent confined concrete strain in compression zone Strain of concrete at the edge of the compression zone The relationship is: in, This represents the distance from the neutral axis to the upper surface of the composite beam when it yields. The distance from the bottom tensile longitudinal reinforcement (6) to the top surface of the beam is denoted as . The distance from the equivalent resultant point of the longitudinal reinforcement (9) of the core beam to the upper surface of the beam is given by the following formula: This is the distance from the upper surface of the equivalent confined concrete zone to the edge of the beam's compression zone.

3. The method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam according to claim 1, characterized in that, In step b, the static equilibrium condition at the mid-span section of the composite beam when it yields is satisfied as follows: in, This represents the total resultant force in the compression zone when the composite beam yields. This represents the total resultant force in the tension zone when the composite beam yields.

4. The method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam according to claim 3, characterized in that, The total force in the pressure zone The equivalent unconfined concrete resultant force in the compression zone Equivalent confined concrete resultant force in the compression zone The combined force of the longitudinal reinforcement (9) of the core beam in the compression zone The sum of The total resultant force in the tension zone The resultant force of the longitudinal reinforcement (6) in the tension zone ,Right now .

5. The method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam according to claim 4, characterized in that, In step b, the equivalent unconfined concrete resultant force in the compression zone and the distance from the point of application of the resultant force to the neutral axis Calculations are performed under the following two conditions: when the concrete at the edge of the compression zone has not reached its peak strain, i.e. hour: When the concrete at the edge of the compression zone reaches or exceeds the peak strain, i.e. hour: in, This refers to the axial compressive strength of concrete. The width of the composite beam section. This represents the peak strain of the concrete.

6. The method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam according to claim 4, characterized in that, In step b, the equivalent confined concrete resultant force in the compression zone The calculation formula is: in, The elastic modulus of concrete. This represents the cross-sectional area of ​​the concrete in the equivalent confined zone.

7. The method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam according to claim 4, characterized in that, In step b, the resultant force of the longitudinal reinforcement (9) of the core beam in the compression zone... The calculation formula is: in, Let be the elastic modulus of the longitudinal reinforcement (9) of the core beam. The total cross-sectional area of ​​the longitudinal reinforcement (9) of the core beam.

8. The method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam according to claim 1, characterized in that, In step c, the resultant force of the tension longitudinal reinforcement (6) in the tension zone The calculation formula is: in, The elastic modulus of the tensile longitudinal reinforcement (6) is given by... The total cross-sectional area of ​​the tension longitudinal reinforcement (6); The equivalent unconfined concrete resultant force in the compression zone Equivalent confined concrete resultant force in the compression zone , The combined force of the longitudinal reinforcement of the core beam in the compression zone (9) The combined force of the tension longitudinal reinforcement (6) in the tension zone Substituting into the static equilibrium equation The height of the compression zone at the yield point of the composite beam is obtained by solving the problem. .

9. The method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam according to claim 1, characterized in that, In step d, the bending moment of each part about the neutral axis of the cross section is calculated using the following formula: equivalent unconfined concrete bending moment in the compression zone. Equivalent confined concrete bending moment in the compression zone ; Bending moment of longitudinal reinforcement (9) of core beam in compression zone ; Tension longitudinal reinforcement in the tension zone (6) Bending moment ;in, Let be the distance from the point of application of the resultant force of the equivalent confined concrete in the compression zone to the neutral axis. The distance from the point of application of the resultant force of the longitudinal reinforcement (9) of the core beam in the compression zone to the neutral axis. The distance from the point of application of the resultant force of the longitudinal reinforcement (6) in the tension zone to the neutral axis.

10. The method for calculating the flexural bearing capacity of a rectangular PVC-FRP pipe reinforced concrete composite beam according to claim 1, characterized in that, In step d, the yield flexural bearing capacity of the composite beam is... The sum of the bending moments of each part is: After substituting the calculation formulas for the bending moments of each part, the final calculation model for the yield flexural bearing capacity of the rectangular PVC-FRP pipe reinforced concrete composite beam is obtained.

Images