Prestressed FRP rib seawater and sea sand concrete beam and design method thereof

Abstract

The invention relates to a prestressed FRP rib seawater and sea sand concrete beam and a design method thereof, and belongs to the technical field of marine building engineering.The method comprises the steps that geometric, material and environmental parameters of components are obtained; on the basis of plane section assumption and a material constitutive relation, a normal section flexural capacity theoretical value is deduced, a bonding influence coefficient and a seawater concentration influence coefficient are introduced for correction, and the designed flexural capacity is obtained; sectional inertia moments of the component in different stages are calculated in a segmented mode, and a short-term rigidity theoretical model is established and corrected to calculate deflection; a maximum crack width theoretical model is established, a bonding influence coefficient is introduced for correction, the high strength of the prestressed FRP rib and the ductility of the SFCB rib are utilized, the problems that a conventional FRP rib beam is low in strength utilization rate and remarkable in brittle failure are solved, a set of accurate and practical design theory is provided, and the method is suitable for the marine environment.

Description

Technical Field

[0001] This invention relates to the field of building engineering technology, specifically to a prestressed FRP reinforced seawater sand concrete beam and its design method, which is particularly suitable for concrete structures in marine environments. Background Technology

[0002] In marine engineering, traditional reinforced concrete structures suffer from insufficient durability due to steel corrosion. Fiber-reinforced composite (FRP) bars, with their corrosion resistance and high strength, have become an ideal alternative to steel reinforcement. Furthermore, the direct use of seawater and sea sand in concrete preparation effectively addresses the shortage of river sand resources. However, FRP bars have a low modulus of elasticity, leading to larger deflections and crack widths in reinforced beams; moreover, as a linear elastic material, their failure is brittle and lacks early warning. More critically, limited by the ultimate compressive strain of concrete, the actual tensile strength utilization rate of FRP bars is typically less than 30%, resulting in material waste.

[0003] Applying prestress is an effective way to improve the utilization rate of FRP (fiberglass reinforced plastic) reinforcement and can significantly improve the load-bearing performance of beams. To improve ductility, steel-fiber composite (SFCB) reinforcement, due to its secondary stiffness after yielding, can provide good deformation capacity and failure indicators. However, studies have shown that SFCB reinforcement suffers significant prestress loss due to slippage at the interface between the internal fibers and the steel core, thus making it unsuitable for prestressing.

[0004] In terms of design theory, existing methods mostly follow the traditional reinforced concrete theory, without fully considering the bond-slip characteristics between FRP bars and concrete, the strengthening constitutive structure of SFCB bars, and the influence of the seawater environment, resulting in insufficient calculation accuracy and restricting the design and application of this type of component.

[0005] Therefore, there is an urgent need for a prestressed FRP reinforced seawater sand concrete beam and design method that combines reasonable reinforcement form with accurate design theory, so as to systematically solve the problems of durability, ductility and design accuracy in marine environment. Summary of the Invention

[0006] The purpose of this invention is to provide a prestressed FRP-reinforced seawater sand concrete beam and its design method, so as to solve the problems of low strength utilization rate of FRP-reinforced concrete beams, large deflection, large cracks, brittle failure and insufficient design accuracy in the prior art.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a prestressed FRP-reinforced seawater sand concrete beam and its design method, comprising: Obtain the geometric parameters, material parameters, and environmental parameters of the component; wherein, the material parameters include: parameters of prestressed fiber-reinforced composite reinforcement (FRP reinforcement), parameters of non-prestressed steel-continuous fiber composite reinforcement (SFCB reinforcement), and parameters of seawater sand concrete; the environmental parameters include seawater concentration; Based on the aforementioned geometric, material, and environmental parameters, and grounded in the plane section assumption and material constitutive relations, by equivalently converting prestressed FRP reinforcement and non-prestressed SFCB reinforcement according to their elastic modulus ratios, the horizontal force equilibrium equation and bending moment equilibrium equation of the cross section are established. Considering the linear elastic characteristics of the prestressed FRP reinforcement and the strengthening behavior of the SFCB reinforcement after yielding, the theoretical value of the flexural bearing capacity of the member under ultimate limit state is derived. Based on experimental and finite element analysis results, a bonding influence coefficient is introduced. ) and the influence coefficient of seawater concentration ( ), for the theoretical value After making corrections, the design flexural bearing capacity is obtained. ; The theoretical value of the normal section flexural bearing capacity of the component under the ultimate state is derived therefrom. Specifically, it includes: The theoretical value of the flexural bearing capacity of the normal section Calculate using the following formula: ; in, Prestressed FRP tendon stress Calculated based on linear elastic constitutive model: ; Stress of non-prestressed SFCB tendons Calculated based on the bilinear constitutive model after yielding: ; Concrete equivalent rectangular stress diagram height The height of the concrete compression zone The following quadratic equation is obtained by solving: ; Its coefficient is: ; ; ; The solution to the equation is: ; The symbols in the formula are defined as follows: Cross-sectional area of ​​prestressed FRP reinforcement and non-prestressed SFCB reinforcement; Effective height of prestressed FRP reinforcement and non-prestressed SFCB reinforcement; Effective prestress of prestressed FRP reinforcement; : The elastic modulus of prestressed FRP reinforcement; Yield strength and yield strain of non-prestressed SFCB reinforcement; : Elastic modulus of non-prestressed SFCB reinforcement after yielding; : Equivalent rectangular stress diagram coefficient for concrete, taken according to the standard; Design value of axial compressive strength of concrete; Width of the rectangular section; Ultimate compressive strain of concrete; The design bending bearing capacity mentioned above Calculated using the following formula: ; Wherein, the adhesion influence coefficient ( ) Calculated using the following formula: ; Because the bond strength between FRP bars and concrete is weaker than that of steel bars, the actual stress of FRP bars does not reach the theoretical value. This coefficient is needed to correct the overestimated bearing capacity. , These are the cross-sectional areas of prestressed FRP reinforcement and non-prestressed SFCB reinforcement, respectively. , These are their measured bond strengths, The standard bond strength is 2.5 MPa. Based on the aforementioned geometric, material, and environmental parameters, and considering the strain compatibility relationship of the SFCB stiffener double-splitter constitutive model using the transformed section method, the section moment of inertia and effective moment of inertia of the member are calculated in segments at three stages: before cracking, after cracking to yielding, and after yielding. A short-term stiffness theoretical model is then established. Based on experimental and finite element analysis results, a stiffness-bond influence coefficient is introduced. The theoretical model is modified to obtain the design short-term stiffness. And accordingly, the deflection of the component under use conditions is calculated; Determining the short-term stiffness and deflection of the component under service conditions specifically includes: Based on the transformed section method, the component is calculated piecewise under different bending moments ( Theoretical short-term stiffness at the level of ) ): when Theoretical short-term stiffness at time (before cracking) ,in To convert the moment of inertia of the cross section; when Theoretical short-term stiffness (from cracking to SFCB bar yielding) ,in The effective moment of inertia is calculated based on the pre-yield parameters of the SFCB reinforcement. when Theoretical short-term stiffness at time (after SFCB reinforcement yielding) ,in The effective moment of inertia is calculated based on the post-yield parameters of the SFCB reinforcement. Calculate the stiffness-bond influence coefficient ( ), and only the theoretical short-term stiffness in the post-cracking stage is modified to obtain the design short-term stiffness ( ): ; According to the design short-term stiffness ( ), calculate the deflection of the component under a given load condition; for a simply supported beam subjected to three-point loading, its maximum deflection at mid-span ( Calculate using the following formula: ; in, This refers to the load value at a single loading point. The calculated span of the beam; To correspond to this load level Design short-term stiffness; The equivalent stress of the steel bars ( Calculated using the following formula: ; in, The design value of the bending moment generated by the external load; The stress-relieving bending moment of the component; As the internal lever arm, take , This is the internal lever arm coefficient, with a value ranging from 0.83 to 0.90; The equivalent reinforcement area is calculated based on the elastic modulus of SFCB reinforcement after yielding: ; The average crack spacing ( Calculated using the following formula: ; in, To account for the correction factor for prestress, ; It is the distance from the outermost edge of the longitudinal tension reinforcement to the bottom edge of the tension zone; For the equivalent diameter of the reinforcing bar, ; The reinforcement ratio is calculated based on the effective tensile concrete cross-sectional area. , ; The strain non-uniformity coefficient between cracks ( Calculated using the following formula: ; in, This refers to the standard value of the tensile strength of concrete. This is a coefficient related to the properties of SFCB reinforcement, with a value ranging from 0.5 to 0.7; Based on the aforementioned geometric parameters, material parameters, and environmental parameters, and considering the equivalent stress of the reinforcing steel under stress relief, average crack spacing, and strain non-uniformity coefficient, a theoretical value for the maximum crack width is established. The calculation model is based on experimental and finite element analysis results, and a crack width bond influence coefficient is introduced. The theoretical value is then corrected to obtain the maximum design crack width. ; The theoretical maximum crack width was calculated ( After that, the crack width bond influence coefficient is introduced. The design maximum crack width is obtained by correcting the crack width. ): ; Because poor bond performance leads to increased crack spacing and reduced concrete contribution between cracks, this coefficient is needed to correct the underestimated crack width; wherein, the crack width bond influence coefficient ( Calculated using the following formula: .

[0008] Preferably, the seawater concentration influence coefficient ( ) Calculated using the following formula: ; Because the mechanical properties of seawater-sand concrete systematically deteriorate with increasing salt concentration, this coefficient is needed to correct for the overestimated bearing capacity; among which, The concentration is for seawater; 0% represents freshwater, and 100% represents all seawater.

[0009] Preferably, the stiffness-bond influence coefficient ( Calculated using the following formula: ; Because bond slip weakens the synergistic effect between FRP reinforcement and concrete, leading to a decrease in the actual stiffness of the member, this coefficient is needed to correct the overestimated stiffness; among which, , These are the cross-sectional areas of prestressed FRP reinforcement and non-prestressed SFCB reinforcement, respectively. , These are their measured bond strengths, The standard bond strength is 2.5 MPa.

[0010] Preferably, the effective moment of inertia ( , Calculated using Branson's formula: ; in, The moment of inertia of the concrete gross section; The moment of inertia of the cracked section is calculated using the following steps: Solve for the neutral axis height under cracked conditions. : ; Calculate the moment of inertia of the cracked section : ; The symbols in the formula are defined as follows: Cracking moment of the component; : The elastic modulus ratio of prestressed FRP reinforcement; The elastic modulus ratio of non-prestressed SFCB reinforcement is used in calculations. (for) (When taking) In calculation (for) (When taking) ; : Elastic modulus of non-prestressed SFCB reinforcement before and after yielding; : Elastic modulus of seawater sand concrete.

[0011] Preferably, determining the maximum crack width of the component under use specifically includes: Based on the plane section assumption, after considering the decompression bending moment, the equivalent stress of the reinforcement in the crack section is calculated. ); Based on the geometric and reinforcement parameters of the component, calculate the average crack spacing ( ) and the coefficient of strain inhomogeneity between cracks ( ); Based on the equivalent stress of the steel reinforcement ( ), average crack spacing ( ) and the coefficient of strain non-uniformity between cracks ( ), calculate the theoretical maximum crack width ( ): ; in, The stress characteristic coefficient of the component is taken as 1.9 for bending. This refers to the elastic modulus of the steel reinforcement.

[0012] Preferably, after obtaining the designed flexural bearing capacity The design short-term stiffness With deflection, and the maximum design crack width The method then includes a design verification and iteration step: The design flexural bearing capacity Design value of bending moment generated by external load Comparison, requirements to be met The ultimate limit state requirement of bearing capacity; the calculated deflection Deflection limits under the corresponding usage environment and working conditions specified in the standard. Comparison, requirements to be met The maximum crack width of the design. Crack width limits as specified in the standard for the corresponding use environment and working conditions. Comparison, requirements to be met ; If any of the above conditions are not met, then adjust one or more of the following design parameters and repeat the steps of the prestressed FRP-reinforced seawater sand concrete beam and its design method as described in claim 1 until all conditions are met: increase the reinforcement area of ​​the prestressed FRP reinforcement and / or non-prestressed SFCB reinforcement ( Increase the tension control stress of prestressed FRP tendons ( Increase the cross-sectional dimensions of the beam, including the cross-sectional width ( or / and section height ( .

[0013] Preferably, the prestressed FRP-reinforced seawater sand concrete beam is specifically configured as follows: The bottom of the beam is provided with prestressed longitudinal reinforcement and non-prestressed longitudinal reinforcement; The prestressed longitudinal reinforcement uses FRP bars to apply prestress in order to control the crack width and deflection of the beam during the service stage. The non-prestressed longitudinal reinforcement uses SFCB reinforcement, which utilizes the deformation capacity of SFCB reinforcement in the yield hardening stage to improve the brittle failure that may occur in the beam due to the linear elasticity and lack of yield stage of FRP reinforcement, and provides significant signs of failure. The beam is also equipped with stirrups and gusset bars. The stirrups and gusset bars are all made of FRP bars, which together with the prestressed FRP bars and SFCB bars form a full fiber composite reinforcement skeleton. The concrete is fiber-reinforced high-performance seawater sand concrete. The fibers include one or more of basalt fibers, polypropylene fibers, polyvinyl alcohol fibers, carbon fibers, and aramid fibers to adapt to the marine environment and utilize locally sourced materials, while improving the toughness and crack resistance of the concrete. The diameters of the FRP bars and SFCB bars are not less than 8mm and not more than 40mm; The net spacing between the outer surfaces of the FRP and SFCB reinforcement bars shall not be less than 2.5 times their diameter; The minimum distance from the outermost edge of the FRP bar and SFCB bar to the surface of the fiber-reinforced marine sand concrete shall not be less than 15mm; The FRP reinforcement includes any one of carbon fiber reinforced composite (CFRP), glass fiber reinforced composite (GFRP), and aramid fiber reinforced composite (AFRP); In the fiber-reinforced high-performance seawater sand concrete, the total volumetric content of the fiber is 0.5% to 3.0%. The prestressing control stress of the prestressed FRP bar is 50% to 80% of its tensile strength; The diameter of the FRP bars for the stirrups and braces shall not be less than 6mm; The spacing of the stirrups is 1 / 4 to 1 / 2 of the beam height.

[0014] Secondly, the present invention provides a prestressed FRP-reinforced seawater sand concrete beam design device for operating the prestressed FRP-reinforced seawater sand concrete beam and its design method, comprising: The parameter acquisition module is used to acquire the geometric parameters, material parameters, and environmental parameters of the component; wherein, the material parameters include prestressed FRP reinforcement parameters, non-prestressed SFCB reinforcement parameters, and seawater sand concrete parameters; the environmental parameters include seawater concentration; The load-bearing capacity calculation module is used to determine the flexural bearing capacity of the component under the ultimate limit state based on the geometric parameters, material parameters, environmental parameters and correction coefficients. The stiffness and deflection calculation module is used to determine the short-term stiffness and deflection of the component under service conditions based on the geometric parameters, material parameters, environmental parameters and correction coefficients. The crack control module is used to determine the maximum crack width of the component under service conditions based on the geometric parameters, material parameters, environmental parameters, and correction coefficients.

[0015] Thirdly, the present invention provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it realizes a prestressed FRP reinforced seawater sand concrete beam and its design method.

[0016] Fourthly, the present invention provides a computer-readable storage medium, characterized in that it stores a computer program thereon, which, when executed by a processor, realizes a prestressed FRP-reinforced seawater sand concrete beam and its design method.

[0017] The present invention has the following beneficial effects: 1. By coordinating the configuration of prestressed FRP reinforcement and non-prestressed SFCB reinforcement, the crack width and deflection of the beam were effectively controlled, brittle failure was improved, and obvious signs of failure were provided. 2. The use of a full fiber composite reinforcement skeleton and fiber-reinforced seawater sand concrete fundamentally solves the problem of steel corrosion and improves the durability of the structure. 3. The design method incorporates the bonding influence coefficient and the seawater concentration influence coefficient, which improves the accuracy of the calculation of flexural bearing capacity, stiffness and crack width, and is highly practical. 4. This invention is applicable to marine environments, uses locally sourced materials, is economical and environmentally friendly, and has broad application prospects. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the prestressed FRP-reinforced seawater sand concrete beam of the present invention; Figure 2 This is a flowchart of the design method of the present invention; Figure 3 A loading schematic diagram of an embodiment of a prestressed FRP-reinforced seawater sand concrete beam provided by the present invention; Figure 4 This is a comparison chart of the theoretical and experimental values ​​of deflection change in Experiment Example 1 of the present invention; Figure 5 This is a comparison chart of the theoretical and experimental values ​​of deflection change in Experiment Example 2 of the present invention; Figure 6This is a comparison chart of the theoretical and experimental values ​​of deflection change in Experiment Example 3 of the present invention; Figure 7 This is a comparison chart of the theoretical and experimental values ​​of crack width development in Experiment Example 1 of the present invention; Figure 8 This is a comparison chart of the theoretical and experimental values ​​of crack width development in Experimental Example 2 of the present invention; Figure 9 This is a comparison chart of the theoretical and experimental values ​​of crack width development in Experimental Example 3 of the present invention; Figure 1 In the middle: 1-Fiber reinforced high-performance seawater sand concrete; 2-Non-prestressed SFCB longitudinal reinforcement; 3-Prestressed FRP longitudinal reinforcement; 4-FRP stirrups; 5-FRP hoop reinforcement. Detailed Implementation

[0019] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be noted that the technical solution and design principle of the present invention will be described in detail below using only one optimized technical solution.

[0020] The embodiments described above are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

[0021] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0022] Example 1: This embodiment details the application of the design method proposed in this invention in a prestressed FRP-reinforced seawater sand concrete beam. The beam is a simply supported beam with a rectangular cross-section, and it employs a three-point loading method.

[0023] 1. Obtaining Design Parameters First, obtain the geometric parameters, material parameters, and environmental parameters of the component.

[0024] Geometric parameters: section width b, section height h, calculated span l, effective height hp of prestressed tendons, effective height h of non-prestressed tendons 0；材料参数：预应力FRP reinforcement: cross-sectional area Ap, elastic modulus Etp, effective prestress σp0, tensile strength ftpκ; non-prestressed SFCB reinforcement: cross-sectional area As, yield strength fsy, yield strain εsy, pre-yield elastic modulus EI, post-yield elastic modulus EII. Concrete parameters: design value of axial compressive strength fc, elastic modulus Ec, ultimate compressive strain εcu, standard value of tensile strength ftk, fiber volume fraction, stirrup spacing, and other structural parameters; environmental parameters: seawater concentration c.

[0025] 2. Calculation of flexural capacity of normal section Based on the geometric parameters, material parameters, and environmental parameters, and using the plane section assumption and material constitutive relations, the bending capacity of the component under the limit state is derived.

[0026] Step 2.1: Calculate the height xc of the concrete compression zone. The height xc of the concrete compression zone is obtained by solving the following quadratic equation:

[0027] The coefficients are calculated as follows:

[0028]

[0029]

[0030] The solution to the equation is:

[0031] Step 2.2: Calculate the stress in the reinforcing bars The stress σtp of prestressed FRP tendons is calculated according to the linear elastic constitutive model:

[0032] The stress σsf of the non-prestressed SFCB tendon is calculated based on the bilinear constitutive model after yielding:

[0033] Step S203: Calculate the theoretical flexural bearing capacity Mu The theoretical value of the flexural bearing capacity Mu of the normal section is calculated according to the following formula:

[0034] Step S204: Calculate the correction factor and obtain the design bearing capacity.

[0035] Calculate the bond influence coefficient γbond, M:

[0036] Calculate the seawater concentration influence coefficient γseawater:

[0037] The theoretical value Mu is corrected to obtain the design flexural bearing capacity. :

[0038] 3. Short-term stiffness and deflection calculation Based on the geometric parameters, material parameters, and environmental parameters, the short-term stiffness and deflection of the component under service conditions are determined.

[0039] Step 3.1: Calculate the cracking moment Mcr and the yield moment My The cracking moment Mcr of the member is calculated using the transformed section method. Based on the plane section assumption and the constitutive relation of the SFCB reinforcement, its yield moment My is calculated.

[0040] Step 3.2: Calculate the theoretical short-term stiffness Bs in segments Based on the transformed section method, the theoretical short-term stiffness (Bs) of the component under different bending moment (M) levels is calculated piecewise: when Theoretical short-term stiffness at time (before cracking) ,in To convert the moment of inertia of the cross section.

[0041] when Theoretical short-term stiffness (from cracking to SFCB bar yielding) ,in The effective moment of inertia is calculated based on the pre-yield parameters of the SFCB reinforcement.

[0042] when Theoretical short-term stiffness at time (after SFCB reinforcement yielding) ,in The effective moment of inertia is calculated based on the post-yield parameters of the SFCB reinforcement.

[0043] The effective moment of inertia (IeI, IeII) is calculated using Branson's formula:

[0044] The moment of inertia Icr of the cracked section needs to be calculated separately according to different elastic modulus ratios (E1 / Ec before yielding and EII / Ec after yielding).

[0045] Step 3.3: Correct the theoretical stiffness to obtain the design stiffness

[0046] Calculate the stiffness-bond influence coefficient γbond, B:

[0047] Only the theoretical short-term stiffness in the post-cracking stage is modified to obtain the design short-term stiffness ( ):

[0048] Step 3.4: Calculate the deflection under operating conditions. According to the design short-term stiffness ( ), calculate the deflection of the component under a given load condition. For a simply supported beam subjected to three-point loading, the maximum mid-span deflection (f) is calculated using the following formula:

[0049] Where P is the load value at a single loading point. Through this process, the theoretical load-deflection curve of the entire process of the component can be plotted.

[0050] 4. Calculation of maximum crack width Based on the geometric parameters, material parameters, and environmental parameters, the maximum crack width of the component under service conditions is determined.

[0051] Step 4.1: Calculate the equivalent stress σsk of the reinforcement at the crack section.

[0052] Where M is the design value of the bending moment generated by the external load; M 0为构件的消压弯矩； z is the internal lever arm, take z = ηh 0，η为内力臂系数； Equivalent reinforcement area:

[0053] Step 4.2: Calculate the average crack spacing (lm).

[0054] Where βp is a correction factor considering prestress. c is the thickness of the protective layer; deq is the equivalent diameter of the reinforcing steel; ρte is the reinforcement ratio calculated based on the effective tensile concrete cross-sectional area.

[0055] Step 4.3: Calculate the strain non-uniformity coefficient ψ between cracks

[0056] Wherein, κ is a coefficient related to the properties of SFCB reinforcement.

[0057] Step 4.4: Calculate the theoretical maximum crack width wmax

[0058] Step 4.5: Correct the theoretical value to obtain the design crack width

[0059] Calculate the bond influence coefficient γbond,w for crack width:

[0060] The theoretical value was corrected to obtain the maximum design crack width. :

[0061] This process allows for the plotting of theoretical curves showing crack width development in the component under different bending moment levels.

[0062] Experimental Example 1: This experimental example designs a prestressed FRP-reinforced seawater sand concrete beam, the schematic diagram of which is shown below. Figure 1 For details of the cross-section reinforcement, please refer to [link / reference]. Figure 4 Calculated span of the beam It is 1800mm, and the cross-sectional dimensions are... The beam structure uses fiber-reinforced high-performance seawater sand concrete with a design strength grade of C80, which incorporates 1% of mixed fibers (0.4% basalt fiber and 0.6% polypropylene fiber) to improve the toughness and crack resistance of the concrete.

[0063] The reinforcement design of the beam is as follows: a 14mm diameter prestressed CFRP bar is used as the prestressed longitudinal reinforcement in the bottom tension zone, and its tensile strength is [not specified]. 2000MPa, elastic modulus The effective prestress is 150 GPa, the tension control stress is taken as 1300 MPa, and the effective prestress is... The yield strength is 1100 MPa; two SFCB bars with a diameter of 14 mm are also configured as non-prestressed longitudinal reinforcements, with a yield strength of 1100 MPa. The elastic modulus before yielding is 450 MPa. The elastic modulus after yielding is 200 GPa. The pressure is 20 GPa. Both stirrups and stirrup bars are made of FRP material, with stirrups being 8mm diameter GFRP bars spaced 160mm apart, and stirrup bars consisting of two 12mm diameter GFRP bars. The concrete cover thickness for all longitudinal reinforcement is 20mm.

[0064] This test case uses a three-point loading method for performance verification. See the loading diagram below. Figure 3 The two loading points are 600mm apart and share the total load. .based on Figure 2The design process shown is used to design and verify the load-bearing capacity, stiffness, and crack width of the beam.

[0065] First, parameters are obtained. In addition to the geometric and material parameters mentioned above, the environmental parameter is the seawater concentration. The average bond strength between the FRP reinforcement and the concrete was measured. Average bond strength between SFCB reinforcement and concrete Standard bond strength Subsequently, based on the plane section assumption and material constitutive relations, the section equilibrium equations were established, and the height of the concrete compression zone was calculated. Prestressed CFRP tendon stress Stress of non-prestressed SFCB tendons Then, the theoretical value of the flexural bearing capacity of the normal section and the influence coefficient of seawater concentration were obtained. After correction, the design flexural bearing capacity and the corresponding ultimate load are obtained. .

[0066] In the stiffness and deflection calculations, the cracking moment and the yield moment of the SFCB reinforcement are first calculated. Then, the short-term stiffness of the beam is calculated piecewise based on the transformed section method, and the stiffness-bond influence coefficient is introduced. The stiffness after cracking is corrected to obtain the design short-term stiffness. The load-deflection curve calculated based on this stiffness is compared with the experimentally measured values, for example... Figure 4 As shown, the two match well, verifying the accuracy of the stiffness model.

[0067] Regarding crack control, the stress-relief bending moment was calculated. Under the bending moment corresponding to the service condition, the equivalent stress in the reinforcing steel was calculated. Average crack spacing and strain non-uniformity coefficient The theoretical maximum crack width was obtained. Then, the crack width bond influence coefficient is introduced. After making corrections, the final design maximum crack width was obtained. The obtained theoretical prediction curve and the crack development observed in the experiment ( Figure 7 This is consistent with the results, verifying the accuracy of the crack prediction model.

[0068] Loading tests conducted on this example beam showed that the beam ultimately failed due to the crushing of the concrete in the compression zone. Furthermore, the non-prestressed SFCB reinforcement had already entered the strengthening stage before failure, providing clear signs of plastic deformation and potential failure, effectively improving the brittle characteristics of the pure FRP-reinforced beam. The measured ultimate bearing capacity was 242 kN, with a relative error of 2.6% compared to the corrected theoretical prediction of 235.7 kN (see Table 1). Within the service load range, the beam's deflection and crack width were effectively controlled, demonstrating good consistency between theoretical calculations and measured results. Figure 4 , Figure 7 This fully demonstrates the effectiveness and reliability of the design method of the present invention in predicting the mechanical behavior of components and ensuring their performance.

[0069] Experimental Example 2: This experimental example aims to compare and study the effects of different loading methods on beam performance and to verify the applicability of the design method of this invention under single-point loading at mid-span. The beam material, cross-sectional dimensions, and reinforcement scheme used in this experimental example are exactly the same as those in Experiment 1.

[0070] The core difference between this experimental example and Experiment 1 lies in the loading method, such as... Figure 3 As shown, the three-point loading is changed to a single-point loading across the mid-span. Load It acts directly at the mid-span of the beam. Based on Figure 2 The design process shown involves recalculating and verifying the beam. First, during the parameter acquisition phase, the loading type is clearly defined as "single-point load at mid-span". Then, in the flexural capacity calculation, since the section reinforcement remains unchanged, the theoretical value of its ultimate limit state flexural capacity is... and the design values ​​after correction for the effects of bonding and seawater concentration. Similar to Example 1, both are [values ​​missing]. However, due to the change in loading method, the corresponding ultimate load is [value missing]. The calculation method changes accordingly, and the calculation formula is as follows: Calculations yielded .

[0071] In stiffness and deflection calculations, cracking moment and SFCB reinforcement yield moment The numerical value remains unchanged, but the calculation of short-term stiffness, especially the effective moment of inertia after cracking, needs to be based on the bending moment diagram under mid-span loading. According to the design method of this invention, for a simply supported beam under single-point loading at mid-span, the formula for calculating the maximum deflection at mid-span is: Calculations show that, under the same total load... The mid-span deflection of the beam under mid-span loading is greater than that of the beam under tri-point loading, due to its more concentrated bending moment distribution. After correction by introducing a corresponding stiffness-bond influence coefficient, the calculated load-deflection curve also shows good agreement with the experimentally measured values ​​(see...). Figure 5This further verifies the adaptability of the stiffness calculation model to different load types.

[0072] In crack width calculation, pressure relief bending moment The average crack spacing remains unchanged. Under the same applied bending moment, the difference in the length of the pure bending segment compared to the three-point loading results in different average crack spacings. and strain non-uniformity coefficient The calculated results differ from those in Experimental Example 1. The final calculated design maximum crack width... The crack width is slightly larger than that in Experiment 1 under the same bending moment. The crack distribution observed in the experiment also confirms that under mid-span loading, the cracks are more concentrated in the pure bending section at mid-span, and the crack width development is consistent with theoretical predictions (see...). Figure 8 ).

[0073] The results of the mid-span loading test on this beam showed that its failure mode was similar to that of Test Example 1, both exhibiting crushing of the concrete in the compression zone accompanied by yielding hardening of the SFCB reinforcement, demonstrating good ductile failure characteristics. The measured ultimate bearing capacity was... , compared with theoretical predictions The relative error is 3.4%, indicating extremely high precision. Under operating conditions, the deflection and crack width increase depending on the loading method, and the theoretical calculation values ​​are in high agreement with the measured values.

[0074] The results of this experiment demonstrate that the design method proposed in this invention is not only applicable to three-point loading, but also has accurate predictive capabilities for other typical load conditions such as single-point loading at mid-span, showcasing its wide applicability and practical engineering value.

[0075] Experimental Example 3: This experimental example aims to verify the applicability of the structural form and design method proposed in this invention to beams of different sizes, especially larger spans. Its basic structural form is the same as in Experimental Example 1, but the geometric dimensions of the beam are significantly increased. The specific design is as follows: Calculated span of the beam. Increased to 3300mm, cross-sectional dimensions adjusted to To withstand greater self-weight and loads, the beam structure still uses fiber-reinforced high-performance seawater sand concrete with a design strength grade of C80, and the fiber content remains consistent with that of Experimental Example 1.

[0076] To accommodate the increased cross-section and internal forces, the reinforcement scheme was adjusted accordingly. Two 16mm diameter prestressed CFRP bars were used in the bottom tension zone, with material properties identical to those in Experimental Example 1. The non-prestressed longitudinal reinforcement was increased to three 16mm diameter SFCB bars. Stirrups were 10mm diameter GFRP bars spaced 150mm apart; stirrups were two 14mm diameter GFRP bars. The protective layer thickness for all longitudinal reinforcement remained at 20mm. The loading method was the same as in Experimental Example 1, using a three-point loading method with a spacing of 1100mm between the two loading points.

[0077] The design method of this invention was applied to perform design calculations on this large-size beam. During the parameter acquisition phase, all geometric parameters were updated. In the flexural bearing capacity calculation, due to the increase in reinforcement and section height, the calculated height of the concrete compression zone was adjusted. Theoretical value of flexural bearing capacity of normal section Significantly improved. After correction for the same bonding and seawater concentration influence coefficients, the design flexural bearing capacity and the corresponding ultimate load were obtained. .

[0078] In stiffness and deflection calculations, the cracking moment is calculated. Due to the increased span, deflection control becomes a more critical design factor. The effective moment of inertia at each stage is calculated using the segmented stiffness model proposed in this invention. After correction using a stiffness-bond influence coefficient, the maximum mid-span deflection under the design load is calculated. The load-deflection curve obtained from the theoretical calculations shows a consistent trend with the results obtained from subsequent experimental measurements (see...). Figure 6 This verifies the effectiveness of the stiffness model for components of different sizes.

[0079] Regarding crack control, the stress-relief bending moment was calculated. Under the equivalent service bending moment, the maximum design crack width was calculated. The observed cracks were uniformly distributed, and the final crack width was close to the calculated value (see...). Figure 9 This indicates that the crack width calculation model proposed in this invention also has high accuracy for large-sized components.

[0080] Table 1. Comparison of theoretical and experimental values ​​of flexural bearing capacity in Experimental Examples 1 to 3 of this invention ; Loading tests conducted on this large-sized beam showed that its failure mode still exhibited the characteristics of ductile failure, namely, crushing of the concrete in the compression zone and ductile failure of the non-prestressed SFCB reinforcement entering the strengthening stage. This demonstrates the ductile performance of this structural form at different scales. The measured ultimate bearing capacity was... , compared with theoretical predictions The relative error was 2.5%. In terms of performance, the development of deflection and crack width both met the design expectations and were in good agreement with the theoretical values.

[0081] The results of this experiment demonstrate that the prestressed FRP-reinforced seawater sand concrete beam and its design method proposed in this invention possess excellent scalability. By adjusting the design parameters, this technology can be successfully applied to components with larger spans. The design method maintains high calculation accuracy and reliability even with dimensional changes, providing strong technical support for its widespread application in practical engineering.

[0082] In summary, this experimental example demonstrates that the prestressed FRP-reinforced seawater sand concrete beam structure proposed in this invention is reasonable and successfully integrates high durability with good ductility. Its supporting design method is scientific, precise, and highly practical, providing a solid theoretical basis and design tool for the engineering application of this type of component in harsh environments such as the ocean.

[0083] The above description is merely a preferred experimental method of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A prestressed FRP-reinforced seawater sand concrete beam and its design method, characterized in that, include: Obtain the geometric parameters, material parameters, and environmental parameters of the component; wherein, the material parameters include: parameters of prestressed fiber-reinforced composite reinforcement (FRP reinforcement), parameters of non-prestressed steel-continuous fiber composite reinforcement (SFCB reinforcement), and parameters of seawater sand concrete; the environmental parameters include seawater concentration; Based on the aforementioned geometric, material, and environmental parameters, and grounded in the plane section assumption and material constitutive relations, by equivalently converting prestressed FRP reinforcement and non-prestressed SFCB reinforcement according to their elastic modulus ratios, the horizontal force equilibrium equation and bending moment equilibrium equation of the cross section are established. Considering the linear elastic characteristics of the prestressed FRP reinforcement and the strengthening behavior of the SFCB reinforcement after yielding, the theoretical value of the flexural bearing capacity of the member under ultimate limit state is derived. Based on experimental and finite element analysis results, a bonding influence coefficient is introduced. ) and the influence coefficient of seawater concentration ( ), for the theoretical value After making corrections, the design flexural bearing capacity is obtained. ; The theoretical value of the normal section flexural bearing capacity of the component under the ultimate state is derived therefrom. Specifically, it includes: The theoretical value of the flexural bearing capacity of the normal section Calculate using the following formula: ; in, Prestressed FRP tendon stress Calculated based on linear elastic constitutive model: ; Stress of non-prestressed SFCB tendons Calculated based on the bilinear constitutive model after yielding: ; Concrete equivalent rectangular stress diagram height The height of the concrete compression zone The following quadratic equation is obtained by solving: ; Its coefficient is: ; ; ; The solution to the equation is: ; The symbols in the formula are defined as follows: Cross-sectional area of ​​prestressed FRP reinforcement and non-prestressed SFCB reinforcement; Effective height of prestressed FRP reinforcement and non-prestressed SFCB reinforcement; Effective prestress of prestressed FRP reinforcement; : The elastic modulus of prestressed FRP reinforcement; Yield strength and yield strain of non-prestressed SFCB reinforcement; : Elastic modulus of non-prestressed SFCB reinforcement after yielding; : Equivalent rectangular stress diagram coefficient for concrete, taken according to the standard; Design value of axial compressive strength of concrete; Width of the rectangular section; Ultimate compressive strain of concrete; The design bending bearing capacity mentioned above Calculated using the following formula: ； Wherein, the adhesion influence coefficient ( ) Calculated using the following formula: ; Because the bond strength between FRP bars and concrete is weaker than that of steel bars, the actual stress of FRP bars does not reach the theoretical value. This coefficient is needed to correct the overestimated bearing capacity. , These are the cross-sectional areas of prestressed FRP reinforcement and non-prestressed SFCB reinforcement, respectively. , These are their measured bond strengths, The standard bond strength is 2.5 MPa. Based on the aforementioned geometric, material, and environmental parameters, and considering the strain compatibility relationship of the SFCB stiffener double-splitter constitutive model using the transformed section method, the section moment of inertia and effective moment of inertia of the member are calculated in segments at three stages: before cracking, after cracking to yielding, and after yielding. A short-term stiffness theoretical model is then established. Based on experimental and finite element analysis results, a stiffness-bond influence coefficient is introduced. The theoretical model is modified to obtain the design short-term stiffness. And accordingly, the deflection of the component under use conditions is calculated; Determining the short-term stiffness and deflection of the component under service conditions specifically includes: Based on the transformed section method, the component is calculated piecewise under different bending moments ( Theoretical short-term stiffness at the level of ) ): when Theoretical short-term stiffness at time (before cracking) ,in To convert the moment of inertia of the cross section; when Theoretical short-term stiffness (from cracking to SFCB bar yielding) ,in The effective moment of inertia is calculated based on the pre-yield parameters of the SFCB reinforcement. when Theoretical short-term stiffness at time (after SFCB reinforcement yielding) ,in The effective moment of inertia is calculated based on the post-yield parameters of the SFCB reinforcement. Calculate the stiffness-bond influence coefficient ( ), and only the theoretical short-term stiffness in the post-cracking stage is modified to obtain the design short-term stiffness ( ): ； According to the design short-term stiffness ( ), calculate the deflection of the component under a given load condition; for a simply supported beam subjected to three-point loading, its maximum deflection at mid-span ( Calculate using the following formula: ; in, This refers to the load value at a single loading point. The calculated span of the beam; To correspond to this load level Design short-term stiffness; The equivalent stress of the steel bars ( Calculated using the following formula: ; in, The design value of the bending moment generated by the external load; The stress-relieving bending moment of the component; As the internal lever arm, take , This is the internal lever arm coefficient, with a value ranging from 0.83 to 0.90; The equivalent reinforcement area is calculated based on the elastic modulus of SFCB reinforcement after yielding: ； The average crack spacing ( Calculated using the following formula: ; in, To account for the correction factor for prestress, ; It is the distance from the outermost edge of the longitudinal tension reinforcement to the bottom edge of the tension zone; For the equivalent diameter of the reinforcing bar, ; The reinforcement ratio is calculated based on the effective tensile concrete cross-sectional area. , ; The strain non-uniformity coefficient between cracks ( Calculated using the following formula: ; in, This refers to the standard value of the tensile strength of concrete. This is a coefficient related to the properties of SFCB reinforcement, with a value ranging from 0.5 to 0.7; Based on the aforementioned geometric parameters, material parameters, and environmental parameters, and considering the equivalent stress of the reinforcing steel under stress relief, average crack spacing, and strain non-uniformity coefficient, a theoretical value for the maximum crack width is established. The calculation model is based on experimental and finite element analysis results, and a crack width bond influence coefficient is introduced. The theoretical value is then corrected to obtain the maximum design crack width. ; The theoretical maximum crack width was calculated ( After that, the crack width bond influence coefficient is introduced. The design maximum crack width is obtained by correcting the crack width. ): ; Because poor bond performance leads to increased crack spacing and reduced concrete contribution between cracks, this coefficient is needed to correct the underestimated crack width; wherein, the crack width bond influence coefficient ( Calculated using the following formula: 。 2. The prestressed FRP-reinforced seawater sand concrete beam and its design method according to claim 1, characterized in that, The seawater concentration influence coefficient ( ) Calculated using the following formula: ; Because the mechanical properties of seawater-sand concrete systematically deteriorate with increasing salt concentration, this coefficient is needed to correct for the overestimated bearing capacity; among which, The concentration is for seawater; 0% represents freshwater, and 100% represents all seawater.

3. The prestressed FRP-reinforced seawater sand concrete beam and its design method according to claim 1, characterized in that, The stiffness-bonding influence coefficient ( Calculated using the following formula: ; Because bond slip weakens the synergistic effect between FRP reinforcement and concrete, leading to a decrease in the actual stiffness of the member, this coefficient is needed to correct the overestimated stiffness; among which, , These are the cross-sectional areas of prestressed FRP reinforcement and non-prestressed SFCB reinforcement, respectively. , These are their measured bond strengths, The standard bond strength is 2.5 MPa.

4. The prestressed FRP-reinforced seawater sand concrete beam and its design method according to claim 1, characterized in that, The effective moment of inertia ( , Calculated using Branson's formula: ; in, The moment of inertia of the concrete gross section; The moment of inertia of the cracked section is calculated using the following steps: Solve for the neutral axis height under cracked conditions. : ; Calculate the moment of inertia of the cracked section : ; The symbols in the formula are defined as follows: Cracking moment of the component; : The elastic modulus ratio of prestressed FRP reinforcement; The elastic modulus ratio of non-prestressed SFCB reinforcement is used in calculations. (for) (When taking) In calculation (for) (When taking) ; : Elastic modulus of non-prestressed SFCB reinforcement before and after yielding; : Elastic modulus of seawater sand concrete.

5. A prestressed FRP-reinforced seawater sand concrete beam and its design method according to claim 1, characterized in that, Determining the maximum crack width of the component under service conditions specifically includes: Based on the plane section assumption, after considering the decompression bending moment, the equivalent stress of the reinforcement in the crack section is calculated. ); Based on the geometric and reinforcement parameters of the component, calculate the average crack spacing ( ) and the coefficient of strain inhomogeneity between cracks ( ); Based on the equivalent stress of the steel reinforcement ( ), average crack spacing ( ) and the coefficient of strain non-uniformity between cracks ( ), calculate the theoretical maximum crack width ( ): ; in, The stress characteristic coefficient of the component is taken as 1.9 for bending. This refers to the elastic modulus of the steel reinforcement.

6. The prestressed FRP-reinforced seawater sand concrete beam and its design method according to claim 1, characterized in that, After obtaining the design flexural bearing capacity The design short-term stiffness With deflection, and the maximum design crack width The method then includes a design verification and iteration step: The design flexural bearing capacity Design value of bending moment generated by external load Comparison, requirements to be met The ultimate limit state requirement of bearing capacity; the calculated deflection Deflection limits under the corresponding usage environment and working conditions specified in the standard. Comparison, requirements to be met The maximum crack width of the design. Crack width limits as specified in the standard for the corresponding use environment and working conditions. Comparison, requirements to be met ; If any of the above conditions are not met, then adjust one or more of the following design parameters and repeat the steps of the prestressed FRP-reinforced seawater sand concrete beam and its design method as described in claim 1 until all conditions are met: increase the reinforcement area of ​​the prestressed FRP reinforcement and / or non-prestressed SFCB reinforcement ( ; Increase the tension control stress of prestressed FRP tendons ( Increase the cross-sectional dimensions of the beam, including the cross-sectional width ( or / and section height ( .

7. The prestressed FRP-reinforced seawater sand concrete beam and its design method according to claim 1, characterized in that: The specific configuration of the prestressed FRP-reinforced seawater sand concrete beam is as follows: The bottom of the beam is provided with prestressed longitudinal reinforcement and non-prestressed longitudinal reinforcement; The prestressed longitudinal reinforcement uses FRP bars to apply prestress in order to control the crack width and deflection of the beam during the service stage. The non-prestressed longitudinal reinforcement uses SFCB reinforcement, which utilizes the deformation capacity of SFCB reinforcement in the yield hardening stage to improve the brittle failure that may occur in the beam due to the linear elasticity and lack of yield stage of FRP reinforcement, and provides significant signs of failure. The beam is also equipped with stirrups and gusset bars. The stirrups and gusset bars are all made of FRP bars, which together with the prestressed FRP bars and SFCB bars form a full fiber composite reinforcement skeleton. The concrete is fiber-reinforced high-performance seawater sand concrete. The fibers include one or more of basalt fibers, polypropylene fibers, polyvinyl alcohol fibers, carbon fibers, and aramid fibers to adapt to the marine environment and utilize locally sourced materials, while improving the toughness and crack resistance of the concrete. The diameters of the FRP bars and SFCB bars are not less than 8mm and not more than 40mm; The net spacing between the outer surfaces of the FRP and SFCB reinforcement bars shall not be less than 2.5 times their diameter; The minimum distance from the outermost edge of the FRP bar and SFCB bar to the surface of the fiber-reinforced marine sand concrete shall not be less than 15mm; The FRP reinforcement includes any one of carbon fiber reinforced composite (CFRP), glass fiber reinforced composite (GFRP), and aramid fiber reinforced composite (AFRP); In the fiber-reinforced high-performance seawater sand concrete, the total volumetric content of the fiber is 0.5% to 3.0%. The prestressing control stress of the prestressed FRP bar is 50% to 80% of its tensile strength; The diameter of the FRP bars for the stirrups and braces shall not be less than 6mm; The spacing of the stirrups is 1 / 4 to 1 / 2 of the beam height.

8. A design device for prestressed FRP-reinforced seawater sand concrete beams for operating the prestressed FRP-reinforced seawater sand concrete beams and their design method as described in any one of claims 1-6, characterized in that, include: The parameter acquisition module is used to acquire the geometric parameters, material parameters, and environmental parameters of the component; wherein, the material parameters include prestressed FRP reinforcement parameters, non-prestressed SFCB reinforcement parameters, and seawater sand concrete parameters; the environmental parameters include seawater concentration; The load-bearing capacity calculation module is used to determine the flexural bearing capacity of the component under the ultimate limit state based on the geometric parameters, material parameters, environmental parameters and correction coefficients. The stiffness and deflection calculation module is used to determine the short-term stiffness and deflection of the component under service conditions based on the geometric parameters, material parameters, environmental parameters and correction coefficients. The crack control module is used to determine the maximum crack width of the component under service conditions based on the geometric parameters, material parameters, environmental parameters, and correction coefficients.

9. An electronic device, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the prestressed FRP reinforced seawater sand concrete beam and its design method as described in any one of claims 1-6.

10. A computer-readable storage medium, characterized in that, It stores a computer program, which, when executed by a processor, implements the prestressed FRP-reinforced seawater sand concrete beam and its design method as described in any one of claims 1-6.

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