Fe-sma reinforced concrete beam bearing capacity calculation method

Abstract

The application provides a Fe-SMA reinforced concrete beam bearing capacity calculation method, and relates to the technical field of reinforced concrete beams, and comprises the following steps: determining the material recovery stress of Fe-SMA strips under complete constraint conditions according to the pre-strain and activation temperature; determining anchoring deformation loss; determining the structural effective pre-stress of Fe-SMA strips on a damaged beam by sequentially deducting the interface slip loss, anchoring deformation loss and beam body active recovery deformation loss from the material recovery stress; solving the neutral axis height through cross-section axial force balance iteration; calculating the ultimate bending moment and converting it into the ultimate load; replacing the original stress with the available stress to re-perform cross-section axial force balance iteration and ultimate load calculation; and the application enables the calculation results of the yield load and the ultimate load to reflect the actual bearing capacity when the interface peeling or anchoring failure occurs prior to the cross-section material damage, instead of separately checking the connection safety after completing the cross-section bearing capacity calculation.

Description

Technical Field

[0001] This invention relates to the field of reinforced concrete beam technology, and in particular to a method for calculating the bearing capacity of Fe-SMA reinforced concrete beams. Background Technology

[0002] After reinforced concrete beams develop tension zone cracks, residual deflection, and degraded flexural stiffness under long-term service or accidental loads, thermally activated self-prestressing strengthening using externally bonded iron-based shape memory alloy strips is an emerging active strengthening method. Existing load-bearing capacity calculation methods typically treat damaged beams as intact beams without initial stress for section analysis, failing to consider the strain remaining in ordinary tensile reinforcement after pre-damage unloading as the starting point for reloading calculations. This leads to an overestimation of the load increment required for the reinforcement to re-yield. Some methods, when determining the strengthening effect provided by Fe-SMA strips, directly use the recovery stress measured under fully constrained conditions in material performance tests as the prestress applied to the beam, without considering the distribution characteristics of interfacial shear stress along the bond length during the transfer of Fe-SMA tension from the strip through the bond layer to the concrete, nor accounting for the consumption of effective prestress by end anchorage deformation and beam camber deformation, thus overestimating the actual effective prestress of the established structure. In existing methods, the calculation of cross-sectional bearing capacity is separated from the interface force transmission verification and the end anchorage verification. The available stress of the Fe-SMA strip in the cross-sectional analysis is not limited by the tensile force that the interface and anchorage can actually transmit. Therefore, it is impossible to determine whether the actual control failure mode of the reinforced beam is cross-sectional material failure, interface peeling, or anchorage failure. Summary of the Invention

[0003] To address the aforementioned technical problems, the technical solution adopted by this invention is as follows: According to a first aspect of this application, a method for calculating the bearing capacity of Fe-SMA-reinforced reinforced concrete beams is provided, comprising: Obtain the geometric parameters, material parameters, and reinforcement parameters of the reinforced concrete beam to be strengthened, and obtain parameters reflecting the residual state of the beam after pre-damage unloading; the residual state parameters include at least the residual strain of ordinary tensile reinforcement. Obtain the cross-sectional parameters, material parameters, pre-strain, activation temperature, bonding length, interfacial bonding parameters, and end anchoring parameters of Fe-SMA strips; The material recovery stress of the Fe-SMA strip under fully constrained conditions is determined based on the pre-strain and activation temperature. Based on the bond-slip constitutive relationship between Fe-SMA strips and concrete, an interface micro-element equilibrium equation is established along the bond length. The actual tensile force transmitted at the interface is obtained by integration. The ratio of the actual tensile force transmitted to the tensile force corresponding to the material recovery stress is taken as the interface force transmission efficiency. The anchorage deformation loss is determined based on the end anchorage stiffness. After deducting the interface slip loss, anchorage deformation loss and active recovery deformation loss of the beam in sequence from the material recovery stress, the effective prestress of the Fe-SMA strip on the damaged beam is determined. Taking the state of the beam after thermal activation and cooling as the starting point for reloading calculation, the residual strain formed after the pre-damage unloading is included in the total strain of ordinary tensile reinforcement, and the effective prestress of the structure is included in the total stress of Fe-SMA strip. The cross-sectional strain compatibility relationship is established by adopting the plane section assumption, and the neutral axis height is solved by cross-sectional axial force balance iteration. Based on the neutral axis height, the yield moment is calculated and converted into a yield load when the ordinary tensile steel reaches the yield strain as the yield state criterion, and the ultimate moment is calculated and converted into an ultimate load when the concrete in the compression zone reaches the ultimate compressive strain as the ultimate state criterion. The allowable tensile force transmitted at the interface is determined based on the bond-slip constitutive relationship, and the allowable tensile force transmitted at the anchorage is determined based on the end anchorage structure. The smaller of the allowable tensile force transmitted at the interface and the allowable tensile force transmitted at the anchorage is used to limit the available stress of the Fe-SMA strip in the ultimate state. When the available stress is less than the Fe-SMA strip stress determined by the section analysis, the available stress is used to replace the original stress, and the section axial force balance iteration and ultimate load calculation are performed again.

[0004] The present invention has at least the following beneficial effects: The method for calculating the bearing capacity of Fe-SMA-reinforced reinforced concrete beams of this invention directly superimposes the strain remaining in the ordinary tensile reinforcement after pre-damage unloading as the initial strain into the cross-sectional strain compatibility relationship during the reloading stage. This ensures that the calculation of the steel yield load is determined by the residual strain state rather than extrapolated from the zero stress starting point, thereby correcting the initial conditions for assessing the inherited load capacity of damaged beams. When determining the reinforcement contribution of the Fe-SMA strips, this method does not directly use the material recovery stress as the effective prestress, but instead calculates the actual tensile force transferred to the beam by integrating the interface shear stress along the bond length, while simultaneously deducting the stress losses caused by end anchorage deformation and beam camber deformation. This ensures that the effective prestress participating in the cross-sectional internal force balance depends on the physical force transmission capacity of the strip-concrete interface and end anchorage, rather than material test values. This method also incorporates the interface-permissible tensile force and the anchorage-permissible tensile force into the limit state calculation. The smaller of the two values ​​is used to control the maximum stress available for the Fe-SMA strip in the cross-sectional analysis. When the control value is less than the stress required for cross-sectional equilibrium, the original stress is forced to be replaced by the control value and the iteration is repeated. This allows the calculation results of yield load and ultimate load to reflect the actual bearing capacity when interface peeling or anchorage failure occurs before the failure of the cross-sectional material, rather than checking the connection safety separately after the cross-sectional bearing capacity calculation is completed. Attached Figure Description

[0005] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0006] Figure 1 A flowchart illustrating the method for calculating the bearing capacity of Fe-SMA-reinforced reinforced concrete beams provided in this embodiment of the invention. Detailed Implementation

[0007] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0008] It should be noted that, based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Furthermore, this device and / or practice the method can be implemented using other structures and / or functionalities besides one or more of the aspects set forth herein.

[0009] The following will refer to Figure 1 The flowchart shown illustrates a method for calculating the bearing capacity of Fe-SMA-reinforced reinforced concrete beams, introducing such a method.

[0010] The method for calculating the bearing capacity of Fe-SMA-strengthened reinforced concrete beams includes the following steps: S100, obtain the geometric parameters, material parameters and reinforcement parameters of the reinforced concrete beam to be strengthened, and obtain the parameters reflecting the residual state of the beam after pre-damage unloading; the residual state parameters include at least the residual strain of ordinary tensile reinforcement.

[0011] This step is the input step of the calculation method of the present invention, and its core lies in obtaining two types of parameters: one type is the basic design parameters of the reinforced concrete beam, including the cross-sectional width b, the cross-sectional height h, and the area A of ordinary tensile reinforcement. s and effective height h0, area of ​​ordinary compression reinforcement A' s and the distance a' from the point of resultant force to the edge under pressure sThe first category includes the material strength and elastic modulus of concrete and reinforcing steel; the second category includes physical state parameters reflecting the beam structure after pre-damage loading and unloading, which at least include the residual strain ε of ordinary tensile reinforcement. sr .

[0012] Residual strain ε of ordinary tensile steel bars sr This is the key input that distinguishes this invention from existing methods. This parameter cannot be directly read through visual inspection; it must be obtained under the known maximum pre-damage load P. d Residual deflection δ after unloading r and residual crack width w r Based on this, it is obtained through cross-sectional strain inversion. During the inversion, the elastic recovery strain of the steel reinforcement after the concrete in the tension zone of the section exits its working state under the maximum pre-damage load is subtracted from the elastic recovery strain of the steel reinforcement during unloading, thus obtaining the residual plastic strain in the steel reinforcement. When direct inversion conditions are lacking, ε sr It can also be calculated through the load-deflection curve of the loading-unloading cycle, or calibrated through static load tests compared with intact beams of the same batch. Weighting coefficients λ1~λ4 are used in subsequent steps to synthesize the various damage indices into a comprehensive equivalent damage coefficient D. The sum of the four is 1, and their specific values ​​are determined by the analytic hierarchy process (AHP), using the stiffness degradation coefficient 1-η. B Residual deflection index η δ Residual crack index η w and the residual strain index η of steel reinforcement s The importance was calculated by comparing each pair of items.

[0013] This step also involves obtaining the flexural stiffness B of the beam section after unloading. d The ratio η of this stiffness to the intact state B0 B Used for subsequent calculation of the comprehensive equivalent damage coefficient. B d It can be determined directly within the elastic range through on-site static load tests, or determined by the initial tangent slope of the load-deflection curve after unloading and reloading.

[0014] In this step, the residual strain ε of ordinary tensile steel bars is obtained through actual measurement or inversion. sr and the bending stiffness B of the section after unloading dAs input parameters, the plastic deformation information remaining in the beam after pre-damage unloading is preserved, eliminating the need for subsequent section analysis to extrapolate the stress history of the reinforcing bars from a zero-stress state. Simultaneously, the residual state of the beam is jointly characterized at the input layer by four measured indices: stiffness degradation, residual deflection, residual cracks, and residual strain in the reinforcing bars. These indices are weighted using the analytic hierarchy process (AHP) and combined into a comprehensive equivalent damage coefficient. This provides a physical basis for subsequent steps to select different crack closure parameters and stiffness recovery parameters based on the damage level, rather than simplifying the damaged beam into an equivalent intact beam with reduced material strength. The independent input of residual strain in ordinary tensile reinforcement allows this strain to be directly superimposed on the strain increment caused by the new load during reloading, avoiding the artificial setting of the reloading starting point for the damaged beam.

[0015] S200, obtain the cross-sectional parameters, material parameters, pre-strain, activation temperature, bonding length, interfacial bonding parameters, and end anchoring parameters of Fe-SMA strips.

[0016] This step is the input step for Fe-SMA strengthening parameters. Its core is to obtain all the physical parameters used for subsequent calculations of material recovery stress, interface force transfer efficiency, and effective prestress of the structure, which are divided into four categories.

[0017] The first category consists of the geometric and material parameters of the Fe-SMA strip itself, including the number of strips n. f Single width b f Single-strand thickness t f Multiplying the three together gives the total cross-sectional area A. f It also includes the initial elastic modulus E. f Nominal yield strength f fy Ultimate strength f fu These parameters are typically provided by the material supplier or obtained through tensile testing of samples from the same batch.

[0018] The second category consists of thermally activated process parameters, including pre-strain ε. pre Activation temperature T a and activation duration t a Pre-strain is the tensile strain applied to Fe-SMA before installation. The activation temperature and duration jointly determine the magnitude and stabilization rate of the material's recovery stress. The recovery stress corresponding to different activation temperatures for the same batch of material needs to be pre-calibrated through a constrained thermal activation test. During the test, the Fe-SMA specimen is fixed in a constrained frame, heated to the preset temperature, and held at that temperature for a predetermined time. After cooling, the residual tensile force in the specimen is measured, and the recovery stress σ under that condition is obtained by dividing it by the cross-sectional area. r .

[0019] The third category is bonding interface parameters, including adhesive layer thickness t. a *Adhesive shear modulus G a Peak bond stress τ at room temperature max,20 Peak slip s 0,20 and curve shape parameter n 20 These parameters were determined through single shear or pull-out tests on Fe-SMA strips and concrete specimens. The load-slip curves were recorded during the tests, and the characteristic values ​​of the bond stress-slip relationship curves were obtained after data processing. Subsequent steps were based on the actual activation temperature T. a These parameters are corrected: τ max,T =k τ,T ·τ max,20 s 0,T =k s,T ·s 0,20 n T =k n,T ·n 20 Correction factor k τ,T k s,T k n,T The determination was made by fitting interface test data at different temperatures.

[0020] The fourth category is end anchorage parameters, including the total length L of the strip. f Effective bonding length at both ends L b End mechanical anchoring form and equivalent stiffness k of anchoring device a Effective bond length L b The maximum tensile force that the interface can actually transmit is affected; when the bond length is insufficient, end anchoring is needed to supplement the force transmission. The equivalent stiffness k of the anchoring device. a The value is calculated from the anchorage details or calibrated through anchorage bearing capacity tests, and is used for subsequent calculations of anchorage slip Δs. a Prestress loss Δσ caused a =E f ·Δs a / L f .

[0021] S300, determine the material recovery stress of the Fe-SMA strip under fully constrained conditions based on the pre-strain and activation temperature.

[0022] This step determines the recovering stress that the Fe-SMA material can generate under fully constrained conditions. This stress is the starting point for subsequent calculations of the effective prestress of the structure and needs to be distinguished from the actual effective prestress transmitted to the beam.

[0023] Fe-SMA material recovery stress σ r From pre-strain ε pre and activation temperature T aJoint control. After pre-stretching, the Fe-SMA strip is in a martensitic phase. When the strip is heated to the activation temperature T under confined conditions... a When the material undergoes a phase transformation to the austenitic phase, macroscopic recovery stress is generated if the deformation is constrained. The fully constrained condition refers to the boundary condition where the length of the strip is fixed and there is no free shrinkage during the thermal activation process. The recovery stress measured under this condition is the maximum usable recovery stress of the material.

[0024] σ r The specific values ​​should be determined primarily through constrained thermal activation tests on the same batch of Fe-SMA strips. During the test, at least three specimens should be taken, each specimen fixed at both ends within a constrained frame, and heated to the target temperature T using the same heating rate as the on-site reinforcement. a And keep warm a After cooling to room temperature, the residual tensile force in the constraint frame is measured, and the recovered stress of the specimen is obtained by dividing it by the cross-sectional area of ​​the specimen. The average value of all specimens is taken as σ. r .

[0025] When experimental conditions are not available, σ r The following empirical model can be used to estimate: σ r =E f ·ε pre ·[1-exp(-α·T a ]; where α is the material phase transformation coefficient, which is calibrated by constrained thermal activation tests of the same batch of materials at at least three different temperatures; a more refined phase transformation kinetic model can also be used to incorporate the effect of activation temperature on phase transformation volume fraction into the calculation.

[0026] It should be noted that σ r This is an inherent property of the material under fully constrained conditions, unaffected by beam stiffness, interface bonding conditions, and end anchorage conditions. Prestress losses caused by interface slip, anchorage deformation, and active beam deformation are deducted sequentially in subsequent steps; these reductions are not involved in this step.

[0027] In this step, the material's restoring stress σ is... r The determination of this parameter is based on constrained thermal activation tests of samples from the same batch, ensuring that the actual value of this input parameter is determined by the phase transformation behavior of the material itself under constrained heating conditions, rather than relying on theoretical model extrapolation or typical values ​​provided by the material supplier. Furthermore, the average value is obtained through repeated tests of at least three samples, offsetting the influence of batch-specific inhomogeneities on the measured recovery stress. The material phase transformation coefficient α is introduced into the empirical model estimation and calibrated through at least three sets of tests at different temperatures, making the parameters in the estimation formula material-specific. Because σ rThe definition is strictly limited to fully constrained conditions. This step does not involve subsequent factors such as interface force transmission, anchorage stiffness, and beam stiffness, so that the determination of material properties and the calculation of structural response are logically independent, avoiding the direct conflation of material test values ​​with the effective prestress of the structure.

[0028] S400, based on the bond-slip constitutive relationship between Fe-SMA strips and concrete, an interface micro-element equilibrium equation is established along the bond length, and the actual tensile force transmitted at the interface is obtained by integration. The ratio of the actual tensile force transmitted to the tensile force corresponding to the material recovery stress is used as the interface force transmission efficiency, and the anchorage deformation loss is determined based on the end anchorage stiffness.

[0029] Furthermore, the method for determining the interface force transmission efficiency is as follows: By taking infinitesimal elements along the bonding length, the axial force of the Fe-SMA strip is established. With interface shear stress Differential equilibrium equations: ; in, The width of a single Fe-SMA strip; combined bond-slip constitutive relation And Fe-SMA axial constitutive relation Formation of relative sliding of the interface The second-order differential equation; The elastic modulus of Fe-SMA This represents the total cross-sectional area of ​​the Fe-SMA. For the axial displacement of the Fe-SMA strip; with the free end Loading end Numerical integration of the boundary conditions yields the slip distribution along the bond length. and shear stress distribution Integrating the shear stress along the entire length yields the actual tensile force transmitted at the interface. The actual transmitted tension and The ratio is the interface force transmission efficiency. .

[0030] Furthermore, the anchorage deformation loss is determined by the allowable tensile force transmitted by the end anchorage, which is the minimum value among the bearing capacity of the anchorage device itself, the local bearing capacity of the concrete in the anchorage zone, and the anchorage slip control force; wherein the anchorage slip control force is determined by multiplying the equivalent stiffness of the anchorage device by the amount of anchorage slip, and the anchorage deformation loss is calculated by dividing the amount of anchorage slip by the total length of the Fe-SMA strip and then multiplying it by the elastic modulus of Fe-SMA.

[0031] This step is the interface force transmission analysis step, the core of which is to calculate the actual residual value of the Fe-SMA strip after the recovery stress is transmitted through the bonding interface and the prestress loss caused by the end anchoring deformation.

[0032] Interface force transmission efficiency η i The calculation requires solving a boundary value problem. The Fe-SMA strip is divided into infinitesimal elements along the bond length, and an axial force equilibrium relationship is established for each element: the rate of change of the axial force along the length is equal to the interfacial shear stress multiplied by the bond width. Substituting the axial constitutive relation of the Fe-SMA strip (axial force equals the elastic modulus multiplied by the cross-sectional area multiplied by the derivative of the axial displacement) into this equilibrium equation, and combining it with the bond-slip constitutive relation (shear stress is a function of relative slip), a second-order ordinary differential equation is obtained with relative slip s(x) as the unknown function. This equation satisfies the boundary condition of zero slip at the free end and the boundary condition of axial force equal to the tensile force corresponding to the material's restoring stress at the loaded end. Since the bond-slip constitutive relation is usually nonlinear, this differential equation generally has no analytical solution and requires numerical integration methods (such as the Runge-Kutta method) to solve it. After solving, the distribution of slip along the bond length is obtained, and then the distribution of shear stress along the bond length is obtained from the bond-slip constitutive relation. Integrating the shear stress along the entire length, we obtain the tensile force N that can actually be transferred to the concrete at the interface. f,trans The tensile force is related to the total tensile force A of Fe-SMA. f ·σ r The ratio is the interface force transmission efficiency η. i When the actual bond length L b Greater than the effective bond length L e At this time, there is an ineffective section of interfacial shear stress along the length direction, and the actual tensile force transmitted at the interface converges to the ultimate bearing capacity of the interface, η. i It approaches a constant value but is always less than 1, and will not grow indefinitely to exceed 1.

[0033] The calculation of anchorage deformation loss depends on the tensile force N that the end anchorage device is allowed to transmit. a N a The minimum value among the three factors—the bearing capacity of the anchorage device itself, the local bearing capacity of the concrete in the anchorage zone, and the anchorage slip control force—is taken, where the anchorage slip control force is equal to the equivalent stiffness k of the anchorage device. a Multiply by the anchorage slip Δs a The equivalent stiffness k of the anchoring device a Calculations based on detailed anchorage drawings are performed. For bolted anchorages, shear stiffness is used; for wedge-type anchorages, frictional stiffness between the wedge and Fe-SMA is used. Values ​​must consider the elastic deformation of the concrete in the anchorage zone and the anchorage's own clearance. Anchorage deformation loss Δσ a The anchorage slip Δs a Divide by the total length L of the strip fThen multiply by the elastic modulus E f get.

[0034] In this step, the material recovery stress σ is not applied. r Instead of directly using it as effective prestress, the actual distribution of shear stress along the bond length is obtained by solving the interface micro-element equilibrium equations. This makes the calculation of the actual tensile force transmitted at the interface depend on the local bond behavior between the strip and the concrete, rather than the global average assumption. Simultaneously, the end anchorage deformation loss is based on the product of the equivalent stiffness of the anchorage device and the anchorage slippage, ensuring that the calculation of anchorage loss depends on the actual force transmission capacity of the anchorage structure, not on empirical reduction factors. Interface force transmission efficiency η i Defined as the ratio of the actual transmitted tensile force to the tensile force corresponding to the material's restoring stress, rather than an empirical constant, η is used in subsequent steps. i Incorporating the effective prestress coefficient provides a mechanical basis for derivation rather than empirical assumptions. The practice of taking the minimum value of the anchorage bearing capacity, local concrete bearing pressure, and slip control force to allow the tensile force to be transmitted in the anchorage ensures that the anchorage deformation loss is always controlled at the weakest link, avoiding overestimation or underestimation of a single controlling factor.

[0035] S500, after deducting the interface slip loss, anchorage deformation loss and active recovery deformation loss of the beam in sequence from the material recovery stress, the effective prestress of the Fe-SMA strip on the damaged beam is determined.

[0036] Furthermore, the effective prestress of the structure is determined by the following formula: ; in, For effective prestressing of the structure, To restore stress in materials; The interface slip loss is calculated by subtracting the interface force transmission efficiency from 1 and then... Determined by multiplication; The anchorage deformation loss is determined by dividing the anchorage slip by the total length of the Fe-SMA strip and then multiplying by the elastic modulus of Fe-SMA. The active recovery deformation loss of the beam is determined by the Fe-SMA shortening caused by the arching deformation and crack closure deformation. The temperature difference deformation loss is determined by multiplying the difference in linear expansion coefficients between Fe-SMA and concrete by the difference between the activation temperature and the ambient temperature.

[0037] Furthermore, the beam actively recovers its deformation loss. The method for determining it is as follows: First, the initial estimate of the effective prestress of the structure. Calculate the effective preload The distance from the point of effect of preload and Fe-SMA combined force to the centroid of the cross section is eccentricity. Multiply to obtain the equivalent preloaded bending moment Based on the remaining bending stiffness of the damaged beam after unloading Calculate the thermally activated anti-arch value The shortening of the Fe-SMA strip is calculated from this anti-arching value, and then converted into the corresponding stress loss; simultaneously, according to The change in strain at the bottom of the beam is used to calculate the crack closure rate. The sum of all crack closure rates is used to calculate another portion of the stress loss. The two losses are then superimposed to obtain the final value. Substitute The effective prestress is corrected, and the anti-arch value and crack closure amount are recalculated based on the corrected effective prestress. The iteration continues until the change in the anti-arch value and crack closure amount is less than the preset allowable value.

[0038] This step involves restoring the stress σ in the Fe-SMA material. r After deducting all types of losses, the final effective prestress σ acting on the damaged beam is determined. pe The key to this step is to identify and quantify all stress losses along the entire path from material recovery to structural stress, rather than directly using material test values ​​as the reinforcement effect.

[0039] σ pe The determination requires deducting four types of losses in sequence: (1) Interface slip loss Δσ i The interface slip loss is calculated from the interface force transmission efficiency η obtained in step S400. i Determine: Δσ i =(1-η i )·σ r This loss reflects the portion of the recovered stress from the Fe-SMA strips that, during its transfer to the concrete through the bond layer, was not fully transferred to the beam due to relative interfacial slippage. Even with a sufficiently long bond length, the uneven distribution of interfacial shear stress along the length direction causes the area near the loading end to slip first, preventing further stress transfer in sections beyond the effective bond length.

[0040] (2) Anchorage deformation loss Δσ a Anchorage deformation loss is determined by step S400: Δσ a =E f ·Δs a / L f , where Δs aThis refers to the end anchorage slippage. This loss reflects the deformation of the end anchorage device under the tension of the Fe-SMA—the anchorage device (anchor plate, bolt, or wedge) undergoes elastic deformation and gap compression after being subjected to force, causing a small displacement of the Fe-SMA strip end in the loading direction, equivalent to the strip freely shortening, thereby releasing part of the restoring stress. The magnitude of this loss depends on the stiffness of the anchorage structure and the construction quality, and is physically independent of the interface slippage loss.

[0041] (3) Active recovery deformation loss of beam Δσ b This loss reflects the process by which the deformation of the damaged beam, in turn, consumes the strain energy of the Fe-SMA when the equivalent prestress applied by the Fe-SMA causes camber and crack closure. An iterative method is used in the calculation: first, an initial estimated value of the effective prestress σ is set. pe (0) (σ can be taken) r Deduct Δσ i and Δσ a (The remaining value after calculation) to calculate the effective preload N. pe (0) =A f ·σ pe (0) Multiply by the eccentricity e from the resultant point to the centroid of the cross section. f The equivalent preloaded bending moment M is obtained. pe (0) =N pe (0) ·e f Based on the remaining bending stiffness B of the damaged beam after unloading. d Calculate the thermally activated anti-arching value δ p (0) =α δ ·M pe (0) ·L 2 / B d The anti-arching value is divided by the total strip length to estimate the shortening of Fe-SMA, and then multiplied by E. f The stress loss caused by the arching is obtained; at the same time, according to M pe (0) The crack closure amount Δw is estimated by the compressive strain change at the bottom of the beam. The sum of the closure amounts at each crack is divided by the total length of the strip to estimate another portion of the shortening, which is then multiplied by E. f The stress loss caused by crack closure is obtained. The sum of the two losses yields Δσ. b (0) Substitute σ pe (1) =σ r -Δσ i -Δσ a -Δσ b(0) -Δσ t The correction value is obtained, in σ pe (1) Recalculate the anti-arch and crack closure, iterating until the difference between the two calculation results is less than the preset allowable value (e.g., the change in anti-arch value is less than 1% or the absolute value is less than 0.1mm).

[0042] (4) Temperature difference deformation loss Δσ t The loss consists of two parts: first, the relative deformation caused by the difference in the linear expansion coefficients of the Fe-SMA strip and concrete during the cooling process, Δσ t1 =E f ·(α f -α c )·(T a -T0), where α f and α c Here, Δσ represents the linear expansion coefficients of Fe-SMA and concrete, respectively, and T0 represents the ambient temperature. Secondly, the uneven temperature distribution along the section height leads to inconsistent deformation between the strip and different parts of the beam, Δσ. t2 0.02σ is taken according to the construction conditions. r ~0.05σ r The sum of the two is Δσ. t .

[0043] In this step, the material recovery stress σ is not applied. r Instead of directly equating it to the effective prestress of the structure, it sequentially deducts four types of losses: interface slippage, anchorage deformation, active recovery deformation of the beam, and temperature difference deformation, so that σ participating in the subsequent section bearing capacity calculation is... pe This only represents the effective prestress actually remaining in the beam after the complete force transmission path. The beam's active recovery deformation loss Δσ b An iterative method is used for calculation instead of single-step estimation. In each iteration, the anti-camber value and crack closure amount are updated with the effective prestress, which in turn is updated with the strain consumption caused by anti-camber and crack closure. This ensures that the final value of the effective prestress and the amount of active recovery deformation of the beam meet the deformation coordination condition rather than being determined independently. The inclusion of temperature difference deformation loss means that the influence of activation temperature on effective prestress is not limited to the temperature sensitivity of material recovery stress, but also includes the additional stress loss caused by the difference in the linear expansion coefficients of the two materials during the cooling stage. This allows the difference in effective prestress under high-temperature activation (e.g., 250℃) and low-temperature activation (e.g., 150℃) conditions to reflect the different temperature responses of the two physical mechanisms of material phase transformation recovery and thermal expansion and contraction.

[0044] S600 takes the state of the beam after thermal activation and cooling as the starting point for reloading calculation. The residual strain formed after the pre-damage unloading is included in the total strain of ordinary tensile reinforcement, and the effective prestress of the structure is included in the total stress of Fe-SMA strip. The cross-sectional strain compatibility relationship is established by adopting the plane section assumption, and the neutral axis height is solved by cross-sectional axial force balance iteration.

[0045] This step is the initialization step for reloading the cross-section analysis. Its core function is to determine the calculation starting point and establish the cross-section strain compatibility relationship.

[0046] Furthermore, the residual state formed after the pre-damage unloading is determined by a comprehensive equivalent damage coefficient. Classify into levels: ; in, This is the ratio of the bending stiffness of the section after unloading to the bending stiffness of the section in its intact state. It is the ratio of the residual mid-span deflection to the reference deflection. It is the ratio of the maximum residual crack width to the reference crack width. This is the ratio of the residual strain to the yield strain of ordinary tensile steel bars; , , , The weighting coefficients for each damage index are determined by pairwise comparisons of four indices—stiffness degradation, residual deflection, residual cracks, and residual strain in the reinforcing steel—using the analytic hierarchy process (AHP), and satisfying the following conditions: ;according to The value classifies the beam into minor, moderate, and severe damage levels.

[0047] Furthermore, the method for establishing the cross-sectional strain compatibility relationship is as follows: The compressive strain of the concrete at the compression edge of the cross section is taken as The height of the neutral axis is As a basic variable, the distance from the compression edge on the cross section is... The strain increment at a given point is linearly distributed according to the following formula: ; in, This represents the increase in concrete strain at the compression edge during reloading, with tension being positive and compression being negative. Location of ordinary tension reinforcement Ordinary compression reinforcement position Fe-SMA strip position Substituting these values ​​into the linear distribution, we obtain the strain increments of each material during the reloading process: The total strain of ordinary tensile steel reinforcement is: ; For ordinary tensile reinforcement, The residual strain of ordinary tensile reinforcement after pre-damage unloading. This refers to the effective height of ordinary tension reinforcement; The total strain of ordinary compression steel bars is: ; This represents the total strain of ordinary compression steel bars. The residual strain of ordinary compression steel bars after pre-damage unloading. This is the distance from the resultant force point of ordinary compression reinforcement to the compression edge of the cross section; The total stress of the Fe-SMA strip is: ; The total stress of the Fe-SMA strip. For effective prestressing of the structure, Additional stress generated by reloading; The residual strain and the effective prestress of the structure As a historical state quantity, it directly participates in the calculation of the internal forces of the section, and its formation path is not repeatedly included in the calculation during the reloading process.

[0048] Furthermore, Determined in the following manner: First, based on the linear elasticity relationship Calculation, where The elastic modulus of Fe-SMA is given by the additional strain: ; In the formula This represents the increase in strain of the concrete at the compression edge. The distance from the resultant force point of the Fe-SMA strip to the compression edge of the cross section is denoted as . The height of the neutral axis. The strain difference between Fe-SMA and the concrete at the bottom of the beam caused by interfacial slip; When the total stress of Fe-SMA strip Exceeding the nominal yield strength Then, the Ramberg-Osgood model was used to determine its stress: ; in, For the total strain of Fe-SMA, The hardening index is determined based on material testing.

[0049] This step first classifies the degree of damage to the beam by using a comprehensive equivalent damage coefficient D. D is determined by the stiffness degradation coefficient (1-η). B ), residual deflection index η δ Residual crack index η w The residual strain index η of ordinary tensile steel bars s The four weighted composite values, with weight coefficients λ1 to λ4 determined using the Analytic Hierarchy Process (AHP), are analyzed as follows: At least five experts with experience in assessing existing concrete structures are invited to conduct pairwise comparisons of the importance of the four damage indicators on the beam's bearing capacity and reinforcement effect. A 1-9 scale (1 indicating equal importance, 9 indicating extreme importance) is used. Each expert independently scores the values, and the geometric mean is taken to form a judgment matrix. The eigenvector corresponding to the largest eigenvalue of this matrix is ​​calculated and normalized to obtain the weights. Finally, a consistency check is performed (consistency ratio CR < 0.1). The D-value classifies the beam into mild, moderate, and severe damage levels. This level is mainly used in subsequent steps to select crack closure parameters and stiffness recovery parameters. However, it must be clarified that the D-value and damage level are only used for selecting correction parameters (such as η in crack closure calculations). wc (Relationship with D), residual strain ε of ordinary tensile reinforcement in reloaded section calculation. sr The values ​​obtained from the S100-step actual measurement or inversion are still used directly, without conversion through the D value.

[0050] After determining the damage level, the reloading calculation starts from the state of the beam after thermal activation and cooling. This state includes two historical state quantities: the residual plastic strain ε in the ordinary tensile reinforcement. sr The effective prestress σ established in the Fe-SMA strip pe The cross-sectional analysis adopts the plane section assumption: the strain increment of each longitudinal material on the cross-section is linearly related to the distance from the compression edge, and the strain increment Δε of the concrete at the compression edge is taken as the value. c The linear distribution is described by the neutral axis height x as the basic variable. Ordinary tensile reinforcement (located at y=h0) and ordinary compressive reinforcement (located at y=a') are respectively... s ) and Fe-SMA bands (located at y=h f Substituting the position of the material into the general formula for linear distribution, we obtain the expression for the strain increment of each material during the reloading process. The total strain of ordinary tensile steel reinforcement is the residual strain ε. sr The sum of the newly added strain increments; the same applies to ordinary compression reinforcement; the total stress of the Fe-SMA strip is the effective prestress of the structure σ. pe With the added additional stress Δσ f The sum of Δσ f The calculations are performed according to linear elasticity when the Fe-SMA stress does not exceed the nominal yield strength, including the strain difference Δε caused by interface slip. ifWhen the nominal yield strength is exceeded, the Ramberg-Osgood model is used. The hardening index m of this model is obtained by fitting uniaxial tensile tests on the same batch of Fe-SMA specimens. After completing the strain and stress expressions, the x-value is solved iteratively by the cross-sectional axial force equilibrium equation. After the iteration converges, the subsequent calculations of yield bearing capacity and ultimate bearing capacity are performed.

[0051] In this embodiment, the damage level of the beam is classified by a comprehensive equivalent damage coefficient D, so that the selection of crack closure parameters and stiffness recovery parameters in subsequent steps is based on the weighted synthesis result of measured damage indices rather than a single index. At the same time, the introduction of the residual strain index η_s of ordinary tensile steel bars in the D value calculation makes the damage level judgment result most sensitive to the plastic deformation of steel bars (λ4 takes the maximum value), reflecting the decisive influence of the residual strain of steel bars on the structural stress performance after reloading. When the calculation starts from the state after thermal activation and cooling, the residual strain of ordinary tensile steel bars and the effective prestress of Fe-SMA are independently calculated: the former determines from which strain value the steel bars continue to be stretched to yield, and the latter determines from which stress value the Fe-SMA continues to bear load. The two historical state quantities are not converted or superimposed, eliminating the uncertainty caused by artificial conversion of steel bar residual strain into equivalent prestress or prestress into equivalent initial strain. Under the plane section assumption, the linear relationship of the strain distribution across the entire cross section is described using the strain increment of the concrete at the compression edge and the height of the neutral axis as basic variables. This ensures that the coordination of strain increments of each material depends only on the geometric position, not the magnitude of the internal forces within the cross section, avoiding redundant degrees of freedom in the iterative path of first assuming the neutral axis and then calculating the strain. The separate treatment of the Fe-SMA additional stress in the linear elastic segment and the post-yield segment prevents the stress behavior of the strips in the cross section analysis from infinitely extrapolating the linear elastic relationship. When the stress exceeds the nominal yield strength, the stress growth rate is controlled by the hardening exponent m, rather than continuing to grow linearly according to the initial elastic modulus. m is obtained by fitting uniaxial tensile tests of the same batch of specimens, ensuring that the parameter source of the constitutive model is consistent with the actual material response.

[0052] S700, based on the neutral axis height, the yield moment is calculated and converted into a yield load by taking the yield strain of ordinary tensile steel bars as the criterion for determining the yield state, and the ultimate moment is calculated and converted into an ultimate load by taking the ultimate compressive strain of the concrete in the compression zone as the criterion for determining the ultimate state.

[0053] This step is the bearing capacity calculation step. Based on the neutral axis height x obtained from step S600, the yield load and ultimate load of the beam after reloading are determined respectively.

[0054] Furthermore, the determination of whether the concrete in the compression zone has reached the ultimate compressive strain is simplified by using an equivalent rectangular stress diagram. The compressive stress in the equivalent rectangular stress diagram is taken as... The height of the pressure zone is taken as ,in, This refers to the axial compressive strength of concrete. and These are preset coefficients.

[0055] Yield state determination: based on the total strain ε of ordinary tensile steel reinforcement. s Reaching the yield strain ε y As a marker of the yield state. ε y =f y / E s , where f y E represents the yield strength of ordinary steel reinforcement. s This is the elastic modulus of ordinary steel reinforcement. In the section analysis, keeping the strain compatibility and internal force equilibrium relationships established in step S600 unchanged, Δε is gradually increased. c (Incremental strain of concrete at the compression edge), after each iteration, the total strain ε at the location of ordinary tensile reinforcement is read. s When ε s First time reaching ε y At that moment, stop loading, record the internal force values ​​of each material, and calculate the bending moment M according to the section bending moment formula. y =C c ·z c +C' s ·z' s +T f ·z f The yield moment is obtained. Based on the beam's support and loading conditions, M is... y Converted to yield load P y For a simply supported beam with concentrated loading at mid-span, P y =4M y / L; For a simply supported beam with three-point loading, P y =6M y / L; For other loading forms, the conversion is performed according to the general relationship between bending moment and load in structural mechanics.

[0056] Limit state determination: The ultimate compressive strain ε of the concrete in the compression zone is reached. cu As a marker of the limiting state. ε cu The value corresponding to the concrete strength grade in the "Code for Design of Concrete Structures" is determined. For concrete of C50 and below, ε... cu The value is taken as 0.0033. When making the determination, an equivalent rectangular stress diagram is used to simplify the stress distribution in the concrete compression zone: the actual parabolic compressive stress distribution is equivalent to a uniformly distributed rectangular stress block, and the compressive stress is taken as α1·f. c The height of the pressure zone is taken as β1·x. Where f cΔε represents the axial compressive strength of concrete. α1 and β1 are coefficients taken according to the specification. For concrete of C50 and below, α1 = 0.85 and β1 = 0.85; for concrete above C50, α1 and β1 are reduced according to the specification formula. Δε is gradually increased. c Monitoring the compressive strain ε of concrete at the compression edge c =Δε c (Since step S600 starts from the thermally activated state, the initial strain at the pressure edge is 0), when ε c First time reaching ε cu Stop loading at that moment, record the internal force values ​​of each material at that instant, and calculate the ultimate bending moment M of the section using the same method. u And convert it to the ultimate load P u .

[0057] This method uses the yield strain reached by ordinary tensile steel reinforcement and the ultimate compressive strain reached by concrete in the compression zone as the criteria for determining the yield state and ultimate state, respectively. This ensures that the calculation of the yield load does not depend on the identification of the inflection point of the section moment-curvature curve, and the calculation of the ultimate load does not depend on external assumptions about the strain distribution of the section. In the yield state determination, ε... s =f y / E s As a threshold, based on the neutral axis height obtained from S600 iterations and the strain expression at the location of ordinary tensile reinforcement, it is directly determined whether the threshold has been reached. When ε s Exceeding ε y Loading is stopped at the point of yielding to avoid the influence of the hardened section of the reinforcing steel on the identification of the yield point. In the ultimate limit state determination, an equivalent rectangular stress diagram is used instead of the actual concrete compressive stress distribution curve. This simplifies the parabolic compressive stress distribution into a uniform rectangular stress block, making the calculation of the ultimate bending moment independent of the numerical integration of the stress distribution in the compression zone of the concrete. This simplifies the calculation while maintaining consistency with the ultimate bearing capacity calculation method in the current concrete structure design code. α1 and β1 are taken according to the code rather than derived separately, making the calculation results of the ultimate limit state comparable to the code method. When converting bending moment to load, appropriate conversion relationships are used for different loading forms, so that the calculation results of yield load and ultimate load can directly correspond to the actual loading condition, rather than just outputting the bending moment value of the section.

[0058] S800, the allowable tensile force transmitted at the interface is determined according to the bond-slip constitutive relationship, and the allowable tensile force transmitted at the anchorage is determined according to the end anchorage structure. The smaller value between the allowable tensile force transmitted at the interface and the allowable tensile force transmitted at the anchorage limits the available stress of the Fe-SMA strip in the ultimate state. When the available stress is less than the Fe-SMA strip stress determined by the section analysis, the available stress replaces the original stress and the section axial force balance iteration and ultimate load calculation are performed again.

[0059] Furthermore, when interface peeling or end anchorage failure is the controlling failure mode, the smaller of the ratio of the allowable tensile force transmitted at the interface to the total cross-sectional area of ​​the Fe-SMA and the ratio of the allowable tensile force transmitted at the anchorage to the total cross-sectional area of ​​the Fe-SMA is used as the available stress limit for the Fe-SMA. After replacing the Fe-SMA strip stress in the original section analysis with this limit, the section axial force balance iteration and ultimate bending moment calculation are re-executed until the section internal force balance, the interface shear stress not exceeding the allowable interface value, and the end anchorage internal force not exceeding the allowable anchorage value are simultaneously satisfied.

[0060] This step is a reverse control step for connection safety. Its core logic is that the ultimate bearing capacity calculated in step S700 is determined based on cross-sectional analysis, where the Fe-SMA strip stress σ f It is only constrained by the material constitutive relation. However, whether the stress can actually be reached depends on whether the bond interface and end anchorage can transfer the tensile force to the beam. If the transfer capacity of the interface or anchorage is insufficient, the section analysis results will be unsafe. S800, in turn, limits the available stress of Fe-SMA in section analysis by limiting the allowable tensile force transferred by the interface and anchorage, and recalculates the bearing capacity if necessary.

[0061] The interface allows the transmission of tensile force N. i Determination: Based on the bond-slip constitutive relation used in step S500, it is obtained by integrating along the effective bond length. When the actual bond length L... b Greater than the effective bond length L e At that time, N i Take the ultimate bearing capacity of the interface (i.e., the shear stress along L) e (a constant value that converges after integration); when L b Less than L e At that time, N i The value is taken from the integral result of the actual bonding length, at which point the interface force transfer efficiency η is obtained. i If the value is less than 1, the interface allows the transmission of tensile force N. i =η i ·A f ·σ r At the same time, the maximum interfacial shear stress τ needs to be checked. max,cal Does it exceed the temperature-corrected peak interfacial bond stress τ? max,T If it exceeds, then it should be τ max,T Control N i The upper limit.

[0062] Anchoring allows the transmission of tensile force N aDetermination: The minimum value among the anchorage device's own bearing capacity, the local bearing capacity of the concrete in the anchorage zone, and the anchorage slip control force is taken. The anchorage device's own bearing capacity is calculated according to the steel structure connection design method based on the anchor plate thickness, bolt diameter, or wedge structure; the local bearing capacity of the concrete in the anchorage zone is calculated according to the local compressive bearing capacity formula in the current concrete structure design code; the anchorage slip control force is equal to the equivalent stiffness k of the anchorage device. a Multiply by the anchorage slip Δs a , where k a The anchorage bearing capacity is determined by calculation based on the detailed anchorage drawings or by testing the anchorage bearing capacity.

[0063] Determination and Iterative Calculation of Controlled Failure Mode: The stress in the Fe-SMA strip in the cross-section analysis is σ. f The corresponding tensile force is T. f =A f ·σ f Comparing T f With N i N a The size of T. f At the same time less than N i and N a If the cross-sectional analysis result indicates the control failure mode, both the interface and anchorage are safe, and the calculation results of step S700 are output. If T f Greater than N i or N a For any value in N, then N i and N a The smaller value in the range is the control value, and the stress limit σ can be used to back-calculate Fe-SMA. f,use =min(N i N a ) / A f Using σ f,use σ in the replacement section analysis f Repeat step S600 for cross-sectional axial force balance iteration (at this time, the Fe-SMA tensile force within the cross-section is forcibly limited to A). f ·σ f,use (Other material internal forces are redistributed to satisfy axial force balance) and the ultimate bending moment is calculated in step S700 to obtain the corrected ultimate bearing capacity. After correction, the interface shear stress and anchorage internal forces are checked again to see if they meet the requirements. If not, σ is further reduced. f,use The process is iterated again until the following conditions are met simultaneously: the internal forces of the cross section are in equilibrium, the interface shear stress is not greater than the allowable value of the interface, and the end anchorage internal force is not greater than the allowable value of the anchorage.

[0064] This method incorporates the allowable tensile force transferred at the interface and the allowable tensile force transferred at the anchorage into the ultimate state calculation, ensuring that the results of the section bearing capacity analysis are not independent of the actual transfer capacity of the connection system. The smaller of these two values ​​is used to limit the available stress of the Fe-SMA strip in the section analysis, so that the final value of the ultimate bearing capacity is controlled by the weakest link in the interface bond or end anchorage, rather than solely determined by the strength of the section material. When the transfer capacity of the interface or anchorage is insufficient, this control value replaces the original section analysis stress, and the axial force balance iteration and ultimate bending moment calculation are re-performed. This ensures that the corrected bearing capacity result satisfies the bearing conditions of the connection system after the redistribution of internal forces in the section, rather than requiring a separate verification of connection safety after the section analysis is completed. The practice of calculating the allowable tensile force transferred at the interface and the allowable tensile force transferred at the anchorage independently and then taking the smaller value ensures that the connection verification does not depend on a prior judgment of the relative strength of the interface and anchorage; the failure mode is automatically identified during the calculation process. The closing point is set after the ultimate load calculation rather than the yield load calculation, so that the modified bearing capacity can still meet the connection safety requirements under the most unfavorable state (when the Fe-SMA tension reaches its peak), rather than only in the elastic stage.

[0065] While specific embodiments of the invention have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and are not intended to limit the scope of the invention. Those skilled in the art should also understand that various modifications can be made to the embodiments without departing from the scope and spirit of the invention.

Claims

1. A method for calculating the bearing capacity of Fe-SMA-reinforced reinforced concrete beams, characterized in that, include: Obtain the geometric parameters, material parameters, and reinforcement parameters of the reinforced concrete beam to be strengthened, and obtain parameters reflecting the residual state of the beam after pre-damage unloading; The residual state parameters include at least the residual strain of ordinary tensile steel bars; Obtain the cross-sectional parameters, material parameters, pre-strain, activation temperature, bonding length, interfacial bonding parameters, and end anchoring parameters of Fe-SMA strips; The material recovery stress of the Fe-SMA strip under fully constrained conditions is determined based on the pre-strain and activation temperature. Based on the bond-slip constitutive relationship between Fe-SMA strips and concrete, an interface micro-element equilibrium equation is established along the bond length. The actual tensile force transmitted at the interface is obtained by integration. The ratio of the actual tensile force transmitted to the tensile force corresponding to the material recovery stress is taken as the interface force transmission efficiency. The anchorage deformation loss is determined based on the end anchorage stiffness. After deducting the interface slip loss, anchorage deformation loss and active recovery deformation loss of the beam in sequence from the material recovery stress, the effective prestress of the Fe-SMA strip on the damaged beam is determined. Taking the state of the beam after thermal activation and cooling as the starting point for reloading calculation, the residual strain formed after the pre-damage unloading is included in the total strain of ordinary tensile reinforcement, and the effective prestress of the structure is included in the total stress of Fe-SMA strip. The cross-sectional strain compatibility relationship is established by adopting the plane section assumption, and the neutral axis height is solved by cross-sectional axial force balance iteration. Based on the neutral axis height, the yield moment is calculated and converted into a yield load when the ordinary tensile steel reaches the yield strain as the yield state criterion, and the ultimate moment is calculated and converted into an ultimate load when the concrete in the compression zone reaches the ultimate compressive strain as the ultimate state criterion. The allowable tensile force transmitted at the interface is determined based on the bond-slip constitutive relationship, and the allowable tensile force transmitted at the anchorage is determined based on the end anchorage structure. The smaller of the allowable tensile force transmitted at the interface and the allowable tensile force transmitted at the anchorage is used to limit the available stress of the Fe-SMA strip in the ultimate state. When the available stress is less than the Fe-SMA strip stress determined by the section analysis, the available stress is used to replace the original stress, and the section axial force balance iteration and ultimate load calculation are performed again.

2. The method according to claim 1, characterized in that, The effective prestress of the structure is determined by the following formula: ； in, For effective prestressing of the structure, To restore stress in materials; The interface slip loss is calculated by subtracting the interface force transmission efficiency from 1 and then... Determined by multiplication; The anchorage deformation loss is determined by dividing the anchorage slip by the total length of the Fe-SMA strip and then multiplying by the elastic modulus of Fe-SMA. The active recovery deformation loss of the beam is determined by the Fe-SMA shortening caused by the arching deformation and crack closure deformation. The temperature difference deformation loss is determined by multiplying the difference in linear expansion coefficients between Fe-SMA and concrete by the difference between the activation temperature and the ambient temperature.

3. The method according to claim 1, characterized in that, The method for determining the interface force transmission efficiency is as follows: By taking infinitesimal elements along the bonding length, the axial force of the Fe-SMA strip is established. With interface shear stress Differential equilibrium equations: ； in, The width of a single Fe-SMA strip; combined bond-slip constitutive relation And Fe-SMA axial constitutive relation Formation of relative sliding of the interface The second-order differential equation; The elastic modulus of Fe-SMA This represents the total cross-sectional area of ​​the Fe-SMA. For the axial displacement of the Fe-SMA strip; with the free end Loading end Numerical integration of the boundary conditions yields the slip distribution along the bond length. and shear stress distribution Integrating the shear stress along the entire length yields the actual tensile force transmitted at the interface. The actual transmitted tension and The ratio is the interface force transmission efficiency. .

4. The method according to claim 1, characterized in that, The anchorage deformation loss is determined by the allowable tensile force transmitted by the end anchorage, which is the minimum value among the bearing capacity of the anchorage device itself, the local bearing capacity of the concrete in the anchorage zone, and the anchorage slip control force. The anchorage slip control force is determined by multiplying the equivalent stiffness of the anchorage device by the amount of anchorage slip. The anchorage deformation loss is calculated by dividing the amount of anchorage slip by the total length of the Fe-SMA strip and then multiplying it by the elastic modulus of Fe-SMA.

5. The method according to claim 1, characterized in that, The residual state formed after pre-damage unloading is determined by the comprehensive equivalent damage coefficient. Classify into levels: ； in, This is the ratio of the bending stiffness of the section after unloading to the bending stiffness of the section in its intact state. It is the ratio of the residual mid-span deflection to the reference deflection. It is the ratio of the maximum residual crack width to the reference crack width. This is the ratio of the residual strain to the yield strain of ordinary tensile steel bars; , , , The weighting coefficients for each damage index are determined by pairwise comparisons of four indices—stiffness degradation, residual deflection, residual cracks, and residual strain in the reinforcing steel—using the analytic hierarchy process (AHP), and satisfying the following conditions: ;according to The value classifies the beam into minor, moderate, and severe damage levels.

6. The method according to claim 1, characterized in that, The method for establishing the cross-sectional strain compatibility relationship is as follows: The compressive strain of the concrete at the compression edge of the cross section is taken as The height of the neutral axis is As a basic variable, the distance from the compression edge on the cross section is... The strain increment at a given point is linearly distributed according to the following formula: ； in, This represents the increase in concrete strain at the compression edge during reloading, with tension being positive and compression being negative. Location of ordinary tension reinforcement Ordinary compression reinforcement position Fe-SMA strip position Substituting these values ​​into the linear distribution, we obtain the strain increments of each material during the reloading process: The total strain of ordinary tensile steel reinforcement is: ； For ordinary tensile reinforcement, The residual strain of ordinary tensile reinforcement after pre-damage unloading. This refers to the effective height of ordinary tension reinforcement; The total strain of ordinary compression steel bars is: ； This represents the total strain of ordinary compression steel bars. The residual strain of ordinary compression steel bars after pre-damage unloading. This is the distance from the resultant force point of ordinary compression reinforcement to the compression edge of the cross section; The total stress of the Fe-SMA strip is: ； The total stress of the Fe-SMA strip. For effective prestressing of the structure, Additional stress generated by reloading; The residual strain and the effective prestress of the structure As a historical state quantity, it directly participates in the calculation of the internal forces of the section, and its formation path is not repeatedly included in the calculation during the reloading process.

7. The method according to claim 6, characterized in that, Determined in the following manner: First, based on the linear elasticity relationship Calculation, where The elastic modulus of Fe-SMA is given by the additional strain: ； In the formula This represents the increase in strain of the concrete at the compression edge. The distance from the resultant force point of the Fe-SMA strip to the compression edge of the cross section is denoted as . The height of the neutral axis. The strain difference between Fe-SMA and the concrete at the bottom of the beam caused by interfacial slip; When the total stress of Fe-SMA strip Exceeding the nominal yield strength Then, the Ramberg-Osgood model was used to determine its stress: ； in, For the total strain of Fe-SMA, The hardening index is determined based on material testing.

8. The method according to claim 7, characterized in that, The determination of whether the concrete in the compression zone has reached the ultimate compressive strain is simplified by using an equivalent rectangular stress diagram. The compressive stress in the equivalent rectangular stress diagram is taken as... The height of the pressure zone is taken as ,in, This refers to the axial compressive strength of concrete. and These are preset coefficients.

9. The method according to claim 1, characterized in that, When interface peeling or end anchorage failure is the controlling failure mode, the smaller of the ratio of the allowable tensile force transmitted at the interface to the total cross-sectional area of ​​the Fe-SMA and the ratio of the allowable tensile force transmitted at the anchorage to the total cross-sectional area of ​​the Fe-SMA is used as the available stress limit for the Fe-SMA. After replacing the Fe-SMA strip stress in the original section analysis with this limit, the section axial force balance iteration and ultimate bending moment calculation are re-executed until the section internal force balance, the interface shear stress not exceeding the allowable interface value, and the end anchorage internal force not exceeding the allowable anchorage value are simultaneously satisfied.

10. The method according to claim 1, characterized in that, The beam actively recovers deformation loss The method for determining it is as follows: First, the initial estimate of the effective prestress of the structure. Calculate the effective preload The distance from the point of effect of preload and Fe-SMA combined force to the centroid of the cross section is eccentricity. Multiply to obtain the equivalent preloaded bending moment Based on the remaining bending stiffness of the damaged beam after unloading Calculate the thermally activated anti-arch value The shortening of the Fe-SMA strip is calculated from this anti-arching value, and then converted into the corresponding stress loss; simultaneously, according to The change in strain at the bottom of the beam is used to calculate the crack closure rate. The sum of all crack closure rates is used to calculate another portion of the stress loss. The two losses are then superimposed to obtain the final value. Substitute The effective prestress is corrected, and the anti-arch value and crack closure amount are recalculated based on the corrected effective prestress. The iteration continues until the change in the anti-arch value and crack closure amount is less than the preset allowable value.

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