Rust RC beam bending-deflection whole process prediction method considering bonding degradation systematically

Abstract

The invention discloses a method for systematically predicting the bending-deflection whole process of a rusted RC beam by considering bonding degradation. The method comprises the following steps: firstly, dividing a rusted RC beam into a plurality of units, and calculating the bonding stress between a rusted steel bar and concrete; giving a small load, calculating the stress strain and deflection deformation of each unit reinforcing steel bar and concrete according to the plane section assumption, if the tensile reinforcing steel bar is found to slip, entering the next step, otherwise, increasing the load, and repeatedly calculating until the RC beam is damaged; after the tensile steel bar slides, calculating the stress-strain and deflection deformation of the steel bar and the concrete according to the fact that the total deformation of the tensile steel bar in the RC beam is equal to the total deformation of the concrete at the corresponding position, increasing the load, and repeatedly calculating until the test beam is damaged; after calculation is finished, results such as a bending-deflection whole-process curve and flexural capacity of the rusted RC beam can be output. According to the method, the influence of corrosion, bonding and degradation of the tensile steel bars on the bending deformation performance of the RC beam can be systematically considered, and a calculation basis is provided for service performance evaluation of the rusted RC beam.

Description

Technical Field

[0001] The invention relates to the technical field of service performance evaluation methods for corroded RC beams, and in particular to a method for predicting the entire bending-deflection process of corroded RC beams taking bond degradation into consideration. Background Art

[0002] In recent decades, corrosion of steel bars in concrete is one of the main causes of deterioration of reinforced concrete (RC) structures. Loss of cross-sectional area, degradation of mechanical properties, spalling of cover, and degradation of the bond between steel and concrete can all lead to deterioration of the performance of RC structures. Accurate prediction of the flexural properties of corroded reinforced concrete beams is crucial for decision-making on their repair and reinforcement. The degradation caused by corrosion, such as reduction in cross-sectional area, degradation of mechanical properties, and degradation of bond, should be considered in the prediction, and the latter is more difficult to consider than the first two because it can lead to uncoordinated deformation between steel and concrete.

[0003] At present, scholars at home and abroad have proposed some methods for calculating the bending capacity of RC beams that take into account the influence of corroded bonding. The most mainstream method is the correction coefficient method based on experimental fitting, which uses the flat section assumption to calculate the steel bar strain value and make corrections to consider the influence of the uncoordinated deformation caused by corroded bonding degradation. This method is simple, but its applicability is limited by the previous fitting test. For this reason, some scholars have established more widely applicable analytical models, but these models are still mainly used to calculate the bending capacity of corroded RC beams, and cannot be used to calculate the deflection deformation of RC beams.

[0004] At present, the commonly used method for predicting the deflection of RC beams is the equivalent stiffness method that considers the influence of section cracking. Although this model is simple, this method can only be used to predict the deflection of RC beams under specific loads. At the same time, it cannot consider the bond changes between steel bars and concrete, and is difficult to use for predicting the deflection of corroded RC beams. For corroded RC beams, finite element simulation is a feasible deflection prediction method, which considers the bond effect between steel bars and concrete through nonlinear spring units. However, finite element modeling is usually complex and computationally expensive, making it difficult to be widely used. In recent years, some scholars have proposed load-deflection prediction models for corroded RC beams that consider the effects of bond degradation, but these models only consider the local bond and slip between bending cracks, and do not consider the slip of corroded steel bars in the entire RC beam section. At present, there is no load-deflection prediction method for corroded RC beams that systematically considers the effects of bond degradation.

[0005] To this end, the present invention proposes a method for predicting the entire bending-deflection process of corroded RC beams that systematically considers bond degradation. The overall slip characteristics between the steel bars and concrete in the entire RC beam section under corrosion bond degradation and the resulting uncoordinated deformation effects are systematically considered. The bending deformation curve and bending bearing capacity of the corroded RC beam can be accurately predicted, providing a calculation basis for the service performance evaluation of the corroded RC beam. Summary of the invention

[0006] The purpose of the present invention is to provide a method for predicting the whole process of bending-deflection of a corroded RC beam taking into account bond degradation, which can quickly and accurately predict the bending deformation curve and bending bearing capacity of the corroded RC beam, and provide a calculation basis for the service performance evaluation of the corroded RC beam.

[0007] In order to effectively solve the above technical problems, the technical solutions adopted by the present invention are as follows:

[0008] A method for predicting the entire bending-deflection process of a corroded RC beam with systematic consideration of bond degradation comprises the following steps:

[0009] (1) The RC beam is divided into multiple units. These units are numbered 1, 2, 3, ... n from the left support to the mid-span. Assume that the length of each unit is l e , calculate the effective bond stress τ between the corroded steel bar and concrete e,ρ and residual bond stress τ r,ρ ;

[0010] (2) Given a small load P, calculate the tensile force F of the tensile reinforcement in unit i (i = 1, 2, 3, ... n) based on the plane section assumption s,i and the cross-sectional curvature φ i , the mid-span deflection Δ of the corroded RC beam can be expressed as formula (1):

[0011]

[0012] Where x i is the distance from the midpoint of unit i to the left support of the RC beam;

[0013] Bond stress τ required for the tensile force of the tensile reinforcement in adjacent units to increase r,i It can be expressed as formula (2):

[0014]

[0015] Where n s and d are the number and diameter of the tensile reinforcement, respectively;

[0016] Whether the tensile reinforcement has slipped is determined according to formula (3):

[0017]

[0018] (3) After the tensile reinforcement slips, the stress-strain response and deflection deformation of each unit reinforced concrete are calculated based on the total deformation of the tensile reinforcement in the RC beam section being equal to the total deformation of the concrete at the corresponding position. Assume that the anchor force at the end of the tensile reinforcement in the RC beam under a given load is F ak , the tensile force F of the tensile reinforcement in element i s,iIt can be expressed as formula (4):

[0019]

[0020] Where m is the number of the last unit of the RC beam bending shear section, τ b,i is the bond stress between the tensile reinforcement and concrete, and τ is taken according to the relative slip between the tensile reinforcement and concrete at each unit. e,ρ or τ r,ρ ;

[0021] Calculate the tensile reinforcement strain ε in element i according to the bilinear constitutive model s,i , the total elongation of the tensile reinforcement in the RC beam ΔL s It can be expressed as formula (5):

[0022]

[0023] The relative slip between the tensile reinforcement and concrete at unit i can be calculated by subtracting the elongation of the concrete from the elongation of the tensile reinforcement at that location. Since the actual elongation of the concrete is very small, it can be ignored. The relative slip S between the tensile reinforcement and concrete at unit i is i It can be expressed as formula (6):

[0024]

[0025] The bonding stress τ in formula (4) b,i The value can be determined by formula (7):

[0026]

[0027] Where s 3 is the critical slip value between the effective bond stress and residual bond stress between the steel bar and concrete. In the prediction process, τ is first taken b,i The value of τ e,ρ Calculate the tensile force and slip S of the tensile reinforcement at unit i i , when S i >s 3 When τ b,i The value of τ r,ρ Calculate the tensile reinforcement forces of all units after unit i;

[0028] After the tensile reinforcement enters the slip state, the deformation of the tensile reinforcement and the concrete section no longer obey the plane section assumption, but the deformation of the concrete section itself still obeys the plane section assumption, that is, in the known unit i, the tensile reinforcement F s,i Based on the plane section assumption, the equivalent strain ε of concrete at the tensile reinforcement position in the unit can be calculated. cs,i , the total elongation of concrete at the tensile reinforcement position in the RC beam ΔLc It can be expressed as formula (8):

[0029]

[0030] Elongation of tensile reinforcement in RC beams ΔL s Should be equal to the elongation of concrete at the tensile reinforcement position ΔL c Otherwise, it is necessary to repeatedly modify the assumed tensile reinforcement end anchor force F ak , until ΔL s =ΔL c , so far the deflection of the RC beam under a given load can be calculated.

[0031] Gradually increase the load and repeat the above calculation process until the test beam is destroyed.

[0032] (4) Output the bending-deflection curve of the corroded RC beam, bending bearing capacity and other results, and the calculation is completed.

[0033] The beneficial effects of the present invention are as follows: the present invention provides a method for predicting the entire bending-deflection process of a corroded RC beam that systematically considers bond degradation, systematically considers the overall slip characteristics between the steel bars and concrete in the entire RC beam section under corrosion bond degradation and the influence of the induced uncoordinated deformation, can quickly and accurately predict the bending deformation curve and bending bearing capacity of the corroded RC beam, and provides a calculation basis for evaluating the service performance of the corroded RC beam. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a schematic diagram of unit division of the RC beam of the present invention.

[0035] Figure 2 It is the bilinear bond-slip model used in the present invention.

[0036] Figure 3 It is a schematic diagram of the effective bonding stage of the tensile steel bars of the RC beam of the present invention.

[0037] Figure 4 It is a schematic diagram of the sliding stage of the tensile reinforcement of the RC beam of the present invention.

[0038] Figure 5 It is a calculation flow chart for predicting the load-deflection curve of the beam of the present invention.

[0039] Figure 6 It is the experimental beam size parameter used to verify the model of the present invention in Experimental Example 3.

[0040] Figure 7 It is a comparison diagram of the load-deflection curve predicted by the present invention and the experimental results in Example 3.

[0041] Figure 81 is the load-deflection diagram of the test beam in Example 3 predicted by the bond degradation MF model of the present invention.

[0042] Fig. 9 3 is the load-deflection diagram of the test beam in Example 3 predicted by the bond degradation MP model of the present invention.

[0043] Fig.10 It is the experimental beam size parameter used to verify the model of the present invention in Example 4.

[0044] Fig.11 It is a comparison diagram of the load-deflection curve predicted by the present invention and the experimental results in Example 4.

[0045] Fig.12 1 and 10 are load-deflection diagrams of the test beam in Example 4 predicted by the present invention using the bond degradation MF and MP models, respectively. DETAILED DESCRIPTION

[0046] The present invention is further described below in conjunction with the accompanying drawings and embodiments. When the following description refers to the drawings, unless otherwise indicated, the same symbols in different drawings represent the same or similar elements.

[0047] Example 1

[0048] like Figure 1 As shown in the figure, the RC beam is divided into multiple units, which are numbered 1, 2, 3, ... n from the left support to the mid-span. Assume that the length of each unit is l e .

[0049] use Figure 2 The bilinear bond-slip model shown in Figure 1 calculates the bond stress between the tensile reinforcement and concrete. As the slip increases, the bond stress is idealized into two average values, namely, the effective bond stress τ e and residual bond stress τ r . Effective bond stress of uncorroded steel bar τ e The model proposed in the literature "Cairns J., Abdullah RBBond strength of black and epoxy-coated reinforcement-A theoretical approach. ACI Materials Journal, 1996, 93 (4): 362-369" can be used for calculation as follows:

[0050]

[0051] Where n is the number of transverse ribs on the steel bar section; A r is the transverse rib area, which can be expressed as A r =πDh r; D is the diameter of the steel bar; h r is the transverse rib height; f coh is the adhesive force between concrete and steel bars; δ is the angle between the transverse rib and the steel bar axis; φ is the friction angle; s r is the transverse rib spacing; C r It is used to characterize the shape coefficient of the transverse rib, and is generally taken as 0.8. Other parameters are: h r =0.007d; δ=45°; tanφ=0.3; s r =0.6d,f coh =3.68MPa. max is the maximum pressure that the steel bar bears when the bond fails, calculated as follows:

[0052]

[0053] Where b is the width of the beam section; n st is the number of tensile reinforcements; Δz is the stirrup spacing; f ct is the tensile strength of concrete, f c ′ is the compressive strength of concrete, and the relationship between the two is:

[0054] Residual bond stress τ r Much smaller than the effective bonding stress τ e , according to the effective bond stress τ proposed in the literature "Giuriani E, Plizzari G, Schumm C. Role of stirrups and residual tensile strength of cracked concrete on bond[J]. Journal of Structural Engineering, 1991, 117(1): 1-18." r 0.4τ e In the case of steel bar pull-out failure and concrete splitting failure, the critical slip s 3 can be taken as c clear (c clear is the clear distance between steel ribs) and 0.5c clear .

[0055] Corrosion deteriorates the bond performance between concrete and steel bars. The empirical values ​​proposed in the literature "Bhargava K, Ghosh AK, Mori Y, et al. Suggested empirical models for corrosion-induced bond degradation in reinforced concrete. Journal of Structural Engineering, 2008, 134 (2): 221-230" are used to represent the bond degradation between corroded steel bars and concrete. In this model, the bond strength after steel bar corrosion is expressed as a function of the steel bar corrosion rate:

[0056] (i) Bond degradation model based on pull-out components (bond degradation MP model):

[0057]

[0058] (ii) Bond degradation model based on flexural-tension members (bond degradation MF model):

[0059]

[0060] Where R(ρ) is the equivalent degradation coefficient of the bond strength of corroded steel bars; ρ is the steel bar corrosion rate.

[0061] The average effective bond stress τ between steel bars and concrete after corrosion e,ρ and residual bond stress τ r,ρ It can be expressed as:

[0062] τ e,ρ =R(ρ)τ e (5)

[0063] τ r,ρ =R(ρ)τ r (6)

[0064] Given a small load P, the strain ε of the tensile reinforcement in unit i (i = 1, 2, 3, ... n) is calculated based on the plane section assumption: s,i and the reinforcement strain ε′ s,i It can be expressed as:

[0065]

[0066] Where ε ct,i and ε cb,i are the concrete strains at the upper and lower edges of section i, respectively; h is the height of the beam section; h 0 and a′ s are the distances from the centroid of the reinforcement of section i to the upper and lower concrete edges respectively.

[0067] According to the elastoplastic model proposed in the literature “El-Tawil, S., Ogunc, C., Okeil, A., and Shahawy, M. Static and fatigue analysis of RC beams strengthened with CFRP laminates. Journal of Composites for Construction, 2001, 5(4), 258-267.”, the stress-strain relationship of the steel bar is expressed as

[0068]

[0069] Where E s 、E sp are the elastic modulus and deformation modulus after yielding of the steel bar; f sy and ε sy are the yield strength and yield strain of the steel bar, respectively. sp It is expressed as:

[0070]

[0071] Where f su and ε su are the ultimate strength and ultimate strain of the steel bar, respectively.

[0072] In the present invention, the tensile force of concrete is ignored, and the pressure of concrete can be calculated as follows:

[0073]

[0074] Where F c,i is the concrete pressure; b is the beam width; y is the distance from the top of the section to any section height.

[0075] The distance from the point where the total concrete pressure acts to the top of the section (y c,i ) can be expressed as:

[0076]

[0077] The forces of the tensile reinforcement, the supporting reinforcement, the concrete and the bending moment of any element i should satisfy the following equilibrium equation:

[0078] F c,i +F′ s,i +F s,i =0 (14)

[0079] F c,i (h 0 -y c,i )+F′s,i (h 0 -a′ s )=M i (15)

[0080] Among them, M i is the bending moment of section i.

[0081] For a given load (P), the bending moment (M i ); Calculate the strain (ε) of the upper and lower edges of any element i according to equations (14) and (15). ct,i &ε cb,i ); the cross-sectional curvature of element i (φ i ) can be expressed as:

[0082]

[0083] The deflection (Δ) of the RC beam under a given load (P) can be calculated from the cross-sectional curvature of the 1-unit to the n-unit.

[0084]

[0085] Where Δ is the mid-span deflection of the beam; x i is the distance from the middle of element i to the beam support.

[0086] As the given load increases, the stress increment of the steel bars between adjacent units may exceed the effective bond strength of the steel bars, and the steel bars will slip. This is judged based on the tensile force increment of the tensile steel bars in the adjacent units and the effective bond strength of the steel bars. The bond stress τ required for the tensile force of the tensile steel bars in the adjacent units to increase r,i The tensile force in the tensile reinforcement of the adjacent unit (F s,i+1 ,F s,i )express:

[0087]

[0088] If the calculated bonding stress τ r,i Less than the effective bond stress τ provided between the tensile reinforcement and concrete e , then increase the load to judge again or failure will occur, otherwise, slippage occurs between the steel bars and concrete.

[0089] The tensile reinforcement is anchored by the bond between the reinforcement and the concrete at the ends of the beam. The anchoring force of the reinforcement will also increase with the increase of the given load (P). Because of the slip between the reinforcement and the concrete, the strain of the reinforcement cannot be calculated using the flat section assumption, but can be determined based on the principle that the total elongation of the tensile reinforcement and the concrete at its corresponding position in the entire beam is equal. First, assume that the reinforcement anchoring force is F ak , then the tensile force F of the tensile reinforcement in any unit of the beam iss,i It can be expressed as:

[0090]

[0091] Where m is the number of elements in the bending-shear zone of the beam; τ b,i is the bond stress between the steel bar and the concrete, and τ is taken according to the slip between the concrete and the tensile steel bar at unit i. e,ρ or τ r,ρ .

[0092] The strain of the tensile reinforcement along the beam in the unit can be expressed as:

[0093]

[0094] The total elongation of the tensile reinforcement in the whole beam (ΔL s ) can be expressed as:

[0095]

[0096] The slip between the tensile reinforcement and concrete at unit i can be calculated by subtracting the elongation of concrete from the elongation of the tensile reinforcement at the same position. The actual elongation of concrete at the tensile reinforcement is very small and can be ignored compared with the elongation of the reinforcement. Therefore, the slip between the tensile reinforcement and concrete at unit i (S i ) can be expressed as:

[0097]

[0098] The bonding stress value (τ b,i ) can be determined by the following formula:

[0099]

[0100] In the prediction process, the bonding stress (τ b,i ) is taken as τ e,ρ , calculate the tension, strain and slip of units 1, 2, ..., i in turn. When the slip exceeds the critical value, the bond stress (τ b,i ) takes the value of τ r,ρ Used for subsequent calculation of unit reinforcement tension.

[0101] The tensile reinforcement (F s,i ) is determined, the concrete (ε ct,i &ε cb,i ) is determined as follows: First, the strain of the reinforcement (F′) is calculated according to formulas (11), (12), (13), (14), and (15). s,i ) and concrete (F c,i ) and then calculate the Fs,i Combined with formula (14) and (15), the strain of concrete (ε ct,i &ε cb,i ).

[0102] Concrete at the location of the tensile reinforcement (ε cs,i ) The equivalent strain can be expressed as:

[0103]

[0104] The total elongation of concrete at the location of the tensile reinforcement in the entire beam (ΔL c ) can be expressed as:

[0105]

[0106] The elongation of the tensile reinforcement in the whole beam (ΔL s ) should be equal to the elongation of the concrete at the tensile reinforcement position (ΔL c Otherwise, the assumed anchor force (F ak ), and repeat the calculation until ΔL s =ΔL c After that, according to equations (16) and (17), the cross-sectional curvature (φ) of all elements can be calculated. i ) and the deflection (Δ) of the beam under a given load (P). With further increase in load (P), successive deflections (Δ) can be calculated until the beam fails, giving a complete load-deflection curve. The ultimate load of the beam can be determined by three criteria: 1. The maximum compressive strain of the concrete ε ct,i Exceeding the limit strain ε cu ; 2 Maximum tensile strain of steel bar ε s,i Exceeding the limit strain ε su ;3 Anchorage force F of steel bars ak Exceeding the critical value F ak,c .

[0107] Example 2

[0108] The present invention is explained more intuitively through a calculation flow chart.

[0109] Figure 5 The calculation flow chart of the present invention is shown in Figure 2. By giving a small initial load and gradually increasing the load, the load-deflection curve of the beam can be predicted. The ultimate load of the beam can be determined by three criteria: 1. The maximum compressive strain of concrete ε ct,i Exceeding the limit strain ε cu ; 2 Maximum tensile strain of steel bar ε s,i Exceeding the limit strain ε su ;3 Anchorage force F of steel bars ak Exceeding the critical value F ak,c .

[0110] First, the beam is divided into multiple units and these units are numbered. Then the effective bond stress (τ e,ρ ) and residual bond stress (τ r,ρ ), in addition, other basic parameters are required, such as the size of the beam, the mechanical parameters of the material, the corrosion rate of the steel bars, etc. The calculation process is as follows:

[0111] The calculation starts with a small load (P). First calculate the bending moment (M i ), and then calculate the strains of the upper and lower edges of the concrete (ε ct,i &ε cb,i ) and the strain and tension of the tensile reinforcement (εs ,i &F s,i Next, we calculate the cross-sectional curvature (φ) of all elements. i ), calculate the deflection (Δ) of the beam under a given load (P). Calculate the required bond stress (τ r,i ), and the effective bonding stress (τ e,ρ ) for comparison. If τ r,i >τ e,ρ , then use formula (19) to calculate the tensile force of the tensile steel bar and rebuild the force and moment balance; otherwise, determine whether the beam exceeds the ultimate load of the beam. If so, end the calculation; otherwise, increase the load (P) and repeat the calculation until a certain judgment result is true.

[0112] When slip occurs between the steel bar and concrete, the bending moment (M i ), assuming that the reinforcement anchorage force is (F ak ), and calculate the stress and strain of each unit tensile reinforcement (F s,i &ε s,i ), and then the total elongation of the tensile reinforcement in the whole beam (ΔL s ). Using the upper and lower edge strains of concrete (ε ct,i &ε cb,i ) indicates the stress of the erected steel bars (F′ s,i ) and concrete pressure (F′ s,i ), and combine the force and moment equilibrium equations to calculate the strains (ε ct,i &ε cb,i ), the strain of the tensile reinforcement out of the concrete (ε cs,i ), calculate the elongation (ΔL c ). Determine ΔL s =ΔL c Are they equal? ​​If yes, calculate the deflection (Δ), otherwise modify the reinforcement anchorage force F ak Repeat the calculation until ΔLs =ΔL c When calculating the deflection, determine whether the beam has reached the limit state. If so, end the calculation. If not, add load after the deflection calculation is completed. Again, assume that the steel anchor force (F ak ) and repeat the calculation until the beam fails.

[0113] Example 3

[0114] Figure 6 As the key parameter of the specimen, the experimental results of the published literature "Yu Dan. Bearing capacity test and finite element simulation of corroded reinforced concrete beams. Master's degree thesis of Guangxi University, 2013" were used to verify the accuracy of the proposed method in predicting the load-deflection curve of corroded RC beams. The length of these beams is 1700mm, and the cross-sectional dimensions are b×h=120×200mm. Two deformed steel bars with a diameter of 14mm were used as tensile steel bars, and two deformed steel bars with a diameter of 10mm were used as stand bars. The yield strength and ultimate strength of the tensile steel bars are 389.2MPa and 566.2MPa, respectively, and the yield strength and ultimate strength of the hanger bars are 267.5MPa and 356.7MPa, respectively. Only the tensile steel bars are subject to accelerated corrosion. The beams are simply supported with a clear span of 1500mm and are loaded symmetrically at two points. The two groups of beams BM1 and BM2 are loaded at 500mm and 700mm, respectively. The main parameters and test results are listed in Table 1.

[0115] Table 1 Experimental data and verification results

[0116]

[0117] Note: cu is the cubic compressive strength of concrete. In this model, f c ′ is taken as 0.76f cu . l is the load span of the beam. c is the thickness of the concrete cover of the tensile reinforcement. exp is the experimental value of the ultimate load of the beam. p,MF and P p,MP The ultimate load of the beam is predicted based on the bond degradation MF and MP models proposed in the literature "Bhargava K, Ghosh AK, Mori Y, et al. Suggested empirical models for corrosion-induced bond degradation in reinforced concrete[J]. Journal of Structural Engineering, 2008, 134(2): 221-230."

[0118] The model proposed in the present invention can predict the load-deflection curve and the ultimate load. The predicted value of the load-deflection curve is compared with the experimental value and the ultimate load. Figure 7 The predicted load-deflection curves are in good agreement with the experimental ones, so the proposed model can accurately predict the degradation of stiffness and ultimate load caused by reinforcement corrosion. All predictions use the bond degradation MF and MP models. For non-corroded and slightly corroded beams, the predicted curves obtained using the two bond degradation models are the same because the bond degradation MF and MP models are similar for slight bond degradation. As the corrosion rate increases, the predicted curves using the MF model show earlier stiffness degradation and slightly smaller ultimate loads than the curves using the MP model because the bond degradation rate of the MF model is faster. This shows that the proposed model can effectively capture the effect of bond degradation on the bending behavior of corroded beams, and the proposed model can accurately predict the load-deflection curves of corroded beams.

[0119] like Figure 8 As shown in Figure 2, the load-deflection curves predicted by the MF model for beams BM1 and BM2 at different corrosion rates are summarized. The results show that the stiffness and ultimate load of the beams decrease with increasing corrosion rate. However, for slightly corroded beams, the attenuation of stiffness is very small. With increasing corrosion rate, the stiffness of the beams also degrades significantly during loading before the tensile reinforcement yields. This causes the corroded tensile reinforcement of the beam to slip relative to the surrounding concrete at a small load. The relative slip reduces the synergy and integrity between the reinforcement and concrete, resulting in stiffness degradation of the beam. The greater the corrosion rate, the earlier the significant stiffness degradation of the beam occurs during loading. In addition, the significant stiffness degradation is also affected by the loading span of the beam. For example, beam BM2-2 has a similar corrosion rate to beam BM2-1, but a longer loading span, so the significant stiffness degradation of BM2-2 occurs much earlier than BM1-2.

[0120] Fig. 9The predictions of the load-deflection curves of the BM1 and BM2 series beams at different corrosion rates using the MP model are summarized. The stiffness degradation of the severely corroded beams occurs earlier when predicted using the MF model than when predicted using the MP model. This is because the bond degradation rate measured by the MF model is faster than that of the MP model. The ultimate loads of the beams predicted using the MF and MP models are summarized in Table 1. For the slightly corroded beams, the ultimate loads predicted by both models are similar. As the corrosion rate increases, the ultimate loads predicted using the MF model become smaller than those using the MP model, due to the faster bond degradation rate measured by the MF model. However, as the corrosion rate increases further, the ultimate loads predicted using the two models become similar again. This may be due to the complete bond degradation of the tensile reinforcement due to severe corrosion predicted by both models. In such cases, the corroded beams almost lose their bond at higher loading states, resulting in similar ultimate load predictions by both models.

[0121] Example 4

[0122] Fig.10 are the parameters of the specific beam. The experimental results of the published literature “Wang, L., Ma, Y., Ding, W., Zhang, J., and Liu, Y., Comparative Study of Flexural Behavior of Corroded Beams with Different Types of Steel Bars. Journal of Performance of Constructed Facilities, 2014, 29 (6), 04014163” were used to further verify the accuracy of the proposed method in predicting the load-deflection curve of corroded RC beams. These beams have the same length of 2400 mm and a cross section of b×h=200 mm×300 mm. Two deformed steel bars with a diameter of 20 / 22 mm and one ordinary steel bar with a diameter of 12 mm are used as tensile reinforcement at the bottom of the beam. Two ordinary steel bars with a diameter of 12 mm are used as frame reinforcement at the top of the beam. The two deformed steel bars at the bottom of the beam are subject to accelerated corrosion. The test beam is loaded at three points with a clear span of 2100 mm. Table 2 lists the main parameters and test results.

[0123] Table 2 Experimental data and verification results

[0124]

[0125] The predicted load-deflection curves are compared with the experimental load-deflection curves and the ultimate load. Fig.11As shown in Table 2, the predicted load-deflection curves are in good agreement with the tested curves, especially when the bond degradation model MF is used. The proposed model can accurately predict the stiffness degradation and ultimate load caused by corrosion of the tensile reinforcement. For the case of the MP bond degradation model, the stiffness prediction of the severely corroded beam is slightly overestimated due to the slower bond degradation of the MP model. Fig.12 A comparison of the curves predicted by the MF and MP models for beams with different corrosion rates is given. It can be found that the stiffness degradation of severely corroded beams occurs much earlier when predicted by the MF model than when predicted by the MP model, which confirms the reliability of the proposed model in including the effects of bond degradation. However, the ultimate load predicted by the MP model is very similar to that predicted by the MF model, which indicates that the bond degradation caused by corrosion has a greater impact on the stiffness of the beam than on the ultimate load. Overall, the proposed model can accurately predict the load-deflection curves of corroded RC beams with a suitable bond degradation model.

[0126] The present invention uses the above embodiments to illustrate the implementation method of the present invention, but the present invention is not limited to the above implementation methods, that is, it does not mean that the present invention must rely on the above methods to be implemented. All equivalent changes and modifications made according to the scope of the patent application of the present invention are within the scope of the present invention.

Claims

1. A method for predicting the whole process of bending-deflection of corroded RC beams with systematic consideration of bond degradation, characterized in that: The method comprises the following steps: (1) Divide the corroded RC beam into multiple units and calculate the bond stress between the corroded steel bars and concrete; (2) Given a relatively small load, the stress-strain response and deflection deformation of the steel bars and concrete in each unit are calculated based on the plane section assumption. If slippage of the tensile steel bars is found, proceed to the next step. Otherwise, increase the load and repeat the calculation until the RC beam fails. (3) After the tensile reinforcement slips, the stress-strain response and deflection deformation of the reinforced concrete of each unit are calculated based on the total deformation of the tensile reinforcement in the RC beam section being equal to the total deformation of the concrete at the corresponding position. The load is increased and the calculation is repeated until the test beam is destroyed. (4) Output the bending-deflection curve of the corroded RC beam, bending bearing capacity and other results, and the calculation is completed; In step (1), the RC beam is divided into multiple units. These units are numbered 1, 2, 3, ... n from the left support to the mid-span. Assume that the length of each unit is l e , calculate the effective bond stress τ between the corroded steel bar and concrete e,ρ and residual bond stress τ r,ρ ; In step (2), the tensile force F of the tensile reinforcement in unit i (i = 1, 2, 3, ... n) is calculated based on the plane section assumption. s,i and the cross-sectional curvature φ i , the mid-span deflection Δ of the corroded RC beam can be expressed as formula (1): Where x i is the distance from the midpoint of unit i to the left support of the RC beam; Bond stress τ required for the tensile force of the tensile reinforcement in adjacent units to increase r,i It can be expressed as formula (2): Where n s and d are the number and diameter of the tensile reinforcement, respectively; Whether the tensile reinforcement has slipped is determined according to formula (3): In step (3), assume that the anchor force at the end of the tensile reinforcement in the RC beam under a given load is F ak , the tensile force F of the tensile reinforcement in element i s,i It can be expressed as formula (4): Where m is the number of the last unit of the RC beam bending shear section, τ b,i is the bond stress between the tensile reinforcement and concrete, and τ is taken according to the relative slip between the tensile reinforcement and concrete at each unit. e,ρ or τ r,ρ ; Calculate the tensile reinforcement strain ε in element i according to the bilinear constitutive model s,i , the total elongation of the tensile reinforcement in the RC beam ΔL s It can be expressed as formula (5): The relative slip between the tensile reinforcement and concrete at unit i can be calculated by subtracting the elongation of the concrete from the elongation of the tensile reinforcement at that location. Since the actual elongation of the concrete is very small, it can be ignored. The relative slip S between the tensile reinforcement and concrete at unit i is i It can be expressed as formula (6): The bonding stress τ in formula (4) b,i The value can be determined by formula (7): Where s3 is the critical slip value between the effective bond stress and residual bond stress between the steel bar and concrete. In the prediction process, τ b,i The value of τ e,ρ Calculate the tensile force and slip S of the tensile reinforcement at unit i i , when S i >s3, take τ b,i The value of τ r,ρ Calculate the tensile reinforcement forces of all units after unit i; After the tensile reinforcement enters the slip state, the deformation of the tensile reinforcement and the concrete section no longer obey the plane section assumption, but the deformation of the concrete section itself still obeys the plane section assumption, that is, in the known unit i, the tensile reinforcement F s,i Based on the plane section assumption, the equivalent strain ε of concrete at the tensile reinforcement position in the unit can be calculated. cs,i , the total elongation of concrete at the tensile reinforcement position in the RC beam ΔL c It can be expressed as formula (8): Elongation of the tensile reinforcement in the RC beam ΔL s Should be equal to the elongation of concrete at the tensile reinforcement position ΔL c Otherwise, it is necessary to repeatedly modify the assumed tensile reinforcement end anchor force F ak , until ΔL s =ΔL c , so far the deflection of the RC beam under a given load can be calculated; Gradually increase the load and repeat the above calculation process until the test beam is destroyed. The bending-deflection curve of the RC beam, the bending bearing capacity and other results can be calculated.

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