Modeling the flexural behavior of corroded reinforced concrete beams with considering stirrups corrosion

This study shows that the stirrups corrosion should receive more attention in the serviceability limit state due to its considerable effect on flexural behavior. Based on a parametric study, it shows that the effect of the crosssection loss of tension reinforcements on the load-carrying capacity of the corroded beam is more significant than the bond strength reduction.

Journal of Science and Technology in Civil Engineering, NUCE 2020 14 (3): 26–39 MODELING THE FLEXURAL BEHAVIOR OF CORRODED REINFORCED CONCRETE BEAMS WITH CONSIDERING STIRRUPS CORROSION Nguyen Trung Kiena , Nguyen Ngoc Tana,∗ a Faculty of Building and Industrial Construction, National University of Civil Engineering, 55 Giai Phong street, Hai Ba Trung district, Hanoi, Vietnam Article history: Received 22/05/2020, Revised 14/07/2020, Accepted 21/07/2020 Abstract The reinforcement corrosion is one of the most dominant deterioration mechanisms of existing reinforced concrete structures In this paper, the effects of the stirrup corrosion on the structural performance of five corroded beams have been simulated using the finite element model with DIANA software These tested beams are divided into two groups to consider different inputs: (i) without corroded stirrups in flexural span, (ii) with locally corroded stirrups at different locations (e.g full span, shear span, middle span) FE model has been calibrated with experimental results that were obtained from the four-point bending test carried out on the tested beams This study shows that the stirrups corrosion should receive more attention in the serviceability limit state due to its considerable effect on flexural behavior Based on a parametric study, it shows that the effect of the crosssection loss of tension reinforcements on the load-carrying capacity of the corroded beam is more significant than the bond strength reduction Keywords: reinforced concrete; beam; stirrup corrosion; finite element model; flexural nonlinear behavior https://doi.org/10.31814/stce.nuce2020-14(3)-03 c 2020 National University of Civil Engineering Introduction The corrosion of reinforcement is one of the most dominant deterioration mechanisms of reinforced concrete (RC) structures It inflicts damages which lead to a decrease in the performance as well as safety of RC structures [1] The corrosion of steel rebars is associated with the loss of crosssection, the propagation of the concrete crack, and the reduction of bond strength between steel and concrete They lead to complex distributions of strains and stresses, highly nonlinear, path-dependent behavior In fact, many studies were conducted by both experimental and theoretical methods on corroded RC beams For example, the effect of the spatial variability of steel corrosion on the structural performances of corroded RC beams has been experimentally investigated and discussed by Lim et al [1] It concluded that if the non-uniform steel weight loss along the steel rebar is adequately assessed, the local damages of corroded RC beams can be physically captured For a low dispersion of cross-section loss, the structural capacity of the corroded beam is governed by the corrosion levels As the dispersion of the steel cross-section loss raises, the pitting corrosion or the local variability of the steel cross-section loss has a more significant impact than the corrosion level Coronelli and Gambarova [2] studied the modeling of corroded RC beams It stated that a critical aspect is an assessment ∗ Corresponding author E-mail address: tannn@nuce.edu.vn (Tan, N N.) 26 Kien, N T., Tan, N N / Journal of Science and Technology in Civil Engineering of pitting corrosion in the finite element (FE) model, which may induce brittle behavior in the steel rebars Therefore, corrosion affects both the strength and the ductility of a structure In order to assess the serviceability of a corroded RC structure, the parameters should be taken into consideration are not only concrete cover depth and steel rebar cross-section loss but also the reduction of the concrete section A two-dimensional nonlinear FE model has been developed in the study of Kallias et al [3] to assess the structural performance of a series of RC beams damaged by ranging corrosion levels at different locations This study shows that the loss of steel cross-section and associated concrete damage/section loss (due to the accumulation of expansive corrosion products) are found to be the main causes of loss of strength and bending stiffness The bond deterioration is responsible for changes in cracking patterns and widths Consequently, modeling bond deterioration is highly significant for performance assessment at the serviceability limit state The study of Sæther et al [4] had been conducted on how to the use of FE analysis to simulate the mechanical response of RC structures with corroded reinforcement In Vietnam, although the major deterioration of coastal structures is related to corrosion of steel reinforcement [5], the number of research works that are related to this subject is still limited Previous studies have been conducted mainly by surveying and statistical methods to assess the extent and damage of corrosion, but have not yet produced results on the behavior of corroded structures In recent years, several research works have been firstly performed to assess the behavior of corroded RC structures in a chloride environment Tan and Hiep [6] analyzed the potential of existing empirical models for prediction of steel corrosion rate by using a series of experimental data collected from the literature In an experimental study on the influence of reinforcement corrosion on steel - concrete bond stress by Tan et al [7], it concluded that when the corrosion level was in the range of to 2%, the bond stress between corroded steel and concrete is larger than that of uncorroded reinforcement and concrete As the corrosion level increases to 6.5% and more than 8.4%, the bond stress of corroded RC components decreases from 30% to 62% compared with the uncorroded case Nguyen and Tan [8] conducted a study on the prediction of the residual carrying capacity of the RC column subjected inplane axial load considering corroded longitudinal steel rebars using the finite element method This study concluded that the residual carrying capacity of corroded RC column is governed by the location and corrosion level of reinforcement The corrosion of longitudinal steel rebars in the tension zone of the column results in a more significant impact on the reduction of carrying capacity compared with the case of corroded rebars in the compression zone Recently, the studies consider mainly the influence of corroded longitudinal reinforcement on the flexural behavior of RC beams, but there are only a few that mention how stirrups corrosion affects structural behavior In this study, to understand the flexural capacity of RC beam with stirrups corrosion, several corroded beams have been simulated to examine the suitable constitutive model using FE analysis in DIANA software The simulation was carried out on five tested RC beams that are divided into two cases: (i) without corroded stirrups in flexural span (only U-type stirrups at middle span); (ii) with corroded stirrups at different locations and of different corrosion levels The validation of the simulation has been based on the load – deflection relationship that is calibrated by the experimental data The simulation results can represent the flexural behavior (e.g load carrying capacity, deflection) of the tested beams Moreover, a parametric study was also realized to assess the effect of the bond strength reduction and the cross-section loss of corroded steel rebars on the flexural behavior of corroded beams 27 2.1 Concrete material law The expansion of corrosion products induces the crack and spalling Consequently, the concrete area that is degraded by corrosion damage-indu Kien, N T., Tan, N N / Journal of Science and Technology in Civil Engineering strength compared to that of the undamaged concrete areas The corrosion Materials law for modeling corroded RCcover beam is considered in the FE model by modifying the the concrete 2.1 Concrete material law relationship of the concrete, as suggested by Lim et al [1] as illustrated in F The expansion of corrosion products induces the crack and spalling of concrete Consequently, the concrete area that is degraded by corrosion damage-induced reduced strength compared to that of the undamaged concrete areas The corrosion damage on the concrete cover is considered in the FE model by modifying the stress-strain relationship of the concrete, as suggested by Lim et al [1] as illustrated in Fig The deterioration of the concrete compressive strength can be described by Eq (1) with fc,d being the compressive strength of the corroded conFigurelaw Constitutive lawinofcompression concrete in and tension Figure Constitutive of concrete of the crete, fc being the compressive strength compression and tension [1] non-corroded concrete, k being the coefficient related to bar roughness and diameter, for the case of medium-diameter ribbed rebars a value k = 0.1 has been proposed by Cape [9], ε0 being the strain at the compressive strength fc , and ε1 being the average smeared tensile strain in the transverse direction fc,d = fc / + k (ε1 /ε0 ) (1) The strain ε1 can be estimated by Eq (2) with b0 being the section width in the state without corrosion crack, b f being the beam width expanded by corrosion cracking ε1 = b f − b0 /b0 (2) b f − b0 = nbars wcr (3) where nbars is the number of rebars; and wcr is the total crack width at a given corrosion level The total crack width wcr can be determined as Eq (4) proposed by Molina et al [10] wcr = (vrs − 1) Xd (4) where vrs is the ratio between the specific volumes of rust and steel that can be assumed to be [10] Xd is the depth of the penetration attack that is determined by Eq (5) proposed in the study of Val [11], with icorr (µA/m2 ) being the corrosion current density in the steel bar and t (years) being the duration of corrosion Xd = 0.0116icorr t (5) 2.2 Steel reinforcement law Previous studies reported that both strength and ductility corroded reinforcement are affected mainly due to variability in steel cross-section loss over their lengths [12] Because of the difficulty in implementing the actual variability of steel corrosion in the numerical model, an alternative approach is suggested by modeling the corroded steel rebar over a length based on average cross-section loss together with empirical coefficients The use of empirical coefficients (whose values are smaller 28 modulus is assumed to be 1% of its elastic modulus Es Where, fy and fsu tensile strength and ultimate tensile strength of steel ey and esu are the yie maximum strain of steel, respectively Kien, N T., Tan, N N / Journal of Science and Technology in Civil Engineering than 1) is to account for the reduction in strength and ductility of corroded rebar attributed to the irregular cross-section loss along the rebar length in addition to the reduction attributed to the average Figure Stress - strain relationship of the steel reinforcement [1] cross-section Since the corrosion damage on the 2.3 Model of steel – concrete deteriorated bond rebar is considered in the FE model by reducing two significant factors that have huge effects on the bond stress the steel cross-sectional areas over the rebarThe length relationship according to steel weight loss, the simplified bilin-are the amount of steel corrosion and the confinement of the There is a consensus on its well-defined trend that the bond strength initially inc ear constitutive stress - strain relationship of steel with the corrosion amount in the pre-cracking stage and then substantially decrea as illustrated in Fig is used without empirical the longitudinal coefficients, where the post-yield modulus is as- corrosion cracking developed along with the steel reinforceme However, bond failure in corroded rebars is mostly by splitting, for the commonl sumed to be 1% of its elastic modulus E s Where, concrete covers and Figure stirrup amounts the of parameters fy and f su are the yield tensile strength and ultiStress - Consequently, strain relationship the steel of the bond Figure Stress - strain relationship of the steel reinforcement [ such brittle reinforcement [1] behavior Therefore, the re mate tensile strength of steel εy and relationship ε su are themust be modified to reproduce bond respecstress curve as deteriorated proposed by Kallias yield strain and maximum strain steel, 2.3 ofModel of steel- slip – concrete bond and Rafiq [3] is used herein f deteriorated bond between steel and concrete as illustrated in Fig For the tively The two significant factors havesteel huge effects isonillustrated the bond corroded steel bar, the good bondthat between and concrete by s 2.3 Model of steel – concreterelationship deteriorated bond slip curve CEB-FIP [13].of steel corrosion and the confinement of are inthe amount There is a consensus The two significant factors that have huge ef- on its well-defined trend that the bond strength initia fects on the bond stress - slip are amount in the pre-cracking stage and then substantially withrelationship the corrosion the amount of steel corrosion and the confinethe longitudinal corrosion cracking developed along with the steel reinfo ment of the concrete There is a consensus on its However, failure in corroded rebars is mostly by splitting, for the co well-defined trend that the bond strengthbond initially covers and stirrup amounts Consequently, the parameters of the increased with the corrosionconcrete amount in the precracking stage and then substantially decreased relationship must be modified to reproduce such brittle behavior Therefore as the longitudinal corrosionbond cracking developed stress - slip curve as proposed by Kallias and Rafiq [3] is used h along with the steel reinforcement [1] However, deteriorated bond between steel and concrete as illustrated in Fig bond failure in corroded rebars is mostly by splitsteel bar, bond between steel and concrete is illustrate ting, for the commonly used corroded concrete covers and the good Figure Constitutive law of the deteriorated slipthe curve in CEB-FIP [13] stirrup amounts Consequently, parameters of bond [1] the bond - stress relationship must be modified to reproduce such brittle behavior Therefore, the residual bond stress - slip curve as proposed by Kallias and Rafiq [3] is used herein for the deteriorated bond between steel and concrete as illustrated in Fig For the non-corroded steel bar, the good bond between steel and concrete is illustrated by stress - slip curve in CEB-FIP [13] The residual bond - slip relationship can be described as the following Eqs (6), (7) and (8) U = U1 (S /S )0.3 S α = S α Umax,D /U1 (6) 1/0.3 (7) S max = S exp (1/0.3) Ln Umax,D /U1 + S Ln U1 /Umax,D (8) where α = 0.7; U1 = 2.57 fc 0.5 with fc is the compressive strength of non-corroded concrete; S = 0.15c0 with c0 = 8.9 mm that is the spacing between the ribs of the steel bar; S = 0.35c0 ; and 29 Kien, N T., Tan, N N / Journal of Science and Technology in Civil Engineering S = 0.15 or 0.4 mm for plain concrete or steel confined concrete, respectively Umax,D = R [0.55 + 0.24 (c/db )] + 0.191 A st fyt /S s db R = A1 + A2 mL (9) (10) The residual bond strength Umax,D can be determined by Eq (9), with c is the concrete cover, db is the diameter of the longitudinal rebar, A st is the cross-section area of the stirrup, fyt is the yield strength of the stirrup, S s is the stirrup spacing R is the factor accountable for the residual contribution of concrete towards the bond strength as a function of A1 = 0.861 and A2 = 0.014, which is related to the current density used in the accelerated corrosion test, and mL is the amount of steel weight loss in percentage (Eq (10)) Eq (9) consists of two separate terms: the first and second terms are attributed to the concrete and stirrup contributions to the bond strength, respectively The effectiveness of this equation is that the level of confinement can be varied with the changes in the stirrup spacing and concrete compressive strength for different specimens Validation of FE models for flexural corroded RC beams 3.1 Corroded beams without corroded stirrups in flexural span a Presentation of the tested beams by Dong et al [14] In this section, two RC beams with the dimensions of 1200 × 250 × 180 mm as illustrated in Fig from an experimentalJournal studyofconducted byTechnology Dong et al.in[14] used for NUCE modeling Science and Civilare Engineering 2020the corroded beams with U-type stirrups in the flexural span These beams were tested to investigate the crack propagation and flexural behavior of RC beams under steel corrosion and sustained loading simultaneously The places theplaces shearinzones of the beams stirrups and tension reinforcements stirrups wereinonly the shear zones of the Both beams.the Both the stirrups and tension reinforcements corroded the laboratory werewere corroded in theinlaboratory Target corrosion area Figure Layout and cross-sections of tested beams [14] Figure Layout and cross-sections of tested beams [14] The tested made ofmade concrete having a 28-day strength of 35.4 MPa.ofThe The beams tested were beams were of concrete having compressive a 28-day compressive strength reinforcements consisted of HRB335 steel rebars for tension longitudinal reinforcement, HPB300 35.4 MPa The reinforcements consisted of HRB335 steel rebars for tension plainlongitudinal steel rebars for compression longitudinal reinforcement and stirrups The mechanical properties reinforcement, HPB300 plain steel rebars for compression longitudinal of these reinforcements are shown in Table 1, characterized by the nominal diameter, yield tensile reinforcement and stirrups The mechanical properties of these reinforcements are strength, ultimate tensile strength, and elastic modulus in Table characterized by the nominal diameter, yieldhave tensile strength, Inshown this study, three1,tested beams named FNN00, FCL03and FCL06 been used to ultimate analyze and tensile and elastic modulus simulate thestrength, flexural behavior using the FE model FNN00 was a non-corroded beam considered as the control beam FCL03 and FCL06 were corroded for the target area in the flexural span (Fig 4), In this study, three tested beams named FNN00, FCL03and FCL06 have been used to analyze and simulate the flexural behavior using the FE model FNN00 was a non30 corroded beam considered as the control beam FCL03 and FCL06 were corroded for the target area in the flexural span (Fig 4), which were simultaneously subjected to a sustained load corresponding to 30% and 60% of the expected ultimate load, Kien, N T., Tan, N N / Journal of Science and Technology in Civil Engineering which were simultaneously subjected to a sustained load corresponding to 30% and 60% of the expected ultimate load, respectively After the failure of the tested beams with a four-point bending test, the corrosion levels of tension reinforcements and stirrups were determined by weighting the remaining mass of each steel rebar compared to the initial mass before corrosion Table presents the actual corrosion levels of reinforcements for these beams It shows that the tension reinforcements were corroded at low levels of to 3% on average, meanwhile, the stirrups were corroded at moderate levels of 11 to 12% on average Table presents the applied load and deflection of three tested beams, which are characterized by the load corresponding to yield strength of tension reinforcement (Fy , kN), the ultimate load at the failure (Fu , kN), the deflections at the mid-span of the tested beam denoted s f and su corresponding to Fy and Fu Table Mechanical properties of steel rebars Rebar type Nominal diameter (mm) Yield strength (MPa) Ultimate strength (MPa) Elastic modulus (MPa) HRB335 HPB300 16 380.5 396.9 552.7 535.7 1.92 × 105 1.98x105 Table Corrosion levels of reinforcements in the tested beams Corrosion level (%) Tested beam FNN00 FCL03 FCL06 Stirrup Tension reinforcement 11.08 12.07 3.10 2.01 Failure mode Flexural Flexural Flexural Table Experimental results of bending test on the tested beams by Dong et al [14] Tested beam F f (kN) s f (mm) Fu (kN) su (mm) su − s f (mm) FNN00 FCL03 FCL06 95.8 92.1 94.3 5.37 3.90 3.84 102.45 100.30 101.40 11.80 9.25 9.40 6.43 4.90 5.56 b Modeling of the corroded beams without stirrups in flexural span In this study, the concrete material has been modeled with an element mesh of 30 × 3030 × 30 mm using a 20-node hexahedron solid element (CHX60 element in DIANA), while the slip reinforcements have been modeled as a three-node numerically integrated truss element (CL9TR element in DIANA) as illustrated in Fig A line-solid interface element has been used in order to simulate the influence of bond - slip behavior because it connects slip reinforcements to the continuum element in which the line element is located Therefore, the interface elements based on the bond stress-slip relation from CEB-FIP 1990 [13] can be applied In the part of the beam where there is no reinforcement, we assigned it as plain concrete with the same compressive strength as given in the previous section 31 located based on located Therefore, Therefore, the the interface interface elements elements based onthe thebond bondstress-slip stress-sliprelation relationfrom from flexural span flexural span CEB-FIP CEB-FIP 1990 1990 [13] [13] can can be be applied applied InIn the the part part ofof the the beam beamwhere wherethere thereisisnono In this analysis, since there is no information for for thethe spatial variability of corrosion In this analysis, since there is no information spatial variability of corrosion reinforcement, we ititas with the compressive strength asas reinforcement, we assigned assigned asplain plainconcrete concrete with thesame same compressive strength for the the stirrups and tension reinforcement, we we have simulated thethe corroded steel rebar for stirrups and tension reinforcement, have simulated corroded steel rebar given section givenain in the the previous previous section over based on average loss In addition, thethe effect of corrosion is is Kien, N T., Tan, N N.cross-section / Journal of Science and Technology in Civil Engineering overlength a length based on average cross-section loss In addition, effect of corrosion modeled by by reducing thethe cross-section of of thethe steel rebars based on on thethe information modeled reducing cross-section steel rebars based information given in Table and modifying the constitutive law of damaged concrete, steel, andand given in Table and modifying the constitutive law of damaged concrete, steel, their interface (bond) their interface (bond) c Validation of FE model c Validation of FE model Fig.Fig shows good agreement between thethe experimental andand numerical results forfor shows good agreement between experimental numerical results the the loadload – deflection curves of two corroded beams FCL03 andand FCL06 FEFE model cancan – deflection curves of two corroded beams FCL03 FCL06 model (a) Concrete mesh (b) Reinforcement mesh (a) Concrete mesh (b) Reinforcement mesh predict thethe ultimate flexural strength of tested beams with good accuracy In fact, thethe (a)ultimate Concrete mesh (b) Reinforcement mesh predict flexural strength of tested beams with good accuracy In fact, applied loads corresponding to model the yield strength of of steel reinforcement thethe Figure Three-dimensional FE ofyield thetensile corroded beams without stirrups in the flexural of span applied loads corresponding to the tensile strength steel reinforcement of corroded beams FCL03 andand FCL06 areare equal to 92.1 kNkN andand 94.3 kN,kN, respectively corroded beams FCL03 FCL06 equal to 92.1 94.3 respectively FEM results are about 1% to 2% different from the experimental results Dong al FEM are about toinformation 2% different from the variability experimental results.forDong et al In thisresults analysis, since there1% is no for the spatial of corrosion theetstirrups and tension reinforcement, we have simulated the corroded steel rebar over a length based on average [14][14] noted thatthat since thethe corrosion levels of tension reinforcements in the tested beams noted since corrosion levels of tension reinforcements in the tested beams 88 is modeled by reducing the cross-section of the cross-section loss In addition, the effect of corrosion were relatively lowlow (2%(2% to 3%), andand thusthus there is aisnegligible difference in the ultimate were relatively to 3%), there a negligible difference in the ultimate steel rebars based on the information given in Table and modifying the constitutive law of damaged loads between twotwo corroded beams andand control beam loads between corroded beams control beam concrete, steel, and their interface (bond) ForFor a target thethe estimated deflection by by thethe FEFE model is slightly lower than aoftarget load, estimated deflection model is slightly lower than c Validation FEload, model 120 120 100 100 100 100 80 60 60 40 40 20 20 0 FCL03 FEMFEM FCL03 FCL03 EXP EXP FCL03 80 80 60 60 40 40 20 20 Load (kN) 80 Load (kN) 120 120 Load (kN) Load (kN) the the measured by by thebetween test.test This result cancan be be explained thatthat the simulated measured deflection the result explained Fig showsdeflection good agreement theThis experimental and numerical results forthe the simulated load – debeam has lower ductility thanthan thethe experimental beam since thecan non-reinforced area hashas flection curves of two corroded beams FCL03 and FCL06 FE model predict the ultimate flexural beam has lower ductility experimental beam since the non-reinforced area strength of tested beams with good accuracy In fact, the applied loads corresponding to the yield been assigned with plain concrete Meanwhile, thethe difference of of thethe stiffness between been assigned with plain concrete Meanwhile, difference stiffness between tensile strength of steel reinforcement of the corroded beams FCL03 and FCL06 are equal to 92.1 kN the the modeled andand experimental beams cancan be ascribed to existing cracks duedue to corrosion modeled experimental beams be ascribed to existing cracks to corrosion and 94.3 kN, respectively FEM results are about 1% to 2% different from the experimental results before which hardly implements the simulation properly Moreover, at the before which hardly in the simulation properly Moreover, at the Dong etloading, al.loading, [14] noted that since theimplements corrosionin levels of tension reinforcements in the tested beams end of the bending test, the failure of two corroded beams FCL03 and FCL06 was the end of the low bending of two corroded difference beams FCL03 and FCL06 the were relatively (2% totest, 3%),the andfailure thus there is a negligible in the ultimate loads was between two corroded beams and control beam flexural mode andand similar to those of the control beam FNN00 flexural mode similar to those of the control beam FNN00 0 10 10 Deflection at mid-span (mm)(mm) Deflection at mid-span 15 15 Beam FCL03 (a)(a)(a) Beam FCL03 Beam FCL03 FCL06 FEMFEM FCL06 FCL06 EXP EXP FCL06 0 10 10 Deflection at mid-span (mm)(mm) Deflection at mid-span 15 15 (b) Beam FCL06 (b) (b) Beam FCL06 Beam FCL06 Figure Load - deflection curves of corroded beams without stirrups by experiment and FEM analysis For a target load, the estimated deflection by the FE model is slightly lower than the measured deflection by the test This result can be explained that the simulated beam has lower ductility than the been assigned with plain concrete Meanwhile, experimental beam since the non-reinforced area9 has the difference of the stiffness between the modeled and experimental beams can be ascribed to existing cracks due to corrosion before loading, which is hardly implemented in the simulation properly 32 In addition, the cracks due to loading developed upwards from the bottom surface of the beam In the flexural span of each corroded beam, these cracks were found to be typically in the vertical direction and parallel as illustrated in Fig (e.g front, bottom, Figure Load - deflection curves of corroded beams without stirrups by experiment and back faces).Kien, Among these or and three majorin cracks with important width N T., Tan, N N.cracks, / Journal oftwo Science Technology Civil Engineering and FEM analysis were experimentally map, whichbeams can be represented FE Moreover, at the end of identified the bending in test,the thecracking failure of two corroded FCL03 and FCL06bywas In addition, the cracks due to loading developed upwards from the bottom surface analysis the flexural mode and similar to those of the control beam FNN00 of beam.the In cracks the flexural of each corroded beam, these found to beam be In the addition, due tospan loading developed upwards from the cracks bottomwere surface of the typically the vertical and parallel as illustrated in Fig (e.g front, In the flexuralinspan of each direction corroded beam, these cracks were found to be typically in bottom, the vertical and back faces) as Among thesein cracks, twofront, or three major with Among important width direction and parallel illustrated Fig (e.g bottom, andcracks back faces) these cracks, twowere or three major cracks with important width were experimentally identified in the cracking map, experimentally identified in the cracking map, which can be represented by FE which can be represented by FE analysis analysis (a) Crack pattern on the beam FCL03 by experiment and numerical analysis Crack pattern onbeam the beam FCL03 by by experiment and and numerical analysis analysis (a) Crack(a)pattern on the FCL03 experiment numerical (b) Crack pattern on the beam FCL06 by experiment and numerical analysis Figure Comparison of the crack pattern on the corroded beam without stirrups using experiment FEM and numerical analysis (b) Crack pattern on the beam FCL06 byand experiment (b) Crack pattern on the beam FCL06 by experiment and numerical analysis 3.2 Corroded beams withoflocally corroded stirrups Figure Comparison the crack pattern on the corroded beam without stirrups using Figure Comparison of the crack pattern on the corroded beam without stirrups using experiment and FEM a Presentation of the tested beamsexperiment by Ullah etand al.FEM [15] Corroded beams locally corroded 3.2.3.2 Corroded beams withwith locally corroded stirrups In the section, three tested beams with stirrups the dimensions of 1800x100x150 mm in the a Presentation of the beams Ullah et al been [15] a conducted Presentation of tested the tested by have Ullah et al [15] study by Ullah et beams al.by[15] used for modeling the flexural beams In the section, three tested beams with the dimensions of 1800 × 100beams × 150 mm in the study with locally corroded Fig presents detail ofofthese with In the section, stirrups three tested beams with thethe dimensions 1800x100x150 mmnumbering in the conducted by Ullah et al [15] have been used for modeling the flexural beams with locally corroded each stirrup thebydiagram ofal.these the bending that was realized to of assess study conducted Ullah [15]four-point havewith beennumbering used for test modeling the beams stirrups Fig 8and presents the detailetof beams each stirrup andflexural the diagram the with locally corroded Fig.to8 assess presents theflexural detail of these beams with numbering their flexural behavior four-point bending test thatstirrups was realized their behavior each stirrup and the diagram of the four-point bending test that was realized to assess P their flexural behavior.P P P 8 500 mm 10 10 11 11 12 12 13 13 14 14 15 15 Figure Layout and cross-section of tested beams [15] 150mm 600 mm 500 mm D13 500 mm 150mm 600 mm 500 mm D13 D13 D13 D13 100mm 100mm The tested beams were made of concrete having 10 the average compressive strength of 32 MPa Longitudinal reinforcements were the steel rebars10 with a nominal diameter of 13 mm having the yield 10 33 Kien, N T., Tan, N N / Journal of Science and Technology in Civil Engineering tensile strength of 395 MPa In the other beams, while the longitudinal reinforcements were coated using epoxy resin to avoid corrosion, the stirrups in the tested beams composed of plain steel rebars with the nominal diameter of mm having the yield tensile strength of 395 MPa In this study, four tested beams named B2-STD, B3-MC-FS, B7-MC-SS, B9-MC-MS have been used to analyze and simulate the flexural behavior using FE models Beam B2-STD was a noncorroded beam considered as the control beam In the other beams, while the longitudinal reinforcements were coated using epoxy resin to avoid corrosion, the stirrups were corroded at different locations in the tested beams, such as: (i) at the full span in beam B3-MC-FS, (ii) at the shear span in beam B7-MC-SS, and (iii) at the middle span in beam B9-MC-MS Table synthesized the experimental results of a four-point bending test on the tested beams All tested beams were fractured by the flexural mode Table Experimental results of bending test on the tested beams by Ullah et al [15] Beam name Corrosion location Peak load (kN) Max deflection (mm) Failure mode B2-STD B3-MC-FS B7-MC-SS B9-MC-MS None Full span Shear span Middle span 39.53 36.49 37.03 32.37 21.96 31.21 21.89 14.90 Flexural Flexural Flexural Flexural The levels were beams determined After thecorrosion failure of the corroded with afor each stirruptest, andthepresented Figure for four-point bending corrosionin levels of stirrups were determined weighting three corrodedbybeams Forthe theremaining simulation mass ofofeach steel rebar compared to the initial corroded beams, an average corrosion mass before corrosion level was calculated for all stirrups Three The corrosion levels were determined for each beams B3-MC-FS, stirrup corroded and presented in Fig for three B7-MC-SS corroded and B9-MC-MS had the corrosion level beams For the simulation of corroded beams, an of average7.2%, corrosion level was for all stir10.5% and calculated 11.6% on average, rups Three corroded beams B3-MC-FS, B7-MCrespectively In particular, it notes that a SS and B9-MC-MS had the corrosion level of stirrup (number 3) in the beam B7 was 7.2%, 10.5% and 11.6% on average, respectively corroded with approximately 30% weight In particular, it notes that a stirrup (number 3) loss B7 was corroded with approximately in the beam 30% weight loss Figure Corrosion profile of corroded Figure 9 Corrosion profile of corroded stirrups in the tested beamsbeams [15] [15] stirrups in the tested b Modelling of the flexural beams with locally corroded stirrups b Modeling of the flexural beams with locally corroded stirrups similarasprocess as in presented in 3.1.2 paragraph 3.1.2 wasforperformed the A similarAprocess presented paragraph was performed modeling for the modeling tested beams tested beams corroded stirrups different locations Themodeled concrete has with corroded stirrups with at different locations Theatconcrete material has been withmaterial an element mesh ofbeen 30 × modeled 30 × 30 mm using a 20-node hexahedron solid element (CHX60 element), while the slip with an element mesh of 30x30x30 mm using a 20-node hexahedron reinforcements are modeled as aelement), three-nodewhile numerically truss element (CL9TRaselement) solid element (CHX60 the slipintegrated reinforcements are modeled a threeThe corroded steel rebar was simulated along the length based on an average cross-section loss For node numerically integrated truss element (CL9TR element) The corroded steel rebar each beam with locally corroded stirrups, the effects of corrosion in a target area were modeled by was along thesteel length based an average cross-section For each beam reducing thesimulated cross-section of the rebars and on modifying the constitutive lawloss of damage materials with locally corroded the effects under corrosion, as well as the stirrups, steel – concrete bond.of corrosion in a target area were modeled by reducing the cross-section of the steel rebars and modifying the constitutive law of damage materials under corrosion, as well 34 as the steel – concrete bond node numerically integrated truss element (CL9TR element) The corroded steel rebar was simulated along was simulated alongthethelength lengthbased basedononananaverage averagecross-section cross-sectionloss loss.For Foreach eachbeam beam with locally corroded stirrups, with locally corroded stirrups,thetheeffects effectsofofcorrosion corrosioninina atarget targetarea areawere weremodeled modeledby by reducing reducingthethecross-section cross-sectionofofthethesteel steelrebars rebarsand andmodifying modifyingthe theconstitutive constitutive law law ofof Kien, N T., Tan, N N / Journal of Science and Technology in Civil Engineering Journal of Science and Technology in Civil Engineering NUCE 2020 damage materials under corrosion, damage materials under corrosion,asaswell wellasasthe thesteel steel– –concrete concretebond bond For mild corrosion (approximately 10% weight loss), the least flexural capacity was observed in the beam B9-MC-MS with an 18.11% reduction from the control beam, and corrosion of stirrups was done in a middle span The maximum capacity of the beam B9 in the test was 32.4 kN compared with approximately 35.0 kN at the same deflection of FEM results The beam B7-MC-SS with corroded stirrups in the shear span has the least reduction in load-carrying capacity (37.0 kN in test versus 39.0 kN in FEM) For the case of the beam B3-MC-FS, the reduction in flexural capacity was 7.69% compared (a) Concrete mesh (b) Reinforcement mesh Concrete mesh (b)Reinforcement Reinforcement mesh38 kN, (a)(a) Concrete with the control beam.mesh The failure load of the beam(b) B3 in FE analysismesh was Figure 10 Three-dimensional FE model of of the corroded beams with corroded stirrups which is10 4% larger than the experimental result In the case oflocally flexural beams, stirrups Figure Three-dimensional model ofthe thecorroded corroded beams with locally corroded Figure 10 Three-dimensional FEFE model beams with locally corroded that subjected to accelerated corrosion in the middle span have more effect on stirrups stirrups than in the shear span However, the corrosion level of c maximum Validation ofcapacity the FE model c Validation of the FE model c Validation of the FE model reinforcement affects theagreement maximumbetween capacity the most and tested results for the load-deflection Fig 11 shows acceptable experimental curves of three beams with differentagreement locations of corroded stirrups FE model cantested predictresults the ultimate Fig shows acceptable between experimental and for Fig 1111 shows acceptable between experimental and Additionally, the stiffness agreement of the simulated beams is similar totested those results of thefor flexural strength of tested beamsof with goodbeams accuracy Fordifferent mild corrosion (approximately 10% weight load-deflection curves three with locations corroded stirrups thethe load-deflection curves of three beams with locations corroded stirrups experimental beams throughout evolution ofdifferent damaging stageswith inofof both the preand loss), the lowest flexural capacity wasthe observed in the beam B9-MC-MS an 18.11% reduction FE model predict ultimate flexural strength ofa tested beams with goodaccuracy accuracy FE model cancan predict thethe ultimate flexural of beams good post-peak regions ductility varied for strength all corroded beams, aswith the location ofcapacity the from the control beam,The and corrosion of stirrups wasthe done in tested middle span The maximum of corrosion the beam B9 in the 32.4 kN compared with approximately 35.0the kN beam at the same deflection was nottest thewas same Based on the deflection results, B3-MC-FS of showed FEM results The beam B7-MC-SS with corroded stirrups in the shear span has the least reduction the highest ductility, followed by B7-MC-SS as the stirrups were corroded in in load-carrying capacity (37.0 kN in test versus 39.0 kN in FEM) For the case of the beam B3-MC12 the shear span and B9-MC-MS shared the 12lowest ductility which can be obtained by FS, the reduction in flexural capacity was 7.69% compared with the control beam The failure load of 40 40 30 30 Load (kN) Load (kN) using a numerical model B3 EXP 20 B3 FEM B7 EXP 20 B7 FEM 10 10 0 10 15 20 25 Deflection at mid-span (mm) 30 35 10 15 20 25 Deflection at mid-span (mm) 30 35 40 Load (kN) 30 B9 EXP 20 B9 FEM 10 0 10 15 20 25 Deflection at mid-span (mm) 30 35 Figure 11 Load - deflection curves of tested beams withbeams locally with corroded stirrups using experiment and FEM Figure 11 Load - deflection curves of tested locally corroded stirrups using experiment and FEM 35 13 Kien, N T., Tan, N N / Journal of Science and Technology in Civil Engineering the beam B3 in FE analysis was 38 kN, which is 4% larger than the experimental result In the case of flexural beams, stirrups that subjected to accelerated corrosion in the middle span have more effect on maximum capacity than in the shear span However, the corrosion level of reinforcement affects the maximum capacity the most Additionally, the stiffness of the simulated beams is similar to those of the experimental beams throughout the evolution of damaging stages in both the pre- and post-peak regions The ductility variedIn forthe all case the corroded beams, as the location of the corrosion was not the same Based on7.2% the In the beam B3-MC-FS, which was corroded in the full span with 7.2% case of the the beam beam B3-MC-FS, which was corroded the full span with of B3-MC-FS, which was corroded inin the full span with 7.2% deflection results, the beam B3-MC-FS showed the highest ductility, followed by B7-MC-SS as the weight loss, many corrosioncracks crackswere wereobserved observedwith withthe therange range crack width from many corrosion corrosion cracks were observed with the range ofof crack width from weight loss, of crack width from stirrups were corroded in the shear span and B9-MC-MS shared the lowest ductility which can be mm [15] The The cracks due loading the failure stage are found 0.05 to by0.25 0.25 The cracks due duetoto toloading loadingatatatthe thefailure failurestage stage are found 0.05 to [15] cracks are found obtained usingmm a numerical model in the thebeam middle span of the beam as illustrated Fig 12(a) concentrated middle spanof ofthe thebeam beam asillustrated illustrated Fig 12(a) In the case in of B3-MC-FS, which wasas corroded in the full span with 7.2% weight loss, concentrated middle span ininin Fig 12(a) many corrosion cracks were observed with the range of crack width from 0.05 to 0.25 mm [15] The In case of at thethebeam beam B7-MC-SS, where the locations corroded were the beam B7-MC-SS, where thelocations locations of corroded stirrups were the of the B7-MC-SS, where the corroded were cracksIn due to case loading failure stage are found concentrated in theofof middle span stirrups ofstirrups the beam as the cracks due to corrosion were found only in a part of the beam [15] in shear span, span, due to corrosion were found only in a part of the beam [15] illustrated in Fig.the 12(a) cracks due to corrosion were found only in a part of the beam [15] the case of the beamthe B7-MC-SS, where the cracks locations of corroded stirrups were in shear span, Fig.In12(b) shows that the spacing between cracks due loading larger than the spacingbetween between cracksdue due loading larger than inthe the shows that spacing tototoloading isisis larger than inin the the cracks due to corrosion were found only in a part of the beam [15] Fig 12(b) shows that the at the the failure failure stage Similarly, the corroded stirrups the middle span B3-MC-FS stirrups ininin the middle span beam B3-MC-FS at failurestage stage.Similarly, Similarly,the thecorroded corroded stirrups the middle span spacing between cracks due to loading is larger than in the beam B3-MC-FS at the failure stage of the the beam beam B9-MC-MS induced more under loading and bigger in the case of B9-MC-MS more under loading and bigger case B9-MC-MS induced more cracks under loading and bigger Similarly, the corroded stirrups in the middleinduced span in the case cracks ofcracks the beam B9-MC-MS induced more cracks under loading and bigger spacing between them than the case of the beam B3-MC-FS spacing between them than the case of the beam B3-MC-FS between them than thanthe thecase caseofofthe thebeam beamB3-MC-FS B3-MC-FS Crack pattern ofbeam the beam B3by by experiment and and numerical analysis analysis (a) pattern of numerical Crack pattern of the beam B3 by experiment and numerical analysis (a) Crack Crack(a) pattern ofthe the beamB3 B3 byexperiment experiment and numerical analysis (b) Crack pattern ofbeam the beam by experiment experiment and and numerical analysis analysis (b) pattern of the B7B7by numerical (b) Crack Crack (b) Crack pattern pattern of of the the beam beam B7 B7 by byexperiment experimentand andnumerical numericalanalysis analysis (c) Crack pattern of the beam B9 by experiment and numerical analysis (c) Crack pattern of the beam B9 by experiment and numerical analysis (c) Crack (c) Crack pattern pattern of of the the beam beam B9 B9 by byexperiment experimentand andnumerical numericalanalysis analysis Figure 12 Comparison of crack patternon on the the corroded beam withwith corroded stirrups stirrups Figure 12 Comparison of crack pattern corroded beam corroded Figure 12 Comparison of crackusing pattern on theandcorroded beam with corroded stirrups experiment FEM Figure 12 Comparison of crack pattern on the corroded beam with corroded stirrups using experiment and FEM using experiment and FEM using experiment and FEM 3.3 Parametric study on the flexural behavior ofofcorroded 3.3 study on the behavior of corroded beam beam 3.3 Parametric Parametric study on flexural the flexural behavior corroded beam 3.3 Parametric study on the flexural behavior of corroded beam section, the tested 6.6.Parametric study In In this this section, the tested beams havebeams identicalhave material properties with for the several In this section, the tested beams dimensions, have Table Table Parametric study forcorroded several beam FCL03 in the study of Dongtested et properties al [14] (cf section Two parameters have study been considered, In this section, the beams have3.1) Table Parametric for several identical dimensions, material with bond strength reductions and crossidentical dimensions, material properties with bond strength reductions and crosswhich are the bond strength reduction and the cross-section loss of tension longitudinal reinforceidentical dimensions, material with bond strength reductions the corroded beam FCL03 in the properties study of Dong section losses and crossthe corroded beam FCL03 in theforstudy of strength Dong reduction ranging section ments Table presents several cases the bond fromlosses 0% to 80%, for the the corroded beam FCL03 in the of Dong section losses et al [14] (cf section 3.1) Twostudy parameters Beams Bond Crosset al [14] (cf section 3.1) Two parameters 36 Beams Bond Crosset al been [14] (cf section which 3.1) Two parameters have considered, are the bond Beams Bond section Crossindex strength have been considered, which are the bond index strength section have been considered, are the strength reduction and the which cross-section lossbond of index strength loss section reduction strength reduction and the cross-section loss of reduction loss strength reduction andreinforcements the cross-section loss 6of tension longitudinal Table (%) (%)loss reduction tension longitudinal reinforcements Table The simulation results of the load – deflection curve are presented in Fig 13 fo assessing the effect of bond strength ranging from 0% to 80% The results obtained show that the bond strength reduction has a negligible effect on the load-carrying capacity of corroded beams, especially on the ultimate load However, the failure of th testedofbeams high reductions bond strength from 30% to 80% can occu Kien, N T., Tan, N N / Journal Sciencehaving and Technology in CivilofEngineering earlier than that of the beam without bond strength reduction For the tested beam cross-section loss ranging from 10% to 50% either parameter is studied, otheratparameters are of 9.0 mm in FCL03When – 0, the applied load is suddenly reduced the deflection declared as the corroded beam FCL03 comparison with approximately 4.2 mm on another 120 Table Parametric study for several bond strength reductions and cross-section losses FCL03–0 FCL03–1 FCL03–2 FCL03–3 Cross-section loss (%) 30 50 80 20 30 50 Load (kN) Beams index Bond strength reduction (%) 100 80 60 FCL03-0 FCL03-1 FCL03-2 FCL03-3 40 20 0 Deflection at mid-span (mm) 10 Figure 13.Figure Load - 13 deflection with several Load -curves deflection curvesbond withstrength severalreductions bond strength reductions b Effect of the cross-section loss Fig 14 shows the simulation results of the load – deflection curves of the tested beams with the cross-sectional tension reinforcement loss ranging from 10% to 50% I a Effect of the bond strength reduction can be seen that the effect of the cross-section loss on the flexural carrying capacity o The simulation results of the load – deflection curve are presented in Fig 13 for assessing the tested beams is more significant than the reduction of bond strength The load-carrying effect of bond strength ranging from 0% to 80% The results obtained show that the bond strength capacity of tested beams is reduced by increasing the cross-section loss of tension reduction has a negligible effect on the reinforcement load-carryingAscapacity of corroded especially on the an example, the ultimatebeams, load of the tested beams decreases by 40% ultimate load However, the failure of thewhen tested beams having high reductions of bond strength from the cross-section loss raises from 0% to 30% (100 kN on the beam FCL03–0 30% to 80% can occur earlier than that versus of the60beam strength the tested kN onwithout the beambond FCL03–2) Thisreduction decrease of For the ultimate load can be up to beam FCL03 – 0, the applied load is suddenly ofloss 9.0 Moreover, mm in comparison more thanreduced 60% with at thethe 50%deflection cross-section the deflection at the middl with approximately 4.2 mm on the other.span is greatly reduced on the beam FCL03-3 The failure mode of the tested beam shifted from ductile to brittle fracture with an important cross-section loss This type o b Effect of the cross-section loss brittle failure can be predicted with the FE simulation Load (kN) 120 Fig 14 shows the simulation results of the load – deflection curves of the tested beams with the 100 cross-sectional tension reinforcement loss ranging 80 15 from 10% to 50% It can be seen that the effect of 60 the cross-section loss on the flexural carrying caFCL03-0 pacity of tested beams is more significant than the 40 FCL03-1 reduction of bond strength The load-carrying caFCL03-2 20 FCL03-3 pacity of tested beams is reduced by increasing the cross-section loss of tension reinforcement As an 10 example, the ultimate load of the tested beams deDeflection at mid-span (mm) creases by 40% when the cross-section loss raises Figure 14 Load deflection curves with several losses Figure- 14 Load - deflection curves withcross-section several from 0% to 30% (100 kN on the beam FCL03–0 cross-section losses Conclusions versus 60 kN on the beam FCL03–2) This decrease of the ultimate load can be up to more than In this paper, the effects of the stirrup corrosion on the flexural capacity 60% with the 50% cross-section loss Moreover, corroded RC beams have been simulated and discussed FE analysis meth the deflection at the middle span is greatly reduced on the beam FCL03-3 The failure mode of the DIANA software has been provided to simulate the structural responses of the c tested beams shifted from ductile to brittle fracture with an important cross-section loss This type of beams with considering two different inputs: (i) without stirrups in flexural s brittle failure can be predicted with the FE simulation with corroded stirrups at different locations The validation of the FE model is p by comparing the numerical and experimental results of the load – deflection c parametric simulation was also realized to assess the effect of the bond reduction and the cross-section loss of tension reinforcements on the flexural 37 of the corroded beam The obtained results allow us to draw the main conclu follows: - The FE model that was adopted in this paper provides a good predictio Kien, N T., Tan, N N / Journal of Science and Technology in Civil Engineering Conclusions In this paper, the effects of the stirrup corrosion on the flexural capacity of five corroded RC beams have been simulated and discussed FE analysis method with DIANA software has been provided to simulate the structural responses of the corroded beams to consider two different inputs: (i) without stirrups in flexural span, (ii) with corroded stirrups at different locations The validation of the FE model is presented by comparing the numerical and experimental results of the load – deflection curves A parametric simulation was also realized to assess the effect of the bond strength reduction and the cross-section loss of tension reinforcements on the flexural capacity of the corroded beam The obtained results allow us to draw the main conclusions as follows: - The FE model that was adopted in this paper provides a good prediction of the flexural capacity (e.g load carrying capacity, load – deflection curve) of the corroded beams by modeling the corrosion damage on the reinforcement, concrete and steel – concrete bond - The FEM analysis can detect the impact of stirrups corrosion on the flexural behavior of the corroded beam by representing the reduction of the deflection at the middle span For a corroded beam with local corroded stirrups, severe corrosion of approximately 30% weight loss for the stirrup in the shear span can be a good example On the other hand, there is no significant change in terms of both flexural capacity and ductility in corroded beams compared with the control beam by only applying uniform corrosion in U-type stirrup - While in the design stage of a structure, engineers not often consider the influence of stirrups in the flexural capacity of the beam However, the obtained results show that the stirrups corrosion should receive more attention in the serviceability limit state due to its considerable effect on flexural capacity, induced reduction of stiffness and ductility of existing reinforced concrete beam - The effect of the cross-section loss of tension reinforcements on the flexural capacity of the corroded beam (e.g ultimate load, deflection) is more significant than the bond strength reduction The failure mode of the corroded beam can be changed from ductile to brittle fracture with an important cross-section loss References [1] Lim, S., Akiyama, M., Frangopol, D M (2016) Assessment of the structural performance of corrosionaffected RC members based on experimental study and probabilistic modeling Engineering Structures, 127:189–205 [2] Coronelli, D., Gambarova, P (2004) Structural Assessment of Corroded Reinforced Concrete Beams: Modeling Guidelines Journal of Structural Engineering, 130(8):1214–1224 [3] Kallias, A N., Rafiq, M I (2010) Finite element investigation of the structural response of corroded RC beams Engineering Structures, 32(9):2984–2994 [4] Sæther, I., Sand, B (2012) FEM simulations of reinforced concrete beams attacked by corrosion ACI Structural Journal, 109(2):15–31 [5] Hai, D T., Yamada, H., Katsuchi, H (2007) Present condition of highway bridges in Vietnam: an analysis of current failure modes and their main causes Structure and Infrastructure Engineering, 3(1):61–73 [6] Tan, N N., Hiep, D V (2020) Empirical models of corrosion rate prediction of steel in reinforced concrete structures Journal of Science and Technology in Civil Engineering (STCE)-NUCE, 14(2):98– 107 [7] Tan, N N., Dung, T A., The, N C., Tuan, T B., Anh, L T (2018) An experimental study to identify the influence of reinforcement corrosion on steel-concrete bond stress Journal of Science and Technology in Civil Engineering (STCE)-NUCE, 12(6):29–38 (in Vietnamese) 38 Kien, N T., Tan, N N / Journal of Science and Technology in Civil Engineering [8] Nguyen, N D., Tan, N N (2019) Prediction of residual carrying capacity of RC column subjected inplane axial load considering corroded longitudinal steel bars Journal of Science and Technology in Civil Engineering (STCE)-NUCE, 13(2V):53–62 (in Vietnamese) [9] Capé, M (1999) Residual service-life assessment of existing R/C structures Master’s thesis, Gothenburg, Sweden: Chalmers University of Technology, and Milan, Italy: Milan University of Technology [10] Molina, F J., Alonso, C., Andrade, C (1993) Cover cracking as a function of rebar corrosion: Part 2—Numerical model Materials and Structures, 26(9):532–548 [11] Val, D V (2007) Deterioration of Strength of RC Beams due to Corrosion and Its Influence on Beam Reliability Journal of Structural Engineering, 133(9):1297–1306 [12] Du, Y G., Clark, L A., Chan, A H C (2005) Residual capacity of corroded reinforcing bars Magazine of Concrete Research, 57(3):135–147 [13] CEB-FIP Model Code (1990) Design code Thomas Telford, London [14] Dong, J., Zhao, Y., Wang, K., Jin, W (2017) Crack propagation and flexural behaviour of RC beams under simultaneous sustained loading and steel corrosion Construction and Building Materials, 151: 208–219 [15] Ullah, R., Yokota, H., Hashimoto, K., Goto, S (2016) Load carrying capacity of RC beams with locally corroded shear reinforcement Journal of Asian Concrete Federation, 2(1):46 39 ... tested beams with the dimensions of 1800 × 10 0beams × 150 mm in the study with locally corroded Fig presents detail ofofthese with In the section, stirrups three tested beams with thethe dimensions... model of of the corroded beams with corroded stirrups which is10 4% larger than the experimental result In the case oflocally flexural beams, stirrups Figure Three-dimensional model ofthe thecorroded... was corroded with approximately in the beam 30% weight loss Figure Corrosion profile of corroded Figure 9 Corrosion profile of corroded stirrups in the tested beamsbeams [15] [15] stirrups in the