Cyclic Behavior of Reinforced Concrete Beams with

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Cyclic Behavior of Reinforced Concrete Beams with Corroded Transverse

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Steel Reinforcement

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Yu-Chen Ou 1, and Hou-Heng Chen

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Abstract

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This study examined the seismic performance of reinforced concrete beams with corrosion only

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induced in the transverse steel reinforcement by using cyclic loading. The beams were designed

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with closely spaced steel hoops as transverse reinforcement conforming to ACI 318 seismic

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design provisions. Seven beams were constructed. One beam was used as a control without

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corrosion. The other six beams were subjected to six levels of corrosion in the potential plastic

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hinge region by using an electrochemical method. Corrosion test results indicate that pitting

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corrosion increased with an increasing corrosion level. The hoops fractured at a corrosion weight

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loss of 35%. Cyclic test results indicated that the beams could sustain a corrosion weight loss of

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6% in the hoops and still maintain a ductile flexural behavior. Corrosion of hoops adversely

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affected the deformation capacity of the beams significantly, yet did not significantly influence

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the load-carrying capacity of the beams. The residual shear strength provided by concrete and

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steel was still sufficient to develop flexural yielding, even for the beams with hoops corroded to

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fracturing. Methods were developed to estimate the residual shear strength and ductility of

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reinforced concrete beams with corroded hoops. The amount of corrosion substances filled in the

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cracks volume was approximately 25% of the reduced volume of the steel due to corrosion.

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Although shear strength estimation based on the average corrosion weight loss was not

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conservative, that based on the minimum residual cross sectional area was too conservative at a

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high corrosion level due to severe pitting corrosion. Shear strength estimation based on average

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weight loss and minimum residual cross sectional area produced results that describe the

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experimental behavior more reasonably.

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Keywords: Reinforced concrete beams; corrosion; transverse reinforcement; seismic;

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cyclic loading; flexural-shear failure. 1

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Associate Professor, Department of Construction Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan. E-mail: [email protected] Formerly Master student, Department of Construction Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan.

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INTRODUCTION

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Corrosion of steel reinforcement in reinforced concrete structures is a common deterioration

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issue. Corrosion reduces the area of steel reinforcement (i.e. uniform corrosion) and causes a

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non-uniform distribution of cross sectional area along the reinforcement (i.e. pitting corrosion).

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Uniform corrosion reduces the load-carrying capacity of the reinforcement, while pitting

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corrosion causes localized yielding, reducing the strength and ductility of the reinforcement. Steel

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expands after corrosion, resulting in cracking, delamination, and spalling of cover concrete,

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ultimately degrading steel-concrete bond and load-carrying capacity of the structure.

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Earlier studies have demonstrated that transverse reinforcement, due to a smaller diameter,

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corrodes faster than the longitudinal reinforcement in terms of volume reduction. Consequently, a

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beam designed to fail in flexure gradually shifts the failure mode from flexural to flexural-shear

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or shear failure with an increasing corrosion level, transforming a ductile failure to a brittle one

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(Rodriguez et al. 1997, and Ou et al. 2012). Based on reliability analysis, Val (2007) investigated

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how uniform and pitting corrosion affects failure probability of beams designed to fail in flexure.

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According to their results, the probability of shear failure increases faster than that of flexural

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failure, especially when pitting corrosion occurs. The probability of shear failure may exceed that

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of flexural failure within a 50 year life span of a typical structure.

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Corrosion of transverse reinforcement generally involves uniform corrosion along the length

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of steel bars. At moderate and severe corrosion levels, pitting corrosion becomes significant and

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typically occurs near the corners of the bents (Higgins and Farrow 2006, Juarez et al. 2011, and

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Wang et al. 2011). Rodriguez et al. (1997) indicated that shear strength estimated using the

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Eurocode (1992) shear strength equation with a reduced section of the transverse reinforcement at

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the corrosion pit and original concrete cross section overestimates the experimental results. A

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conservative estimation can be obtained if cover concrete is removed completely when

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calculating the shear strength. Juarez et al. (2011) estimated the residual shear strength of

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corroded beams by using the ACI 318 (2008) shear strength equation. According to their results,

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shear strength calculated based on the average residual diameter of the transverse reinforcement

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overestimates the measured shear strength; meanwhile, that based on the minimum residual

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diameter can provide conservative estimation of shear strength. The shear strength of concrete is 1

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assumed in Juarez’s study to remain constant after corrosion. Xia et al. (2011) proposed

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empirical equations to predict the ratio of the shear strength of a corroded beam to that of the

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corresponding uncorroded beam based on the average cross-sectional loss of corroded transverse

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reinforcement, average corrosion crack width, or maximum corrosion crack width. Note that the

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above studies on shear behavior used monotonic loading to test specimens.

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Under a seismic condition, the plastic hinge regions of a beam are expected to undergo

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inelastic deformation reversals. As is well known, shear strength of concrete degrades under

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inelastic reversals with an increasing ductility (Aschheim and Moehle, 1992). Therefore, the

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ACI-318 code requires more transverse reinforcement for shear reinforcement in the seismic

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design of beam plastic hinge regions. Moreover, transverse reinforcement plays an important role

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in providing confinement to concrete and delaying buckling of longitudinal reinforcement,

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ensuring a satisfactory ductility capacity of the plastic hinge region under seismic loading

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reversal. Consequently, corrosion of transverse reinforcement is more detrimental to the

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structural performance under seismic condition than under monotonic loading condition.

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Figure 1 illustrates examples of transverse reinforcement corrosion in reinforced concrete

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buildings. Exactly how transverse reinforcement corrosion affects the inelastic shear behavior of

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beams has received limited attention in the literature. Kato (2006) and Ou et al. (2012)

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investigated the cyclic behavior of beams with corroded transverse reinforcement, indicating that

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corrosion of transverse reinforcement influences the beam ductility. However, most of the

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specimens investigated incurred corrosion both in the longitudinal and transvers reinforcement,

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making it difficult to differentiate between the effects of transverse and longitudinal

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reinforcement corrosions on the structural performance. This study conducted cyclic tests on

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beams with corrosion induced only in the transverse reinforcement. Six corrosion levels were

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examined. Results of this study shed further light on the seismic behavior of beams with corroded

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transverse reinforcement and develop residual shear strength and ductility capacity models.

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EXPERIMENTAL PROGRAM

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Specimen Design The specimen was designed in compliance with the ACI 318 code (2008). Figure 2(a) 2

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illustrates the side view of the specimen. The specimen contains a beam connected to an

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anchorage block. The end of the beam connected to the anchorage block is referred to as fixed

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end while the other end referred to as free end. Figure 2(b) illustrates the cross-sectional view of

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the beam. The specified and actual concrete compressive strengths f c' are 28 and 38 MPa,

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respectively. The beam was designed with three #9 bars in the top and bottom sides of the beam

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and with #4 hoops as transverse reinforcement having a horizontal spacing of 10 cm. The

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specified and actual: yield strengths of longitudinal reinforcement f y are 412 and 444 MPa,

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respectively; in addition, those for transverse reinforcement are 412 and 432 MPa, respectively.

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The beam has a tension longitudinal reinforcement ratio of 1.5% and a volumetric ratio of

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transverse reinforcement to the concrete core of 1.8%. Shear strength of the beam was designed

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based on shear demand, which corresponds to moment strength assuming 1.25 specified yield

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strength in the longitudinal reinforcement. Concrete shear strength was not considered in the

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shear strength calculation based on the seismic provisions of the ACI 318 code. Figure 2(c)

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illustrates the corrosion observation specimen. The specimen is a replication of the portion of the

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beam from the fixed end extending 60 cm towards the free end. Figure 2(d) shows the

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construction of the beam and corrosion observation specimens. There were a total of seven sets of

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specimens. One set was used as the control group without corrosion, while the other six sets were

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subjected to different corrosion levels.

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Test Setup

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Accelerated Corrosion

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Corrosion in the transverse reinforcement was accelerated using an electrochemical method

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by imposing an electrical current to the reinforcement. The current density was approximately

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600 µ A/cm 2 . Corrosion was controlled to occur only in the potential plastic hinge region of the

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beam, from the fixed end extending 60 cm to the free end of the beam. Six hoops from the fixed

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end of the beam were imposed with an electrical current by connecting the ends of the hoops to

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the anodes of DC power supplies. The 60-cm region was enclosed with a water tank infilled with

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a NaCl solution of 5%. Four copper plates were placed on the four sides of the beam in the water

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tank. The cathodes of the power supplies were connected to the copper plates. Figures 3(a) and

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3(b) illustrate the elevation and cross-sectional views of the accelerated corrosion setup,

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respectively. Figure 3(c) illustrates the electric wires connecting the hoops to the power supplies. 3

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Figure 3(d) illustrates the overall view of the test setup. The beam specimen and the corrosion

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observation specimen in each set were subjected to the corrosion process starting from the same

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time and lasted for the same period.

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Cyclic Testing

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Following the corrosion, the corrosion observation specimen was demolished and the

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reinforcement was removed for corrosion measurement. The beam specimen was subjected to

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cyclic loading to evaluate the seismic performance. Figure 4 shows the test setup for cyclic

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loading. The anchorage block of the specimen was fixed to the strong floor. Cyclic load was

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applied using a hydraulic actuator attached to the beam at 120 cm from the fixed end. The beam

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was cyclically loaded up to drift levels of 0.25%, 0.375%, 0.5%, 0.75%, 1.0%, 1.5%, 2.0%, 3.0%,

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4.0%, 5%, and 6%. Each drift level was repeated twice. The actuator was controlled by using the

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relative displacement measured during testing between the loading point and the fixed end of the

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beam to achieve the prescribed drift levels precisely.

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RESULTS AND DISCUSSION

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Corrosion Test Results

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Table 1 lists, for all of the specimens, the corrosion weight loss, ∆w , average and minimum

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residual cross-sectional areas, Aavg and Amin , maximum pit depth, pmax , and total crack width,

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Wcr . The values of ∆w , Aavg , Amin , and pmax represent the average of the values from the six

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hoops subjected to corrosion. The average residual cross-sectional area was calculated based on

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the residual weight. The minimum residual cross-sectional area was calculated based on the

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average of three diameters measured at the smallest cross section. The corrosion pit was

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measured by a caliper with respect to a nearby point with negligible corrosion. Note that

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corrosion measurements on steel reinforcement were obtained from the corrosion observation

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specimens. To calculate the total crack width, crack patterns were first recorded with the width of

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each crack measured for both the beam specimens and corrosion observation specimens. Then,

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the total crack width was determined by summing all of the crack widths along the perimeter of a

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selected cross section. The 60-cm corroded portions of the beams and corrosion observation 4

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specimens were divided equally into five regions, and the total crack width was determined for

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each region. Table 1 presents the average value of the total crack widths from the five regions,

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indicating that the beam specimen and the corresponding corrosion observation specimen have

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similar corrosion crack widths for medium to high corrosion levels.

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Table 1 indicates that an increasing corrosion levels increases the difference between the

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average and minimum residual cross-sectional area. This finding suggests that pitting corrosion

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becomes more significant with an increasing corrosion level. This phenomenon is owing to that

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severe pitting corrosion typically occurred near corrosion cracks. Corrosion cracks facilitated the

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reaction of ferrous iron with hydroxide to form corrosion substances. Due to the volumetric

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expansion, the corrosion substances subsequently widened the cracks, exacerbating the corrosion

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further. For the specimen with 35% corrosion, every hoop was corroded in the accelerated

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corrosion process until it broke. This was achieved by continuing the accelerated corrosion

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process for each hoop until a sudden increase of electrical resistance, which is a sign of the hoop

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breakage, as confirmed upon the retrieval of the corroded hoops (Fig. 5). The electric-chemical

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process was then terminated by turning off the electrical current to the broken hoop. Note that

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severe pitting corrosion is evident in Fig. 5. Figure 6 illustrates the distribution of cracks on the

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four faces of the 60-cm region of the beam specimen subjected to accelerated corrosion. Note that

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the direction of most of the cracks is along the longitudinal direction of the beam, rather than

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along the transverse direction. This is likely because the longitudinal reinforcement, which did

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not corrode, restrained the development of cracks along the transverse direction of the beam.

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Cyclic Test Results

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Figure 7 illustrates the damage distribution of the specimens at selected drift levels. Figure 8

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illustrates the hysteretic behavior of all specimens with the instances of spalling of cover concrete

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and fracture of hoops indicated. Table 2 lists various performance indicators for the specimens.

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The symbols used in Table 2 are defined as follows: ∆ y denotes idealized yield drift; ∆ u

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denotes ultimate drift, defined when the applied load declines more than 20% from the peak

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value; Ppeak denotes peak applied load; µ denotes ductility, defined by the ratio of ∆ u to

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∆ y ; and ∆ p denotes plastic rotation, defined as the difference between ∆ u and ∆ y (FEMA

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267). The idealized yield drift refers to the drift at the intersection of two lines in the hysteretic

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behavior plot (Fig. 8): one line starts from the origin and intersects the envelope of the hysteretic

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behavior at approximately 60% of the force at the idealized yield drift; the other line ends at the

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ultimate drift with zero stiffness. The intersection of the two lines was chosen so that the area

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beneath the envelop response equals that beneath the two lines. The values listed in Table 2 are

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the average value of those from positive and negative drift responses.

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The specimen without corrosion (Bt-0) exhibited a typical flexural-dominant behavior. At the

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first cycle of the 5% drift (Fig. 7(a)), flexural-shear cracks were well distributed within the region

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approximately 70 cm from the fixed end. Significant spalling of concrete started to occur. During

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the second cycle of the 5% drfit loading, the core concrete near the fixed end of the beam started

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to spall off. Consequently, the beam lost its load-carying capacity, showing a significant

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distortion in the 40-cm region of the beam from the fixed end. The applied load dropped

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significantly. This specimen failed in a flexural failure mode. For specimen Bt-3, during the

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second cycle of 4% drfit loading, significant spalling of cover concrete occurred. At 5% drift,

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most of the cover concrete of the 40-cm region spalled off (Fig. 7(b)). A significant portion of the

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core concrete also spalled off. The beam failed with a significant distortion in the 40-cm region

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from the fixed end. The failure mode is a flexural type same as specimen Bt-0. Specimen Bt-6

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exhibited a flexural failure pattern similar to the previous two specimens, except for that the hoop

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closest the fixed end of the beam fractured during the second cycle of the 4% drift loading.

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Figures 7(a), 7(b) and 7(c) compare specimens Bt-0, Bt-3 and Bt-6 at the first cycle of 5% dirft,

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respectively, revealing that an increasing corrosion level increased the extent of spalling of cover

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concrete. Additionally, the peak applied load and ultimate drift decreased with an increasing

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corrosion level (Table 2), due to the reduced load-carrying capacity of cover concrete and

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confinement capacity of the corroded hoops. However, the corroded beams (Bt-3 and Bt-6) still

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possess a drift capacity higher than 4% and a plastic rotation capacity exceeding 3% with a fairly

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ductile behavior (Figs. 8(b) and 8(c)) similar to the control specimen. This finding suggests that a

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beam designed based on the current design code can sustain a corrosion weight loss of 6% in the

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hoops without significantly impairing the seismic capacity. Note that this finding is based on a

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beam with a moderate shear stress level of 0.46

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approximately 55% the maximum average shear stress allowed by the ACI 318 Code (2008) and

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an equal amount of tension and compression longitudinal reinforcement.

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f c' (MPa) at the peak applied load, i.e.

Specimens Bt-11, Bt-12 and Bt-36 showed a flexural-shear failure mode. The failure of these 6

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specimens was preceded by a major diagonal shear crack, as shown in Figs. 7(d), 7(e) and 7(f),

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respectively. Subsequently, a large portion of cover concrete spalled and then fracture of transvers

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reinforcement occurred, as shown in Figs. 8(d), 8(e) and 8(f), respectively. Note that negative

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drift loading was applied before positive drift loading in each cycle of loading. With a corrosion

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weight loss between 11% and 16%, the corroded hoops appeared to be unable to restrain the

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diagonal shear cracking. The beams failed immediately after the formation of a major diagonal

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crack. The peak applied loads of these specimens resembled that of specimen Bt-6 (Table 2).

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However, the drift capacities were reduced significantly with ultimate drifts ranging from 2% to

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3% and plastic rotations from 1.7% to 2.2%. The higher the corrosion level, the lower the drift

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capacity. These three beams exhibited a hysteretic behavior substantially less ductile than the

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previous three specimens (Bt-0 to Bt-6). The hoops of specimen Bt-35 were corroded to fracture

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before cyclic testing. Several major diagonal cracks formed at the first negative 2% drift loading

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(Fig. 7g). When the load was reversed to a positive 2% drift, a large portion of cover concrete

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spalled, exposing several fractured hoops and ultimately leading to failure of the beam (Fig.

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8(g)).

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All specimens developed yielding of longitudinal reinforcement, as evidenced by the clear

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softening of hysteretic behavior (Fig. 8h) before failure. Even for specimen Bt-35, which had

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hoops already broken before cyclic testing, the specimen still appeared to possess a significant

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amount of shear strength. This amount is largely owing to the shear strength contribution from

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concrete and the fact that critical shear cracks may cut the hoops at locations a distance from the

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broken locations, in which a certain amount of shear strength of the hoops remained. For instance,

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according to Fig 5(f), one leg of the hoop was broken, while a significant cross-sectional area

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remained for the other leg. It is likely that before the spalling of cover concrete, the unbroken leg

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could still provide a significant shear resistance. When the cover concrete started to spall, the

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shear strength dropped drastically, as mentioned earlier. Since the longitudinal reinforcement of

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all of the specimens yielded before failure, the peak applied load did not decrease significantly

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with an increasing corrosion level (Fig. 8h). The reduction of the peak applied load in specimen

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Bt-35 is only 13% compared to the control specimen. However, the ultimate drift, ductility and

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plastic rotation capacity significantly decreased with an increasing corrosion level. This

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phenomenon is because corrosion decreased the ability of the hoops to confine the core concrete

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(specimens Bt-3 and Bt-6) and restrain shear cracks (specimens Bt-11, Bt-12, Bt-16, and Bt-35), 7

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thus accelerating failure of the beams and ultimately reducing deformation capacity.

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Residual Shear Strength

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The shear strength of beam Vn consists of concrete contribution Vc and shear

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reinforcement contribution Vs (Eq. 1). Vc decreases after corrosion due to the softening of

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concrete caused by corrosion cracks. Vs decreases due to the reduction of cross sectional area.

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The effect of bond reduction on Vs is not considered since hoops rely mainly on anchorages to

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develop stress and anchorages (hooks) of the hoops are better protected by a thicker cover than

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the other region of the hoops (Fig. 5).

Vn = Vc + Vs

(1)

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where Vn is shear strength; Vc is shear strength provided by concrete; and Vs is shear strength

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provided by shear reinforcement

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The softening effect of concrete due to corrosion cracks is assumed to occur only in the cover.

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The expansion of corrosion substances exerts an outward pressure to the cover concrete, leading

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to splitting cracks in the cover concrete. These cracks decrease the ability of cover concrete to

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withstand the compression loading. This effect is simulated in this study based on the softening

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theory proposed by Hsu (1992), as shown in Eq. (2). According to the softening theory, the

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concrete compressive strength f c' decreases to ζ f c' after corrosion.

ζ =

εr =

0.9 1 + 600ε r

Wcr = pcp

∑W

cri

pcp

(2)

(3)

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where ε r is tensile strain; Wcr is total crack width; Wcri is width of crack i as illustrated in Fig.

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9(a); and pcp is outside perimeter of beam cross section.

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As illustrated in Fig. 9(a) by the shaded regions, a portion of the corrosion substances fills in

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the space surrounding the bars released by corrosion volume reduction of the hoop; in addition, a

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portion of the corrosion substances fills in the corrosion cracks. Eq. (4) calculates the ratio of the

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amount of corrosion substance filled in the cracks to the volumetric loss of a hoop due to

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corrosion, α . α was 0.20, 0.24, 0.26, 0.30, 0.27, and 0.25 for specimens Bt-3, Bt-6, Bt-11, 8

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Bt-12, Bt-16, and Bt-35, respectively, using the measured values of Wcr as listed in Table 1. The

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value of α remains relatively constant with an average value of 0.25. Figure 9(b) reveals

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another portion of the corrosion substances escaping from the concrete. Wcr = α

∆w γ steel sCc

(4)

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where s is horizontal spacing the hoops; Cc is clear cover of the hoops; and γ steel is specific

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weight of steel.

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Vc is estimated using the ACI 318 code shear strength equation (ACI 2008) provided by concrete, as defined in the following equation.

 Vd Vc =  0.16 f c' + 17 ρ w u  bw d (MPa) Mu  

(4)

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where f c' is concrete compressive strength; ρ w is tension reinforcement ratio; d is beam

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effective depth; Vu is factored shear; M u is factored moment; and bw is beam web width. In

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this study M u Vu is assumed to be the shear span, 120 cm. For corroded specimens, f c' in Eq.

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(4) is replaced with ζ f c' for cover concrete area. For the core concrete area, f c' remains the

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same. Vc degrades with an increasing ductility of the specimen during the cyclic loading. The

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degradation parameter k , as defined by Eq. (5) and proposed by Aschheim and Moehle (1992)

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is used to estimate the degraded concrete shear strength, kVc . 1≥ k =

4−µ ≥0 3

(5)

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where µ is the ductility. Table 3 lists the residual values of Vc of all specimens. Corrosion

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generally does not significantly decrease Vc . The maximum loss (specimen Bt-35) is

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approximately 7.5%. However, ductility significantly reduces Vc . Since specimens Bt-0 to Bt-11

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have a ductility capacity larger than 4, Vc of these specimens drops to zero before failure.

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Vs is estimated by the following equation. Vs =

Av f y d s

9

(6)

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where Av is cross-sectional area of shear reinforcement; and f y is yield stress of shear

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reinforcement. Since a hoop contains two legs, Av represents the total cross sectional area of the

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two legs. This study considers three cases of Av . In the first case, average residual

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cross-sectional area Aavg is assumed for two legs. In the second case, the minimum residual

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cross-sectional area Amin is assumed for two legs to consider an extreme corrosion condition. In

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the third case, one leg of the hoop is assumed to have Aavg while the other leg has Amin . This

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third case reflects the fact that the critical shear crack unlikely cuts both of the two legs at or near

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the minimum residual cross section (Fig. 5). The values of Vs , as estimated based on the first,

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second, and third cases, are referred to as Vs _ avg , Vs _ min , and Vs _ min_ avg , respectively. Table 4

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lists the value of Vs calculated based on the three cases.

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The shear strength of beam Vn is obtained by summing up Vc and Vs . Figure 10(a)

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summarizes those results. This figure also reveals the experimental peak applied loads. According

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to this figure, shear strengths calculated based on Vs _ avg always exceed the experimental peak

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loads, even when considering reduction due to ductility, implying a flexural failure mode of all

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specimens. This does not correspond to the shear failure mode of specimens Bt-11, to Bt-35. The

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values of Vn based on Vs _ min or Vs _ min_ avg and reduced by duality are lower than the test

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results for specimens Bt-11 to Bt-35. This finding suggests that these two shear calculation

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methods can provide a conservative estimation of shear strength. Vn based on Vs _ min may be

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too conservative, especially for high corrosion levels such as specimen Bt-35. This specimen had

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a severe pitting corrosion and had a large difference between the minimum cross sectional area

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and the cross sectional areas of the other portions of the hoop, which possibly provided a certain

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amount of shear resistance, as mentioned earlier. Vn based on Vs _ min_ avg is closer to

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experimental values both under low and high corrosion levels.

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Figure 10(b) illustrates the relationship between parameter (Vc + Vs − Vy ) (Vinc + Vins ) and

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the ductility, µ , of the specimens. Vinc and Vins are initial uncorroded shear strengths by

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concrete and by shear reinforcement, respectively. The ductility capacity decreases with a

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decreasing residual shear strength. The figure also shows the regression results, which are

10

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expressed by Eq. (7). These regression models can be used for ductility evaluation of beams with

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corroded transverse reinforcement.

µ=β

Vc + Vs − Vy Vinc + Vins

+γ

(7)

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where β is 15.92, 9.18, and 6.34 and γ is -1.30, 2.16, and 3.58 for Vn based on Vs _ avg ,

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Vs _ min_ avg , and Vs _ min , respectively; Vy is shear corresponding to the first yielding of

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longitudinal reinforcement of the beam. R 2 for the three regressions are 0.89, 0.79, and 0.74,

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respectively.

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CONCLUSIONS

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The effects of transverse steel reinforcement corrosion on the seismic behavior of reinforced

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concrete beams designed conforming to the ACI 318 seismic design provisions, and with a

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moderate shear stress level of 0.46

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longitudinal reinforcement were examined using cyclic loading. Important conclusions are

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summarized as follows.

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(1) As the increase of the corrosion level, the difference increased between the average

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cross-sectional area of the corroded hoop and the minimum residual cross-sectional area. This

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suggests that pitting corrosion increased as the corrosion level increased. The hoops fractured

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at a corrosion weight loss of approximately 35%.

f c' (MPa) and equal amount of tension and compression

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(2) The specimens was able to sustain approximately a 6% corrosion level while still maintaining

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a satisfactory ductile flexural behavior with plastic rotation capacities larger than 3%. Further

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increase of corrosion level changed the failure mode of the beam from flexural failure due to

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crushing of core concrete to flexural-shear failure due to diagonal tension failure. As the

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corrosion level increased, the deformation capacities reduced significantly including the

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ultimate drift, ductility, and plastic rotation capacities. However, the peak applied load did not

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show a significant reduction even for the specimens with hoops broken by corrosion. The

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residual shear strength of concrete and the hoops were sufficient to develop flexural yielding.

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For the specimen with broken hoops, the remaining portions of the hoops still preserved a

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significant cross-sectional area due to severe pitting corrosion. It appears that the hoops were 11

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still able provide a certain amount of shear resistance before spalling of cover concrete.

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(3) Methods to estimate the residual shear strength and residual ductility of the corroded beams

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are proposed. In the estimation of the residual shear strength of concrete, the core concrete is

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assumed not affected by corrosion. The shear strength of cover concrete decreases due to the

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splitting cracks by corrosion. This is modeled using softening of concrete in compression due

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to transverse tensile strain. Experimental results showed that amount of corrosion substances

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filled in the cracks volume was approximately 25% of the reduced volume of the steel due to

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corrosion. In the estimation of the residual shear strength by steel reinforcement, three

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residual steel cross sectional areas are used. Comparison with the experimental results show

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that residual shear strength based on the average weight loss is not conservative. On the other

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hand, the residual shear strength estimated based on minimum residual cross-sectional area

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provides conservative results. However, the estimated shear strength becomes too

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conservative at severe corrosion levels due to significant pitting corrosion. Shear strength

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estimated based on both average weight loss and minimum residual cross-sectional area yield

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results that reasonably reflect experimental behavior both under low and high corrosion

359

levels.

360 361

ACKNOWLEDGMENTS

362 363

The authors would like to thank the National Science Council of Taiwan under Contract No. NSC

364

100-2628-E-011-019-MY3 and Architecture and Building Research Institute of Taiwan for

365

financially supporting this research.

366 367

REFERENCES

368 369 370

ACI Committee 318. (2008). Building Code Requirements for Structural Concrete (ACI 318-08)

and Commentary (ACI 318R-08), American Concrete Institute, Farmington Hills, MI.

371

Aschheim, M., and Moehle, J. P. (1992). “Shear strength and deformability of RC bridge columns

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subjected to inelastic displacements,” Report No. UCB/EERC-92/04, Earthquake Engineering

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Research Center, University of California, Berkeley, CA.

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Eurocode 2 (1992). Design of concrete structures. General rules and rules for buildings. 12

375 376 377 378 379

European Committee for Standardization. FEMA-267b. (1999). Interim Guidelines, Advisory No. 2, Supplement to FEMA 267. Federal

Emergency Management Agency, Washington, DC. Higgins, C., and Farrow, III W.C. (2006). “Tests of reinforced concrete beams with corrosion-damaged stirrups,” ACI Structural Journal, 103(1), 133-141.

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Hsu, T. T. C. (1992). Unified Theory of Reinforced Concrete, CRC Press, Boca Raton, FL.

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Juarez, C. A., Guevara, B., Fajardo, G., and Castro-Borges P. (2011). "Ultimate and nominal

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shear strength in reinforced concrete beams deteriorated by corrosion," Engineering Structures,

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33(12), 3189-3196.

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Kato, E., Iwanami, M., and Yokota, H. (2006). “Deterioration in ductility of RC beams with

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corroded reinforcement,” Proceedings of the 2nd fib International Congress, Naples, Italy,

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1-8.

387

Ou, Y. C., Tsai, L. L., and Chen, H. H. (2012). “Cyclic performance of large-scale corroded

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reinforced concrete beams,” Earthquake Engineering and Structural Dynamics, 41(4),

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593-604.

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Rodriguez, J., Ortega, L. M., and Casal, J. (1997). “Load carrying capacity of concrete structures with corroded reinforcement,” Construction and Building Materials, 11(4), 239-248. Val, D. V. (2007). "Deterioration of strength of RC beams due to corrosion and its influence on beam reliability," Journal of Structural Engineering, ASCE, 133(9), 1297-1306.

394

Wang, X. H., Gao, X. H., Li, B., and Deng, B. R. (2011). “Effect of bond and corrosion within

395

partial length of shear behavior and load capacity of RC beam,” Construction and Building

396

Materials, 25, 1812-1823.

397 398

Xia, J., Jin, W. L., and Li, L. Y. (2011). “Shear performance of reinforced concrete beams with corroded stirrups in chloride environment,” Corrosion Science, 53, 1794-1805.

13

Table 1 Click here to download Table: Table. 1.doc

Table 1: Corrosion measurement Specimen

∆w (%)

Bt-0 0.00 Bt-3 2.90 Bt-6 5.87 Bt-11 11.73 Bt-12 12.40 Bt-16 15.67 Bt-35 35.06 ∆w is weight loss; Aavg is

2

Aavg (mm

126.67 121.57 116.44 106.19 105.15 99.33 65.58 average

Wcr (mm) ) Amin (mm ) pmax (mm) Observation Beam specimen specimen 126.67 0.00 0.00 0.00 98.85 1.47 0.17 0.27 83.91 2.56 1.28 0.65 70.45 2.62 0.97 1.38 77.98 2.97 1.74 1.70 59.29 4.73 1.82 1.93 0.00 6.35 4.56 4.06 residual cross-sectional area; Amin is minimum residual 2

cross-sectional area; pmax is maximum pit depth; and Wcr is total crack width.


Table 2. Performance indicators Specimen Bt-0 Bt-3 Bt-6 Bt-11 Bt-12 Bt-16 Bt-35  y is idealized

 y (%)

Ppeak (kN)

 u (%)



 p (%)

0.80 365.40 4.97 6.21 4.17 0.70 354.57 4.67 6.66 3.97 0.70 333.38 4.27 6.10 3.57 0.70 340.49 2.87 4.09 2.17 0.68 336.88 2.67 3.97 1.99 0.70 331.68 2.44 3.49 1.74 0.65 318.80 1.79 2.77 1.14 yield drift;  u is ultimate drift; Ppeak is peak applied load;  is

ductility; and  p is plastic rotation.


Table 3 Residual shear strength by concrete Specimen

Initial Vc (kN)

Vc at ultimate (kN)

Bt-0 Bt-3 Bt-6 Bt-11 Bt-12 Bt-16 Bt-35

137.03 133.94 132.76 130.95 130.29 129.84 126.69

0.00 0.00 0.00 0.00 1.31 22.26 52.14

Vc loss due to

Vc loss due to

corrosion (%) 0.00 2.25 3.11 4.43 4.92 5.24 7.54

ductility (%) 100.00 100.00 100.00 100.00 98.99 82.86 58.85


Table 4 Residual shear strength by shear reinforcement Vs _ avg (kN) Vs _ min (kN) Vs _ min_ avg (kN) Specimen Bt-0 473.45 473.45 473.45 Bt-3 454.37 411.91 369.45 Bt-6 435.19 374.39 313.60 Bt-11 396.88 330.09 263.29 Bt-12 392.99 342.23 291.47 Bt-16 371.25 296.42 221.59 Bt-35 245.12 122.56 0.00 Vs _ avg is based on average residual cross-sectional area Aavg ; Vs _ min is based on the

minimum residual cross-sectional area Amin ; and Vs _ min_ avg is based on Aavg for one leg and Amin for the other leg.

Figure 1 Click here to download Figure: Fig. 1.pdf

Figure 1. Examples of transverse reinforcement corrosion in reinforced concrete buildings


50

50

#4@100

50

1850

40 #4@100

#4@100

900

50

500

500

490 490

800

#4@75

#9

300 #9

Unit : mm

Unit : mm

(b)

200

(a)

600

#9

#4@100

500

Unit : mm

(c)

(d)

Figure 2. Specimen design: (a) side view; (b) cross-sectional view; (c) corrosion observation specimen; and (d) construction of specimens.


Cupper plate hoop longitudiual bars

Cupper plate longitudiual bars hoop

5% NaCl Solution

5% NaCl Solution

+ D.C Power -

+ D.C Power -

Source

Source

(a)

(b)

(c)

(d)

Figure 3. Accelerated corrosion process: (a) elevation view; (b) top view; (c) electric wires; and (d) overall view of test setup


-

P

0 4 0 5

0 4 r o o l f g d n n o r e t ds en ee o r t F d de ex xi i F F 5 6 m c : t i n U

0 5 2 7 1 2

0 9

Figure 4. Cyclic loading setup


(a)

(b)

(c)

(d)

(e)

(f)

Figure 5.Corroded hoops for specimen Bt-35 from the fixed end of the beam: (a) the first hoop; (b) the second hoop; (c) the third hoop; (d) the fourth hoop; (e) the fifth hoop; (f) the sixth hoop.


0.15 0.04

0.04

0.5

0.15

0.1 0.05

0.15

0.14

0.08

0.1

1.3

0.3

0.2

0.08

0.1

0.04

0.06

0.25 0.04

0.1

0.08

0.15

0.35

0.45 0.35

0.35

0.3

0.08 0.2

0.1

F

T

R

0.2

B

F

T

R

(a)

B

(b)

0.2

0.08

0.2

0.25

0.04

0.75

0.04

0.08

0.08

0.04

0.04

0.02

0.04

0.08 0.6

0.25

0.85

0.04

0.1 0.1

0.1

1.42

0.04

0.25

0.06

0.04

0.04

0.04

1.6

0.06

0.04

0.08

0.4

0.2

0.04

F

T

R

0.1

B

F

T

R

(c) 0.04

0.1 0.04

0.1

0.04

0.1

0.15

0.2

0.04 0.04

0.04

0.04

0.35

0.25

0.15

0.5

0.5

1.6 0.06

0.5 0.04

0.04

0.7 0.04

0.5

0.1

0.35

0.04

0.04

0.04

0.8

0.04 0.3

0.1

B

(d) 0.04

0.2

0.6

0.04

0.75

0.04 0.1

0.08

0.35

0.55 0.2 0.2

F

0.2

T

0.1

(e)

R

0.1

0.35 0.06

0.35

0.04

0.45

0.5 0.3

0.2

0.04 0.4

B

3.5 1.0

F

0.04

0.2

T

0.3

0.04

R

0.35

B

(f)

Figure 6. Corrosion crack pattern: (a) Bt-3; (b) Bt-6; (c) Bt-11; (d) Bt-12; (e) Bt-16; and (f) Bt-35 (the number shown in the figure denotes crack width (mm); F, T, R, and B denote front, top, rear, and bottom faces of the beam, respectively; the front face is the face shown in Fig. 7)


(a)

(b)

(c)

(d)

(e)

(f)

(g) Figure 7. Damage distribution: (a) Bt-0 at -5% drift (1st cycle); (b) Bt-3 at -5% drift (1st cycle); (c) Bt-6 at -5% drift (1st cycle); (d) Bt-11 at -3% drift (1st cycle); (e) Bt-12 at -3% drift (1st cycle); (f) Bt-16 at -3% drift (1st cycle); and (g) Bt-35 at -2% drift (1st cycle) (Negative drift denotes the beam is displaced downward at the loading end)


400

400

300

300

Idealized response

200 Applied load (KN)

Applied load (KN)

Test result

Test result

100 0 -100 -200

100 0 -100 -200

:cover spalling :hoop fracture :yield point :Ultimate point

-300

Idealized response

200


-300

-400

-400

-6

-4

-2

0 Drift (%)

2

4

6

-6

-4

-2

(a)

6

Test result

300

Idealized response

200

Applied load (KN)

Applied load (KN)

4

400 Test result

300

100 0 -100 -200

Idealized response

200 100 0 -100 -200


-300


-300

-400

-400 -6

-4

-2

0 Drift (%)

2

4

6

-6

-4

-2

(c) 400

0 Drift (%)

2

4

6

(d) 400

Test result

300

Test result

300

Idealized response

200

Applied load (KN)

Applied load (KN)

2

(b)

400

100 0 -100 -200

Idealized response

200 100 0 -100 -200


-300


-300

-400

-400 -6

-4

-2

0 Drift (%)

2

4

6

-6

-4

-2

(e)

2

4

6

2

4

6

400

Test result

300

0 Drift (%)

(f)

400

Bt-0 Bt-3 Bt-6 Bt-11 Bt-12 Bt-16 Bt-35

300

Idealized response

200 Applied load (KN)

Applied load (KN)

0 Drift (%)

100 0 -100 -200

100 0 -100 -200


-300

200

-300 -400

-400 -6

-4

-2

0 Drift (%)

2

4

6

-6

-4

(g)

-2

0 Drift (%)

(h)

Figure 8. Hysteretic behavior: (a) Bt-0; (b) Bt-3; (c) Bt-6; (d) Bt-11; (e) Bt-12; (f) Bt-16; (g) Bt-35; and (h) envelope responses of all specimens


Rust Uncorroded d bars ‫ݓ‬௖௥௜

‫ܥ‬௖

(a)

(b)

Figure 9. Corrosion substances: (a) filled in the space surrounding the bar and cover cracks; and (b) escaping out of concrete


700

7

600

6

Shear (kN)

500

5

400



300

4 Ppeak Vn(Vs _avg) Vn(Vs _min) Vn(Vs _avg_min)

200 100 0

Vn(Vs _avg) Vn(Vs _avg_min) Vn(Vs _min) Vn(Vs _avg)_regression Vn(Vs _avg_min)_regression Vn(Vs _min)_regression

0

10

3

20 Weight loss (%)

30

40

2 -0.3

-0.15

(a)

0 0.15 0.3 (Vc+Vs-Vy)/(Vinc+Vins)

0.45

0.6

(b)

Figure 10. (a) Residual shear strength estimation; and (b) relationship between residual shear strength and ductility

Figure Caption List

1

FIGURE CAPTIONS

2 3

Figure 1. Examples of transverse reinforcement corrosion in reinforced concrete buildings

4 5

Figure 2. Specimen design: (a) side view; (b) cross-sectional view; (c) corrosion observation specimen; and (d) construction of specimens.

6 7

Figure 3. Accelerated corrosion process: (a) elevation view; (b) top view; (c) electric wires; and (d) overall view of test setup

8

Figure 4. Cyclic loading setup

9 10 11

Figure 5.Corroded hoops for specimen Bt-35 from the fixed end of the beam: (a) the first hoop; (b) the second hoop; (c) the third hoop; (d) the fourth hoop; (e) the fifth hoop; (f) the sixth hoop.

12 13 14

Figure 6. Corrosion crack pattern: (a) Bt-3; (b) Bt-6; (c) Bt-11; (d) Bt-12; (e) Bt-16; and (f) Bt-35 (the number shown in the figure denotes crack width (mm); F, T, R, and B denote front, top, rear, and bottom faces of the beam, respectively; the front face is the face shown in Fig. 7)

15 16 17 18

Figure 7. Damage distribution: (a) Bt-0 at -5% drift (1st cycle); (b) Bt-3 at -5% drift (1st cycle); (c) Bt-6 at -5% drift (1st cycle); (d) Bt-11 at -3% drift (1st cycle); (e) Bt-12 at -3% drift (1st cycle); (f) Bt-16 at -3% drift (1st cycle); and (g) Bt-35 at -2% drift (1st cycle) (Negative drift denotes the beam is displaced downward at the loading end)

19 20

Figure 8. Hysteretic behavior: (a) Bt-0; (b) Bt-3; (c) Bt-6; (d) Bt-11; (e) Bt-12; (f) Bt-16; (g) Bt-35; and (h) envelope responses of all specimens

21 22

Figure 9. Corrosion substances: (a) filled in the space surrounding the bar and cover cracks; and (b) escaping out of concrete

23 24

Figure 10. (a) Residual shear strength estimation; and (b) relationship between residual shear strength and ductility

25