influence of both stirrup spacing and anchorage

Journal of Advanced Concrete Technology Vol. 9, No. 3, 261-275, October 2011 / Copyright © 2011 Japan Concrete Institute 261

Scientific paper

Influence of Both Stirrup Spacing and Anchorage Performance on Residual Strength of Corroded RC Beams Wei Dong1, Yuki Murakami2, Hideki Oshita3, Shuichi Suzuki4 and Tomoaki Tsutsumi5

Received 11 October 2010, accepted 25 September 2011

Abstract In this study, the influences of both stirrup spacing and anchorage performance on the residual strength of corroded RC beams are investigated. With the increase of stirrup spacing, the applied load is easily transferred to the anchorage region, and with the increase of the corrosion ratio of rebar, the mechanism of corroded RC beams shifts from beam action to arch action. In the case of non-uniform corrosion of the main rebar, the maximum deviation ratio of the corrosion ratio of main rebars is over 0.9, and the beam suffers flexural failure due to the yielding of rebars in the extremely corroded region. In the case of uniform corrosion of the main rebars, the maximum deviation ratio of the corrosion ratio of main rebars is below 0.9, and there are two situations. If the bottom portions of the stirrups are sufficient, the applied load is restricted in the support span, and the corroded beam presents a flexural failure mode. On the other hand, if the bottom portions of the stirrups are insufficient, the applied load is transferred to the anchorage, and the corroded beam is inclined to suffer bond failure. Moreover, when the beam suffers bond failure, the residual strength depends on the anchorage performance.

1. Introduction

Many infrastructures have been built more than fifty years ago not only in Japan but also worldwide, and many of these infrastructures have become more or less damaged by various factors at the service stage, such as carbonation, salt damage, and alkali-silica reaction. One possible way to save capital is to maintain the damaged infrastructures and to extend their service lives. However, serious accidents are known to have occurred in spite of proper maintenance. For example, an overpass fell down in Pennsylvania in December 2005, due to the corrosion of rebars caused by snowmelt agent. This accident, which happened just four months after an inspection, points to deficiencies in the system of predicting the residual strength of corroded infrastructure. Hence, it is urgent to find a method to accurately predict the residual strength of damaged infrastructure, which will serve also as the base for maintenance activities. Among the factors that can degrade the strength of infrastructure, the cor-rosion of rebars is the most serious and has a direct in-fluence. Many fundamental results have been accumu-lated in the last thirty years by studying a variety of

specimens with corroded rebars (Aoyama et al. 1998; Iwanami et al. 2002; JSCE. 2006; Lee et al. 1995; Kato et al. 2003; Kayser et al. 1989; Oyado et al. 2001; Val and Chernin 2009; Wang and Li 2010; Xue and Seki 2010); even so, how to accurately predict residual strength is still an unsolved problem that is still receiving worldwide attention.

In real construction, both stirrups and hooks are ar-ranged. In the case of non-corroded beams, stirrups are used to prevent the propagation of diagonal cracks and to improve the shear capacity. Hooks are used to avoid pull-out failure. Whereas in the case of corroded beams, the effects of stirrups and hooks are not clear. In previous research (see for instance, Aoyama et al. 1998; Iwanami et al. 2002; Kato et al. 2003), the arrangements of rebars are so complex that it is difficult to clearly identify the effect of each component (main rebar, stirrup, hook, and so on) on residual strength. An efficient process is to identify the effect of each component first, and then their combined effects. Thus, beams with a simple arrange-ment of rebars were adopted in this study.

It is reported that the residual strength of corroded RC beams increases due to arch action (Kani 1964; Ikeda et al. 1979), and that corroded beams are inclined to ex-perience bond failure rather than shear compressive failure. Although the condition leading to the formation of arch action has not been clarified yet, the deterioration of the rebar-to-concrete bond (bond performance) is regarded as the reason for the change of mechanism. It is obvious that bond performance is mostly related to the amount of stirrups and to the corrosion level. Hence, it is necessary to investigate the effect of the amount of stir-rups and of the corrosion level. Moreover, corroded beams often experience bond failure before a perfect arch action forms, which indicates that anchorage perform-ance (peak bond stress in anchorage) has a great effect on

1 Ph.D. student, Faculty of Science and Engineering, Chuo University, Japan. E-mail: [email protected] 2Assistant Professor, Department of Civil Engineering, Nagaoka National College of Technology, Japan. 3Professor, Department of Civil Engineering, Chuo University, Japan. 4Civil Engineers, Tokyo Electric Power Services Co., LtdJapan. 5Researcher, Institute for Technology Development, Tokyo Electric Power Co., Ltd, Japan.

262 W. Dong, Y. Murakami, H. Oshita, S. Suzuki and T. Tsutsumi / Journal of Advanced Concrete Technology Vol. 9, No. 3, 261-275, 2011

the residual strength of beams undergoing bond failure. Against this background, corroded beams with dif-

ferent stirrup spacing and different anchorage types were tested to investigate the effect of stirrups on failure mode and the effect of anchorage performance on residual strength.

2. Experiment

2.1 Experiment and parameters The specimens are shown in Fig. 1, and the parameters in Table 1. The beams are rectangular RC beams of 240 mm width, 200 mm height and 2100 mm length. Main rebars with D16 (SD295A) deformed bars were arranged at 60 mm intervals, and stirrups with D6 (SD295A) de-formed bars were arranged in some beams. In the ex-periment, the rebars were simply arranged, and no rebars were provided in the compression zone, because it is difficult to investigate the effects of both main rebars and stirrups on residual strength if there are corrosion cracks along the compressive rebars. In series S0, only main rebars were arranged, to investigate the effect of the corrosion pattern of main rebars on residual strength. In series S1, stirrups with different spacing were arranged, to investigate the effect of stirrups in the shear span on failure mode and on residual strength. As already men-tioned, it is obvious that the residual mass of stirrups has an effect on the transmission of bond stress. To investi-gate how the failure mode changes as the stirrups become insufficient, two methods are used: one is to increase the corrosion level, and the other is to widen the stirrup spacing. Thus, beams with larger stirrup spacing were also investigated in this study. In series S2, two stirrups were arranged in the anchorage region, to investigate the effect of stirrups in anchorage on residual strength. In series SF, main rebars were perfectly anchored at the ends of the beam with steel plates. In series F90, 90 degree hooks were arranged. Both series SF and series F90 were used to investigate anchorage performance on residual strength. Moreover, two identical beams, beam S240-20A and beam S240-20B, were made. The stirrups in beam S240-20B were thinly coated with modified epoxy resin three times. The modified epoxy resin is a kind of anticorrosive paint, which does not degrade the bond performance. However, it was not coated on the stirrups in beam S240-20A. Additionally, in order to identify the rebars, the two outer main rebars were la-beled as R and L respectively, and the intermediate rebar were labeled as M (see Fig. 1). 2.2 Material properties The mix proportion of concrete is given in Table 2. 5% sodium chloride solution, a corrosion catalyst, was mixed with water to speed up the galvanic corrosion testing. The design strength of concrete was 30 N/mm2 at 28 days, and the compressive strength of concrete at the loading stage is shown in Table 1. All the compressive strengths were in the vicinity of 30 MPa. The deviation

Fig. 1 Specimen dimensions and rebars.

120

60@4=240

40

40

L M R

(b) Series S80

1800 2100

350 P/2 P/2 Stirrups D6@80

Main rebars D16

200 CLCLCLCLCLCLCLCL

(a) Series S0 2100

CLCLCLCLCLCL350 P/2 P/2

200

1800

Main rebars D16

60@4=240

40 120 40

L M R

CLCLCLCLCLCLCLCL

(c) Series S160

350 P/2 P/2

2100

1800

200

StirrupsD6@160 Main rebars

D16

120

60@4=240

40

40

L M R

(e) Series S2

L M R200

350

12040

40

60@4=240 1800

2100

200

(d) Series S240

350 P/2 P/2

2100 1800

Stirrups D6@240 Main rebars

D16

120

60@4=240

40

40

L M R

Steel plate

L M R

(f) Series SF

200

350

1800

2100

12040

40

60@4=240

Steel plate

200

350P/2 P/2

21001800

200

350P/2 P/2

21001800

(g) Series F90 (Beam F90-S0-20)

(H) Series F90 (Beam F90-S240-20)

60@4=240

120L M R

60@4=240

120L M R

200

350P/2 P/2

2100 1800

unit: mm

W. Dong, Y. Murakami, H. Oshita, S. Suzuki and T. Tsutsumi / Journal of Advanced Concrete Technology Vol. 9, No. 3, 261-275, 2011 263

for compressive strength was 10.7%, which only con-tributes 1.2% to the bending capacity. Hence it can be concluded that the differences in compressive strength had almost no influence on the load capacity.

The data of uniaxial tensile tests for both main rebars and stirrups are shown in Table 3. The flexural capacity and the shear capacity of non-corroded beams calculated by the JSCE code are shown in Table 4. They are all for the flexural failure mode.

2.3 Corrosion method In order to estimate the residual strength of real struc-tures, which experience wide-ranging degradation by salt damage, the entire length of the main rebars was cor-roded. To achieve the expected corrosion ratio in a short period of time, the method of galvanic corrosion testing was adopted (Murakami et al. 2006). As shown in Fig. 2, the beam is placed in a water tank filled with 5% sodium chloride solution. Three rebars act as the anode, and a copper plate as the cathode. 20 A direct current flows through the two electrodes until a given amount of elec-tricity is achieved, which is shown in Table 1. The main rebars and stirrups were taken out from the corroded beams after the loading test and then immersed in a 10% diammonium hydrogen citrate solution for 24 hours to dissolve the rust.

All the main rebars were cut into 42 parts with a length of 50 mm (see Fig. 4), except the rebars in series S0,

which were cut into 5 parts (see Fig. 3). Regarding the corrosion ratio of stirrups, three regions (entirety of each stirrup, upper portion, and lower portion of each stirrup) were measured as shown in Fig. 5.

Here, the percent loss of weight compared to the original weight of the local rebar is defined as the local corrosion ratio, as shown in Eq. 1. The corrosion ratio is the average of local corrosion ratios of the main rebars in the beam.

Table 1 Parameters.

Series Specimen Cement1) Expected corrosion ratio (%)

Stirrup spacing Stirrup ratio

Compressive strength (N/mm2)

Quantity of electricity(A·hr)

S0-0 0 30.8 - S0-10 10 31.6 1110 S0-20 20 35.5 2220 S0

S0-30

N

30

-

36.2 3330 S80-0 0 27.0 - S80-5 5 29.6 2050

S80-10 10 26.5 4100 S80

S80-20

N

20

80 mm (0.33%)

27.2 8200 S160 S160-10 H 10 33.5 2550

S240-0 N 0 32.4 - S240-10 H 10

160 mm (0.18%)34.9 2070

S240-20A 20 34.5 4140

S1

S240

S240-20B 20 240 mm (0.11%) 30.8 4140 S2-0 0 30.3 -

S2-10 10 30.4 1360 S2 S2-20 28.0 2720

SF SF-20

only in anchorage

34.2 2720 F90-S0-20 - 25.7 2620 F90 F90-S240-20

N

20

240 mm (0.11%) 32.4 4880 1) N: normal cement, H: high early strength cement.

Table 2 Mix proportion of concrete.

Unit weight (kg/m3) Gmax (mm)

W/C (%)

SL (cm)

Air (%) W C S G CA NaCl

20 60 10 5 168 280 826 996 2.8 8.8

Table 3 Reinforcement properties.

Diameter D16 D6 Yield stress (N/mm2) 369 438

Ultimate stress (N/mm2) 523 557 Elastic modulus (N/mm2) 2.0×105 2.0×105

Table 4 Theoretical load capacity.

Series Flexual capacity (kN) Shear capacity (kN)S0 80.8

S80 161.4 S160 121.1 S240 107.7

S2 80.8 SF

80.5

80.8

Direct current stabilizedpower supply

Reinforcement（Anode）

Copper plate（Cathode）

5% NaCl solution

Data logger

Direct current stabilizedpower supply

Reinforcement（Anode）

Copper plate（Cathode）

5% NaCl solution

Data logger

Fig. 2 Details of corrosion test.


'100 (%)i i

ii

m mm

α−

= × (1)

where iα = corrosion ratio of part i , im = mass of part i before corrosion, and 'im = residual mass of part i .

It is possible to get the real corrosion ratio if the re-sidual strains are known. However, it has been pointed out in the literature (Kim et al. 2007) that the capacity of elongation degrades to less than 1% due to corrosion, and it seems that the residual strain after yielding can be safely ignored when the measured corrosion ratio is near 20%. On the other hand, for the rebars not to yield, the difference between the measured corrosion ratio and real corrosion ratio needs to be much smaller. In addition, the average of local corrosion ratios is used as the corrosion ratio of a beam, and thus the effect of elongation on the average corrosion ratio is very small and can be ne-glected.

2.4 Loading test and measured item Four-point static bending tests were conducted under displacement control at the velocity of 0.5 mm/minute. The loading span and support span were 350 mm and 1800 mm, respectively. The measured items included

midspan deflection and the longitudinal strains of the main rebars.

To avoid disrupting the bond behavior around the pe-rimeter of the rebars and to protect strain gauges from corrosion, the gauges were set inside the rebars as shown in Fig. 6 (Scott 1996; Murakami et al. 2006). The strain gauged rebars were manufactured as follows: first, the rebar was cut into two halves along the longitudinal axis, then a 4 mm wide and 2 mm deep groove was sawed axially on the cutting plane of both halves. Next, strain gauges (2 mm length, at a spacing of 48 mm) were af-fixed to the surface of one groove, wiring was then in-stalled in the groove, and finally the two halves were bound back together with epoxy resin to give the ap-pearance of a normal deformed bar. The strain gauged rebar was only used as intermediate rebar M. The main rebars for beams S160-10 and S240-10 were all normal deformed bars with no gauges attached, and the strain gauges for beam S240-20A were corroded. Hence there are no strain data for the three beams mentioned above.

3. Corrosion behavior of rebars and corrosion crack behavior in concrete cover

3.1 Corrosion behavior of main rebars The corrosion ratios of series S0 and series S1 are shown in Table 5. The average corrosion ratio of each beam is relatively near the expected corrosion ratio. Moreover, the corrosion ratios of the three rebars in each beam are similar to each other too, except for beams S0-30, S80-20 and S240-20A

In series S0, the distribution of the corrosion ratio of each beam is shown in Fig. 7. It is obvious that the dis-persion of the corrosion ratio is small in beams S0-10 and S0-20, which indicates that the rebars are relatively uniformly corroded. On the other hand, the corrosion ratio for beam S0-30 in region 4 (near 1450 mm) is much larger with a value of 50.7%, which indicates that beam S0-30 is relatively non-uniformly corroded. It can be considered that this kind of difference in local corrosion ratio is caused by the difference in the width of corrosion cracks. The relationship between the coefficient of variation of corrosion ratio and the average corrosion ratio is shown in Fig. 8. It indicates that the larger the corrosion ratio, the larger the variation of the corrosion ratio. And it also indicates that the variation of corrosion ratio in series S1 is larger than in series S0. Moreover, the smaller the spacing of the stirrups, the larger the coeffi-cient of variation. Hence, the coefficient of variation does not only depend on the difference in corrosion crack

2100

CL

100100 100 100 100

0-1000 -500 500 1000

(mm)Measurement Region

Region ① end Region ② middle Region ③ center Region ④ middle Region ⑤ end

2100

CLCL

100100 100 100 100

0-1000 -500 500 1000

100100 100 100 100100100 100 100 100

0-1000 -500 500 1000

(mm)Measurement Region Measurement Region

Region ① endRegion ① end Region ② middleRegion ② middle Region ③ centerRegion ③ center Region ④ middleRegion ④ middle Region ⑤ endRegion ⑤ end

Fig. 3 Measured region of corrosion ratio (series S0).

( )

iregioninratiocorrosionaverage

ratiocorrosionaverage

regionofnumbernn

i

RiMiLii

n

iRi

n

iMi

n

iLi

:

:3/

:3/

avg

111avg

α

ααααα

αααα

++=

⎟⎟⎠

⎞⎜⎜⎝

⎛++= ∑∑∑

===

ＬＭＲ

42i-21 2 3 i i+2 4140

ＬＭＲ

ＬＭＲ

42i-21 2 3 i i+2 4140

Fig. 4 Calculation of corrosion ratio.

H: sum of radius of both main rebar and stirrup

1 Entire stirrup 3 Bottom portion

2 Upper portion H

H

Fig. 5 Measured regions of corrosion ratio.

Cut along longitudinal axis Bind together Sectional area

Strain gauge4 mm

2 m

m

Cut along longitudinal axis Bind together Sectional area

Strain gauge4 mm

2 m

m

Fig. 6 Details of rebar M.


pattern and corrosion ratio of the main rebars, but also on the stirrup spacing.

3.2 Corrosion behavior of stirrups The average corrosion ratio of stirrups is larger than that of main rebars as shown in Table 5, because the concrete cover and the diameter of stirrups are much smaller.

Moreover, the average corrosion ratio of stirrups for beam S240-20B is 40%, about 27% less than beam S240-20A. It can be concluded that modified epoxy resin can reduce the corrosion ratio dramatically. 3.3 Corrosion crack behavior on concrete cover 3.3.1 Series S0 (without stirrups) The corrosion cracks in the concrete cover of beam S0-20 is shown in Fig. 9. It can be observed that the corrosion cracks only occurred in the concrete cover along two outside rebars (L and R), but no crack propa-gated along rebar M. Figure 10, which shows the beam ends, indicates that corrosion cracks developed toward two side surfaces of the beam. Figure 11 shows one side surface of beam S0-20. It can be seen that a reddish liquid (rust) penetrates near the side surface, which indicates that the corrosion crack tips are reaching the side surface. In the other corroded beams of series S0, the corrosion crack patterns are similar. The mechanism is shown in Fig. 12. Internal radial stress, which is caused by the expansion of rust, acts on the concrete surrounding the

Table 5 Corrosion ratio of reinforcements. Real corrosion ratio (%) Average corrosion ratio of stirrup (%)

Entire stirrup (Fig.5-1) Bottom portion (Fig.5-3) Series Specimen L M R Average

Coeffcient of

variatin Left span Right span Average Left span Right span AverageS0-0 -

S0-10 10.7 9.5 10.3 10.2 0.1 S0-20 18.6 18.4 18.8 18.6 0.2 S0

S0-30 29.3 22.8 27.1 26.4 0.5 S80-0 -

-

S80-5 3.7 3.5 4.0 3.7 0.4 17.5 16.9 17.2 13.3 12.6 13.0 S80-10 14.9 16.7 12.8 14.8 0.6 61.7 63.5 62.6 61.3 65.5 63.4 S80

S80-20 24.2 14.0 16.7 18.3 0.6 71.6 75.7 73.7 44.5 70.2 57.4 S160 S160-10 12.3 8.7 11.3 10.8 0.3 45.1 41.0 43.1 38.5 38.0 38.3

S240-0 - - S240-10 11.3 9.7 10.9 10.6 0.2 44.1 45.7 44.9 34.3 38.5 36.4

S240-20A 20.7 32.2 18.7 23.9 0.6 72.3 61.8 67.1 90.9 57.6 74.3

S1

S240

S240-20B 19.4 22.4 17.3 19.7 0.4 43.0 38.7 40.9 35.0 33.5 34.3 S2-0 -

S2-10 11.4 7.5 11.4 10.1 0.1 43.7 34.6 39.2 34.0 23.5 28.8 S2 S2-20 14.3 21.6 13.2 16.4 0.2 42.8 42.4 42.6 26.4 16.3 21.4

SF SF-20 25.0 21.0 17.8 21.3 0.2 25.2 31.1 28.2 16.5 30.9 23.7 F90-S0-20 16.1 15.2 16.5 15.9 0.1 - F90 F90-S240-20 21.5 18.8 17.8 19.4 0.4 58.5 54.1 56.3 42.1 59.9 51.0

0

20

40

60

80

100

1 2 3 4 5Number of region

Cor

rosio

n ra

tio (%

)

Main rebar L (S0-10)Main rebar M (S0-10)Main rebar R (S0-10)Main rebar L (S0-20)Main rebar M (S0-20)Main rebar R (S0-20)

(a) Beam S0-10 and S0-20 (uniform corrosion)

0

20

40

60

80

100

1 2 3 4 5Number of region

Cor

rosio

n ra

tio (%

)

Main rebar L (S0-30)Main rebar M (S0-30)Main rebar R (S0-30)

(b) Beam S0-30 (non-uniform corrosion)

Fig. 7 Corrosion of tensile reinforcement (series S0).

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25 30Corrosion ratio of beam (%)

Dev

iatio

n ra

tio

-

Series S0Series S80Series S160Series S240

Fig. 8 Deviation ratios and corrosion ratio.


corroded rebars. Two sides of the beam are free ends, which means there is no external force to counterbalance the expansion force. As a result, it is easier for corrosion cracks to propagate along rebars L and R. However, internal radial force acts on the concrete surrounding rebar M too, but the expansion stresses of the two outside rebars also act on the concrete surrounding rebar M as compressive stress. Thus the tensile stress in concrete surrounding rebar M decreases. Hence, it is difficult for corrosion cracks to occur along the intermediate rebar. 3.3.2 Series S1 (with stirrups) First, let us take beam S80-20 as an example. The crack pattern in the concrete cover is shown in Fig. 13. Corro-sion cracks are present not only along the two outside main rebars, but also along a portion of intermediate main rebar M. Second, the relationship between the av-erage width of the corrosion cracks and the average corrosion ratio of main rebars L and R is shown in Fig. 14. It is evident that the corrosion crack width in the cover concrete of series S1 is greatly smaller than that of series S0, which proves that stirrups can restrict the ex-pansion of corrosion cracks. If the average corrosion ratio is less than 20%, the average crack width along rebars L and R becomes smaller, as the stirrup spacing decreases. However, if the average corrosion ratio is

larger than 20%, this trend is not so clear due to the considerable corrosion ratio of the stirrups. Finally, as shown in Fig. 15, the corrosion crack in the beam ends indicates that there are almost no corrosion cracks pene-trating toward the two side surfaces. This phenomenon also happens in other corroded beams of series S1. The mechanism is illustrated in Fig. 16. The stirrup is under tensile stress due to the expansion of rust, and bond stress forms between the stirrups and concrete. The bond stress of stirrups can restrict the opening of corrosion cracks in the side surface and corrosion cracks along rebars L and M. Regarding rebar M, the compressive stress, caused by the expansion of rust of rebars L and M, acts on the concrete around rebar M. But with the bond between the stirrups and concrete in the concrete cover, the effect of the compressive stress mentioned above is degraded. Hence, it is easier for corrosion cracks to propagate along rebar M, compared to the beams in series S0.

L M

R

Fig. 9 Corrosion cracks on bottom surface (S0-20).

(a) Beam S0-10 (b) Beam S0-20 Fig. 10 Corrosion cracks on beam end (series S0).

Fig. 11 Sign of rust on side (S0-20).

両側面鉄筋による膨張圧

膨張圧腐食膨張

自由端

自由端 Crack Crack

Crack CrackCrackCrack



自由端

自由端 Crack Crack

Crack CrackCrackCrack

Expansibility of rust Expansion pressure

Fig. 12 Mechanism of corrosion crack (series S0).

L M R

Fig. 13 Corrosion cracks on bottom surface (S80-20).

0.0

0.5

1.0

1.5

2.0

2.5

0 5 10 15 20 25 30Average corrosion ratio of rebar L and R (%)

Ave

rage

cra

ck w

idth

[L a

nd R

] (m

m))

Series S0Series S80Series S160Series S240

Fig. 14 Width of corrosion crack.

(a) Beam S80-10 (b) Beam S80-20 Fig. 15 Corrosion cracks on ends (series S80).

CrackCrack

せん断補強筋

による抑制


CrackCrackCrack

Crack Crack


せん断補強筋

による抑制

CrackCrack

せん断補強筋

による抑制


CrackCrackCrack

Crack Crack


せん断補強筋

による抑制

Expansibility of rust Expansion pressure

Effect of stirrup Effect of stirrupExpansion pressure of side reinforcement

Fig. 16 Mechanism of corrosion crack (series S1).


4. Influence of corroded rebars on residual strength in beams with no stirrups

4.1 Load-midspan deflection and failure mode The curves of load-midspan deflection of series S0 is shown in Fig. 17. The residual strength and failure mode are shown in Table 6. The main rebars in beam S0-0 yield at the applied load of 85 kN. As shown in Fig. 18(a), the beam undergoes typical flexural failure with the occurrence of many flexural cracks in a wide area.

Regarding the corroded beams S0-10 and S0-20, they all undergo bond failure and the rebars do not yield. As shown in Figs. 18 (b) and (c), there are a few flexural cracks in beams S0-10 and S10-20 at the failure stage, which indicates that the capability of crack distribution has been reduced due to corrosion. The failure cracks of the two beams have the same pattern (the failure cracks are the cracks that occur when the load falls dramati-cally). First, flexural cracks initiate near the projective point of the loading point at the bottom face of the beam and extend upwards, and then a diagonal crack propa-gates. Finally, a horizontal crack extends along the main rebars. When the horizontal crack gets near the support point, the beam fails suddenly.

Regarding the corroded beam S0-30 (see Fig. 18 (d)), only a few cracks occur in the final stage, and the hori-zontal crack halts at an extremely corroded point, where the rebars yield.

4.2 Distribution of strain and bond strength The distribution of strains of the main rebars in series S0 is shown in Fig. 19. As shown in Figs. 19 (a) and (b), the shape of strain distribution in beams S0-10 and S0-20 at the early stage is almost the same as that in non-corroded beam S0-0. However, when the applied load is up to 50 kN, the strains in the shear span of beam S0-10 become uniform and the gradient of strain in the anchorage be-come larger. Similarly, when the applied load is up to

0102030405060708090

100

0 5 10 15 20 25 30 35 40Deflection (mm)

Load

(kN

)

S0- 0S0-10S0-20S0-30

S0-0S0-10 S0-30

S0-20

Fig. 17 Load-deflection (series S0).

(b) Beam S0-10

(c) Beam S0-20

(d) Beam S0-30

Before peak After peak

(a) Beam S0-0

flake

Fig. 18 Cracks in the final stage (series S0).

Table 6 Load capacity and failure mode. Corrosion ratio (%) Series Specimen Load

capacity (kN) Failure mode Entire length Constant moment regionMaximum

deviation retio Position

(mm) S0-0 94.9 flexural failure - S0-10 53.1 bond failure 10.2 10.9 0.07 1050 S0-20 34.3 bond failure 18.6 22.5 0.23 1500 S0

S0-30 45.9 flexural failure 26.4 25.8 0.93 1501 S80-0 91.3 flexural failure - S80-5 77.0 flexural failure 3.7 5.8 1.10 1025

S80-10 57.9 flexural failure 14.8 21.3 1.34 1125 S80

S80-20 56.7 flexural failure 18.3 16.9 1.23 1475 S160 S160-10 77.8 flexural failure 10.8 13.1 0.53 1225

S240-0 91.8 flexural failure - S240-10 75.7 flexural failure 10.6 12.1 0.36 1225

S240-20A 43.3 bond failure 23.9 30.6 0.67 625

S1

S240

S240-20B 57.2 shear failure 19.7 20.9 0.67 775 S2-0 91.4 flexural failure - S2-10 69.8 bond failure 10.1 9.2 0.13 S2 S2-20 59.2 bond failure 16.4 19.4 0.22

F90-S0-20 64.5 anchorage failure 15.9 010 F90 F90-S240-20 62.7 anchorage failure 19.4 - 0.35

-


maximum (about 30 kN), the strains in the right shear span of beam S0-20 become smooth and the gradient of strain in the right anchorage becomes larger. As for beam S0-30, the strains in the right shear span are larger than those of the non-corroded beam compared at the applied load of 30 kN; also, the strain at the extremely corroded point becomes very large, which means that the beam undergoes flexural failure due to the yielding of rebars.

In this research, variations in bond stress along the length of rebars is analyzed from the differences in strains in rebars. The bond stress can be given by Eq. 2.

(1 )4

s s sD E ddx

α ετ

−= − (2)

where α = corrosion ratio, sE = the elasticity module of rebars, sε = the strain of main rebars, sD = diameter of main rebars (non-corroded ), assuming that the cross-sections of corroded rebars are circles, and x = distance to one end of beams along the longitudinal di-rection of main rebar.

As an example, the distribution of bond stress of beam S0-10, undergoing bond failure, at the applied load of 50 kN is shown in Fig. 20. It is evident that, in non-corroded beams, the bond stress in the shear span is larger, and that it is close to zero in anchorage. On the other hand, in corroded beams undergoing bond failure, the bond stress in the shear span is close to zero, and it is larger near the anchorage.

The relationships between load and average bond stress of beams S0-10 and S0-20 near the anchorage (0 mm to 250 mm, same below) and near the shear span (250 mm to 750 mm, same below) are shown in Fig. 21 (where the bond stresses are in the failure span, same below). In beam S0-0, bond stress in the shear span in-creases until failure, but the stress in the anchorage is very small at any load level. Regarding beams S0-10 and S0-20, at the early stage, there is no obvious difference with beam S0-0. However, when nearing the failure stage, the bond stress in the shear span declines rapidly, and the bond stress in the anchorage increase simultaneously. This indicates that in uniformly corroded beams, the applied load is transferred to the anchorage due to the corrosion of the main rebars. Based on the experimental data in this study, when there are only main rebars ar-ranged and the corrosion ratio of the main rebars is larger than 10%, the applied load is transferred to the anchorage and the beam undergoes pull-out failure due to bad an-chorage performance.

4.3 Influence of non-uniform corrosion on re-sidual strength As shown in Fig. 19(c), the strain in the right shear span of beam S0-30 is much larger at position 1450 mm when the applied load is up to 30 kN. Beam S0-30 undergoes flexural failure due to the yield of the rebars, which dif-fers from beams S0-10 and S0-20. The distribution of corrosion ratio of the main rebars in series S0 is shown in Fig. 7. It is evident that in beams S0-10 and S0-20, the

0

400

800

1200

1600

2000

0 350 700 1050 1400 1750 2100Position (mm)

Stra

in (μ

)

10kN (S0-10)30kN (S0-10)51kN (S0-10)10kN (S0-0)30kN (S0-0)50kN (S0-0)

(a) Beam S0-10

0

400

800

1200

1600

2000

0 350 700 1050 1400 1750 2100Position (mm)

Stra

in (μ

)

10kN (S0-20)20kN (S0-20)31kN (S0-20)10kN (S0-0)20kN (S0-0)30kN (S0-0)

(b) Beam S0-20

0

400

800

1200

1600

2000

0 350 700 1050 1400 1750 2100Position (mm)

Stra

in (μ

)

10kN (S0-30)30kN (S0-30)46kN (S0-30)10kN (S0-0)30kN (S0-0)

(c) Beam S0-30

Fig. 19 Distribution of strain (series S0).

-3

-2

-1

0

1

2

3

0 350 700 1050 1400 1750 2100Position (mm)

τ (N

/mm2 )

S0-0S0-10

Fig. 20 Bond stress at load level of 50 kN.


unevenness of corrosion ratio is minor. However in beam S0-30, the unevenness of corrosion ratio is much larger, as the corrosion ratio in region 4 even reaches to 50.7%. In other words, beams S0-10 and S0-20 are uniformly corroded, while beam S0-30 is non-uniformly corroded. With regard to beam S0-30, the plastic hinge forms at the position where the rebars are extremely corroded, which results in localized plastic deformation at that point. For this reason, the applied load cannot be transferred to the anchorage smoothly. Thus beam S0-30 undergoes flex-ural failure due to yielding rather than pull-out failure.

The relationship between the average corrosion ratio of the beam and the residual strength ratio, which is defined as the value of the residual strength divided by the strength of the non-corroded beam in the same series, is shown in Fig. 22. (The theoretical value of the cor-roded beam is based on the JSCE code, as the main rebar ratio decreases with the corrosion ratio.) Only the beams undergoing flexural failure are shown in the figure. Since there are no non-corroded beams in series S160, the residual strength ratio of beam S160-10 is calculated based on beam S240-0. As shown in the figure, the re-sidual strength ratio declines linearly, with increases of the average corrosion ratio. This indicates that the re-sidual strength of beams undergoing flexural failure is mainly dependent on the residual mass of the main rebars. As shown in the figure, the residual strengths of beams S160-10 and S240-10 agree well with the theoretical values. However, the residual strengths of other beams

undergoing flexural failure are a little below the theo-retical value. This difference is caused by the unevenness of the corrosion ratio. In other words, beams S160-10 and S240-10 are uniformly corroded, and the other beams are non-uniformly corroded.

In this study, whether a beam is uniformly corroded or not is evaluated by the maximum deviation ratio of cor-rosion ratio, as shown below.

max{| | / }i avg avgk α α α= − (3)

where k = maximum deviation ratios, iα = local corro-sion ratio, and avgα = average corrosion ratio.

The maximum deviation ratio and its position in each beam are shown in Table 6. First, in series S0, the maximum deviation ratios of beams S0-10 and S0-20 undergoing bond failure are 0.07 and 0.23 respectively. The index for S0-30, which undergoes flexural failure due to non-uniform corrosion, is 0.93, at the point in which the rebars are extremely corroded. The maximum deviation ratios in series S80 are all greater than 0.9. The rebars in beams S80-5 and S80-10, with the index of 1.10 and 1.34 respectively, yield at the extremely corroded point in the constant moment region. The index for beam S80-20 is 1.23, and the rebars fracture at the extremely corroded point in the shear span. The indexes for beams S160-10 and S240-10 are 0.53 and 0.36, respectively, and their residual strengths are near the bending theo-retical values. Therefore, in this experiment, the thresh-old for non-uniform corroded bars can be defined as 0.9. However, in the experiment, the extremely corroded points are all near the constant moment region. In those cases where the point with the maximum deviation ratio of over 0.9 is far from the constant moment region, not only the corrosion ratio of the rebars but also the distri-bution of moment should be considered. This should be studied in the future.

5. Influence of stirrups on residual strength of RC beam with stirrups 5.1 Load-midspan deflection The residual strength and failure mode of series S1 are shown in Table 6, and the load-midspan deflection curves of series S80 are shown in Fig. 23. All of the beams undergo ductile failure. Beam S80-5 undergoes flexural compression failure. Beams S80-10 and S80-20 undergo fracture failure when deflection reaches 30 mm.

The load-midspan deflection curves of beams S160-10 and S240-10 is shown in Fig. 24 (a), whose stirrup ratios are 0.18% and 0.11%, respectively. Both of the two corroded beams undergo ductile failure, regardless of the stirrup ratio. In beams S160-10 and S240-10, the corro-sion ratio of the main rebars and the corrosion ratio of the stirrups are almost the same, and nor is there a significant difference in deformation capacity, although the stirrup spacing differs. However, the residual strength of beam S80-10 is lower than that of the two beams mentioned above, owing to the larger corrosion ratio of the rebars.

The load-midspan deflection curves of beams

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60Load (kN)

Ave

rage

bon

d str

ess (

N/m

m2 ) S0-0S0-10S0-20S0-0S0-10S0-20

Shear span

Anchorage region

Fig. 21 Bond stress.

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40Average corrosion ratio (%)

Res

idua

l stre

ngth

ratio

)

Experimental valueTheoretical flexural strength

S160-10 and S240-10

Fig. 22 Residual strength ratio-average corrosion ratio. (flexural failure mode).


S240-20A and S240-20B are shown in Fig. 24 (b). The residual capacity of beam S240-20B is no less than that of beam S80-20. But the residual capacity of beam S240-20A is somewhat small and declines rapidly when the deflection is up to 8 mm. The reason for this differ-ence will be discussed later.

The cracks of series S1 at the failure stage are show in Fig. 25. The number of flexural cracks declines with the increase of corrosion level. The figure shows that the capability of crack distribution has been reduced due to corrosion. Moreover, it can be seen that the flexural cracks stretch upward along the corrosion cracks of the stirrups. In addition, the horizontal crack along the main rebars only appeared in beams S240-20A and S240-20B.

5.2 Strain and bond performance The distribution of strains in beam S80-10 is taken as an example and shown in Fig. 26. The strains of beam

S0-10 are also shown in the figure as red lines for com-parison purposes. The strains of beam S0-10 in the shear span become uniform at the applied load of 50 kN. However, the curve of beam S80-10 has a parabola shape at any load level. This indicates that the applied load is restricted in the shear span and has not been transferred to the anchorage owing to the confining effect of the stirrups. (The stirrups can prevent the propagation of failure cracks along the main rebars, and can also restrict the slip between mains rebar and concrete. These prop-erties are called the confining effect of stirrup.) It can be deduced that, in the beams with larger stirrup spacing, the applied load can be transferred to the anchorage, due to the decline of the confining effect of stirrups.

The load and the average bond stress relationships for beams S80-10 and S240-20B in both the anchorage re-gion and the shear span are shown in Fig. 27. As for beam S80-10, almost all the applied load is restricted in the shear span until failure. In beam S240-20B, the av-

0102030405060708090

100

0 5 10 15 20 25 30 35 40Deflection (mm)

Load

(kN

)

S80-0S80-5S80-10S80-20

S80-5

S80-0

S80-20

S80-10

Fig. 23 Load deflection relationship for series S80.

0102030405060708090

100

0 5 10 15 20 25 30 35 40Deflection (mm)

Load

(kN

)

Ｓ80-10S160-10S240-10

S240-10

S160-10

S80-10

(a) Corrosion ratio 10%

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40Deflection (mm)

Load

(kN

)

S80-20S240-20AS240-20BS240-20B

S80-20

S240-20A

(b) Corrosion ratio 20%

Fig. 24 Load-deflection relationship for series S240.

(a) Beam S80-0

(b) Beam S80-5

(c) Beam S80-10

(d) Beam S80-20

(e) Beam S160-10

(f) Beam S240-10

Corrosion crack Before peak load After peak load

(g) Beam S240-20A

(h) Beam S240-20B Fig. 25 Failure cracks pattern (series S1).


erage bond stress in the shear span reaches the maximum level when the applied load is about 45 kN. Then the bond stress in the shear span declines, but the bond stress in the anchorage increases rapidly while the applied load increases. Finally beam S240-20B undergoes bond fail-ure, which indicates that the failure mode can shift from the flexural mode to bond failure due to corrosion.

Therefore in the corroded beams, when the main re-bars in the shear span cannot endure the bond stress, the bond stress is transferred to the anchorage. And the ap-plied load is easily transferred to the anchorage in the corroded beams with larger stirrup spacing as the con-fining effect is weaker. In this situation, the performance of the anchorage has a great influence on residual strength. If the anchorage performs badly, beams un-dergo pull-out failure at a lower load level. Based on the experimental data in this study, this phenomenon will occur when the stirrup spacing is larger than 240 mm and the corrosion ratio of the main rebars is larger than 19%.

5.3 Influence of corrosion pattern of stirrups The difference in average corrosion ratios of beams S80-10 and S80-20 is 3.5% (S80-10 = 14.8% and S80-20 = 18.3%, see Table 5), and their residual strengths and failure mode are almost the same. However, the differ-ence in average corrosion ratio of beam S240-20A and beam S240-20B is only 4.2%, whereas the residual strengths differ greatly. The applied load of beam S240-20A declines drastically, and the beam undergoes brittle failure, rather than ductile failure. The major rea-son is the difference in corrosion pattern of the stirrups, as shown in Fig. 28. The corrosion ratios of the stirrups are shown in Fig. 29. Almost all the upper portions of the stirrups in the two beams disappeared completely. Many bottom portions of the stirrups in beam S240-20A dis-appeared too. However, in beams S240-20B, the corro-sion ratio of the bottom portion of the stirrups is just near 40%. Thus, it can be concluded that the stirrups, espe-cially the bottom portions of the stirrups, can improve the residual strength and ductility owing to the confining effect of stirrups.

Therefore, the bottom portion of the stirrups has a great effect on residual strength due to the confining

effect of stirrups. In the case of extreme corrosion, the applied load is transferred to the anchorage easily and the beam undergoes brittle failure at a lower load level. The threshold of the corrosion ratio of stirrups is related to the corrosion ratio of main rebars and to the stirrup spacing. To clearly identify the threshold, more test data should be accumulated.

6. Influence of anchorage performance on residual strength

6.1 Influence of stirrups in anchorage The relationship between load and midspan deflection of series S2 is shown in Fig. 30. The curves for series S0 and S80 are also shown in the figure for comparison purposes. First, compared with series S0, in which there are no stirrups arranged, the residual strengths of the corroded beams in series S2 are higher, and the deflec-tions of series S2 are improved. This indicates that the

0

400

800

1200

1600

2000

0 350 700 1050 1400 1750 2100Position (mm)

Stra

in (μ

)

30kN (S0-10)51kN (S0-10)30kN (S80-10)50kN (S80-10)

Fig. 26 Distribution of strain for beam S80-10.

0.0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50 60Load (kN)

Ave

rage

bon

d str

ess (

N/m

m2 ) S0-0S80-10S0-0S80-10

Shear span

Anchorage region

(a) Beam S80-10

0.0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50 60Load (kN)

Ave

rage

bon

d str

ess (

N/m

m2 ） S0-0S240-20BS0-0S240-20B

Shear span

Anchorage region

(b) Beam S240-20B

Fig. 27 Average bond stress in each region.

(b) Beam S240-20B (a) Beam S240-20A

rebars rebars

Corrosion ratioWhole：67.7% Bottom：89.8%

Corrosion ratio Whole：42.9% Bottom：22.2%

Fig. 28 corrosion behavior of stirrup.


stirrups in the anchorage can improve the residual strength and the capacity of deformation of corroded beams. Second, compared with series S80, in which stirrups are arranged at 80 mm intervals, although the average corrosion ratio of rebars in beam S2-10 is 6% higher than in beam S80-5, the residual strengths of the two beams are almost the same. Moreover, the residual strengths of beam S2-20 (corrosion ratio of main rebars = 16.4%) and beam S80-20 (corrosion ratio of main rebars = 18.3%) are similar too. It is evident that the residual strength of beams with only two stirrups in the anchorage region is relatively close to that of beams with stirrups. However, beams like series S2, which have no stirrups in the shear span, undergo brittle failure.

The load-midspan deflection curve of beam SF-20 is shown in Fig. 32. The residual strength is about 10 kN higher than for S2-20, and beam SF-20 has the ductility failure mode. The cracks in the final stage are shown in Fig. 33. First, diagonal cracking initiates at the applied load of 50 kN. With a little drop in the applied load, horizontal cracks along the main rebar occur and pro-gress to the anchorage region. While the horizontal cracks progress, the applied load increases again. Finally, the beam fails. Moreover, the strains of the rebars in the anchorage region increase just after the slight drop in applied load. This means that the applied load is trans-ferred to the anchorage after the applied load of 50 kN. Hence, arch action forms and resists the applied load, owing to the steal plates by which the main rebars are firmly anchored.

The relationships between the load and the average bond stress near the anchorage region and shear span are shown in Fig. 31. First, in Fig.31 (a), the distributions of stress of beam S0-10 and beam S2-10 are similar. At the early stage, the bond stress in the shear span increases, and the bond stress in the anchorage is very small. When close to the failure stage, the bond stress in the shear span declines rapidly while the bond stress in the anchorage increases. The maximum average bond stress of beam S2-10 in the anchorage is 3.1 N/mm2, which is twice the value of beam S0-10. Second, as shown in Fig. 31 (b), the distributions of average bond stress of beams S0-20 and S2-20 are similar with those of beams S0-10 and S2-10. The maximum average bond stress in the an-chorage of beam S2-20 is about 1.5 N/mm2, which is 3 times the value of beam S0-20.

Regarding beam SF-20, the relationships between load

Failure side

0

20

40

60

80

100

120

0 350 700 1050 1400 1750 2100Position (mm)

Cor

rosi

on ra

tio (%

)

S240-20AS240-20B

Disappeared

Measuredregion

(a) Bottom portions of stirrups

Failure side

0

20

40

60

80

100

120

0 350 700 1050 1400 1750 2100Position (mm)

Cor

rosio

n ra

tio (%

)

S240-20AS240-20B

Measured region

Disappeared

(b) Upper portions of stirrups

Fig. 29 Corrosion ratio for stirrups (series S240).

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40Deflection (mm)

Load

(kN

)

S2-0 S2-10S2-20 S0-0S0-10 S0-20S80-5 S80-20

S0-0

S2-0S2-10

S80-5

S2-20S0-10

S0-20

S80-20

Fig. 30 Load-deflection (series S2).

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 10 20 30 40 50 60 70Load (kN)

Ave

rage

bon

d str

ess (

N/m

m2 ) S0-0S0-10S2-10S0-0S0-10S2-10

Shear span

Anchorage region

(a) Corrosion ratio 10%

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 10 20 30 40 50 60 70Load (kN)

Ave

rage

bon

d str

ess (

N/m

m2 ) S0-0S0-20S2-20S0-0S0-20S2-20

Shear span

Anchorage region

(b) Corrosion ratio 20%

Fig. 31 Average bond stress and load of series S2.


and average strain in the constant moment region, shear span and anchorage region are shown in Fig. 34. Strains in the constant moment region and shear span increase rapidly as the applied load increases. Strains in the an-chorage region also increase when the applied load reaches 50 kN. This indicates that firm arch action can result by anchoring the main rebars on the beam ends with steel plates.

In the corroded beam of series S0, because there are no stirrups in the anchorage, the rebars are pulled out from the anchorage at a lower load level. In the corroded beam of series S2, both the slip of the main rebars and the failure crack along the main rebars are restrained due to the confining effect of the stirrups in the anchorage. Hence, applied loads of the beams in series S2 keep on increasing, instead of failing immediately. In beam SF-20, firm arch action occurs for perfect anchorage perform-ance. Therefore, it can be concluded that the residual strength can be improved significantly by means of im-proving the anchorage performance.

6.2 Influence of hooks The relationship between load and midspan deflection of series F90 is shown in Fig. 35. The residual strength for beam F90-S0-20 is 10 kN larger than for beam S0-10, although the corrosion ratio of beam F90-S0-20 is 5% larger than that of beam S0-10. However, flexural cracks appear on the upper concrete fiber near the supports and then extend along the hooks, causing anchorage failure of beam F90-S0-20. (see Fig. 36). The reason for the occurrence of the cracks can be explained as follows. There is almost no bond between the concrete and main rebars due to corrosion of the rebars, so that the beam can be treated as an upper beam and a bottom beam, delim-ited by the border of the main rebars, as shown in Fig. 37. Negative moment forms in the region above the supports, for the purpose of keeping continuity in the anchorage.

When the negative moment exceeds the flexural strength of concrete, flexural cracks appear, and then propagate to the upper region at the support point, finally causing the beam to fail.

Regarding beam F90-S240-20, the average corrosion ratio is 19.4%, only 0.3% less than that of beam S240-20B, and the average corrosion ratio of the bottom portion of the stirrups is 51%, 16.7% larger than that of beam S240-20B. However, the residual strength of beam F90-S240-20 is almost the same as that of beam S240-20B. In addition, beam F90-S240-20 fails at the deflection of 40 mm, which is 10 mm larger than for beam S240-20B. Therefore, hooks are found to effec-tively reduce the decline of residual strength.

The distribution of strains of series F90 is shown in Fig. 38. In this figure, strains in beam F90-S0-20 become relatively uniform at the applied load of 50 kN, similar with beam S0-10; then a horizontal crack initiates at the bottom near the loading point and halts at the supports at the applied load of 53 kN; finally, the beam fails when the load reaches 63 kN. It can be concluded that arch action occurs in the beam.

Average corrosion ratio

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40Deflection (mm)

Load

(kN

)

SF-20(21.1%)S2-20(16.4%)S0-20(18.6%)

Fig. 32 Load-deflection relationship of beam SF-20.

Before peak load After peak loadCorrosion crack

Fig. 33 Cracks in the final stage (beam SF-20).

Anchorage Shear span Constant moment region

0

10

20

30

40

50

60

70

80

0 300 600 900 1200 1500Strain (μ)

Load

(kN

)

S0-0SF-20S2-20

Anchorage Shear span Constant moment regionAnchorage Shear span Constant moment region

0

10

20

30

40

50

60

70

80

0 300 600 900 1200 1500Strain (μ)

Load

(kN

)

S0-0SF-20S2-20

0

10

20

30

40

50

60

70

80

0 300 600 900 1200 1500Strain (μ)

Load

(kN

)

S0-0SF-20S2-20

Fig. 34 Load-average strain in each region (beam SF-20).

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40Deflection (mm)

Load

(kN

)

F90-S0-20S0-10F90-S240-20S240-20B

Fig. 35 Load-deflection relationship of series F90.

Tensile reinforcement

Anchorage

Flexural crack

Fig. 36 Failure cracks of beam F90-S0-20.


As for beam F90-S240-20 shown in Fig. 38 (b), the strains in the left anchorage increase to the same value as beam S0-10, but the gradient near the support point is much larger, owing to the effect of both hooks and stir-rups in the anchorage. It can be deduced that arch action will result if the stirrups in the shear span are corroded to the point where they disappear.

Thus, hooks are found to restrain the degradation of anchorage performance significantly. However, flexural cracks above the support point occur before firm arch action.

6.3 Anchorage performance and residual strength The relationship between the residual strength and cor-rosion ratio of the beams performing bond failure is shown in Fig. 39. All the residual strengths of the beams are much lower than specified by the JSCE code (the blue straight line represents the shear capacity contributed by concrete in which the reduction of the cross-sectional area of main rebars is considered). For series S0, the residual strengths decline dramatically as the corrosion ratios increase. This is because there are no stirrups in series S0, and the reinforcements are pulled out from the anchorages easily. However, for the beams in series S2, the residual strengths are higher than series S0 because of the confining effects of stirrups. The residual strength of SF-20 is significantly larger than that of the beams in series S2. In these beams, the bond strengths in the shear span decline and the applied loads are transferred to the anchorages. On this occasion, anchorage performance plays a very important role in residual strength. If the anchorage performs perfectly, the reduction in residual strength can be reduced by a wide margin.

The relationship between residual strength and the maximal bond stress in the anchorage of the beams ex-hibiting bond failure is shown in Fig. 40. It is revealed that there is a significant linear correlation between the two variables. Therefore, it is possible to predict the residual strength of beams that exhibit bond failure based on anchorage performance. However, the relationship between residual strength and span to depth ratio should be researched in future.

7. Conclusions

This study examines the influence of the corrosion ratio of main rebars, stirrups and anchorage performance on the residual strength of corroded reinforced concrete beams with span-to-depth ratio of 4.5. The following conclusions can be drawn.

(1) In the case of no stirrups, when the ratio of rebar diameter to cover depth is 0.4, corrosion cracks easily occur along the two outside main rebars. However, cracks do not occur along intermediate

Unify

Tensile stress Tensile

Fig. 37 Failure mechanism for beam F90-S0-20.

0

400

800

1200

1600

2000

0 350 700 1050 1400 1750 2100Position (mm)

Stra

in (μ

)

10kN (S0-10)30kN (S0-10)51kN (S0-10)10kN (F90-S0-20)30kN (F90-S0-20)50kN (F90-S0-20)

(a) Beam F90-S0-20

0

400

800

1200

1600

2000

0 350 700 1050 1400 1750 2100Position (mm)

Stra

in (μ

)10kN (S0-10)30kN (S0-10)51kN (S0-10)10kN (F90-S240-20)30kN (F90-S240-20)60kN (F90-S240-20)

(b) Beam F90-S240-20 Fig. 38 Distribution of strain (series F90).

0102030405060708090

100

0 10 20 30 40Corrosion ratio of beams (%)

Res

idua

l loa

d ca

paci

ty (k

N)

Series S0Series S2Series S240SF-20Theoretical shear capacity

Firmly anchored

Influence of anchorage performance

Weak anchorage performance

Fig. 39 Load-corrosion ratio for beams (shear failure).

Pv = 14.80τmax + 28.17R2 = 0.91

0

20

40

60

80

100

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Max bond stress in anchorage τmax (N/mm2)

Load

Pv (

kN)

Series S0Series S2Series S240-20BSF-20Straight line approximation

Fig. 40 Residual strength - bond stress in anchorage.


rebar; when the stirrup ratio is less than 240 mm, cracks occur along the intermediate rebar too.

(2) When the bottom portions of the stirrups have cor-roded to an extreme degree, the residual strength and failure mode vary depending on the corrosion pat-tern of the main rebars. If the main rebars are non-uniformly corroded, the beam undergoes flex-ural failure. If the main rebars are uniformly cor-roded, the beam undergoes bond failure. The threshold of the corrosion ratio of the stirrups is re-lated to the corrosion ratio of the main rebars and to the stirrup spacing.

(3) It is possible to judge whether the main rebars are uniformly corroded or not by the index of deviation ratio. The threshold of the index is 0.9. That is to say, if the index is below 0.9, beam reinforcements are uniformly corroded and vice-versa.

(4) In the corroded beam with stirrups, the degradation of bond stress is restricted due to the confining effect of stirrups, especially the confining effect of the bottom portion of the stirrups.

(5) If the bond force in the shear span cannot resist the applied load, the bond stress in the shear span de-creases, whereas the bond stress in the anchorage increases. On this occasion, anchorage performance has a great influence on residual strength. Based on the experimental data, this occurs when the stirrup spacing is larger than 240 mm and the corrosion ra-tio of the main rebars is larger than 19%, or when there are only main rebars arranged and the corro-sion ratio of the main rebars is greater than 10%.

(6) When the index of deviation corrosion ratio is lower than 0.9, there is no difference in residual strength between the beam with only two stirrups in the an-chorage region and the beam with stirrups in the shear span with spacing of 80 mm. However, the former shows brittle failure, whereas the latter shows ductile failure.

(7) When the main rebars are uniformly corroded and are anchored at the beam ends firmly, the residual strength can be improved by a large amount as arch action occurs.

(8) Hooks can reduce the decline of residual strength effectively. However, if the rebars are not arranged in the compressive region, flexural cracks propagate to the upper region at the support point by the nega-tive moment.

(9) It is possible to estimate the residual strength of beams undergoing bond failure based on anchorage performance.

References Aoyama, T., Shimomura, T. and Maruyama, H., (1998).

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Murakami, Y., Yamauchi, Y., Tsutsumi, T. and Ohshita, H., (2006). “Study on influence of stirrup on residual strength for corroded RC reinforced beam.” Proceedings of the Japan Concrete Institute, 28(2), 727-732. (in Japanese)

Oyado, S., Nishiwa, K., Kasegawa, M. and Nakaoka, T., (2001). “Corrosion pattern and ultimate load for RC beams long term exposure to atmosphere.” Proceedings of the Japan Concrete Institute, 23(3), 315-1320. (in Japanese)

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Xue, X. and Seki, H., (2010). “Influence of longitudinal bar corrosion on shear behavior of RC beams.” Journal of Advanced Concrete Technology, 8(2), 145-156.

influence of both stirrup spacing and anchorage

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