# Corroded zero and two respectively. The spring stiffness

Corroded Steel

Elements

Corroded reinforcement has a

stress-strain diagram similar to that of non-corroded steel with a definite

yield plateau. However, the yield strength and the cross-sectional area of

corroded bars were derived using the empirical equations (Eq. 1, Eq. 2, and Eq.

3) (Du

et al., 2010).

Spring

Elements

Combin14 spring elements modeled the loss of bond between

steel reinforcement and surrounding concrete. The springs were set as linear

longitudinal springs with a vertical degree of freedom UY by setting KEYOPT(1)

and KEYOPT(2) to zero and two respectively. The spring stiffness was set to

100,000 N/mm (571 kip/in.), whereas the damping

coefficients and initial force were set to zero.

1.1. Comparison

of FEA and Experimental Results

Due to the lack of existing experimental data that studies

the behavior of RC beams with corroded reinforcement on the compression side of

the cross-section, the authors were able to compare the FEA model to two beam

specimens (Du et al., 2007) as shown

in Fig. 2

and Fig. 3.

However, the model was compared to 29 experimental beams (Du et al. 2007, Sharaf and Soudki 2002, El

Maaddawy et al. 2005, and Cairns and

Zhao 1993), of which two were structurally sound, 12 where exposed to different

corrosion levels on the tension side of the cross-section, while the rest were

subjected to unbond between steel and surrounding concrete.1.

Analytical Model 1.1. Introduction In beams with corroded reinforcement, the assumption that

the strain in steel is equal to the strain in the adjacent concrete is no

longer valid. This is due to the unbond between the steel reinforcement and the

surrounding concrete, which is caused by corrosion. Therefore, rendering the

code equations for calculating the ultimate flexural capacity of RC beams with

perfect bond invalid. 1.2. Creating

the Model In order to estimate the strain in the compression steel

reinforcement at ultimate in the absence of bond, the FEA model was employed to

analyze different cases of RC beams with unbond between the steel reinforcement

bars and the adjacent concrete in the compression zone. In all the cases

studied, the concrete cover was removed. A total of 36 beams, all of which were

subjected to different unbond lengths between steel reinforcement and adjacent

concrete, were studied. The above beams had three different compression steel

reinforcement ratios ?’ = 0.25?, ?’ = 0.40?,

and ?’ = 0.56?.

The unbonded length over the span varied from 0.013 to 1. In order to

compute the buckling stress of steel reinforcement bars in the compression

zone, the authors employed Eq. 4 and Eq. 5. The adopted equations account for

the critical buckling stress of solid circular columns (Chen and Lui, 1987). Fig. 5

demonstrates the developed graph to calculate the critical buckling stress of

the reinforcing bars. The authors assumed that the bars are pinned at both ends

(Rodriguez et al., 1994).

As mentioned above, the FEA model was employed to study 36

different cases. Of all cases studied, the normalized strains in the compression

steel at ultimate were obtained from the FEA model; then plotted against the

normalized buckling strains as shown in Fig. 6.

Fig. 6 shows

that all the points are below the diagonal line. This indicates that the stress

in the compression bars at ultimate exceeds the buckling stress. In other

words, in all of the cases studied, the steel reinforcing bars buckled. Therefore,

the buckling stress in the compression reinforcement can define the lower bound

values of the stress in the compression bars when analyzing RC beams with

unbonded bars in the compression side of the cross-section. This is because in the case of concrete cover spalling, the

compression steel bars are at the same level as the extreme compression

concrete fibers, which increases the strain in steel, leading to buckling of

compression rebars at lower stress levels. Moreover, Fig. 5

indicates that the increase of unbonded length is associated with a dramatic

decrease in the critical buckling stress, which allows the compression reinforcement

bars to buckle at low levels of loading. Fig. 7

demonstrates an algorithm derived to calculate the ultimate strength of RC

beams subjected to corrosion in the compression steel reinforcement. 1.1. Comparison

of Analytical and FEA Results

The

authors employed the analytical model to calculate the ultimate strength of all

the cases studied by the FEA model. One can note, however, reduction of

ultimate capacity of RC beams with corroded compression reinforcement is

primarily due to the removal of the concrete cover on the compression side of

the cross-section resulted from corrosion. This is in response to the minor

contribution of the compression steel reinforcement to the flexural strength of

the beam. Fig.

8

displays a comparison of the ultimate capacity of all the studied cases

obtained by the FEA model and the analytical model. Note that the analytical model

demonstrates very good agreement with the FEA modal.

1.1. Comparison

of Analytical and Experimental Results

The authors compared the analytical model to the only two

available experimental data of concrete beams with corroded compression

reinforcement (Du et al. 2007). Fig. 9

shows that the analytical model can compute the ultimate flexural strength of

compression corroded concrete beams with good accuracy. 1. Effects

of Different Parameters

1.1. Introduction

The authors employed the analytical model to investigate the

effects of corrosion rate, corrosion length Lcorr,

concrete compressive strength f’c,

and compression reinforcement ratio on the ultimate flexural strength of

concrete beams with corroded compression reinforcement. The investigated beams have

L/d = 15, f’c = 30

MPa (4.35 ksi), 40 MPa (5.8 ksi), and 50 MPa (7.25 ksi), with varying

steel corrosion rates and lengths. The authors computed the ultimate flexural

strength of 670 cases and compared the results to structurally sound beams

according to ACI 318-11 (2011).

1.2. Effect

of Concrete Cover

Since the main function of compression reinforcement is to

control the beam deflection rather than increasing the ultimate flexural

strength of RC beams, corrosion of compression reinforcement does not

significantly affect the ultimate capacity of the beam. However, corrosion of compression

steel bars leads to cracking and spalling of the concrete cover on the

compression side of the cross-section. The vertical axis in Fig. 10

represents the values of Mcorr/M for a beam with a span to depth ratio

of 15 and different corrosion levels. The horizontal axis shows the corrosion

rate, while each of the series represents a different corrosion length. The

reference beam has a reinforcement ratio of about 0.47 of the maximum

reinforcement ratio as given by ACI 318-11 (2011). The concrete compressive

strength is 40 MPa (5.8 ksi), and the yield strength of steel is 450 MPa (65.27

ksi).The corrosion rates varied from 0 to 60%, and the corrosion length over

the span of the beam varied from 0 to 1. Note that the length to depth ratio

increases from 15 to 17; this is due to the removal of the concrete cover on

the compression side of the cross-section as a result of corrosion. By

inspecting the first series (i.e., Lcorr/L = 0) when the corrosion rate is also

equal to 0, one can note that the removal of concrete cover is responsible for

almost 14% of the decrease in ultimate strength.1.1. Effect

of Corrosion Length Fig. 11

shows the effect of corrosion length on the ultimate flexural strength of RC

beams subjected to corrosion on the compression side of the cross-section. The

reference beam has a reinforcement ratio of about 0.47 of the maximum

reinforcement ratio as given by ACI 318-11 (2011) and a span to depth of 15,

the concrete compressive strength is 40 MPa (5.8 ksi) and the yield strength of

steel is 450 MPa (65.27 ksi). The corrosion length over the span of the beam

varied from 0 to 1, while the corrosion rate varied from 0 to 60%. The vertical

axis shows the ultimate capacity of corroded beams as a percent of the

reference beam, whereas, the horizontal axis represents the corrosion length

over the total length of the beam. Each of the series represents a different

corrosion rate. It is important to mention that in order to investigate the

effect of corrosion length without the effect of concrete cover spalling, the

ultimate flexural strength was compared to the same cross-section after

removing the concrete cover on the compression side.One can note from Fig.

11

that, regardless of the corrosion rate, the increase in the corroded length is

associated with a decrease in the ultimate flexural strength. In addition, as

the corrosion length increases from 0 to 20% of the span, there is a sudden

drop in the ultimate capacity. This drop is approximately 5.5%, and can be

attributed to the increase of unbraced length of the compression reinforcing

bars, which causes the steel bars to buckle.

Moreso, when the corroded length exceeds 40% of the beam

span, there is no further decrease in the ultimate flexural strength. This is

because when the unsupported length exceeds a certain limit, the buckling

stress of compression steel bars approaches zero (Fig. 5).

Consequently, the compression reinforcement can be ignored.1.1. Effect

of Corrosion Rate

The

influence of corrosion rate on the ultimate flexural strength of corroded

reinforced concrete beams was studied by means of Mcorr/M, which

is the ratio of the ultimate moment of a corroded beam over the ultimate moment

of the same beam with no corrosion. The vertical axis in Fig. 12 presents

the values of Mcorr/M for a beam with a span to depth ratio

of 15 and different corrosion levels. The horizontal axis shows the corrosion

rate and each of the series represents a different corrosion length. The

reference beam has a reinforcement ratio of about 0.47 of the maximum

reinforcement ratio as given by ACI 318-11 (2011). The concrete compressive

strength is 40 MPa (5.8 ksi), and the yield strength of steel is 450 MPa (65.27

ksi).The corrosion rates varied from 0 to 60%, and the corrosion length over

the span of the beam varied from 0 to 1. Fig. 12

shows that the increase in corrosion rate is accompanied by a decrease in the

ultimate flexural strength. This occurs when corrosion causes a reduction in

the steel cross-sectional area and strength. However, by inspecting the first

series (i.e., Lcorr/L = 0), one can note that the effect of

the corrosion rate is minor: the maximum decrease in ultimate flexural strength

(i.e. when the corrosion rate is 60%) is only 3%. Furthermore, when the

corrosion length is larger than 20% of the span, the decrease in ultimate

capacity due to the corrosion rate is less than 1%. It is important to mention

that in order to investigate the effect of corrosion length without the effect

of concrete cover spalling, the authors compared the ultimate flexural strength

to the same cross-section after removing the concrete cover on the compression

side. 1.1. Effect

of Compression Reinforcement Ratio The authors studied the influence of the compression

reinforcement ratio on the ultimate capacity of reinforced concrete (RC) beams

with corroded compression reinforcement w by means of Mcorr/M, which

is the ratio of the ultimate moment of a beam with corroded compression

reinforcement over the ultimate moment of the same beam with no corrosion. Fig. 13

shows the values of Mcorr/M for a beam with a span to depth ratio

of 15 and three different compression reinforcement ratios ?’ = 0.25, 0.50, and 0.75?.

The tensile reinforcement ratio is about 0.47 of the maximum reinforcement

ratio as given by ACI 318- (2011), the concrete compressive strength is 40 MPa

(5.8 ksi), and the yield strength of steel is 450 MPa (65.27 ksi). The corrosion

rate is set to 30% and the corrosion length varies from 0 to 100% of the beam

span. Fig. 13

illustrates that compression reinforcement ratio has a minimal effect on the

decrease of ultimate flexural strength due to corrosion in the compression

steel reinforcement. For instance, for a corrosion rate of 30%, corrosion

length of 60% of the span, and ?’ =

0.25?, the decrease in ultimate

capacity is about 3.5%, whereas the decrease in ultimate strength is 7% when

the compression reinforcement ratio is 75% of the tensile reinforcement ratio.

1.

Summary and Conclusion

Based on this investigation, the following conclusions could

be drawn:

– Both

the FEA model and the analytical model predict the ultimate flexural strength

of RC beams with corroded compression reinforcement.

– Corrosion

of compression steel reinforcement leads a to maximum flexural strength

reduction of 20%, of which 14-15% is due to the spalling of the concrete cover

on the compression side of the cross-section.

– The

length of the corroded zone is responsible for approximately 5-6% of the loss

ultimate flexural strength.

– If

the corrosion length exceeds 40% of the span, the compression steel

reinforcement can be ignored.

– The

decrease in ultimate capacity due to corrosion rate does not exceed 3%.

– When

the corrosion length is greater than 20% of the span, the decrease in the

ultimate capacity due to the corrosion rate is less than 1%.

– Compression

reinforcement ratio has a minimal effect on the decrease of ultimate flexural

strength due to corrosion in the compression steel reinforcement.