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).

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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the strain in steel is equal to the strain in the adjacent concrete is no
longer valid.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.

 

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