Corroded zero and two respectively. The spring stiffness

Corroded SteelElementsCorroded reinforcement has astress-strain diagram similar to that of non-corroded steel with a definiteyield plateau. However, the yield strength and the cross-sectional area ofcorroded bars were derived using the empirical equations (Eq.

1, Eq. 2, and Eq.3) (Duet al., 2010).SpringElementsCombin14 spring elements modeled the loss of bond betweensteel reinforcement and surrounding concrete.

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The springs were set as linearlongitudinal 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 to100,000 N/mm (571 kip/in.), whereas the dampingcoefficients and initial force were set to zero. 1.

1.  Comparisonof FEA and Experimental Results Due to the lack of existing experimental data that studiesthe behavior of RC beams with corroded reinforcement on the compression side ofthe cross-section, the authors were able to compare the FEA model to two beamspecimens (Du et al., 2007) as shownin Fig. 2and Fig. 3.However, the model was compared to 29 experimental beams (Du et al. 2007, Sharaf and Soudki 2002, ElMaaddawy et al. 2005, and Cairns andZhao 1993), of which two were structurally sound, 12 where exposed to differentcorrosion levels on the tension side of the cross-section, while the rest weresubjected to unbond between steel and surrounding concrete.

1.    Analytical Model 1.1.  Introduction In beams with corroded reinforcement, the assumption thatthe strain in steel is equal to the strain in the adjacent concrete is nolonger valid. This is due to the unbond between the steel reinforcement and thesurrounding concrete, which is caused by corrosion. Therefore, rendering thecode equations for calculating the ultimate flexural capacity of RC beams withperfect bond invalid.

 1.2.  Creatingthe Model In order to estimate the strain in the compression steelreinforcement at ultimate in the absence of bond, the FEA model was employed toanalyze different cases of RC beams with unbond between the steel reinforcementbars and the adjacent concrete in the compression zone. In all the casesstudied, the concrete cover was removed. A total of 36 beams, all of which weresubjected to different unbond lengths between steel reinforcement and adjacentconcrete, were studied. The above beams had three different compression steelreinforcement ratios ?’ = 0.

25?, ?’ = 0.40?,and ?’ = 0.56?.The unbonded length over the span varied from 0.013 to 1. In order tocompute the buckling stress of steel reinforcement bars in the compressionzone, the authors employed Eq. 4 and Eq. 5.

The adopted equations account forthe critical buckling stress of solid circular columns (Chen and Lui, 1987). Fig. 5demonstrates the developed graph to calculate the critical buckling stress ofthe 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 36different cases. Of all cases studied, the normalized strains in the compressionsteel at ultimate were obtained from the FEA model; then plotted against thenormalized buckling strains as shown in Fig. 6.

Fig. 6 showsthat all the points are below the diagonal line. This indicates that the stressin the compression bars at ultimate exceeds the buckling stress. In otherwords, in all of the cases studied, the steel reinforcing bars buckled. Therefore,the buckling stress in the compression reinforcement can define the lower boundvalues of the stress in the compression bars when analyzing RC beams withunbonded bars in the compression side of the cross-section. This is because in the case of concrete cover spalling, thecompression steel bars are at the same level as the extreme compressionconcrete fibers, which increases the strain in steel, leading to buckling ofcompression rebars at lower stress levels.

Moreover, Fig. 5indicates that the increase of unbonded length is associated with a dramaticdecrease in the critical buckling stress, which allows the compression reinforcementbars to buckle at low levels of loading. Fig. 7demonstrates an algorithm derived to calculate the ultimate strength of RCbeams subjected to corrosion in the compression steel reinforcement. 1.

1.  Comparisonof Analytical and FEA Results Theauthors employed the analytical model to calculate the ultimate strength of allthe cases studied by the FEA model. One can note, however, reduction ofultimate capacity of RC beams with corroded compression reinforcement isprimarily due to the removal of the concrete cover on the compression side ofthe cross-section resulted from corrosion. This is in response to the minorcontribution of the compression steel reinforcement to the flexural strength ofthe beam. Fig.8displays a comparison of the ultimate capacity of all the studied casesobtained by the FEA model and the analytical model. Note that the analytical modeldemonstrates very good agreement with the FEA modal. 1.

1.  Comparisonof Analytical and Experimental Results The authors compared the analytical model to the only twoavailable experimental data of concrete beams with corroded compressionreinforcement (Du et al. 2007). Fig. 9shows that the analytical model can compute the ultimate flexural strength ofcompression corroded concrete beams with good accuracy. 1.     Effectsof Different Parameters 1.1.

  Introduction The authors employed the analytical model to investigate theeffects of corrosion rate, corrosion length Lcorr,concrete compressive strength f’c,and compression reinforcement ratio on the ultimate flexural strength ofconcrete beams with corroded compression reinforcement. The investigated beams haveL/d = 15, f’c = 30MPa (4.35 ksi), 40 MPa (5.8 ksi), and 50 MPa (7.25 ksi), with varyingsteel corrosion rates and lengths. The authors computed the ultimate flexuralstrength of 670 cases and compared the results to structurally sound beamsaccording to ACI 318-11 (2011).

 1.2.  Effectof Concrete Cover Since the main function of compression reinforcement is tocontrol the beam deflection rather than increasing the ultimate flexuralstrength of RC beams, corrosion of compression reinforcement does notsignificantly affect the ultimate capacity of the beam. However, corrosion of compressionsteel bars leads to cracking and spalling of the concrete cover on thecompression side of the cross-section. The vertical axis in Fig.

10represents the values of Mcorr/M for a beam with a span to depth ratioof 15 and different corrosion levels. The horizontal axis shows the corrosionrate, while each of the series represents a different corrosion length. Thereference beam has a reinforcement ratio of about 0.47 of the maximumreinforcement ratio as given by ACI 318-11 (2011). The concrete compressivestrength is 40 MPa (5.8 ksi), and the yield strength of steel is 450 MPa (65.

27ksi).The corrosion rates varied from 0 to 60%, and the corrosion length overthe span of the beam varied from 0 to 1. Note that the length to depth ratioincreases from 15 to 17; this is due to the removal of the concrete cover onthe compression side of the cross-section as a result of corrosion. Byinspecting the first series (i.e., Lcorr/L = 0) when the corrosion rate is alsoequal to 0, one can note that the removal of concrete cover is responsible foralmost 14% of the decrease in ultimate strength.1.1.

  Effectof Corrosion Length Fig. 11shows the effect of corrosion length on the ultimate flexural strength of RCbeams subjected to corrosion on the compression side of the cross-section. Thereference beam has a reinforcement ratio of about 0.47 of the maximumreinforcement 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 ofsteel is 450 MPa (65.

27 ksi). The corrosion length over the span of the beamvaried from 0 to 1, while the corrosion rate varied from 0 to 60%. The verticalaxis shows the ultimate capacity of corroded beams as a percent of thereference beam, whereas, the horizontal axis represents the corrosion lengthover the total length of the beam. Each of the series represents a differentcorrosion rate. It is important to mention that in order to investigate theeffect of corrosion length without the effect of concrete cover spalling, theultimate flexural strength was compared to the same cross-section afterremoving the concrete cover on the compression side.One can note from Fig.11that, regardless of the corrosion rate, the increase in the corroded length isassociated with a decrease in the ultimate flexural strength. In addition, asthe corrosion length increases from 0 to 20% of the span, there is a suddendrop in the ultimate capacity.

This drop is approximately 5.5%, and can beattributed to the increase of unbraced length of the compression reinforcingbars, which causes the steel bars to buckle.Moreso, when the corroded length exceeds 40% of the beamspan, there is no further decrease in the ultimate flexural strength. This isbecause when the unsupported length exceeds a certain limit, the bucklingstress of compression steel bars approaches zero (Fig. 5).

Consequently, the compression reinforcement can be ignored.1.1.  Effectof Corrosion Rate Theinfluence of corrosion rate on the ultimate flexural strength of corrodedreinforced concrete beams was studied by means of Mcorr/M, whichis the ratio of the ultimate moment of a corroded beam over the ultimate momentof the same beam with no corrosion. The vertical axis in Fig.

12 presentsthe values of Mcorr/M for a beam with a span to depth ratioof 15 and different corrosion levels. The horizontal axis shows the corrosionrate and each of the series represents a different corrosion length. Thereference beam has a reinforcement ratio of about 0.47 of the maximumreinforcement ratio as given by ACI 318-11 (2011). The concrete compressivestrength is 40 MPa (5.8 ksi), and the yield strength of steel is 450 MPa (65.

27ksi).The corrosion rates varied from 0 to 60%, and the corrosion length overthe span of the beam varied from 0 to 1. Fig. 12shows that the increase in corrosion rate is accompanied by a decrease in theultimate flexural strength. This occurs when corrosion causes a reduction inthe steel cross-sectional area and strength. However, by inspecting the firstseries (i.

e., Lcorr/L = 0), one can note that the effect ofthe corrosion rate is minor: the maximum decrease in ultimate flexural strength(i.e.

when the corrosion rate is 60%) is only 3%. Furthermore, when thecorrosion length is larger than 20% of the span, the decrease in ultimatecapacity due to the corrosion rate is less than 1%. It is important to mentionthat in order to investigate the effect of corrosion length without the effectof concrete cover spalling, the authors compared the ultimate flexural strengthto the same cross-section after removing the concrete cover on the compressionside. 1.1.  Effectof Compression Reinforcement Ratio The authors studied the influence of the compressionreinforcement ratio on the ultimate capacity of reinforced concrete (RC) beamswith corroded compression reinforcement w by means of Mcorr/M, whichis the ratio of the ultimate moment of a beam with corroded compressionreinforcement over the ultimate moment of the same beam with no corrosion. Fig. 13shows the values of Mcorr/M for a beam with a span to depth ratioof 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 reinforcementratio 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 corrosionrate is set to 30% and the corrosion length varies from 0 to 100% of the beamspan. Fig. 13illustrates that compression reinforcement ratio has a minimal effect on thedecrease of ultimate flexural strength due to corrosion in the compressionsteel reinforcement.

For instance, for a corrosion rate of 30%, corrosionlength of 60% of the span, and ?’ =0.25?, the decrease in ultimatecapacity is about 3.5%, whereas the decrease in ultimate strength is 7% whenthe compression reinforcement ratio is 75% of the tensile reinforcement ratio. 1.    Summary and Conclusion Based on this investigation, the following conclusions couldbe drawn:- Boththe FEA model and the analytical model predict the ultimate flexural strengthof RC beams with corroded compression reinforcement.- Corrosionof compression steel reinforcement leads a to maximum flexural strengthreduction of 20%, of which 14-15% is due to the spalling of the concrete coveron the compression side of the cross-section.

– Thelength of the corroded zone is responsible for approximately 5-6% of the lossultimate flexural strength.- Ifthe corrosion length exceeds 40% of the span, the compression steelreinforcement can be ignored.- Thedecrease in ultimate capacity due to corrosion rate does not exceed 3%.

– Whenthe corrosion length is greater than 20% of the span, the decrease in theultimate capacity due to the corrosion rate is less than 1%.- Compressionreinforcement ratio has a minimal effect on the decrease of ultimate flexuralstrength due to corrosion in the compression steel reinforcement. 

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