Behavior of Corroded Reinforced Concrete Beams Under Cyclic Loading - Coursework Example

Introduction There is a great need in having knowledge on effects corrosion on fatigue in concrete structures as concrete structures like offshore structures, bridges and bridges are always under loading of cyclic nature. It is expected that concrete overlays for highway bridge decks are to have the ability of withstanding cycles of repeated axle loads which range in millions during the structures active service life (Zhang et al., 2001). A bridge can undergo 7x108 cycles in its 120 years lifespan (Barnes and Garden, 1999). The two reasons which have been cited to be importance of considering fatigue during the process of structural design are: there maybe occurrence of fatigue failure in the structure and due to the repeated loading the characteristics of materials stiffness, toughness, strength and durability are affected during service loading. According to Täjlsten (2002) the problems that are related to fatigue failure in structures have been of great interest in the recent years because of the following There has been advancement in the methods of design and analysis. Earlier designs involved approximate calculations and conservative safety measures that could account for risk of fatigue, but in the current designs there is need to evaluate for safety of fatigue separately. With the improvement in structural materials there is achievement of high strength, but the increase in strength results in materials being more brittle and the fatigue strength is lowered. The new type of structures that are being constructed in the modern world register high rates of fatigue failure than experienced earlier. Fatigue behaviour of plain concrete The properties of concrete under fatigue are dependant on the irreversible energy deformation that is manifested as inelastic strains that come in the forms of creep and cracks. The factors governing this behaviour include the environmental conditions, history, the range of load, material properties, rate and frequency of loading and loading eccentricity. Initial cracking, propagation and failure are three phases that are manifested in a fatigue process. The relationship between stress and strain in concrete will always vary with the number of cyclic loads experienced (ACI, 1974, Neville, 1996). The curve will first exhibit a concave shape which will quickly transition to a straight line and the straight line will then transition to a characteristic convex shape. According to the observations which have been made reveal that there will be a more convex shaped curve in stress strain response as the concrete approaches failure. The response of concrete subjected to cyclic loading can have a shape that will approximately be enveloped by a quasi-static loading as shown in figure 1. Failure of concrete under cyclic loading will take place as the value of strain in the concrete reaches the strain that matches cyclic stress on a reducing branch of the quasi-static stress-strain curve. In the tests that was performed by Holmen (1982) it was observed that the maximum value of strain in compressed concrete subjected to cyclic loading manifested distinct stages; a quick increase to approximately 10% of total fatigue life (Stage 1), an increase which from 10% to about 80% (Stage2) which is uniform then a rapid increase to failure complete the cycle. Figure 1 Figure 2 According to a proposition by Holmen (1982) the first and second stages could be given by Stage 1  (1.1) Stage 2  (1.2) In the equation  represents maximum strain,  represents the secant modulus at the first cycle,  gives the maximum stress to concrete strength, Sc stands for the characteristics level which is given as Sm+RMS. Sm is the mean stress ratio which is equal 0.5(Smin + Smax ) Smin being the ratio of minimum stress to concrete strength, N represents the number of cycles of loads, Nf is the number of loads cycles before failure in a specified probability failure while t represents the duration of the alternating lpad in hours. RMS is the room mean square value of the stress ratio. If the case in consideration is sinusoidal loading EN which is the secant modulus after first cycle will be reduced throughout the fatigue life in accordance to Smax Fatigue behaviour of steel reinforcement There are many research that have been done on cyclic failure of reinforcing steel in air and when used in concrete beams (Helgason and Hanson, 1974; Moss, 1980). The number of cycles that will lead to failure for specific reinforcing steel is given by the expression Where  represent the number of cycles that will cause, failure  gives the range of stress for specified constant loading amplitude and a being the slope inverse on a log-log graph. When data for experiments done by Tilly (1988) and Moss 1988 was plotted it was found to have a significant scatter. In new designs it is a common practice to use axially tested fatigue failure values but in terms of stress range performance it is found to be 20% higher for bending in concrete than the axial testing in air, this being when 16mm bars are compared. The variation is brought about by concrete influence between cracks which reduces the tensile stress in adjacent bar a phenomenon referred to as tension stiffening. This results to the probability for the critical section for fatigue which coincides with a maximum stress point being reduced in addition to reduction of the probability of failure for a specific cyclic stress range. Loading of cyclic nature will result in micro cracking which in-turn brings about stress concentration on the surface of the bar. There will be crack propagation with the continuation of stress cycle and eventually at a critical crack length there will be instability in propagation process which will result in a sudden fracture. The lowest stress range of 145MPa to cause fatigue failure when tests were being done on concrete beams was reported by Helgason and Hanson (1974). A maximum stress range of 161 MPa for reinforcing steel is recommended in ACI Committee 215 (1974) Fatigue behaviour of corroded reinforcement According to the fatigue data compiled on 6mm diameter 250 grade plain bar after being in service for 20 years in a bridge deck the bar was found to have experienced pitting corrosion (Tilly, 1988). The loss in fatigue strength cold not fully be accounted for by loss in cross section of the bar. There was a proposition that there is need to have a reduction factor of 1.35 and 1.7 in bars where the section loss of up to 255 and greater than 25% were being experienced. Apostolopoulos and Papadopoulos (2007) tested the cyclic behaviour of S400 grade reinforcing steel whose yield strength is 400MPa where 10 mm bars were subjected to salt spray tests between 10 to 90 days so as to induce corrosion before being tested cyclic failure. In the test a mass ranging between 1.6% to 8.5% were reported. When corroded bars were put under a sinusoidal load equivalent to % strain it was found that with a mass loss of 2% there was a reduced number of cycles to failure of 22% while ±3% resulted in a reduction of 47% in number of cycles to failure. Another study on corrosion of reinforcing steel and fatigue was done by Booth etal (1986). The study involved 33mm diameter bars that were immersed in seawater. In the study the bars under investigation were loaded at two frequencies, 0.1 Hz and 3Hz where it was found that the former registered fatigue life of bars that was significantly lower. From the study a design curve for loading at 0.1 Hz was recommended to be Where  represent the stress range which has been applied  is the number of cycles that would cause failure. Mallet (1999), basing on test data of Booth et al (1986) made a recommendation that a design curve to be represented by a different relationship that was dependant on the range of stress. This relationship is applicable in straight bars in the splash zone in marine structures which are likely to be subjected to corrosion. The curves recommended are given by  for 235MPa  for 65MPa    Coronel and Gambarova (2004) came up with a numerical model for the behaviour of corroded reinforcing steel in which there was use of both chloride and corrosion induced through carbonation. In the infinite element model it is possible to reduce the caused by carbonation by the reduction of each section of the bar element. In order to consider pitting corrosion the results of experiment by Cairns and Millard (1999) and Castel et al. (2000) were used. To take into account the effect caused on the steel bar ductility, lower ultimate strains as compared to that of sound steel is introduced. The expression the reduction factor in the cross section ( ) is In the expression  represents the reduction in are brought about by pitting,  gives the cross section area of the bar. The expression for the ultimate strain of corroded steel () was given by =+(-) for the case where  <  In the expression  represents sound steel ultimate strain represents the yield strain in sound steel and  gives the maximum percentage of the cross-section of the bar whose value can be 0.5 (Cairns and Millard,1999) or 0.1 according to Castel et al. (2000). Fatigue behaviour of conventional RC beams There is a variation in the level of susceptibility of reinforced concrete to fatigue in different parts of the member as the level of fatigue is a function of the level of stress on the components at different sections, these being the concrete and the reinforcing steel. There is a variation in the governing failure depending on how the way the reinforced concrete beam has been designed. In case there in adequate reinforcement of it’s the performance of its flexural fatigue will be dominated by the main longitudinal steel while heavy reinforcement will result in flexural or shear failure. With progress in fatigue loading of a beam and subsequent propagation in cracks the results is stress redistribution (Barnes and Mays, 1999). This is a clear manifestation that fatigue failure of structural members is not always the same mechanism as that experienced in static loading conditions. A maximum stress range  limit for straight, deformed and reinforcement in beams that has been recommended by ACA Committee 215(1974) is given by With  being the minimum stress in MPa. Suppose the steel and concrete are of uniform quality, there can be determination of fatigue performance in both components with precision by testing of individual materials and observation of the same performance for fatigue testing in the composite materials (CEB-FIP ,1988). In loaded reinforced concrete elements the calculation of stresses is done by applying simplified models due to the fact that the stresses are complicated. While the real stresses are used in the determination the performance of the elements under test, the model stresses are not the real ones, thus the end result being the exhibition of a large scatter amount. Fatigue behaviour of corroded RC beams A study undertaken by Roper and Hetherington (1982) involved the investigation of fatigue performance reinforced concrete beam which were 1.8m in length in sea water, in air and in 3% salt water. In the study there was use of hot-rolled and cold-worked deformed bars all of which had having similarity in their chemical composition. The following results were found in the case of hot-rolled bars. The beams were put under a test at 6.7Hz with the fatigue variation ranging from 200000 cycles to greater than 10 000 000 cycles. It was found that with the level of stress being put constant the shortest fatigue lives was registered in salt water that for air was longest while that for sea water lied between the two. There was observation of pitting corrosion in both the reinforcement for beams whose tests were done in sea water and in 3 % salt solution. In the study there was no report on the exact mass losses. Another study which was done by Radain (1989) involved the investigation of fatigue performance of beams of 900mm length which were submerged in seawater subjected to a load range of 41 to 92% of static failure load. In all the beams under study failure was by fatigue fracture in the reinforcing bars that were under tensile loading. From the electrical potential measurements that were undertaken there was a high probability of having corrosion in the reinforcement but the test did not report on mass loss. In the study by Oyando et al (2003) where 2.1m long reinforced concrete beams put under highly accelerated corrosion. The parameters that were investigated the level of damage experienced by the beams where there was a mass loss of 8%, 15% and 20%. In the study the diameter of steel reinforcement were 13mm and 16mm while the design load cycles leading to failure that were recorded were 0.2 million, 0.5 millions and 2.0 millions. Experiment design This section gives the experiment design procedure under the following heading: test specimens, concrete mix designs, construction and loading protocol and instrumentation. Test Specimens The loading specimens will be composed of deformed steel reinforcing bars which will be et in concrete prisms which will have three stirrups so as to provide confinement. By use of PVC pipe the bonded length will be restricted to four times the diameter of the bar. As a way of ensuring that the bar will not yield, Ф = 20 mm, Grade 500E steel, typical to New Zealand, will be used for the main while the stirrup of size R6 will be constructed using Grade 300 steel. The details are shown in figure Figure 3: Test specimen Source : Kivell, A. Palermo and A. Scott Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, 8140, New Zealand. Concrete Mix Design When designing the concrete a compressive strength of at least 45MPa targeted and a water content of 0.4 will be used. The concrete mix to be used will of 155kg/m3 of water, 744 kg/m3 sand, 387 kg/m3 cement (general purpose), 1136 kg/m3 stone of about 13mm and 2.11/m3 of water reducer. Construction Before the specimens are put under the corrosion the specimens will be constructed such that they will be all identical. The bars to be used in the construction will be cleaned so as to get rid of any corrosion together with any machining fluid that may have come in contact with the bars surface before pouring of specimens. After the construction the specimens will undergo accelerated corrosion. Loading Protocol and Instrumentation After the specimens have gone through accelerated corrosion they will be tested through cyclic loading as shown in the figure. The load measurement will be done through a load cell wile the displacement will be through a potentiometer where the accuracy will be ±0.002 mm. Figure 4: Testing frame set up Source : Kivell, A. Palermo and A. Scott Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, 8140, New Zealand. References ACI Committee 215, 1981. “Fatigue of concrete structures”, American Concrete Institute, Farmington Hills, USA, 401 pp. Apostolopoulos, C.A. and Papadopoulos, M.P., 2007. “Tensile and low cycle fatigue behavior of corroded reinforcing steel bars S400”, Construction and Building Materials, Vol. 21, No 4, pp: 855-864. Barnes, R.A. and Mays, G.C., 1999. “Fatigue performance of concrete beams strengthened with CFRP plates”, Journal of Composites for Construction, ASCE, Vol. 3, No. 2, pp: 63-72. Booth, E.D., Leeming, M.B., Paterson, W.S. and Hodgkiess, T., 1986. “Fatigue of reinforced concrete in marine conditions”, Proceedings of the International Conference on Concrete in the Marine Environment, London., UK, pp: 1878-198. Cairns, J. and Millard, S., 1999. “Section 13.2: Reinforcement corrosion and its effect on residual strength of concrete structures”, Proceedings of the Eighth International Conference on Structure Faults and Repair, Edinburgh, U.K, edited M. Forde. Castel, A., Francois, R., and Arliguie, G., 2000. “Mechanical behaviour of corroded reinforced concrete beams. II: Bond and notch effects” Materials and Structures, RILEM, Vol. 33, pp: 545-551. CEB-FIP, 1988. Fatigue of Concrete Structures: State of the Art Report Bulletin d'Information no. 190 , CEB-FIP Comité Euro-International du Béton, Paris, France. Coronelli, D. and Gambarova, P., 2004. “Structural assessment of corroded reinforced concrete beams: Modeling guidelines”, Journal of Structural Engineering, Vol. 130, No. 8, pp: 1214-1224. Helgason, T. and Hanson, J.M., 1974. “Investigation of Design Factors Affecting Fatigue Strength of Reinforcing Bars – Statistical Analysis”, Abeles Symposium on Fatigue of Concrete, SP-41, American Concrete Institute, Farmington Hills, USA, pp: 107-138. Holmen, J.O., 1982. “Fatigue of concrete by constant and variable amplitude loading”, Fatigue of Concrete Structures, American Concrete Institute, Detroit, pp: 71-110. Kivell, A. Palermo and A. Scott Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, 8140, New Zealand. Moss, D.S., 1982. “Bending fatigue of high yield reinforcing bars in concrete”, TRRL Report SR748, Transport and Road Research Laboratory, Department of Transport, Crowthorne, UK. Mallett, G.P., 1991. “Fatigue of Reinforced Concrete” State of the Art Review 2, Transport and Road Research Laboratory, HMSO Publications, London, 166 pp. Neville, A.M., 1996. “Properties of concrete”, John Wiley & Sons Inc., 844 pp. Oyado, M., Hasegawa, M. and Sato, T. 2003. “Characteristics of fatigue and evaluation of RC beam damaged by accelerated corrosion”. Quarterly Report of RTRI, Vol. 44, No. 4 pp: 72-77. Täjlsten, B., 2002. “FRP strengthening of existing concrete structures design guideline” Luleå University of Technology, Luleå, Sweden, 2nd Edn. Tilly, G.P., 1988. “Durability of Concrete Bridges”, Journal of the Institution of Highways and Transport. Radain, T.A., 1989. “Effect of corrosion, freeze-thaw cycles, and their combined effects on the fatigue behavior of reinforced concrete”. PhD thesis, University of Rhode Island, Rhode Island, USA. Roper H. and Hetherington G. B., 1981. “Fatigue of reinforced concrete beams in air, chloride solution and sea water”, Recent Research on Fatigue of Concrete Structures, American Concrete Institute, Detroit, USA. Zhang J., Li, V.C. and Stang, H., 2001. “Size effect on fatigue in bending of concrete”, Journal of Materials in Civil Engineering, Vol. 13, No. 6, pp: 446-453. Read More

When data for experiments done by Tilly (1988) and Moss 1988 was plotted it was found to have a significant scatter. In new designs it is a common practice to use axially tested fatigue failure values but in terms of stress range performance it is found to be 20% higher for bending in concrete than the axial testing in air, this being when 16mm bars are compared. The variation is brought about by concrete influence between cracks which reduces the tensile stress in adjacent bar a phenomenon referred to as tension stiffening.

This results to the probability for the critical section for fatigue which coincides with a maximum stress point being reduced in addition to reduction of the probability of failure for a specific cyclic stress range. Loading of cyclic nature will result in micro cracking which in-turn brings about stress concentration on the surface of the bar. There will be crack propagation with the continuation of stress cycle and eventually at a critical crack length there will be instability in propagation process which will result in a sudden fracture.

The lowest stress range of 145MPa to cause fatigue failure when tests were being done on concrete beams was reported by Helgason and Hanson (1974). A maximum stress range of 161 MPa for reinforcing steel is recommended in ACI Committee 215 (1974) Fatigue behaviour of corroded reinforcement According to the fatigue data compiled on 6mm diameter 250 grade plain bar after being in service for 20 years in a bridge deck the bar was found to have experienced pitting corrosion (Tilly, 1988). The loss in fatigue strength cold not fully be accounted for by loss in cross section of the bar.

There was a proposition that there is need to have a reduction factor of 1.35 and 1.7 in bars where the section loss of up to 255 and greater than 25% were being experienced. Apostolopoulos and Papadopoulos (2007) tested the cyclic behaviour of S400 grade reinforcing steel whose yield strength is 400MPa where 10 mm bars were subjected to salt spray tests between 10 to 90 days so as to induce corrosion before being tested cyclic failure. In the test a mass ranging between 1.6% to 8.5% were reported.

When corroded bars were put under a sinusoidal load equivalent to % strain it was found that with a mass loss of 2% there was a reduced number of cycles to failure of 22% while ±3% resulted in a reduction of 47% in number of cycles to failure. Another study on corrosion of reinforcing steel and fatigue was done by Booth etal (1986). The study involved 33mm diameter bars that were immersed in seawater. In the study the bars under investigation were loaded at two frequencies, 0.1 Hz and 3Hz where it was found that the former registered fatigue life of bars that was significantly lower.

From the study a design curve for loading at 0.1 Hz was recommended to be Where  represent the stress range which has been applied  is the number of cycles that would cause failure. Mallet (1999), basing on test data of Booth et al (1986) made a recommendation that a design curve to be represented by a different relationship that was dependant on the range of stress. This relationship is applicable in straight bars in the splash zone in marine structures which are likely to be subjected to corrosion.

The curves recommended are given by  for 235MPa  for 65MPa    Coronel and Gambarova (2004) came up with a numerical model for the behaviour of corroded reinforcing steel in which there was use of both chloride and corrosion induced through carbonation. In the infinite element model it is possible to reduce the caused by carbonation by the reduction of each section of the bar element. In order to consider pitting corrosion the results of experiment by Cairns and Millard (1999) and Castel et al. (2000) were used.

To take into account the effect caused on the steel bar ductility, lower ultimate strains as compared to that of sound steel is introduced. The expression the reduction factor in the cross section ( ) is In the expression  represents the reduction in are brought about by pitting,  gives the cross section area of the bar.

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