SHEAR BEHAVIOR OF DOUBLY REINFORCED CONCRETE BEAMS WITH AND WITHOUT STEEL FIBERS AFFECTED BY DISTRIBUTED CRACKS

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1 SHEAR BEHAVIOR OF DOUBLY REINFORCED CONCRETE BEAMS WITH AND WITHOUT STEEL FIBERS AFFECTED BY DISTRIBUTED CRACKS Ionut Ovidiu TOMA 1, Tomohiro MIKI 2 and Junichiro NIWA 3 1 Member of JSCE, Ph.D. Candidate, Dept. of Civil Eng., Tokyo Institute of Technology ( M1-17 O-okayama, Meguro-ku, Tokyo , Japan) iotoma@cv.titech.ac.jp 2 Member of JSCE, Assistant Professor, Dept. of Civil Eng., Tokyo Institute of Technology ( M1-17 O-okayama, Meguro-ku, Tokyo , Japan) mikitomo@cv.titech.ac.jp 3 Fellow of JSCE, Professor, Dept. of Civil Eng., Tokyo Institute of Technology ( M1-17 O-okayama, Meguro-ku, Tokyo , Japan) jniwa@cv.titech.ac.jp The present study is aimed at investigating the shear behavior of reinforced concrete beams with doubly reinforced rectangular cross-section, with and without steel fibers, affected by distributed cracks. The influence of the distributed cracks was mathematically quantified with the help of a crack density parameter. Monotonic loading tests were conducted on the RC beams and their failure indicated a mixed mode between both diagonal tension and diagonal compression failures. Due to the reinforcement layout, the effect of the longitudinal compression reinforcement on the shear carrying capacity should be taken into account. The distributed cracks were shown to have less influence on the peak load of doubly reinforced concrete beams. Key Words :crack density, shear crack location, dowel effect, shear failure 1. INTRODUCTION Shear failure of reinforced concrete beams is quite difficult to predict accurately. In spite of many years of research 1), 2) it is still not fully understood. If a beam without properly designed shear reinforcement is overloaded, the failure is most likely to occur suddenly with no advance warning. This is in strong contrast with the flexural failure. For typically under-reinforced concrete beams, flexural failure occurs by yielding of the longitudinal reinforcement accompanied by obvious cracking and large deflections, that gives ample warning about the imminent failure of the beams and provides the opportunity to take corrective measures. The probability of brittle failure to occur in reinforced concrete beams that have been affected by deleterious agents (e.g. Alkali-Silica Reaction) is much higher. That is why it is important to know the shear carrying capacity of such concrete members and, if possible, to also predict the shear span where the failure is more likely to happen. Currently there are many studies focusing on the shear carrying capacity of RC beams without web reinforcement 2) - 5). However, there is little research for RC beams with doubly reinforced cross-sections and their shear behavior. Such a reinforcement layout is often met in the RC members made out of high strength concrete that are part of the structures located in seismic areas. The reinforcement in the compression area is used to increase the ductility of the structural concrete members 6) and to prevent the brittle failure of the high strength concrete elements 7). The present study is aimed at investigating the shear behavior of doubly reinforced concrete beams, with or without steel fibers, affected by distributed cracks. For this purpose, monotonic loading tests were carried out on a series of eight RC beams. Prior to testing, the surface of the beams was inspected for 590

2 the presence of distributed cracks. The crack density parameter introduced in the earlier research work 8) was used to mathematically quantify the influence of the distributed cracks on the shear carrying capacity of the beams. The beams exhibited a mixed mode of failure between both diagonal tension and diagonal compression failures. 2. RESEARCH MOTIVATION While most of previous research works focused on the mechanical properties of undamaged RC members, this study investigates the behavior of RC beams affected by distributed cracks. Since concrete structures are subjected to both external factors (severe environment, loads) and internal factors (chemical reactions within the concrete) that lead to the formation of cracks, it is important to know the strength reserve of such concrete members or structures. One of the undesired phenomena occurring in concrete structures is the formation of distributed cracks. Among the factors that can lead to such cracking pattern, Alkali-Silica Reaction (ASR) is very important. Because ASR induced cracking takes a lot of time and special conditions to develop, the use of an expansion agent came as an alternative to have extensive cracking in a short period of time. From the results of previous research work 8) it was concluded that using expansion agents to generate distributed cracks in RC beams leads to a crack pattern similar to those obtained in actual structures 9). The present study will further investigate the similarities between the two crack patterns. Since controlling the distributed cracks by means of conventional reinforcement would lead to overly-reinforced concrete members, short steel fibers were also used in this study. Being randomly distributed throughout the concrete mass, steel fibers can better control the cracking in any direction. Adding short fibers to the concrete mix has several benefic effects ranging from reducing the crack opening 8) to an increase in the deformability and shear carrying capacity of RC beams 10), 11). As stated before, there are few studies concerned with the doubly reinforced concrete beams 12). The present research tries to bring its contribution to a better understanding of the shear behavior of RC beams with longitudinal reinforcement both at the top and bottom parts of the cross section. 3. MATERIALS (1) Concrete A concrete with a designed compressive strength of 30 N/mm 2 obtained at 7 days through the uniaxial compression test, was considered. For each of the concrete mix proportions summarized in Table 1 the tests were conducted according to JIS A 1108 and JIS A 1113 for the compressive strength and the tensile strength, respectively. (2) Longitudinal reinforcement The characteristics of the longitudinal reinforcement used in this study are as follows: PC bar size D22 (nominal diameter: d = 21.4 mm), yield strength: f y = 930 N/mm 2 and the ultimate strength f u = 1080 N/mm 2. The specifications for PC bars are according to JIS G (3) Steel fibers The steel fibers have crimped ends 8). The length is L f = 30 mm and the diameter is d f = 0.6 mm. The material properties are: the tensile strength f u = 1000 Concrete Type W *1 [kg/m 3 ] Table 1 Mix Proportions for Each of the Concrete Batches C *2 [kg/m 3 ] W/C [%] S *3 [kg/m 3 ] G *4 [kg/m 3 ] EA *5 [kg/m 3 ] SF *6 [kg/m 3 ] AE *7 [kg/m 3 ] SP *8 [kg/m 3 ] C F130EA-DL F135EA-DL F135EA-DL F140EA-DL F145EA-DL F145EA-DL F150EA-DL *1 Water, *2 High early strength Portland cement, specific gravity = 3.14, *3 Fine aggregate, specific gravity = 2.64, *4 Coarse aggregate, specific gravity = 2.64, G max = 20 mm, *5 Expansion agent, specific gravity = 3.14, *6 Steel fibers, specific gravity = 7.85, *7 Air entraining agent, specific gravity = 1.03, *8 Superplasticizer, high performance water reducing agent, specific gravity =

3 A A Fig.1 Beam Geometry and Reinforcement Layout (dimensions are in mm) D22 PC bar D6 (SD295A) D22 PC bar 148 D22 PC bar Strain gage for steel Fig.3 Location of the Steel Strain Gages 69 Fig.2 Cross Sectional View at Section A-A (dimensions are in mm) N/mm 2 and the Young s modulus E s = N/mm 2. (4) Expansion agent The amount of expansion agent was to replace a part of the fine aggregate mass and not of the cement mass. This was based on the fact that with the quality control commonly achieved in modern cement factories the flaws are more likely to come from the aggregates that are used in the mixing than from the cement itself. Moreover, in some deleterious processes that affect concrete elements, for example ASR, the silica in the aggregate reacts with the alkali in the cement to create the ASR gel. Therefore, the expansion agent could be considered to be a part of the fine aggregate. 4. TEST PROGRAM 26 The test program consisted in a number of eight specimens. For each of the concrete mixes in Table 1 a beam with the dimensions of mm (L H B) was cast. The beams were designed to fail in shear and had a longitudinal reinforcement ratio of p w = 3.29%, for tension reinforcement, and a shear span to effective depth ratio a/d = According to the reinforcement layout used in previous research 8) the influence of the chemical prestressing was quite important. A different reinforcement layout is adopted in the present study. Longitudinal reinforcement, with the same characteristics presented above, was placed at the top part of the cross section. The beam geometry and the reinforcement layout are presented in Fig. 1 and the section view in Fig. 2. Such a reinforcement layout will help in distributing the longitudinal tensile strains, created by the use of expansion agent, more uniformly throughout the concrete section. This will lead to a decrease in the chemical prestressing as it will be shown later. Moreover, as it can be seen from Fig. 1, there are no stirrups in the shear span. The reason for such a reinforcement layout is that we wanted to evaluate the shear carrying capacity of the concrete itself without the help of shear reinforcement. After casting, the formwork was covered in wet cloth and kept at room temperature for 24 hours. In the next day, the formwork was stripped off and the 592

4 Table 2 Compressive Strength of Concrete in the RC Beams Given by Schmidt Hammer Test, f ' c,schmidt Concrete type ' f c,schmidt [N/mm 2 ] C F130EA-DL F135EA-DL F135EA-DL F140EA-DL F145EA-DL F145EA-DL F150EA-DL 16.6 specimen was placed in an environmental chamber where it was kept for curing at 21 C constant temperature and 75% relative humidity until the day of testing. On a 12-hour interval the beams were also sprinkled with water so that to ensure enough moisture for concrete curing. The strain induced in the reinforcement was measured by means of strain gages connected to the steel bars and the results were recorded by a data logger on a 10-minute interval. In this way, the strain development in the steel bars was monitored regularly. The location of the steel strain gages is shown in Fig. 3. After a curing period of time of 7 days, monotonic loading tests were conducted on the RC beams. The notation of the specimens and mix proportions is kept similar to the one used in the previous reasearch 8) with the difference that a DL suffix was added to the names. This is to denote that the beams are doubly reinforced. 05F135EA-DL means that the concrete contains 0.5% fiber (05F), 135 kg/m 3 of expansion agent (135EA) are used in the mix proportion and the beam is doubly reinforced (DL). 5. RESULTS AND DISCUSSIONS (1) Concrete strength Uniaxial compression tests and splitting tests according to JIS A 1108 and JIS A 1113, respectively, were carried out after 7 days. The obtained values for the control case C were f c = 31.5 N/mm 2 for the compressive strength and f t = 2.2 N/mm 2 for the tensile strength. For the other mix proportions containing expansion agent, Table 1, the uniaxial compression tests could not be performed. The degree of degradation of concrete in the cylinders was too high and they 100 mm mm Fig.4 Damaged Compression Cylinder for the 05F145EA-DL Case either tended to break when lifted from the ground or they were already deformed. Such a deformed shape of a compression cylinder is shown in Fig 4. Because it was needed to quantify the compressive strength of the concrete, a non-destructive Schmidt hammer test was conducted on the RC beams themselves. The confining effect of the conventional reinforcement that cannot be simulated in the compression cylinders is expected to be much larger than in the previous research 8). The non-destructive test was conducted on the control specimen C, as well. The results are summarized in Table 2. The value of the compressive strength for the control case obtained by Schmidt hammer test is slightly higher than the value obtained through the uniaxial compression test. Moreover, it is important to notice that Schmidt hammer test gives quite accurate values, for the confined condition within the RC beams, compared to the uniaxial compression test. The increase in the values of the compressive strengths obtained by Schmidt hammer tests on the RC beams compared to the values obtained following standard procedures has been reported in the previous study 8). The number of rebound values recorded for each specimen in this study was fifty. The location of the measuring points was within the area bound by the tensile and compressive longitudinal reinforcement, Fig. 1, and only one reading was recorded at each point. The direction of measuring was perpendicular to the side of the RC beam. Since concrete is a highly heterogeneous material and taking into account the confinement effect of the longitudinal reinforcement, the concrete strength in the longitudinal direction is expected to be slightly higher than the obtained value measured in the transversal direction along which the concrete could expand more freely. 593

5 Steel strain (x10-6 ) Steel strain (x10-6 ) 800 C 500 Bottom part Top part Time(hours) F135EA-DL Top part 500 Bottom part Steel strain (x10-6 ) Steel strain (x10-6 ) F130EA-DL Bottom part 500 Top part Time (hours) F135EA-DL Bottom part 500 Top part Time (hours) Time (hours) Steel strain (x10-6 ) F140EA-DL Bottom part Top part Steel strain (x10-6 ) F145EA-DL Top part Bottom part Steel strain (x10-6 ) Time (hours) 10F145EA-DL Top part Bottom part Time (hours) Steel strain (x10-6 ) Time (hours) 10F150EA-DL Bottom part Top part Time (hours) Fig.5 Steel Strain Histories for All Specimens It is also known that the results given by the Schmidt hammer test are highly dependent on the size and shape of the specimen, moisture contest of concrete, type of cement and coarse aggregate used in each mix proportion. In order to ensure the consistency of the results, all the beams tested in this study had the same shape and size, same curing conditions (which leads to a more or less the same moisture content in the concrete) and the same type of cement and aggregate was used in all concrete mixes. In the subsequent calculations for the shear carrying capacity of RC beams, the values of f c will be the ones presented in Table 2 for all the cases. (2) Strain history in the longitudinal reinforcement With the data recorded during the curing period of time, the strain histories in the longitudinal steel bars were plotted in Fig. 5. It can be clearly seen that the difference between the steel strains at the top and bottom parts is quite small and tends to be negligible for the control case C. Moreover, according to the JSCE standard 594

6 specifications for concrete structures 13), the influence of the axial force, which in this study is given by the chemical prestress, on the shear carrying capacity of RC beams is taken into account by the factor β n, defined as: 2 M β 0 n = 1+ (1) M in which M u is the ultimate resisting moment of the RC beam and M 0 is the decompression moment. The decompression moment M 0 was calculated in two steps. The first step consists in calculating the equivalent stress in the concrete starting from the strain in the longitudinal reinforcement recorded at the end of the curing period of time. The equivalent stress in the concrete was calculated using the following equation: u top bottom ( ε + ε ) Es As s s σ c, eq = (2) b h in which E s is the elastic modulus for steel, N/mm 2, A s is the area of steel, mm 2, ε s top is the steel strain at the top part, ε s bottom is the steel strain at the bottom part, b is the width of the web, mm, h is the height of the cross section, mm and σ c,eq is the equivalent compressive stress in the concrete, N/mm 2. In the above equation no difference has been made between the area of tension or compression steel, A s, since the beams have the same amount of reinforcement both at the bottom and top parts. The second step for calculating the decompression moment consists in the following: due to the difference in steel strains at the top and bottom parts, Fig. 5, an additional bending moment acts on the RC beams. This will result in a compressive or tensile stress that is added to the σ c,eq. The additional stress was calculated as: top bottom ( ε ε ) h As Es s s c 2 h σ = (3) I 2 where I is the moment of inertia of the cross section, mm 4 and c is the distance from the extreme concrete fiber to the centroid of the longitudinal reinforcement, mm. Since the RC beams are symmetrically reinforced, c is the same for both the tension and compression reinforcement. Moreover, the distance from the neutral axis to the extreme fiber is half of the height of the cross section. Finally, the compressive stress in the lower fiber that the decompression moment has to balance was calculated as: σ decomp = σ c, eq ± σ (4) in which σ c,eq and ε are calculated according to equation (2) and equation (3), respectively. The ± sign depends on the difference between the steel strain at the top part and the steel strain at the bottom top part being greater or smaller than 0. If ε s ε bottom s > 0 then σ σ + σ decomp = c, eq. In equation (2), ε s top and ε s bottom are each calculated as the arithmetic mean of four values (see Fig. 1, for the reinforcement layout, and Fig. 3, for the location of the steel strain gages.). If ε s top ε s bottom > 0 it means that the beam bends upwards, Fig. 6a, and if ε s top ε s bottom < 0, the beam bends downwards, Fig. 6b. On the other hand, due to the reinforcement layout, Fig. 1, higher values for the ultimate resisting moment M u are obtained. This means that the values of the second term in equation (1) decrease.the calculated values for β n are presented in Table 3. Values of β n closer to 1.0 mean that the influence of the chemical prestressing, due to the use of expansion agent, is greatly decreased because of the reinforcement layout adopted in this study. In equation (1) the material parameters required to compute M 0 and M u are either known or can be easily determined. As shown above M 0 can be calculated with the data that is readily available from the material characteristics of the reinforcement. On the other hand, the ultimate resisting moment of the beam, M u, was calculated based on the equivalent stress block. The values of the compressive strength of concrete are the ones determined by the Schmidt hammer test, summarized in Table 2. It is important to specify at this stage that in the decompression moment method recommended by the JSCE standard specifications for concrete structures 13), shown in equation (1), the influence of Table 3 Values of β n Computed from the Steel Strain Histories Concrete type β n C 1 00F130EA-DL F135EA-DL F135EA-DL F140EA-DL F145EA-DL F145EA-DL F150EA-DL

7 pre-stressing, in this research chemical pre-stressing, is considered only in terms of the lower fiber stress. Because of this, the distribution of stresses along the height of the beam cross section is neglected. In other words, the upper fiber stress is neglected, leading to the scattering and conservative prediction of the results as it was shown by Hamada et al. 14) and Tamura et al 15). (3) Definition of crack density The previously introduced crack density parameter 8) is also used in the present research. The parameter was defined as the ratio between the area of the cracks and the initial area of concrete. The crack density depends on the average crack width and on the total length of cracks within a specified area of concrete; multiplying the two terms, the area of cracks is obtained. The method is easy to use and it showed good results in terms of predicting the shear crack location in RC beams that showed distributed crack patterns before loading. The equation used for calculating the crack density parameter is shown below: Ω i = m wi L j j= 1 (5) A where wi is the average crack width for each area A i and L j is the length of each crack, m being the total number of cracks for the area A i. The method is further investigated to check whether there is any dependency of the obtained results on the division of the concrete surface or not. i For this purpose, the surfaces of the beams are divided using two distinct patterns. The first pattern applied is the one that was already presented in an earlier paper 8), shown in Fig. 7a, and the new pattern is shown in Fig. 7b. For each of the areas A 1 through A 5 in Fig. 7a, the crack density parameter Ω 1 through Ω 5 is computed based on equation (5). The distributed crack patterns corresponding to the type of surface area division shown in Fig. 7a are depicted in Fig. 8. At the same time, the values of the crack density paramenter are presented under their corresponding areas for all the cases that showed distributed cracks before loading. The average crack width, in equation (5), for each of the areas A 1 through A 5 was calculated based on 120 values of the crack width measured at different locations within each area. The device used to conduct these measurements was a digital camera connected to a handheld computer. The camera took close up shots of the concrete surface and the software in the computer directly gave the values of the widths for the cracks present in the picture taken by the camera. The range of crack openings for which this devise case be used is between 0.05 mm and 2.5 mm. The second term that makes up the numerator in equation (5) was computed as follows: after the crack widths at different locations on the concrete surface were measured, high resolution digital pictures of the beam surface were taken. The pictures were then inserted into specialized software and, after manually tracing all the visible cracks, the total crack length or the desired area of concrete was automatically given by the software. Deformed shape Initial shape Initial shape a) The Beam Bends Upwards (ε s > 0) b) The Beam Bends Downwards (ε s < 0) Fig. 6 Deformed Shape of the RC Beam Due to Chemical Prestressing a) Previous Type of Surface Area Division 8) b) New Type of Surface Area Division Fig.7 Types of Surface Area Division 596

8 Doboku Gakkai Ronbunshuu E Vol.63 No.4, , F130EA-DL 00F130EA-DL Ω1=1.43 % Ω2=1.34 % Ω3=1.17 % Ω4=1.29 % Ω5=1.48 % Ω1=1.30 % 00F135EA-DL 0.58 Ω2=1.24 % 00F135EA-DL Ω2=1.55 % Ω3=1.22 % Ω4=1.76 % Ω5=2.97 % Ω1=1.59 % 05F135EA-DL Ω2=1.83 % 05F135EA-DL Ω1=1.72 % Ω2=1.34 % Ω3=0.84 % Ω4=1.26 % Ω5=1.68 % Ω1=1.44 % 05F140EA-DL Ω2=1.33 % 05F140EA-DL Ω1=1.98 % Ω2=1.40 % Ω3=0.99 % Ω4=1.89 % Ω5=2.35 % Ω1=1.44 % 05F145EA-DL Ω2=1.89 % 05F145EA-DL Ω1=2.08 % Ω1=2.47 % Ω2=1.95 % Ω3=1.66 % Ω4=2.53 % Ω5=3.49 % 10F145EA-DL Ω2=2.59 % 10F145EA-DL Ω1=2.04 % Ω2=1.46 % Ω3=0.63 % Ω4=1.12 % Ω5=1.72 % Ω1=1.48 % 10F150EA-DL Ω2=1.17 % 10F150EA-DL Ω1=1.67 % Ω2=1.25 % Ω3=0.82 % Ω4=1.42 % Ω5=2.04 % Ω1=1.31 % Ω2=1.44 % Fig.9 Crack Densities as a Percentage of the Initial Area of Concrete for a Different Type of Surface Area Division Fig.8 Crack Densities as a Percentage of the Initial Area of Concrete for One Type of Surface Area Division It should be noted that during the course of measuring the crack openings, there were cases when the crack opening could not be measured as it fell outside of the range of the measuring device (<

9 mm). However, those cracks, hairline cracks, were not entirely neglected as they were taken into account through their crack length that was added to the total crack length for the area of concrete they belonged to. The same procedure is applied to the new divison pattern that focuses only on the two shear spans of the beam, neglecting the rest of the concrete surface, Fig. 7b. Consequently, there will result two areas, denoted A 1 and A 2, for which the crack density parameters Ω 1 and Ω 2 are computed. The calculated values for the crack density parameters Ω 1 and Ω 2 are shown in Fig. 9 below each of the concrete beams that exhibited distributed cracks before testing. As reported earlier by Toma et al. 8) the shear carrying capacity of the RC beams with distributed cracks is influenced by the crack densities of the areas that are entirely located in the shear span. Either of the corresponding crack density parameters will result in the shear failure occurring in the shear span with the higher value for Ω. If the proposed method is truly independent of how the concrete surface area is divided, a similar trend should be observed for the new surface area division (Fig. 9). By comparing the values of the crack densities Ω 2 and Ω 4 in Fig. 8 with the Ω 1 and Ω 2 from Fig. 9, it can be seen that for the cases when Ω 4 > Ω 2 in Fig. 8, Ω 2 > Ω 1 in Fig 9. The same thing holds true for the cases when Ω 4 < Ω 2 in Fig. 8 as they lead to Ω 2 < Ω 1 in Fig. 9. This simple comparison shows the fact that the qualitative information given by the crack density parameter is accurate for different choices of surface area division. Until now, the focus was only on one side of the RC beams (from now on referred to as front side ). The question is: would the qualitative results given by the crack density parameter change if the other side of the beam was considered for inspection? In order to be able to answer this question, the opposite side of each of the beams (from now on denoted as back side ) was also inspected. Figure 10 shows the developed shape of the beam. For the drawing to be simpler and easier to understand, only the front side, the top side and the back side are shown. The bottom side and the end face of the 3D beam are not shown. Moreover, the distributed crack patterns of the front side and the back side for the 0F130EA-DL case are shown. Only the new type of surface area division is considered, Fig. 7b, because the qualitative results in terms of the shear span where the failure is more likely to occur, given by the crack density parameter do not depend on the type of surface area division, as previously shown. Additionally, the values of the crack Ω 1b = 1.33% Back side Top side Ω 1f = 1.30% Ω 2f = 1.24% Front side Ω 2b = 1.22% Fig.10 Developed Shape of the Beam and Distributed Crack Patterns for 0F130EA-DL density parameter is presented for each area on the front and back sides. By looking at the values of the crack density parameter shown in Fig. 10, it can be concluded that even though they are slightly different in values, the qualitative result remains the same: the shear failure is more likely to occur in the shear span with the higher value of the crack density parameter and the predicted shear span is the same for both sides of the RC beam. The same trend was observed for all the other RC beams used in this study that showed distributed cracks before loading. Of particular interest are the cracks inside the RC beams. The geometry of the inside cracks can be estimated by using various stereological methods 16) that were successfully applied to concrete 17) and that were adopted from the field of rock mechanics. Such methods can predict with reasonable accuracy the 3D distribution of cracks in concrete under loading starting from 2D images of the cracks taken from the samples that are cut along parallel planes at more than two different locations on the specimen. However, the method has been applied only to small size concrete specimens 18) for which special devices had to be constructed to preserve the cracking condition 19, 20) inside concrete under loading. Given the current limitations of applying such methods to full size concrete specimens, the crack density parameter was considered a more suitable method for a quick estimation of the degree of damage in a concrete structure that shows distributed crack patterns. 598

10 a) Highway Bridge Pier in USA 16) 15 cm b) Railway Bridge Pier in Japan 15 cm Fig.11 Examples of ASR Induced Distributed Cracks in Actual Structures (4) Distributed crack patterns comparison with actual structures In plain concrete, expansive ASR generally results in map cracking caused by differential stress due to variation in the amount of expansion within the concrete element. In reinforced or prestressed concrete cracks may show a preferred orientation parallel to the main reinforcement 21). In concrete affected by ASR the strength may drop below the ultimate. It was shown that the expansion has a greater effect on the tensile strength than on the compressive strength 22). The modulus of elasticity, generally, decreases and the variations in this parameter may be more sensitive to expansive ASR than strength changes 23), 24). Severely damaged concrete members may show loss of prestress and corrosion of steel; but where deterioration is less severe, the bond is largely unaffected and so concrete expansion may lead to substantial increase in the tensile stress in steel. This effect has been termed chemical pre-stress 25), 26). As it can be seen from either Fig. 8 or Fig. 9, using expansion agent was successful to create distributed cracks. It is interesting to observe that the pre-cracks obtained in this study have a preferred orientation that is parallel to the longitudinal reinforcement. Only towards the both ends of the beams the crack orientation changes to become parallel to the stirrups (Fig. 1). A similar distribution of cracks has been observed in the actual structures affected by ASR 9), 27), 28). Two examples of actual structures affected by ASR are presented in Fig. 11. More recent studies in the field of prestressed concrete have confirmed the preferred orientation of 600 mm 900 mm Fig.12 Crack Pattern for a Selected Area of a Road Bridge Pier in Japan the ASR induced cracks parallel to the main reinforcement 29). It can be confirmed that the obtained distributed crack patterns by using expansion agent are visually similar to the ones induced by ASR expansion in real RC structures. The chemical prestress phenomenon due to the use of expansion agent is also similar to the phenomenon reported in earlier research 25), 26). There is, however, a difference between the crack created by the expansion agent and those caused by ASR in concrete structures. The cracks induced by 599

11 the presence of the expansion agent originate and are entirely located in the concrete matrix. In the real RC structures affected by ASR, the cracks form at the interface between the reactive aggregate and cement paste and, sometimes, can pass through the aggregates as well and not only through the concrete matrix. Because of this, a slightly different state of stress is induced in the RC beams used in this study compared to real life cases. The crack pattern for a portion of a bridge pier for which the crack density parameter was calculated is shown in Fig. 12. The pier showed extensive damage due to ASR, with crack openings ranging from 0.05 mm to 1.15 mm. The value of the crack density parameter for the selected area was 1.64%. Since at this stage of the research there is no clear mathematical relationship betweent the shear carrying capacity and the crack density parameter, the above value of the crack density parameter is able to give information only about the state of damage in a concrete member compared to other concrete members affected by distributed cracks. Further tests should be conducted in order to establish the dependency of the shear carrying capacity of a concrete member on the crack density parameter. (5) Shear testing and shear carrying capacity of the control case Figure 13 shows the load-displacement curve for the control case, C. After the formation of the first diagonal crack, the load slightly dropped but soon after it continued to increase. Shortly, another shear crack occurred in the opposite span from where the first diagonal crack formed. The load dropped again but by continuing to load the beam, the carrying capacity further increased. The beam reached its peak load at a mid-span displacement of about 6 mm. The order in which the diagonal cracks formed on the RC beam for the control case is shown in Fig. 13 by the numbers 1, 2 and 3. It is interesting to observe that compared to previous researches 2), 4) the load did not drop suddenly after or shortly after the formation of the diagonal crack but it continued to increase further. This means that there are additional reserves of shear strength in the RC beams. The two possible influencing factors are the dowel action of the longitudinal reinforcement and the aggregate interlocking effect. Both the effect of the dowel action and the aggregate interlock are highly dependent on the opening of the shear crack. Moreover, the maximum size of the coarse aggregate is an influencing factor for the aggregate interlocking effect. This effect tends to decrease for larger size beams, for the same size of Load (kn) Formation of the first shear crack (1) 150 Formation of the second shear 120 crack (2) Midspan displacement (mm) Fig.13 Load-Displacement Curve for the Control Case the coarse aggregate, and it becomes more important for the smaller size specimens. When computing the shear carrying capacity of RC beams without web reinforcement, these effects are insignificant 4) 2), 12). In previous research works there was no vertical reinforcement in the clear span of the RC beams. Because of that, after the formation of the diagonal crack, the dowel effect of the longitudinal reinforcement was greatly dependent on the part of concrete beneath it from the point where the diagonal crack intersects the reinforcement to the support. With the increase in the load and with the opening of the diagonal crack, the pressure exerted by the reinforcement on the cover concrete beneath it became too large and lead to the formation of a splitting crack along the longitudinal steel bar. Consequently, the dowel effect of the reinforcement was lost. However, in the present case, the bottom reinforcement is linked to the top reinforcement through the stirrups that were used under the loading points. Due to the increased stiffness of the reinforcement, taking into account its layout, the opening of the diagonal crack is limited. Consequently, the dowel effect of the longitudinal reinforcement is higher in this case and should be taken into account. Another consequence of the limited width of the shear crack opening could be an increase in the aggregate interlocking effect, as well. Moreover, the compressive stresses are resisted both by the concrete area above the neutral axis and by the longitudinal reinforcement located at the top part of the beam. The presence of the longitudinal reinforcement in the compression zone leads to a slower propagation of the shear crack above the neutral axis of the beam and further acts to limit the crack opening once it succeeded propagating towards the loading point. This could explain why there is an increase in the shear (3) 600

12 C F130EA-DL 00F135EA-DL 05F135EA-DL 05F140EA-DL 05F145EA-DL 10F145EA-DL 10F150EA-DL Fig.14 Crack Patterns at the Onset of Shear Failure carrying capacity after the formation of the diagonal cracks in the specimen C and why a more ductile behavior of the beam was observed instead of a brittle failure. However, a slight increase in the load after the formation of the shear crack, followed by a second peak, was also reported for the RC beams with longitudinal reinforcement only at the bottom part 30). On the other hand, significant increase in the shear carrying capacity after the formation of the diagonal crack, similar to the present study, was observed during tests on RC beams with both tension and compression reinforcements. 31) The experimental results were later confirmed by means of non-linear FEM 32). While the first diagonal crack occurred at a load that was consistent with the diagonal tension failure, equation (6), the load continued to increase further instead of decreasing. The failure mode observed in this experiment is neither a pure diagonal tension failure 2), 4) nor a pure diagonal compression failure 33), 34) but a combined mode of failure between the two. Such a mixed mode of failure was previously reported to occur in RC beams without shear reinforcement with longitudinal reinforcement located only at the bottom part 35). The dowel effect of the longitudinal reinforcement and the aggregate interlocking effect are believed to have influenced such a behavior of the RC beams. The shear carrying capacity of the control case was computed as follows: first, the shear carrying capacity of the concrete itself was calculated, using the equation proposed by Niwa et al. 3) in 1986: V c = 0.2 f ' 1/ 3 c p w 1/ d a d / 4 b w d (6) where f c is the compressive strength of concrete given by Schmidt hammer test (N/mm 2 ), p w is the longitudinal reinforcement ratio, d is the effective depth (mm), a is the shear span (mm) and b w is the width of the web (mm). The effect of the chemical prestress is additionally taken into account by the factor β n. Finally, the calculated formula for the shear carrying capacity that was used in this study is: V cal =β V (7) in which β n is according to equation (1). However, the contribution of the compression reinforcement to the shear carrying capacity of the RC beam was not taken into account. Its influence on the shear behavior of the RC beams can be described as a more significant contribution of the longitudinal reinforcement to the shear carrying capcity after the n c 601

13 formation of the diagonal crack as well as a higher aggregate interlocking effect. These two improvements can be explained by a smaller opening of the diagonal crack. Due to the reduced number of experimental studies conducted on the RC beams with both longitudinal tensile and compression reinforcement, the contribution of the latter cannot be accurately quantified mathematically. Further tests should be conducted in order to address this matter in future research works. The ratio of the experimentally obtained value V exp and the calculated value V cal for the control case shows sufficient accuracy of the estimation method. The value of V exp /V cal is (6) Shear testing and shear carrying capacity of the specimens with distributed cracks a) Diagonal crack location in terms of the shear span Figure 14 shows the crack patterns at the onset of the shear failure for all the specimens used in this study. The shear span where the failure occurred is highlighted in grey for each beam. By looking at Fig. 8, Fig. 9 and Fig. 14, it can be seen that for all the specimens that showed distributed pre-cracks, the failure occurred in the shear span for which a higher value of either Ω 2 or Ω 4 was obtained (Fig. 8) or for either Ω 1 or Ω 2 (Fig. 9). This once again proves that the crack density parameter is able to predict the shear span where the failure is more likely to occur. In addition, the results show that the qualitative prediction is independent of the surface area division. b) Estimation for diagonal crack location within the shear span where failure occurred In the previous sub-section it was shown that the crack density parameter can predict the location of the shear crack in terms of the shear span. The question is whether it can still predict the location more accurately, for example within the shear span where the failure occurs. In order to find out whether this is possible or not, the surface of the beam in the shear span, that is more likely to fail, was further divided by a square grid with a constant 50 mm interval in both vertical and horizontal directions, as shown in Fig. 15. For each of the squares, the crack density parameter was calculated. Once the values were obtained, it had to be decided where the shear crack will be located. A first step was to look for the squares with high values for the crack density parameter that were located close to the line of thrust that connects the loading point to the support. The second step was to look at the values of the crack density parameter of the squares adjacent to the ones selected in the previous step. If the value for Ω is higher than or equal to the value of the squares previously selected, the current square is also taken into account. If the value is smaller, the respective square is discarded. Moreover, the squares with high values for Ω that are closer to the vertical lines passing either through the support or through the loading point are not taken into account since those areas have little influence in the shear failure of the RC beams. The obtained locations of the critical diagonal cracks within the shear spans for all the beams, except the control case, are presented in Fig. 16 by means of highlighted squares. The values of crack density parameter are also shown in bold within the highlighted squares. The crack patterns at the onset of the shear failure are overlapped on the grid. It can be seen that the crack density parameter can give a reasonable approximation of the diagonal crack location within the shear span. There are still cases when the predicted area is wider than the actual location of the critical shear crack. However, it is believed that the method shows sufficient accuracy. It can also be observed that the location of the diagonal crack is, in most of the cases, consistent with the squares that are crossed by the line of thrust than by the squares chosen by their high values of the crack density parameter. However, the area within which most of the cracking due to shear occurs is accurately predicted by taking into account both types of squares (the squares selected according to the two steps procedure explained above). The location of the critical crack could be more accurately predicted if a smaller step size is chosen for the grid. c) Shear behavior of RC beams with distributed pre-cracks The load-displacement curves for the RC beams with distributed pre-cracks are presented in Fig. 17, Fig. 18 and Fig. 19. Only the beams without steel fibers showed a small drop in the load after the formation of the shear crack, similar to the control case. For all the other specimens, such a drop could not be observed. This could be explained by the added ductility that steel fibers confer to the beams. While the absence of a visible drop in the load for the RC beams with steel fibers is somehow expected, a similar behavior could be observed for the RC beams with distributed cracks but without steel fibers. It is also interesting to observe that the load displacement curves shown in Fig. 17 are also smooth without larger and more often drops in the load as it was observed for the control case, Fig. 13. This might seem a bit unusual but it can be explained by the presence of the distributed cracks before 602

14 00F130EA-DL F135EA-DL F135EA-DL F140EA-DL F145EA-DL F145EA-DL F150EA-DL 50 mm mm mm mm Fig.15 Area Division within the Shear Span where Failure Occurs loading. In undamaged RC beams, the formation of the diagonal crack is accompanied by a drop in the load. This drop can be larger or smaller depending on the beam having longitudinal reinforcement only at the bottom part or having both tension and compression reinforcement. The drop in the load is caused by the sudden occurrence of the diagonal crack through the Fig.16 Shear Crack Location Within the Shear Span where Failure Occurred Using the Crack Density Parameter Ω(%) entire shear span. In the RC beams with distributed cracks, however, the diagonal crack occurred gradually as it bridges the already existing cracks, due to the use of expansion agent, over much sorter distances compared to the shear span of the beam. Thus, the presence of distributed cracks before loading may be the cause of obtaining such smooth load-displacement curves for the specimens without 603

15 Load (kn) Formation of the diagonal cracks F130EA-DL F135EA-DL Midspan displacement (mm) Load (kn) F135EA-DL 05F140EA-DL 05F145EA-DL Midspan displacement (mm) Fig.17 Load-Displacement Curves for Beams with Pre-Cracks and without Steel Fibers Fig.18 Load-Displacement Curves for Beams with Pre-Cracks and Containing 0.5% Steel Fibers Load (kn) F145EA-DL 10F150EA-DL Vexp/Vcal Control case 0 % fiber 0.5 % fiber 1.0 % fiber Midspan displacement (mm) Crack density Ω (%) Fig.19 Load-Displacement Curves for Beams with Pre-Cracks and Containing 1.0% Steel Fibers steel fibers. The behavior of RC beams with distributed cracks was similar to the one observed for the control case but with smaller drops in the load leading to smoother curves. Therefore, it can be said that for all the beams with distributed cracks tested in this study, a combined mode between diagonal tension failure and diagonal compression failure could be observed. The dowel effect of the longitudinal reinforcement and the aggregate interlocking effect are believed to have influenced such a behavior of the RC beams. This was possible due to the reinforcement layout that limited the opening of the shear crack. Moreover, the effect of adding steel fibers acted further towards a limitation of the crack opening. A close look at both Fig. 17 and Fig. 18 will shown that the addition on steel fibers in small percentages (in this case 0.5%) has not a significant effect in terms of the peak resisting load. There is only a slight increase in the peak load from the specimen 00F135EA-DL in Fig. 17 to the specimen 05F135EA-DL in Fig. 18. For the case of low fiber percentages the benefit of adding steel fibers resides Fig. 20 Dependency of V exp /V cal on the Crack Density Parameter Ω of the Shear Span where Failure Occurred in an increased deformability of the RC beams under loading and a leaner post peak branch in the load-displacement curve compared with the specimens without steel fibers. With the increase in the fiber percentage from 0.5% to 1.0%, a higher peak resisting load can be observed for the RC beams, Fig. 19. Again, the post peak behavior shows a slow decrease in the resisting load with the increase of midspan deflection. The specimens that had 1.0% steel fibers in their mixes not only showed a higher peak resisting load (compared with the RC beams with only 0.5% fibers or the RC beams without fibers) but also an increased deformability under loading. d) Shear carrying capacity of RC beams with distributed pre-cracks The shear carrying capacity of RC beams with distributed pre-cracks and without steel fibers was calculated following the steps presented in sub-section 5.(5). For the beams that had steel fibers in their concrete mix, the effect of fibers was taken into account by means of the following empirical equation 10) : 604

16 v= τ L f 0.37 V f (8) d f where v is the shear stress (N/mm 2 ), τ is the bond strength, taken as 4.15 N/mm 2 for the steel fibers having crimped-ends in the absence of any pull-out tests, V f is the volume of fibers, L f is the fiber length (mm) and d f is the fiber diameter (mm). Equation (8) has been proven to be quite accurate 36) for the case of RC beams containing steel fibers. The shear carrying capacity of the RC beams with steel fibers was calculated as: V cal, f =β n Vc + v bw d (9) in which b w is the width of the web (mm) and d is the effective depth (mm). The obtained results using equation (7), for the beams without steel fibers, and equation (9), for the beams with steel fibers, are summarized in Table 4. The prediction method has reasonable accuracy. Contrary to what was expected, the presence of distributed pre-cracks had no major influence in the shear carrying capacity of the tested specimens. Figure 20 shows the variation of the V exp /V cal ratio with respect to the crack density parameter Ω expressed as a percentage of the initial area of concrete. The diamond shaped dot represents the control case, the squares represent the specimens with expansion agent but without steel fibers, the triangles show the specimens with expansion agent and 0.5% steel fibers and the crosses depict the specimens with expansion agent and 1.0% steel fibers. The values for Ω that were used in Fig. 20 are the ones corresponding to the shear span where the failure occurred (Fig. 13) and calculated according to the surface area division presented in Fig. 8. Those values should be used because the corresponding areas are entirely located in the shear spans of the RC beams with little influence from the support areas or from the area that is associated to the bending cracking. As it can be seen from Fig. 20, increasing the amount of expansion agent, for the same percentage of steel fibers, leads to higher values for the crack density and consequently to a decrease of the V exp /V cal ratio to the point when it becomes smaller than 1.0. However, even for high values of Ω, the calculated values for the peak loads are still smaller than the experimental ones. Consequently, it was concluded that the presence of distributed pre-cracks does not have a significant influence on the overall behavior of doubly-reinforced concrete beams. Table 4 Calculated Results Versus Experimental Values V cal Concrete Type [kn] [kn] V exp /V cal C F130EA-DL F135EA-DL F135EA-DL F140EA-DL F145EA-DL F145EA-DL F150EA-DL CONCLUSIONS V exp Using expansion agent to create distributed pre-cracks proves to be successful. Moreover, it is shown that the obtained crack pattern is similar to those present in actual structures affected by ASR. The crack density parameter Ω can predict the location of the critical shear crack in terms of the shear span. It is also shown that Ω does not depend on the division of the concrete surface area when it comes to predict the shear span where the failure is more likely to occur. Moreover, a further division of the area within the failed shear span leads to a better prediction of the shear crack location. Even though in some cases the predicted location of the critical crack is wider than the actual result obtained from the experiments, the method shows reasonable accuracy. A combined mode between diagonal tension and diagonal compression failures can be observed for the doubly-reinforced beams tested in this study. The behavior is similar to the one previously observed on RC beams with longitudinal reinforcement in the compression area and is thought to be due to the reinforcement layout that prevents large openings of the shear crack. Because of this, additional factors like the dowel action of the longitudinal reinforcement and the aggregate interlocking, contribute to the increased shear carrying capacity. The calculation method for the peak loads resisted by the RC beams in this study leads to an under-estimation of the experimental results. Further testing is necessary in order to account for all the effects that contribute to the shear mechanism of the doubly-reinforced concrete beams. The crack density does not have a significant influence on the overall behavior of the beams tested in this study. Even though it was expected that the presence of distributed pre-cracks will act towards a decrease in the shear carrying capacity, the predicted 605