ACI STRUCTURAL JOURNAL TECHNICAL

ACI STRUCTURAL JOURNAL

TECHNICAL PAPER

Title no. 105-S18

Shear Behavior of Large Concrete Beams Reinforced with High-Strength Steel by Tarek K. Hassan, Hatem M. Seliem, Hazim Dwairi, Sami H. Rizkalla, and Paul Zia This paper presents test results of six large-size concrete beams reinforced with either conventional- or high-strength steel and tested up to failure. The beams were constructed without web reinforcement to evaluate the nominal shear strength provided by the concrete. The shear behavior, ultimate load-carrying capacity, and mode of failure are presented. The applicability of the current ACI design code to large-size concrete beams constructed without web reinforcement is discussed. The influence of the shear spandepth ratio, concrete compressive strength, as well as the type and the amount of longitudinal steel reinforcement is investigated. The study shows that using high-strength steel alters the mode of failure from diagonal tension to shear compression failure and results in higher shear strength compared with using conventional steel. It was also found that the current ACI shear design provisions are unconservative for large-size concrete beams without web reinforcement. Keywords: beams; high-performance steel; high-strength steel; shear.

INTRODUCTION The demand for high-performance reinforcing materials has been increasing over the past few years to combat unnecessary repair costs, which are estimated to exceed billions of dollars a year in the U.S.1,2 Extensive research has been conducted in the past few years to evaluate the materials characteristics of different types of high-performance steel. Nevertheless, the resulting impact on existing building codes is sparse in relation to the effort put into research. The lack of information regarding the behavior of concrete members reinforced with this type of material prevents design engineers from using the full strength of the material. Different types of high-performance reinforcing bars are currently being examined by different research institutions and universities worldwide for various structural engineering applications. By metallurgically modifying the microstructure of the steel, the bars are less susceptible to corrosion compared with conventional steel and have a yield strength that is almost twice that of conventional steel. Several demonstration projects including bridge decks, airport control towers, bridge piers, and high-rise condominiums have been constructed successfully using high-strength steel.2 Nevertheless, in most of these applications, the highstrength bars have been used by direct substitution of the amount required for conventional steel and, thus, neglecting the benefits of the higher yield strength of the material. It has been recently reported that the higher yield strength of the material could strongly influence the shear behavior, ultimate load-carrying capacity, and mode of failure of concrete beams reinforced with this type of material.3 The use of highperformance steel reinforcement in concrete footings and mat foundations has an emergent potential to increase longevity and, therefore, lead to substantial savings in the ACI Structural Journal/March-April 2008

life-cycle cost of concrete structures. The high yield strength of the material combined with its enhanced corrosion resistance makes it ideal for substructure applications. In most cases, the depth of footings and mat foundations is controlled by either one- or two-way shear. Therefore, understanding the shear behavior of concrete members reinforced with highperformance steel is essential for a safe and economic design of foundations. Despite numerous comprehensive studies over the last 50 years, understanding of the shear behavior of conventionally-reinforced concrete beams remains unclear. Several international codes,4-6 including the current ACI Building Code (ACI 318-05),4 are based on semi-empirical considerations. The calculated shear strength could vary significantly among different code approaches. Discrepancies up to 250% in the allowable shear stress according to different codes of practice have been reported.7 There is also substantial evidence that the shear stress at failure decreases as the depth of the member increases and as the aggregate size decreases.8-10 Such a phenomenon raises doubt about the use of current shear design provisions for beams without web reinforcement. It should be highlighted that 86% of all available test data compiled by the Subcommittee F of Joint ACI-ASCE Committee 445 pertain to beam depths less than 500 mm (20 in.).9 One of the main factors affecting the nominal concrete shear strength is the ability of concrete to transfer shear across cracks in the web of the beams. Softening of the concrete due to the biaxial state of tension-compression in the web of beams loaded in shear has been investigated by many researchers, and different formulations have been proposed in the past 25 years. It has been observed that these models vary widely even for concrete beams reinforced with conventional steel. Some theories of biaxial softening of concrete do not even predict concrete crushing at very high deformations.11 This paper presents test results of six large-size concrete beams reinforced with either high-strength or conventional Grade 420 MPa (60 ksi) steel and tested up to failure. All the beams were constructed without web reinforcement to evaluate the concrete shear strength. The influence of the shear spandepth ratio (a/d) as well as the type and the amount of longitudinal steel reinforcement is investigated. RESEARCH SIGNIFICANCE Efficient use of the high tensile strength characteristics of the high-performance steel is expected to provide durable ACI Structural Journal, V. 105, No. 2, March-April 2008. MS No. S-2006-398.R1 received October 11, 2006, and reviewed under Institute publication policies. Copyright © 2008, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the JanuaryFebruary 2009 ACI Structural Journal if the discussion is received by September 1, 2008.

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a total length of 4900 mm (16 ft). The dimensions of the beams were selected to be much larger than those used in developing the ACI shear design provisions established in 1962.12 The beams were cast in three batches of different concrete strengths, producing three groups (A, B, and C) of identical dimensions. One beam of each group was reinforced with conventional Grade 420 MPa (60 ksi) steel while the other beam was reinforced with high-strength steel bars. No transverse reinforcement was provided in any of the specimens to evaluate the nominal concrete shear strength. The first group of beams (Group A) was tested at an a/d of 1.9. The influence of the concrete compressive strength on the shear behavior was investigated by testing the second group of beams (Group B) using the same a/d of 1.9, but with a lower concrete compressive strength. The third group of beams (Group C) was tested using an a/d of 2.7 to examine the flexural shear behavior of the beams. The longitudinal reinforcement ratio used in the concrete beams reinforced with high-strength steel was 40% less than that used in concrete beams reinforced with Grade 420 MPa (60 ksi) steel. This reduction in the reinforcement ratio is based on using a yield strength of 690 MPa (100 ksi) for the highstrength steel. The beams are identified by a numbering code. The first letter denotes the type of the longitudinal steel: G for Grade 420 MPa (60 ksi) steel and M for high-strength steel. The second term represents the a/d, while the third number denotes the concrete compressive strength in MPa. Details of the test specimens are given in Table 1. The longitudinal steel was evenly distributed along the width of the specimens leaving 40 mm (1.5 in.) concrete cover on each side. Bottom cover was chosen according to ACI 318-054 for beams subjected to interior exposure. The bottom longitudinal steel bars were hooked upward beyond the supports to preclude the possibility of anchorage failure.

Tarek K. Hassan is an Associate Professor in the Department of Structural Engineering, Ain Shams University, Cairo, Egypt. He received his MSc and PhD from the University of Manitoba, Winnipeg, MB, Canada, in 1999 and 2002, respectively. He is currently a part-time Senior Structural Engineer at Dar Al Handasah Consultants, Cairo, Egypt. His research interests include nonlinear analysis and design of concrete structures, and repair and strengthening of concrete structures using advanced composite materials. ACI member Hatem M. Seliem is a Postdoctoral Research Associate in the Department of Civil, Construction, and Environmental Engineering at North Carolina State University (NCSU), Raleigh, NC. He received his PhD from NCSU in 2007 and his BSc and MSc from Cairo University, Cairo, Egypt, in 2000 and 2002, respectively. His research interests include design of concrete structures using innovative materials and retrofitting of reinforced concrete structures using advanced composite materials. Hazim Dwairi is an Assistant Professor in the Department of Civil Engineering, Hashemite University, Jordan. He received his PhD from North Carolina State University in 2004. His research interests include design and analysis of concrete structures and behavior of structures under lateral loads. Sami H. Rizkalla, FACI, is a Distinguished Professor of Civil and Construction Engineering in the Department of Civil, Construction and Environmental Engineering; Director of the Constructed Facilities Laboratory (CFL); and Director of the NSF Industry/University Cooperative Research Center at North Carolina State University. He is also the immediate Past President and the founder of the Network of Centers of Excellence on Intelligent Sensing of Innovative Structures (ISIS Canada). He is Past Chair and a current member of ACI Committees 118, Use of Computers; 440, Fiber Reinforced Polymer Reinforcement; E803, Faculty Network Coordinating Committee; and a member of Joint ACI-ASCE Committees 423, Prestressed Concrete, and 550, Precast Concrete Structures. ACI Honorary Member Paul Zia is a Distinguished University Professor Emeritus at North Carolina State University. He is a member of ACI Committees 363, HighStrength Concrete, and 440, Fiber Reinforced Polymer Reinforcement; Joint ACIASCE Committees 423, Prestressed Concrete, and 445, Shear and Torsion; ACI TAC Technology Transfer Committee; and the Concrete Research Council.

concrete structures with smaller reinforcement ratios and significantly reduced maintenance requirements compared with conventional steel. The present experimental study allows quantifying the benefits of using high-strength steel and provides experimental evidence of its high strength capabilities. The impact of the high tensile strength of the material on the shear behavior of concrete beams is demonstrated. The study also evaluates the limitations of the current shear design provisions in the ACI Code4 to develop design guidelines that recognize its contribution to the shear strength of concrete beams.

Materials High-strength steel—A commercially available highperformance steel known as microcomposite multistructural formable (MMFX) steel, which conforms to ASTM A1035,13 was selected for this study. Tension coupons were tested according to ASTM A37014 to determine the material characteristics of the bars. Typical stress-strain behavior of the MMFX bars compared with Grade 420 MPa (60 ksi) steel bars is shown in Fig. 1. The high-strength steel bars exhibited a linear stress-strain relationship up to a stress level of 690 MPa (100 ksi), followed by a nonlinear behavior up to failure without a well-defined yield point. According to

EXPERIMENTAL INVESTIGATION Test specimens Six large-size concrete beams were constructed and loaded to failure under concentrated load acting at midspan. The main variables included in the study are the a/d, concrete compressive strength, and the type and amount of the longitudinal steel reinforcement. All the beams had identical nominal cross-sectional dimensions of 460 x 915 mm (18 x 36 in.) with Table 1—Details of test specimens Group A

Group B

Group C

Specimen

G-1.9-51

M-1.9-51

G-1.9-38

M-1.9-38

G-2.7-32

Shear span-depth ratio (a/d)

1.9

1.9

1.9

1.9

2.7

G-2.7-32 2.7

Concrete compressive strength, MPa (psi)

51 (7400)

51 (7400)

38 (5500)

38 (5500)

32 (4650)

32 (4650)

Type of longitudinal reinforcement

G*

M†

G*

M†

G*

M†

Bottom reinforcement ratio, %

0.72

0.44

0.72

0.44

0.72

0.44

Top reinforcement ratio, %

0.36

0.22

0.36

0.22

0.36

0.22

Diagonal cracking load, kN (kips)

670 (150)

670 (150)

670 (150)

670 (150)

445 (100)

445 (100)

Failure load, kN (kips)

871 (195)

1560 (350)

753 (170)

1364 (306)

552 (124)

638 (143)

Predicted failure load using ACI 318-05, kN (kips)

1103 (248)

1917 (431)

1103 (248)

1418 (319)

690 (155)

690 (155)

PTest /PACI 318-05

0.8

0.81

0.68

0.96

0.80

0.92

*

G refers to Grade 60 steel. †M refers to high-strength steel.

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ACI Structural Journal/March-April 2008

ASTM A37014 offset method (0.2%), the yield strength of the bars was determined to be 827 MPa (120 ksi). The measured initial modulus of elasticity of the bars was 200 GPa (29,000 ksi) up to a stress level of 690 MPa (100 ksi), beyond which a considerable reduction in the modulus of elasticity was observed. Based on test results, the average ultimate tensile strength was 1120 MPa (162 ksi). Grade 420 MPa (60 ksi) steel—The Grade 420 MPa (60 ksi) reinforcing bars used in the current study met the requirements of ASTM A615.15 Based on tension coupon tests, the bars had an average modulus of elasticity and yield strength of 200 GPa (29,000 ksi) and 469 MPa (68 ksi), respectively.

Fig. 1—Typical stress-strain behavior for conventional and high-strength steel.

Concrete—All beams were cast with normal-strength concrete with a maximum aggregate size of 19 mm (0.75 in.) using three different batches of concrete. The compressive strength of the concrete was determined based on the average of at least three 100 x 200 mm (4 x 8 in.) cylinders cast from the same batch of concrete and cured under the same conditions as the beams. The measured concrete compressive strength for different specimens is given in Table 1. Test setup The beams were tested under a concentrated load acting at midspan, as shown in Fig. 2. The load was applied using a 2000 kN (450 kips) hydraulic actuator. The beams were supported on either steel I-beams or concrete blocks secured to the strong floor. Neoprene pads were placed between the concrete beam and the supports to allow for rotation at both ends of the beam. A 25 mm (1 in.) thick steel plate was attached to the actuator to distribute the load to the beam. Neoprene pads were placed between the loading plate and the concrete surface to prevent local crushing of the concrete. Each beam was instrumented to measure the vertical deflections at midspan and at the supports using string potentiometers. Twelve horizontal and vertical linear potentiometers were used to measure diagonal crack widths. Two PI gauges were attached to the top and bottom of the beam at midspan to measure the concrete deformation. All the data were continuously recorded up to failure. Instrumentation layout is shown in Fig. 3 and 4 for beams with a/d of 1.9 and 2.7, respectively. EXPERIMENTAL RESULTS AND DISCUSSION Deflections The load-deflection behavior of the test specimens of Group A having an a/d of 1.9 and a concrete compressive

Fig. 2—Details of test specimens. ACI Structural Journal/March-April 2008

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Fig. 4—Instrumentation layout of beams with a/d of 2.7.

used in Specimen M-1.9-51, resulting in higher steel strain and probable higher localized bond slip. The behavior of concrete beams having the same a/d of 1.9 but constructed with a lower concrete compressive strength of 38 MPa (5500 psi) was investigated using Group B test specimens. To simulate overloading conditions, both Specimens G-1.9-38 and M-1.9-38 of Group B were initially loaded to a load level of 450 kN (100 kips) and unloaded. The specimens were reloaded up to failure to evaluate the post-cracking stiffness for both specimens. The load-deflection behavior of the second load cycle is shown in Fig. 6. The measured post-cracking stiffness of Specimen G-1.9-38, reinforced with Grade 420 MPa (60 ksi) steel, was 50% higher than that of Specimen M-1.9-38, which is reinforced with high-strength steel but with a reduced reinforcement ratio. The load-deflection behavior of Group C beams with an a/d of 2.7 and concrete strength of 32 MPa (4650 ksi) is shown in Fig. 7. Similar to Group B specimens, the two specimens, G-2.7-32 and M-2.7-32, were loaded to 225 kN (50 kips) and unloaded before loading to failure to simulate overloading conditions. The beam reinforced with high-strength steel (M-2.7-32) exhibited higher deflections than the beam reinforced with Grade 420 MPa (60 ksi) steel (G-2.7-32) at the same load level. This behavior is attributed to the smaller area of reinforcing steel used and higher induced steel strain and probable more localized bond slips. In general, concrete beams reinforced with Grade 420 MPa (60 ksi) steel reinforcement exhibited less post-cracking deflection at the same load level compared with beams reinforced with high-strength steel because the latter had a reduced reinforcement ratio. For beams reinforced with Grade 420 MPa (60 ksi) steel, failure was sudden and was preceded by relatively little cracking. The measured ultimate midspan deflection for the three beams reinforced with Grade 420 MPa (60 ksi) steel was less than the span/470. A less brittle behavior was observed for the beams reinforced with high-strength steel. Considerable deflections and much wider cracks were observed for these beams prior to failure. At failure, the deflections for the beams reinforced with the high-strength steel and having an a/d of 1.9 were equivalent to the span/230, twice the deflections of the beams reinforced with Grade 420 MPa (60 ksi) steel.

Fig. 5—Load-deflection behavior of Group A specimens.

Fig. 6—Load-deflection behavior of Group B specimens.

strength of 51 MPa (7400 psi) is shown in Fig. 5. For both specimens, linear behavior was observed up to the initiation of the first flexural crack at a load level of 370 kN (83 kips) followed by nonlinear behavior up to failure. Following the formation of the flexural cracks, a major diagonal shear crack developed and became visible in both specimens at a load level of 670 kN (150 kips). After cracking, the measured deflections of the concrete beam reinforced with high-strength steel (Specimen M-1.9-51) were significantly higher than those measured for the concrete beam reinforced with Grade 420 MPa (60 ksi) steel (Specimen G-1.9-51). This behavior is attributed to the reduced reinforcement ratio

Fig. 3—Instrumentation layout of beams with a/d of 1.9.

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Crack pattern For all specimens, flexural cracks were first initiated under the applied load. With further increase of load, new flexural cracks formed in the shear spans and curved toward the loading area. The first diagonal shear crack was observed at the same load level for identical specimens regardless of the type of reinforcement. For specimens reinforced with Grade 420 MPa (60 ksi) steel with an a/d of 1.9, the first diagonal shear crack was observed at a load level equivalent to 80% of the ultimate load. A similar crack was observed at a load level of approximately 45% of the ultimate load for the beams reinforced with high-strength steel. Such a phenomenon demonstrates the reserved capacity for these beams and provides adequate warning prior to shear failure. Figure 8(a) depicts a typical crack pattern at the initiation of diagonal shear cracks for Specimens M-1.9-51 and M-2.7-32, reinforced with high-strength steel and having a/d of 1.9 and 2.7, respectively. Diagonal cracking loads for all the specimens are given in Table 1. The width of the major diagonal shear crack for different specimens is shown in Fig. 8(b). The figure clearly shows that the major diagonal shear crack in the beams reinforced with high-strength steel was almost three times wider than that observed in identical beams reinforced with Grade 420 MPa (60 ksi) steel before failure. This is attributed to the reduced reinforcement ratio used for high-strength steel.

Beams reinforced with high-strength steel—Failure was controlled primarily by the compressive strength of the diagonal strut (compression shear failure). The high yield strength of the materials precluded diagonal tension failure and allowed the failure to take place in the concrete strut at much higher

Failure mode Beams reinforced with Grade 420 MPa (60 ksi) steel— Diagonal tension failure was observed for the three concrete beams reinforced with Grade 420 MPa (60 ksi) steel. Failure occurred due to extension of the diagonal shear crack rapidly toward the load point shortly after its initiation. Strain measurements at the bottom of the concrete beams at midspan implied that yielding of the conventional steel reinforcement governed the failure mode. A separate nonlinear finite element study16 confirmed the observed behavior and indicated yielding of the longitudinal conventional reinforcement at the location of shear cracks, as shown in Fig. 9 for Specimen G-1.9-51. Upon yielding of the longitudinal steel reinforcement at the location of a shear crack, the section was no longer capable of resisting any additional increase in load and the concrete beams failed abruptly in shear. Detailed information about the finite element modeling is reported elsewhere.16

Fig. 8—(a) Crack pattern at initiation of diagonal shear crack; and (b) diagonal crack width of different specimens.

Fig. 7—Load-deflection behavior of Group C specimens. ACI Structural Journal/March-April 2008

Fig. 9—Typical tensile strain distribution at ultimate of concrete beams reinforced with conventional Grade 60 steel.16 177

loads. Typical tensile strains at the midspan section, for Groups B and C, are shown in Fig. 10 and 11, respectively. The figures show that at ultimate, the measured tensile strain in the high-strength steel bars exceeded its yield strain defined by the 0.2% offset method. Typical shear failure of concrete beams reinforced with Grade 420 MPa (60 ksi) and high-strength steel is shown in Fig. 12. Concrete shear strength Despite the reduction in the reinforcement ratio, the shear strength of concrete beams reinforced with high-strength steel was significantly higher than that of the beams reinforced with Grade 420 MPa (60 ksi) steel. The high yield strength of the material maintained the capacity of the tension tie and allowed the beams to resist more load until crushing of the diagonal strut occurred. This behavior was highly pronounced for beams with a small a/d (a/d = 1.9). The ultimate load-carrying capacity of Specimen G-1.9-51, reinforced with Grade 420 MPa (60 ksi) steel and having an a/d of 1.9, was 871 kN (195 kips). Test results showed that the concrete shear strength could be increased by 80% but using 40% less area of high-strength steel (Specimen M-1.9-51). Similar behavior was observed for Specimens G-1.9-38 and M-1.9-38. As the tensile stress in the high-strength steel bars approached its yield strength, wide cracks were observed

and the beneficial effect of using high-strength steel started to attenuate. Such a phenomenon was clearly observed for beams with an a/d of 2.7. Using high-strength steel as main longitudinal reinforcement in these beams increased the shear strength by only 16% while using 40% less steel. Failure loads for all specimens are summarized in Table 1. COMPARISON WITH ACI 318-05 Beams with a/d of 1.9—A simple strut-and-tie model was developed as required by the ACI 318-054 for beams with a clear span less than four times the depth of the beam. The strut-and-tie model consisted of a direct strut extending from the loading plate to the reaction bearing plate, as shown in Fig. 13. Failure mechanisms governing the strength were typically crushing of the compressive strut or yielding of the tie reinforcement. To account for the nonlinear stress-strain behavior of high-strength steel, an exponential stress-strain relationship was assumed as reported by the Concrete Innovation Appraisal Services.17 The bearing dimensions were sufficiently large to avoid crushing of the concrete at the nodes in the strut-and-tie model. The predicted ultimate capacities for different specimens are given in Table 1. In

Fig. 10—Load-tensile strain behavior of Group B specimens.

Fig. 12—Typical shear failure for beams reinforced with conventional and high-strength steel.

Fig. 11—Load-tensile strain behavior of Group C specimens. 178

Fig. 13—Strut-and-tie model for beams with a/d of 1.9. ACI Structural Journal/March-April 2008

general, the analysis indicates that ACI 318-054 overestimated the capacity of concrete beams reinforced with either conventional- or high-strength steel. For Specimens G-1.9-51 and G-1.9-38 reinforced with Grade 420 MPa (60 ksi) steel, failure was controlled by yielding of the tie. The predicted capacity was independent of the concrete compressive strength and, therefore, identical capacities were predicted for both specimens. Conversely, crushing of the compressive strut was the governing mode of failure for Specimens M-1.9-51 and M-1.9-38, reinforced with high-strength steel. Increasing the concrete compressive strength by 34% increased the predicted capacity by the same magnitude. The analysis demonstrated the influence of the concrete compressive strength on the shear strength of the concrete beams reinforced with high-strength steel. The capacity of the compressive strut was taken as 0.51fc′, where fc′ is the specified compressive strength of concrete. It should be highlighted that, according to ACI 318-05, the compressive capacity of the strut is independent of the tensile strain in the reinforcement. Beams with a/d of 2.7—The nominal concrete shear strength vc was predicted according to ACI 318-05 using Eq. (1) vc = 0.167 f c′ (MPa) (1 MPa = 145 psi)

(1)

The ACI 318-054 design method considerably overestimated the shear strength of large-size concrete beams constructed without web reinforcement. The diagonal shear crack was initiated in the beams with an a/d of 2.7 and became visible at a load level of 445 kN (100 kips), which corresponds to 0.11 f c′ MPa. The predicted capacity for Specimen G-2.7-32, reinforced with conventional steel, was 25% higher than the measured value (shear strength corresponds to 0.134 f c′ MPa). It should be noted that the current ACI shear provisions were based on testing shallow beams,13 which did not account for the size effect of large-size beams. CONCLUSIONS Based on the findings of this investigation, the following conclusions can be drawn: 1. High-strength steel strongly influenced the shear behavior of the concrete beams tested in the current study and constructed without web reinforcement. Ignoring the high strength characteristics of the material could provide unreliable predictions of the ultimate load-carrying capacity and mode of failure; 2. The diagonal cracking strength is a measure of the concrete contribution at ultimate for members reinforced with conventional steel and constructed without web reinforcement. Such a relationship is inappropriate for high-strength steel as the behavior is strongly influenced by the a/d and the stress level in the bars. Test results showed that initiation of diagonal shear cracks is independent of the type or the amount of the longitudinal reinforcement; 3. Concrete beams reinforced with Grade 420 MPa (60 ksi) steel and constructed without web reinforcement exhibited a very brittle failure due to yielding of the longitudinal steel reinforcement. Shear failure occurred shortly after initiation of the shear crack; 4. Despite the reduction in the reinforcement ratio by 40%, the shear strength of concrete beams reinforced with highstrength steel was significantly higher than that of the beams reinforced with Grade 420 MPa (60 ksi) steel. The high yield strength of the material maintained the capacity of the


tension tie, and thus enabled the beams to resist more load until crushing of the diagonal strut occurred; 5. A significant reserve in strength was observed for beams reinforced with high-strength steel after diagonal cracking. Failure was due to crushing of the diagonal concrete strut at much higher loads compared with beams reinforced with conventional steel; and 6. The ACI 318-05 simplified expression for the shear contribution of concrete is unconservative for large-size concrete beams without web reinforcement. The expression needs to account for the size effect and the reinforcement characteristics. ACKNOWLEDGMENTS The authors gratefully acknowledge the donation of the materials provided by MMFX Technologies Corp., CA. Special thanks are extended to A. Hosny, E. Thorup, and J. Atkinson at the Constructed Facilities Laboratory for their valuable help during the experimental program.

REFERENCES 1. Reis, H.; Ervin, B. L.; Kuchma, D. A.; and Bernhard, J. T., “Estimation of Corrosion Damage in Steel Reinforced Mortar Using Guided Waves,” Journal of Pressure Vessel Technology, V. 127, No. 3, 2005, pp. 255-261. 2. Darwin, D.; Browning, J.; Nguyen, T. V.; and Locke, C., “Mechanical and Corrosion Properties of a High-Strength, High Chromium Reinforcing Steel for Concrete,” SM Report No. 66, University of Kansas, Lawrence, KS, 2002, 106 pp. 3. Seliem, H.; Hosny, A.; Dwairi, H.; and Rizkalla, S., “Shear Behavior of Concrete Beams Reinforced with MMFX Steel Without Web Reinforcement,” Report No. IS-06-08, Constructed Facilities Laboratory, North Carolina State University, Raleigh, NC, 2006, 21 pp. 4. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (318R-05),” American Concrete Institute, Farmington Hills, MI, 2005, 430 pp. 5. Commission of the European Communities, “Design of Concrete Structures. Part 1: General Rules and Rules for Buildings,” Eurocode 2, 2003, 330 pp. 6. DIN 1045-1, Deutsche Norm, “Concrete, Reinforced and Prestressed Concrete Structures—Part 1: Design,” Normenausschuss Bauwesen (NABau) im DIN Deutsches Institut fur Normung e. V. Beuth Verlag, Berlin, Germany, 2001, pp. 1-48. 7. Hawkins, N. M.; Kuchma, D. A.; Mast, R. F.; and Reineck, K., “Simplified Shear Design of Structural Concrete Members,” NCHRP Report 549, Washington, DC, 2005, 54 pp. 8. Kani, G. N. J., “How Safe are Our Large Reinforced Concrete Beams?” ACI Structural Journal, V. 64, No. 4, Apr. 1967, pp. 128-141. 9. Bažant, Z. P., and Yu. Q., “Designing Against Size Effect on Shear Strength of Reinforced Concrete Beams without Stirrups: Formulation,” Journal of Structural Engineering, ASCE, V. 131, No. 12, 2005, pp. 1877-1885. 10. Sherwood, E. G.; Bentz, E. C.; and Collins, M. P., “Evaluation of Shear Design Methods for Large, Lightly-Reinforced Concrete Beams,” Proceedings of the Advances in Engineering Structures, Mechanics and Construction, ON, Canada, 2006, pp. 153-164. 11. Duthinh, D., “Senstivity of Shear Strength of Reinforced Concrete and Prestressed Concrete Beams to Shear Friction and Concrete Softening According to Modified Compression Field Theory,” ACI Structural Journal, V. 96, No. 4, July-Aug. 1999, pp. 495-508. 12. Joint ACI-ASCE Committee 326, “Shear and Diagonal Tension,” ACI JOURNAL, Proceedings V. 59, No. 1-3, Jan.-Mar., 1962, pp. 1-30, 277-344, and 352-396. 13. ASTM A1035-07, “Standard Specification for Deformed and Plain, Low Carbon, Chromium, Steel Bars for Concrete Reinforcement,” ASTM International, West Conshohocken, PA, 2007, 5 pp. 14. ASTM A370-07, “Standard Test Methods and Definitions for Mechanical Testing of Steel Products,” ASTM International, West Conshohocken, PA, 2007, 47 pp. 15. ASTM A615-06, “Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement,” ASTM International, West Conshohocken, PA, 2006, 6 pp. 16. Hassan, T., “Behavior of Concrete Deep Beams Reinforced with High Strength Steel,” Ain Shams Scientific Bulletin, V. 41, No. 3, 2007, pp. 109-127. 17. Concrete Innovation Appraisal Services, (CIAS), “Structural Design Criteria for High-Strength MMFX Microcomposite Reinforcing Bars,” CIAS Report: 04-1, 2004, 34 pp.

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