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    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME TECHNOLOGY (IJCIET) ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October, pp. 152-167 © IAEME: www.iaeme.com/ijciet.asp Journal Impact Factor (2013): 5.3277 (Calculated by GISI) www.jifactor.com IJCIET ©IAEME EXPERIMENTAL VERIFICATION OF THE MINIMUM FLEXURAL REINFORCEMENT FORMULAS FOR HSC BEAMS M. SAID1 & T. M. ELRAKIB2 1 Lecturer, Civil Eng. Dep., Shoubra Faculty of Eng., Benha University, Egypt 2 Lecturer, Housing and Building National Research Center, Cairo, Egypt ABSTRACT The main objective of the current research is to establish experimental data for minimum flexural reinforcement, ρmin, of high strength concrete (HSC) rectangular beams. Nine full-scale singly reinforced beams with flexural reinforcement ratios varying from 50% to 100% of the minimum limit specified by the ACI 363R-35 were tested in flexure. Concrete compressive strengths of 52, 73 and 96.5 MPa were used. The test results including crack patterns, deflections and strains in the tensile flexural steel bars show that a 25 % reduction of the ACI 363R-35 limit for the ρmin would result in a satisfactory flexural beam behavior. The experimental results of this study are compared with the limits specified by available codes and researches. Keywords: High Strength Concrete, Beams, Minimum Reinforcement, Ductility. INTRODUCTION High strength concrete (HSC) provides a better solution for reducing sizes and weights of concrete structural elements. The major part of the application of high strength concrete concerns particular structures such as offshore platforms and the lower story columns of high-rise buildings. HSC correlates with improvements in its other engineering properties (tensile strength, creep coefficient, etc.), however, it fractures suddenly and forms a smooth failure plane [1, 2]. However, in designing a reinforced concrete member, it is important to insure that the member will not exhibit brittle failure and will be capable of sustaining large deformations near maximum load. This capability gives ample prior warning before failure. Because concrete becomes increasingly more brittle as its compressive strength is increased, guaranteeing adequate ductility represents one of the primary design concerns when HSC is involved. Moreover, in some situations and for one reason or another, the concrete section dimensions are bigger than required by strength consideration to the extent that the flexural element does not need tensile 152
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME steel reinforcement to carry its service loads. If the amount of flexural reinforcement is very small, the cracking moment (i.e. the flexural strength computed from the modulus of rupture of concrete) will exceed the flexural strength of the reinforced concrete section and a suddenly brittle failure may occur with the formation of first crack, [3-5].Accordingly, a l l current national and international codes of practice of reinforced concrete structures s t i l l require a minimum amount of flexural reinforcement to be provided in these elements, including beams. According to most of these codes, the minimum flexural reinforcement ratio, ρmin is the one that would result in the ultimate moment of the cracked section being at least equal or larger than the cracking moment of the gross section (i.e. Mu /M cr≥1.0). This condition is stated to be adequate enough to fulfill the previous requirements of crack control and prevention of the b r i t t l e failure[2-5].According to the previous condition, the minimum flexural reinforcement ratio ρmin is inversely proportional with fyand it should be pointed out that Mu would be higher if the strain hardening of the reinforcing steel is considered. If this is taken into account, it will be possible to reduce the required ρmin. Boscoet al[1] Proposed a dimensional analysis criterion based on a fracture mechanics model to compute the minimum amount of reinforcement for HSC beams in flexure. He concluded that the minimum flexural reinforcement provided by the ACI Code expression is inadequate for HSC, Eq.1. ρmin=1.4/fy(MPa) (1) Equation [1] does not include the concrete strength as a parameter. With the extensive use of higher strength concrete, it was shown that Eq. [1] would yield inadequate reinforcement ratios because it was based on test results obtained from beams made of NSC. The expression given below is provided by ACI 318-08 [6] and ACI 363R-35[7] to be effective for HSC as well as the NSC. ρmin = 0.25(f’c)0.5/fy>1.4/fy(MPa) (2) The expression of the Canadian standards CSA (A23.3-04)[8] for ρmin is as follows: ρmin = 0.20(f’c)0.5/fy(MPa) (3) The limit of validity is given as 20MPa >f’c>80MPa. It is clearly noted that the ACI 363R-35 expression results in 25% more reinforcement than the CSA (A23.3-04). In addition, the formula of the Japanese Standards JSCE [9] for ρmin is: ρmin = 0.058 (h/d)2(f’c)0.66/fy(MPa) (4) Where h is the total height of beam and d is the effective depth. JSCE code states that the previous formula should be used only for f’c≥35 MPa with a fixed value of ρmin = 0.002 for lower values of f’c. On the other hand, El-Saie, A. [10] tested seven T-section beams to determine the minimum amount of flexural reinforcement in HSC with fcu equals only 80 MPa for all tested beams. One of the beams was plain concrete, three beams reinforced with high grade steel and three beams reinforced with mild-grade steel. The tensile strength of the HSC was measured by using the modulus of rupture fr .Test results show that the tensile strength of HSC as measured by the modulus of rupture fr =0.98 (f’c) 0.5MPa which is higher than the ACI 363 R-35 formula by about 48%. Based 153
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME on a proposed empirical expression, Mu/Mcr=1.45, a new formula for the ρmin in HSC beams was suggested as follows: ρmin = 0.25{(f’c)0.5/fy}{1-0.5(1+[((B/b)-1)*(ts/t)2]/+[((B/b) -1)*(ts/t)]} (5) Where B= flange width, b= web width, ts = slab thickness and t= total beam height. Accordingly, in case of rectangular section, ρmin = 0.125 (f’c) 0.5/fy which represents 50% of the ACI 363R-35 limit. However, the researcher didn't mention any results about the ductility of the tested beams. Recently, Rizk et al [4] tested sex thick HSC slabs having small ratios of flexural reinforcement. The main test variables included concrete compressive strength, reinforcement ratio and slab effective depth. Based on the experimental test results, it was concluded that ACI 318-08[6] and CSA (A23.3-04) [8] codes overestimate ρmin required for thick HSC slabs greater than 250 mm. It was also reported that the value of ρ min tends to be inversely proportional to the slab effective depth. A new model that uses the fracture mechanics concepts to account for the size effect was suggested as follows: ρmin = 0.236(125/d)0.33(f’c)0.5/fy(MPa) (6) Where d is the effective depth. It was mentioned that the application of the new formula can result in a saving of steel reinforcement. However, all the previous limits for ρmin are based on empirical equations that sometimes are conservative and, hence, may be uneconomic. In addition, Rashid M. et al [5] stated that, based on the current code provisions it can be analytically observed that an increase in concrete strength leads to higher ductility. Experimental evidence reported by other researchers [11-13] supports this prediction except for Ashour[2]. In his study, [2], test results showed enhanced ductility for higher strength concrete beams but only up to a concrete strength of around 80MPa then ductility decreases as the concrete strength are increased. So, further experimental evidence embracing concrete with compressive strength greater than 80MPa is therefore necessary. The diversity of the previous limits and observations clearly reveals the need for further research in t h i s area, in order to evaluate the validity of the available formulas from the economic point of view, as well as try to establish a more accurate limit for the minimum reinforcement ratio in HSC beams. This paper presents experimental results of nine full scale rectangular HSC beams reinforced in flexure w i t h small amounts of steel bars to examine the available formulas for ρmin in HSC. The tested parameters are flexural reinforcement ratio, ρ, and the concrete compressive strength, fcu. The flexural reinforcement ratio ranges from 0.50 to 1.0 times ρmin specified by the ACI 363R-35 and the target concrete compressive strength is 50, 75 and 100MPa. EXPERIMENTAL WORK Test Specimens The experimental test program included nine RC beams 250x400x3500 mm. All beams were constructed in the laboratory of the Housing and Building National Research Center and tested under two point loads. Details of the beams are shown in Fig.1. The shear spans were the same for all beams, i.e. (a/d) =3.60. Since very low ratios of flexural reinforcement were used, the flexural capacity of all test specimens was lower than the diagonal cracking capacity. Therefore, no shear cracks were expected. However, steel stirrups, R8@150mm, were provided in the shear span as an extra precaution, R denotes normal grade bars. These stirrups and the top bars holding the stirrups 154
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME were terminated at the boundaries of the constant moment region. Test specimens were grouped into three series according to their concrete compressive strength (50, 75 and 100MPa). Each series consisted of three beams. In each series, three different reinforcement ratios were used. The properties of the test specimens are summarized in Table 2. In some specimens, two bars different in size and yield stress were used in the longitudinal reinforcement. In calculating the required minimum flexural reinforcement ratio, the weighted average of the yield stress was used for these specimens. Concrete clear cover of approximately 15 mm was provided for all beams. After casting, test beams were cured for fourteen days by continuous spraying of water. In addition, six standard cubes 150*150*150 mm were cast from each mix as control specimens to evaluate the actual concrete compressive strength fcu. These cubes and beams were cured and tested on the same day of testing the corresponding specimens. Table 2 Details of test specimens Series Specimen Target compressive strength fcu, MPa B501 ^ + Longitudinal reinforcement, As Yield stress fy ,MPa #ρmin*10-3 ρ*10-3 #(ρ/ρmin) 1.69 0.51 2 T 12 515 3.10 2.39 0.77 2 T 12 + 1 T 10 501 3.17 3.23 1.02 1 T 12 + 1 T 10 495 3.93 2.04 0.52 1 T 12 + 2 T 10 501 3.96 2.89 0.73 B753 2 T 12 + 2 T 10 495 3.93 4.05 1.03 B1001 3 3.31 B751 2 480 B503 1 2 T 10 3 T 10 480 4.68 2.48 0.53 4 T 10 480 4.68 3.37 0.72 3 T 12 + 1 T 10 506 4.44 4.45 0.99 B502 B752 B1002 B1003 50 75 100 + T denotes high grade deformed bars, and the following number indicates the diameter in mm. fy was calculated using the weighted average of the yield strength for different sizes of bars. #According to ACI 363-R35 ^ Materials Three different concrete mixes were used in casting the test specimens. The mixes were designed to obtain compressive strengths of 50,75 and 100MPa. Ordinary Portland cement, siliceous sand, coarse aggregates size 10 mm, Silica fume and super-plasticizer type F [7] were used with the quantities shown in Table 3 for each mix. Concrete compressive strength, fcu, given in Table 3for each mix represents the average of six uniaxially loaded standard cubes. Two different sizes of deformed steel bars were used as flexural reinforcement, 10 and 12 mm in diameter, having yield stress of 480, 515MPa, respectively. Mild steel with fy=380 MPa, denoted R, was used for stirrups and top bars. 155
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME Table 3 Mix Proportions of the Three Concrete Grades Super plasticizer Liter/m3 Actual compressive strength, fcu (MPa) 0.30 10 52 580 0.24 18 74 580 0.20 40 96.5 Series Cement (kg/m3) Silica fume Kg/m3 Dolomite Kg/m3 Sand Kg/m3 W/C 1 450 15 1180 640 2 575 50 1100 3 750 100 1200 Instrumentation and Test Procedure Test specimens were instrumented to measure the applied load, mid-span deflection, and strains of longitudinal reinforcement in the constant moment region. A general view of the instrumentation is shown in Fig.1. A Linear variable displacement transducer (LVDT) for measuring vertical deflection was mounted at the bottom side of the midspan for each specimen. Two electrical resistance strain gauges mounted on the bottom reinforcing bars were used to measure the strains up to yielding. The locations of the strain gauges are also shown in Fig1. The load was distributed equally by a spreader beam to two points along the specimen to generate a constant moment region at midspan. At each load stage, the electrical strain gauges, load cells and (LVDT) voltages were fed into the data acquisition system. The voltage excitations were read, transformed and stored as micro strains, force, and displacement by means of a computer program that runs under the Lab View software. All specimens were tested three months after casting. HYDRAULIC JACK P LOAD CELL 250 R8@150 mm 400 400 2R8 * As, refer to Table 2 x sec.x 1300 100 1300 3300 * strain gauge 250 y sec.y 100 Elvation LVDT Fig. 1: Test Setup and Details of the Tested Beams 156
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME TEST RESULTS AND ANALYSIS The adequacy of the flexural reinforcement for the tested beams will be evaluated by considering both of the reserve strength beyond flexural cracking and displacement ductility index. Presently, there are no generally accepted criteria for such an evaluation. A reserve strength parameter can be defined as the ratio of the yield load to the cracking load (Py/Pcr) or as the ratio of the ultimate load to the cracking load (Pu/Pcr). Since tested beams, having low flexural reinforcement, are under reinforced, their behavior was expected to be ductile. Behavior of Test Specimens In all specimens, flexural cracks were observed first in the constant moment region. As the load was increased, tension reinforcement yielded, which resulted in a significant increase in the crack width and the deflection. No shear cracks were observed till the end of the test. Crack patterns of the tested beams at the end of the test indicate that the final crack width increased as the reinforcement ratio decreased. Table 4 presents the experimentally obtained cracking, yielding and ultimate loads for the tested beams. The experimental cracking load, Pcr corresponds to the load at which the initial cracking was observed on the test specimen and was confirmed by the deviation of the load-deflection curve. The experimental yielding load, Py, corresponds to the load at which yielding flat plateau is observed in the load-deflection curve. The experimental ultimate load, Pu is the peak load reached during testing. The test results showed that the concrete compressive strength had more influence on the cracking load than the flexural reinforcement ratio, and that the flexural reinforcement had an obvious influence on the yielding and ultimate loads. At this very low range of flexural reinforcement ratios for the tested beams, lower or around the ρmin limit of the ACI 363R-35, it was noted that the initiation, the development, the distribution and the widths of flexural cracks were highly sensitive to the flexural reinforcement ratio. In addition, the beams behavior, the ratio between their ultimate to cracking loads were also sensitive to the flexural reinforcement ratios provided, see in Table 4. Beams B 5 0 1 , B 7 5 1 a n d B 1 0 0 1 w i t h flexural reinforcement ratio ρ≈ 0.5ρmin, according to ACI 363R-35 formula, had ultimate loads of45.6, 50.7 and 66.5kN, after the initiation of the first crack at a load of 37.5, 39.2 and 43.9 kN, respectively. The failure mode of these beams was characterized by a few flexural wide cracks, as shown in Fig. 2. This semi-ductile type of failure of t h e s e b e a m s and the low margin between its cracking and ultimate loads, refer to Table 4, are clearly due to flexural reinforcement ratio which is much lower than the minimum limit required by the ACI 363R-35. Beams B 5 0 2 , B 7 5 2 a n d B 1 0 0 2 with flexural reinforcement ratio ρ≈ 075 ρmin, according to ACI 363R-35, had ultimate loads of 76.3, 81.2and89.3kN, respectively. The first crack loads were 44.5, 46.1 and 47.8 kN, respectively. Unlike the previous group (B 5 0 1 , B 7 5 1 a n d B 1 0 0 1 ) , the failure of these beams (B 5 0 2 , B 7 5 2 a n d B 1 0 0 2 ) was characterized by a larger number of cracks with smaller widths, as shown in Fig. 2. Although the flexural reinforcement ratios µ of (B 5 0 2 , B 7 5 2 a n d B 1 0 0 2 ) were still lower than the minimum limit ρmin required by the ACI 363R-35, it can be noted that a better uniform crack distribution and a higher margin between the cracking and the ultimate loads were the main outlines of the behavior, see Table 4 . This gives an initial indication that the ρmin of the ACI 363R35 is overestimated and could be reduced by about 25 % without harmful effect on the beam behavior. Other tested beams with flexural reinforcement ratios ≈ ρmin, according to ACI 363R-35, which are B 5 0 3 , B 7 5 3 a n d B 1 0 0 3 , had ultimate loads of 90.2, 114.9 and 134.3kN, 157
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME respectively. The cracking loads of these beams were 47.3, 50.5 and 53.4kN. The failure of these beams was characterized by an increasingly growing number of cracks with smaller widths, as shown in Fig.2. Such expected increased uniformity in the crack distribution as well as the increased margin between the cracking and the ultimate loads were due to the increase in the corresponding flexural reinforcement ratio, ρ that resulted in a better moment distribution and hence, a better beam behavior. However, it was noted that the ratio of the yield load to the cracking load increased with increasing the reinforcement ratio, ρ, see Table 4 . Table 4: Experimental Results of the Tested Beams Beam Pcr, (kN) Py, (kN) Pu, (kN) Py,/Pcr Pu,/Pcr, ∆y mm ∆f mm *λ∆=∆f/∆y B501 B502 B503 37.6 44.5 47.3 39.4 56.9 83.1 45.6 76.3 90.2 1.05 1.29 1.76 1.21 1.72 1.91 6.7 7.3 8.2 56.3 76.2 91.8 8.4 10.3 11.2 B751 B752 39.3 46.1 45.3 63.5 50.7 81.2 1.15 1.38 1.29 1.76 6.9 7.5 74.5 92.3 10.8 12.3 B753 50.5 103.5 114.9 2.01 2.23 8.6 115.2 13.4 B1001 43.9 53.8 66.5 1.22 1.51 9.8 63.7 6.5 B1002 47.8 78.2 89.3 1.63 1.87 11.8 99.1 8.5 B1003 53.4 113.7 134.3 2.13 2.51 12.6 123.5 9.8 *Displacement Ductility Index Fig 2-a: Crack Pattern of Series 1 158
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME Fig 2-b: Crack Pattern of Series 2 Fig 2-c: Crack Pattern of Series 3 Load-Deflection Behavior The applied load was plotted against the vertical deflection measured at midspan for all tested beams as shown in Fig3. It may be seen that four distinctly different segments, separated by four significant events that took place during the loading history, can idealize a typical load-deflection curve. Labeled as A, B, C and D, these events may be identified as first cracking, yielding of tensile reinforcement, initiation of concrete crushing and failure of concrete compression zone, respectively. The first two events were associated with a reduction in beam stiffness, while the remaining two events led to a reduction in the applied load. In between, a straight line may approximate the curve, 159
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME Fig. 3-a. The effects of different parameters on the load-deflection behavior of test beams are presented in Figs. 3-b to 3-d. C Applied Load B A ABCD- F ir s t c r a c k D S t e e l y ie ld in g I n itia ti o n o f c o n c r e te c r u s h in g C o n c r e te C r u s h in g D e f l e c t io n Fig 3-a: Idealized Load- Deflection Curve 100 B503 80 Load, kN 60 B502 40 B501 B501,ρ=0.50ρmin 20 B502,ρ=0.75ρmin B503,ρ=ρmin 0 0 20 40 60 80 100 Displacement, mm Fig 3-b: Load-Deflection Relationship for Series 1, fcu=50MPa 120 B753 B751 100 Load, kN 80 B752 B751 60 40 B751 B751 20 B751,ρ=0.50ρmin B752,ρ=0.75ρmin B753,ρ=ρmin 0 0 20 40 60 80 100 120 140 Displacement, mm Fig 3-c: Load-Deflection Relationship for Series 2,fcu=75MPa 160
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME 140 B1003 120 Load, kN 100 80 B1002 60 B1001 40 B1001,ρ=0.50ρmin 20 B1002,ρ=0.75ρmin B1003,ρ=ρmin 0 0 20 40 60 80 100 120 140 Displacement, mm Fig 3-d: Load-Deflection Relationship for Series 3,fcu=100MPa Fig. 4-a shows the reserve flexural parameter (Py,/Pcr) at first yielding beyond the cracking strength as a function of the f lexural reinf orcement ratio ρ. Generally, it was noted that the ratio (Py,/Pcr) was increased with increasing f lexural reinforcement ratio µ. Examining Fig. 4-a, it can be concluded that as the concrete compressive strength increases a higher reinforcement ratio is required to achieve a specific reserve flexural capacity. ACI 318-08 requires providing at least one-third more flexural reinforcement than t h a t required by analysis, i . e . , (Py,/Pcr) ≥1.30. Fig.4-b gives t h e experimental minimum reinforcement ratios ρmin needed to assure t h i s one-third reserve strength for the different concrete strength and it can be drawn that providing (ρ/ρmin)=0.75 will lead to attain a reserve flexural parameter(Py,/Pcr)=1.29 for all concrete grades. In addition, Fig.5 shows the reserve ultimate flexural parameter (Pu,/Pcr)for ultimate load beyond the cracking strength as a f unction of (ρ/ρmin)and it was observed that this reserve strength parameter,(Pu,/Pcr,), increases for higher strength concrete. 2.50 Py / Pcr 2.00 1.50 1.00 fcu = 52 Mpa fcu = 73 Mpa fcu =96.5 Mpa ACI318-08 limit 0.50 0.00 1.5 2 2.5 3 3.5 Flexural reinforcement ratio, ρ*10-3 4 4.5 Fig. 4-a: Relationship between the Actual Flexural Reinforcement Ratio ρ and the Experimental Reserve Flexural Capacity (Py/Pcr) 161
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME 2.50 Py / Pcr 2.00 1.50 1.00 fcu = 52 Mpa fcu = 73 Mpa fcu =96.5 Mpa ACI318-08 limit 0.50 0.00 0.5 0.6 0.7 0.8 0.9 1 1.1 (ρ/ρmin), ACI 363-35 Fig. 4-b: Relationship between the ratio (ρ/ρmin) due to ACI363-R35 and the Experimental Reserve Flexural Capacity (Py/Pcr) 3.00 2.50 Pu/Pcr 2.00 1.50 1.00 fcu = 52 Mpa fcu = 73 Mpa 0.50 fcu =96.5 Mpa 0.00 0.5 0.6 0.7 0.8 0.9 1 1.1 (ρ/ρmin), ACI 363-35 Fig. 5: Relationship between the Ratio(ρ/ρmin)According to ACI 363-R35 and the Experimental Ultimate Reserve Flexural Capacity(Pu/Pcr) Ductility Ductility of a structural member may be defined as its ability to deform at or near the failure load without a significant loss in strength. In the case of a flexural member, sectional ductility based on curvature and/or member ductility based on deflection is usually considered. In the present study, the definition of displacement ductility is investigated. Displacement ductility index, λ∆, may be defined as λ∆= (∆f/∆y) in which ∆f and∆y are the midspan deflections of the beam at failure and at yielding of the longitudinal tensile reinforcement, respectively [5, 7]. Deflection at yield load was calculated from the load-deflection curve as the corresponding displacement of the intersection of the secant stiffness at a load value of 80% of the ultimate lateral load and the tangent at the ultimate load. Also, failure is assumed to have occurred at a load equal to 80% of the ultimate load in the descending branch of the load-deflection curve. Table 4 presents the values of the deflections at yielding of tensile reinforcement ∆y and at failure load ∆f. In general, it was noted that both of ∆y and∆f increase as ρ increases. Considering the displacement ductility index λ∆in Table 4, it is shown that, everything else remaining the same, λ∆increased slightly as fcu increased from 52 to 73MPa, but then decreased obviously as fcu increased further from 73 to 96.5MPa, see Fig. 6. The same trend has been reported by Rashid et al [4].According to ACI 363-R35, it is evident that increasing f’c leads to increase the minimum reinforcement ratio, ρmin. Thus, for a certain flexural 162
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME reinforcement ratio, ρ, the ratio (ρ/ρmin) decreases as f’c increases. The variation of the displacement ductility index, λ∆ , as a function of (ρ/ρmin) for different concrete grades is shown in Fig. 7 where λ∆increases as (ρ/ρmin) increases. A displacement ductility index, λ∆,in the range of 5 is considered imperative for adequate ductility, especially in the areas of seismic design and the redistribution of moments [2,5]. Therefore, assuming that aλ∆value of 5 represents an acceptable lower limit to ensure the ductile behavior of flexural members, it appears that beams with (ρ/ρmin)≈ 0.70-0.80, according to ACI 363-R35, would meet that requirement Fig. 7. This gives another indication that the ρmin of the ACI 363-R35 can be reduced by 25 % with attaining an acceptable ductility index. 14 fcu = 52 Mpa fcu = 73 Mpa fcu =96.5 Mpa Ductility index, λ∆ 12 10 8 6 1.5 2 2.5 3 3.5 Flexural reinforcement ratio, ρ*10-3 4 4.5 Fig. 6: Relationship between Flexural Reinforcement Ratio ρ and the Ductility Index λ∆ 14 Ductility index, λ∆ 12 10 8 fcu = 52 Mpa fcu = 73 Mpa 6 fcu =96.5 Mpa 4 0.5 0.6 0.7 0.8 0.9 1 1.1 (ρ/ρmin), ACI 363-35 Fig. 7: Relationship between the Ratio (ρ/ρmin) due toACI 363-R35 and the Ductility Index λ∆ Strains in the Longitudinal Steel Reinforcement Strain measurements on the longitudinal reinforcing steel bars of all the tested beams recorded tension steel strain values >4000 µ s at the ultimate load level which indicate that the longitudinal reinforcement developed yielding, where µ s means micro strain= strain x 10-6 , see Fig.8 . 163
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME 140 120 100 Load kN 80 60 40 B501 B503 B1003 B753 20 B502 B1002 B751 0 0 2000 4000 6000 8000 10000 Strain *10 -6 Fig. 8: Load- Steel Strain Relationship for all Tested Beams COMPARISON OF AVAILABLE FORMULAS FOR THE MINIMUM FLEXURAL REINFORCEMENT IN HSC BEAMS Fig.9 shows a comparison between the different formulas for the minimum flexural reinforcement ratio versus the concrete compressive strength and it can be concluded that ACI 363R-35[7] formula represents the upper limit, i.e. the most conservative one, while El-Saie[10] formula represents the lower limit. Fig.10 represents a comparison between all of the available limits for the minimum flexural reinforcement ratio in the light of the experimental results and from the ductility point of view. In this respect, Rizk[4], ACI 363R-35[7],CSA-A23.3-04[8], JSCE [9],and the El-Saie [10] formulas are considered. If 5.0 is considered as an adequate ductility index [2,5], then for a singly reinforced section it can be shown that all the formulas of the previous limits lead to achieve a reasonable ductility index for all concrete tested grades. However, forfcu> 100 MPa and (ρ/ρmin) =1,El-Saie[10] formula seem to lead to inadequate ductility. 5.00 ρmin*10 -3 4.00 3.00 2.00 ACI363-R35 [7] JSCE [9] ELASI [10] CSA [8] Rizk [4] 1.00 40 60 80 100 Concrete Compressive Strength, f’c MPa Fig. 9: Relationship between the Concrete Compressive Strength and ρmin for Available Formulas 164
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME Ductility index, λ∆ 12 11 (a) fcu=52MPa 10 ACI363-R35 [7] CSA [8] JSCE[9] Rizk[4] ELASI[10] 9 8 0.50 1.00 1.50 2.00 2.50 ρ/ρmin Ductility index, λ ∆ 13 12 (b)fcu=73MPa Rizk[4] CSA [8] JSCE[9] ACI363-R35 [7] ELASI[10] 11 10 0.50 1.00 1.50 2.00 2.50 ρ/ρmin 11 Ductility index, λ ∆ 10 9 (c)fcu=96.5MPa 8 ACI363-R35 [7] CSA [8] JSCE[9] Rizk[4] ELASI[10] 7 6 0.50 1.00 1.50 ρ/ρmin 2.00 2.50 Fig. 10: Relationship between the Ratio (ρ/ρmin) According to Different formulas and the Ductility Index λ∆ : (a) fcu=52 , (b) fcu=73 and (c) fcu=96.5 MPa 165
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME CONCLUSIONS Within the range of the investigated parameters and properties of the materials used in this work, the following conclusions could be drawn: 1. The ACI 3 63 R -35 f o r m u l a for minimum flexural reinforcement ratio in HSC can be reduced by 25% without any harmful affect on the flexural behavior and i t w i l l achieve an adequate ductility index which may lead to good savings in the amount of the flexural reinforcement. 2. Also, reducing the l i m i t of ρmin to 75% of the limit specified by the ACI 36 3R -35 will lead to attain a reserve flexural paramete r (Py,/Pcr)≥ 1.29 for all concrete grades. 3. For the same longitudinal reinforcement, it was observed that the reserve strength parameters, (Pu,/Pcr,) and (Py,/Pcr,) decrease for higher strength concrete. 4. For the same concrete compressive strength with low values of flexural reinforcement ratio, ρ, the displacement ductility index increases as ρ increases. 5. The displacement ductility index λ∆ increases as concrete compressive strength increases for the same ratio (ρ/ρmin) up to 75 Mpa and then decreases as fcu increases. 6. For concrete compressive strength> 100 MPa and (ρ/ρmin) =1, El-Saie [10] f o r m u l a for minimum flexural reinforcement ratio, which represents50% of the ACI 36 3R - 35 limit, seem to lead to inadequate ductility index, i.e.λ∆<5. However, the other available formulas achieved a ductility index λ∆>6 for all concrete grades. ACKNOWLEDGEMENT The researcher expresses his great gratitude to the staff of both "Building Materials and Quality Control Institute" and " Reinforced Concrete Institute", Housing & Building National Research Center for their great effort through all experimental stages of this research. REFERENCES 1) 2) 3) 4) 5) 6) 7) Bosco, C.; Debernardi, P. G. and Carpinteri, A. (1990), “Minimum Reinforcement in HSC," Journal of Structural Engineering, ASCE, Vol.116, No.2, pp 427-437. Ashour, S. A. (2000), "Effect of Compressive Strength and Tensile Reinforcement Ratio on Flexural Behavior of HSC Beams,” Engineering Structures Vol.22, No5, pp 413-423. El-Ghandour, A. (2001), “Minimum Flexural Reinforcement in RC Beams,” Ninth International Colloquium On Structural and Geotechnical Engineering, Ain Shams University, Egypt. Rizk, E. and Marzouk, H. (2011), "Experimental Validation of Minimum Flexural Reinforcement for Thick HSC Plates, "ACI Structural Journal, V108, No. 3, pp 332340. Rashid, M. A. and Mansur, M. A. (2005), "Reinforced HSC Beams in Flexure, "ACI Structural Journal, Vol.102, No. 3, pp 462-471. ACI Committee 318 (2008), "Building Code Requirements for Structural Concrete (ACI 31 8- 08) and Commentary (318R-02)," American Concrete Institute. ACI Committee 363 "State of the Art Report on High Strength Concrete (ACI 3 63 R 35), “American Concrete Institute. 166
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 5, September – October (2013), © IAEME 8) 9) 10) 11) 12) 13) 14) 15) 16) CSA A23.3-04 (2004),"Design of Concrete Structures," Canadian Standard Association, Rexdale, Canada. Japanese Society of Civil Engineers (2005)"Standard Specifications for Design and Construction of Concrete Structures-2002," Design Part. El-Saie, A. (2000), "Minimum Amount of Reinforcement in HSCT-Sections," M.Sc. thesis, Faculty of Engineering, Cairo University. Chin, M. S. and Wee, T.H. (1997), “Flexural Behavior of High Strength Concrete Beams “ACI Structural Journal, Vol. 94, No. 6, pp663- 674. Pendyala,R. and Patnaikuni, I.(1996), “Full-Range Behavior of High Strength Concrete Flexural Members: Comparison of Ductility Parameters of High and Normal Strength Concrete Members,” ACI Structural Journal, Vol. 93, No. 1, pp30-35. Shin S. W.;Ghosh, S. K.; and Moreno, J. (1989), “Flexural Ductility of High Strength Concrete Members,” ACI Structural, Vol. 86, No.4, pp.394-400. Dr. K.V.Ramana Reddy, “Non- Destructive Evaluation of In-Situ Strength of High Strength Concrete Structures”, International Journal of Civil Engineering & Technology (IJCIET), Volume 4, Issue 4, 2013, pp. 21 - 28, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316. D.B.Mohite and S.B.Shinde, “Experimental Investigation on Effect of Different Shaped Steel Fibers on Flexural Strength of High Strength Concrete”, International Journal of Civil Engineering & Technology (IJCIET), Volume 4, Issue 2, 2013, pp. 332 - 336, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316. Javaid Ahmad and Dr. Javed Ahmad Bhat, “Ductility of Timber Beams Strengthened using CFRP Plates”, International Journal of Civil Engineering & Technology (IJCIET), Volume 4, Issue 5, 2013, pp. 42 - 54, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316. 167