Strength, cracking and deflection performance of large-scale self-consolidating concrete beams subjected to shear failure

Engineering Structures 32 (2010) 1262–1271

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Strength, cracking and deflection performance of large-scale self-consolidating concrete beams subjected to shear failure A.A.A. Hassan ∗ , K.M.A. Hossain, M. Lachemi Department of Civil Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, Canada, M5B 2K3

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Article history: Received 20 June 2009 Received in revised form 2 January 2010 Accepted 4 January 2010 Available online 25 January 2010 Keywords: Self-consolidating concrete Shear resistance Aggregate interlock Dowel action Code-based predictions

abstract An experimental investigation was conducted to study the shear strength, cracking behavior and deflection characteristics of large-scale concrete beams made with both self-consolidating concrete (SCC) and normal concrete (NC). Twenty concrete beams without shear reinforcement were tested to shear failure under simply supported three-point loading conditions. The variables were concrete type, coarse aggregate content, beam depth (150–750 mm) and longitudinal reinforcing steel ratio (ρw ) (1% and 2%). The performance was evaluated based on crack pattern, crack width, load at first flexure/diagonal (shear) crack, ultimate shear resistance, post-cracking shear resistance/ductility, load–deflection response and failure mode. The results showed that the ultimate shear strength of SCC beams was slightly lower than that of their NC counterparts. The results also validated the performance of various Code-based equations in predicting the crack width and first flexural cracking moment/load. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction Self-consolidating concrete (SCC) is the latest innovation in concrete technology. It is a highly flowable mixture that spreads readily under its own weight, without the use of vibrators for consolidation, and it achieves good compaction without segregation, even in congested reinforcement members. SCC is produced by increasing the fine aggregate content through the incorporation of mineral admixtures and/or viscosity-modifying admixtures (VMAs) [1–7]. The coarse aggregate content in SCC is usually lower than in normal concrete (NC), and the minimum slump flow value is limited to 550 mm to enhance the workability and flowability. The maximum size of coarse aggregates in SCC depends on the particular application [8]. Based on an investigation of the shear strength of NC beams without shear reinforcement, Taylor [9] reported that the contributions of the uncracked concrete compression zone, the dowelling action of the flexural reinforcement, and the aggregate interlock along the cracks to overall shear capacity were about 25%, 25% and 50%, respectively. There are two main concerns among designers/engineers about the lower shear resistance of SCC compared to NC: the comparatively lower coarse aggregate volume and the development of a weak aggregate interlock mechanism at the smooth fractured surfaces formed during loading [10]. The substantial difference in the rheology of the cement paste matrix in SCC compared to NC, which is related to the average aggregate diameter

∗

Corresponding author. E-mail address: [email protected] (A.A.A. Hassan).

0141-0296/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2010.01.002

and spacing [11–14], also affects the shear resistance of SCC. Lack of research warrants a full-scale experimental investigation of SCC beams subjected to shear failure. The investigation should consider various SCC mixture parameters (aggregate size, aggregate volume) and beam parameters (size and longitudinal reinforcement ratio) [15,16]. A study of the performance of Code-based procedures in predicting the shear strength and cracking characteristics of SCC beams is also warranted. The objective of this paper is to present the results of an investigation comparing the shear strength of full-scale SCC beams without shear reinforcement to that of NC beams. The aggregate interlock mechanism, which affects the shear load, cracking and deflection behavior, is greatly influenced by the beam size [17–21]. The beam size effect on the shear strength was investigated by testing SCC and NC beams of variable depth and a constant shear span to total depth ratio. The longitudinal tensile steel ratio (ρw ) is also an influencing factor on the shear capacity and deformability of reinforced concrete (RC) beams [21,22]. To study the effect of the longitudinal steel ratio, SCC and NC beams were designed to have low ρw (1%) and comparatively high ρw (2%). The experimental crack widths from both the SCC and NC beams were compared with those obtained from the Gergely–Lutz equation [23]. Experimental first flexural cracking moments were compared with those calculated from the Canadian Code (CSA) [24], ACI Code [25], Australian Standard (AS) [26] and Eurocode (EC2) [27]. The recommendations of this paper may be of special interest to designers considering the use of SCC in structural applications.

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Table 1 Details of experimental beams. Beam designation

1SCC150 1NC150 2SCC150 2NC150 1SCC250 1NC250 2SCC250 2NC250 1SCC363 1NC363 2SCC363 2NC363 1SCC500 1NC500 2SCC500 2NC500 1SCC750 1NC750 2SCC750 2NC750

Total length (L) (mm)

Effective span (S) (mm)

Total depth (h) (mm)

Effective depth (d) (mm)

Longitudinal steel ratio (ρw = As/bd) %

Reinforcement

Top

Bottom

1050

750

150

102.5

1

–

3 # 15

1050

750

150

100.0

2

–

4 # 20

1750

1250

250

202.5

1

2 # 10

5 #15

1750

1250

250

197.5

2

2 # 10

4 #25

2340

1815

363

310.5

1

2 # 15

3 # 25

2340

1815

363

305.5

2

2 # 15

3 # 35

3200

2500

500

447.5

1

2 # 15

4 # 25

3200

2500

500

442.5

2

2 # 15

4 # 35

4500

3750

750

667.5

1

2 # 15

6 # 25

4500

3750

750

650.5

2

2 # 15

6 # 35

As = area of tensile longitudinal steel, b = width of the beam = 400 mm, a = shear span = S /2, # is the bar number, bottom and side cover of the beam = 40 mm, a/d = 2.5.

2. Experimental program

Table 2 Mixture proportions and fresh/hardened properties of SCC and NC mixtures. Concrete type

2.1. Description of the test beams Twenty reinforced concrete beams (ten made of SCC and ten made of NC) with no shear reinforcement were tested (Table 1). The beams were 400 mm in width (b) and the shear span to total depth ratio (a/h) was kept constant at a value of 2.5 to ensure shear failure rather than bending failure [28]. The ten reinforced concrete beams of each concrete type made up two identical groups of five beams with a variable total depth (h) of 150 to 750 mm, and a longitudinal tensile steel ratio (ρw ) of 1% or 2%. The tested beams were classified by their total depth and longitudinal steel ratio (Table 1). For example, an SCC beam having 1% ρw with a total depth of 750 mm was designated as 1SCC750, while 2NC363 represented an NC beam with a total depth of 363 mm and a longitudinal steel ratio of 2% (Table 1). 2.2. Materials Both the SCC and NC mixtures were prepared from the same materials with different mix proportions. Table 2 presents the fresh and hardened properties for both mixtures. Canadian Type 10 Portland cement (similar to ASTM Type I) and ground granulated blast furnace slag (GGBFS) served as cementitious materials for both types of concrete. Natural sand and 10 mm maximum size crushed limestone were used as fine and coarse aggregates, respectively. The difference between the two mixtures was in the coarse aggregate content; the NC mixture contained 25% more coarse aggregate in volume than the SCC mixture. The intent of having such varied content was to investigate the effect of aggregate interlock on shear strength reduction. To adjust the flowability and cohesiveness of the mixtures, a high-range water reducer (HRWR), similar to Type F of ASTM C 494 [29], was used for the SCC mixture, and a water reducer (WR), similar to Type A of ASTM C 494 [29], was used in the NC mixture. Bars #10, #15, #20, #25 and #35 were used and tested. All bars had an average yield strength of 480 MPa and an average tensile strength of 725 MPa.

SCC Type 10 Cement (kg/m ) Ground granulated blast furnace slag (kg/m3 ) 10-mm coarse aggregate (kg/m3 ) Fine aggregate (kg/m3 ) Water (kg/m3 ) HRWR mL/100 kg of binder WR mL/100 kg of binder Slump (mm) Slump flow 3

V-funnel flow time (s) L-box

NC

315 135

300 100

900 930 180 850 0 –

1130 725 160 0 300 80

Flow (mm) T 500 (s)

700 3 5.5

– – –

H2/H1 (%) T 200 (s) T 400 (s)

90 1.5 2 45 3.8

– – –

28-d fc0 (MPa) 28-d fct0 (MPa)

47 4

T 500: flow time to achieve 500 mm slump flow, T 200 and T 400: times taken by concrete to travel a horizontal distance of 200 and 400 mm, respectively, H2: the height of concrete at the far end of the L-box, H1: the height of concrete behind the L-box gate.

2.3. Casting and curing of specimens The ready-mixed concrete mixtures were delivered to Ryerson University Structures Laboratory in trucks. The delivered SCC mixture was similar to that used in the Pearson International Airport project in Toronto in 2000 [30]. Immediately after concrete delivery, the fresh properties of both mixtures were tested. A traditional slump test [31] was conducted to obtain the slump value of the NC. The slump flow test [32] evaluated the viscosity and flowability of the SCC mixture, and a V-funnel test [33] was used to evaluate its stability. The V-funnel was filled with about 12 L of concrete, and the time it took for the concrete to flow through the apparatus was measured. An L-box [34] test evaluated the passing ability of the SCC mixture. The SCC beams were cast without vibration in one lift; the concrete was poured into the formwork at one end and flowed to the

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Fig. 1. Test setup, instrumentation and testing of a beam specimen.

other end. In contrast, the NC beams were cast by pouring concrete into the formwork, then compacting it with electrical vibrators. The control cylinders were also cast in the same manner. After casting, the beams and control cylinders were moist-cured for four days, then air-cured until the day of the test. The mean values of both the compressive strength (fc0 ) and splitting tensile strength (fct0 ) were determined from control specimens for the 28day duration of the investigation.

observed at about 20% of the failure load, and diagonal cracks were observed at 32%. The large beams showed their first flexural cracks at about 35% of the failure load, and diagonal cracks at about 60%. The number of cracks and the crack widths at various levels of loading are presented in Table 3. The large test beams had more cracks than the small ones (for both SCC and NC samples) with either 1% or 2% ρw . The small test beams showed a total of five to six cracks before failure; the large beams showed eleven to twelve. The NC beams exhibited more cracks than the SCC beams, particularly in terms of the number of diagonal (shear) cracks. The presence of more aggregate in the NC beams extended the path of shear cracking around the aggregate, leading to the development of more shear cracks and improvement of the post-cracking shear resistance. Figs. 2 and 3 show marked similarities between the SCC and NC beams in terms of crack width, crack height and failure mode. The failure crack widths varied between 2 and 3 mm in the small/shallow beams, while crack widths of up to 25 mm were observed in the large beams (Figs. 2–3 and Table 3). Beams with 2% ρw had lower crack widths compared to beams with 1% ρw (for both SCC and NC), as the presence of higher ρw enhances the resistance for the cracks to open wider. The maximum crack height before failure was higher in beams with 1% ρw (about 71% of beam depth) than those with 2% ρw (63% of beam depth).

2.4. Beam test setup and loading procedure 3.2. Experimental and theoretical analyses of crack width The beams were simply supported and tested under a threepoint loading condition (Fig. 1). A hydraulic jack was used to gradually apply the concentrated load at the mid-span of the beams until failure. Four linear variable differential transducers (LVDTs) were attached to the front surface of each beam at a 45◦ angle to measure the shear strain (Fig. 1). Another LVDT was installed directly under the mid-span to measure the central deflection. To monitor the development of strain in the longitudinal steel reinforcement, two electrical strain gauges were installed at the mid-span of the lower layer of the reinforcement. A computer-aided data acquisition system was used to monitor the load, displacements and strains throughout the loading history at pre-selected time intervals. The load was applied in a load-control fashion in three stages: at 50%, 75% and 100% of the expected failure load. 3. Results and analyses 3.1. Cracking and failure characteristics Figs. 2 and 3 present schematic diagrams of the SCC and NC test beams showing crack patterns and crack widths at 50% and 75% of the expected failure load, and at failure. As expected, during the early stages of loading, fine vertical flexural cracks appeared around the mid-span of all of the beams. With an initial increase in load, new flexural cracks formed away from the mid-span area. With a further increase, the flexural cracks started to propagate diagonally towards the loading point, and other new diagonal cracks began to form separately farther away from the mid-span along the beam (Figs. 2–3). In most cases, shear failure occurred shortly after a dominant diagonal shear crack (within one shear span or zone) extended to the top fibre, as indicated in Figs. 2–3. The volume of sound at shear failure was positively related to the beam size; the larger beams were noticeably louder than the smaller ones. In both the SCC and NC test beams, cracks extended up to 50% of the beam depth at 50% of the failure load, and up to 70% of the beam depth at 75% of the failure load. The angle of the early diagonal dominant shear cracks was around 55◦ (to the beam longitudinal axis). The angle of the failure diagonal cracks was approximately 35◦ . In the case of the small beams, the first flexural cracks were

Early ACI 318 provisions adopted the Gergely–Lutz equation to predict crack widths. Part of this investigation was to study the accuracy of that equation in predicting crack widths in the tested SCC and NC beams. In addition, the current Canadian Code requires computation of a crack width parameter based on the same equation; this equation is as follows [23]:

p w = 11 × 10−6 β fs 3 dc A = 11 × 10−6 β z 1/3

(1)

where z = fs (dc A) ; w is the crack width in mm; β is the distance from the neutral axis to the bottom fiber divided by the distance to the centre of tensile reinforcement; fs is the stress in the longitudinal reinforcement in MPa; dc is the distance from the extreme tension fiber to the centre of the reinforcing bar located closest to it in mm; and A is the area of effective tension surrounding the tension reinforcement with the same centroid as the tension reinforcement, divided by the number of bars or wires in mm2 . Eq. (1) was derived by running a statistical analysis on crack width data from a number of investigations. Its intent was to predict the maximum crack width at the surface of beams in areas of flexural tension. Because of the large scatter in the crack width data, 10% of the measured crack widths used to derive Eq. (1) exceeded 1.5 times the values given by the equation, while 2% were less than 0.5 times the calculated width [35]. Table 3 compares the experimental and calculated (predicted) crack widths from Eq. (1) for the NC and SCC beams with 1% and 2% ρw . There is an overall similarity between the beams in terms of crack width. The investigation found that the calculated crack width values were close to those obtained from experiments on both the 1% or 2% ρw NC and SCC beams, when applying up to 50% of the failure load (Table 3). As the applied load increased to 75%–100% of the failure load, the calculated crack widths significantly exceeded the experimental values. The close results for calculated versus experimental crack widths up to 50% of failure load can be attributed to the fine flexural cracks that formed in the mid-span, opening wider as the load increases. With an increase in load beyond 50% of the failure load, widening was reduced or stopped, because new diagonal cracks formed away from the mid-span

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Fig. 2. Crack development and crack widths at 50%, 75%, and 100% of failure load in beams with 750 and 500 mm depths.

(typical for shear failure). At up to 50% of load, the maximum crack width was predominantly governed by flexural (F) cracks (Table 3). Eq. (1) provides good prediction when the crack width is governed by flexural cracks resulting from the flexural failure of beams. It also should be noted that in this investigation Eq. (1) predicted

the crack widths at rebar stresses below the yielding stress for all beams even at failure load (Table 5). Because the tested beams failed in shear, the stresses in the longitudinal bars for all beams did not reach a very high level as that in the case of beams under bending failure.

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Fig. 3. Crack development and crack widths at 50%, 75%, and 100% of failure load in beams with 363, 250 and 150 mm depths.

The difference between the calculated crack widths and those obtained from the experiments was comparatively high in smallsize beams and decreased with the increase of beam depth. This can be attributed to the assumption of a constant value of β . However, β can change with beam depth. The variation of the ratio

β used in Eq. (1) with beam depth and ρw is shown in Table 3. The value of β is relatively high in shallow (small) beams (β = 1.93 in 2NC150), and is lower in deeper (large) beams (β = 1.21 in 1NC750). The Canadian Code does not limit the crack width. However, it does limit the value of z in Eq. (1) to 30 000 N/mm for

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Table 3 Calculated and experimental crack widths for SCC and NC beams. Beam Number of cracks at different % designation of failure load level

1NC150 1SCC150 2NC150 2SCC150 1NC250 1SCC250 2NC250 2SCC250 1NC363 1SCC363 2NC363 2SCC363 1NC500 1SCC500 2NC500 2SCC500 1NC750 1SCC750 2NC750 2SCC750

50%

75%

100%

3 3 4 3 5 3 3 5 4 5 4 3 5 4 4 6 7 3 6 5

3 5 6 6 5 4 4 7 5 8 5 5 7 10 8 8 12 9 8 10

7 9 7 11 8 7 7 11 10 11 10 9 11 14 11 14 23 16 14 16

β Eq. (1)

1.71 1.71 1.93 1.93 1.35 1.35 1.47 1.47 1.25 1.25 1.33 1.33 1.17 1.17 1.22 1.22 1.21 1.21 1.33 1.33

Calculated crack width at different % of failure load level (Eq. (1)) (mm)

Experimental maximum crack width at different % of failure load (mm)

50%

75%

100%

50%

*

75%

*

100%

*

0.28 0.32 0.20 0.26 0.19 0.21 0.18 0.17 0.20 0.17 0.18 0.12 0.16 0.15 0.10 0.11 0.14 0.13 0.13 0.11

0.49 0.48 0.33 0.42 0.29 0.31 0.27 0.24 0.28 0.28 0.24 0.22 0.23 0.22 0.18 0.18 0.22 0.20 0.19 0.18

0.69 0.67 0.50 0.52 0.37 0.36 0.33 0.31 0.37 0.35 0.3 0.28 0.29 0.27 0.24 0.23 0.3 0.28 0.27 0.25

0.20 0.20 0.14 0.18 0.20 0.18 0.18 0.12 0.16 0.18 0.16 0.10 0.18 0.16 0.12 0.10 0.18 0.16 0.14 0.10

F F FD FD F F F FD F F F F F F F F F F F F

0.22 0.22 0.20 0.18 0.30 0.20 0.28 0.14 0.20 0.22 0.20 0.12 0.30 0.22 0.14 0.14 0.24 0.20 0.18 0.12

F F D FD F F F FD F F F FD F F FD FD F F F F

0.40 0.50 0.20 0.18 0.30 0.20 0.28 0.14 0.20 0.22 0.20 0.12 0.30 0.22 0.14 0.14 0.24 0.20 0.18 0.12

D D D FD F F F FD D F F FD F F FD FD F F F F

* Governing crack type; F: Flexure crack; D: Diagonal crack; FD: Flexure–diagonal crack.

interior exposure and 25 000 N/mm for exterior exposure [24]. This limitation assumes a constant value of 1.2 for β in order to limit the critical crack width to 0.40 and 0.33 mm for interior and exterior exposure, respectively [35]. As per Table 3, the mean value of β for beams, having 1% ρw and beam depth greater than 250 mm, is 1.21, which closely matches the value (β = 1.2) assumed in CSA A23.3. For beams with 2% ρw and a beam depth greater than 250 mm, the experimental mean value of β is found to be 1.29, which leads to lower estimation of z values than those obtained from CSA A23.3. For beams less than 250 mm in depth, the assumption of a constant value of β (=1.2) as per CSA A23.3 is significantly lower than values obtained from experiments. 3.3. Experimental load–deflection response and strength characteristics 3.3.1. Experimental load–deflection response Typical load–central deflection responses of the SCC and NC beams (Fig. 4) showed a similar trend of variation throughout loading. The load and deflection were recorded at the first flexural crack, the first diagonal crack, and at various load levels (50%, 75% and 100% of failure load). The first flexural cracking load was marked by the first step or slope change in the load–central deflection response (Fig. 4) and by load–longitudinal bar strain curves at mid-span. Both SCC and NC beams with 1% ρw showed a higher deflection than those with 2% ρw . The presence of several peaks in the load–deflection response of some beams could be due to the formation of additional wide, extended diagonal cracks before failure, while the presence of a single peak is due to the formation of a single-failure diagonal crack. Table 4 summarizes the total experimental load at the first flexural crack, as well as the total load and deflection at the first diagonal crack and at failure. The first cracking loads for both NC and SCC were more or less the same, and the effect of ρw (between 1% and 2%) in the two mixtures was found to be insignificant. The longitudinal steel strain development in both SCC and NC beams was similar. Table 5 represents the longitudinal steel strains at mid-span at three stages of loading (50%, 75%, and 100% of failure load). In general, the strain in longitudinal steel at different load levels decreased with increase in beam depth and ρw . The longitudinal steel in all the beams (except 1NC150 and 1SCC150) did not reach yielding, since they were designed to fail in shear.

3.3.2. Ultimate shear strength To compare the shear strength results for SCC and NC beams, the ultimate shear load was normalized to account for the difference in compressive strength. According to ACI 318 and other studies [36], the effect of concrete compressive strength (fc0 ) is adequately captured by assuming the shear strength to be approximately proportional to the square root of fc0 . The normalized shear load was therefore calculated by dividing the ultimate shear load by the square root of fc0 for each type of concrete. Tables 4 and 5 summarize the ultimate shear√load (peak load) Vu , normalized ultimate shear load Vunz (=Vu / fc0 ) and normalized ultimate shear stress ‘vunz (=Vunz /bd) of all beams. The SCC beams showed lower ultimate shear strength (load) than their NC counterparts in all beam depths and in both longitudinal steel ratios (ρw = 1% or 2%) (Table 4). The greatest difference in shear strength was observed in larger beam depths with lower longitudinal steel ratios. The maximum difference was observed in 1NC750, which shows a 17% higher ultimate shear load than 1SCC750. The 25% lower coarse aggregate content in the SCC is the main reason for the lower ultimate shear load of all the SCC beams; shear transfer due to the aggregate interlock mechanism decreases significantly with the reduction of coarse aggregate content. It should be noted that the SCC/NC mixtures used in the study are considered to be conventional-strength concrete. In high-strength concrete, diagonal cracks penetrate the aggregate instead of surrounding it, producing a shorter crack path that causes lower resistance due to aggregate interlock. The ultimate shear stress decreased for both SCC and NC, irrespective of the 1% or 2% ρw , as beam depth increased. For SCC, when the beam depth increased from 150 to 750 mm, the shear stress dropped by 32% and 22% in beams with 1% and 2% ρw , respectively, compared to a shear stress drop of 23% and 20% for the NC beams. The ultimate stress drop due to an increase in beam depth seemed to be higher in the SCC beams than in the NC beams. Besides the lower quantity of coarse aggregates, the reduction of the ultimate shear stress in SCC beams can also be attributed to the development of longer, wider cracks in deeper beams. With regard to the effect of the longitudinal steel ratio, the results indicate that the ultimate shear capacity for all SCC or NC beams containing 2% ρw was higher than for those with 1% ρw . This increase in overall shear resistance can be attributed to the enhanced dowel action of the longitudinal reinforcement, and to

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Fig. 4. Experimental load–mid-span deflection responses.

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Table 4 Strength–deflection results of SCC and NC beams with 1% and 2% ρw . Beam Total load (kN) designation

1SCC150 1NC150 2SCC150 2NC150 1SCC250 1NC250 2SCC250 2NC250 1SCC363 1NC363 2SCC363 2NC363 1SCC500 1NC500 2SCC500 2NC500 1SCC750 1NC750 2SCC750 2NC750

Central deflection (mm)

At first flexural crack (Pf )

At first diagonal crack (Pd )

At failure (Pu )

At first diagonal crack (δd )

At failure (δu )

32 32 33 33 58 60 60 54 90 90 96 94 109 120 120 135 180 188 222 205

49 50 53 50 74 82 83 85 141 135 146 132 200 190 240 205 320 325 390 350

146 154 161 168 228 243 252 269 298 330 325 349 348 403 438 456 471 567 601 650

0.65 0.56 0.56 0.34 0.64 0.81 0.58 0.62 0.97 0.77 0.72 0.77 1.35 1.09 1.15 0.95 1.81 0.91 1.58 0.97

2.5 3.25 3.2 2.5 2.66 2.79 3.08 2.06 2.77 3.2 1.9 2.23 2.9 3.35 2.4 2.7 3.4 3.67 2.6 2.2

(δu /δd ) (%)

Shear load at first diagonal crack (Vd )

Ultimate shear load (Vu ) (kN)

(Vu /Vd ) (%)

385 580 571 735 416 344 531 332 286 416 264 290 215 307 209 284 188 403 165 227

25 26 27 26 39 43 43 44 74 71 77 70 106 101 126 108 175 177 210 190

74 78 81 85 116 123 128 136 153 169 166 178 181 209 226 235 250 298 315 340

294 304 298 331 298 287 295 306 206 237 216 255 172 208 180 218 143 168 150 179

Table 5 Shear strength and longitudinal steel strain development in SCC/NC beams. Beam designation

1SCC150 1NC150 2SCC150 2NC150 1SCC250 1NC250 2SCC250 2NC250 1SCC363 1NC363 2SCC363 2NC363 1SCC500 1NC500 2SCC500 2NC500 1SCC750 1NC750 2SCC750 2NC750

Longitudinal steel strain (εs ) microstrain

Normalized

50%

75%

100%

Ultimate shear load, (Vunz ) kN MPa−1/2

Ultimate shear stress, (vunz ) kN mm−2 /MPa1/2

1018 881 775 600 990 920 626 687 700 825 429 639 722 760 457 422 572 642 395 475

1503 1548 1240 990 1468 1380 920 1006 1120 1125 780 869 1037 1100 749 763 915 1006 666 721

2100 2180 1550 1500 1700 1755 1180 1250 1400 1500 1000 1070 1280 1380 970 1030 1260 1340 920 1000

11 11 12 12 17 18 19 20 23 25 25 26 27 30 34 34 37 44 47 50

0.183 0.189 0.202 0.206 0.173 0.18 0.191 0.199 0.157 0.17 0.171 0.179 0.135 0.152 0.169 0.172 0.125 0.145 0.157 0.165

the increased uncracked compression concrete resistance resulting from the movement of the neutral axis away from the top compression layer of the beam. The ultimate shear capacities of the 750 mm depth beams with 2% ρw were 28% (SCC) and 18% (NC) higher than for those with 1% ρw . This difference can be attributed to increased dowel action and uncracked compression concrete resistance, which contribute to extra shear for greater overall shear resistance. The results of the effect of the beam depth and longitudinal steel ratio on the ultimate shear stress match with the findings of Reineck et al. [37]. A qualified database of the shear test results was created by Reineck et al. for beams that do not contain shear reinforcement. The overwhelming number of tests in their database indicated that the ultimate shear stress decreased as the longitudinal steel ratio and beam depth increased.

3.3.3. Post-cracking shear resistance and ductility The mechanisms of aggregate interlock and dowel action play significant roles in the increase of shear resistance from Vd (shear resistance at the development of the first diagonal crack) to Vu (ultimate shear resistance of concrete). To characterize the performance of SCC and NC, it is important to analyze the postcracking shear resistance of concrete beams due to aggregate interlock and dowel action. This can be described by the percentage ratio of Vu to Vd (100Vu /Vd ), as shown in Table 4. As the beam depth increased from 150 mm to 750 mm, the percentage ratio of Vu to Vd in SCC beams decreased from 298% to 147% in 1% ρw , and from 304% to 154% in 2% ρw . In NC beams, this ratio decreased from 308% to 174% in 1% ρw and from 336% to 186% in 2% ρw . This result supports the theory that the development of lower post-cracking shear resistance in SCC is due to the presence of 25% less coarse aggregate

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Fig. 5. % error of prediction for first cracking load by Codes with respect to experiments.

than in NC. The influence of increased longitudinal reinforcement on post-diagonal cracking shear resistance is minimal. Table 4 presents the post-cracking shear ductility expressed as a percentage ratio of the experimental deflection values at peak failure load (δu ) to the experimental first diagonal crack deflection (δd )(= 100δu /δd ). As the beam depth increased from 150 mm to 750 mm, the percentage ratio of δu to δd in SCC beams decreased from 416% to 188% in 1% ρw and from 571% to 165% in 2% ρw . In NC beams, it decreased from 580% to 307% in 1% ρw and from 735% to 227% in 2% ρw . This decrease indicates that the post-cracking shear ductility is higher in NC beams than in their SCC counterparts. The difference between SCC and NC is more pronounced in beams with a lower steel ratio (ρw ). The shear ductility also grew with the increase of longitudinal reinforcement in both types of beam. Shear design should take into account the reduced post-cracking shear resistance and ductility of SCC mixtures that contain less coarse aggregate than NC. 3.4. Theoretical formulations of cracking moment The values of cracking moment (Mcr ) associated with the first flexural crack can be calculated based on various Codes. As per ACI [25]: Mcr =

fr Ig

(2)

yt

where fr = 0.62 fc0 for normal weight concrete; yt is the distance from centroidal axis of the gross section and Ig is the second moment of area of the gross section (the steel bars are not considered). As per CSA [24]:

p

Mcr =

fr Ig

(3)

yt

where fr = 0.6λ fc0 for normal weight concrete; λ is taken equal to 1 for normal density concrete; yt is the distance from centroidal axis of the gross section to the extreme tension fiber and Ig is the second moment of area of the gross section (the steel bars are not considered). As per the Australian Standard (AS) [22]:

As per Eurocode (EC2) [27]: Mcr = fctm Iu (h − xu )

(5)

where fctm is the mean value of axial tensile strength of concrete, equal to 0.3fck0.67 , where fck is the characteristic compressive cylinder strength of the concrete at 28 days; Iu is the second moment of area of the uncracked section; xu is the distance from the centroidal axis of the section to the extreme tension fiber; and h is the height of the cross section of the beam. The characteristic strength of concrete (fck and fcf ) is defined as the value of concrete strength, which is exceeded by 95% of the control specimens. 3.5. Comparison of experimental and theoretical shear load /moment Eqs. (2)–(5) are used to calculate the cracking moment (Mcr ), and hence the first cracking load of the experimental beams. The tested beams were subjected to three-point loading, where the maximum moment occurs in a localized region under the applied load at mid-span. With four-point loading, the maximum moment occurs over a greater length of the mid-span region, and therefore the moment at first cracking reduces compared to that of threepoint loading. Fig. 5 shows the percentage error in predicting the first cracking load by different Codes, as compared to experiments for SCC/NC beams with both 1% and 2% ρw . For small beams (shallow beams up to 200 mm depth), the calculated values from the Codes were very close to the experimental values, with a maximum percentage error of 8%. For large beams, the maximum percentage of error was 38%. Both ACI and CSA predictions yield lower values compared to experiments, while both AS and EC2 yield higher values, especially in large beams. This difference can be attributed to the fact that ACI and CSA Codes neglect the effect of longitudinal reinforcement, while AS and EC2 take it into account in the calculation of the second moment of area of the uncracked section.

p

Mcr = Zfcf0

(4)

where fcf is the characteristic flexural tensile strength of the p concrete = 0.6 fc0 and Z is the section modulus of the uncracked section, referred to the extreme fiber at which cracking occurs [22].

4. Conclusions The study investigated the overall shear resistance of full-scale self-consolidating concrete (SCC) beams in comparison to their normal concrete (NC) counterparts. The investigation included a total of 20 concrete beams; there were ten NC and ten SCC beams of variable depth (150–750 mm) and longitudinal reinforcement ratio (1% and 2%) with no shear reinforcements. The focus was on the crack pattern, crack width, crack loads (at the first flexural crack and the first diagonal crack), ultimate shear resistance,

A.A.A. Hassan et al. / Engineering Structures 32 (2010) 1262–1271

load–deflection response, and failure modes. The results of the study have led to the following conclusions.

• An overall similarity was noted between SCC and NC beams in

•

•

•

•

terms of crack widths, crack heights, crack angles and overall failure mode. The ultimate shear load of SCC/NC beams grew with the increase of longitudinal reinforcement, while the ultimate shear stress decreased with the increase of beam depth, irrespective of either 1% or 2% longitudinal reinforcement ratios. SCC beams showed lower ultimate shear strength than their NC counterparts. The shear strength reduction was higher in deeper beams with lower longitudinal steel ratios. A maximum ultimate shear strength increase of 17% was observed in NC beams. The post-diagonal cracking shear resistance and ductility of SCC beams were also low compared to NC beams, due to less aggregate interlock as a consequence of a lower quantity of coarse aggregate in SCC. The reduced post-cracking shear resistance and ductility of SSC should be taken into consideration in the shear design of SCC beams. Beams with a higher longitudinal steel ratio (2%) generally showed narrower crack widths than those with a low longitudinal steel ratio (1% for both SCC and NC beams). For SCC/NC, the Gergely–Lutz equation predicted the crack width at 50% of the failure load reasonably well, but significantly overpredicted the crack widths at 75% and 100% of the failure load. For large-size beams, both ACI and CSA equations underestimated the first flexural cracking load, while the AS and EC2 equations overestimated it. For shallow beams, all four Codebased equations predicted values close to those obtained from experiments.

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