Blast response of beams built with high-strength concrete and high-strength ASTM A1035 bars

International Journal of Impact Engineering 130 (2019) 41–67

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International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng

Blast response of beams built with high-strength concrete and high-strength ASTM A1035 bars

T

Yang Li, Hassan Aoude

⁎

Department of Civil Engineering. University of Ottawa, Ottawa, Canada

ARTICLE INFO

ABSTRACT

Keywords: Blast High-strength reinforcement HSC Shock-tube Beams

The work reported in this paper is aimed towards better understanding the behavior of reinforced concrete flexural members built with high-strength reinforcement (HSR) under blast loading. As part of the study, a series of high-strength concrete (HSC) beams built with ASTM A1035 Grade 690 MPa bars are tested under simulated blast loads using a shock-tube. Parameters investigated include the effect of steel type (Grade 690 MPa vs. 400 MPa), concrete strength (100 MPa vs. 50 MPa) and reinforcement ratio (ρ = 1%–2.2%). The effect of loading rate is investigated by testing a companion set of beams under slowly applied (quasi-static) loading. The results show that use of high-strength steel in HSC beams results in increased blast capacity and improved control of displacements at equivalent blasts. The use of high-strength concrete is also found to be better suited for beams reinforced with high-strength bars. The results further demonstrate the importance of ensuring beams designed with high-strength bars are under-reinforced and provided with sufficient shear reinforcement. The blast response of the beams is predicted analytically using dynamic analysis.

1. Introduction It is becoming increasingly important to protect critical buildings and infrastructure against the effects of blast loads. Events such as the Oklahoma City Bombing (1995) and Lac-Mégantic Disaster (2013) demonstrate the devastating human and economic costs that can be caused by bomb blasts and accidental explosions. To ensure greater safety, guidelines for the blast-resistant design of structures have recently been developed and enacted worldwide, including in the United States, the UK and Canada [1]. The use of high-strength reinforcing bars in concrete structures is becoming more common. High-strength bars with yield strengths (fy) greater than 500 MPa have been developed in several markets worldwide, including: Japan (USD 685, fy = 690 MPa), Taiwan (SD 685, fy = 690 MPa), China (HRB 600, fy = 600 MPa) and Korea (KS SD600, fy = 600 MPa). In North America, Grade 550 MPa reinforcement is referenced in the ASTM A615 and A706 specifications, while guidelines have also been developed for SAS670 steel, a German-produced highstrength reinforcing bar with a yield strength of 670 MPa [2]. The steel used in this study is referenced in the ASTM A1035 specifications, and includes Grade 690 MPa and Grade 830 MPa steel bars [3]. Over the years, important research has studied the behavior structures built with high-strength bars under static and earthquake loading [2,4].

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Consequently, design guidelines for the structural use of high-strength reinforcement have been developed and continue to be optimized [5]. In contrast, studies on the blast behavior of concrete structures built with high-strength bars are very limited. Moreover, much of the available data comes from early impact studies on members designed with reinforcing bar types that are no longer used in practice (see Background section). This study aims to better understand the blast behavior of reinforced concrete beams built high-strength bars. As part of the study, a series of beams built with Grade 690 MPa ASTM A1035 reinforcement are tested using a high-capacity shock-tube. As part of the analytical investigation, the behavior of the beams is predicted using dynamic inelastic SDOF analysis. 2. Background 2.1. Properties of Grade 690 MPa reinforcement The lack of a well-defined yield point is a key characteristic of the stress-strain response of Grade 690 MPa ASTM A1035 reinforcement (see Fig. A1a), and this in turns affects the flexural response of beams [6]. Fig. A1c shows the load-deflection responses of three beams tested by Yotakhong [7]; the tests included one specimen reinforced with 3-

Corresponding author. E-mail address: [email protected] (H. Aoude).

https://doi.org/10.1016/j.ijimpeng.2019.02.007 Received 20 September 2018; Received in revised form 22 February 2019; Accepted 23 February 2019 Available online 25 February 2019 0734-743X/ © 2019 Elsevier Ltd. All rights reserved.

International Journal of Impact Engineering 130 (2019) 41–67

Y. Li and H. Aoude

No.6 ASTM A615 bars (fy = 420 MPa) and two companion specimens with equal (3- No.6) and reduced (2-No.6) amounts of Grade 690 MPa reinforcement. As seen in the figure, the beams with high-strength bars do not show any distinct yield points and continue to carry loads with increasing deflections until failure occurs due to crushing of concrete at mid-span. This behavior contrasts the response of the beam with conventional reinforcement which shows a clear deflection plateau after yielding [5]. As shown in Fig. A1a, the stress-strain curves of different high-strength bars are quite different. While the quasi-static properties of ASTM A1035 reinforcing bars are readily available, there exists no information on the properties of this bar type under high strain-rates. Nonetheless, a few studies have examined the effect of steel grade on the dynamic properties of steel reinforcement [8–12]. Malvar [8] presented a comprehensive review in this area which gathered data from static and dynamic tests on steel bars with yield stresses ranging from 290 to 710 MPa. The study found that the dynamic increase factor (DIF) at both yield and ultimate is inversely proportional to the steel yield stress itself; that is, higher grade steel shows reduced rate dependence when compared to steel with a lower yield stress.

2.2.3. Effect of longitudinal steel ratio Several previous studies have also investigated the effect of steel ratio on the dynamic performance of beams. Among them, Zhan et al. [24], Yoo et al. [26] and Louw et al. [45] have reported that maximum and residual displacements tend to decrease with the increase in steel increment. Adhikary et al. [20] similarly reported that increasing the steel ratio improves impact response by reducing maximum deflections. On the other hand, this study found that beams with larger steel ratios experienced increased damage near the impact point. Increasing the compression steel ratio was found to reduce the degree of local failure. Likewise, Goldston [25] reported that increasing the ratio of GFRP bars improved performance, but resulted in greater damage. Similarly, Magnusson et al. [37] found that the use of large steel ratios in HSC beams had a tendency to change failure from flexure to shear under blast. 2.2.4. Effect of reinforcement grade Experimental studies on the dynamic behaviour of beams built with high-strength bars is scarce [47–53] (see Table A3). Moreover, a review of previous studies indicates most available data comes from early impact tests on members built with reinforcing bar types that are no longer used in practice (see Table A4, Fig. A1b and reference [54] for additional information on these older bar types). Likewise, there exists no data on the dynamic performance of beams built with Grade 690 MPa ASTM A1035 reinforcement. Moreover, there is limited data on the dynamic performance of beams built with high-strength concrete 55 MPa ) and high-strength bars (see Fig. A2). Nonetheless, most ( fc of these early impact studies demonstrate that the use of higher strength bars improves the performance of beams under dynamic loading (see the conclusions from Mylrea [47], Mavis and Stewart [51], Cernica and Charignon [52] and Miyamoto et al. [53] in Table A3). Data on the blast behavior of beams built with high-strength bars is extremely scarce, however Keenan [36] conducted an early analytical & experimental study on this topic. The blast tests included sixteen beams reinforced with high-strength bars having a specified yield stress of 620 MPa. The study concluded that greater blast resistance can be gained with high-grade steel when compared to lower grade steel, however the author noted that the limited strain-capacity of highstrength steel may restrict its use in blast-resistant design. More recent blast studies in this area have been conducted on slabs. Among them, Thiagarajan et al. [55] examined the effect of concrete type and reinforcement grade. The tests included four slab specimens with different combinations of normal-strength concrete (NSC), high-strength concrete (HSC), normal strength reinforcement (NSR) and highstrength low-alloy vanadium reinforcement (HSLA-V). When compared to the control slab with conventional materials (NSC & NSR), substitution with either HSC concrete or HSLA-V bars led to enhanced blast performance with reductions in peak deflections. Optimal results were obtained when both high-strength concrete and steel were used. Li et al. [56] reported similar benefits when combining ultra-high performance concrete and high-strength reinforcing bars in slabs subjected to closein blasts.

2.2. Previous impact and blast tests Over the years, a significant number of studies have investigated the behavior of reinforced concrete beams under impact loading. Table A1 provides an overview of some of this research [13–32] (refer to references [33,34] for compressive reviews of previous studies). Experimental studies on the blast behaviour of reinforced concrete beams are more limited, especially in the case of members subjected to far-field blasts (see Table A2 for previous experimental [35–41] and numerical studies [42–44]). Previous findings related to the effects of loading rate, concrete strength, steel ratio and steel grade are summarized below. 2.2.1. Effect of loading-rate Previous research confirms that reinforced concrete beams exhibit increased capacities under dynamic loading [13–24,29–31,45]. For example, Adhikary et al. [20] conducted low-velocity impact tests on beams subjected to varying strain-rates (0.005–3.1 s−1) and reported dynamic strength ratios which ranged from 1.16 to 1.42. Similarly, Magnusson et al. [37] tested a series of beams with varying concrete grades under far-field blast loads and reported dynamic strength ratios of 1.04 to 1.81. This study further reported that the failure mode of some beams changed from flexure to shear under dynamic conditions; plain HSC beams with large steel ratios were found to be especially susceptible to suffering such failures. 2.2.2. Effect of concrete strength The effect of concrete strength on the dynamic behavior of beams has been studied by several researchers. Chen and May [15] studied the impact response of beams having concrete strengths ( fc ) of 35 and 50 MPa and found that beams with higher concrete strengths sustained larger impact loads. On the other hand, in their numerical study, Pham and Hao [29] concluded that varying fc from 20 to 100 MPa does not considerably affect impact resistance. Louw [45] studied the impact response of cantilever beam-columns having fc of 19–37 MPa and reported concrete strength more greatly affected shear resistance when compared to flexural strength; for shear-critical beams doubling fc was found to increase impact strength by 33%, compared to 17% for static conditions. Recently, Li et al. [46] examined the blast behavior of HSC beams having fc = 50 and 100 MPa and reported that increasing the concrete strength had limited effects on blast resistance but improved control of deflections. Goldston et al. [25] reported similar performance benefits when increasing the concrete strength from 40 to 80 MPa in beams designed with large amounts of GFRP bars.

2.3. Research significance In summary, research on the blast behavior of beams built with high-strength reinforcement is limited, and data on beams designed with Grade 690 MPa ASTM A1035 bars is lacking. Moreover, most existing dynamic test data comes from early impact tests, on beams designed with bar types that are no longer used in practice. Likewise, there exists limited data on the dynamic performance of beams built with HSC concrete and high-strength bars. The research reported in this paper is intended to provide greater

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International Journal of Impact Engineering 130 (2019) 41–67

Y. Li and H. Aoude

understanding on the blast behavior of reinforced concrete beams built with high-strength reinforcement. More specifically, the paper reports the results from shock-tube blast tests on medium-scale beams built with high-strength concrete and reinforced with Grade 690 MPa ASTM A1035 bars. Test specimens were designed to investigate the effects of steel type (high-strength vs. normal strength bars), concrete strength (100 vs. 50 MPa), longitudinal steel ratio (1–2.2%) and loading rate (blast vs. static loads), providing important insights into the effects of various parameters affecting the blast performance of beams reinforced with high-strength bars. The analytical study examines the applicability of using dynamic inelastic SDOF analysis to predict the blast response of HSC beams designed with Grade 690 MPa ASTM A1035 reinforcement.

Longitudinal steel in the beams consisted of 2-No.4, 2-No.5 or 2-No.6 Grade 690 MPa ASTM A1035 bars, resulting in steel areas, As = 258 mm2, 400 mm2 and 568 mm2 and tension steel ratios of ρ = 1%, 1.5% and 2.2%. The reinforcement details were chosen to match those of a companion set of beams built with conventional (Grade 400 MPa) bars (see Table 1). Reinforcement in the control set consisted of either 2-No.4 bars (As = 258 mm2), or 2–15 M/2–20 M Canadian size bars (As = 400 and 600 mm2, respectively). The steel ratios in this control set were chosen based on the limits prescribed in the CSA S850 blast standard [1]. In all cases, the beams were reinforced with stirrups made from 6.3 mm wire spaced at 100 mm in the shear spans (it is noted closed hoops were not used to allow for comparison with the companion beams tested by Li et al. [46]; it is expected that the use of such reinforcement would enhance ductility). To facilitate construction, 2–6.3 mm bars were provided at the top of the beams in the shear spans only. Specimen nomenclature in Table 1 indicates concrete type (C100 or C50), steel type (HSR or NSR) and longitudinal bar size (No.4/No.5/No.6 or 15 M/20 M bars). For example, beam C100-No.5(HSR) is built with 100 MPa concrete and 2-No.5 highstrength bars, while C100-15M(NSR) refers to the companion beam built with normal-strength reinforcement.

3. Experimental program 3.1. Description of test specimens A total of eight reinforced concrete beams were studied in this research study. Five of the beams were tested under blast loads, with the three remaining beams tested under static conditions. As shown in Table 1, six specimens were cast using high-strength concrete having a specified strength of 100 MPa (C100), with the remaining beams cast using a lower-strength 50 MPa concrete (C50). As shown in Fig. 1, the beams had cross-sectional dimensions of 125 mm × 250 mm, a length of 2440 mm and were tested under four-point loading over a span of 2232 mm. The constant moment region and shear spans in all beams were 750 mm and 741 mm, respectively (shear-span ratio, a/d = 3.7).

3.2. Material properties Two concretes were used in this study. The first mix consisted of a high-strength concrete with a specified strength of 100 MPa (designated as C100). Table 2 shows the quantities of cement, coarse aggregate,

Table 1 Beam properties and average concrete properties. Beam ID

C50-No.4(HSR) C50-No.5(HSR) C100-No.4(HSR) C100-No.5(HSR) C100-No.6(HSR) C50-No.4(NSR)a C100-No.4(NSR)a C100-15M(NSR)a C100-20M(NSR)a a b

Concrete

Longitudinal reinforcement

Type

Comp. Strength, f′c (MPa)

Type

Details

Reinf. ratio ρ (%)

Ratio ρ/ρb

C50

61.8

HSR (690 MPa)

2- No.4

1.0

0.80

22222222-

1.5 1.0 1.5 2.2 1.0 1.0 1.5 2.4

1.28 0.57 0.90 1.17 0.24 0.17 0.31 0.44

C100 C50 C100

61.8 96.4 95.0 96.2 58.2 106.8 110.6 105.5

NSR (400 MPa)

No.5 No.4 No.5 No.6 No.4 No.4 15M 20M

Companion beams with normal-strength reinforcement tested by Li et al. [46]. ρb: balanced reinforcement ratio.

Fig. 1. Beam design details.

43

b

Transverse steel (6 mm wire)

Loading type (Dynamic/ Static)

U-shaped stirrups @ 100 mm in shear spans

D D&S D D&S

International Journal of Impact Engineering 130 (2019) 41–67

Y. Li and H. Aoude

Table 2 High strength concrete mix properties. Cement (kg/m3)

Slag (kg/m3)

Silica Fume (kg/m3)

Sand (kg/m3)

Aggregate 13 mm [1/2″] (kg/m3)

Aggregate 19 mm [3/4″] (kg/m3)

Water (kg/m3)

SP (L/m3)

Retarder (L/m3)

373

164

48

734

560

560

157

13.1

3.3

Fig. 2. Material stress-strain curves.

Table 3 Reinforcement steel properties. Type

Steel wire ASTM A1035 Gr. 690 MPa

⁎

ID

6 mm wire No.4 HSR No.5 HSR No.6 HSR

Bar Diameter db(mm)

Bar Area Ab (mm2)

Yield Strain ɛy

Strength fy (MPa)

Strain ɛu

6.35 12.7 15.9 19.1

32 129 200 284

0.0028 0.0067 0.0070 0.0066

577 904* 929* 855*

0.0701 0.0560 0.0485 0.0528

Ultimate

Rupture

Ramberg–Osgood parameters

Strength fu (MPa)

Strain ɛu

A

B

C

645 1077 1217 1153

– 0.062 0.060 0.059

– 0.0030 0.0025 0.0035

183 166 178

1.8 2.0 1.9

Determined using 0.2% offset method.

sand, slag, silica fume and admixtures in this concrete. The second mix consisted of a pre-packaged, self-consolidating concrete mix with a lower specified strength of 50 MPa (designated as C50). This mix had a sand-to-total aggregate ratio of 0.55, a maximum aggregate size of 10 mm, a water-cement ratio of 0.42 and had various admixtures which are added in dry powder form (a super plasticizer, a viscosity-modifying admixture and an air-entraining admixture) (see Aoude et al. [57] for further details on this mix). Table 1 shows the average concrete strengths in each beam, as determined by testing 100 mm × 200 mm cylinders at 28 days, while Fig. 2a shows sample stress-strain curves for the two concretes. The properties of the reinforcing steel are reported in Table 3 and were obtained by testing three samples for each bar type in direct tension. Stress–strain curves for the Grade 690 bars as well as the Grade 400 MPa steel bars used in the control beams are shown in Fig. 2b and c.

sketch of the supports used in the static tests. Strain readings in the longitudinal steel were monitored using strains gauges applied on the bars at mid-span. The displacements, applied loads, and strains were recorded using a data acquisition system. Blast tests were conducted using a shock-tube at the University of Ottawa blast laboratory [58]. Fig. 4a shows the four main components of the shock-tube which is capable of simulating the blast waves caused by the far-field detonation of high explosives. For further details on the shock-tube and its capabilities, refer to Lloyd et al. [58]. Fig. 4b shows the setup used in this study. Since the beams are non-planar, a load transfer device (LTD) was used to collect and redirect the blast pressure at the 2 m × 2 m end-frame opening onto the specimens as two point loads [59]. The LTD configuration during testing is shown in Fig. 4c; it can be seen that the loading pattern is consistent with that used in the static tests. The boundary conditions can have a significant influence on the dynamic response of beams [15,23,29] . In this study, the beams were secured to the shock-tube using simply-supported boundary conditions which were similar to those used in the static tests (see Fig. 4d for a photo and sketch of the support detail). It is noted that while the boundary conditions are similar, their effects under static and dynamic loads may be different and this should be considered when comparing the results from the static and dynamic tests. Load-cells were used to captured the dynamic reactions at the beam supports, while the shockwave data was captured using two dynamic pressure gauges installed near the end-frame. The displacement response of the beams was

3.3. Test setup and procedure This study included four-point bending tests on companion beams tested under static and dynamic loading. In both cases the beams had the same span, loading pattern and similar boundary conditions which consisted of simple supports. Fig. 3a shows the setup used in the static tests. Loading was applied using a hydraulic jack in 10 kN increments and was measured using a load-cell, while displacements at mid-span were measured using an LVDT and cable transducer. Fig. 3b shows a 44

International Journal of Impact Engineering 130 (2019) 41–67

Y. Li and H. Aoude

Fig. 3. Beam static test setup, load-deflection results and approximate method to determine the yield point.

measured using linear variable differential transducers (LVDTs) placed at mid-height and one-third span. Strains in the tension steel bars were recorded using strain-gauges. A high-speed camera was used to record videos and images of the specimens at a frame rate of 500 frames per second. The shockwave, displacement and strain data was captured using a 16 channel high-speed digital oscilloscope at a sampling rate of 100,000 Hz (refer to Lloyd et al. [58] for further details). In this study, the specimens were subjected to varying blast intensities to examine their behavior under elastic, yield and ultimate conditions. Sample shockwaves for Blasts 1 to 4 are shown in Fig. 4e and the key blast parameters used to define the shockwaves are summarized in Table 4. They include: the positive reflected impulse (Ir), peak reflected pressure (Pr) and positive phase duration (td). These blast parameters are obtained by varying the driver length and driver pressure. For all tests the driver length was kept at 2800 mm, while the driver pressure was increased gradually. To correlate the shockwave data with actual blast conditions the procedure in Annex A of the CSA S850 standard [1] was used to estimate the scaled distance (Z) for the blasts (see Table 4). For example, Blast 4 (Ir = 744 kPa•ms, Pr = 76 kPa, td = 23 ms) corresponds to a scaled distance Z = 5.82 m/kg1/3 and simulates the shockwave generated by the detonation of 635 kg of TNT at a distance of 50 m.

Park [61], and illustrated in Fig. 3d. The toughness parameter gives an indication of the energy-absorption capacity and was obtained by computing the total area under the load-deflection curves until failure (see Fig. 3d). Fig. 5 shows photos of the beams at failure. The results from the blast tests are summarized in Table 6. In addition to reporting the shockwave data (Pr, td and Ir) for each test, the table summarizes the response of each specimen in terms of maximum mid-span displacements, support rotations (δmax and θmax) and residual mid-span displacements (δres) (the residual displacements correspond to the postblast deformations in the specimens after they come to rest). Fig. 4f shows a sample pressure-displacement time history along with an overview of key blast and response parameters. Fig. 6 shows photos of the damage in the beams, while Fig. 7–10 can be used to study the influence of the test variables on the displacement response of the specimens. 4.2. Effect of high-strength reinforcement ratio The effect of high-strength steel ratio (ρ) is examined by comparing the static and dynamic responses of beams C100-No.4(HSR), C100No.5(HSR), and C100-No.6(HSR). In all cases the beams had 100 MPa concrete but varying amounts of tension steel, consisting of two No.4, No.5 or No.6 Grade 690 MPa bars, resulting in steel ratios, ρ = 1%, 1.5% and 2.2%. As noted earlier, the steel ratios were chosen to match those in the companion beams built with normal-strength bars. The ρ/ρb ratios, where ρb is the balanced steel ratio, are reported in Table 1. Fig. 3c shows the static response of the beams in both sets. As expected, the strength and stiffness of the beams built with normalstrength bars increased as the reinforcement ratio became larger. This same effect was observed in the beams designed with high-strength bars. The maximum load resisted by beam C100-No.5(HSR) (ρ = 1.5%) was 54% larger when compared to the peak load sustained by beam C100-No.4(HSR) (ρ = 1%). Similarly, the specimen with No.5 HSR bars showed a response which was 46% stiffer when compared to the

4. Experimental results 4.1. Summary of results The results from the static four-point bending tests are shown in Fig. 3c. To study the load-deflection curves, various parameters defined in Fig. 3d are summarized in Table 5. These include the maximum load s s (Pmax ), failure displacement ( max ), stiffness (Ks), displacement ductility s s s ( max / y ) and toughness ( Au ). Since the beams with high-strength bars do not show well-defined yield points, the yield displacement ( sy ) was approximated using the procedure suggested by Pam et al. [60] and 45

International Journal of Impact Engineering 130 (2019) 41–67

Y. Li and H. Aoude

Fig. 4. Details of the dynamic test setup and sample shockwave & response time histories.

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International Journal of Impact Engineering 130 (2019) 41–67

Y. Li and H. Aoude

Table 4 Driver length/pressure and average reflected shockwave data for Blast 1–4. Blast ID Blast Blast Blast Blast Blast a b

1 2 3a 3b 4

a

Driver pressure kPa (psi)

Driver length mm (ft)

Average reflected pressure, Pr (kPa)

Average reflected impulse, Ir (kPa•msec)

Average positive phase duration, td (msec)

Scaled distance Z (m/kg1/3)

Equivalent charge weight (kg)b

117 207 276 345 483

2743 2743 2743 2743 2743

24.5 41.0 49.6 57.7 75.9

240 380 462 548 744

21.5 21.3 21.5 21.8 22.8

11.9 8.4 7.4 6.8 5.8

73 212 304 399 635

(17) (30) (40) (50) (70)

(9) (9) (9) (9) (9)

Beam with No.4 bars tested under Blasts 1, 2, 3a, 3b; Beams with No.5 & No.6 bars tested under Blasts 1, 2, 3b and 4. Note: Assumed stand-off distance = 50 m.

Table 5 Results from static and dynamic resistance curves. Static test results Load Beam

C100-No.4(HSR) C100-No.5(HSR) C100-No.6(HSR) C100-No.4(NSR) C100-15M(NSR) C100-20M(NSR) a

Dynamic results Displacement

(kN)

Yield Pys

Peak s Pmax (kN)

Yield

118.4 185.4 191.8 58.1 94.5 118.2

126.7 194.7 199.0 75.5 104.6 137.5

29.2 31.4 – 10.9 14.6 15.0

(mm)

s y

Load

Toughness

Failure s max (mm)

Stiffness Ks (N/mm)

Ductility s s max / y

Toughness Aus (kN•mm)

Peak dynamic

D s Pmax /Pmax

Dynamic

AuD / Aus

35.2 34.0 27.2 58.6 40.7 31.0

4054 5904 7765 5330 6342 7880

1.21 1.09 – 5.35 2.74 2.07

2655 3686 3096 3180 3272 2998

152.0 240.1 -a 106.2 138.5 205.2

1.20 1.23 – 1.40 1.32 1.49

4015 5123 – 3113 4461 4706

1.51 1.39 – 0.98 1.36 1.57

D load, Pmax (kN)

toughness, AuD (kN)

Data unavailable due to malfunction of equipment during testing.

Fig. 5. Failure modes of beams tested under static loading.

companion with No.4 HSR bars. However, it can be observed that increasing the high-strength steel ratio further to 2.2% in beam C100No.6(HSR) did not lead to a further increase in capacity. This can be explained by the fact that this beam was over-reinforced (ρ/ρb > 1), with failure occurring due to crushing of concrete prior to the development of yield stresses in the high-strength bars. The results clearly show the importance of ensuring that beams with high-strength bars are designed to be “under-reinforced”. Using the approximate method des / sy ) of the beams with No.4 fined in Fig. 3d, the ductility ratios ( max and No.5 high-strength bars were found to be 1.2 and 1.1, although beam C100-No.5(HSR) showed a 39% increase in overall toughness when compared to beam C100-No.4(HSR). The over-reinforced No.6 specimen failed in a brittle manner without yielding of the highstrength reinforcement and showed reduced toughness when compared to the beam with No.5 bars (see Table 5). Examination of the failure photos in Fig. 5 shows that the damage at failure became more severe as the high-strength reinforcement ratio was increased; this was especially true for the beam with No.6 bars which suffered a sudden compression failure.

The steel ratio also had a significant influence on the blast response of the beams built with Grade 690 MPa bars. As seen in Fig. 7, increasing the ratio of high-strength bars from 1% to 1.5% resulted in improved control of deformations at similar blasts. No trend was seen at Blast 1, however beam C100-No.5(HSR) showed a 20% reduction in δmax at Blasts 2 and 3b when compared to beam C100-No.4(HSR). On the other hand, increasing the steel ratio beyond balanced conditions in beam C100-No.6(HSR) (ρ = 2.2%, ρ/ρb = 1.17) did not lead to any further enhancement in displacement control when compared to C100No.5(HSR). No maximum displacement data was collected for the beam with the No.6 bars at Blast 4, however the residual displacement was 25% higher when compared to the specimen with No.5 bars. Increasing the high-strength steel ratio also affected blast capacity and failure mode (see Fig. 6). Failure of beam C100-No. 4 (HSR) occurred at Blast 3b (Ir = 480 kPa•ms), while beam C100-No.5(HSR) survived this impulse and failed at Blast 4 (Ir = 750 kPa•ms). No further enhancement in resistance was observed in beam C100-No.6(HSR) which also failed at Blast 4. In terms of failure mode, the C100No.4(HSR) and C100-No.5(HSR) beams failed in flexure with crushing 47

1 2 3a 3b 1 2 3b 4 1 2 3a 3b 1 2 3b 4

C50-No.4 (HSR)

Z (m/ kg1,/3)

22.9 38.5 50.1 60.3 22.1 41.7 61.1 78.0 27.6 40.4 52.0 58.2 22.3 43.8 59.1 77.6

231.7 357.5 443.2 515.3 258.5 394.1 568.0 743.7 281.1 403.6 479.6 540.3 216.4 377.6 547.5 749.7

48 12.0 8.8 7.9 12.2 8.2 6.7 12.3 8.6 6.8 6.2

22.9 20.8 21.8 22.0 21.1 22.2 22.4 21.0 21.6 23.7

13.2 30.4 44.5 11.5 21.4 79.6 10.4 15.1 32.9 118.1

10.9 16.6 26.2 –

13.4 24.3 37.3 64.5 13.0 20.1 34.0 77.2 10.2 22.4 33.8 52.7 9.1 17.7 26.8 64.7

3.6 14.2 6.6 2.7 4.7 22.1 2.0 0.2 12.4 71.7

2.1 1.0 1.9 25.2

2.6 1.4 6.6 20.2 3.7 1.2 0.8 39.8 1.0 1.3 3.9 8.7 3.6 3.1 1.2 20.0

23.7 23.9 26.4 23.0 23.3 42.5 23.3 21.5 22.3 54.1

23.5 21.7 21.5 –

23.8 22.4 23.9 29.6 23.6 21.7 21.9 38.9 23.3 22.5 23.7 27.7 23.2 21.6 21.7 29.4

tmax (ms)

0.7 1.6 2.3 0.6 1.1 6.4 0.6 0.8 1.7 6.1

0.5 0.8 1.2 –

0.6 1.1 1.7 3.0 0.6 0.9 1.6 3.5 0.5 1.0 1.5 2.4 0.4 0.8 1.2 3.0

θmax (o)

Minor F cracks Moderate F cracks Cover spalling Hairline F cracks Moderate F cracks Severe crushing No damage Minor F cracking Moderate F cracking Severe crushing

Hairline F cracks Hairline F&S cracks Moderate F&S cracks Severe cover spalling No damage Minor F&S cracks Moderate F&S cracks Shear failure Hairline F cracks Moderate F&S cracks Further cracking Severe cover spalling No damage Minor F cracking Moderate F cracking Cover spalling & Severe crushing No damage Minor F cracking Moderate F&S cracks Shear & bond failure

Observed damage




Superficial Moderate Heavy Superficial Moderate Hazardous Superficial Superficial Moderate Hazardous

Superficial Superficial Moderate –

Superficial Moderate Moderate Heavy Superficial Superficial Moderate Heavy Superficial Moderate Moderate Heavy Superficial Superficial Moderate Heavy

CSA S850 response limits and component damage3 Response Expected damage limit level

Note: 1 Pr = Reflected pressure; Ir = Reflected impulse; td = positive phase duration; Z = calculated scaled distance;. 2 δmax = maximum mid-span displacement; δres = residual mid-span displacement; tmax = time to reach maximum displacement; θmax = maximum support rotations. 3 CSA component damage and response limits: “Blowout” (Component is overwhelmed by blast load causing debris with significant velocities) = response greater than B4; “Hazardous failure” (component has failed with no significant velocities) = response in between B4 and B3; “Heavy damage” (Component has not failed but has significant permanent deflections causing it to be unrepairable) = response in between B3 and B2; “Moderate damage” (Component has permanent deflections but is repairable) = response in between B2 and B1; “Superficial damage” (component has no visible permanent damage) = response less than B1. a Data unavailable due to malfunction of equipment during testing.

11.9 8.6 7.0 –

12.6 8.7 7.4 6.6 12.9 8.3 6.6 5.7 11.0 8.5 7.2 6.8 12.8 8.1 6.7 5.8

22.4 20.4 20.1 –

22.6 21.4 22.3 21.4 22.8 20.6 21.6 21.8 21.9 21.1 21.1 22.6 20.0 20.6 20.5 24.4

δres (mm)

δmax (mm)

td (ms)

Pr (kPa)

Ir (kPa*ms)

Specimen response2

Shockwave properties1

1 24.7 222.8 2 39.7 334.6 3b 55.5 539.2 a 4 – Data from companion NSR beams tested by Li et al. [46]. C100-No.4(NSR) 1 24.4 229.0 2 38.2 348.0 3a 45.0 421.0 C100-15M(NSR) 1 23.9 223.0 2 42.9 340.7 3b 58.6 516.0 C100-20M(NSR) 1 23.6 244.3 2 39.2 360.0 3b 57.4 538.2 4 68.8 702.6

C100-No.6 (HSR)

C100-No.5 (HSR)

C100-No.4 (HSR)

C50-No.5 (HSR)

Blast ID

Beams

Table 6 Results of the dynamic experimental program.

Y. Li and H. Aoude

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Fig. 6. Evolution of blast damage in beams (HSR vs. NSR steel).

of concrete and cover spalling at mid-span. As shown in Fig. 6, crushing was more significant in the more heavily reinforced specimen. Previous researchers have reported the failure pattern becomes more severe with increasing steel ratio [23]. The failure mode of the C100-No.6(HSR) specimen was different; in addition to the damage at mid-span, large diagonal shear cracks were visible in the shear span, with signs of loss of reinforcement bond at this location (see Fig. 6). The blast results clearly point to the importance of properly detailing the longitudinal and transverse reinforcement in beams designed with high-strength bars (i.e. ensuring ρ < ρb, providing sufficient transverse reinforcement to deal with increased shear demands, and ensuring longitudinal bars are properly anchored). The provision of compression bars and transverse reinforcement in the form of closely spaced ties (closed hoops) throughout the span is also recommended to enhance the ductility and flexural performance of beams designed with high-strength bars.

in each set had identical properties (2-No.4 or 2-No.5 high-strength bars) but were constructed with concretes having specified strengths of 100 MPa and 50 MPa, respectively. Fig. 8 compares the response of specimens C100-No.4(HSR) & C50No.4(HSR) under dynamic loading and shows that the use of higher strength concrete improved the control of displacements at equivalent blasts. At Blasts 1, 2, 3a and 3b, maximum displacements for the C100No.4(HSR) specimen were decreased by 24%, 8%, 9% and 18%, when compared to the companion built with C50 concrete. Similarly, residual displacements were reduced by 62%, 7%, 41% and 57% at these same blasts when comparing the results of the C100 and C50 beams. It can be concluded that the use of higher strength concrete improves blast performance by reducing maximum and residual displacements in this set. The results match the observations made by Li et al. [46] for the companion beams built with normal-strength bars (C100-No.4(NSR) & C50-No.4(NSR)). Several previous studies have reported that increasing concrete compressive strength enhances the flexural behavior, stiffness and ductility of HSC beams, and this may explain the observed enhancement in blast performance [62]. Fig. 6 shows the failure mode of the two specimens; it can be observed that both beams failed at the same blast intensity (Blast 3b) due to severe spalling of the cover concrete in the mid-span region, with crushing of concrete in the compression zone. While spalling in both cases was severe, it can be observed that the damage states are quite similar. The effect of concrete strength is further examined by comparing the responses of beams C100-No.5(HSR) & C50-No.5(HSR). Both beams

4.3. Effect of concrete strength Design of beams with high-strength bars may be more efficient with high-strength concrete (HSC). Increasing the concrete strength increases the balanced reinforcement ratio (limit between under- and over-reinforced behavior) which can allow for an increase steel reinforcement area [5]. The effect of concrete strength is studied by comparing the responses of two sets of beams: (1) C100-No.4(HSR) & C50-No.4(HSR) and (2) C100-No.5(HSR) & C50-No.5(HSR). The beams 49

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Fig. 7. Effects of reinforcement ratio on displacements under blast loads.

Fig. 8. Effects of concrete strength on displacements under blast loads.

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had the same longitudinal and transverse steel ratios, however the reduced concrete strength in beam C50-No.5(HSR) results in over-reinforced conditions (ρ/ρb = 1.28, which compares to ρ/ρb = 0.9 for beam C100-No.5(HSR)). As with the previous set, the C100 specimen with No.5 bars showed reduced mid-span displacements when compared to the companion beam built with C50 concrete. As shown in Fig. 8, maximum displacements were reduced by 30%, 12% and 21% at Blasts 1, 2 and 3b when comparing the results of the C100 and C50 specimens. At the failure shot (Blast 4), the maximum and residual displacements for the C100 specimen were 16% and 50% lower when compared to the C50 beam. Both beams failed at Blast 4, but with different failure modes. Specimen C100-No.5(HSR) failed in flexure, with crushing of concrete at mid-span and spalling of the cover in the tension zone. In contrast, the use of lower-strength concrete in beam C50-No.5(HSR) resulted in a brittle shear failure, which indicates that the amount of transverse reinforcement was insufficient in this specimen. Louw et al. [45] previously reported that doubling the concrete strength enhanced the shear resistance of reinforced concrete beamcolumns by 33% under dynamic impact loading. To examine the effect of concrete strength on shear capacity, the nominal shear resistance of beams C100-No.5(HSR) & C50-No.5(HSR) was predicted using the CSA A23.3-14 standard [63]. According to this model, the shear resistance of a reinforced concrete member (Vr) can be taken as the combination fc b w d v (where β = aggregate interof a concrete component, Vc = lock factor; fc = concrete cylinder strength; and bwdv = are the web

when compared to their NSR companions. However, the beams with high-strength bars showed reduced ductility when compared to the beams with conventional steel bars. Using the approximate method s / sy ) of the beams with No.4 defined in Fig. 3d, the ductility ratios ( max and No.5 high-strength bars were found to be 1.2 and 1.1, which compare to values of 5.4 and 2.7 for the companions with No.4 and 15 M normal-strength bars. In the No.6/20 M set, the beam with normal-strength bars showed a ductile “steel-controlled” failure, while the companion beam with high-strength bars showed a brittle “concrete-controlled” failure, with crushing occurring prior to the development of yield stresses in the bars. As noted before, the C100No.6(HSR) specimen was “over-reinforced”, which explains the difference in failure mode. Despite the reduction in ductility, the beams with HSR bars showed similar energy-absorption capacity when compared to their NSR companions. When examined in terms of toughness Aus , beam C100-No.4(HSR) showed a reduction of only 17% in toughness when compared to beam C100-No.4(NSR). Similarly, beam C100-No.5(HSR) showed a 13% increase in toughness when compared to the companion with 15 M normal-strength bars. Likewise, despite the difference in failure mode, the beams in the No.6/20 M set showed comparable toughness ( Aus = 3100 vs. 3000 kN mm). The failure photos in Fig. 5 shows that spalling and crushing were somewhat more severe in the beams with HSR bars when compared to the NSR companions. The responses of the HSC beams built with high-strength versus normal-strength bars under dynamic loading are compared in Figs. 9,10 and Table 6. The comparisons show that use of high-strength reinforcement results in important enhancements in blast performance, both in terms of displacement control and overall blast capacity. In the No.4 set (C100-No.4(HSR) vs. C100-No.4(NSR)) the use of highstrength reinforcement reduced maximum displacements by 22%, 26% and 24% at Blasts 1, 2 and 3a, respectively (see Fig. 9). The reductions in residual displacements were more significant and correspond to 72%, 91% and 41% at these blast intensities. Similarly, the inclusion of highstrength bars in No.5/15 M set (C100-No.5(HSR) vs. C100-15M(NSR)) led to reductions of 21%, 17% and 66% in maximum displacements at Blasts 1, 2 and 3b (see Fig. 10). Residual displacements were also better controlled in the beam with high-strength bars when compared to beam C100-15M(NSR), with reductions of 34% and 95% at Blast 2 and 3b. Substitution of conventional reinforcement with high-strength bars also increased blast capacity. As shown in Fig. 6, failure of beams C100No.4(HSR) and C100-No.5(HSR) occurred at Blast 3b and 4, respectively (Ir = 540 & 750 kPa•ms); in comparison companion beams C100No.4(NSR) and C100-15M(NSR) failed at Blast 3a and 3b, respectively (Ir = 421 & 516 kPa•ms). The beams in each set show similar failures, however damage was greater in the beams with high-strength bars (in particular, spalling was more extensive). As noted earlier, beam C100-No.6(HSR) was over-reinforced, with a ρ/ρb ratio = 1.17 which limited the benefit of the high-strength reinforcement. As shown in Fig. 10 the C100-No.6(HSR) and C100-20M (NSR) specimens showed similar displacements at Blasts 1 and 2, as the reinforcement in both beams remained in the elastic range. At Blast 3b, the beam with high-strength bars showed reductions of 20% and 85% in maximum and residual displacements when compared to its NSR companion. However, unlike the previous two sets, the use of highstrength bars did not lead to an increase in blast capacity, with both specimens failing at Blast 4 pressures. Moreover, the over-reinforced steel ratio in the specimen with No.6 HSR bars affected failure mode, with significant shear cracking and signs of bond failure observed in the beam with high-strength reinforcement (see Fig. 6). Goldston [25] previously noted that increasing the steel ratio in over-reinforced beams results in more prominent local damage and increased shear cracking. Magnusson et al. [37] also noted that high steel ratios in HSC beams can change the failure mode from flexure to shear, which corresponds to the result in this study.

Av f y

width and shear depth), and a steel component, Vs = s d v cot , which depends on the number of stirrups that cross the diagonal shear crack (where fy = yield strength of the reinforcement, s = spacing of the shear reinforcement; and θ = angle of the diagonal shear crack with respect to the longitudinal axis). Using the simplified method in the CSA A23.3 standard ( = 0.18 and = 35 ), the nominal shear capacities of beams C50-No.5(HSR) and C100-No.5(HSR) are predicted to be 119 kN and 132 kN, respectively, due to the difference in concrete cylinder strength. At Blast 4, the peak reflect pressure (Pr) was approximately 78 kPa for both beams. Multiplying this pressure by the area of the load transfer device (A) results in a maximum applied shear force of Vf = 0.5*Pr A 132 kN, which can partly explain the shear failure observed in beam C50-No.5(HSR). In addition to having insufficient shear resistance, beam C50-No.5(HSR) was over-reinforced (ρ/ρb > 1) which may have also contributed to its failure mode. The results show that the use of HSC is better suited when designing reinforced concrete beams with high-strength bars for blast effects, as it increases shear resistance and increases the balanced steel ratio (ρb) which can prevent over-reinforced conditions. 4.4. Effect of reinforcement type in the C100 series The influence of reinforcement type was a key parameter investigated in this study. The effect of this parameter is studied by comparing the static and dynamic responses of the following three sets of high-strength concrete specimens: (1) C100-No.4(HSR) & C100No.4(NSR) and (2) C100-No.5(HSR) & C100-15M(NSR) and (3) C100No.6(HSR) & C100-20M(NSR). The beams in each set were built with C100 concrete and had similar steel ratios, but were constructed with high-strength and normal-strength bars (HSR vs. NSR), respectively. Fig. 3c compares the static responses of the companion specimens in each set and shows that the use of HSR bars had a significant effect on the load-deflection curves. While the beams with normal-strength reinforcement showed clear yield points and deflection plateaus, the beams with high-strength bars showed more linear responses, with no distinct yield points, and slight rounding of the load-deflection curves before failure occurred due to concrete crushing. Nonetheless, the use of Grade 690 MPa reinforcement resulted in significant enhancements s in HSC beam capacity, with increased in maximum load (Pmax ) of 68%, 86%, and 45% for the specimens with No.4, No.5 and No.6 HSR bars 51

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Fig. 9. Effects of steel type on displacements under blast loads (part 1 of 2).

Fig. 10. Effects of steel type on displacements under blast loads (part 2 of 2).

4.5. Effect of reinforcement type in the C50 series

built with C50 concrete and No.4 Grade 690 MPa vs. 400 MPa bars, respectively. Continuing the trend observed in the C100 series, the use of high-strength bars in the C50 beams led to a better control of maximum and residual displacements at equivalent blasts (see Fig. 9).

The effect of reinforcement type is further examined by comparing the response of beams C50-No.4(HSR) vs. C50-No.4(NSR) which were 52

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While displacements were similar at Blast 1, reductions of 18% and 22% in maximum displacement were recorded for beam C50No.4(HSR) at Blasts 2 and 3a when compared to its NSR companion. Similarly, residual displacements were also significantly reduced by 89% and 74% at these blasts for the beam containing high-strength bars. The use of high-strength reinforcement also led to an increase in blast capacity, with failures occurring at Blast 3b vs. Blast 3a (Ir = 515 vs. 448 kPa ms) for beams C50-No.4(HSR) vs. C50-No.4(NSR) (see Fig. 6). Both specimens failed in a similar manner, with spalling of cover concrete in the mid-span tension region, however spalling was more extensive in the C50-No.4(HSR) specimen. As shown in Fig. 8, increasing the high-strength reinforcement ratio further to ρ = 1.5% in beam C50-No.5(HSR) led to some reductions in maximum and residual displacements when compared to beam C50No.4(HSR) (ρ = 1%). However, as noted before, the increased shear demand, coupled with the over-reinforced conditions, transformed the failure from flexure to shear in the beam with C50 concrete and No.5 HSR bars (Fig. 6).

Increased damage at failure was also observed when comparing the dynamic and static failure photos of the C100 beams with No.5 highstrength bars (C100-No.5(HSR)). As with the previous set, the dynamic companion showed more important spalling in the constant moment region. Likewise, the specimen tested under blast loads showed more severe crushing in the mid-span region (see Figs. 6 and 11b). A study of the displacement time-history graphs and high-speed video also shows that the beams suffered large rebound deformations during dynamic testing. The large rebound displacements combined with the repeated blast tests may have therefore weakened the unreinforced compression zone prior to failure. The results pointed to the importance of providing well-confined compression bars to improve the resistance of the midspan compression region. Previous research indicates that the use of closely-spaced hoops and compression bars can reduce damage and increase the ductility of beams subjected to dynamic loading, and also increase the capacity of the compression zone and prevent bar buckling [16,20,35]. The effect of concrete and steel type on failure mode can further be illustrated by comparing the high-speed video stills in Fig. 12. In the No.4 series (see Fig. 12a), it can be seen that concrete strength (C100 vs. C50) does not alter the failure process (regardless of steel type), however spalling and flying debris was clearly more significant in the beams with high-strength bars when compared to their NSR companions. In the No.5/15 M series (see Fig. 12b), severe crushing occurred in the companion C100 beams built with either high-strength or normal-strength bars, whereas the combined use of lower-strength C50 concrete and high-strength bars results in shear failure.

4.6. CSA S850 response limits The CSA S850 blast standard defines various response limits designated as B1 through B4 which can be used in the blast assessment of reinforced concrete structures [1]. These limits correlate with specific support rotations (θmax) and ductility ratios (μmax) which define component damage levels which go from “Superficial” (less than B1) to “Blowout” (greater than B4); for example, in the case of beams µmax = 1, max = 2 , max = 5 and max = 10 , correlate with limits B1, B2, B3 and B4, respectively. Table 6 compares the support rotations observed in the experiments with the response/damage limits in the standard. In general, the results show that the damage states are underpredicted in some cases, particularly at failure. For example, beam C100-No.5(HSR) sustained a support rotation of 3° under Blast 4, which corresponds to “Heavy” damage according to the standard (component has not failed …). However, the severe crushing and spalling failure would be better classified as being “hazardous” in this case (component has failed …). As a comparison, the companion beam with normalstrength bars (C100-15M(NSR)) showed similar severe damage but a much larger rotation of 6.1° at failure, and the standard correctly classifies the damage state as “hazardous” in this case (see Table 6). In general, the results indicate that the response limits in the CSA S850 blast standard need to be modified if they are to be applied to beams with high-strength ASTM A1035 bars, as such beams may show lower than expected rotations at failure.

4.8. Dynamic vs. static resistance Fig. 13a shows a comparison of the static and dynamic resistance curves for beams C100-No.4(HSR) and C100-No.5(HSR). The dynamic results were obtained by summing the support reactions recorded by the load-cells during testing. It can be seen that static and dynamic resistance curves follow similar trends. The maximum loads under dyD s / Pmax namic and static loading, and their ratio (Pmax ) are also reported in the plots. Table 5 presents the results for all specimens, including the companion beams built with normal-strength bars. In general, higher loads were recorded for the high-strength concrete beams in both the HSR and NSR sets under blast loading when compared to static loading, which corresponds with the observations of other researchers [37]. The dynamic-to-static strength ratios were found to be 1.20 and 1.23 for beams C100-No.4(HSR) and C100-No.5(HSR) at Blast 3b and 4, respectively. The increase in capacity can be explained by the increase in concrete and reinforcement strengths under high strain-rates. However, as shown in Fig. 13a (iii), the strength ratios were noticeably larger for the beams with normal-strength bars when compared to the compaD s / Pmax nions with high-strength steel (average Pmax ratios of 1.40 and 1.22 in the NSR and HSR series, respectively). Previous research indicates that the strain-rate dependence of steel reinforcement reduces as the yield strength is increased [8], and this can possibly explain the reduced load ratios in the HSR series. In general, higher toughness results ( AuD / Aus ratios greater than 1.0) were also observed for the beams in both sets under blast loads, with larger dynamic toughness ( AuD ) results for the beams with high-strength versus normal-strength bars (see Table 5). The effect of the test parameters on the dynamic resistance curves is further studied in Fig. 13b and c. Examining the effect of concrete strength (see Fig. 13b), it can be observed that the C100 and C50 specimens built with No.4 high-strength bars showed similar dynamic capacities and resistance curves. In the No.5 series, the beam with C100 D concrete showed larger maximum dynamic resistance (Pmax = 240 kN vs. 210 kN) when compared to its C50 companion, due to the difference

4.7. Effect of loading-rate and concrete/steel type on failure mode The failure modes of the beams under static and dynamic conditions can be examined by studying the failure photos in Fig. 5and 6. In the case of the C100 beams with No. 4 high-strength bars (C100No.4(HSR), the static and dynamic specimens showed similar flexural failure modes, however damage under dynamic loading was more prominent and was associated with more severe spalling of cover concrete. High-speed video shows that the sudden spalling results in significant flying debris, which can pose dangers to building occupants (see Fig. 11a). Burrell et al. [64] noted that the addition of steel fibers in columns subjected to blasts can prevent cover spalling. Similarly, Magnusson et al. [37] reported that the use of fibers is effective in enhancing damage control in HSC beams under blast loads. Previous studies have also reported that fibers increase shear resistance and improve ductility under dynamic effects [28,32]. Research on the benefits of fibers in HSC beams designed with high-strength bars is recommended.

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Fig. 11. High-speed stills showing failures in beams C100-No.4(HSR) & C100-No.5(HSR).

Fig. 12. Effect of concrete & steel type on beam failures.

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Fig. 13. Dynamic resistance curves.

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Table 7 Constitutive material and dynamic increase factor models. Material model Concrete in compression

fc c ( c ) c0 c ) ck c 1+( c0

Popovics [65]: Stress-strain relationship: fc =

c

Concrete in tension

DIF model

= 0.8 +

fc ; 17

Ec = 3320 fc + 6900;

c0

=

fc · c Ec c 1

Saatciogluet al. [66]:

Where:

DIFc={

1.0 Ascending k={

0.67 +

Linear–elastic model with: Peak stress: ft = 0.33 fc Peak strain:

t

fc 62

Descending

=

ft Ec

0.03ln ( ) + 1.30 1.0 30s 0.55ln ( ) 0.47 > 30s 1

Malvar and Ross [67]: DIFt={

1

( ) ,

1s

s

* ( )1/3, s

Log * = 6 Steel in tension

0.0024 s s 2.96 0.0024 < s s + 0.0019

1040 0.02 <

s

0.02

At ultimate

0.06

Case 2: Ramberg-Osgood equation: fs = 200, 000 s × (A +

1

=

1 ; (1 + 8fc / 10)

s

Saatcioglu et al. [66]: At yield DIFy = 0.034 ln ( ) + 1.30

200, 000 Case 1: ACI-ITG-6R [5]: fs ={1170

2;

A

1 [1 + (B )C ] C

)

1

> 1s

1

= 10 6s

1

Where:

1.0

DIFu = 0.0101 ln ( ) + 1.10

1.0

fu

200, 000 s s 0.00345 690 s > 0.00345 200, 000 s s 0.00275 Case 4: Elasto-plastic with fy = 550 MPa fs ={ 550 s > 0.00275 Case 3: Elasto-plastic with fy = 690 MPa fs ={

Note: fc – concrete stress at strain ɛc; fc – peak concrete stress; ɛc0 – peak concrete strain; Ec – concrete elastic modulus; k – slope control parameter; βc – curve fitting factor; ft – peak concrete tensile stress at strain ɛt; fs – steel stress at strain ɛs; fy – steel yield stress; ɛy – steel yield strain; fsh – steel hardening stress; ɛsh – steel hardening strain; fu – steel ultimate stress; ɛu – steel ultimate strain; s – static strain rate; – dynamic strain rate; α, γ, β*and δ = various curve fitting parameters; DIFc, DIFt, DIFy & DIFu: Dynamic increase factors for concrete in compression & tension and steel at yield & ultimate; Parameters A,B,C in R-O function obtained from coupon stress-strain data (see Table 3).

in failure mode (flexure vs. shear). Examining the effect of reinforcement ratio, it can be seen that the C100 beam with No.5 bars showed D larger stiffness and an increased dynamic strength (Pmax = 240 kN) D when compared to the companion with No.4 bars (Pmax = 152 kN). As observed in Fig. 13c, the beams with high-strength reinforcement showed similar stiffness but larger peak strengths under dynamic loading when compared to the companions with normal-strength bars. Finally, examining Fig. 13d, it can be seen that the peak dynamic loads increased with an increase in blast intensity; for example, beam C100D s / Pmax No.4(HSR) showed strength ratios of Pmax = 1.16 & 1.20 at Blasts 3a & 3b, while the responses remained elastic at Blasts 1 and 2.

components exhibit increased capacities when subjected to dynamic loading. To account for this apparent strain-rate effect, the expressions proposed by Saatcioglu et al. [66] and Malvar and Ross [67] were used to predict the dynamic increase factors of concrete in compression (DIFcf) and concrete in tension (DIFt). Based on the strain readings taken at the center of the steel reinforcement, the strain-rates ( ) during the tests varied between 0.1 and 1 s−1 (see Fig. A3(a)), however given the variability in the strain-readings a constant strain-rate of 1 s−1 was used in the analysis. Using this assumed strain-rate, the models predicted dynamic response factors of DIFc= 1.14 and DIFt= 1.20. No model exists for the dynamic increase factor of Grade 690 MPa reinforcement conforming to ASTM A1035 [8]. In this paper, the relationships proposed by Saatcioglu et al. [66] were selected to modify the static stressstrain curve of the high-strength steel bars. Previous research indicates that the dynamic increase factor of steel is reduced at yield when compared to ultimate [8]; since the high-strength bars do not show a well-defined yield point, the entire stress-strain curve was modified with a single factor of 1.10, corresponding to the dynamic increase factor at ultimate stress (DIFu) when = 1 s−1. Sample stress-strain curves for the HSC concrete and high-strength reinforcement under static and high strain-rates are shown in Fig. 14a. In the next step, sectional analysis was used to develop moment-curvature relationships (M ) for each beam using the procedure shown in Fig. 14b. The beams were then discretized into m equal segments along their halflength. Using the M- ϕ relationships and integration, the load-deformation relationships were then obtained using the procedure outlined in Fig. 14c.

5. Prediction of response of beams with HSR bars 5.1. Development of resistance curves The dynamic response of the beams with high-strength bars was predicted using dynamic inelastic single-degree-of-freedom (SDOF) analysis [44]. In this study, the SDOF approach was only used to capture the global (maximum displacement) response of the specimens. In the first step, resistance functions were developed using the dynamic material models shown in Table 7. For concrete, the static response in compression was defined using the Popovics [65] model, while tensile response was modelled using a linear relationship having a peak stress of ft = 0.33 fc and a slope equal to Ec (where fc = compressive strength and Ec = elastic modulus). Four different stress-strain models were initially considered for the high-strength reinforcement, including: (1) a three-part function proposed in the ACI ITG-6R guide [5], (2) a Ramberg-Osgood (R-O) function which closely replicates the experimental stress-strain behavior of the ASTM A1035 bars and (3 & 4) elastic-perfectly plastic relationships having yield strengths of 690 and 550 MPa, respectively. Based on the results of the static analysis (see next section), the ACI ITG function was used to develop the dynamic resistance curves. Reinforced concrete structural

5.2. SDOF analysis procedure The dynamic response of a single-degree-of-freedom (SDOF) system can be determined by solving the equation of motion shown below, where m = mass, c = damping coefficient, k = stiffness, F(t) = timedependent applied load, and u = displacement:

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Fig. 14. Material models, sectional analysis & resistance curve procedures.

mu¨ (t ) + cu (t ) + k (u (t )) = F (t )

(1)

where u¨ (t ) and u(t) = acceleration and displacement of the beam at mid-span; k(u(t)) = resistance as a function of displacement; and where KM, KL and KLM = mass, load and load-mass factors used to transform the real system into the equivalent SDOF model. In this study, KLM factors of 0.6 and 0.56 were used to reflect the change in assumed beam deflected shape before and after yield, respectively (refer to Biggs [68] or UFC 3-340-02 [73] for further details). The mass, m, was taken as the mass of the beam plus the load-transfer device (450 kg), while the forcing function was taken as F (t ) = APr (t ) , where Pr(t) = idealized triangular pressure-time history having the same peak pressure and impulse found in the tests (see Table 6), and where A = loaded-area of the load-transfer device (3.4 m2). With the idealized pressure-time histories, transformation factors and resistance functions defined, the equations of motion were solved using the average acceleration method in software RCBlast [74].

In this study, maximum response under blast loading typically occurred during the first-cycle of response (see Table 6 and Fig. A3(b)), therefore the effects of damping were conservatively ignored [68,69]. To determine specimen response, each beam was transformed into an equivalent SDOF system by selecting a governing degree of freedom (in the case, the beam mid-span), where the mass, stiffness, and applied force of the real system were lumped. Transformation factors were used to transform the real system into the equivalent SDOF [68]. Eq. (2) shows the generalized form of the equation of motion for the equivalent SDOF system [69–72]:

KM mu¨ (t ) + KL k (u (t )) = KL F (t ) or KLM mu¨ (t ) + k (u (t )) = F (t )

(2) 57

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Y. Li and H. Aoude

Fig. 15. Comparison of experimental and analytical resistance curves (static and dynamic).

Table 8 Results of the static beam analysis. Analytical peak load and maximum displacement predictions a s a (Peak load Ratio: Pmax ) Pmax /Pmax

C100-No.4(HSR) C100-No.5(HSR) C100-No.6(HSR) Average Ratio Coefficient of variation

a max

(Displacement Ratio:

s a max / max )

Case 1

Case 2

Case 3

Case 4

Case 1

Case 2

Case 3

Case 4

126.7 (1.00) 169.4 (1.15) 205.0 (0.97) 1.04 0.092

139.4 (0.91) 196.6 (0.94) 211.0 (0.95) 0.95 0.043

91.2 (1.39) 136.3 (1.43) 183.1 (1.09) 1.30 0.144

73.5 (1.72) 111.0 (1.75) 163.2 (1.22) 1.57 0.192

46.1 (0.76) 30.6 (1.11) 24.5 (1.11) 0.99 0.201

41.2 (0.85) 31.3 (1.09) 23.9 (1.14) 1.03 0.147

42.6 (0.83) 34.0 (1.00) 26.1 (1.04) 0.96 0.120

74.6 (0.47) 38.8 (0.88) 28.3 (0.96) 0.77 0.340

a s s Note: Pmax and amax = predicted peak load and max. displ.; Pmax and max = experimental peak load and max displ.;. Case 1: ACI ITG-6R; Case 2: R-O curve; Case 3: 690 MPa elasto-plastic; Case 4: 550 MPa elasto-plastic.

5.3. Static analysis results

uses the experimental stress-strain data. The displacement ratios for Cases 1 and 2 were not as accurate, with average ratios of 0.99 and 1.03, but high coefficients of variation. With the exception of the beam with No.4 HSR bars, the analytical maximum displacements are underpredicted by both models due to over-estimation of HSC beam stiffness (this same effect has previously been reported by Shahrooz et al. [4]). The mean peak-load ratios were 1.30 and 1.57 for Cases 3 and 4, which used elastic-perfectly plastic models with fy of 690 and 550 MPa. Based on these results, the ACI ITG model was used in the development of the dynamic resistance curves.

Fig. 15 compares the analytical and experimental static load-deflection curves for beams C100-No.4(HSR) and C100-No.5(HSR) obtained using the procedure described in Section 5.1. The analytical resistance curves were predicted using the four steel models described previously, and are labeled as Cases 1–4 in the charts. The computed-tos a /Pmax measured peak-load ratios (Pmax ) and maximum displacement ras a / max tios ( max ) for all beams are shown in Table 8. Considering all specimens, the average load ratios for Cases 1 and 2 (ACI ITG and R-O) are 1.04 and 0.95, with higher capacities predicted for Case 2, which

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Y. Li and H. Aoude

No.5(HSR) when compared to the experimental data. In both cases, the analytical resistance curves show a more rounded ascending branch, with an over-prediction of stiffness, when compared to the experiments. Fig. 16 compares the experimental and predicted mid-span displacements (δmax and δanls) for beams C50-No.4(HSR), C100No.4(HSR), C100-No.5(HSR) and C100-No.6(HSR) at Blasts 1–4. The results for all tests along with statistical data are reported in Table 9. The mean displacement ratio (δmax/δanls) is found to be 1.07, with a coefficient of variation of 0.153, when considering all blasts, which confirms that the SDOF procedure can predict the blast response of the beams with high-strength bars with reasonable accuracy. At Shots 1, 2 and 3, the mean displacement ratios are found to be 1.01, 1.03 and 1.07, while the accuracy is found to reduce at Shot 4 (Blast 3b in the No.4 series and Blast 4 in the No.5/No.6 series), which shows a mean displacement ratio of 1.18. One possible reason for the reduced accuracy is the effect of accumulated damage from repeated blast testing which was not considered in the analysis. Another possible source of error is the over-prediction of stiffness in the analytical resistance curves. In general, the results are also not as well predicted for the beam with No.6 high-strength bars, which was over-reinforced. Other possible sources of error in the SDOF analysis include inaccuracies in the material and DIF models, resistance function procedure, assumption of constant strain-rate, choice of transformation factors, blast load idealizations and the assumptions regarding the boundary conditions and distributions of mass and loading in the real structure. In this study, the SDOF approach was used to predict the global response of the specimens, however it did not capture local response characteristics. Alternative analysis methods such as FEM analysis can possibly be used to better capture the response of HSC beams reinforced with high-strength bars and allow for an evaluation of other response characteristics such as cracking, spalling, failure mode and load-time histories. Further FEM research as presented by Chen et al. [42] and Qu et al. [43] and others are recommended.

Fig. 16. Dynamic analysis results.

5.4. Dynamic analysis results Fig. 15 also shows the computed and measured dynamic resistance curves for beams C100-No.4(HSR) and C100-No.5(HSR). The experimental resistance functions were obtained by summing the dynamic reactions from the load cells, while the analytical resistance curves were obtained using the ACI-ITG steel model and the previously defined concrete and DIF models. In general, the analytical predictions follow the same trends observed in the experiments. The predicted and measured peak dynamic strengths are similar for beam C100-No.4(HSR), while the predicted strength is approximately 16% lower for beam C100Table 9 Results of the dynamic (SDOF) analysis. Beams

C50-No.4(HSR)

C100-No.4(HSR)

C100-No.5(HSR)

C100-No.6(HSR)

Statistical data

1 2 a

Shot #

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 δmax/δanls Mean Coefficient of variation Max. Min.

Blast ID

1 2 3a 3b 1 2 3a 3b 1 2 3b 4 1 2 3b 4 Overall 1.07 0.153 1.30 0.76

Idealized shockwave properties1

Maximum mid-span displacements2

Pr (kPa)

Ir (kPa•msec)

td (msec)

δmax (mm)

δanls (mm)

δmax/δanls

% Error

22.9 38.5 50.1 60.3 27.6 40.4 52 58.2 22.3 43.8 59.1 77.6 24.7 39.7 55.5 -a Shot 1 1.01 0.222 1.30 0.76

231.7 357.5 443.2 515.3 281.1 403.6 479.6 540.3 216.4 377.6 547.5 749.7 222.8 334.6 539.2 – Shot 2 1.03 0.162 1.26 0.87

20.2 18.6 17.7 17.1 20.4 20.0 18.4 18.6 19.4 17.2 18.5 19.3 18.0 16.9 19.4 – Shot 3 1.07 0.141 1.26 0.93

13.4 24.3 37.3 64.5 10.2 22.4 33.8 52.7 9.1 17.7 26.8 64.7 10.9 16.6 26.2 – Shot 4 1.18 0.06 1.26 1.13

13.3 23.6 32.8 57.0 13.5 25.9 34.9 41.7 9.4 18.5 28.8 56.0 8.4 13.2 20.8 –

1.01 1.03 1.14 1.13 0.76 0.87 0.97 1.26 0.97 0.96 0.93 1.16 1.30 1.26 1.26 –

1.4% 3.2% 13.7% 13.2% −24.4% −13.5% −3.1% 26.5% −2.9% −4.0% −7.0% 15.6% 30.0% 25.6% 25.7% –

Pr = Reflected pressure; Ir = Reflected impulse; td = positive phase duration;. δmax = experimental mid-span displacement; δanls = analytical mid-span displacement. No data recorded during testing.

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6. Conclusions

modes and collapse mechanisms under static and dynamic loading. However, specimens tested under blast loads were susceptible to sudden cover spalling and more severe crushing failures. It is recommended that beams designed with high-strength reinforcement be provided with compression bars and closely-spaced ties to increase the capacity of the compression zone and prevent bar buckling [20]. The use of fibers may also be a solution to better control spalling & reduce flying debris. (4) Comparison of dynamic and static resistance curves shows that the strength of HSC beams designed with both normal-strength and high-strength bars increases under blast loads. However, the strength-ratios were lower for the beams with high-strength bars, which may be due to the reduced strain-rate sensitivity of higher grade reinforcement. (5) The results confirm that dynamic inelastic SDOF analysis can be used to predict the blast response of reinforced concrete beams designed with Grade 690 MPa high-strength bars, although the accuracy reduced at later blasts due to the effects of accumulated damage.

As the use of high-strength reinforcement becomes more prevalent, there is an important need for data to gain better understanding of the blast behavior of reinforced concrete structures designed with highstrength bars. This paper presented results from shock-tube blast tests on high-strength concrete beams reinforced with Grade 690 MPa ASTM A1035 bars. Parameters investigated included the effects of steel type, concrete strength, steel ratio and loading rate. The following conclusions can be drawn from this study: (1) The use of high-strength reinforcement in HSC beams improved blast performance by increasing blast capacity and better controlling peak displacements. Increasing the high-strength steel ratio further improved blast performance. However, the benefit of the high-strength bars was negated when increasing the steel ratio beyond balanced conditions. (2) The results show that the use of higher strength concrete is better suited for beams designed with high-strength bars. In the No.4 HSR series, doubling the specified concrete strength from 50 to 100 MPa led to improved control of maximum and residual displacements. In the No.5 HSR series, increasing the concrete strength improved blast capacity and prevented shear failure. In general, the results also point to the importance of carefully detailing the transverse reinforcement in beams built with high-strength bars. (3) Companion beams with high-strength bars showed similar failure

Acknowledgment This research program was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors wish to express their gratitude to MMFX Technologies, a Commercial Metals Company for the donation of the steel materials used in this study.

Appendix Figs. A1–A3 and Tables A1–A4.

Fig. A1. Stress-strain relationship of high-strength reinforcement and effect on beam response.

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Y. Li and H. Aoude

Fig. A2. Summary of previous research on effect of steel grade in beams and slabs tested under impact and blast loads (distribution of specimens based on concrete strength).

Fig. A3. (a)Typical strain readings at center of longitudinal steel reinforcing bars and (b) typical pressure and displacement time-history showing positive phase duration (td) and time to maximum response (tmax).

61

62

Beam

Beam Beam Beam Beam Beam Beam

Beam Beam (GFRP) Beam Beam Beam Beam Beam Beam

FM

FM FM FM FM FM FM

FM FM FM FM FM FM FM FM

NSC NSC/HSC UHPC FRC NSC FRC FRC FRC

NSC NSC NSC NSC NSC NSC

NSC

NSC

Concrete type

27–40 40–80 200 42–60 46 42–51 42–45 49–64

36–50 42 24 24–39 40 40

47–55

34

Concrete strength (MPa)

235 732–1605 523 415–464 500 413 498 500

510 400 345 373–407 371 371

464

600

Tension steel strength (MPa)

1.0–2.6 0.5–2 0–1.7 2.1 0.5–0.8 0.8 2.3 1.6

0.9 1.3–2.5 0.6–1.3 0.8–3.2 0.8–2.4 2.4

1.6

0.1–0.2

Tension steel Reinf. ratio (%) Tension steel strength / grade

×

× ×

×

Concrete strength

Parameters investigated

× × ×

×

× × × ×

×

Tension reinf. ratio

×

×

× ×

×

×

Shear reinf. ratio

×

×

Comp. reinf. ratio

× × ×

×

Beam dimensions

Note: FM: Falling mass; NSC: normal-strength concrete, HSC: high-strength concrete, FRC: fiber-reinforced concrete, UHPC: ultra-high performance concrete.

Column

FM

Remennikov & Kaewunruen [13] Saatci & Vecchio [14] Chen & May [15] Fujikake et al. [16] Tachibana et al. [17] Kishi & MIkami [18] Somraj et al. [19] Adhikary et al. [20–23] Zhan et al. [24] Goldston et al. [25] Yoo et al. [26,27] Jin et al. [28] Pham & Hao [29] Chopreza [30] Lee et al. [31] Ulzurrun and Zanuy [32]

Specimen type

Test method

Study

Table A1 Previous experimental research on the impact performance of reinforced concrete beams.

× × ×

× ×

Fiber reinforcement

×

×

×

Boundary conditions

× × ×

×

×

× × × × × ×

×

×

Impact test parameters (mass, height,)

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International Journal of Impact Engineering 130 (2019) 41–67

63

⁎

Closein Closein Closein Closein Closein Closein Farfield NSC

NSC

Beam

Beam

NSC/HSC

NSC

NSC

NSC

NSC

NSC/HSC

NSC

NSC

Concrete type

Beam

Beam

Beam

Beam

Beam

Beam

Beam

Beam

Specimen type

20–40

40

40–70

31–42

27

30

40

40–200

42–56

45

Concrete strength (MPa)

450

395

450

509

322–388

235

395

544–604*

620

328

Tension steel strength (MPa)

0.5–1.0

0.4–1.0

–

0.23

0.8

1.17

0.4–1.0

1.2–2.5

1.1

1.5–3.3

Tension steel Reinf. ratio (%)

×

Tension steel strength/ grade

Parameters investigated

×

×

×

Concrete strength

×

×

×

×

×

Tension reinf. ratio

×

×

Prestressing index

×

×

Shear reinf. ratio ×

Comp. reinf. ratio

×

Beam dimensions

the steel reinforcement in Magnusson's tests had a specified yield stress of 500 MPa (Swedish Grade B500T steel) and the effect of steel grade was not specifically studies.

Stochino [44]

Numerical (FEM) Numerical (FEM) Numerical (SDOF)

Live test

Live test

Live test

Live test

Farfield

N/A

Blast simulator Shock-tube

Magnusson et al. [37] Zhang et al. [38] Zhai et al. [39] Nagata et al. [40] Lee et al. [41] Chen et al. [42] Qu et al. [43]

N/A

Blast simulator

Feldman & Siess [35] Keenan [36]

Type of blast

Test Method

Study

Table A2 Previous experimental and numerical research on the blast performance of beams.

×

×

Fiber reinforcement

×

×

×

Blast test parameters/ scaled distance

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International Journal of Impact Engineering 130 (2019) 41–67

Impact: SL

Impact: SL

Mavis & Greaves [50] Mavis & Stewart [51]

64

Blast: PBS

Blast: ST

Blast: LE

Keenan [36]

Thiagarajan et al. [55]

Li et al. [56]

RC slabs

RC Slabs

PS/RC Beams

RC Beams

RC Beams

RC Beams

RC Beams RC Slabs

5

4

16

19

42

27

4

8

Not reported

8

No. of specimens

305

160–180

191

279

150

127

200 150

406

H (mm)

4572

1300

2743

2590

1981

1981

2133 1828

2438

L (mm)

Slab length × width × thickness 2000 × 1000 × 100

Slab length × width × thickness 1652 × 876 × 102

200

150

127

147

104

127

100 508

254

B (mm)

Beam dimensions

57–129

28–107

42–56

38–84

53

39–43

45

25–44

20 26

20

Concrete strength (MPa)

300–1750

400–572

620

353–685

285–464

285–464

327–464

274–522

124–310

310- 772

Tension steel yield strength (MPa)

Not reported [43, 87, 250]

HSLA-V [80]

ASTM A15 Intermediate [40] ASTM A432 Hard [60] ASTM A431 Hard [75] Other [90]

SD30/685 [40,100]

ASTM A15 Structural [33] ASTM A15 Intermediate [40] ASTM A432 Hard [60]

ASTM A15 Structural [33] ASTM A15 Intermediate [40] ASTM A15 Hard [50]

ASTM A15 Structural [33] ASTM A16 Rail [40] ASTM A15 Hard [50] ASTM A15 Intermediate [40] ASTM A431 Hard [75]

Steel designation [Specified Grade in ksi]

▪ Excessive deflections may be better controlled by prestressing the tensile steel. ▪ When compared to the control slab with convention materials (NSC & NR), substitution with either HSC concrete or HSLA-V bars led to enhanced blast performance. Optimal results when combining HSC and high-strength reinf. ▪ UHPC beam with high-strength steel had the best behavior in terms of displacement control and overall damage tolerance. Introduction of ultra-high-strength steel in UHPC led to a 40% reduction in maximum displacement when compared to mild steel. While the NSC slab with conventional reinforcement suffered a brittle collapse, no damage was observed in the UHPC slab with ultra-high-strength reinforcement.

▪ Falling height needed to rupture the steel reinforcement was found to increase with the increase in the amount and yield strength of the steel reinforcement. ▪ While beam static strength increased when the high-strength steel was substituted for mild steel, beams reinforced with mild steel were better able to withstand severe impact forces. In general, beams with high-strength steel showed poor performance under impact when compared to beams with equal amounts of mild steel. ▪ Majority of beams having hard-grade bars showed higher residual capacity when compared to companions with structural or intermediate type bars. ▪ Beams reinforced with one hard grade bar matched the performance of beams with two structural grade bars. ▪ Beams having higher reinforcement ratios had higher residual capacities, with the best performance obtained for the beam with two hard grade bars, followed by two intermediate grade bars and finally two structural grade bars. ▪ Beams reinforced with high-strength reinforcement showed equal or better performance when compared to those with structural or intermediate grade bars when evaluated in terms of ultimate and residual strength capacity. ▪ Beams with high-strength bars showed increase in deformation capacity with increase in loading-rate (opposite trend observed for beam with conventional reinforcement). ▪ Total energy required to cause failure was lower for beam with high-strength bars when compared to beam with conventional bars at lower loading-rates, however better performance was observed at high loading-rates. ▪ Failure region was smaller (greater damage) in the beam with high-strength bars at low loading-rates, although the failure condition improved at higher loading-rates. ▪ More resistance can be gained with a larger amount of highgrade steel than lower grades of steel.

Primary conclusions

Note: FM: Falling mass, SL: Spring-loaded, DC: Deformation controlled, PBS: pneumatic blast simulator, ST: shock-tube, LE – Live explosive testing, PS: prestressed concrete beam.

FEM

Miyamoto et al. [53]

Impact: SL

RC Beams

Impact: DF

Mavis & Richards [49]

Cernica & Charignon [52]

RC Beams

Impact: FM

Simms [48]

RC Beams

Impact: FM

Mylrea [47]

Specimen type

Dynamic testing method

Study/Authors

Table A3 Previous impact and blast studies investigating the effect of steel reinforcement grade in beams and one-way slabs.

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International Journal of Impact Engineering 130 (2019) 41–67

65

1999

SAS670c

Present

1966 1966 1966 1966 1972 1986 1966 1966 1999 1964 1966 1999 Present Present Present Present

End

Billet Billet Billet Billet Billet Billet Rail Rail Rail Axle Axle Axle Carbon Low-Alloy Stainless Low-Carbon Chromium –

Notes on Steel Type

33 33

33 33

55 55

55 55

Grade 33 (Structural) Min. Min. yield Tensile

70 70 70 70

70 70

40 40

40 40 40 40

70 70

Min. Tensile

40 40

Min. yield

Grade 40 (Intermediate)

80 80 80 80

50 50 50

80 80

Min. Tensile

50

50 50

Min. yield

Grade 50 (Hard)

90 90 90 90 90 90 90 80 90

60 60 60 60 60 60 60

90

Min. Tensile

60 60

60

Min. yield

Grade 60

Note: Grades are indicated in ksi (1 ksi = 6.9 MPa). Note: Source of data: CRSI Report 48: Evaluation of reinforcing bars in old reinforced concrete structures (see reference [54]). a Grade 75 steel in ASTM A615 steel was re-instated in 1987. Grade 80 and 100 added in 2008 and 2012, respectively. b Grade 80 steel in ASTM A706 added in 2008. c SAS670 steel is a German-produced high-strength steel available for use in North America.

1911 1957 1959 1959 1968 1974 1913 1963 1968 1936 1965 1968 1987a 1974b 1996 2003

Start

Year

A15 A408 A432 A431 A615 A615 A16 A61 A616 A160 A160 A617 A615 A706 A955M A1035

ASTM Spec

Table A4 Reference standards and properties of older and currently used high-strength steels in North America (1911 to current).

100 100

75

100 100

Min. Tensile

75

75 75

Min. yield

Grade 75

80 80

Min. yield

Grade 80

105 100

Min. Tensile

97

100

100

Min. yield

116

150

115

Min. Tensile

Grade 100

120

Min. yield

150

Min. Tensile

Grade 120

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