Shear Behavior of High-Strength and Lightweight Cementitious Composites Containing Hollow Glass Microspheres and Carbon Nanotubes

Abstract

In this study, an experimental program was conducted to investigate the shear behavior of beams made of high-strength and lightweight cementitious composites (HS-LWCCs) containing hollow glass microspheres and carbon nanotubes. The compressive strength and dry density of the HS-LWCCs were 87.8 MPa and1.52 t/m³, respectively. To investigate their shear behavior, HS-LWCC beams with longitudinal rebars were fabricated. In this test program, the longitudinal and shear reinforcement ratios were considered as the test variables. The HS-LWCC beams were compared with ordinary high-strength concrete (HSC) beams with a compressive strength of 89.3 MPa to determine their differences; the beams had the same reinforcement configuration. The test results indicated that the initial stiffness and shear capacity of the HS-LWCC beams were lower than those of the HSC beams. These results suggested that the low shear resistance of the HS-LWCC beams led to brittle failure. This was attributed to the beams’ low elastic modulus under compression and the absence of a coarse aggregate. Furthermore, the difference in the shear capacity of the HSC and HS-LWCC beams slightly decreased as the shear reinforcement ratio increased. The diagonal compression strut angle and diagonal crack angle of the HS-LWCC beams with shear reinforcement were more inclined than those of the HSC beams. This indicated that the lower shear resistance of the HS-LWCCs could be more effectively compensated for when shear reinforcement is provided and the diagonal crack angle is more inclined. The ultimate shear capacities measured in the tests were compared with various shear design provisions, including those of ACI-318, EC2, and CSA A23.3. This comparison showed that the current shear design provisions considerably overestimate the contribution of concrete to the shear capacity of HS-LWCC beams.

1. Introduction

Lightweight aggregate concrete is defined by its lower density compared with normal concrete. The maximum density of lightweight aggregate concrete ranges from 1850 to 2200 kg/m³, depending on the design codes [1,2,3]. This low density can reduce the self-weight of structural members and transportation costs, leading to savings in construction costs. Since the early 1920s, lightweight aggregate concrete has been used in various structures [4] (such as buildings, bridges, and marine structures), due to its low density, cost effectiveness, and high heat resistance. With technological advancements, the demand for lightweight and high-strength structural members has increased, especially in the construction of skyscrapers and long-span bridges. Increasing the concrete strength while reducing the self-weight improves the structural capacity to resist loads in the same area, reduces the cross section of the members, and decreases dead loads. In buildings, a reduced cross section also provides more space. Furthermore, the enhanced structural strength is expected to increase the structure’s lifespan.

Several types of lightweight aggregate (including vermiculite [5], oil palm shell [6], scoria [7], and fly ash cenosphere [8]) have been researched to enhance structural performance or to reduce self-weight. Because natural lightweight aggregate is subject to depletion, research on lightweight aggregate using industrial wastes [9,10,11] or artificial lightweight aggregate [12,13] has been actively conducted in recent years. In the review article by Samson et al. [14], it was indicated that an increase in compressive strength is typically accompanied by an increase in density. However, Lee et al. [15] developed high-strength and lightweight cementitious composites (HS-LWCCs) with a density and compressive strength of less than 1.5 g/cm³ and 97 MPa, respectively, using hollow glass microspheres (HGMs). This verified the possibility of concurrently improving material strength and reducing self-weight.

In addition to the enhanced performance achieved through the use of lightweight aggregate, the performance of structural members can also be improved using additional materials, including carbon nanotubes (CNTs). Research has shown that the addition of CNTs has various advantages, such as improved mechanical performance [16], the inhibition of microcrack propagation [17], increased resistance against chloride penetration [18], and improved resistance against deterioration after exposure to high temperatures [19]. According to one study [20], the effect of CNTs on density is insignificant, although the partial absorption of water molecules on the surface may occur [21]. Due to the benefits of using CNTs, Jeong et al. [22] studied the mixing of these nanotubes into lightweight cementitious composites. However, because of the van der Waals interface, CNTs in powder form tend to aggregate, hindering the benefits of these materials in lightweight cementitious composites. Thus, CNT dispersion is necessary. The study found that the best mechanical performance was attained by dispersing CNTs in a polyvinyl pyrrolidone suspension. The foregoing studies have sufficiently confirmed that CNT addition can improve the performance of lightweight cementitious composites.

In addition to the research focusing on the material behavior of high-strength lightweight concrete, several studies have investigated the structural behavior of lightweight concrete members. The flexural performance of high-strength lightweight cement composites (HSLCCs) incorporating CNTs was experimentally evaluated by Hong et al. [23]. Their study found that HSLCCs containing CNTs exhibited sufficient ductility and could be applied to flexural structural members. Because shear failure can cause sudden structural collapse, the shear behavior of lightweight concrete has also been investigated by several research groups [24,25,26]. In general, the shear transfer mechanisms in beams are dominated by shear reinforcement. However, in beams without shear reinforcement, a number of parameters contribute to the mechanism. These include uncracked concrete in a compression zone, aggregate interlocking, and the dowel action of longitudinal reinforcement [27,28]. Several studies [24,25,26] considering these parameters have been conducted, and have examined the changes in the shear behavior of members due to variations in the type of lightweight aggregate, compressive strength, and longitudinal reinforcement ratio. Yang et al. [25] confirmed that the aggregate size had a significant effect on the shear behavior. They observed that cracks penetrated lightweight aggregate when cracking occurred in lightweight concrete. However, according to Bentz et al. [29], both normal-weight and lightweight concrete beams with a compressive strength exceeding 70 MPa are presumed to ignore the shear stress transferred through the aggregate interlocking along a crack surface. To understand the shear behavior of HS-LWCC beams, experiments are necessary. This is because the shear behavior of these beams may differ from that of normal-strength lightweight aggregate concrete beams.

Accordingly, an experimental program was implemented in this study to investigate the shear behavior of HS-LWCC beams with and without shear reinforcement. Longitudinal and transverse reinforcement ratios were included as the test variables. By comparing the test results of these beams with those of ordinary high-strength concrete (HSC) beams, which were also prepared in this study, the effects of HS-LWCCs were investigated in detail. Subsequently, by comparing the test results with design provisions, the applicability of these provisions to HS-LWCC beams was determined.

2. Research Significance

Research on lightweight concrete has been conducted extensively in the past. However, studies specifically focused on high-strength lightweight concrete intended for structural applications are still insufficient. In this study, experimental research was conducted to understand the shear behavior of HS-LWCC beams with various longitudinal and shear reinforcement ratios. For the comparison of their shear behavior, conventional concrete beams with the same reinforcement ratios and concrete compressive strength were also prepared. The test results revealed that the shear capacity of the HS-LWCC beams was considerably lower than that of the HSC beams, particularly in cases without shear reinforcement. Additionally, a comparison with various shear design provisions suggested that the shear contribution of HS-LWCCs should be acknowledged as reduced. This study is expected to contribute to a better understanding of the structural characteristics of HS-LWCC beams and to improving shear design provisions.

3. Test Program

3.1. Materials

This study adopted the HSC mix proportion used in Lee. et al. [30], and the HS-LWCC mix proportion developed by Jeong et al. [22], as summarized in

Table 1. Mix proportion.

Type	W/B 1	C 2	FA 3	Silica Fume	Silica Powder	Aggregate		Lightweight Materials		SP 6	W 7	CNTs (wt.%)
						Coarse	Fine	LA 4	HGMs 5
HSC	0.22	542.0	70.0	83.0	-	920.0	661.0	-	-	10.3	153.0	-
HS-LWCC	0.25	739.1	-	110.9	208.0	-	-	111.0	211.0	25.3	212.5	0.05

¹ W/B: water/binder ratio; ² C: cement (kg/m³); ³ FA: fly ash (kg/m³); ⁴ LA: lightweight aggregate (<2 mm) (kg/m³), density of 1770 kg/m³; ⁵ HGMs: hollow glass microspheres (kg/m³), noted as S60HS and manufactured by 3M™, with average diameter of 30 $\mathsf{\mu }$m and density of 600 kg/m³; ⁶ SP: superplasticizer (kg/m³); ⁷ W: water (kg/m³).

. Both mix designs used ordinary Portland cement and silica fume as the binders. In addition, composite materials, including silica powder, silica sand, HGMs, and lightweight fine aggregate with a diameter of 2 mm or less, were utilized in the HS-LWCC. An aqueous solution of sonicated multi-wall CNTs (MWCNTs), used to prevent aggregation, was provided by a manufacturing company and incorporated into the HS-LWCC. The amount added was 0.05 wt.%, based on the existing literature [22]. Meanwhile, composite materials, including fly ash, fine aggregate, and coarse aggregate with a maximum diameter of 20 mm or less, were utilized in the HSC.

To investigate the behavior of the materials under compression, Ø100 × 200 mm cylindrical specimens were fabricated, with three specimens for each concrete material. The specimens were cured at 21 °C and 95% relative humidity (RH) for 24 h before demolding. Then, to enhance the initial and 28 d strength, the specimens were cured at 90 °C and 99% RH for 48 h. Following the high-temperature curing, dry curing was conducted at 21 °C and 65% RH for the remaining curing period, until the age of 28 d. It should be noted that this experimental program adopted the curing procedure presented in the literature [15], as the target compressive strength of the concrete was achieved in this previous study. Figure 1 shows the test setup for the compression test and the measured stress–strain responses. The compressive strains were taken as the average of three strains measured using strain gauges attached to the sides of the cylindrical specimens. The measured compressive strengths were 89.3 and 87.8 MPa for the HSC and HS-LWCC, respectively. Based on ASTM C469/C469M [31], the elastic modulus was calculated as 37.7 GPa for the HSC and 17.7 GPa for the HS-LWCC, respectively. Notably, the measured dry density of the HS-LWCC (1.52 t/m³) was considerably lower than that of the HSC (2.43 t/m³).

3.2. Design of Beams

To investigate the shear behavior of the HS-LWCC beams with reinforcement, 14 beams (7 HSC and 7 HS-LWCC) were prepared. In the test program, the longitudinal and shear reinforcement ratios were considered as the test variables. The details of each beam are shown and summarized in Figure 2 and

Table 2. Design of specimens.

Specimen	a	b	d	h	Longitudinal Reinforcement		Shear Reinforcement		Shear Capacity (kN)	Deflection (mm)	Failure Mode
					${\mathit{\rho }}_{\mathit{s}}$ (%)	${\mathit{f}}_{\mathit{y}}$ (MPa)	${\mathit{\rho }}_{\mathit{v}}$ (%)	${\mathit{f}}_{\mathit{v}\mathit{y}}$ (MPa)
N-L1.2	1000	220	400	440	1.16	446	-	-	110.6	4.2	Shear
N-L1.7	1000	220	400	440	1.74	446	-	-	120.2	2.4	Shear
N-L2.3	1000	220	400	440	2.32	446	-	-	139.1	3.1	Shear
N-L2.9	1000	220	400	440	2.93	485	-	-	231.6	6.5	Shear
N-V.18	1000	220	400	440	1.16	446	0.18	449	192.0	9.3	Shear
N-V.27	1000	220	400	440	1.16	446	0.27	449	216.6	27.9	Flexure
N-V.36	1000	220	400	440	1.16	446	0.36	449	210.5	29.8	Flexure
L-L1.2	1000	220	400	440	1.16	446	-	-	53.2	4.2	Shear
L-L1.7	1000	220	400	440	1.74	446	-	-	37.1	2.4	Shear
L-L2.3	1000	220	400	440	2.32	446	-	-	47.0	3.1	Shear
L-L2.9	1000	220	400	440	2.93	485	-	-	126.8	6.5	Shear
L-V.18	1000	220	400	440	1.16	446	0.18	449	147.2	12.1	Shear
L-V.27	1000	220	400	440	1.16	446	0.27	449	177.9	12.1	Shear
L-V.36	1000	220	400	440	1.16	446	0.36	449	194.9	17.8	Shear

, respectively.

Figure 3 shows the beam designations. The beams are first categorized by mix type: N and L denote the HSC and HS-LWCC, respectively. The second letter represents the test variable: L and V for longitudinal and shear reinforcements, respectively. The number at the end of the designation indicates the longitudinal reinforcement ratio for the L-series beams and the shear reinforcement ratio for the V-series beams. All the beams were fabricated following the curing procedure used for the cylindrical specimens.

The figures and table indicate that the beams had the same cross section, 220 mm × 440 mm. The shear span-to-depth ratio was fixed at 2.5, as primarily adopted in the literature [30,32,33,34], to minimize the effect of arch action, which can significantly increase the shear strength of the beams. In the N-L and L-L test series (Table 2), the longitudinal reinforcement ratio was considered as the test variable. The longitudinal reinforcement was classified into four types: 2-D25 (1.2%), 3-D25 (1.7%), 4-D25 (2.3%), and 4-D29 (2.9%). No shear reinforcement was provided. As Eurocode 2 [3] considers the effect of the longitudinal reinforcement ratio up to 2.0%, a broader range of longitudinal reinforcement ratios was covered in the testing. In the N-V and L-V test series (Table 2), the shear reinforcement ratio was considered as the test variable. The longitudinal reinforcement ratio was maintained at 1.2%, whereas the shear reinforcement ratio was varied (0.18, 0.27, and 0.36%) by adjusting the spacing of the stirrups. These values correspond to the minimum shear reinforcement ratio, as well as to 1.5 and 2.0 times the minimum specified in Eurocode 2. The shear reinforcement was in the form of a single leg with a 135° standard hook. The shear reinforcement was arranged by placing two D10 compression rebars at the top part of the beams.

The nominal diameters of the rebars (D10, D25, and D29) were 9.53, 25.4, and 28.6 mm, respectively. The yield strengths of D10, D25, and D29, measured by direct tension test, were 449, 446, and 485 MPa, respectively.

3.3. Test Setup

To investigate the shear behavior of the HSC and HS-LWCC beams, three-point bending tests were conducted using a hydraulic testing machine with a capacity of 500 kN. The load was applied to the top center of the beam at a monotonic rate of 0.3 mm/min. Each test was paused every 50 kN to observe the crack pattern occurring during each loading step. The deflection of the beam was simultaneously measured using two linear variable differential transformers (LVDTs) placed underneath the center of the beam. To measure the average strain during loading, three LVDTs with a rosette configuration were placed on the side of the beam, as illustrated in Figure 4. From the loading point, the LVDT rosette was placed at a distance equal to the beam depth; this location could be considered as a shear-critical section. Based on the average strain measured by the LVDT rosette, the principal strain and corresponding angle were calculated. The angle, which represents that of the diagonal compression strut, has a significant effect on the shear capacity and has been actively studied [35,36,37]. This angle is used to determine the extent to which the shear reinforcement contributes to the shear resistance.

4. Test Results

4.1. Overall Behavior and Failure Mode

Figure 5 shows the crack pattern after failure. This pattern is extremely useful for understanding the overall behavior and failure mode of the beams. For the HSC beams without shear reinforcement, flexural cracks initially occurred at the center of the beams, followed by flexural cracks in the shear span. As the load increased, the flexural cracks located in the shear span progressed to flexural–shear cracks. Subsequently, the beams suddenly failed due to the propagation of these flexural–shear cracks. In contrast, flexural cracks were observed in the HS-LWCC beams without shear reinforcement; however, their extent was less than that in the HSC beams. Ultimately, the HS-LWCC beams failed abruptly with shear cracks. The crack patterns in the HS-LWCC beams were found to be straighter than those in the HSC beams. This might be attributed to the weak aggregate interlocking in HS-LWCCs [25]. Furthermore, the diagonal cracks in the HS-LWCC beams were more inclined than those in the HSC beams.

For the HSC beams with shear reinforcement, the failure transitioned from shear mode to flexural mode as the shear reinforcement ratio increased. All the HSC beams developed flexural cracks at the bottom during the initial loading steps. As the load increased, the flexural cracks in the shear span progressed to flexural–shear cracks. Both the flexural and flexural–shear cracks propagated to the loading point, where localized concrete failure was observed. The extent of the localized failure increased with the shear reinforcement ratio. Subsequently, the width of the flexural–shear cracks in N-V.18 increased, leading to sudden shear failure. In contrast, the failure of N-V.27 and N-V.36 shifted from shear mode to flexural mode because the amount of shear reinforcement was sufficient. Contrastingly, the trend of crack patterns in the HS-LWCC beams differed from those observed in the HSC beams. The crack initiation process, from flexural cracks to flexural–shear cracks with localized failure at the loading point, was similar between the HS-LWCC and HSC beams. However, all the HS-LWCC beams exhibited shear failure. These differences are mainly due to the mechanical behavior of HS-LWCCs, which have lower shear resistance and tensile performance at a crack surface than HSC. The crack patterns and failure modes indicate that the HS-LWCC beams require more shear reinforcement than the HSC beams.

The contribution of the shear reinforcement varied with the crack angle; however, this requires verification. Based on the observed crack patterns after failure, the crack angle was determined using the average slope of the most significant inclined crack in the web. The crack angles in N-V.18, N-V.27, and N-V.36 were found to be 33.9°, 34.9°, and 35.3°, respectively. The crack angles in the HS-LWCC beams were calculated to be lower than those in the HSC beams: 26.9°, 32.5°, and 24.8° for L-V.18, L-V.27, and L-V.36, respectively.

4.2. Load–Deflection Responses

The load–deflection responses, used for investigating the effect of the materials and reinforcement configurations on the shear behavior, are compared in Figure 6. The HSC beams without shear reinforcement exhibited virtually identical stiffness until crack formation, regardless of the amount of reinforcement. After the formation of flexural cracks, the overall stiffness decreased. This stiffness was observed to decrease as the longitudinal reinforcement ratio decreased. Virtually all the HSC beams experienced a sudden load drop upon the occurrence of shear failure. However, L2.9 exhibited a continuous increase in load after two sudden load drops; the test was terminated due to limitations in the capacity of the loading equipment. The unusual structural behavior of L2.9 was attributed to the increased load resulting from dowel action even after shear cracking occurred, due to the high longitudinal reinforcement ratio. A similar behavior was observed by Jeli et al. [38] and Han et al. [39]. The initial stiffness of the HS-LWCC beams without shear reinforcement was considerably lower than that of the HSC beams. This difference was attributed to the lower stiffness of the HS-LWCC beams under compression (Figure 1). Furthermore, the longitudinal reinforcement ratio was found to have a significant influence on the stiffness of the HS-LWCC beams. This was presumed to be due to the lower tensile strength of the HS-LWCC compared with that of HSC, resulting in early cracking. All the HS-LWCC beams without shear reinforcement exhibited shear failure accompanied by a sudden load drop.

In the case of the HSC beams with shear reinforcement, N-V.18 exhibited shear failure with a rapid load drop after reaching the maximum load. This occurred because the longitudinal reinforcement did not yield due to the small shear reinforcement ratio. In contrast, N-V.27 and N-V.36 showed a ductile flexural behavior because the amount of shear reinforcement was sufficient to prevent shear failure. These beams displayed similar load–deflection responses because the same longitudinal reinforcement was provided. For the HS-LWCC beams with shear reinforcement, the maximum load increased with the shear reinforcement. However, all the beams exhibited brittle shear failure with a sudden load drop. Because only L-V.36 showed slightly ductile behavior, the shear failure of this specimen was inferred to have occurred after the yielding of the longitudinal reinforcement. This is because lightweight aggregate concrete has a lower tensile strength and fracture energy than normal-weight aggregate concrete [40]. Furthermore, aggregate interlocking in lightweight concrete is less effective than that in normal-weight concrete [25]. As a result, the shear resistance from aggregate interlocking in HS-LWCCs and HSC cannot be expected to be the same. Consequently, the HS-LWCC beams exhibited a predominantly shear failure behavior. Similar to the beams without shear reinforcement, the overall stiffness of the HS-LWCC beams was considerably lower than that of the HSC beams. This was attributed to the low elastic modulus of HS-LWCCs.

4.3. Shear Capacity and Corresponding Deflection

The shear capacities of the HSC and HS-LWCC beams are compared in Table 2 and Figure 7. As presented in Figure 7a, all the HS-LWCC beams without shear reinforcement exhibit shear capacities lower than those of the HSC beams. The shear capacity of the HSC beams gradually increases as the longitudinal reinforcement ratio increases up to 2.3%. This trend aligns with current design standards [3], indicating that the shear strength increases with a longitudinal reinforcement ratio of up to 2%. In contrast, the HS-LWCC beams do not show a significant change in their shear capacity, despite an increase in the longitudinal reinforcement ratio of up to 2.3%. Therefore, the shear capacity of the HS-LWCC specimens, for L1.2 to L2.3, shows a reduction ratio of 52%, 69%, and 66%, respectively, compared to the shear capacity of the HSC, as illustrated in Figure 8a. The low shear strength of the HS-LWCC beams and the slight influence of the longitudinal reinforcement ratio on these beams were attributed to the low aggregate interlocking effect at the crack surface. Consequently, the flexural–shear cracks rapidly propagated toward the loading point in the HS-LWCC beams. Meanwhile, when the longitudinal reinforcement ratio was increased to 2.9%, the HSC and HS-LWCC beams showed a significant increase in their shear capacity. Autrup et al. [41] presented a summary of the models of the dowel force provided by a conventional deformed rebar. In the models [42,43,44], the dowel force increased with the diameter of the deformed rebar, to the extent that even a reinforced concrete member failed with splitting cracks. Therefore, the high shear capacity of N-L2.9 was inferred to be due to the significant dowel action resulting from the large rebar diameter and high reinforcement ratio. Due to this influence, the shear capacity reduction ratio of L2.9 was found to be 45%, which differs from the trend observed in the other L series specimens.

In the case of the beams with shear reinforcement, the shear strength of the HS-LWCC beams was consistently lower than that of the HSC beams. This is indicated by the comparison in Figure 7b, showing the low shear resistance performance of the HS-LWCC beams. The HSC and HS-LWCC beams show an increase in shear capacity with the shear reinforcement ratio. The difference in the shear capacity between the HSC and HS-LWCC beams is also observed to slightly decrease when the shear reinforcement ratio is 0.18%, compared to that when no shear reinforcement is provided. Furthermore, when the shear reinforcement ratio is 0.36%, the difference in the maximum load capacity between the two beams significantly decreases, due to the flexural failure of the HSC beams. The shear strengths of the HSC and HS-LWCC beams increase with the shear reinforcement ratio. However, after the failure shifts from the shear mode to the flexural mode, the HSC beams demonstrate no further increase in their maximum load. Accordingly, when the shear strengths of the HSC and HS-LWCC beams with identical shear reinforcement ratios are compared, the disparity in their loading capacities tends to diminish as the shear reinforcement ratio increases. As shown in Figure 8b, when comparing the shear capacity of the HSC and HS-LWCC beams with the same shear reinforcement ratio, the shear capacity reduction ratio is 23%, 18%, and 7%, for V.18 to V.36, respectively. The reduction in shear capacity due to the lightweight aggregate is found to be not as significant as that for the L series. These results indicate that the role of shear reinforcement in shear strength is more distinct in the HS-LWCC beams than in the HSC beams. Kockal and Ozturan [45] confirmed that the elastic modulus and splitting tensile strength of lightweight concrete are lower than those of conventional concrete. Additionally, using lightweight HSC may result in a greater reduction in the load transfer capacity of larger structures compared to smaller ones [46]. The aggregate size used in the HS-LWCC is smaller than that in the HSC, making it difficult to achieve the interlocking effect of the aggregates [25]. Nevertheless, given that HS-LWCCs exhibit a lower crack angle than HSC, the contribution of shear reinforcement to shear strength is more significant in HS-LWCCs than in HSC. Consequently, the shear strength of the HS-LWCC beams can be increased by placing additional shear reinforcement.

Figure 9 presents the center deflection of each beam at maximum load. For the beams with no shear reinforcement (Figure 9a), the deflection of the HS-LWCC beams at maximum load is significantly greater than that of the HSC beams. This is due to the substantially lower elastic modulus of HS-LWCCs compared with that of HSC. Regardless of the concrete material, the deflection at maximum load decreases as the longitudinal reinforcement ratio increases up to 2.3%. This is due to the increase in flexural stiffness provided by the longitudinal reinforcement after the onset of flexural cracking. However, in L2.9, the deflection increases significantly, deviating from the previous trend. This deviation is presumed to be due to changes in the shear resistance mechanics, possibly influenced by the dowel action of the longitudinal reinforcement.

In the case of the beams with shear reinforcement (Figure 9b), the HS-LWCC beams with a relatively low shear reinforcement ratio exhibit a higher deflection at maximum load than the HSC beams. In addition, the deflection at maximum load increases with the shear reinforcement ratio, and is accompanied by an improvement in the shear capacity. In the case of the beams with relatively high shear reinforcement ratios (V.27 and V.36), the HSC beams exhibit significantly greater deflection at maximum load than the HS-LWCC beams, as the failure of the HSC beams shifts from shear mode to flexural mode. Therefore, when shear failure occurs in beams with the same shear reinforcement ratio, the HS-LWCC beams have a smaller deflection at maximum load than the HSC beams. This weakness of the HS-LWCC beams could be resolved by providing sufficient shear reinforcement.

4.4. Average Strain and Diagonal Compression Strut Angle

The average strain measured by the LVDT rosette attached to the side of each beam is presented in Figure 10. Except for the strain in beams N-V.27 and N-V.36, the figure shows the average strain measured in the shear span where shear failure occurred. In these beams, because the main diagonal crack was not within the measurement range of the LVDT rosette, the measurements of the LVDTs attached to the opposite shear span were used. The figure indicates that vertical strain is predominant in the deformation of the web.

Figure 11 shows the average principal and shear strains, which are evaluated from three average strain values. As presented in the graph, under the same applied load, the principal and shear strains decrease due to the enhanced shear resistance provided by the shear reinforcement with an increasing ratio. In the HSC beams, significant increases in the principal and shear strains are observed when the load exceeds 200 kN. In contrast, in the HS-LWCC beams, similar increases are noted for loads between 50 and 100 kN. This indicates that the flexural–shear crack propagates through the web in the HS-LWCC beams at an earlier loading step than in the HSC beams, due to the lower shear resistance of HS-LWCCs.

The diagonal compression strut angle in the beams with shear reinforcement is evaluated based on the average strains measured by the LVDT rosette (Figure 12). When the average strain is extremely low, numerical instability in the angle calculation is observed; these instances are excluded from the figure. As presented in the figure (except for N-V.36, which exhibited flexural failure), the angle of the diagonal compression strut decreases as the applied load increases. In addition, this angle increases with the shear reinforcement ratio. In analyzing its effect on concrete materials, the difference in the diagonal compression strut angle is found to be insignificant at the maximum load when the shear reinforcement ratio is 0.18%. However, when the shear reinforcement ratios are 0.27% and higher, the strut angles in the HS-LWCC beams are considerably smaller than those in the HSC beams. This finding can be explained by the lower shear resistance contribution of HS-LWCCs compared with that of HSC. The low resistance results in a large web deformation, resulting in a small diagonal compression strut angle. This indicates that the diagonal compression strut angle is closely related to the shear crack angle. Thus, a consideration of the characteristics of HS-LWCCs is necessary when assessing the shear strength provided by shear reinforcement.

The actual crack angle measured from the images and those calculated using the LVDTs rosette data in Figure 12 are compared in

Table 3. Comparison of actual and LVDTs rosette-calculated crack angles.

Specimen	Actual Crack Angle (°)	LVDTs Rosette (°)	Actual Crack Angle/ LVDTs Rosette
N-V.18	34	26	1.30
N-V.27 *	35	40	0.87
N-V.36 *	35	38	0.93
L-V.18	27	25	1.08
L-V.27	32	28	1.16
L-V.36 *	25	32	0.78
average			1.02

* Crack measurement in the span opposite to the shear span with failure crack.

. Due to the failure crack, some parts of the LVDTs rosette in N-V.27, N-V.36, and L-V.36 became detached during measurement, so the crack angles from the opposite shear span were compared. These specimens showed actual crack angles lower than those calculated using the LVDTs rosette. This is believed to be due to the lower vertical strain (${\epsilon }_{90}$) in the span opposite to the shear span where the failure crack occurred. Even considering this point, a comprehensive comparison of the actual crack angle with those calculated using the LVDTs rosette showed that the two results were similar.

5. Comparison with Design Provisions

Most design provisions incorporate factors in the shear strength calculations to account for the effect of lightweight concrete. To evaluate the applicability of current design provisions to the high-strength lightweight concrete beams tested in this study, the test results were compared with the shear design provisions of ACI 318-19 [1], CSA A23.3: 19 [2], and Eurocode 2 (EC2) [3]. The design provisions are summarized in

Table A1. Shear capacity equations presented by design provisions.

ACI 318-19 (2019)	$V=V_c+V_s$
	$V_s={\displaystyle \frac{A_v{f}_{vy}d}{s}}$
	w/o stirrups	$V_c=\left[0.66{\lambda }_s\lambda {\left({\rho }_l\right)}^{1/3}\sqrt{f_c^{\prime }}+{\displaystyle \frac{N_u}{6A_g}}\right]b_{w}d$
		${\lambda }_s$: $\sqrt{2/(1+0.004d)}\le 1$
	w/ stirrups	$V_c=\left[0.66\lambda {\left({\rho }_l\right)}^{1/3}\sqrt{f_c^{\prime }}+{\displaystyle \frac{N_u}{6A_g}}\right]b_{w}d$
	$\lambda :$ material factor of lightweight concrete, 0.75
CSA A23.3:19 (2019)	$V=V_c+V_s\le V_{r,max}$
	$V_c=\lambda \beta \sqrt{f_c^{\prime }}{b}_w{d}_v$   $\sqrt{f_c^{\prime }}\le 8\mathrm{M}\mathrm{P}\mathrm{a}$
	$\lambda :$ material factor of lightweight concrete, 0.75
	$\beta =\left[{\displaystyle \frac{0.40}{\left(1+1500{\epsilon }_x\right)}}\right]\left[{\displaystyle \frac{1300}{\left(1000+s_{ze}\right)}}\right]$
	$V_s={\displaystyle \frac{f_{vy}{A}_v{d}_v\cot \theta }{s}}$
	$\theta =29+7000{\epsilon }_x$
	$V_{r,max}=0.25f_c^{\prime }{b}_w{d}_v$
EC2 (2004)	w/o stirrups	$V_c=\left[C_{Rd,c}{\eta }_{1}k{\left(100{\rho }_l{f}_c^{\prime }\right)}^{1/3}\right]b_{w}d$
		$k$: $1+\sqrt{200/d}\le 2.0$
	w/ stirrups	$V_s={\displaystyle \frac{A_v}{s}}z{f}_{vy}\cot \theta$   $1.0\le \cot \theta \le 2.5$
	$C_{Rd,c}:$ $0.18$ for concrete, $0.15$ for lightweight concrete
	${\eta }_1:0.40+0.60\rho /2200$ for lightweight concrete
$A_g:$ gross area of concrete section, mm2 $A_v:$ area of shear reinforcement, mm2 $N_u:$ factored axial force normal to cross section, N $a_g:$ specified nominal size of coarse aggregate, mm; $a_g=0$, if $f_c^{\prime }$ is greater than 70 MPa $b_w:$ web width of cross section, mm $d:$ effective depth, mm $d_v:$ effective shear depth, mm; shall be taken as the greater of $0.72h$ or $0.9d$ $f_c^{\prime }:$ specified compressive strength of concrete, MPa $f_{vy}:$ specified yield strength of shear reinforcement, MPa $k_{dg}:$ maximum size of aggregate, mm $k_v:$ aggregate interlocking factor $s:$ longitudinal spacing of shear reinforcement, MPa $s_z:$ crack spacing parameter, mm; shall be taken as $d_v$ or the maximum distance between the layers of distributed longitudinal reinforcement $s_{ze}:$ equivalent crack spacing parameter, mm; $s_{ze}=35s_z/(15+a_g)$ $z:$ internal lever arm, mm $\beta :$ factor used to account for shear resistance of cracked concrete $\rho :$ oven-dry density of lightweight concrete ${\rho }_l:$ longitudinal reinforcement ratio; $A_s/b_{w}d$ $\theta :$ angle between web compression and axis of member (°) ${\epsilon }_x:$ mid-depth strain at section; ${\epsilon }_x=(M_f/d_v+V_f-0.5N_f)/2E_s{A}_s$, ${\epsilon }_x\le 3.0\times {10}^{-3}$

. The shear capacities evaluated from the design provisions are compared with the test results, as summarized in

Table 4. Comparison of shear capacity between test results and design provisions.

Specimen	${\mathit{V}}_{\mathit{t}\mathit{e}\mathit{s}\mathit{t}}\left(\mathbf{k}\mathbf{N}\right)$	${\mathit{V}}_{\mathit{c}\mathit{o}\mathit{d}\mathit{e}}$			${\mathit{V}}_{\mathit{t}\mathit{e}\mathit{s}\mathit{t}}/{\mathit{V}}_{\mathit{c}\mathit{o}\mathit{d}\mathit{e}}$
		${\mathit{V}}_{\mathit{A}\mathit{C}\mathit{I}}$ (kN)	${\mathit{V}}_{\mathit{C}\mathit{S}\mathit{A}}$ (kN)	${\mathit{V}}_{\mathit{E}\mathit{C}2}$ (kN)	ACI	CSA	EC2
N-L1.2	110.6	95.7	103.5	127.0	1.16	1.07	0.87
N-L1.7	120.2	109.5	119.7	145.3	1.10	1.00	0.83
N-L2.3	139.1	120.6	131.8	152.3	1.15	1.06	0.91
N-L2.9	231.6	130.2	141.6	152.3	1.78	1.64	1.52
N-V.18	192.0	195.1	157.4	159.4	0.98	1.22	1.20
N-V.27	216.6	flexural failure
N-V.36	210.5	flexural failure
L-L1.2	53.2	71.8	95.4	85.6	0.74	0.56	0.62
L-L1.7	37.1	82.1	109.9	98.0	0.45	0.34	0.38
L-L2.3	47.0	90.4	120.6	102.7	0.52	0.39	0.46
L-L2.9	126.8	97.7	129.3	102.7	1.30	0.98	1.23
L-V.18	147.2	163.2	153.7	159.4	0.90	0.96	0.92
L-V.27	177.9	198.6	180.4	239.1	0.90	0.99	0.74
L-V.36	194.9	234.1	205.5	318.8	0.83	0.95	0.61
Average					0.98	0.93	0.86
CoV					0.36	0.39	0.39

and shown in Figure 13. Specimens N-V.27 and N-V.36, which exhibited flexural failure, were excluded from the comparison. The shear capacity calculation is based on the actual measured mechanical properties. It does not include values, such as strength reduction and safety factors, which are typically considered in design.

All the design provisions were found to predict the shear capacity of the HSC beams without shear reinforcement reasonably. However, they significantly underestimated the shear capacity of N-L2.9. The dowel action in N-L2.9 was inferred to be more considerable than that in the other HSC beams because this beam had an excessive rebar diameter and longitudinal reinforcement ratio. Therefore, except for abnormally over-reinforced beams, each design provision reasonably reflected the effect of the longitudinal reinforcement ratio. Nevertheless, the difference between the test and predicted shear capacity values varied depending on the design provisions.

All the design provisions seemed to predict that the HSC beams with shear reinforcement (except for N-V.36) had an adequate shear capacity and would exhibit flexural failure. Upon a more detailed investigation, the provisions of EC2 (unlike those of ACI-318 and CSA A23.3) showed a more sensitive decrease in the ratio $V_{test}/V_{provision}$ with an increasing shear reinforcement. This result can be explained by two considerations: EC2 only acknowledges the shear reinforcement contribution and ignores the concrete contribution when the shear reinforcement ratio is relatively low. In addition, EC2 permits a lower angle for the diagonal compression strut than the other design provisions.

In the case of the HS-LWCC beams without shear reinforcement (except for L-L2.9), all the design provisions considerably overestimated the shear capacity, although the effect of lightweight concrete is considered in the code provisions with the material factor ($\lambda$ or ${\rho }_l$). This indicates that the contribution of lightweight concrete to the shear capacity should be more conservatively acknowledged, especially when HS-LWCC is employed, as tested in this study.

In contrast, the code design provisions appear to evaluate the shear capacity of the L-V series better than that of the L-L series. However, when the contributions of the HS-LWCC and shear reinforcement are separately examined, the comparison results differ. In the case of ACI-318, when shear reinforcement is provided, the contribution of the HS-LWCC is assumed to be the same as that for a beam without shear reinforcement, leading to an overestimation of the contribution of the concrete. Consequently, the shear capacity is also overestimated when shear reinforcement is provided. Therefore, a more reasonable prediction of the shear capacity could be expected by reducing the contribution of the HS-LWCC by more than what is currently considered. The best agreement with the test results is exhibited by CSA A23.3. However, the estimated shear crack angle, i.e., 38.4°–41.4°, is larger than the experimentally observed angle of 24.8°–32.5°. This indicates that the contribution of the shear reinforcement is underestimated, whereas the contribution of the HS-LWCCs is overestimated. The provisions of EC2 disregard the contribution of HS-LWCCs; however, they predict the inclined shear crack angle to be excessively small, resulting in an overestimation of the shear reinforcement contribution. Therefore, stricter limits on the lower bound of the inclined shear crack angle are deemed necessary when calculating the shear capacity of HS-LWCC beams with shear reinforcement.

In summary, based on the comparison between the test results and the predicted shear capacity of the HS-LWCC beams, reducing the assumed contribution of the HS-LWCC is necessary to calculate the shear capacity of these beams reasonably. Additionally, to prevent the overestimation of the contribution of the shear reinforcement, stricter limitations on the lower bound of the inclined shear crack angle must be implemented.

6. Conclusions

In this study, an experimental program was conducted to determine the shear behavior of HS-LWCC beams with a compressive strength and dry density of approximately 80 MPa and 1.52 t/m³, respectively. For comparison, tests were also conducted on conventional HSC beams with a similar compressive strength and identical configuration. The longitudinal and shear reinforcement ratios of the specimens were included as the test variables. Fourteen specimens were fabricated and tested by three-point bending tests. The effects of the concrete material on the crack patterns, load–deflection responses, maximum shear capacity, deflection at maximum load, and angle of diagonal compression strut were investigated based on the test results. In addition, the measured shear capacity was compared with that evaluated using current shear design provisions. The conclusions of this study can be summarized as follows.

• The shear cracks in the HS-LWCC beams, when compared with those in the HSC beams, appeared straighter. This was attributed to the significantly lower shear resistance of HS-LWCCs along the crack surface. Compared with HSC, HS-LWCCs have a lower tensile strength and aggregate interlocking effect.
• Without shear reinforcement, the increase in the shear capacity with the longitudinal reinforcement ratio was more distinct in the HS-LWCC beams than in the HSC beams. Meanwhile, when excessive longitudinal reinforcement was provided using D29 bars at a ratio of 2.9%, both the HSC and HS-LWCC beams exhibited a significant increase in their shear capacity.
• In both the HSC and HS-LWCC beams, the shear capacity increased with the shear reinforcement ratio. The HSC beams exhibited flexural failure when the shear reinforcement ratio was 0.27 or 0.36%, whereas the HS-LWCC beams experienced shear failure. This was because the contribution of the concrete to the shear capacity of the HS-LWCC beams was smaller than that to the shear capacity of the HSC beams.
• When comparing the shear capacity of HSC and HS-LWCCs, the shear capacity of the HS-LWCC beams without shear reinforcement showed a reduction of 52%, 69%, 66%, and 45% compared to the HSC beams for L1.2 to L2.9, respectively, at the same longitudinal reinforcement ratio. In the case with shear reinforcement, there was a reduction of 23%, 18%, and 7% for V.18 to V.36, respectively. When shear reinforcement was provided, the difference between the HSC and HS-LWCC beams was not as significant as in the case without shear reinforcement.
• In the HSC and HS-LWCC beams, the diagonal compression strut inclination angle obtained from the measurements of the LVDT rosette was found to be similar to the inclined shear crack angle. Additionally, the inclined shear crack angle and diagonal compression strut angle were observed to be smaller in the HS-LWCC beams than in the HSC beams. Therefore, the contribution of the shear reinforcement to the HS-LWCC beams was expected to be more considerable than that to the HSC beams.
• Current design provisions overestimate the shear capacity of HS-LWCC beams without shear reinforcement compared with that of HSC beams. Therefore, the contribution of concrete to the shear capacity of HS-LWCC beams must be evaluated as lower than the contribution suggested by the current design provisions.
• The provisions of CSA A23.3 were found to predict the shear strength of the HS-LWCC beams with shear reinforcement most accurately. However, when the contribution of concrete to the shear strength of HS-LWCCs is reduced, the shear reinforcement contribution should be evaluated more rationally. The provisions of ACI 318 tended to overestimate the contribution of concrete to the shear capacity of HS-LWCC beams. Conversely, the provisions of EC2 tended to overestimate the shear reinforcement contribution from the small angles of inclined shear cracks. Therefore, for a more reasonable shear design of HS-LWCC beams, the contributions of both the concrete and shear reinforcement must be evaluated more accurately.
• The test results indicate that an HS-LWCC beam tends to require more shear reinforcement than a conventional HSC beam. However, since the dry density of HS-LWCCs is only 63% of that of HSC (1.52 compared to 2.43 t/m³), the self-weight of an HS-LWCC element is significantly lower than that of an HSC element. Consequently, HS-LWCCs are advantageous due to their reduced self-weight, which could result in the smaller dimensions of a reinforced concrete member.