# Strengthening Shear Resistance of Beams without Web Reinforcements Using Vertical Prestressed Steel Bars

Authors: Zihui Liu; Yujun Cui; Weiqi Wang; Wei Cao; Xuan Wang; Xingwei Xue
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

Ensuring the shear capacity of concrete structures is crucial. The vertical prestressed steel bar (VPSB) strengthening method is effective for improving the shear behaviour of concrete structures. Four concrete beams are investigated to reveal the effect of VPSBs on the shear capacity of concrete beams without web reinforcement. Test results indicate that the shear capacity of the test beam strengthened by VPSBs in the beam is significantly increased by more than 95%, and the failure mode of the test beam changes from diagonal tension failure to shear compression failure. Additionally, the results provide insights into the strengthening mechanism of VPSBs, i.e., the shear contribution of the VPSBs can be categorised into two stages. The vertical compressive stress provides shear contribution in the first stage and provides control in terms of crack development; meanwhile, in the second stage, the stirrup action by VPSBs contributes to shear.


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## Body

## 1. Introduction

Concrete structures are currently the most important structures in the construction industry. Improving the mechanical properties of reinforced concrete structures is always a hot research field [1–5]. Shear design is an important aspect in concrete structure design for preventing shear failure, which may cause instantaneous brittle failure; the damage incurred is severe and can result in catastrophic consequences. Therefore, enhancing the shear capacity of concrete structures is an important research topic.Researchers have attempted to strengthen the shear capacity of concrete structures by improving concrete materials. For example, steel fibre–reinforced concrete [6–9], ultra-high-performance concrete [10–15], polymer mortar [16, 17], and other materials [18–20] have been used to improve the mechanical properties of concrete beams, thereby enhancing their shear capacity. Steel plates or fiber reinforced polymer [12, 21–26] have been used to enhance the shear strength of beams. However, these methods are passive strengthening methods. Therefore, as an active and effective shear strengthening method, the vertical prestressed steel bar (VPSB) strengthening method has been investigated.As early as 1991, VPSBs [27] were used in retrofitted prestressed composite beams. Since then, many VPSB strengthening experiments pertaining to rectangular beams [28–31], T-shaped beams [32, 33], and box girders [34] have been performed, and the test results have consistently proved that VPSBs can effectively improve the shear strength, rigidity, and ductility of concrete beams. Compared with other shear reinforcement methods, the VPSB method is the most effective shear strengthening method [31].Numerical analysis is an effective method to study the mechanical properties of structures [35–38]. The shear reinforcement mechanism of VPSBs has been investigated via numerical analysis. A shear-sensitive fiber beam formulation proposed by Ferreira et al. [39] was extended to account for the effects of unbonded vertical external prestressed reinforcement on the structural response of RC beams. Li et al. [40] used the total strain crack model of concrete and established a nonlinear three-dimensional finite element analysis to model shear strength in Midas/FEA, in which the parameters included the vertical compressive stress degree and VPSB stirrup ratio, and the optimal arrangement of VPSBs were discussed. Fiset et al. [41] investigated the behaviour of thick concrete members strengthened in shear with unbonded VPSBs, as well as performed loading tests and numerical analysis. The main parameters of the numerical analysis were the shear span ratio, vertical prestress, shear span ratio, and vertical reinforcement rigidity.A few theoretical studies pertaining to the prediction of the vertical prestressed shear capacity have been performed. Xue et al. [42] established a shear strength prediction model for concrete beams without web reinforcement strengthening based on VPSBs by modifying the critical shear crack theory, which assumes the contribution of the shear strength, including VPSBs as stirrups, as well as the compression zone of concrete, dowelling action, aggregate interlock, and residual tensile strength. The compression zone of concrete, dowelling action, and residual tensile strength account for the effect of vertical compressive stress on the tensile strength of concrete. In a model developed by El-Shafiey and Atta [43], concrete, stirrups, and prestressing forces were considered in shear capacity prediction.Studies involving the mechanism of VPSBs in enhancing the shear capacity are scarce. This paper emphatically studies the shear reinforcement method by using VPSBs, focuses on the shear strengthening influence parameters and tries to reveal its shear reinforcement mechanism.


## 2. Experimental Program

Four rectangular beams of reinforced concrete without web reinforcement were used in this study. Among them, two test beams were used as control beams, and the others were strengthened with VPSBs. The shear strengthening effect of VPSBs on concrete beams without web reinforcement was investigated.


### 2.1. Specimens

Four reinforced concrete rectangular beams were tested, two of which were control beams, denoted as RC1 and RC2, correspondingly. The other two beams were prestressed vertically by VPSBs and were labelled as IP_F22_S240 and IP_F22_S160. The details of the components are presented next.The control beam measured 250 mm (b) × 500 mm (h) × 3000 mm (l), and its effective span was 2600 mm. Five longitudinal tensile reinforcements with a diameter of 22 mm were arranged at the bottom of the specimen (longitudinal reinforcement ratio, ρ = 1.81%). Two compression steel bars with a diameter of 22 mm were arranged at the top of the specimen. The specimens were segregated into two groups along the longitudinal direction. The shear span area on the left was not arranged with stirrups, and shear failure is expected to occur in this region; meanwhile, the shear span area on the right was arranged with stirrups with a spacing of 100 mm and a diameter of 12 mm, and the cross-zone stirrup rate ρsv was 0.9048%. The geometrical dimensions and reinforcement arrangement of the control beams are shown in Figure 1(a).Figure 1
Geometry and arrangement of specimen reinforcement (units: mm).
(a)(b)The other two shear-reinforced specimens were strengthened by setting VPSBs in the left shear span area, as shown in Figure1(b). Ducts were reserved in the beams when concrete was poured, whereas the VPSBs were set in these ducts and tensioned. Through the vertical compressive stress provided by the VPSBs and the action of the VPSBs as stirrups, the shear capacity of the concrete beam improved. The tensile force applied to the VPSBs was 22 kN, and the spacing of the VPSBs was 240 and 160 mm. In terms of the specimen labels, “IP” refers to the “internal vertical prestressed steel bar,” “F” represents the “tensile force applied by the VPSBs in the body” (units: kN) and “S” represents the “spacing between the VPSBs in the body” (units: mm). For example, IP_F22_S240 refers to a specimen that is strengthened by setting VPSBs in the left shear span area, with a tensile force of 22 kN applied to each VPSB and a spacing of 240 mm between the VPSBs.Vertical displacement was applied in the middle of the beam using one hydraulic ram. The load was applied to a structural steel frame connected to the floor. The beam was supported by two horizontal steel cubes. A ball-bearing unit was used under the ram to ensure the transfer of the pure axial load to the specimen. The hydraulic jacks were 1400 and 1200 mm away from the left and right supports, respectively. Relative to the support on the left, the shear span ratio was 3.3, which reduced the arching effect. A YLR-3F pressure sensor was used to determine the value of the loading force. The strain gauges arranged on the VPSBs were labelled PS1-L (R), PS2-L(R), PS3-L(R), and PS4-L(R), where “L” and “R” indicate that the strain gauges were located on the left and right sides of the specimen section, respectively. Using the data from the strain gauges, the tensile force of the VPSBs can be effectively controlled, and the strain values during loading can be obtained. Strain gauges TS1, TS2, and TS3 were installed on the tensile longitudinal reinforcements to measure the strain of the longitudinal tensile reinforcements such that the occurrence of test beam flexural failure during loading can be confirmed.After tightening the nuts with a wrench to apply force to the VPSBs, a jacking hydraulic jack was used to load the test beam at a load rate of 20 min for each loading step, and the load was sustained for 10 min.


### 2.2. Strengthening Technique

The strengthening structural system was primarily composed of the following components: (1) two steel bars with a diameter of 14 mm and a length of 800 mm, which were prestressed before they were loaded onto the specimens; (2) M14 nuts at both ends of the steel bars. The pretension force can be applied to the steel bars by tightening the nuts; (3) four 10-mm-thick steel plates with holes measuring 20 mm in diameter under the nuts, as shown in Figure2.Figure 2
Structure form of a beam strengthened by VPSBs.The VPSBs were tensioned as follows: after the strain gauges were attached to the VPSBs and connected to the strain collecting instrument, the nuts were tightened using a wrench to apply the tension force. For strengthening specimens were IP_F22_S240 and IP_F22_S160. The tension force applied was 22 kN. Finally, vertical compressive stresses of 0.73 and 1.1 MPa were achieved by IP_F22_S240 and IP_F22_S160, respectively, owing to the tensile force. In addition, the secondary tension method, which is based on the difference between the test strain value read from the strain collecting instrument and the theoretical value, was adopted to reduce the effect of short-term tension force loss.


### 2.3. Materials

The specimens were fabricated using commercial concrete with a strength grade of 30 MPa and were poured simultaneously. The compressive strength (30.2 MPa) and splitting strength (2.88 MPa) of concrete were obtained using test cubes measuring 150 mm × 150 mm × 150 mm.Longitudinal tensile reinforcements with a diameter of 22 mm, stirrups with a diameter of 12 mm, and VPSBs with a diameter of 14 mm were used. The mechanical properties of the three types of reinforcements, including yield strength, tensile strength, and elastic modulus, are listed in Table1.Table 1
Mechanical properties of steel rebars.
TypeDiameter (mm)Yield strength (MPa)Tensile strength (MPa)Elastic modulus (MPa)Longitudinal reinforcements224556702.0 × 105Stirrups12445630VPSBs143505152.1 × 105The main parameters of the test beams are listed in Table2.Table 2
Main parameters of test beams.
SpecimensDimensionb × h × l (mm3)Longitudinal tension rebarsLongitudinal compression rebarsStirrupsVPSBsDiameter (mm)Spacing (mm)Tensile force (kN)RC_1250 × 500 × 30005Φ222Φ22Φ12@100———RC_2IP_F22_S2401424022IP_F22_S1601416022


## 2.1. Specimens

Four reinforced concrete rectangular beams were tested, two of which were control beams, denoted as RC1 and RC2, correspondingly. The other two beams were prestressed vertically by VPSBs and were labelled as IP_F22_S240 and IP_F22_S160. The details of the components are presented next.The control beam measured 250 mm (b) × 500 mm (h) × 3000 mm (l), and its effective span was 2600 mm. Five longitudinal tensile reinforcements with a diameter of 22 mm were arranged at the bottom of the specimen (longitudinal reinforcement ratio, ρ = 1.81%). Two compression steel bars with a diameter of 22 mm were arranged at the top of the specimen. The specimens were segregated into two groups along the longitudinal direction. The shear span area on the left was not arranged with stirrups, and shear failure is expected to occur in this region; meanwhile, the shear span area on the right was arranged with stirrups with a spacing of 100 mm and a diameter of 12 mm, and the cross-zone stirrup rate ρsv was 0.9048%. The geometrical dimensions and reinforcement arrangement of the control beams are shown in Figure 1(a).Figure 1
Geometry and arrangement of specimen reinforcement (units: mm).
(a)(b)The other two shear-reinforced specimens were strengthened by setting VPSBs in the left shear span area, as shown in Figure1(b). Ducts were reserved in the beams when concrete was poured, whereas the VPSBs were set in these ducts and tensioned. Through the vertical compressive stress provided by the VPSBs and the action of the VPSBs as stirrups, the shear capacity of the concrete beam improved. The tensile force applied to the VPSBs was 22 kN, and the spacing of the VPSBs was 240 and 160 mm. In terms of the specimen labels, “IP” refers to the “internal vertical prestressed steel bar,” “F” represents the “tensile force applied by the VPSBs in the body” (units: kN) and “S” represents the “spacing between the VPSBs in the body” (units: mm). For example, IP_F22_S240 refers to a specimen that is strengthened by setting VPSBs in the left shear span area, with a tensile force of 22 kN applied to each VPSB and a spacing of 240 mm between the VPSBs.Vertical displacement was applied in the middle of the beam using one hydraulic ram. The load was applied to a structural steel frame connected to the floor. The beam was supported by two horizontal steel cubes. A ball-bearing unit was used under the ram to ensure the transfer of the pure axial load to the specimen. The hydraulic jacks were 1400 and 1200 mm away from the left and right supports, respectively. Relative to the support on the left, the shear span ratio was 3.3, which reduced the arching effect. A YLR-3F pressure sensor was used to determine the value of the loading force. The strain gauges arranged on the VPSBs were labelled PS1-L (R), PS2-L(R), PS3-L(R), and PS4-L(R), where “L” and “R” indicate that the strain gauges were located on the left and right sides of the specimen section, respectively. Using the data from the strain gauges, the tensile force of the VPSBs can be effectively controlled, and the strain values during loading can be obtained. Strain gauges TS1, TS2, and TS3 were installed on the tensile longitudinal reinforcements to measure the strain of the longitudinal tensile reinforcements such that the occurrence of test beam flexural failure during loading can be confirmed.After tightening the nuts with a wrench to apply force to the VPSBs, a jacking hydraulic jack was used to load the test beam at a load rate of 20 min for each loading step, and the load was sustained for 10 min.


## 2.2. Strengthening Technique

The strengthening structural system was primarily composed of the following components: (1) two steel bars with a diameter of 14 mm and a length of 800 mm, which were prestressed before they were loaded onto the specimens; (2) M14 nuts at both ends of the steel bars. The pretension force can be applied to the steel bars by tightening the nuts; (3) four 10-mm-thick steel plates with holes measuring 20 mm in diameter under the nuts, as shown in Figure2.Figure 2
Structure form of a beam strengthened by VPSBs.The VPSBs were tensioned as follows: after the strain gauges were attached to the VPSBs and connected to the strain collecting instrument, the nuts were tightened using a wrench to apply the tension force. For strengthening specimens were IP_F22_S240 and IP_F22_S160. The tension force applied was 22 kN. Finally, vertical compressive stresses of 0.73 and 1.1 MPa were achieved by IP_F22_S240 and IP_F22_S160, respectively, owing to the tensile force. In addition, the secondary tension method, which is based on the difference between the test strain value read from the strain collecting instrument and the theoretical value, was adopted to reduce the effect of short-term tension force loss.


## 2.3. Materials

The specimens were fabricated using commercial concrete with a strength grade of 30 MPa and were poured simultaneously. The compressive strength (30.2 MPa) and splitting strength (2.88 MPa) of concrete were obtained using test cubes measuring 150 mm × 150 mm × 150 mm.Longitudinal tensile reinforcements with a diameter of 22 mm, stirrups with a diameter of 12 mm, and VPSBs with a diameter of 14 mm were used. The mechanical properties of the three types of reinforcements, including yield strength, tensile strength, and elastic modulus, are listed in Table1.Table 1
Mechanical properties of steel rebars.
TypeDiameter (mm)Yield strength (MPa)Tensile strength (MPa)Elastic modulus (MPa)Longitudinal reinforcements224556702.0 × 105Stirrups12445630VPSBs143505152.1 × 105The main parameters of the test beams are listed in Table2.Table 2
Main parameters of test beams.
SpecimensDimensionb × h × l (mm3)Longitudinal tension rebarsLongitudinal compression rebarsStirrupsVPSBsDiameter (mm)Spacing (mm)Tensile force (kN)RC_1250 × 500 × 30005Φ222Φ22Φ12@100———RC_2IP_F22_S2401424022IP_F22_S1601416022


## 3. Test Results and Discussion

### 3.1. Shear Capacity and Failure

As control beams, RC_1 and RC_2 behaved elastically before the concrete beams formed cracks, and the vertical displacement exhibited a linear proportional relationship with the load. As the load increased continuously, three cracks and five cracks formed on the left side of RC_1 and RC_2, respectively, with a spacing of 18–24 cm. In both RC_1 and RC_2, a main crack developed and formed. The main crack expanded rapidly to the left support and loading point. The width of the crack widened rapidly, and the specimens failed abruptly. This exemplifies the typical brittle shear failure, and typical forms of shear failure are shown in Figures3(a) and 3(b). The shear capacities of RC_1 and RC_2 were 234.4 and 256.5 kN, corresponding to deflections in the middle span of 3.0 and 3.6 mm, respectively.Figure 3
Cracking mode of a partial specimen under shear failure. (a) RC_1. (b) RC_2. (c) IP_F22_S240. (d) IP_F22_S160.
(a)(b)(c)(d)Specimen IP_F22_S240 exhibited five diagonal cracks on the left side, and the main crack was formed when the load reached 285 kN. Owing to the effect of the vertical compressive stress and the stirrup effect of the VPSBs, the main crack developed relatively slowly toward the left support and loading point. When VPSB PS3-R yielded, the specimen reached the ultimate shear capacity (530.1 kN), and the corresponding vertical deflection was 12.4 mm, as shown in Figure3(c).The crack development and failure mode of specimen IP_F22_S160 were similar to those of specimen IP_F22_S240. As the load increased, three flexural shear cracks appeared on the left side of the specimen. When the load reached approximately 300 kN, the main crack was formed and gradually developed toward the left support and loading point. When the load reached 490 kN, the nuts of the VPSB PS4 detached, which caused shear compression failure and a loud crisp noise with a corresponding vertical deflection of 8.4 mm, as shown in Figure3(d). When the nuts detached, the VPSBs failed to yield and could not fully serve as stirrups. Therefore, the shear capacity of IP_F22_S160 was lower than that of IP_F22_S240.As shown in Figure3, the shear failure processes of RC_1 and RC_2 were rapid. No clear indications were shown before the specimens were destroyed. Although severe cracks were formed in specimens IP_F22_S240 and IP_F22_S160 at loads of 280–300 kN, the specimens managed to continue to sustain the load and maintain their rigidity owing to the effect of the VPSBs. Finally, the failure mode was transformed from shear diagonal tension failure to shear compression failure. When IP_F22_S240 and IP_F22_S160 were destroyed, a certain extent of ductility was demonstrated, i.e., numerous cracks developed more fully, with a deflection-to-span ratio of 1/200–1/310. The shear capacity of specimens IP_F22_S240 and IP_F22_S160 increased to 530.1 and 490 kN, respectively, which were 115.97% and 99.61% higher than the average shear strengths of RC_1 and RC_2, respectively.In addition, comparing the load–displacement curves of specimens IP_F22_S240 and IP_F22_S160 strengthened by VPSBs with different spacings (Figure4), it was observed that as the VPSB spacing decreased, the crack development of the specimen was restrained more effectively and the rigidity of the specimen was maintained well.Figure 4
Load–displacement curve of specimens.The main results of the specimens are presented in Table3, where PMC, PSC, PCSC, PU, and δU are the corresponding loads for the initial crack, first diagonal crack, formation of critical diagonal cracks, ultimate shear capacity, and deflection value, respectively.Table 3
Main experimental results of specimens.
SpecimensPMC (kN)PSC (kN)PCSC (kN)PU (kN)δU (mm)Failure modeRC_153.4142.4234.4234.43.0Diagonal tension failureRC_276.5131.6256.5256.53.6Diagonal tension failureIP_F22_S24053135285530.112.4Shear compression failureIP_F22_S16057.1158.43004908.4Shear compression failure


### 3.2. Prestressing Rebars

Specimens IP_F22_S240 and IP_F22_S160 were equipped with VPSBs measuring 14 mm in diameter. The VPSBs were applied with a tensile force of 22 kN before loading. The initial strain of the VPSBs can be calculated using the following equation:(1)ϵs=σsEs,where εs is the initial strain of the VPSBs; σs is the initial stress of the VPSBs, which is equal to the tensile force divided by the cross-sectional area of the steel bars; Es is the elastic modulus of the VPSBs. Therefore, as shown in Figure 5, the initial tensile strain of all VPSBs was approximately 680με.Figure 5
VPSBs stress–strain curve and cracking pattern at shear failure of specimens. (a) IP_F22_S240. (b) IP_F22_S160.
(a)(b)As shown in Figure5(a), before the load reached 260 kN, the strain of the VPSBs of specimen IP_F22_S240 changed slightly. Owing to the vertical compressive stress generated by the VPSBs on the specimen, the development of cracks in the specimen was effectively suppressed, and the shear capacity was retained at this stage. As the load increased, the strain on the VPSBs increased, and the VPSBs served as stirrups gradually. Diagonal cracks formed on the specimen and developed slowly, and the number of cracks increased. At this stage, the strain of the VPSBs increased linearly; in particular, the strains of PS3 and PS4 VPSBs located in the main cracks increased rapidly (Figure 6(a)). Finally, the main crack passed through the lower region of VPSB PS3 and extended along the longitudinal reinforcements toward the left support. PS3-R first reached the yield strain, and specimen IP_F22_S240 exhibited shear failure.Figure 6
Depiction of cracking pattern at shear failure for IP_F22_S240 and IP_F22_S160 (units: mm).
(a)(b)For the same tensile force of the VPSBs, the vertical compressive stress of the specimen increased as the spacing of the VPSBs decreased. The vertical compressive stress changed from 0.73 MPa of specimen IP_F22_S240 to 1.1 MPa of specimen IP_F22_S160. The vertical compressive stress of specimen IP_F22_S160 increased, which restrained the development of cracks more effectively and maintained the shear capacity well; therefore, the effect of the vertical prestressed reinforcement as stirrups appeared gradually until 340 kN (Figure5(b)). Before the load reached 340 kN, the preservation of the shear capacity of the specimen depended on the vertical compressive stress. This shows that the shear contribution of the VPSBs can be categorised into two stages: at the initial stage of loading, the main shear contribution was vertical compressive stress. As the load increased, the contribution of the VPSBs as stirrups increased gradually. In addition, the vertical compressive stress was greater, and the contribution of the VPSBs as stirrups occurred later.The main crack in specimen IP_F22_S160 passed through PS3 and PS4 (Figure6(b)). When the load reached approximately 490 kN, the nuts of VPSB PS4 detached, and the specimen was destroyed. At this time, the vertical prestressed steel did not yield.


### 3.3. Crack Pattern

No stirrups were embedded in the left side of the four specimens, and sufficient stirrups were arranged on the right side. Therefore, shear failure occurred on the left side of the test beam. Only the left-side cracks of the test beams are described below.


#### 3.3.1. RC_1 and RC_2

First, a vertical crack was generated on the bottom surface of the mid-span of RC_1 and RC_2, and the corresponding loads were 53.4 and 76.5 kN, respectively. Subsequently, as the load increased, several vertical cracks appeared along the support direction, and the crack spacing was relatively large, i.e., 14–28 mm. When the load increased to 142.4 and 131.6 kN, diagonal flexural cracks developed gradually in RC_1 and RC_2. When the load increased to 234.4 and 256.5 kN, main cracks formed in RC_1 and RC_2, and their diagonal angles were 31.5° and 38.9°, respectively; the cracks developed rapidly toward the loading point and left support, whereas the width increased significantly, as shown in Figures7(a) and 7(b). The specimens exhibited diagonal shear failure accompanied by a loud noise.Figure 7
Depiction of cracking pattern at shear failure for RC_1 and RC_2 (units: mm).
(a)(b)


#### 3.3.2. IP_F22_S240 and IP_F22_S160

The VPSBs applied to the left side of the specimen did not significantly affect the formation of vertical cracks; however, they did affect the formation of the initial diagonal cracks.The loads corresponding to the first flexural crack of specimens IP_F22_S240 and IP_F22_S160 were 60 and 50 kN, respectively, which were similar to the load of the initial crack in the control beam.The loads corresponding to the first diagonal crack of specimens IP_F22_S240 and IP_F22_S160 were 160 and 135 kN, respectively. Compared with the control beam, the generation of diagonal cracks lagged behind by approximately 20 kN. This implies that the vertical compressive stress provided by the VPSBs can effectively suppress the generation of diagonal cracks.When the load increased to 285 and 300 kN, main cracks formed in specimens IP_F22_S240 and IP_F22_S160, with inclination angles of 42.1° and 44.2°, respectively. Compared with the control beam, the formation of the main crack was delayed owing to the vertical compressive stress.As the load increased gradually, the effect of the vertical prestressed reinforcement as stirrups become more prominent, which contributed to a significant restraining effect on the development of the diagonal crack.When the specimen exhibited shear failure, five diagonal cracks were formed in specimen IP_F22_S240. The vertical prestressed steel PS3-R yielded and caused the shear failure of the specimen. As shown in Figure6(a), the angle of the main crack of specimen IP_F22_S240 was approximately 45°, and the bottom of the main crack developed along the longitudinal reinforcement toward the support.For specimen IP_F22_S160, because the VPSBs provided a higher vertical compressive stress and the stirrup ratio was greater, the suppression effect on the diagonal cracks was more prominent. Before the nuts of the VPSB PS4 detached, the number of diagonal cracks in specimen IP_F22_S160 (three cracks) was less than that of specimen IP_F22_S240 (five cracks), and the crack width was relatively small, which indicated that the compressive stress of the VPSBs and the ratio of stirrups significantly affected the shear capacity and crack suppression, as shown in Figure6(b).During the entire test process, the strain of the longitudinal reinforcements remained less than the yield strain.


## 3.1. Shear Capacity and Failure

As control beams, RC_1 and RC_2 behaved elastically before the concrete beams formed cracks, and the vertical displacement exhibited a linear proportional relationship with the load. As the load increased continuously, three cracks and five cracks formed on the left side of RC_1 and RC_2, respectively, with a spacing of 18–24 cm. In both RC_1 and RC_2, a main crack developed and formed. The main crack expanded rapidly to the left support and loading point. The width of the crack widened rapidly, and the specimens failed abruptly. This exemplifies the typical brittle shear failure, and typical forms of shear failure are shown in Figures3(a) and 3(b). The shear capacities of RC_1 and RC_2 were 234.4 and 256.5 kN, corresponding to deflections in the middle span of 3.0 and 3.6 mm, respectively.Figure 3
Cracking mode of a partial specimen under shear failure. (a) RC_1. (b) RC_2. (c) IP_F22_S240. (d) IP_F22_S160.
(a)(b)(c)(d)Specimen IP_F22_S240 exhibited five diagonal cracks on the left side, and the main crack was formed when the load reached 285 kN. Owing to the effect of the vertical compressive stress and the stirrup effect of the VPSBs, the main crack developed relatively slowly toward the left support and loading point. When VPSB PS3-R yielded, the specimen reached the ultimate shear capacity (530.1 kN), and the corresponding vertical deflection was 12.4 mm, as shown in Figure3(c).The crack development and failure mode of specimen IP_F22_S160 were similar to those of specimen IP_F22_S240. As the load increased, three flexural shear cracks appeared on the left side of the specimen. When the load reached approximately 300 kN, the main crack was formed and gradually developed toward the left support and loading point. When the load reached 490 kN, the nuts of the VPSB PS4 detached, which caused shear compression failure and a loud crisp noise with a corresponding vertical deflection of 8.4 mm, as shown in Figure3(d). When the nuts detached, the VPSBs failed to yield and could not fully serve as stirrups. Therefore, the shear capacity of IP_F22_S160 was lower than that of IP_F22_S240.As shown in Figure3, the shear failure processes of RC_1 and RC_2 were rapid. No clear indications were shown before the specimens were destroyed. Although severe cracks were formed in specimens IP_F22_S240 and IP_F22_S160 at loads of 280–300 kN, the specimens managed to continue to sustain the load and maintain their rigidity owing to the effect of the VPSBs. Finally, the failure mode was transformed from shear diagonal tension failure to shear compression failure. When IP_F22_S240 and IP_F22_S160 were destroyed, a certain extent of ductility was demonstrated, i.e., numerous cracks developed more fully, with a deflection-to-span ratio of 1/200–1/310. The shear capacity of specimens IP_F22_S240 and IP_F22_S160 increased to 530.1 and 490 kN, respectively, which were 115.97% and 99.61% higher than the average shear strengths of RC_1 and RC_2, respectively.In addition, comparing the load–displacement curves of specimens IP_F22_S240 and IP_F22_S160 strengthened by VPSBs with different spacings (Figure4), it was observed that as the VPSB spacing decreased, the crack development of the specimen was restrained more effectively and the rigidity of the specimen was maintained well.Figure 4
Load–displacement curve of specimens.The main results of the specimens are presented in Table3, where PMC, PSC, PCSC, PU, and δU are the corresponding loads for the initial crack, first diagonal crack, formation of critical diagonal cracks, ultimate shear capacity, and deflection value, respectively.Table 3
Main experimental results of specimens.
SpecimensPMC (kN)PSC (kN)PCSC (kN)PU (kN)δU (mm)Failure modeRC_153.4142.4234.4234.43.0Diagonal tension failureRC_276.5131.6256.5256.53.6Diagonal tension failureIP_F22_S24053135285530.112.4Shear compression failureIP_F22_S16057.1158.43004908.4Shear compression failure


## 3.2. Prestressing Rebars

Specimens IP_F22_S240 and IP_F22_S160 were equipped with VPSBs measuring 14 mm in diameter. The VPSBs were applied with a tensile force of 22 kN before loading. The initial strain of the VPSBs can be calculated using the following equation:(1)ϵs=σsEs,where εs is the initial strain of the VPSBs; σs is the initial stress of the VPSBs, which is equal to the tensile force divided by the cross-sectional area of the steel bars; Es is the elastic modulus of the VPSBs. Therefore, as shown in Figure 5, the initial tensile strain of all VPSBs was approximately 680με.Figure 5
VPSBs stress–strain curve and cracking pattern at shear failure of specimens. (a) IP_F22_S240. (b) IP_F22_S160.
(a)(b)As shown in Figure5(a), before the load reached 260 kN, the strain of the VPSBs of specimen IP_F22_S240 changed slightly. Owing to the vertical compressive stress generated by the VPSBs on the specimen, the development of cracks in the specimen was effectively suppressed, and the shear capacity was retained at this stage. As the load increased, the strain on the VPSBs increased, and the VPSBs served as stirrups gradually. Diagonal cracks formed on the specimen and developed slowly, and the number of cracks increased. At this stage, the strain of the VPSBs increased linearly; in particular, the strains of PS3 and PS4 VPSBs located in the main cracks increased rapidly (Figure 6(a)). Finally, the main crack passed through the lower region of VPSB PS3 and extended along the longitudinal reinforcements toward the left support. PS3-R first reached the yield strain, and specimen IP_F22_S240 exhibited shear failure.Figure 6
Depiction of cracking pattern at shear failure for IP_F22_S240 and IP_F22_S160 (units: mm).
(a)(b)For the same tensile force of the VPSBs, the vertical compressive stress of the specimen increased as the spacing of the VPSBs decreased. The vertical compressive stress changed from 0.73 MPa of specimen IP_F22_S240 to 1.1 MPa of specimen IP_F22_S160. The vertical compressive stress of specimen IP_F22_S160 increased, which restrained the development of cracks more effectively and maintained the shear capacity well; therefore, the effect of the vertical prestressed reinforcement as stirrups appeared gradually until 340 kN (Figure5(b)). Before the load reached 340 kN, the preservation of the shear capacity of the specimen depended on the vertical compressive stress. This shows that the shear contribution of the VPSBs can be categorised into two stages: at the initial stage of loading, the main shear contribution was vertical compressive stress. As the load increased, the contribution of the VPSBs as stirrups increased gradually. In addition, the vertical compressive stress was greater, and the contribution of the VPSBs as stirrups occurred later.The main crack in specimen IP_F22_S160 passed through PS3 and PS4 (Figure6(b)). When the load reached approximately 490 kN, the nuts of VPSB PS4 detached, and the specimen was destroyed. At this time, the vertical prestressed steel did not yield.


## 3.3. Crack Pattern

No stirrups were embedded in the left side of the four specimens, and sufficient stirrups were arranged on the right side. Therefore, shear failure occurred on the left side of the test beam. Only the left-side cracks of the test beams are described below.


### 3.3.1. RC_1 and RC_2

First, a vertical crack was generated on the bottom surface of the mid-span of RC_1 and RC_2, and the corresponding loads were 53.4 and 76.5 kN, respectively. Subsequently, as the load increased, several vertical cracks appeared along the support direction, and the crack spacing was relatively large, i.e., 14–28 mm. When the load increased to 142.4 and 131.6 kN, diagonal flexural cracks developed gradually in RC_1 and RC_2. When the load increased to 234.4 and 256.5 kN, main cracks formed in RC_1 and RC_2, and their diagonal angles were 31.5° and 38.9°, respectively; the cracks developed rapidly toward the loading point and left support, whereas the width increased significantly, as shown in Figures7(a) and 7(b). The specimens exhibited diagonal shear failure accompanied by a loud noise.Figure 7
Depiction of cracking pattern at shear failure for RC_1 and RC_2 (units: mm).
(a)(b)


### 3.3.2. IP_F22_S240 and IP_F22_S160

The VPSBs applied to the left side of the specimen did not significantly affect the formation of vertical cracks; however, they did affect the formation of the initial diagonal cracks.The loads corresponding to the first flexural crack of specimens IP_F22_S240 and IP_F22_S160 were 60 and 50 kN, respectively, which were similar to the load of the initial crack in the control beam.The loads corresponding to the first diagonal crack of specimens IP_F22_S240 and IP_F22_S160 were 160 and 135 kN, respectively. Compared with the control beam, the generation of diagonal cracks lagged behind by approximately 20 kN. This implies that the vertical compressive stress provided by the VPSBs can effectively suppress the generation of diagonal cracks.When the load increased to 285 and 300 kN, main cracks formed in specimens IP_F22_S240 and IP_F22_S160, with inclination angles of 42.1° and 44.2°, respectively. Compared with the control beam, the formation of the main crack was delayed owing to the vertical compressive stress.As the load increased gradually, the effect of the vertical prestressed reinforcement as stirrups become more prominent, which contributed to a significant restraining effect on the development of the diagonal crack.When the specimen exhibited shear failure, five diagonal cracks were formed in specimen IP_F22_S240. The vertical prestressed steel PS3-R yielded and caused the shear failure of the specimen. As shown in Figure6(a), the angle of the main crack of specimen IP_F22_S240 was approximately 45°, and the bottom of the main crack developed along the longitudinal reinforcement toward the support.For specimen IP_F22_S160, because the VPSBs provided a higher vertical compressive stress and the stirrup ratio was greater, the suppression effect on the diagonal cracks was more prominent. Before the nuts of the VPSB PS4 detached, the number of diagonal cracks in specimen IP_F22_S160 (three cracks) was less than that of specimen IP_F22_S240 (five cracks), and the crack width was relatively small, which indicated that the compressive stress of the VPSBs and the ratio of stirrups significantly affected the shear capacity and crack suppression, as shown in Figure6(b).During the entire test process, the strain of the longitudinal reinforcements remained less than the yield strain.


## 3.3.1. RC_1 and RC_2

First, a vertical crack was generated on the bottom surface of the mid-span of RC_1 and RC_2, and the corresponding loads were 53.4 and 76.5 kN, respectively. Subsequently, as the load increased, several vertical cracks appeared along the support direction, and the crack spacing was relatively large, i.e., 14–28 mm. When the load increased to 142.4 and 131.6 kN, diagonal flexural cracks developed gradually in RC_1 and RC_2. When the load increased to 234.4 and 256.5 kN, main cracks formed in RC_1 and RC_2, and their diagonal angles were 31.5° and 38.9°, respectively; the cracks developed rapidly toward the loading point and left support, whereas the width increased significantly, as shown in Figures7(a) and 7(b). The specimens exhibited diagonal shear failure accompanied by a loud noise.Figure 7
Depiction of cracking pattern at shear failure for RC_1 and RC_2 (units: mm).
(a)(b)


## 3.3.2. IP_F22_S240 and IP_F22_S160

The VPSBs applied to the left side of the specimen did not significantly affect the formation of vertical cracks; however, they did affect the formation of the initial diagonal cracks.The loads corresponding to the first flexural crack of specimens IP_F22_S240 and IP_F22_S160 were 60 and 50 kN, respectively, which were similar to the load of the initial crack in the control beam.The loads corresponding to the first diagonal crack of specimens IP_F22_S240 and IP_F22_S160 were 160 and 135 kN, respectively. Compared with the control beam, the generation of diagonal cracks lagged behind by approximately 20 kN. This implies that the vertical compressive stress provided by the VPSBs can effectively suppress the generation of diagonal cracks.When the load increased to 285 and 300 kN, main cracks formed in specimens IP_F22_S240 and IP_F22_S160, with inclination angles of 42.1° and 44.2°, respectively. Compared with the control beam, the formation of the main crack was delayed owing to the vertical compressive stress.As the load increased gradually, the effect of the vertical prestressed reinforcement as stirrups become more prominent, which contributed to a significant restraining effect on the development of the diagonal crack.When the specimen exhibited shear failure, five diagonal cracks were formed in specimen IP_F22_S240. The vertical prestressed steel PS3-R yielded and caused the shear failure of the specimen. As shown in Figure6(a), the angle of the main crack of specimen IP_F22_S240 was approximately 45°, and the bottom of the main crack developed along the longitudinal reinforcement toward the support.For specimen IP_F22_S160, because the VPSBs provided a higher vertical compressive stress and the stirrup ratio was greater, the suppression effect on the diagonal cracks was more prominent. Before the nuts of the VPSB PS4 detached, the number of diagonal cracks in specimen IP_F22_S160 (three cracks) was less than that of specimen IP_F22_S240 (five cracks), and the crack width was relatively small, which indicated that the compressive stress of the VPSBs and the ratio of stirrups significantly affected the shear capacity and crack suppression, as shown in Figure6(b).During the entire test process, the strain of the longitudinal reinforcements remained less than the yield strain.


## 4. Conclusions

In this study, four test beams with a shear-to-span ratio of 3.3 were investigated, two of which were control beams without web reinforcement, and the other two were strengthened by VPSBs. The effect of shear enhancement by VPSBs on reinforced concrete beams without webs was investigated in this experiment. Based on the experiment, the following conclusions were obtained:(1)
Control beams with a large shear-to-span ratio exhibited diagonal tension failure under a concentrated load. After being strengthened by VPSBs, the failure mode of the test beams changed from diagonal tension failure to shear compression failure. The VPSBs significantly increased the shear capacity of the test beam, i.e., from 234.4 to 256.5 kN of the control beam to 490 and 530.1 kN of the other two shear reinforced specimens that were strengthened by setting the VPSBs in the left shear span area, respectively (as shown in Figure1(b)); the increased capacities were 99.61% and 115.97% higher than the average shear capacity of the control beams, respectively.(2)
the number of cracks in the control beam was relatively small. When the main crack formed, it developed rapidly toward the support and loading points. The width of the crack increased rapidly, and the beam exhibited shear failure abruptly. For the test beams strengthened with VPSBs, numerous cracks appeared under the load. Owing to the restraint of the VPSBs, the cracks developed relatively slowly. After the main cracks were formed, the test beams were still able to sustain the load. The cracks developed more fully until the test beam was destroyed.(3)
The shear failure of the VPSBs involved primarily two stages. (i) Stagei: shear resistance was primarily provided by the vertical compressive stress generated by the VPSBs on the beam body in the early stage of loading, and the vertical compressive stress effectively suppressed the occurrence and development of cracks. At this stage, the strain of the VPSBs remained unchanged. (ii) Stage ii: As the load increased, the strain of the VPSBs increased linearly, and the contribution of the prestressed steel bars as stirrups increased gradually. Consequently, the shear capacity of the test beam improved significantly. In addition, the greater the vertical compressive stress applied in the first stage, the later the formation of the second stage.(4)
The spacing and tensile force of the VPSBs significantly affected the shear capacity and crack development. The stirrup ratio and vertical compressive stress of the VPSBs increased as the VPSB spacing decreased, thereby facilitating the development of specimen cracks as well as preserving the shear capacity and rigidity.The compressive stress and stirrup effect provided by the VPSBs make an important contribution to the improvement of the shear capacity of reinforced concrete beams. In the future, it is recommended to carry out research on the following two aspects: size effect and structural structure in actual engineering.



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*Source: 3869978-2022-08-12.xml*