Shear behavior of ultra-high-performance concrete beams prestressed with external carbon fiber-reinforced polymer tendons

Abstract

The ultra-high-performance concrete (UHPC) and fiber-reinforced polymer (FRP) are well-accepted high-performance materials in the field of civil engineering. The combination of these advanced materials could contribute to improvement of structural performance and corrosion resistance. Unfortunately, only limited studies are available for shear behavior of UHPC beams reinforced with FRP bars, and few suggestions exist for prediction methods for shear capacity. This paper presents an experimental investigation on the shear behavior of UHPC beams reinforced with glass FRP (GFRP) and prestressed with external carbon FRP (CFRP) tendons. The failure mode of all specimens with various shear span to depth ratios from 1.7 to 4.5 was diagonal tension failure. The shear span to depth ratio had a significant influence on the shear capacity, and the effective prestressing stress affected the crack propagation. The experimental results were then applied to evaluate the equations given in different codes/recommendations for FRP-reinforced concrete structures or UHPC structures. The comparison results indicate that NF P 18-710 and JSCE CES82 could appropriately estimate shear capacity of the slender specimens with a shear span to depth ratio of 4.5. Further, a new shear design equation was proposed to take into account the effect of the shear span to depth ratio and the steel fiber content on shear capacity.

Graphical abstract

Keywords

beam / external prestressing / ultra-high-performance concrete / fiber-reinforced polymers / shear behavior / design equation

1 Introduction

Owing to their high strength-to-weight ratio, excellent durability, and good fatigue properties, fiber-reinforced polymers (FRPs) are considered an advantageous alternative to steel for the reinforcement of concrete structures in severe environments. However, because of the linear elastic behavior without a discernible yield point of FRP reinforcements, the ductility of FRP-reinforced components is mainly dependent on the compressive plasticity of concrete. Thus, FRP-reinforced concrete members are prone to brittle failure [1]. Moreover, resulting from the low elastic modulus of FRP bars, FRP-reinforced concrete members experience increased deflection and reduced shear capacity compared to those reinforced with traditional steel reinforcement [2].

Based on the unique strain-hardening response of ultra-high-performance concrete (UHPC), the combined use of UHPC and FRP reinforcements was proposed as a potential method to improve the structural ductility. Compared to traditional concrete, UHPC has much greater compressive and tensile strengths, higher toughness, and better structural durability [3,4]. The application of UHPC can contribute to the creation of lighter, thinner, and more sustainable civil structures. However, because the reduced thickness of the UHPC beam section causes difficulty in arranging the internal prestressed tendons, using external prestressing technique becomes a reasonable choice. As the external tendons are directly exposed to the environment, protection against detrimental effects is of particular concern. UHPC beams prestressed with external FRP tendons could be an effective method for improving structural durability.

Much existing literature has reported methods for improving bearing capacity and deformation ability of reinforced concrete members [5–9]. However, although a number of investigations have been conducted to study the shear behavior of concrete beams reinforced with FRP bars [10–14], studies on the shear behavior of concrete beams prestressed with external tendons are relatively limited, and are generally related to the application of steel strands and normal-strength concrete [15–17]. Ghallab et al. [18] tested five prestressed concrete beams with external Aramid FRP (AFRP) tendons. The test results demonstrated that the shear span to depth ratio had a notable effect on the shear capacity and failure pattern of the externally prestressed beams. The presence of the external FRP tendons increased the shear capacity of the tested beams by approximately 75%. Ng and Soudki [19] tested 15 concrete specimens externally prestressed with carbon FRP (CFRP) rods and examined the effect of the shear span to depth ratio, external prestressing level, and shear reinforcement setup. The experimental results showed that the prestressed specimens could reduce the effective shear span to depth ratio. However, the stirrups did not have a great influence on the shear behavior due to their limited shear contribution. In addition, the greatly enhanced shear strength of the prestressed specimens could not be appropriately predicted using the current American Concrete Institute (ACI) design equations. Furthermore, Mészöly and Randl [20] tested 20 I-shaped UHPC specimens to study the effect of steel fibers and shear reinforcements on shear behavior. For the stirrup-free UHPC specimens, the applied load suddenly decreased after the formation of the critical shear crack. The consistently developed critical crack caused the shear failure of the beams. For the stirrup-reinforced specimens, almost all the stirrups reached yield stress when subjected to 60% to 80% of the peak load, and the formation of the shear cracks was also obviously delayed.

The application of UHPC will obviously increase the shear capacity contribution of the concrete [21,22]. The steel fiber content has a significant influence on the cracking resistance and residual strength, which is related to the structural ductility [20]. The higher quantity of fibers in UHPC results in better bond performance between the internal reinforcements and concrete [23]. This novel FRP-reinforced and prestressed UHPC beam thus has the potential to improve the shear behavior of FRP-reinforced beams. As such, more experimental data are required to describe the shear behavior accurately.

Unfortunately, to the best of the authors’ knowledge, few if any studies have reported the shear behavior of FRP (GFRP)-reinforced UHPC beams prestressed with external CFRP tendons. The experimental and analytical investigations described herein are based on the following objectives:

1) to provide a reference for the shear behavior of FRP-reinforced UHPC beams prestressed with external FRP tendons;

2) to quantify the effects of the shear span to depth ratio (a/d) and effective prestressing stress (f_pe) on the shear behavior in detail;

3) to use the experimental results to evaluate the accuracy of the prediction equations in different guidelines;

4) to propose a design method for calculating the shear capacity of FRP-reinforced UHPC beams.

2 Experimental program

2.1 Details of specimens

Six simply supported UHPC beams were subjected to two concentrated loads and tested to failure. The geometric dimensions and reinforcement layout of the specimens are shown in Figs. 1 and 2, respectively. The details of the specimens are given in Table 1. It should be noted that the specimen code, e.g., B-X/Y-Z, indicates the main parameters of the specimen, where B means beam, X/Y is the value of a/d, and Z is the f_pe applied to the external tendons (as a percentage of the tensile strength, f_fp, of the CFRP tendon).

All tested beams were 2440 mm in length with a depth of 200 mm. The external CFRP tendons were anchored at the two ends of the specimen and pitted with deviators at the mid-span. According to ACI 440.4R-04 guideline [24], the deviators were saddle-shaped, with radius of curvature designed as 400 mm. Thus, the theoretical strength reduction of CFRP tendons was limited to no more than 5% of the tensile strength. The internal tensile reinforcements comprised three 12-mm-diameter deformed GFRP bars with 10 mm cover. Considering the tensile resistance of the steel fiber content in UHPC and the thin web layout of the beam specimens, 6-mm-diameter single-legged GFRP stirrups spaced at 100 mm within the shear span were used as the shear reinforcements, which meets the requirement of ACI 440.1R-15 [25] provision about the minimum shear reinforcement. To ensure shear failure, all of the specimens were designed to be over-reinforced in bending based on ACI 440.4R-04 and NF P 18-710 [26] guidelines. As a result, the longitudinal tensile reinforcement ratio, ρ_f, was 4.66%, and the shear reinforcement ratio, ρ_sv, was 0.71%.

The conventional anchor used for steel tendons was not suitable for FRP, hence a bond-type anchor grouted with UHPC [27] was employed in the present study. Moreover, a rubber protective cover was wrapped around the CFRP tendon at the deviating and anchoring positions to protect the strands. Because this rubber cover was less than 2 mm in thickness, it had a negligible effect on the mechanical property of the external tendons.

2.2 Material characterization

2.2.1 CFRP tendons

The CFCC^® strand manufactured by Tokyo Rope was selected for the external tendons in the tested beams. This type of CFRP strand with a diameter (D) of 12.54 mm consists of one straight wire and six twisted wires. The nominal diameter, d, and effective diameter, d_e, of each wire were 4.18 and 3.72 mm, respectively, as shown in Fig. 3. The mechanical properties of the CFRP tendons are listed in Table 2.

2.2.2 GFRP bars

As shown in Fig. 4, ribbed GFRP bars were used as the internal longitudinal reinforcements and stirrups. These composite bars were manufactured using the pultrusion process and comprised continuous unidirectional glass fibers in a vinyl ester resin matrix; their properties are also listed in Table 2.

2.2.3 UHPC

UHPC with a steel fibers volume fraction of 2% was used to cast the specimens. The quality mix proportion was cement: water: silica fume: ground quartz: quartz sand: water reducing agent = 1 : 0.2 : 0.25 : 0.3 : 1.1 : 2.5%. The steel fibers used in the present study had a length of 13 mm, a diameter of 0.2 mm, and a tensile strength of more than 2000 MPa. The tested beams and anchors were hot-cured (24 h at room temperature followed by 72 h of steam curing at 85°C ± 5°C). The mechanical properties of UHPC at 28 d were tested according to GB/T 31387-2015 [28], as shown in Table 3. The cubic compressive strength, f_cu, was obtained using standard 100 mm cubes. The axial compressive strength, f_c, and modulus of elasticity, E_c, were determined using 100 mm × 100 mm × 300 mm prisms. The initial cracking and ultimate tensile strengths (f_r0 and f_ru, respectively) under bending tension were obtained using 100 mm × 100 mm × 400 mm prisms.

2.3 Tensioning procedure, loading method, and measurements

To reduce the local stress concentration, 30-mm-thick steel anchor plates were bonded to the beam ends. Anchors were secured to the anchor plates with nuts after being tensioned with a hydraulic jack. The prestressing force of each external tendon was measured using a pressure sensor incorporated at the dead end of the anchor during the tensioning process. To minimize the short-term loss of the prestressing force, both tendons were over tensioned to a stress value of 1.05f_pe. The prestressing losses were all below 0.04f_pe before the loading test, which were calculated by the measured prestressing values after the tensioning procedure and before the loading process. As shown in Fig. 5, all of the specimens were tested under four-point bending loading. The load was applied with a loading rate of 2.5 kN/min through the load control mode. Then, it switched to a displacement-controlled mode after shear cracking, and the mid-span deflection increased 2 mm at every load level. The deflections at the mid-span and supports were measured using dial indicators. The strain in the top flange of the mid-span was measured by strain gauges. The distribution of cracks was recorded manually by tracing the crack propagation on the surface of the specimens, and a hand-held microscope was employed to detect the widths of cracks.

3 Test results

3.1 Failure mode

The observed shear failure phenomena were consistent for the six specimens tested in the present study. Diagonal tension failure occurred in all specimens, as shown in Fig. 6. In the typical failure process, web-shear cracks appeared within the shear span. Then, one web-shear crack suddenly developed and became a critical diagonal crack, after which the tensile stress of the longitudinal GFRP bars increased correspondingly to maintain cross-sectional equilibrium. The critical diagonal crack developed rapidly with the increasing load, and propagated toward the loading position. Finally, abrupt shear failure occurred with little warning, and the test beam was divided into two parts by the critical crack. The angles between the critical diagonal crack and the beam axis (inclination angle) varied between 35° and 42°.

As mentioned above, all of the specimens with various a/d values failed in a consistent manner. This could be attributed to the transverse strength of FRP being much lower than its tensile strength [29]; thus, the single-leg GFRP stirrups tended to fail in shear rather than in tension. Once the critical diagonal shear crack formed, this diagonal crack progressively developed into the compression flange and induced shear failure. Hence, the steel fiber content in UHPC showed marginal influence on restraining the propagation of the critical diagonal crack. The concrete at the two sides of the critical crack was subject to the forces from the applied load and the support reaction, and thus slid along the crack interface [30]. As a result, the GFRP stirrups located in the critical cracking region were prematurely cut off, leading to relative displacement of the two sides. The specimens mainly relied on the tensile resistance of the UHPC and the compression stress generated by the external tendons to resist the tensile stress during the post-cracking stage. The specimens fractured along the critical crack in the ultimate state. It should be noted that the measured strains of the mid-span in the ultimate state remained well below the ultimate compressive strain (discussed in Section 3.5), and thus the tested beams did not fail in compressive failure of the UHPC, such as top flange crushing and web crushing. Voo et al. [31] reported that a consistent diagonal tension failure was observed in stirrup-free internally prestressed UHPC beams with a/d ranged from 1.8 to 4.5. It confirmed that the prestressed UHPC beams without shear reinforcements were able to fail in diagonal tension, even under the condition of a small a/d.

An additional feature was observed at failure: the shear dowel action provided by the longitudinal reinforcements led to complete fracture of the tensile GFRP bars in the vicinity of the critical diagonal crack. In addition, for all specimens (particularly for B-1.7-30, B-2.8-30, and B-4.5-15), splitting of the UHPC along the longitudinal GFRP reinforcements within the shear span was observed at failure. Owing to the smoother cracked interfaces of fine powder concrete beams [31,32], the contribution of aggregate interlock in transferring shear stresses was limited. Consequently, the dowel forces in the GFRP bars crossing the critical crack were increased, thus causing higher vertical tensile stress in the surrounding concrete. This vertical tensile stress combined with the bond stress between the surrounding concrete and GFRP bars resulted in splitting failure along the longitudinal GFRP bars. This phenomenon could be regarded as a secondary failure. A similar splitting failure pattern was observed in the shear tests conducted by El-Sayed et al. [10] on high-strength concrete beams without stirrups. The single-legged GFRP stirrups provided an insignificant tensile force, and thus the beams in the present study behaved similarly to UHPC beams without stirrups.

3.2 Load-deflection relationships

The load-deflection relationships of the tested beams are presented in Fig. 7. The important experimental results, such as the flexural cracking loads, shear cracking loads, and ultimate loads, are listed in Table 4. In general, all of the load-deflection relationships for the GFRP-reinforced UHPC beams prestressed with external CFRP tendons showed a bilinear trend, indicating the brittle nature of the shear failure. The load-deflection relationships of the specimens could be described as two stages. The first phase, up to the flexural cracking, indicates the linear elastic stage. The second phase, cracking to failure, represents the declined stiffness of the cracked beams. As shown in Fig. 7(a), for specimens with the same a/d, the post-cracking flexural stiffness was almost consistent, owing to the same longitudinal reinforcement layout of the specimens. In addition, increasing the f_pe of the external prestressed tendons led to a reduced ductile behavior with decreased deflection at higher ultimate loads. This result indicates that a higher f_pe is favorable for reducing the mid-span deflection of the specimens, which is a critical drawback limiting the extensive application of FRP-reinforced structures [22].

Moreover, it is widely accepted that beam action is the critical mechanism in slender beams with a/d of more than 2.5, and arch action is critical in short beams with a/d of less than 2.5 [19]. For slender beams B-2.8-30 and B-4.5-30, more of the shear load was transferred through beam action, which caused high tensile stress level in the web and accelerated the shear cracking. Hence, the shear cracking loads of slender beams B-2.8-30 and B-4.5-30 were significantly smaller than that of short beam B-1.7-30, as shown in Fig. 7(b). On the other hand, the application of external tendons could reduce the effective a/d and sustain the arch action even in slender beams [19], because the negative moment induced by the external prestressing force reduced the total moment under the same applied load. As a result, the slender beams could resist a larger ultimate shear load instead of failing progressively after shear cracking. The P_u/P_cri ratios of beams B-2.8-30 and B-4.5-30 were 2.27 and 1.86, respectively, which are significantly higher than the value of 1.37 for short beam B-1.7-30.

3.2.1 Effect of the shear span to depth ratio

Specimens B-1.7-30, B-2.8-30, and B-4.5-30 (the short and slender beams) were considered to compare the effects of a/d. Figure 8 shows the influence of a/d on the shear capacity of the specimens. As a/d decreased from 4.5 to 2.8 and 1.7, the shear cracking load increased by 95.2% and 428.2%, and the shear capacity increased by 55.5% and 154.5%, respectively. This implies that a/d significantly influenced the shear capacity of the specimens. The flexural stress on the cross section was higher in the specimen with a larger a/d under the same applied load. Consequently, the principal tensile stress on the cross section was higher, which affected the shear cracking and diagonal tension failure.

3.2.2 Influence of the effective prestressing stress

Specimens B-4.5-5, B-4.5-15, B-4.5-30, and B-4.5-45 were considered to compare the effects of f_pe. It can be concluded from Table 4 and Fig. 9 that as f_pe increased from 0.05f_fp to 0.15f_fp, 0.30f_fp, and 0.45f_fp, the shear cracking load increased by 22.2%, 53.3%, and 121.4%; the shear capacity slightly increased by 3.3%, 7.6%, and 8.9%; and the ultimate deflection decreased by 8.5%, 18.5%, and 34.3%, respectively. The enhanced shear capacity and reduced ultimate deflection could be attributed to the compression stress provided by the external tendon, which offset the principal tensile stress, restrained the spread of cracks, and thus sustained the post-cracking stiffness of the beams. Compared to the effect of a/d, f_pe had a relatively slight influence on the shear capacity of the beams.

3.3 Crack distribution

Figure 10 shows the crack patterns of the specimens at failure, and the bold lines represent the critical diagonal cracks. Overall, a similar crack distribution was observed for each specimen. Because of the crack-bridging action of the steel fibers, the total number of cracks in UHPC specimens were limited. In the crack formation process, flexural cracks appeared first within the pure bending span between the two concentrated loads, followed by the appearance and propagation of several web-shear cracks and flexural-shear cracks in the shear span. These diagonal cracks progressively developed toward the load points because of the dominance of the principal tensile stress. Then, one dominant diagonal crack would suddenly widen into the critical diagonal crack. Specifically, for the shear cracks, web-shear cracks appeared earlier in short beam B-1.7-30, whereas flexural-shear cracks appeared earlier in slender beams B-2.8-30 and B-4.5-30. This might be because the flexural-shear cracking was governed by the tensile stress level in the tension zone, whereas the web-shear cracking was governed by the principal tensile stress level in the web. A smaller a/d led to a lower tensile stress in the extreme tension fiber under the same applied load, and thus web-shear cracking occurred before flexural-shear cracking.

Overall, flexural cracks developed more rapidly than shear cracks before failure, as shown in Fig. 11. When shear cracking occurred, the width of the major flexural crack usually increased to greater than 1 mm; as a result, the major flexural cracks were wider than the major shear cracks during the loading process. The variation in the maximum widths of the flexural crack exhibited an approximately linear relationship with the increasing load, and the maximum widths of the flexural cracks varied between 0.7 and 1.9 mm in the ultimate state. In addition, the distribution of flexural cracks in specimen B-4.5-5 was narrower than in specimens with higher f_pe. This result indicates that a higher prestressing force is favorable for controlling the propagation and extension of flexural cracks. Compared to the number of flexural cracks, fewer shear cracks originated within the shear span. The principal tensile stress was more significant in the section in the vicinity of the loading point; hence, most of the shear cracks were concentrated near the loading points. The distributions of the shear cracks in the specimens other than B-4.5-5 were basically similar because the shear crack spacing was mainly affected by the configuration of the stirrups. Specifically, several web-shear cracks appeared within the shear bending section of specimen B-4.5-5. Because of the much smaller a/d of specimen B-4.5-5, the development of the critical diagonal crack was slower, and thus B-4.5-5 showed a multiple diagonal cracking pattern.

3.4 Stress variation in CFRP tendons

The stress in the external tendons was calculated from the value of the force measured by the pressure sensor. Overall, the increment of the tendon stress was insignificant before cracking because the mid-span deflection was limited before flexural cracking. However, the tendon stress was approximately proportional to the mid-span deflection after cracking. Figure 12 illustrates that as f_pe increased from 0.05f_fp to 0.15f_fp, 0.30f_fp, and 0.45f_fp, the ultimate stress (f_u) increased by 9.7%, 43.4%, and 58.6%, respectively. The f_pe of the external tendons significantly influenced the utilization efficiency of the external CFRP tendon. In contrast, the corresponding ultimate stress increment (f_u − f_pe) decreased by 18.8%, 33.4%, and 66.1%, respectively, because a larger f_pe led to a smaller mid-span deflection in the ultimate state.

3.5 Concrete strain variation

Figure 13 illustrates the development of the UHPC strain at the top surface of the mid-span section. It can be observed that the compressive strain at the top surface of the beam increased almost linearly with the increasing applied load. The maximum compressive strain of the mid-span UHPC in the ultimate state ranged from approximately 2100με (B-1.7-30) to 2900με (B-4.5-30), which are values well below the ultimate compressive strain of approximately 4500με [32,33]. This indicates that no compression failure occurred before the shear failure. Moreover, f_pe only had a limited influence on the maximum compressive strain (Fig. 13(a)) owing to the slight influence of f_pe on the shear capacity and bending moment in the mid-span. However, a/d significantly affected the growth rate of the compressive strain at the top surface in the mid-span (Fig. 13(b)) because a smaller a/d would lead to a smaller bending moment in the mid-span, and thus induce a smaller measured compressive strain.

3.6 Post-cracking capacity and nominal shear strength

Table 4 indicates that as f_pe increased from 0.05f_fp to 0.45f_fp, the ratio of the ultimate load (P_u) to the shear cracking load (P_cri) sharply decreased by 50.9%, indicating that a further increase in f_pe might result in immediate failure after shear cracking occurred. Herbrand and Classen [34] noted that a P_u/P_cri value of 1.2 represented the safety margin of concrete beams. The P_u/P_cri ratios of the specimens in the present study were greater than 1.3 (above 1.8 in most cases), indicating a good post-shear-cracking capacity of the UHPC beams. This could be attributed to the tensile resistance provided by both the external CFRP tendons and the crack-bridging effect of steel fibers, which restrained the propagation of cracks and improved the post-cracking shear behavior. In addition, to characterize the shear bearing capacity of flexural members, Herbrand defined the nominal shear strength, ν_u (ν_u = V_u/(b_wh₀), where V_u is the shear capacity; V_u = 0.5P_u in the present study). An experimental database of 1479 reinforced normal concrete beams (with a/d ranging from 2 to 4 and ρ_sv ranging from 0.1% to 9.3%) in Ref. [30] indicates that the average value of ν_u is approximately 1.9 MPa (ranging from approximately 0.2 to 6.0 MPa). In contrast, the ν_u values of the UHPC beams in this study varied between 8.27 (B-4.5-5) and 22.61 MPa (B-1.7-30), showing that the application of UHPC ought to obviously enhance the ν_u of reinforced concrete beams.

4 Analytical investigation

The shear capacity, V_u, of an UHPC beam prestressed with external tendons could be calculated as follows:

(1)V_{\mathrm{u}}=V_{\mathrm{c}}+V_{\mathrm{s}}+V_{\mathrm{p}},

where V_c is the shear resistance provided by the concrete, V_s is the shear resistance provided by the shear reinforcement, and V_p is the shear resistance provided by the prestressing force.

However, the shear resistance provided by steel fibers is considered separately in some design codes [26,35]. Thus, the ultimate shear capacity, V_u, could be obtained using Eq. (2).

(2)V_{\mathrm{u}}=V_{\mathrm{c}}^{\prime }+V_{\mathrm{f}}+V_{\mathrm{s}}+V_{\mathrm{p}},

where V_{\mathrm{c}}^{\prime } is the shear resistance supplied by the cement matrix, and V_f is the shear resistance provided by the steel fibers.

The equations recommended by different design codes/recommendations to evaluate the contributions of the different shear-resisting components are presented in the following section.

4.1 Typical design predictions for FRP-reinforced concrete structures

Shear prediction equations for FRP-reinforced beams have been proposed and included in the design codes/recommendations of many countries. Most of these equations were proposed by modifying the existing equations for concrete members with steel reinforcements, considering the difference in the elastic modulus.

4.1.1 Chinese code

According to the Chinese code GB 50608-2020 [36], for flexural members with FRP stirrups, the shear resistance provided by concrete (V_c) is given by Eq. (3).

(3)V_{\mathrm{c}}=0.86f_{\mathrm{t}}b{}_{w}c,

(4)c=k{h}_0,

(5)k=\sqrt{2{\rho }_{\mathrm{f}}{\alpha }_{\mathrm{f}}+{({\rho }_{\mathrm{f}}{\alpha }_{\mathrm{f}})}^2}-{\rho }_{\mathrm{f}}{\alpha }_{\mathrm{f}},

where f_t is the axial tensile strength of concrete (f_t = 0.668f_r0 [26]), b_w is the width of the web, c is the depth from the neutral axis to the edge of the compression zone, h₀ is the effective depth of the cross section, ρ_f = A_f/(b_wh₀), A_f is the area of the longitudinal FRP reinforcement, and α_f is the ratio of the elastic modulus of the longitudinal FRP bar (E_f) to that of the concrete (E_c).

The shear resistance provided by the vertical stirrups, V_s, could be calculated using Eq. (6).

(6)V_{\mathrm{s}}=\frac{f_{\mathrm{f}\mathrm{v}}{A}_{\mathrm{f}\mathrm{v}}}{s}{h}_0,

(7)\{\begin{array}{rl}& f_{\mathrm{f}\mathrm{v}}=\mathrm{m}\mathrm{i}\mathrm{n}\left\{0.004E_{\mathrm{f}\mathrm{v}},{\phi }_{\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{d}}{f}_{\mathrm{f}\mathrm{u}}\right\},\\ & {\phi }_{\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{d}}=\left(0.3+0.05\frac{r_{\mathrm{v}}}{r_{\mathrm{d}}}\right),\end{array}

where f_fv is the designed tensile strength of the FRP stirrup, which is determined using Eq. (7), A_fv is the area of the FRP stirrups, s is the stirrup spacing, E_fv is the modulus of elasticity of the FRP stirrup, f_fu is the tensile strength of the FRP stirrup, r_v is the internal bending radius of the FRP stirrup, and r_d is the diameter of the stirrups.

The shear resistance supplied by the prestressing force, V_p, could be predicted as follows:

(8)V_{\mathrm{p}}=0.05N_{\mathrm{p}0},

where N_p0 is the force resulting from the bending moment of the prestressed tendons and longitudinal reinforcements could cancel the stress from the axial force at the extreme tension fiber.

The predicted results, V_u,GB, using GB 50608-2020 are listed in Table 5.

4.1.2 ACI guidelines

According to the US code ACI 440.1R-15 [25], V_c is determined by Eq. (9):

(9)V_{\mathrm{c}}=\frac{2}{5}\sqrt{f_{\mathrm{c}}^{\prime }}{b}_{\mathrm{w}}(k{h}_0),

where kh₀ is the neutral axis depth (the calculation of k is the same as in Eq. (5)), and f_{\mathrm{c}}^{\prime } is the specified compressive strength of concrete.

ACI 440.1R-15 also gives the shear resistance provided by vertical stirrups, V_s:

(10)V_{\mathrm{s}}=\frac{f_{\mathrm{f}\mathrm{v}}{A}_{\mathrm{f}\mathrm{v}}}{s}{h}_0,

(11)\{\begin{array}{rl}& f_{\mathrm{f}\mathrm{v}}=0.004E_{\mathrm{f}\mathrm{v}}⩽f_{\mathrm{f}\mathrm{b}},\\ & f_{\mathrm{f}\mathrm{b}}=\frac{\left(0.3+0.05{\displaystyle \frac{r_{\mathrm{v}}}{r_{\mathrm{d}}}}\right)f_{\mathrm{f}\mathrm{u}}}{1.5}⩽f_{\mathrm{f}\mathrm{u}},\end{array}

where f_fb is the strength of the bent portion of the FRP stirrups.

Moreover, because ACI 440.1R-15 does not account for V_p, ACI 318M-08 [37] introduced the shear resistance provided by the prestressing force as follows:

(12)V_{\mathrm{p}}=V_{\mathrm{p}\mathrm{y}},

where V_py is the vertical component of the effective prestressing force.

The predicted results, V_u,ACI, using ACI 440.1R-15 are listed in Table 6.

4.1.3 CAN/CSA S806-12 standard

According to the Canadian standard CAN/CSA S806-12 [38], the V_c of members with longitudinal FRP reinforcements and stirrups could be determined using Eq. (13). Notably, V_c should not be greater than 0.22\sqrt{f_{\mathrm{c}}^{\prime }}{b}_{\mathrm{w}}{d}_{\mathrm{v}} or less than 0.11\sqrt{f_{\mathrm{c}}^{\prime }}{b}_{\mathrm{w}}{d}_{\mathrm{v}}.

(13)V_{\mathrm{c}}=0.05{\lambda }_{\mathrm{d}}{k}_{\mathrm{m}}{k}_{\mathrm{r}}(f_{\mathrm{c}}^{\prime }{)}^{1/3}{b}_{\mathrm{w}}{d}_{\mathrm{v}},

where λ_d is the concrete density factor (λ_d = 1.0 for normal-density concrete and 1.3 for low-density concrete), k_{\mathrm{m}}=\sqrt[]{V_{\mathrm{f}}{h}_0/M_{\mathrm{f}}}⩽1.0, V_f is the factored shear force, M_f is the factored moment, k_{\mathrm{r}}=1+(E_{\mathrm{f}}{\rho }_{\mathrm{f}}{)}^{1/3}, and d_v is the effective shear depth, taken as the greater of 0.9h₀ or 0.72h.

The contribution of V_s is given by the following equation:

(14)V_{\mathrm{s}}=\frac{0.4f_{\mathrm{f}\mathrm{v}}{A}_{\mathrm{f}\mathrm{v}}{d}_{\mathrm{v}}}{s}\cot \theta ,

where θ is the angle of the diagonal compressive stress; θ should not be greater than 60° or less than 30°.

The shear resistance provided by the prestressing force, V_p, is given by the following:

(15)V_{\mathrm{p}}=0.5V_{\mathrm{p}\mathrm{y}}.

The predicted results, V_u,CSA, using CAN/CSA S806-12 are listed in Table 7.

4.2 Typical design predictions for fiber-reinforced concrete structures

Compared to normal-strength concrete structures, the shear design equations for fiber-reinforced concrete structures are more complicated owing to the different considerations in computing the favorable effect of the fiber content. In particular, the use of the characteristic coefficient of steel fiber to modify existing equations for normal concrete members has been introduced in some design codes (e.g., CECS38-2004 [39]). In contrast, the shear contributions of the cement matrix, V_{\mathrm{c}}^{\prime }, and steel fibers, V_f, are separately considered in some design recommendations for UHPC members (e.g., NF P 18-710 and JSCE CES82).

4.2.1 NF P 18-710 standard

In the French standard NF P 18-710 [26], the shear resistance provided by the cement matrix, V_{\mathrm{c}}^{\prime }, taking into account the favorable influence of the prestressing stress on the shear capacity, could be predicted as follows:

(16)V_{\mathrm{c}}^{\prime }=\frac{0.24}{{\gamma }_{\mathrm{c}\mathrm{f}}{\gamma }_{\mathrm{E}}}{k}_{\mathrm{p}}\sqrt{f_{\mathrm{c}}}{b}_{\mathrm{w}}{\mathit{\text{z}}}_1,

where γ_cf is a partial safety factor taken as equal to 1.30; γ_cf, γ_E could be adopted as 1.5; k_p is a factor for the case of the prestressed member, k_p = 1 + 3f_peA_p/A_cf_c, where A_p is the area of CFRP tendons; A_c is the cross-sectional area of the UHPC; and z₁ is the lever arm of the internal forces, taken as equal to 0.9h₀.

The shear resistance of steel fibers, V_f, could be calculated as:

(17)V_{\mathrm{f}}=(A_{\mathrm{f}\mathrm{b}}{\sigma }_{\mathrm{r}\mathrm{d},\mathrm{f}})/\tan \theta ,

where A_fb is the area of the UHPC with A_fb = b_wz₁ for rectangular or T sections, θ is the angle between the principal compression stress and the beam axis, and σ_rd,f is the residual tensile strength. The residual tensile strength could be determined by the following equation:

(18){\sigma }_{\mathrm{r}\mathrm{d},\mathrm{f}}=(1/K{\gamma }_{\mathrm{c}\mathrm{f}})(1/w_{\mathrm{l}\mathrm{i}\mathrm{m}}){\displaystyle {\int }_0^{w_{\mathrm{l}\mathrm{i}\mathrm{m}}}{\sigma }_{\mathrm{f}}}(w)\mathrm{d}w,

(19)w_{lim}=max\{w_{\mathrm{u}},w_{max}\},

where K is the fiber orientation factor, which is taken as equal to 1.25, σ_f(w) is a function of the tensile stress and crack width, w_u is the ultimate crack width attained in the ultimate limit state, and w_max is the maximum crack width according to the provisions of NF P 18-710.

The shear contribution provided by the shear reinforcement is given by the following equation:

(20)V_{\mathrm{s}}=(A_{\mathrm{f}\mathrm{v}}/s)\mathit{\text{z}}{f}_{\mathrm{y}\mathrm{w}\mathrm{d}}^{}\cot \theta ,

where f_ywd is the design elastic limit of the shear reinforcement.

The predicted results, V_{u,NF P}, using NF P 18-710 are listed in Table 8.

4.2.2 JSCE CES82 recommendations

According to the Japanese code JSCE CES82 [35], the shear strength provided by the cement matrix, V_{\mathrm{c}}^{\prime }, could be expressed as follows:

(21)V_{\mathrm{c}}^{\prime }=({\beta }_{\mathrm{d}}{\beta }_{\mathrm{p}}{\beta }_{\mathrm{n}}{f}_{\mathrm{v}\mathrm{c}\mathrm{d}}{b}_{\mathrm{w}}{h}_0)/{\gamma }_{\mathrm{b}},

where {\beta }_{\mathrm{d}}=\sqrt[4]{1/h_0}, which is assigned a value of 1.5 when β_d > 1.5; {\beta }_{\mathrm{p}}=\sqrt[3]{100\rho } with ρ = A_f/(b_wh₀), and β_p is assigned a value of 1.5 when β_p > 1.5; {\beta }_{\mathrm{n}}=1+M_0/M_{\mathrm{d}}, which is assigned a value of 2 when β_n > 2, where M₀ is the bending moment required to cancel the stress from the axial force at the extreme tension fiber, and M_d is the design bending moment; f_{\mathrm{v}\mathrm{c}\mathrm{d}}=0.7\times 0.20\sqrt[3]{f_{\mathrm{c}}} with f_vcd ≤ 0.50 MPa; and γ_b is generally equal to 1.3.

The contribution of steel fibers, V_f, can be calculated as follows:

(22)V_{\mathrm{f}}=(f_{\mathrm{v}\mathrm{d}}/\tan {\beta }_{\mathrm{u}})b_{\mathrm{w}}{\mathit{\text{z}}}_2/{\gamma }_{\mathrm{b}},

where f_vd is the mean tensile strength perpendicular to the diagonal crack of the UHPC; β_u is the angle of the diagonal crack relative to the beam axis, β_u = 45°; z₂ is equal to h₀/1.15; and γ_b is generally equal to 1.3.

The shear resistance of the shear reinforcement is determined by the following equation:

(23)V_{\mathrm{s}}=[A_{\mathrm{f}\mathrm{v}}{f}_{\mathrm{w}\mathrm{y}\mathrm{d}}^{}(\sin {\alpha }_{\mathrm{s}}+\mathrm{c}\mathrm{o}\mathrm{s}{\alpha }_{\mathrm{s}})/s]\mathit{\text{z}}/{\gamma }_{\mathrm{b}},

where α_s is the angle of shear reinforcements to the member axis, and f_wyd is the yield stress of the shear reinforcement, taken as 400 MPa or less.

The contribution of the prestressing force, V_p, is calculated as follows:

(24)V_{\mathrm{p}}=P_{\mathrm{e}\mathrm{d}}\sin {\alpha }_{\mathrm{p}}/{\gamma }_{\mathrm{b}},

where P_ed is the effective prestressing force; α_p is the deviated angle of the external tendons; and γ_b is generally equal to 1.1.

The predicted results, V_u,JSCE, using JSCE CES82 are listed in Table 9.

4.2.3 MCS-EPFL recommendations

In the Swiss recommendation MCS-EPFL [40], V_c can be calculated using Eq. (25).

(25)V_{\mathrm{c}}=[b_{\mathrm{w}}\mathit{\text{z}}0.5(f_{\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{d}}+f_{\mathrm{u}\mathrm{t}\mathrm{u}\mathrm{d}})]/\tan \theta ,

where f_uted is the design value of the elastic limit stress of UHPC in tension, and f_utud is the designed tensile strength of UHPC.

The shear resistance provided by the stirrups, V_s, is given as follows:

(26)V_{\mathrm{s}}=\frac{f_{\mathrm{s}\mathrm{d}}{A}_{\mathrm{f}\mathrm{v}}}{s}\mathit{\text{z}}(\cot \theta +\cot {\alpha }_{\mathrm{s}})\sin {\alpha }_{\mathrm{s}},

where f_sd is the yield stress of the shear reinforcement.

The predicted results, V_u,MCS, using MCS-EPFL are listed in Table 10.

4.3 Proposed equation for predicting the shear capacity

As mentioned above, the shear design equations for typical design predictions of FRP-reinforced normal-strength concrete structures and steel bar-reinforced UHPC structures were adopted to predict the shear capacity of the beam specimens in the present study. The mechanical properties of the UHPC and FRP reinforcements were taken as the tested values when using these specifications, and the material component coefficients were assigned in accordance with the corresponding provisions. In addition, the yield stress of the stirrups in the NF P 18-710, JSCE CES82, and MCS-EPFL approaches was chosen as 0.004E_fv (approximately 180 MPa, 0.21f_fd), which was the recommended value for FRP stirrups in both the Chinese and ACI codes.

The comparison clearly shows that the GB 50608-2020, ACI 440.1R-15, and CSA S806-12 approaches developed for FRP-reinforced normal concrete structures were quite over-safe. The reasons for the greater errors could be attributed to the addition of steel fibers, which significantly improved the tensile strength of the UHPC as well as the post-cracking behavior of the beams. In contrast, the means of the ratios of V_u to V_{u,NF P} and V_u to V_u,JSCE for the tested beams with a/d = 4.5 were equal to approximately 0.96 and 0.99, respectively, indicating that NF P 18-710 and JSCE CES82 could appropriately calculate the shear capacity of the slender specimens. Unfortunately, because the equations for V_{\mathrm{c}}^{\prime } were not a function of a/d in the NF P and JSCE recommendations, the predicted shear capacity of the shorter specimens became very conservative. Moreover, because the prediction equation for V_c in MCS-EPFL did not consider the material component coefficient, the calculated shear capacity of the slender specimens was overestimated with an average error of 36%.

The predicted contributions of the V_{\mathrm{c}}^{\prime } and V_f components based on NF P 18-710 and JSCE CES82 were approximately 0.87 and 0.90 times the corresponding predicted shear capacity, respectively. Thus, the shear resistance was closely related to the fiber-reinforced UHPC in both the NF P and JSCE approaches. In addition, the contribution of V_f computed based on JSCE CES82 (approximately 0.85V_u,JSCE) was significantly higher than that of NF P 18-710 (approximately 0.65V_{u,NF P}), implying that the contribution of the steel fibers was considered to be more important in the JSCE approach.

To overcome the above deficiencies, the modified parameter α was introduced to consider the influence of a/d on the shear capacity, as given by Eq. (27). Based on CECS38-2004, Zheng [41] proposed Eq. (28) to predict the shear strength f_ft of fiber-reinforced concrete. Hence, the shear contribution of the concrete and steel fibers can be determined using Eq. (29).

(27)\alpha =m/(\lambda +n),

(28)f_{\mathrm{f}\mathrm{t}}=(1+{\beta }_{\mathrm{v}}{\lambda }_{\mathrm{f}})\sqrt{f_{\mathrm{c}}},

(29)V_{\mathrm{c}}=\alpha f_{\mathrm{f}\mathrm{t}}{b}_{\mathrm{w}}k{h}_0,

where α is the influence coefficient of the shear span to depth ratio λ; k is the ratio between c and h₀, which can be evaluated using Eq. (5); m and n can be obtained by regressing the experimental data of the present study, m = 5.49 and n = −0.26; β_v is the coefficient related to the form of the steel fibers (e.g., 0.6 for straight fibers); and λ_f is the characteristic coefficient of the fiber content, λ_f = v_fl_f/d_f, where v_f is the volume fraction of steel fibers, l_f is the length of the steel fibers, and d_f is the diameter of the steel fibers.

In addition, Eqs. (6) and (8) can be applied to predict the shear resistance provided by V_s and V_p. Hence, the shear capacity of the FRP-reinforced UHPC beams prestressed with external FRP tendons can be determined using Eq. (30). As shown in Table 11, the mean ratio and standard error between the predicted results (V_u,cal) and experimental results were approximately 1.02 and 0.03, respectively. Hence, the proposed equation yields more accurate results with a much lower scatter.

(30)V_{\mathrm{u}}=\left(\frac{5.49}{\lambda -0.26}\right)\sqrt{f_{\mathrm{c}}}(1+{\beta }_{\mathrm{v}}{\lambda }_{\mathrm{f}})k{h}_0{b}_{\mathrm{w}}+\frac{f_{\mathrm{f}\mathrm{v}}{A}_{\mathrm{f}\begin{array}{}\end{array}}}{s}{h}_0+0.05N_{\mathrm{p}0},

where λ = a/d, and the recommended values of λ are 1.5–4.5.

4.4 Performance of the proposed shear design equation

As mentioned above, few studies have focused on FRP-reinforced UHPC beams prestressed with external FRP tendons. To verify the applicability of the proposed method, the results obtained with Eq. (30) was compared with the results of an experimental study of five CFRP-reinforced UHPC beams with CFRP stirrups [42], as summarized in Table 12. Five beam specimens had a rectangular cross section of 150 mm × 300 mm and a length of 3000 mm. The f_cu of the UHPC was 149 MPa. The results of this comparison show that the proposed equation could calculate the shear capacity of the beams with a maximum error of 14%. The mean ratio and standard error between the predicted and experimental shear capacities were approximately 0.96 and 0.11, respectively. Thus, the proposed equation is suitable for predicting the shear capacity of UHPC flexural members reinforced with FRP reinforcements.

5 Conclusions

This paper investigated the shear behavior of an innovative beam based on the high-performance materials FRP and UHPC. Six T-shaped beams were tested to investigate the influence of shear span to depth ratio and effective prestressing stress on the shear behavior. Then, a comparison between the existing prediction equations and the proposed method in the present study was discussed. Based on the results of experimental and analytical studies, the following conclusions could be drawn.

1) The failure mode of GFRP-reinforced UHPC beams prestressed with external CFRP tendons was diagonal tension failure, due to the weak transverse strength of the GFRP shear reinforcement. The application of UHPC containing steel fibers with volume fraction of 2% did not change the failure mode of the specimens. The ratios of the shear capacity to the shear cracking load ranged from 1.30 to 2.65, ensuring ductile post-cracking behavior. The presence of UHPC significantly enhanced the nominal shear strengths of concrete beams.

2) The shear span to depth ratio significantly influenced the shear capacity. The application of the external CFRP tendons sustained the arch action even in slender beams after shear cracking. Thus, slender beams with shear span to depth ratios greater than 2.5 could resist a larger ultimate shear load, instead of abrupt failing after shear cracking. Besides, the effective prestressing stress had a relatively limited influence on the shear capacity. However, the increase in effective prestressing stress greatly improved the cracking resistance and restrained the propagation of cracks.

3) NF P 18-710 and JSCE CES82 equations seem to be reliable for calculating the shear capacity of slender beams with a shear span to depth ratio greater than 2.8. Unfortunately, GB 50608-2020, ACI 440.1R-15, CAN/CSA S806-12, and MCS-EPFL approaches cannot reasonably predict the shear capacity of the GFRP-reinforced UHPC beams prestressed with external CFRP tendons.

4) A proposed prediction method, which takes into account the effects of the steel fibers and shear span to depth ratio on the shear capacity, could appropriately predict the shear capacity of GFRP-reinforced UHPC beams.

References

[1] Zhu H, Cheng S, Gao D, Neaz S M, Li C. Flexural behaviour of partially fiber-reinforced high-strength concrete beams reinforced with FRP bars. Construction & Building Materials, 2018, 161 : 587– 597

[2] Au F, Du J S. Deformability of concrete beams with unbonded FRP tendons. Engineering Structures, 2008, 30( 12): 3764– 3770

[3] Xue J, Briseghella B, Huang F, Nuti C, Tabatabai H, Chen B. Review of ultra-high performance concrete and its application in bridge engineering. Construction & Building Materials, 2020, 260 : 119844–

[4] Li J, Wu Z, Shi C, Yuan Q, Zhang Z. Durability of ultra-high performance concrete—A review. Construction & Building Materials, 2020, 255 : 119296–

[5] Shishegaran A, Ghasemi M R, Varaee H. Performance of a novel bent-up bars system not interacting with concrete. Frontiers of Structural and Civil Engineering, 2019, 13( 6): 1301– 1315

[6] Shishegaran A, Karami B, Rabczuk T, Shishegaran A, Naghsh M A, Mohammad Khani M. Performance of fixed beam without interacting bars. Frontiers of Structural and Civil Engineering, 2020, 14( 5): 1180– 1195

[7] Zheng H, Fang Z, Chen B. Experimental study on shear behavior of prestressed reactive powder concrete I-girders. Frontiers of Structural and Civil Engineering, 2019, 13( 3): 618– 627

[8] Wang X, Shi J Z, Wu G, Yang L, Wu Z S. Effectiveness of basalt FRP tendons for strengthening of RC beams through the external prestressing technique. Engineering Structures, 2015, 101 : 34– 44

[9] Elrefai A, West J, Soudki K. Fatigue of reinforced concrete beams strengthened with externally post-tensioned CFRP tendons. Construction and Building Materials, 2012, 29 : 246– 256

[10] El-Sayed A K, El-Salakawy E F, Benmokrane B. Shear capacity of high-strength concrete beams reinforced with FRP bars. ACI Structural Journal, 2006, 103( 3): 383– 389

[11] Ahmed E A, El-Salakawy E F, Benmokrane B. Performance evaluation of glass fiber-reinforced polymer shear reinforcement for concrete beams. ACI Structural Journal, 2010, 107( 1): 53– 62

[12] Jumaa G B, Yousif A R. Size effect on the shear failure of high-strength concrete beams reinforced with basalt FRP bars and stirrups. Construction & Building Materials, 2019, 209 : 77– 94

[13] Fang Z, Hu R, Jiang R N, Xiang Y, Liu C. Fatigue behavior of stirrup free reactive powder concrete beams prestressed with CFRP tendons. Journal of Composites for Construction, 2020, 24( 4): 04020018–

[14] Ferrier E, Confrere A, Michel L, Chanvillard G, Bernardi S. Shear behaviour of new beams made of UHPC concrete and FRP rebar. Composites. Part B, Engineering, 2016, 90 : 1– 13

[15] Qi J, Wang J, Ma Z, Tong T. Shear behaviour of externally prestressed concrete beams with draped tendons. ACI Structural Journal, 2016, 113( 4): 677– 688

[16] Wang J, Qi J, Zhang J. Optimization method and experimental study on the shear strength of externally prestressed concrete beams. Advances in Structural Engineering, 2014, 17( 4): 607– 615

[17] Tan K H, Ng C K. Effect of shear in externally prestressed beams. ACI Structural Journal, 1998, 95( 2): 116– 128

[18] Ghallab A H, Khafaga M A, Farouk M F, Essawy A. Shear behavior of concrete beams externally prestressed with Parafil ropes. Ain Shams Engineering Journal, 2013, 4( 1): 1– 16

[19] Ng S, Soudki K. Shear behavior of externally prestressed beams with carbon fiber-reinforced polymer tendons. ACI Structural Journal, 2010, 107( 4): 443– 450

[20] Mészöly T, Randl N. Shear behaviour of fiber-reinforced ultra-high performance concrete beams. Engineering Structures, 2018, 168 : 119– 127

[21] Pourbaba M, Joghataie A, Mirmiran A. Shear behaviour of ultra-high performance concrete. Construction & Building Materials, 2018, 183 : 554– 564

[22] Yoo D Y, Banthia N, Yoon Y S. Predicting service deflection of ultra-high-performance fiber-reinforced concrete beams reinforced with GFRP bars. Composites. Part B, Engineering, 2016, 99 : 381– 397

[23] Alkaysi M, El-Tawil S. Factors affecting bond development between ultra high performance concrete (UHPC) and steel bar reinforcement. Construction & Building Materials, 2017, 144 : 412– 422

[24] ACI 440.4R-04. Prestressing Concrete Structures with FRP Tendons. Farmington Hills: American Concrete Institute (ACI), 2004

[25] ACI 440.1R-15. Guide for the Design and Construction of Structural Concrete Reinforced with Fiber-reinforced Polymer (FRP) Bars. Farmington Hills: American Concrete Institute (ACI), 2015

[26] NF P 18–710. National Addition to Eurocode 2—Design of Concrete Structures: Specific Rules for Ultra-High Performance Fibre-Reinforced Concrete. Saint-Denis Cedex: Association Française de Normalisation (AFNOR), 2016

[27] Fang Y W, Fang Z, Jiang R N, Xiang Y, Huang D. Transverse static and low-velocity impact behavior of CFRP wires under pretension. Journal of Composites for Construction, 2019, 23( 5): 04019041–

[28] GB/T 31387-2015. Reactive Powder Concrete. Beijing: Ministry of Housing and Urban-rural Development of the People’s Republic of China, 2015

[29] Yuan Y, Wang Z Y. Shear behaviour of large-scale concrete beams reinforced with CFRP bars and handmade strip stirrups. Composite Structures, 2019, 227 : 111253–

[30] Qi J, Ma Z J, Wang J, Bao Y. Post-cracking shear behaviour of concrete beams strengthened with externally prestresssed tendons. Structures, 2020, 23 : 214– 224

[31] Voo Y L, Poon W K, Foster S J. Shear strength of steel fiber-reinforced ultrahigh-performance concrete beams without stirrups. Journal of Structural Engineering, 2010, 136( 11): 1393– 1400

[32] Wang Q, Song H L, Lu C L, Jin L Z. Shear performance of reinforced ultra-high performance concrete rectangular section beams. Structures, 2020, 27( 8): 1184– 1194

[33] Yang J, Fang Z, Dai G L. Flexural behaviour of prestressed UHPC beams. Advanced Materials Research, 2011, 243– 249: 2011-1155

[34] Herbrand M, Classen M. Shear tests on continuous prestressed concrete beams with external prestressing. Structural Concrete, 2015, 16( 3): 428– 437

[35] Concrete Engineering Series No. 82. Recommendations for Design and Construction of High Performance Fiber Reinforced Cement Composites with Multiple Fine Cracks. Tokyo: Japan Society of Civil Engineers (JSCE), 2008

[36] GB50608-2020 . Technical Standard for Fiber Reinforced Polymer (FRP) in Construction. Beijing: Ministry of Housing and Urban-rural Development of the People’s Republic of China, 2020

[37] ACI 318M-08. Building Code Requirements for Structural Concrete ACI 318M–08 and Commentary. Farmington Hills: American Concrete Institute (ACI), 2008

[38] CAN/CSA S806-12. Design and Construction of Building Structures with Fibre-reinforced Polymers. Rexdale: Canadian Standards Association (CSA), 2012

[39] CECS38-2004 . Technical Specification for Fiber Reinforced Concrete Structures. Beijing: China Association for Engineering Construction Standardization (CECS), 2004

[40] MCS-EPFL Recommendation UHPFRC. Ultra-high performance fibre reinforced cement-based composites (UHPFRC) construction material, dimensioning and application. Lausanne: Swiss Federal Institute of Technology (MCS-EPFL), 2016

[41] Zheng H. Experimental study on shear behaviour of concrete box beams. Dissertation for the Doctoral Degree. Changsha: Hunan University, 2015 (in Chinese)

[42] Cao T. Experimental study on shear behaviours of CFRP tendons reinforced FRCC flexural components. Thesis for the Master’s Degree. Nanjing: Southeast University, 2016 (in Chinese)

RIGHTS & PERMISSIONS

Higher Education Press 2021.