Introduction

Quantity and size of coarse aggregate in self-compacting concrete (SCC) is generally lower than that of CC of the same strength class. Recycled aggregate concrete (RAC) has two interfacial transition zones, one is the old one between mortar and coarse aggregate and the other is between the recycled coarse aggregate (RCA) and mortar. The old ITZ is generally considered as the weak link in RAC.

Shear strength is one of the most investigated parameters of all the structural aspects of reinforced concrete due to the fact that shear failure usually occurs without giving any warning and may lead to casualties. Most of the research studies on shear strength were confined to the beams produced using conventional concrete (CC). Today, use of self-compacting concrete (SCC) and recycled aggregate concrete (RAC) is increasing enormously in the construction industry due to their numerous advantages. Use of SCC reduces the energy required for the transportation and compaction of concrete especially in high-rise buildings and structural elements with dense reinforcement. It also reduces the noise pollution due to the elimination of the use of concrete vibrators (Sonebi and Bartos 2002; Okamura and Ouchi 2003; Khatib 2008). RAC is a need of present time due to increasing rate of demolition of existing structures. Waste generated in the process is utilized for the production of concrete in the construction industry at a large scale (Xiao et al. 2005; Kapoor et al. 2016a, b; Xiao 2018).

Shear forces imposed on a beam are resisted by its internal shear forces generated through aggregate interlock, uncracked concrete in compression zone, dowel force of the longitudinal reinforcement and shear resisted by shear reinforcement (if present). Aggregate interlock plays a significant role in the transfer of shear stresses through a crack in concrete (Zsutty 1971; Okamura and Higai 1980; Mphonde and Frantz 1984; Ashour et al. 1992; Ahmad et al. 2018). SCC has lower amount of coarse aggregate content than CC (Sonebi and Bartos 2002; Ahmad and Umar 2018). It is established from the previous studies that reducing the content of coarse aggregate in concrete will reduce shear transfer through aggregate interlock action resulting in the reduction of its shear strength (Walraven 1981). As far as the shear strength of SCC beams is concerned, conclusions given by different authors are contradictory. Experimental results of Hassan et al. (2008) and Helincks et al. (2013) suggested that the difference in shear strength of SCC and CC beams with identical characteristics was found to be insignificant. Lin and Chen (2012) tested CC beams, SCC1 beams and SCC2 beams for the shear strength. Amount of coarse aggregate in CC and SCC1 beams was kept equal while SCC2 beams had lower coarse aggregate content than CC and SCC1 beams. Shear strengths of SCC1 and SCC2 beams were found to be greater and smaller than that of CC beams, respectively. Lima de Resende et al. (2016) concluded that ultimate shear stress of CC and SCC beams may or may not be equal depending upon the composition of concrete, beams size and the shear reinforcement ratio. Ultimate shear stress of the high-strength SCC beams with small transverse reinforcement ratio was found to be significantly lower than that of CC beams with identical characteristics.

Researchers also have different opinions that the shear strength of RAC beams will decrease or increase as compared to that of CC beams with the same strength class. Gonzalez-Fonteboa and Martinez-Abella (2007) tested beams having 50% RCA with a longitudinal reinforcement ratio of 3%. No significant differences in terms of deflection and shear strength were observed between CC beams and RAC beams. On the basis of experimental study on 20 beams having 0, 30, 50 and 100% RCA replacement ratio, Choi et al. (2010) concluded that shear strength of beam reduces for higher percentages of RCA. Fathifazl et al. (2010) reported that shear strength of RAC beams, both in terms of ultimate shear strength and deflection, are superior to that of beams made entirely with NCA.

In the literature, some papers discussed the accuracy of shear strength models for conventional concrete beams but none of them addressed the accuracy of shear strength models for beams produced with SCC and RAC (Hirata et al. 2013; Ahmad and Bhargava 2018). The inconsistencies among the results of shear strength of SCC and RAC beams raises a question that whether the provisions of shear in current design codes can be used to calculate the shear capacities of SCC and RAC beams? To answer this question, a database of SCC and RAC slender beams with and without shear reinforcement is generated. Experimental shear strengths are compared with those calculated by the ACI building code ACI-314-14, JSCE guideline no. 15 (2007), New Zealand concrete structures standard NZS 3101-2006 and Australian standard AS 3600-2009.

Shear design provisions

This section briefly discusses the shear design provisions of the above-mentioned design codes. This study is confined to the reinforced concrete beams without axial force; therefore, design provisions of non-prestressed members without axial forces are discussed. All the equations presented in this section are based on SI units.

ACI-318-14

Nominal shear strength of slender RC beams is calculated by adding the concrete contribution \((V_{\text{c}} )\) and shear reinforcement contribution \((V_{\text{s}} )\):

$$V_{\text{n}} = V_{\text{c}} + V_{\text{s}} ,$$
$$V_{\text{c}} = \left( {\sqrt {f_{\text{c}}^{\prime } } + 120\rho \frac{{V_{\text{u}} d}}{{M_{\text{u}} }}} \right)\frac{bd}{7}\; \le \;0.3\sqrt {f_{\text{c}}^{\prime } } bd,$$

where \(f_{\text{c}}^{\prime }\) is the cylindrical compressive strength of concrete. ρ is the percentage of longitudinal reinforcement. \(V_{\text{u}}\) and \(M_{\text{u}}\) are the maximum factored shear force and bending moment, respectively, in the beam during application of external load. b and d are the width and effective depth of the beam, respectively.

$$V_{\text{s}} = \frac{{A_{\text{v}} f_{\text{vy}} d}}{s} \le 0.66\sqrt {f_{\text{c}}^{\prime } } bd,$$

where \(A_{v}\) is the total area of shear reinforcement placed in \(s\). \(s\) is the spacing of shear reinforcement. \(f_{\text{vy}}\) is the yield strength of stirrups ≤ 420 MPa.

Japanese code (JSCE guideline no. 15, 2007)

Design shear capacity of a member \((V_{\text{yd}} )\) is calculated by the following equation:

$$V_{\text{yd}} = V_{\text{cd}} + V_{\text{sd}} ,$$

where \(V_{\text{cd}}\) is the design shear capacity of members without shear reinforcement, which is given by

$$V_{\text{cd}} = \beta_{\text{d}} \beta_{\text{p}} \beta_{\text{n}} f_{\text{cvd}} bd/\gamma_{\text{b}} ,$$

where \(f_{\text{cvd}} = 0.20\sqrt[3]{{f_{\text{cd}} }} \le 0.72 {\text{MPa}}\). \(\beta_{\text{d}} = \sqrt[4]{1000/d}\), when \(\beta_{\text{d}}\) > 1.5 take \(\beta_{\text{d}}\) = 1.5; d is in mm. \(\beta_{\text{p}} = \sqrt[3]{100\rho }\), when \(\beta_{\text{p}}\) > 1.5 take \(\beta_{\text{p}}\) = 1.5. \(\beta_{\text{n}} = 1\) for members without axial force. \(f_{\text{cd}}\) is the design compressive strength of concrete in MPa. b and d are the width and effective depth of the beam, respectively. ρ is the percentage of longitudinal reinforcement. \(V_{\text{sd}}\) is the shear capacity provided by shear reinforcement:

$$V_{\text{sd}} = \frac{{A_{\text{w}} f_{\text{wyd}} d}}{{S_{\text{s}} }} \times \frac{z}{{\gamma_{\text{b}} }},$$

where \(A_{\text{w}}\) is the total area of shear reinforcement placed in \(S_{\text{s}}\). \(S_{\text{s}}\) is the spacing of shear reinforcement. \(f_{\text{wyd}}\) is the design yield strength of shear reinforcement. \(f_{\text{wyd}}\) ≤ 400 MPa if \(f_{\text{c}}^{\prime }\) < 60 MPa up to 800 MPa if \(f_{\text{c}}^{\prime }\) > 60 MPa. \(z\) is the distance between resultant of compressive stress and centroid of tension reinforcement, generally taken as 0.87d. \(\gamma_{\text{b}}\) is the member factor, generally taken as 1.10.

New Zealand standard (NZS 3101-2006)

As in ACI 318-14, NZS 3101-2006, calculate the nominal shear strength of an RC beam (\(V_{\text{n}}\)) by combining the concrete contribution (\(V_{\text{c}}\)) and shear reinforcement contribution (\(V_{\text{s}}\)):

$$V_{\text{n}} = V_{\text{c}} + V_{\text{s}} ,$$
$$V_{\text{c}} = k_{\text{a}} k_{\text{d}} v_{\text{b}} bd,$$
$$0.08\sqrt {f_{\text{c}}^{\prime } } \le v_{\text{b}} \le (0.07 + 10\rho )\sqrt {f_{\text{c}}^{\prime } } \le 0.2\sqrt {f_{\text{c}}^{\prime } } ,$$

where \(k_{\text{a}}\) is a factor that accounts for the maximum size of the aggregate. \(k_{\text{a}}\) = 0.85 if maximum aggregate size is 10 mm or less. \(k_{\text{a}}\) = 1.0 if maximum aggregate size is 20 mm or more. The value of \(k_{\text{a}}\) is linearly interpolated if the maximum aggregate size is between 10 and 20 mm. \(k_{\text{d}}\) is a factor that accounts for the size of the beam. \(k_{\text{d}} = \left( {{\raise0.7ex\hbox{${400}$} \!\mathord{\left/ {\vphantom {{400} d}}\right.\kern-0pt} \!\lower0.7ex\hbox{$d$}}} \right)^{0.25}\), when d > 400 mm. d is in mm. \(k_{\text{d}}\) is taken as unity for the beams having shear reinforcement equal to or more than the minimum shear reinforcement. \(f_{\text{c}}^{\prime }\) is the cylindrical compressive strength of the concrete. \(\rho\) is the percentage of longitudinal reinforcement. b and d are the width and effective depth of the beam, respectively. \(V_{\text{s}}\) is same as defined in “ACT-318-14”. But \(f_{\text{vy}}\) ≤ 500 MPa.

Australian standard (AS 3600-2009)

The nominal shear strength of a beam is calculated by adding the ultimate shear strength provided by concrete (\(V_{\text{uc}}\)) and shear reinforcement (\(V_{\text{us}}\)):

$$V_{\text{n}} = V_{\text{uc}} + V_{\text{us}} ,$$
$$V_{\text{uc}} = \beta_{1} \beta_{2} \beta_{3} b_{\text{v}} d_{\text{o}} f_{\text{cv}} \left( {\frac{{A_{\text{st}} }}{{b_{\text{v}} d_{\text{o}} }}} \right)^{1/3} .$$

For members with shear reinforcement equal to or greater than minimum shear reinforcement

$$\beta_{1} = 1.1\left( {1.6 - {\raise0.7ex\hbox{${d_{\text{o}} }$} \!\mathord{\left/ {\vphantom {{d_{\text{o}} } {1000}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${1000}$}}} \right) \ge 1.1.$$

Otherwise,

$$\beta_{1} = 1.1\left( {1.6 - {\raise0.7ex\hbox{${d_{\text{o}} }$} \!\mathord{\left/ {\vphantom {{d_{\text{o}} } {1000}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${1000}$}}} \right) \ge 0.8.$$

For members subjected to pure bending, i.e., without axial tension or compression

\(\beta_{2} = 1\), for members without axial loads. \(\beta_{3} = 1\), or \(2d_{\text{o}} /a_{\text{v}}\) but not greater than 2, if diagonal compression is generated over the length \(a_{\text{v}}\). \(a_{\text{v}}\) is the distance between support and the section where shear force is considered. \(f_{\text{cv}} = f^{\prime 1/3}_{\text{c}} \le 4\;{\text{MPa}}\). bv and do are the width and effective depth of the beam, respectively. Ast is the area of steel provided in the tension zone.

$$V_{\text{us}} = \left( {\frac{{A_{\text{sv}} f_{{{\text{sy}} \cdot {\text{f}}}} d_{0} }}{s}} \right){ \cot }\theta_{\text{v}} ,$$

\(A_{\text{sv}}\) is the cross-sectional area of shear reinforcement provided in \(s\). \(s\) is the spacing of shear reinforcement. \(f_{{{\text{sy}} \cdot {\text{f}}}}\) is the yield strength of stirrups or fitments ≤ 500 MPa. \(\theta_{\text{v}}\) is the angle between compression strut and longitudinal reinforcement.

Comparison between experimental and calculated shear strengths

Experimental shear strengths (Vexp) are compared with the nominal shear capacities (Vn) calculated using the procedures of ACI 318-14, JSCE-2007, NZS 3101-2006 and AS 3600-2009 as discussed above. All the beams considered in this study were slender beams (a/d > 2.5) tested in pure flexure without any axial loads. Beams were having rectangular cross section, with or without shear reinforcement. Ratio of experimental to nominal shear strength (Vexp/Vn) of beams calculated as per the procedure of the above-mentioned building codes is termed as the strength ratio in this paper. Strength ratio greater than unity shows that the prediction is conservative while the shear strength ratio less than unity indicates unconservative predictions. Nominal shear strengths of the beams were calculated without considering the strength reduction factors.

Self-compacting concrete beams

Summary of the SCC beams considered in the study are given in Table 1 and their details are given in “Appendix”. A total number of 103 beams were considered in the study out of which 75 were without stirrups and 28 were with stirrups. Range of concrete compressive strength (\(f_{\text{c}}^{\prime }\)), shear-span-to-depth ratio (a/d), width (b), effective depth (d), percentage of longitudinal reinforcement (ρ), shear reinforcement index (ρvfy) are given in Table 1.

Table 1 Summary of SCC beams considered in the study
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Overall evaluation

For SCC beams, maximum, minimum and average strength ratios, coefficient of variation and percentage of the unconservative results for different code provisions are given in Table 2. Graphical representations of strength ratio (Vexp/Vn) with experimental ultimate shear stress for SCC beams are shown in Fig. 1a, b. Statistical parameters given in Table 2 and graphical representation in Fig. 1a, b show that procedure of AS 3600-2009 produced least scatter for SCC beams with and without shear reinforcement since most of the points are concentrated near the line representing a strength ratio of unity. At the same time, this procedure produced maximum number of unconservative strength ratios.

Table 2 Statistical parameters for SCC beams
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Fig. 1
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a Strength ratios for SCC beams without shear reinforcement. b Strength ratios for SCC beams with shear reinforcement

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Detailed evaluation

ACI 318-14 For beams without shear reinforcement, average strength ratio and coefficient of variation of strength ratio were found to be 1.36 and 18%, respectively. Only 6.67% of the results were found to be unconservative. Unconservative results include the beams tested by Hassan et al. (2008) having an effective depth of more than 450 mm and Biolzi et al. (2014) having longitudinal reinforcement smaller than 1%. For beams with shear reinforcement, maximum strength ratio, minimum strength ratio, average strength ratio and coefficient of variation of strength ratio were found to be 1.97. 1.04, 1.57 and 18%, respectively. None of the strength ratios was found to be unconservative.

JSCE-2007 Average strength ratio and COV were found to be 1.28 and 15%, respectively, for SCC beams without shear reinforcement. 6.67% of the results were found to be unconservative when JSCE method was found for calculating the nominal shear strength of SCC beams without stirrups. Unconservative strength ratios were found for the beams tested by Biolzi et al. (2014) with longitudinal reinforcement smaller than 1%. Strength ratios for the beams tested by Alghazali and Myers (2017) having high-volume fly ash and effective depth greater than 400 mm were also found to be unconservative. For beams with shear reinforcement, average strength ratio and COV were found to be 1.55 and 17%, respectively. Out of 28 beams with shear reinforcement, strength ratio of only one beam tested by Lima de Resende et al. (2016) having a concrete compressive strength of 71.6 MPa was found to be unconservative.

NZS 3101-2006 Average strength ratio and COV for SCC beams without shear reinforcement were found to be 1.22 and 18%, respectively. 14.67% predicted results were found to be unconservative. Unconservative results include the beams tested by Arezoumandi and Volz (2013) having beam depth greater than 450 mm and beams prepared with high-volume fly ash tested by Alghazali and Myers (2017). For beams with shear reinforcement, average strength ratio and COV were found to be 1.51 and 19%, respectively. None of the shear strength ratios were found to be unconservative.

AS 3600-2009 For beams without shear reinforcement, average strength and COV were found to be 1.11 and 14%, respectively. 18.67% of the unconservative results were from the beams tested by Arezoumandi and Volz (2013) having a depth greater than 450 mm, Biolzi et al. (2014) having a longitudinal reinforcement smaller than 1% and beams tested by Alghazali and Myers (2017) prepared from SCC containing high-volume fly ash. For SCC beams with shear reinforcement, average strength ratio and COV were found to be 1.2 and 16%, respectively. Strength ratio for the beams with shear reinforcement tested by Lima de Resende et al. (2016) having concrete compressive strength 71.6 MPa were found to be unconservative.

Recycled aggregate concrete beams

Summary of the RAC beams considered in the study are given in Table 3 and their details are given in “Appendix”. 109 RAC beams were considered in the study, 77 were without stirrups and 32 were with stirrups. Range of recycled aggregate replacement ratio (Rr), cylindrical compressive strength of concrete (\(f_{\text{c}}^{\prime }\)), shear-span-to-depth ratio (a/d), width (b), effective depth (d), percentage of longitudinal reinforcement (ρ), shear reinforcement index (ρvfy) are given in Table 3.

Table 3 Summary of RAC beams considered in the study
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Overall evaluation

For RAC beams, statistical parameters maximum, minimum and average (Vexp/Vn), coefficient of variation and percentage of the unconservative results found for different code provisions are given in Table 4. Graphical representations of strength ratio (Vexp/Vn) with experimental ultimate shear stress for SCC beams are shown in Fig. 2a, b. Statistical parameters given in Table 4 and graphical representation in Fig. 2a, b show that procedure of AS 3600-2009 and JSCE-2007 produced least scatter for RAC beams with and without shear reinforcement. But, the procedure of JSCE produced only 7.8% unconservative results for RAC beams without shear reinforcement, contrary to AS 3600-2009 which produced 23.37% unconservative results.

Table 4 Statistical parameters for RAC beams
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Fig. 2
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a Strength ratios for RAC beams without shear reinforcement. b Strength ratios for RAC beams with shear reinforcement

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Detailed evaluation

ACI 314-14 Average strength ratio and COV for RAC beams without shear reinforcement were found to be 1.32 and 18%, respectively. Unconservative strength ratios were found for the beams tested by Arezoumandi et al. (2015) with Rr = 100% and Rahal and Alrefaei (2017) having a longitudinal reinforcement of 0.79%. For RAC beams with shear reinforcement average values of strength ratio and COV were 1.68 and 24%, respectively. None of the strength ratios were found to be unconservative for RAC beams with shear reinforcement.

JSCE-2007 For RAC beams without shear reinforcement, average strength ratio and COV were 1.25 and 15%, respectively. Unconservative strength ratios were found for the beams tested by Gonzalez-Fonteboa and Martinez-Abella (2007), Katkhuda and Shatarat (2016) and Rahal and Alrefaei (2017). These beams were either having smaller amount of longitudinal reinforcement or 100% recycled aggregate replacement ratio. Average of the strength ratio and COV for RAC beams with shear reinforcement were 1.59 and 20%, respectively. JSCE method does not yield unconservative estimate of the shear strength of RAC beams with shear reinforcement.

NZS 3101-2006 This method yielded an average strength ratio and COV of 1.15 and COV of 17%, respectively, for the RAC beams without shear reinforcement. This method gives unconservative strength ratios for the beams tested by Choi et al. (2010) and Knaack and Kurama (2014) having Rr = 100%, Arezoumandi et al. (2015) having beam depth greater than 400 mm and Rr = 100%, and Rahal and Alrefaei (2017) having a longitudinal reinforcement ratio of 0.79%. Average strength ratio and COV were found to be 1.44 and 24%, respectively, for RAC beam with shear reinforcement. Unconservative estimate was found for only one beam tested by Al-Zahra et al. (2011).

AS 3600-2009 Australian standard gives an average strength ratio of 1.11 and a COV of 15% for RAC beams without shear reinforcement. Strength ratios for 16 out of 77 beams were found to be unconservative. Unconservative estimates of strength ratios were found for the beams tested by Choi et al. (2010), Knaack and Kurama (2014), Arezoumandi et al. (2015), and Rahal and Alrefaei (2017). These beams were having either 100% recycled aggregate replacement ratio, depth greater than 400 mm or longitudinal reinforcement percentage smaller than 1%. Average strength ratio and COV were 1.32 and 19%, respectively, for the RAC beams with shear reinforcement. Strength ratio of one beam tested by Al-Zahra et al. (2011) was found to be unconservative.

Revision proposed in AS 3600-2009

After detailed statistical analysis, it was found that AS 3600-2009 has the minimum strength ratio and scatter for the collected database. A modification in the size effect factor of AS 3600-2009 is recommended and the results are plotted in Fig. 3. The use of modified size effect factor reduced the unconservative results from 18.67 to 7.8% for SCC beams and 24.67% to 8% for RAC beams.

Fig. 3
figure 3

a Strength ratios for SCC beams without shear reinforcement as per AS 3600-2009. b Strength ratios for SCC beams without shear reinforcement after reducing size factor in AS 3600-2009. c Strength ratios for RAC beams without shear reinforcement as per AS 3600-2009. d Strength ratios for RAC beams without shear reinforcement after reducing size factor in AS 3600-2009

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Conclusions and recommendation

SCC is different from CC in terms of quantity and size of coarse aggregate while RAC is different from CC in terms of type of aggregate. Provisions for shear strength given in international code of practices are for CC beams. This paper evaluated shear strength provisions of four design codes: ACI 318-14, JSCE-2007, NZS 3101-2006 and AS 3600-2009 for the beams produced with SCC and RAC. On the basis of evaluation, the following conclusions can be made:

  • In general, all the four design codes produced more scatter for RAC beams as compared to SCC beams. Average strength ratios were also found to be more for RAC beams as compared to SCC beams.

  • For SCC and RAC beams without shear reinforcement, all the four codes produced unconservative estimates of the shear capacities having effective depths larger than 450 mm or longitudinal reinforcement ratio less than 1%. Minimum average strength ratio with least scatter was found for AS 3660-2009 but at the same time it produced 18.67% and 24.67% unconservative results for SCC and RAC beams, respectively. Critical assessment of the strength ratios showed that most of the unconservative estimates were for the beams with larger depths. Therefore, it is recommended to modify the factor β1 to \(1.1\left( {1.5 - {\raise0.7ex\hbox{${d_{\text{o}} }$} \!\mathord{\left/ {\vphantom {{d_{\text{o}} } {1000}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${1000}$}}} \right) \ge 0.8\) to account for the size effect of the member. This modification reduced the percentage of unconservative results to 8% for both SCC and RAC beams with a COV of 13% for SCC beams and 15% for RAC beams.

  • All the four codes produced conservative estimates of the shear strength for SCC and RAC beams with shear reinforcement. AS 3600-2009 produced conservative estimates with minimum average strength ratio and least scatter.