1 Introduction

The resilience of reinforced concrete structures in regards of torsional forces is critical in regions prone to seismic activity [1,2,3]. Torsion failure in concrete beams can have brittle and catastrophic consequences, emphasizing the significance of appropriate shear reinforcement measures [4,5,6]. To address this challenge, extensive investigations have been undertaken to improve the torsional behavior of reinforced concrete beams [7,8,9,10,11,12,13].

It is to be noted that, a truss is a structure made up of connecting lines arranged in different configurations and is able to support other structures. Triangles are especially favored in truss designs [14,15,16,17]. Triangles are frequently used in truss constructions for three primary reasons: their remarkable geometric features, effectiveness in transferring loads, and spatial openness [18, 19]. Trusses incorporate many triangles to provide robust support for enormous loads, making them a common component in road traffic bridges and building roofs [20]. There are different kinds of trusses available, and it is expected that rearranging the reinforcement pattern of RCC beams to resemble trusses will improve their performance. Furthermore, using welds in connecting joints greatly enhances its ability to bear heavy loads [21]. Mahzuz [22] conducted a study on the vertical load-bearing capacity of four beam types with varying reinforcement schemes; the results were compared to the conventional Non-welded Rectangular Stirrup Beam (NRSB). At a mix ratio of 1:1.5:1.5, the ultimate load for Welded Rectangular Stirrup Beam (WRSB), Non-welded Warren Truss Beam (NWTB), and Welded Warren Truss Beam (WWTB) increased by 17.6%, 14.9%, and 34.2%, respectively. When the mix ratio was set at 1:2.5:2.5, the increase of final load was 17.3% for WRSB, 11% for NWTB, and 30.2% for WWTB. The lack of experimental comparisons of such a beam's torsional strength was, however, a shortcoming of the research.

Moreover, Tibhe and Rathi [23] compared the torsional behavior of RCC beams wrapped in CFRP and GFRP. Using epoxy-bonded fiber-reinforced polymer (FRP) fabric as transverse reinforcement of RCC beams is the subject of this research. In terms of ductility factor, torsional moment, and angle of twist, a controlled beam specimen is compared to two groups of beams: 1. CFRP fabric bonded beams and 2. GFRP fabric bonded beams. The latter exhibited higher torsional strength. Additionally, the torsional behavior of reinforced concrete beams coated with aramid fibers was investigated by Kandekar and Talikoti [24]. Beams that are wrapped in strips show significant raise in torsional strength. Their study concluded that a fully wrapped RCC beam provides greater torsional strength than a controlled beam. Moreover, Chalioris [25] conducted an experimental investigation to strengthen rectangular and flanged beams against torsional loads using carbon fiber-reinforced polymers. This research focuses on the use of epoxy-bonded carbon fiber-reinforced polymer (FRP) sheets and strips as an external transverse reinforcement to provide torsional strength to concrete beams that do not have stirrups. The experimental program includes a moderate experimental test setup that encompasses 14 rectangular and T-shaped beams that are tested under pure torsion. A steel spreader beam was positioned diagonally on top of two steel arms, which were fastened to the ends of each tested beam, and the load was applied through these arms. Rectangular beams that were strengthened by complete enclosure in continuous FRP sheets outperformed their FRP strip counterparts in terms of capacity and torsional behavior.

A study on the torsional behavior of beams made of steel fiber reinforced concrete was carried out by Okay and Engin [26]. Beams reinforced with steel fiber reinforced concrete (SFRC) were subjected to torsional moment tests in order to determine their failure mode. The specimens that were tested underwent a consistent twisting process. Not only does adding steel fiber reinforcement (SFR) change the beam’s torque capability, but it drastically changes the energy absorption capacity. They also developed and tested an empirical equation that relates torque to twist for SFRC beams using the test data. Likewise, Rathi, Kandekar [27] looked at the torsional behavior of RC beams strengthened with carbon fiber. For the purpose of studying their torsional behavior, three of the twelve beams were reinforced using various patterns of unidirectional carbon fiber with the same qualities, while the remaining nine beams were built as standard beams. By utilizing ANSYS software, a more thorough examination was conducted to determine the impact of various carbon fiber kinds and configurations on the beams’ failure mechanism, ultimate load carrying capability, and first crack load. The observation revealed that the use of CFRP significantly enhances the strength of the retrofitted beam, surpassing that of the normal beam by 45–140%.

From the above literature review, it can be concluded that different researchers have used various experimental techniques and reinforcement patterns to compare the shear and torsional behavior of reinforced concrete beams. Experimental comparisons of flexural strength of beams have already been conducted for the patterns of NRSB, WRSB, and WWTB. However, the shear and torsional behavior of such beams still need to be addressed for clarity in these comprehensive studies. Therefore, the primary focus of this research is to examine the torsional resistance of three distinct beam types: NRSB, WRSB, and WWTB. The next step is to compare the best alternative shear reinforcement pattern to the standard NRSB. This study aims to provide elementary experimental data and a discussion that can be useful for further research in this field to analyze and compare the performance of various shear reinforcement systems. The significance of this research lies not only in its contribution to existing knowledge but also in its potential to pave the way for further advancements in this field. By offering elementary experimental data and engaging in thorough discussions, this study seeks to provide a solid foundation for future research endeavors.

2 Experimental program

All the beams were of the same dimensions and reinforcement, i.e., 1220 mm (4 feet) long, 127 mm (5 inch) wide, and 203 mm (8 inch) deep. Nine beams were used for both ratios, i.e., 1:1.5:1.5 and 1:2.5:2.5. In all beams, 16 mm bars were used for top and bottom longitudinal reinforcements, and 10 mm bars were used as shear reinforcements. Stone chips, sand, and cement were also used as coarse aggregate, fine aggregate, and binder material, respectively. Three cylindrical molds were also cast for each mix ratio to determine the compressive strength (fc') of concrete. All the molds were 152 mm (6 inch) in diameter and 304 mm (12 inch) in height. The overall research framework is presented in Fig. 1, which will be explained in the subsequent sections.

Fig. 1
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Flowchart of the present study

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2.1 Preparation of reinforcement specimens

Three distinct types of beams were tested, each using two distinct concrete mix ratios. For each pattern of reinforcement, 3 beams were prepared and tested. Therefore, a total of 18 beams were prepared. For all the 18 beams, two 16 mm bars of 1143 mm (45 inch) length were used as the top and bottom longitudinal reinforcements. The shear reinforcement pattern for NRSB and WRSB was the same, i.e., 10 mm rectangular tie bars having dimensions of 102 mm × 152 mm (4 inch × 6 inch) with a center to center spacing of 133 mm (5.25 inch), as shown in Fig. 2. On the other hand, in WWTB, 10 mm bars were used in the shape of a warren truss as shear reinforcement. Transverse horizontal links of 10 mm bars were also used at the top and bottom to connect two collateral trusses at every joint, as shown in Fig. 3. The casing of reinforcement for all beams was such that the weight was the same (10.2 ± 0.2 kg, each). This was done to maintain homogeneity in terms of the weight and cost. The welding of WRSB and WWTB is shown in Figs. 4 and 5, respectively. The geometric information of the reinforcements is given in Fig. 6. Before the welding of the WRSB and WWTB specimens, GI wires were used to hold the joints of the reinforcement in place, similar to the case of NRSB. Then all the specimens were brought to a workshop and welded at the joints properly. The electrode used for welding was E6012.

Fig. 2
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Reinforcement for Non-welded Rectangular Stirrup Beam (NRSB) and Welded Rectangular Stirrup Beam (WRSB)

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Fig. 3
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Transverse links and truss elements of a Welded Warren Truss Beam (WWTB)

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Fig. 4
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Welding of WRSB

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Fig. 5
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Welding of WWTB

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Fig. 6
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Geometric information of the reinforcements

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2.2 Materials for concrete

All the required materials were collected upon ensuring the specific qualities. Well-graded, sharp-edged stone chips of two different sizes (19 mm and 12.7 mm) were used as coarse aggregate. For fine aggregate, Sylhet Sand with a Fineness Modulus of 2.86 was collected. Ordinary Portland Cement (OPC, ASTM C-150, Type-1) was used as the binding material. The composition of the cement was 95–100% Clinkers and 0–5% Gypsum. The materials used for concrete preparation are depicted in Fig. 7a–d.

Fig. 7
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Materials used in concrete casting

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2.3 Preparation of formwork and placement of reinforcement specimens

The conventional formwork was prepared for 18 beams by utilizing wood slices joined by nails while maintaining the required dimensions. In order to prevent moisture loss, a layer of paper and a double layer of polythene were placed under the formwork, as shown in Fig. 8. After preparing the reinforcement specimens, they were placed into the formwork accordingly, as depicted in Fig. 9. Small mortar blocks with a depth of 19 mm were used under the bottom bars to maintain the clear cover. The specimens were carefully marked to allow separate recognition of each beam.

Fig. 8
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Wooden formwork

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Fig. 9
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Reinforcement in formwork

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2.4 Preparation of concrete mixture, casting, and curing

Two types of concrete mixtures were used: 1:1.5:1.5 and 1:2.5:2.5 by volume (cement: sand: stone). Each ratio was employed for nine beams, the certain mixtures were prepared separately, one after another. The water cement ratio was 0.5 for the mix ratio of 1:1.5:1.5 mix ratio and 0.45 for that of 1:2.5:2.5. The stone chips were washed properly, and the sand was adjusted to saturated surface dry condition before mixing. All the aggregates were mixed well after ensuring uniformity, and careful measures were taken to prevent the entry of any debris or unwanted particles. The slump value of the concrete was 82 ± 5 mm (3.2 inches). The mixing process is illustrated in Fig. 10a–d.

Fig. 10
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Concrete mixing is going on

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Initially, nine beams for the 1:1.5:1.5 mix ratio were cast followed by the casting of the other nine beams for the mix ratio of 1:2.5:2.5. For each mix ratio, three cylindrical specimens were also cast to find out the compressive strength of concrete. The cast beams are shown in Fig. 11. For curing, the beams and the cylinders were marked according to different types and immersed in water for 28 days. A curing tub with sufficient volume capacity was built in the meantime. The curing process is depicted in Fig. 12.

Fig. 11
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Cast beams

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Fig. 12
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Beams in curing

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2.5 Test setup and testing

The test setup included an angle (50 mm × 50 mm × 5 mm; 500W), four plate bars (350 mm × 200 mm × 16 mm) and channel (150 mm × 16 kg/m). Eight steel bolts (200 mm in length & 16 mm in diameter) were used in plate bars and four steel bolts (50 mm in length & 10 mm in diameter) were used as simple supports. Then the angles were cut and welded for the moment arm shown in Fig. 13a. Figure 13b and c demonstrate welding of the angle to form the lever arm and the dimensions of the lever arm, respectively. An I-beam of 600 mm long was also procured, which is shown in Fig. 13d. The channel section was then welded to the side of the arm where the load was to be applied through the I beam and the other side was welded to the plate bar.

Fig. 13
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Preparation of the lever arm

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Torsional moment is applied by attaching the lever arm around the concrete beams. Figure 14 illustrates the schematic diagram of the test setup, wherein a single vertical load, when applied, is evenly distributed to the lever arms. Consequently, the middle section of the reinforced concrete beam experiences pure torsion. These lever arms were 610 mm long and were bolted around the beam. A long steel wide flange I-beam (2000 mm) was diagonally laid down, resting on hinged end supports on top of the lever arms. The specimen was placed over the two steel roller bearings, with a 0.15 m gap between them, as shown in Fig. 15. The test setup was placed on the base of the UTM machine for each beam specimen. The UTM model utilised is the UTE 60, with serial number 2/2008-3849, and a maximum capacity of 800 KN, as depicted in Fig. 16.

Fig. 14
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Schematic Diagram of Torsion Setup

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Fig. 15
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Mechanism of Torsion sketch

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Fig. 16
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Real-life picture in UTM

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3 Result and discussion

3.1 Results of compressive strength test of cylinders

Three cylinders were cast and tested for each mix ratio. The total number of cylinders was 6. The cylinders had a diameter of 152.4 mm (6 inches) and a height of 304.8 mm (12 inches). Table 1 displays the results. The average compressive strength of cylinders C-01, C-02, and C-03 for the mix ratio of 1:1.5:1.5 is 43.34 MPa, whereas it is 22.92 MPa for that of 1:2.5:2.5.

Table 1 Compressive strength of concrete, fc'
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3.2 Test results of beams

A total of 18 beams were tested in the UTM for four different patterns of shear reinforcement and two different concrete mix ratios. It was observed that each beam had the identical pattern of torsional cracks. Cracks were typically formed in an inclined pattern, beginning at the support and finishing near the bracket of the moment arm. A nearly 45° angle was produced by the formation of cracks with the longitudinal direction of the beam. Figure 17 displays a few instances of the failures which have taken place. Moreover, as illustrated in Fig. 18a–f, the UTM provided load vs. displacement graphs for all the tested beams. The calculated ultimate torsional moment and average ultimate load are shown in Tables 2 and 3, respectively, for both mix ratios.

Fig. 17
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Failure mode (45° angle) of some tested beams

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Fig. 18
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Load vs Deflection graphs of three types of beams for both mix ratios

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Table 2 Detailed test results of the beams having a mix ratio of 1:1.5:1.5
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Table 3 Detailed test results of the beams having mix ratio of 1:2.5:2.5
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3.3 Angle of twist calculation

The angle of twist in torsion experiments for beams is a critical parameter in understanding the behavior of materials under torsional loading [28, 29]. The angle of twist was calculated by using the elastic theory for both mix ratios of 1:1.5:1.5 and 1:2.5:2.5 as shown in Tables 4 and 5 respectively. The following equations for the angle of twist are used [26, 30,31,32]:

$$\Phi = \frac{{{\text{TL}}}}{{{\text{KG}}}}$$
(1)
$$E = 5000\sqrt {f_{c} \prime } \left( {{\text{Mpa}}} \right)$$
(2)
$$G = \frac{{\text{E}}}{{2\left( {1 + {\upgamma }} \right)}}$$
(3)
$$K = ab^{3} \left[ {\frac{16}{3} - 3.36\frac{b}{a}\left( {1 - \frac{{b^{4} }}{{12a^{4} }}} \right)} \right]$$
(4)

where, Φ = Angle of twist; T = twisting moment (force–length); L = Beam length; E = modulus of elasticity of concrete; G = modulus of rigidity (force per unit area); K = Torsional stiffness constant/polar moment of inertia (length to the fourth); 2a = longer edge length; 2b = shorter edge length; \({\text{f}}_{{\text{c}}}^{\prime}\)= Compressive strength; \(\upgamma\) = Poison’s ratio.

Table 4 Angle of twist having a mix ratio of 1:1.5:1.5
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Table 5 Angle of twist having a mix ratio of 1:2.5:2.5
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3.3.1 Angle of twist for mixing ratio 1:1.5:1.5

The measurement of twist in torsion experiments for beams holds paramount importance in structural engineering. The twist, represented by the angle of rotation a beam undergoes when subjected to torsional forces, serves as a critical indicator of material behavior and structural integrity. It enables a comprehensive understanding of how a material responds to torsional stress, aiding in the characterization of its mechanical properties. By assessing the angle of twist, engineers gain insights into potential failure modes, allowing for the identification of vulnerable points within the structure.

3.3.2 Angle of twist for mixing ratio 1:2.5:2.5

Calculating the angle of twist in torsion experiments is crucial for understanding material behavior, assessing structural integrity, and predicting failure modes. The analysis of twist in torsion experiments is an indispensable tool for guiding the development of safer and more resilient structural elements.

A graphical representation of the relationship between the average ultimate torsional moment and average ultimate angle of twist for the aforementioned mix ratios are shown in Fig. 19, demonstrating compressive strengths of 43.47 MPa and 22.92 MPa respectively. Both mix ratios exhibit a linear change in the average ultimate torsional moment with respect to the average ultimate angle of twist.

Fig. 19
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Average Ultimate Torsional Moment vs. Average. Angle of twist for both mix ratios

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3.4 Comparison based on ultimate torsional moment

The ultimate torsional moment is a critical parameter in the analysis and design of structures subjected to torsional forces. It represents the maximum twisting moment that a structural element, such as a beam or a shaft, can withstand before reaching the point of failure. Determining the ultimate torsional moment is essential for ensuring the structural integrity and safety of a system as it helps to evaluate the torsional capacity of materials and design elements. The ultimate load and ultimate torsional moment for each beam type were determined and subsequently compared with those for NRSB. The comparison of the three types of beams is demonstrated in Figs. 20 and 21 for the mix ratios of 1:1.5:1.5 and 1:2.5:2.5 respectively. In Figs. 20 and 21, it is seen that the ultimate torsional moment of WRSB increased by 4.4% and 10% compared to that of NRSB for 1:1.5:1.5 (\({\text{f}}_{{\text{c}}}^{\prime} = 43.34{\text{ MPa}}\)) and 1:2.5:2.5 (\({\text{f}}_{{\text{c}}}^{\prime} = 22.92\text{ MPa}\)) respectively. But the ultimate torsional moment of WWTB increased by 1% compared to NRSB for 1:1.5:1.5 while it decreased by 2.4% compared to NRSB for 1:2.5:2.5. Therefore, for the qualitative comparison, it can be said that NRSB ≈ WWTB < WRSB. The relation between concrete compressive strength and percent increase of torsional moment of WRSB and WWTB with respect to NRSB are shown in Fig. 22. This can be used for other compressive strengths as well. Specifically, for WWTB, it can be said that 26 MPa (interpolated from Fig. 22) is the minimum concrete compressive strength up to which the percentage increase of torsional moment is zero with respect to WRSB.

Fig. 20
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Comparison of the three types of beam for 1:1.5:1.5 mix ratio

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Fig. 21
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Comparison of the three types of beam for 1:2.5:2.5 mix ratio

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Fig. 22
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Percentage increase of torsional moment of WRSB and WWTB at different compressive strengths with respect to NRSB

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As mentioned in Sect. 1, shear tests conducted by Mahzuz, Ahmed [22] revealed a 17.6%, 14.9% and 34.2% increase in ultimate load for WRSB, NWTB and WWTB, respectively, compared to conventional NRSB for a mix ratio of 1:1.5:1.5. For a mix ratio of 1:2.5:2.5, the ultimate load increments for WRSB, NWTB and WWTB were 17.3%, 11% and 30.2% respectively. It is noteworthy that the torsional behavior of NWTB was examined in the present study. The qualitative comparison can be presented as NRSB < WRSB < WWTB. Using the Ansys software for simulations, Hasan, Alam [33] conducted research on four types of shear reinforced beams with concrete compressive strengths of 20.5, 22.3, and 28.7 MPa. The study revealed that WWTB and WRSB have a higher percentage of load enhancement compared to NRSB. Conversely, for each fc′, NWTB showed poor shear performance compared to NRSB. This indicates results similar to those in Mahzuz, Ahmed [22]. Combining the findings from the two studies, it is evident that WWTB provides the maximum shear strength among all the beams, with the value exceeding 30% compared to NRSB. In the present study, WRSB yields the maximum torsional moment, while NRSB and WWTB provide almost identical values. Therefore, based on the experimental data, WWTB can be proposed as the best alternative to the conventional NRSB.

4 Conclusion

In this research, an equal weight of shear reinforcement for all types of beams was maintained to ensure accurate comparison of torsional moments. The costing for each type of beam is approximately the same, as identical dimensions and weights of reinforcements were used despite variations in shear reinforcement patterns. The present study discloses that WRSB specimens exhibit the maximum torsional moment (including the angle of twist) values for both mix ratios, with a range of 4.4% to 10% when compared to NRSB. However, for the WWTB specimens, the values are nearly the same, ranging from − 2.4% to 1% compared to NRSB. Additionally, considering the results of shear tests from previous studies, WWTB emerges as the best alternative to NRSB, demonstrating more than a 30% load increase. Overall, WWTB can be proposed as the best alternative of the conventional NRSB. It is essential to note that all tested beams in this research shared the same spacing of shear reinforcement, yield strength of steel, beam size, and span. This study has provided valuable insights into optimizing the torsional behavior of reinforced concrete beams. The continuation of similar research with diverse inputs could yield more generalized and robust insights into shear reinforcement strategies. Exploring alternative truss patterns and different fiber types in beams may further contribute to advancements in achieving optimal torsional moments. Modified Warren truss and swimmer bars can be employed as shear reinforcement and can be tested to enhance the torsional moment performance.