The enormous growth of human population worldwide along with rising economic challenges, are in lockstep exacerbating the lack of affordable housing associated with the high cost of building construction, especially in developing countries (Weldetsadik and Hirbaye, 2022). As such, the construction industry is continually seeking measures that could alleviate building costs without compromising engineering safety. For example, utilization of plastic aggregates in concrete has been suggested to be a potential cost – effective and energy saving measure (Mohammed and Hama, 2023). But an interesting emerging development on issues of basic housing construction, is use of rectangular beams and lintels made with the triangular cage of steel (TRC) layout or triangular reinforcing, hereafter referred to as TRC beams.
Expectedly, TRC beams are more cost – effective than the conventional beams reinforced with the rectangular cage (RRC) of steel layout or rectangular reinforcing, owing to less amount of steel used in the former. Hence use of TRC beams could contribute towards affordability of housing. Indeed in some developing countries, TRC beams are already being informally employed in basic housing construction, owing to cost effectiveness of the triangular reinforcing layout used. However, use of the TRC steel layout in beams, has not been widely investigated to fully understand its effects on structural performance. A quick scan of the literature shows that nearly all researches done on structural performance of reinforced concrete (RC) beams, have been based on the conventional RRC layout of steel. However, few papers have began to emerge on TRC layout of steel reinforcement, as later discussed (Section 1.2).
1.1 Ring beams in building construction
1.1.1 Ties for retrofit
Buildings that are not designed and built as rigid frame structures, are typically constructed in a manner that incorporates a ring beam(s). In housing construction, RC ring beams are built at the lintel level crossing at the top of window and door openings. Various types of low to medium storey buildings such as ordinary houses, apartments, schools, offices, hospitals, shopping malls etc., incorporate RC ring beams to partly serve as a horizontal structural tie system. Ring beams are particularly essential in masonry structures wherein bricks and blocks are used as walling units. In such structures, the ring beam supports the upper wall section, roof or floor, and transfers these loads uniformly to walls beneath it, while bridging across door or window openings.
As already mentioned, ring beams partly serve as a structural tie system making the building formidable and sturdy to resist horizontal forces. Earthquake events are among the most destructive combination of external vertical and horizontal natural forces that can severely damage the structural joint and tie system of buildings. Earthquake damage of buildings is often associated with joint failures and lack of major structural components. Satyarno (2011) identified the lack of ring beams in buildings, to be one of the main reasons responsible for the damage or collapse of 200,000 houses during the earthquake disaster in Indonesia. Infact, incorporation of ring beams is one of the important recommendations in earthquake guidelines for resistance of buildings to seismic damage (Arya et al., 2014). Finite element analysis was done by Rao et al. (2004) to evaluate seismic behaviour of masonry buildings built with or without ring beams. They reported that the wall sections enclosed by ring beams, also collectively referred to as horizontal bands, provided remarkable resistance to earthquake damage of buildings. Horizontal bands are wall sections typically enclosed between three RC ring beams located at the plinth level, lintel and roof - eve level of the same building (DMMD, 2005; Yadav et al., 2021). Indeed, Bothara et al. (2018) reported that school buildings constructed with horizontal bands of ring beams along with other fittings, exhibited effective seismic resistance, incurring no damage during the 2015 Gorkha epic earthquake that occurred in Nepal destroying entire community houses.
1.1.2 Structural role
In conventional housing construction wherein seismic retrofit is not incorporated or not of concern, one RC ring beam is typically installed usually only at the lintel level, for normal structural purposes. As such, RC ring beams are also flexural elements that must possess adequate structural capacity. This aspect was the main focus of the present study, aimed at evaluating structural performance of TRC beams. Although the construction practice of employing TRC in lieu of the conventional RRC ring beams, emanated from the need to reduce building costs for affordability of housing, it is essential that structural performance of the former is fully understood. As such, the present investigation was conducted to evaluate effects of the TRC steel layout or triangular reinforcing, on structural behaviour of concrete beams.
1.2 Concrete beams reinforced with the triangular steel layout
Al-Ansari (2015) conducted a limited investigation comprising experimental testing and finite element analysis of two (2) triangular beams and one (1) T – beam of reinforced concrete. All the beams were 2 m long. The triangular beams were of two different cross - section sizes 250 mm base x 217 mm height or 300 mm base x 260 mm height, while the T – beam was of cross - section 150 mm web width x 200 mm overall height x 350 mm wide flange. Both beam types were reinforced with 2T12 mm tension steel, along with stirrups spaced at 200 mm centre to centre (c/c). The yield strength of steel bars used, was 550 MPa. Compared to T – beams, it was reported that the triangular beams exhibited greater ductility along with less cracking.
The paper by Mahzuz (2011) was a theoretical analysis of triangular RC beams relative to the conventional rectangular beams. In the analysis, an attempt was made to modify the standard theory equations that are conventionally used for design of rectangular beams, then the modified formulae were employed to analyse triangular beams. The Working Stress Design (WSD) philosophy was employed, but their study focused mainly on the resulting cost saving of materials owing to use of triangular RC beams. Compared to rectangular beams, use of triangular beams reportedly reduced the concrete section area by 42.8–45.1%, while steel area reduced by 8.9–12.5%. Mahzuz (2011) also reported that triangular beams performed better than rectangular beams, with the former giving higher moment capacity and higher shear resistance. However, this claim was flawed since no thorough theoretical analysis was done to show superior performance of triangular beams, nor were experiments conducted to validate the proposed modifications made to the standard design equations.
Ambroziak et al. (2020) conducted a study wherein triangular precast lintels, were evaluated for shear resistance. The lintels were of size 120 mm base x 180 mm height x 1200 mm long, reinforced with 3Y6 mm tension steel at the bottom and 1Y6 mm compression steel at the top. The triangular links were spaced at 75 mm c/c at support for a distance of 300 mm from the beam end, while a wider spacing of 150 mm was used along midspan length of the beam. The 25 MPa concrete was used, along with longitudinal and shear reinforcement bars of yield strengths 500 MPa and 235 MPa, respectively. The test arrangement specified in Eurocode EN 845-2 (2016) was employed in the experiment. Accordingly, the test was done by applying a single point load, located at a distance = 75 mm + height (mm) of the lintel, from its end. It was reported (Ambroziak et al., 2020) that standard theory gave accurate prediction of measured shear capacity values of the triangular lintels. Their findings showed that the general performance of triangular lintels didn’t seem to significantly differ from that of conventional rectangular lintels.
The experiment by Bhakare and Pise (2020) was an investigation into the shear behaviour of rectangular concrete beams reinforced with spiral - shaped reinforcement cage (SRC) of steel layout, RRC or TRC steel layout. A total of 27 rectangular beams of size 150 x 150 x 700 mm were made, comprising nine (9) RRC, nine (9) TRC and nine (9) SRC beams. The spacing of stirrups was varied to 70, 90 and 110 mm c/c. The beams were reinforced with tension or compression steel of 3Y10 bars, while stirrups were made using R6 mm steel. The Y10 and R6 mm bars were of Fe 500 and Fe 250 steel grades. The 27 beams were cast using 20 MPa concrete, then cured in water for 28 days prior to testing using the two – point loading arrangement.
As expected, their results (Bhakare and Pise, 2020) showed that spacing of stirrups significantly influenced shear and flexural responses of the different beams. At 70 mm spacing of stirrups, the load carrying capacity of TRC beams, was similar to that of their counterpart RRC beams, But at wider link spacings of 90 and 110 mm, the load carrying capacity levels of TRC beams were respectively 7.1% and 17.9% lower. Interestingly, however, TRC beams consistently showed significantly reduced maximum deflection results relative to those of their counterpart RRC beams. At link spacings of 70, 90 and 110 mm, TRC beams gave deflection values that were 42.0%, 21.2% and 23.6% lower than those of the control RRC beams, respectively. The foregoing experimental results showed that while TRC beams tended to become increasingly vulnerable to flexural failure as link spacing increased, they exhibited significantly lower deflections relative to those of the corresponding conventional RRC beams. It may be noted that although different steel cage layouts were used in the study (Bhakare and Pise, 2020), all the beams were reinforced with the same amount of tension and compression steel areas, hence no cost saving of materials was associated with the TRC beams investigated.
Sathya (2017) conducted an experiment to investigate shear behaviour of triangular concrete beams. Five (5) triangular beams of size 230 mm base x 400 mm height x 1200 mm length were cast, along with one (1) RRC beam to serve as the control. Two (2) triangular beams were made with triangular stirrups that were equally spaced at 85 mm c/c. The other three (3) triangular beams were made with triangular stirrups that were spaced at 85 mm c/c at beam supports, then spacing was gradually increased towards midspan of the beam length. The concrete beams were reinforced with the tension and compression steel bars 3Y16 and 3Y12 mm, respectively. After casting, the concrete beams were cured in water for 28 days, following which they were tested using the two – point loading arrangement. It was reported that triangular beams showed 12.71% higher load carrying capacity relative to that of the control. However, it is quite notable that only one (1) control RRC beam was cast and tested, which is a major flaw since the single value reported may not be representative of the true result. Typically, testing of at least two beams would be necessary to obtain a representative average result, especially for the control.
In another experimental study, Chavan and Joshi (2020) tested a total of nine (9) square beams of size 200 x 200 x 1000 mm long, reinforced with the square steel cage layout, lattice - shaped steel cage layout or TRC steel layout. For the beams reinforced with the square – shaped steel cage, two bars were embedded as tension or compression steel. But for the TRC beams, a single bar was embedded as compression steel along with two bars of tension reinforcement. The bar size(s) and spacing of stirrups used, were not mentioned in the paper, but the steel reinforcement was reportedly of Fe 500 grade. The beams were cast using 25 MPa concrete and cured in water for 28 days, then subjected to flexural testing. Results showed that TRC beams gave 19.2% lower peak load, but also exhibited a significant 26.8% lower deflection. It is possible or even likely that the link spacing used in the study by Chavan and Joshi (2020), may have been fairly wide to the extent of adversely affecting the peak load values of TRC beams (Bhakare and Pise, 2020). Meanwhile the observation by Chavan and Joshi (2020) showing that TRC beams gave a deflection reduction of 26.8%, is consistent with findings by Bhakare and Pise (2020) who reported deflection reductions of 21–42%, depending on the link spacing.
In summary, the literatures reviewed in the foregoing, give contradictory findings regarding the effects of TRC steel layout or triangular reinforcing, on load bearing response of RC beams, with some studies reporting increase while others showed decrease in peak load. Two aspects are, however, evident:- Firstly, link spacing influences the load bearing responses of beams. Studies (Bhakare and Pise, 2020) have shown that peak load decreases with increase in link spacing, and vice - versa. Secondly, deflection values of TRC beams are consistently and significantly lower than those of their counterpart RRC beams.