PSI - Issue 70

Abutu Simon John Smith et al. / Procedia Structural Integrity 70 (2025) 11–18

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318-83 equations. Khuntia et al. predicted lower estimates of the beams’ shear strength/ultimate load because of the indirect representation of the fibre- UHPFRC matrix bond stress as an estimate of SFRC beam’s compressive strength. Imam et al. ’s (1997) prediction of very low estimates for the beams’ shear strength/ultimate load was due to the way that steel fibre topology (which was the only fibre term in the equation) was represented in the equation to produce insignificant effect on the beams’ shear resistance. The high shear strength/ultimate load predicted by NF P 18-710 (2016) was because: (1) a /d term (which is a very important shear influencing factor) was not included in the equation and (2) the use of the mean value of the post-cracking strength along the shear crack to represent the shear resistance provided by steel fibres. Hussein (2015) overestimated the shear strength/ultimate load of the beams because it represented shear span ( a ) as moment shear force ratio (M/V) in the equation; whose effect translates to increased estimate of the beams’ shear strength/ultimate load . The overestimation of the beams’ shear strength/ultimate load by Kwak et al. (2002) is because the equation was originally developed for SFRC beam. Additionally, Kwak et al.’s (2002) representation of concrete compressive strength, a /d and ρ in the equation leads to at least triple multiplier effect when used for predicting UHPFRC beams’ shear strength/ultimate load. Aoude et al. (2012) predicted high values for the beams’ shear strength/ultimate load because the term added to specially account for the contribution of hooked end fibre yields too much value for the steel fibre’s contribution during analysis. Despite the fact that RILEM TC 162-TDF (2003) reasonably predicted good estimates for b8, b9, b10 and b11, it however produced highly deviated estimates for b1, b2, b3, b4, b5, b6, b7 and b12 due to the absence of a /d variable in the equation as seen in b8 and b12 having the same shear strength/ultimate load even when a /d changed from 2.8 to 2.08. Smith and Xu’s (2023) equation as can be seen in Table 2 and Table 3 produced the most accurate estimate of the beams’ shear strength/ultimate load. This comes from the fact that the equation contains both direct ( a /d, V f , s and ρ ) and indirect (compressive strength and coarse aggregate size) factors that affect the shear capacity of UHPFRC beams. Furthermore, the equation also considered the shear failure mechanism of UHPFRC beams in terms of steel fibre’s resistance at both pre -cracking and post-cracking stages by including both fibre topology and fibre-UHPFRC matrix bond stress in the equation; making it a very robust shear capacity equation that can be used for estimating any UHPFRC beam’s shear capacity irrespective of the shear variables under consideration including UHPFRC with coarse aggregate (i. e. UHPFRC-CA). Analysis also revealed that the consistency of Smith and Xu’s (2023) equation in predicting slightly lower deviated shear strength/ultimate load of the considered beams was over 85%; meaning that it is so far, one of the best shear capacity equation that can be used to safely design UHPFRC/UHPFRC-CA beams since the deigned beams, when practically subjected to shear loading will have a little higher shear strengths/ultimate loads than the predicted ones. 4. Conclusions The analyses of different existing shear capacity equation for UHPFRC beams was done in this present paper to point out the most reliable equation that can be used to design UHPFRC beams against shear loading. The conclusions drawn from this investigation include: • The shear capacity equations developed in CECS2020 (2020), SIA 2052 (2016), JSCE (2006), Imam et al. (1997), Khuntia et al. (1999), Ashour et al. (1992), Al- Ta’an and Al-Feel (1990), and Narayanan and Darwish (1987) underestimate UHPFRC beams’ shear strength/ultimate load. • The underestimation of UHPFRC beams’ shear capacity by some equations from literature was a direct result of the lack of a wholesome term to account for steel fibre. • Hussein (2015), Aoude et al. (2012), Kwak et al. (2002) and NF P 18-710 (2016) overestimate the shear strength/ultimate load of UHPFRC beams. • The indirect representation of steel fibres and a /d in some of the equations from existing literature is responsible for the overestimation of the UHPFC beams’ shear capacity. • The shear capacity equation developed in RILEM TC 162-TDF (2003) reasonably estimates UHPFRC beams’ shear strength/ultimate load but with inconsistencies in deviations from experimental values. • The shear capacity equation developed by Smith and Xu (2023) for UHPFRC beams perfectly predicts the shear strength/ultimate load of UHPFRC beams with over 92% consistent correlation with experimental values.