PSI - Issue 70

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

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The various equations and standards developed for analyzing the shear capacity of UHPFRC beam have their shortcomings because no single equation has accurately captured all the direct and indirect factors that contribute to UHPFRC beam’s shear resistance. This is why researchers are still proposing new shear capacity equations that take their research parameters into consideration. The discrepancies in the different existing equations for evaluating the shear capacity of UHPFRC beams call for their assessment in order to determine the equation that can best predict UHPFRC beam’s shear capacity with the highest degree of accuracy. So, this study analyzes the different existing shear capacity equations to check their level of accuracy when compared with experimental shear capacities. In terms of novelty, the findings from this study can be practically applied to the structural design of UHPFRC/UHPFRC-CA beams subjected to shear loading at experimental design stage to ensure that the beam fails in shear instead of flexure (i.e. through the use of the most robust shear capacity equation as recommended by this study). The application of th is study’s findings can also be extended to the experimental testing of UHPFRC/UHPFRC-CA beams as the rightly predicted ultimate load/shear strength will be used to allocate the correct amount of load to be applied at each loading stage of the experiment; therby ensuring that the true first flexural cracking load, first shear cracking load, ultimate load and their corresponding crack widths and deflections are obtained. 2. Method of Analyses The method of analyses employed for this study involves the selection of different shear capacity equations that have been developed by researchers and in different standards as well as the selection of some beams from existing literatures, so that their experimental shear capacities/ultimate loads can be compared with those evaluated using the selected shear capacity equations. The selection of the different shear capacity equations used in this study was based on the equations that have at least 2 of the following shear design parameters or UHPFRC/UHPFRC-CA properties: volume of steel fibre ( V f ), shear span-depth ratio ( a /d), stirrups, longitudinal reinforcement ratio ( ρ ), fibre factor (an equation containing volume, length, diameter and bond factor of steel fibre as a single term), bond strength of steel fibre-UHPFRC/UHPFRC- CA matrix (τ), and compressive strength ( f cu ) of UHPFRC/UHPFRC-CA. These parameters and properties contain both direct and indirect shear influencing factors that affect the shear performance of any UHPFRC beam subjected to shear loading; and these are the variables considered before selecting all the shear capacity equations used for this study’s analyses. The selected experimental beams from literature were chosen based on the condition that the following variables can be established about the beam: compressive strength, tensile strength, volume of steel fibre ( V f ), length of steel fibre ( l f ), diameter of steel fibre ( d f ), longitudinal tensile reinforcement ratio ( ρ ), shear span-depth ratio ( a /d), depth of the beam (d), breadth of the beam (b), height of the beam (h), depth of the UHPFRC/UHPFRC-CA beam ’s compression zone (x 0 ), angle of the shear/diagonal crack to the longitudinal tensile reinforcement (θ), yield strength of the longitudinal tensile reinforcement ( f yl ), and area of the longitudinal tensile reinforcement ( A s ). The selected shear capacity equations include: Imam et al. (1997), Khuntia et al. (1999), Aoude et al. (2012), Ashour et al. (1992), Al- Ta’an and Al-Feel (1990), Kwak et al. (2002), Narayanan and Darwish (1987), Hussein (2015), Smith and Xu (2023), JSCE (2006), RILEM TC 162-TDF (2003), SIA 2052 (2016), NF P 18-710 (2016), CECS2020 (2020). The selected beams from existing literature include: beams US2-1.5-3.0 and US2-1-3.0 from Hussein (2015) taken as b1 and b2 respectively; beams SB1, SB2 and SB3 from Lim and Hong (2016) taken as b3, b4 and b5 respectively; beam M-6/015-1 from Gustafsson and Noghabai (1999) taken as b6; beam BS-100-2.0 from Son et al. (2011) taken as b7; beams B(1-6)a, B1b, B2b, B3b and B4b from Smith and Xu (2024) taken as b8, b9, b10, b11 and b12 respectively. The research variables inputted into the various equations considered in this study for the analyses of the different beams’ shear capacity/ultimate load are presented in Table 1 . Nomenclature UHPFRC Ultra-high performance fibre reinforced concrete UHPFRC-CA Ultra-high performance fibre reinforced concrete containing coarse aggregate SFRC Steel fibre reinforced concrete