PSI - Issue 70

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

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Table 2. Estimation of UHPFRC beams’ ultimate shear capacity using existing equations Equations from existing literatures

Shear capacity/ultimate load of UHPFRC beams from existing literatures (kN) b1 b2 b3 b4 b5 b6 b7 b8 b9

b10 b11 b12

Experiment

455 395 4.03 1.6 160 137 7782 3147 240 219 251 225 923 913 254 239 429 323 429 367 999 560 278 276 1106 591 1666 991 216 166

476 537 552 325 493

273 258 283 265 360

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)

91

133 216 0.03 0.2

53

53

53

0.4 53

262 304 388 195 216 2782 3353 1824 1023 2503 307 348 432 303 362 343 407 452 286 338 856 898 982 418 698 334 376 460 277 296 772 957 703 379 563 453 517 550 310 492

207 211 213 154 234 940 707 535 639 1101 250 253 254 197 320 239 263 231 201 304 1296 1234 1351 1243 1907 231 231 237 178 277 468 418 336 378 490 273 261 278 215 340 210 171 167 176 199 283 269 295 236 283

Hussein (2015)

Smith and Xu (2023)

JSCE (2006)

554 596 599 286

-

RILEM TC 162-TDF (2003) SIA 2052 (2016) NF P 18-710 (2016) CECS2020 (2020)

333 371 447 402 283

654 735 724 214

-

169 113 99

115 152

1012 1097 1061 676 1002

412 330 328 304 391 178 171 186 178 195

261 303 387 159

-

Table 3. Percentage deviation of existing equations from experiment Equations from existing literatures

Percentage deviation (%) of existing shear capacity equations’ results from experimental results b1 b2 b3 b4 b5 b6 b7 b8 b9

b10 b11 b12

Imam et al. (1997)

-99.1 -99.6 - 80.8

- 75.2 - 43.4 - 35.2 - 24.2

- 60.9 - 29.7 - 21.7 - 18.1

- 99.9

- 99.9 - 56.2 - 26.6 - 31.4

-80.6 -79.5 -81.3 -99.8 -85.3 -24.2 -18.2 -24.7 -41.9 -35 -8.4 -1.9 -10.2 -25.7 -11.1 -12.5 1.9 -18.4 -24.2 -15.6 374.7 378.3 377.4 369.1 429.7 -15.4 -10.5 -16.3 -32.8 -23.1 244.3 174 89 141.1 205.8 0 1.2 -1.8 -18.9 -5.6 -23.1 -33.7 -41 -33.6 -44.7 3.7 4.3 4.2 -10.9 -21.4 -38.1 -56 -65 -56.6 -57.8 50.9 27.9 15.9 14.7 8.6 -34.8 -33.7 -34.3 -32.8 -45.8 71.4 62 18.7 42.6 36.1

Khuntia et al. (1999) -64.8 -65.3 - 45

- 40

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) JSCE (2006) RILEM TC 162 TDF (2003) SIA 2052 (2016) NF P 18-710 (2016) CECS2020 (2020)

1610 696.7

484.5 524.4 230.4 214.8 407.7

-47.3 -44.6 - 35.5 -44.8 -43 - 27.9

- 6.8 - 12

102.9 131.1

79.8 67.2 77.9 28.6 41.6

-44.2 -39.5 - 29.8

- 30

- 16.7

- 14.8

- 40

-5.7 -18.2

62.2 78.2 27.4 16.6 14.2

Smith and Xu (2023) -5.7 -7.1 - 4.6

- 3.7

- 0.4 8.5

- 4.6 - 12

- 0.2

219.6 41.8

16.4 11

-

-38.9 -30.1 - 30

- 30.9

- 19 23.7

- 42.6

243.1 49.6 266.2 150.9

37.4 36.9 31.2

- 34.2

-

112.6 104.3 92.2 108 103.2

-52.5 -58 - 45.2

- 43.6

- 29.9

- 51.1

-

The reason why Narayanan and Darwish (1987) seriously underestimated the beams’ shear strength/ultimate load is that, it was not developed for UHPFRC beams but for SFRC beams. This means that the data used for its development were those of SFRC beams; and this makes it to be an inappropriate equation for evaluating the shear capacity of UHPFRC. For CECS2020 (2020), the underestimation was as a result of the lack of a term to account for fibre pull out force in the equation, as fibre topology term considered in the equation was not enough to represent the total contribution of steel fibre to shear resistance. The lower shear strength/ultimate load predicted by SIA 2052 (2016) was due to the non-representation of both fibre-UHPFRC matrix bond stress and fibre topology in the equation. JSCE (2006) predicted lower shear strength/ultimate load for the beams because there was no inclusion of steel fibre term in the equation; and the indirect use of design average tensile strength and angle between member axis and diagonal crack to account for steel fibre factors have no reasonable effect on the beams’ shear strength/ultimate load. Al- Ta’an and Al - Feel’s (1990) lower prediction of the beams’ shear strength/ultimate load was because it indirectly used the product of the post cracking strength (σ pc ) and the area through which the steel fibres act to account for the steel fibre’s topology in the equation. Ashour et al. (1992) underestimated the beam’s shear strength/ultimate load because it used SFRC beams’ data to find the constants in the modified Zsutty and ACI