PSI - Issue 70

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

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Table 1. Research variables used for evaluating the selected beams’ shear capacity/ultimate load Research variables Beams from existing literature b1 b2 b3 b4 b5 b6 b7 b8 b9

b10

b11

b12

Compressive strength (N/mm 2 )

153.9 152.8 166.9 166.9 166.9 108.9 100

154.6 142.4 165.2 154.6 154.6

Tensile strength (N/mm 2 ) V f (%) l f (mm) d f (mm)

12.9 9.3

11.5 11.5 11.5 4.32

-

5.5

5.3

5.5

5.5

5.5

1.5 1

1.5 1.5 1.5 1

2 6

2

2

3

2

2

13

13

19

19

19

6

13

22

13

13

13

0.2 0.2

0.2 0.2 0.2 0.15 0.15

0.2

0.3

0.2

0.2

0.2

s(mm)

-

-

165 110 66

-

-

175

175

175

175

175

0.081 0.081 0.078 0.078 0.078 0.031 0.032 0.0373 0.0373 0.0373 0.0373 0.0373

ρ

a /d(mm)

3

3

3

3

3

2.9 2

2.8

2.8

2.8

2.8

2.08 350

a (mm)

642 642

660 660 660 1250 600

475

475

475

475

d ca (mm) d(mm) b(mm) h(mm) x 0 (mm)

0

0

0

0

0

16

0

10

10

10

10

10

254 254 150 150 300 300

220 220 220 410 300 150 150 150 200 200 290 290 290 500 350

168.5 168.5 168.5 168.5 168.5

100 200

100 200

100 200

100 200

100 200

15.5 0

49.9 0

88 30

117.3 0

58 42

30 53

55 57

30 53

7

θ ( o )

15

20

25

30

45

37

45

f yl (N/mm ′ (N/mm 2 ) - f ys (N/mm 2 ) - 2 )

468 468

600 600 600 590 400

653 414 414 628

653 414 414 628

653 414 414 628

653 414 414 628

653 414 414 628

- -

-

-

-

- -

- -

400 400 400

A s (mm

2 )

2800 2800

2642 2642 2642 2513 2454

′ (mm 2 ) 2 )

- -

- -

-

-

-

- -

- -

66.37 66.37 66.37 66.37 66.37 66.37 66.37 66.37 66.37 66.37

A ss (mm

157 157 157

3. Results of Analyses and Discussions The results obtained from analyzing all the beams considered in this study using the various selected shear capacity equations are presented in Table 2; and it revealed that CECS2020 (2020), SIA 2052 (2016) (with the exception of b1, b2, b3, b4 and b5), JSCE (2006) (with the exception of b1, b2, b3, b4 and b5), Imam et al. (1997), Khuntia et al. (1999), Ashour et al. (1992) (except for b9), Al- Ta’an and Al-Feel (1990) (except for b9), Narayanan and Darwish (1987) seriously underestimated the beams’ shear strength/ultimate load even though the equations were developed with the inclusion of shear design variables that directly affect UHPFRC shear capacity. The possible implications of the identified underestimations of the UHPFRC/UHPFRC- CA beams’ ultimate load/shear capacity in practice include: (1) designing UHPFRC/UHPFRC-CA beams with insufficient shear reinforcement to resist shear force which may lead to brittle failure. (2) reducing the safety margin of the structure and subjecting the beam to failure under normal or unexpected loads. The equations that seriously overestimated the beams’ shear strength/ultimate load as can be seen in Table 2 include: Hussein (2015) (with the exception of b1 and b2), Aoude et al. (2012), Kwak et al. (2002) and NF P 18-710 (2016). The main implication of overestimating UHPFRC/UHPFRC- CA beams’ shear capacity in practice is the fact that it leads to over -designing for shear, which in turn leads to uneconomical design. Comparative analysis of RILEM TC 162-TDF (2003) with the other equations (excluding Smith and Xu (2023)) showed that it gave a better estimate of all the beams’ shear strength/ultimate load. However, the deviations of RILEM TC 162-TDF (2003) from experimental results were inconsistent in terms of lower and higher values that reached a high value of -42.6% (see Table 3). The shear strength/ultimate load predicted using Smith and Xu (2023) equation as presented in Table 2 provided the best results that showed very high correlation (over 92% consistent correlation) with the experimental shear strength/ultimate load.