Issue 72

M. A. M. Khalil, Fracture and Structural Integrity, 72 (2025) 193-210; DOI: 10.3221/IGF-ESIS.72.14

Beam thickness (mm)

Specimen code RC1GI-I RC1GI-E RC1GI-I-F RC2GI-I RC2GI-E RC2GI-I-F RC3GI-I RC3GI-E RC3GI-I-F RC1 RC2 RC3

Yield point ( δ y ) (mm)

Ultimate point ( δ u ) (mm)

Ductility index (µ δ )

µ δ /µ δ CTR .

5.76 4.44 6.65 5.87 3.28 6.07 6.61 7.68 3.25 4.63 5.23 5.75

49.10 17.60 17.93 24.17 35.22 29.22 10.68 34.00 31.40 16.47 12.61 22.65

8.99 4.26 2.70 4.61

1.00 0.47 0.30 1.08 1.00 0.59 0.15 1.01 1.00 0.40 0.24 1.15

300

10.45 6.14 1.62 6.19 9.97 3.95 2.41 4.55

400

500

Table 6: Ductility index (µ δ ) of tested specimens.

1.20

RC RCGI-I RCGI-E RCGI-I-F

1.00

1.00

1.00

1.00

0.80

0.59

0.59

0.60

0.51

0.47

0.46

0.40

0.40 Ductility Ratio

0.30

0.24

0.16

0.20

0.00

T=300mm

T=400mm

T=500mm

Figure 12: Ductility ratio for specimens.

Ductility of energy The ductility of energy (µ E ), as shown in equation is based on the energy theory which was proposed by Naaman et al. [25]. This equation could be used to calculate the ductility without identifying the yield point of the specimen.

1 E T



μ = (

1)

(1)

E 2 E

E

where E T is the total energy calculated by the area under the load mid-span deflection curve. E E is the elastic energy (Fig. 13), which is calculated by the area under the slope of the elastic behavior. Traditionally, the weighted value of S 1 and S 2 is used to obtain the slope of the elastic zone region (S) in Eqn. 2 below.   P1S1 (P2 P1 )S2 S= P2 (2)

where S 1 and S 2 are the slopes of the initial two lines on the load mid-span deflection curve P 1 and P 2 are the loads at the end of the two lines, respectively.

Tab. 7 shows the energy ductility of the beam specimens. In terms of ductility energy area ratio, 0–69% represents brittleness, 70%–74% represents semi-ductility, and 75%–100% represents ductility [26]. All specimens are more ductile (86 to 95%), but only 81% for RC1GI-I specimen only.

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