Issue 73

N. Laouche et alii, Fracture and Structural Integrity, 73 (2025) 88-107; DOI: 10.3221/IGF-ESIS.73.07

Frequency parameter

Non-dimensional crack location s l

0.15

0.25

0.35

0.55

0.85

 1

2.6398 10.0401 21.4903 5.8540 15.5466 27.9505 0.9071 5.8088 15.5645

2.6058 9.9588 21.9814 5.8731 15.1812 27.9649 0.9219 5.8142 15.1540

2.5749 10.1158 22.2333 5.7957 15.1895 28.4982 0.9342 5.7110 15.2095

2.5568 10.3264 21.6440 5.7233 15.5170 27.7916 0.9506 5.5769 15.5278

2.6398 10.0401 21.4903 5.8540 15.5466 27.9505 0.9580 5.8063 15.3165

 2  3

S-S

 1

 2  3

C-C

 1

 2  3

C-F

Table 4: Effects of the steel outer layer crack location s l , where

 s a 0.35 , on the frequency parameter. (uncracked inner core

composite polymer concrete)

Critical buckling parameter

Non-dimensional crack location s l

0.15

0.25

0.35

0.55

0.85

cr N 1 cr N 2 cr N 3 cr N 1 cr N 2 cr N 3 cr N 1 cr N 2 cr N 3

3.4389 4.6609 4.6686 4.6612 4.6684 5.9447 0.8054 3.0655 4.6607

3.3468 4.6615 4.6685 4.6610 4.6684 5.9370 0.8122 3.0678 4.6608

3.2662 4.6620 4.6685 4.6608 4.6685 5.9354 0.8212 3.0700 4.6607

3.2210 4.6623 4.6684 4.6606 4.6685 5.9351 0.8431 3.0721 4.6600

3.4389 4.6609 4.6686 4.6612 4.6684 5.9447 0.8724 3.0665 4.6598

S-S

C-C

C-F

Table 5: Effects of the steel outer layer crack location s l , where

 s a 0.35 , on the critical buckling parameter. (uncracked inner core

composite polymer concrete).

Frequency parameter

Non-dimensional crack depth c a

0

0.25

0.5

0.75

1

 1

2.6711 10.3727 22.3181 5.8866 15.6187 28.5679 0.9582 5.8362 15.6695

2.6702 10.3630 22.2927 5.8854 15.6162 28.5492 0.9567 5.8352 15.6660

2.6695 10.3550 22.2720 5.8844 15.6140 28.5334 0.9555 5.8342 15.6627

2.6689 10.3487 22.2556 5.8834 15.6121 28.5205 0.9545 5.8334 15.6597

2.6684 10.3440 22.2435 5.8826 15.6104 28.5104 0.9538 5.8327

 2  3

S-S

 1

 2  3

C-C

 1

 2  3

C-F

15.6568 Table 6: Effects of the inner core composite polymer concrete crack depth c a , where  c l 0.15 , on the frequency parameter. (uncracked steel outer layer)

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