Issue 73

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

Critical buckling parameter

Non-dimensional crack depth c a

0

0.25

0.5

0.75

1

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

3.5259 5.9663 5.9709 5.9725 5.9726 5.9914 0.8784 3.0722 5.9723

3.5236 5.9565 5.9676 5.9681 5.9684 5.9841 0.8763 3.0720 5.9681

3.5216 5.9265 5.9423 5.9386 5.9437 5.9778 0.8746 3.0718 5.9386

3.5200 5.8621 5.8840 5.8673 5.8858 5.9764 0.8732 3.0717 5.8673

3.5188 5.7654 5.8059 5.7672 5.8069 5.9760 0.8722 3.0716

S-S

C-C

C-F

5.7672 Table 7: Effects of the inner core composite polymer concrete crack depth c a , where  c l 0.15 , on the critical buckling parameter. (uncracked steel outer layer). Frequency parameter Non-dimensional crack location c l 0.15 0.25 0.35 0.55 0.85

 1

2.6699 10.3596 22.2839 5.8850 15.6153 28.5425 0.9562 5.8348 15.6647

2.6686 10.3557 22.3025 5.8859 15.6008 28.5415 0.9568 5.8351 15.6509

2.6673 10.3619 22.3128 5.8829 15.6001 28.5621 0.9573 5.8312 15.6522

2.6666 10.3704 22.2896 5.8800 15.6129 28.5346 0.9579 5.8260 15.6632

2.6699 10.3596 22.2839 5.8850 15.6153 28.5425 0.9582 5.8350 15.6564

 2  3

S-S

 1

 2  3

C-C

 1

 2  3

C-F

Table 8: Effects of the inner core composite polymer concrete crack location c l , where

 c a 0.35 , on the frequency parameter.

(uncracked steel outer layer).

Critical buckling parameter

Non-dimensional crack location c 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

3.5227 5.9477 5.9620 5.9613 5.9626 5.9806 0.8756 3.0719 5.9613

3.5193 5.9501 5.9574 5.9553 5.9574 5.9824 0.8759 3.0720 5.9553

3.5160 5.9515 5.9552 5.9534 5.9556 5.9860 0.8762 3.0721 5.9534

3.5140 5.9525 5.9539 5.9528 5.9549 5.9902 0.8771 3.0722 5.9529

3.5227 5.9477 5.9620 5.9613 5.9626 5.9806 0.8782 3.0720 5.9599

S-S

C-C

C-F

Table 9: Effects of the inner core composite polymer concrete location c l , where

 c a 0.35 , on the critical buckling parameter

(uncracked steel outer layer).

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