Issue 73

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

2

cr N L

12



N

(37)

cr

3

Ebh

s

In the following tables, the results are presented for different boundary conditions: Simply-Supported-Simply-Supported (S-S), Clamped-Clamped (C-C), and Clamped-Free (C-F). These boundary conditions represent distinct support configurations that significantly influence the dynamic behavior of the beam, including its natural frequencies and critical buckling loads.

Frequency parameter

Non-dimensional crack depth s 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

2.6433 10.0768 21.5775 5.8574 15.5544 28.0199 0.9127 5.8118 15.5780

2.6350 9.9909 21.3750 5.8494 15.5360 27.8555 0.8995 5.8047 15.5440

2.6287 9.9281 21.2285 5.8430 15.5214 27.7268 0.8897 5.7989 15.5103

2.6251 9.8922 21.1440 5.8386 15.5111 27.6430 0.8838 5.7945

 2  3

S-S

 1

 2  3

C-C

 1

 2  3

C-F

15.4799 Table 2: Effects of the steel outer layer crack depth s a , where  s l 0.15 , on the frequency parameter. (uncracked inner core composite polymer concrete).

Critical buckling parameter

Non-dimensional crack depth s 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

3.4488 4.7154 4.7344 4.7158 4.7343 5.9572 0.8134 3.0662 4.7151

3.4257 4.5529 4.5582 4.5531 4.5581 5.9027 0.7946 3.0646 4.5527

3.4084 4.3818 4.4020 4.3818 4.4020 5.8018 0.7805 3.0633 4.3816

3.3980 4.3449 4.3684 4.3449 4.3684 5.7767 0.7722 3.0626

S-S

C-C

C-F

4.3447 Table 3: Effects of the steel outer layer crack depth s a , where  s l 0.15 , on the critical buckling parameter. (uncracked inner core composite polymer concrete).

99