PSI - Issue 68

Victor Rizov et al. / Procedia Structural Integrity 68 (2025) 146–152 V. Rizov / Structural Integrity Procedia 00 (2025) 000–000

149

4

#

!

#

=

!

,

(13)

"!

!

!

!

!

"

!

$

!

#

=

!

.

(14)

#"

"

!

!

!

"

!

!" !

The reader can find details for determination of the shear stresses,

, as a function of torsion moment in

Chobanian (1997). After resolving the static indeterminacy, the SERR is obtained from the strain energy via formula 15.

" ! # ! !

$ B

=

,

(15)

"

!

!

where

is the width of the beam. Actually, formula 15 is aimed for calculating the SERR at increase of

delamination in the delamination tip in cross-section of the beam (Fig. 1). The SERR at increase of delamination in the delamination tip in cross-section ! !

of the beam is derived by

! !

formula 16, i.e.

" ! # ! !

$ B

=

.

(16)

"

!

Formulas 17 and 18, derived by the compliance method, are used here for check-up of the SERR determined via 15 and 16:

!

! ! " "

!

"

B

#

=

,

(17)

"

!

C

C

"

$

!

"

!

!

B

#

=

.

(18)

!

"

C

C

!

!

$

!

!

!

The compliance, , is given by

!

#

=

!

!

.

(19)

"

!

!

The findings from (17) and (18) confirm the SERR obtained from (15) and (16).

3. Results It is studied how the SERR (in normalized form) varies as a result of change of different parameters (refer to Figs. 2, 3 and 4). This is done in order to see the effects of these parameters on the delamination in fixed-ended beams under twisted support. The numerical data that are used here are as follows: m, m, m, m, m, rad, and . "#!"" = ! !#!!" = ! !#!"! = ! "#!"" #$!"# !#!!" ! = ! !

! = !

% = !

" = !

$ = ! !