PSI - Issue 59

Mykola Pidgurskyi et al. / Procedia Structural Integrity 59 (2024) 322–329 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

324

3

Let’s reduce equation (1) to the standard form used in fracture mechanics (Anderson (2017)):

   

   

1 1 1 

  

2

6 

M

b





2 (2) where σ are the normal bending stresses, MPa; F(L) is a correction function that takes into account the change in the geometry of the cross-section, 1 2 ( ) 6 K L   L F L I I b L                 ,

6 M b  

1 I I     1 1 1 2

 

2

b









( )

F L

, and



.

  

2

6

L



The development of the method (Kienzler and Hermann (1986)) was obtained in work (Pidgurskyi et al. (2021)) when determining the SIF for a С -channel profile with a crack. In order to verify the results obtained on the basis of the proposed engineering methods for determining SIF, its comparison with the results of computer simulation of crack development in the thin-walled cross-section of the channel, obtained by finite element method (FEM) is conducted. 3. Research results and discussion In order to analytically determine the SIF of the normal separation for a crack in an I-beam using the method of change in the inertia moments, consider the case when an edge crack of length L develops in one of the flanges of the I-beam profile (Fig. 1).

Fig. 1. Scheme of crack development in the cross-section of the I-beam.

We take into account that during bending of an element with a crack in the cross-section, nominal stresses arise, which will be determined by the change in the inertia moment and the coordinates of the center of mass of I-beam net cross-section. The results of the calculations show that the vertical coordinate Z has a significant effect, while the Y coordinate of the center of mass changes slightly (0.1 b ) and has no significant effect on the nominal stresses. We accepted next assumptions: – the radii of roundings are neglected when calculating the moment of inertia;