PSI - Issue 59

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

325

4

– the displacement of the main axes of the cross-section of the profile in the horizontal direction is neglected, as it does not affect the change in the vertical coordinate of the cross-section of the I-beam (it does not affect the change of stresses in the flange of the I-beam); – we believe that when a defect develops in the cross-section of the I-beam under the action of a bending moment, the nature of the load on the beam does not change and is implemented according to the “ pure bending ” scheme. For this stage of crack development, the nominal stresses are determined by the dependences:

1         1 2

M z

(3)

,

1 



I

1

Y

1 

1 

H











   1 2

2

b L 

H  

1  b H



1 

2     

2

2

(4)

,

z











1

2

1  b L H

1 2     1 b

  





3

2

2

2

H

2 



1 

3

1  2 12      H b 

1 

  

  

  





1  2 H z

I

1  b H z



2   

  

1

1

1

Y

12

2

(5)

,





2

3

b L 

1 

1 









1 1 b L z 



 

2     

12

where z 1 is the distance from the lower edge of the profile (axis Y 0 ) to the center of mass of the net section (running axis Y def ), m; 1 Y I is the moment of inertia of the net section of the I-beam profile relative to the Y def axis passing through the running center of its mass, m 4 ; H is the height of the beam of the I-beam profile, m; Then, based on the dependences (2-5), it is possible to write down the expression for determining the SIF for a crack in the shelf of a I-beam under the action of a bending moment:

1 1 1 



(1) K M 

(6)

,

1      Y Y I I

I

1 

or

1

H

 

(1) K M 

(7)

L F L

,



 

1

I

2

I

Y



 3

   

   

2

2

H



2 

1 

3

b

1 

1 

H

1 2 Y H I

  

  

2

I

b

  , and

M









1 

,

Y

12

12

2 2

where  are the normal stresses in the defect-free section of the I-beam, MPa. Y I is the moment of inertia of the transverse section of a defect-free I-beam, m 4 . F(L) = 1.1 + 0.0213 L - 0.0008 L 2 + 0.00009 L 3 is a correction function that takes into account the change in the

geometry of the complex net cross-section of the I-beam (Fig. 2). Note that the correction function is given for I-beam type 25B1.