PSI - Issue 59

Andrii Pavluk et al. / Procedia Structural Integrity 59 (2024) 566–574 Andrii Pavluk et al./ Structural Integrity Procedia 00 (2019) 000 – 000

569

4

The distribution of stresses and deformations in the normal cross-section of the beam under oblique bending is presented in Fig. 1.

Fig. 1. Distribution of stresses and deformations in the normal cross-section of the beam.

The equilibrium equations can be expressed as:

(7)

. . c М М М М     0; н л

,

t

(8)

0; c N N N   

,

t

Stresses in the normal cross-section are described by two functions (3) and (4), concerning three different segments (Fig. 1): the first segment is the tensile segment from the bottom of the element to the neutral axis; the second segment is from the neutral axis to the maximum stress in the compressed zone; the third segment is from the maximum stress in the compressed zone to the top of the element. Taking into account functions (3) and (4), coefficients of polynomials (5) and (6), as well as equilibrium equations (7) and (8), the compressive force in the normal cross-section of the element will be equal to:

(9)

,

1 c N N N   c c

2

2

3

z

z

z

z

z

(10)

1

1

1

1

1

1

1

2 2 ( ) )

2

1

1

с

с

( ) N fudA fubdz b E z k     ( ) (

( z dz b E 

( )

),

k









2

3









1

1

1

2

2

c

с

с

0

0

0