PSI - Issue 36

A. Babii et al. / Procedia Structural Integrity 36 (2022) 203–210 A. Babii, T. Dovbush, N. Khomuk et al. / Structural Integrity Procedia 00 (2021) 000 – 000

207

5

For the supporting system under consideration the function of bending moment on the interval ( ) 1 21 11 ... n a a a + + + ( ) ( ) 1 1 1 21 11 ... +   + + + + n n a a s a a (Fig. 5) will be written as ( ) ( ) ( ) ( ) ( ) , 1 1 ... ... 1 11 21 1 11 21 + − + + + + + +  −  − + = c n a s a a c a a a s s s s Q M s Q n n (2) where 1 11 21 ... n a a a Q + + + is value of resultant transverse force acting on sections ( ) 1 11 21 , ..., , n a a a , is described by

 + + + ...

a a

a

11 21

1

n

q s ds  ( )

Q

=

,

the dependence

+ + + ...

a a

a

11 21

1

n

0

1 11 21 ... n a a a Q + + + ,

c s is coordinate of resultant transverse force application

+ + + 21 ...

+ + + 21 ...

   

   

a a 11

a

a a 11

a

1

1

n

n

( ) 1 11 21 ... n a s a a Q − + + + are value of resultant transverse force acting on the

;

 0

 0

  q s s ds ( )

/

 q s ds ( )

s s

= −

c

s

= 

q s ds  ( )

Q

;

section interval ( n+ 1)1,

(

)

s a a − + + + 11 21 ...

a

1

n

( ) 1 1 + c n s is coordinate of resultant transverse force application (

) 1 11 21 ... n a s a a Q − + + + relating to the coordinates

central point

   

   

 s

 s

  q s s ds ( )

/

 q s ds ( )

s

= − s

.

( ) +

1 1

c n

+ + + ...

+ + + ...

a a

a

a a

a

11 21

1

11 21

1

n

n

Fig. 5. Scheme of influence of determined operational loading patterns.

The function of bending moment is taking the form

   

   

21 ... + + +

21 ... + + +

21 ... + + +

   

   

11 a a

a

11 a a

a

11 a a

a

 x

 s

 s

1

1

1 

n

n

n

(3)

( )

0 

0 

0 

( ) q s ds s

( ) q s s ds  

/

( ) q s ds

( ) q s ds s

( ) q s s ds  

/

( ) q s ds 

.

M s

=

  −

+

  −

21 ... + + +

21 ... + + +

21 ... + + +

11 a a

a

11 a a

a

11 a a

a

1

1

1

n

n

n

Dependence (3) enables us write the functions in order to determine internal force factors for any element of fertilizer distributor structural system due to arbitrary loading. A mathematical model has been built describing unequal loading on the supporting frame system of the fertilizer distributor.

During consideration, the change of non uniformly distributed load in cross-sectional longitudinal plane was taken into account as a function of arbitrary shape impulse loading (Fig. 6), which is closest real loading conditions. Fertilizer distributor frame is supported in six points where some vertical reactions are taking place R 11 , R 21 ,. R 31 , R 12 , R 22 , R 32 , R 11 , R 21 are the reactions of hauling chains mounting, R 31 , R 12 , R 22 ,

Fig. 6. Scheme of fertilizer distributor design model loading.