Issue 22

S. Bennati et alii, Frattura ed Integrità Strutturale, 22 (2012) 39-55; DOI: 10.3221/IGF-ESIS.22.06

kB

   

2

2   

2

a

c

tanh cos ) d c   

( sin 









h

M

f

0

A







6

4 3  

EJ

c

d c 

EJ

cos

tanh sin 









2   3

M a

1(

2  

2 2 0

0 2 a c l d M ( )

1

)

)(   









2 EJ E A h a     0 2 ) f f

2

   

2   (

2

c M

) sin

 





2   ( 

2

0

a c

b

)[ ( 

]

tanh





0

0

c

d c EJ 

cos

tanh sin 







M

M

2   ( 

2

tanh sin  b

c

0

)







2 kB h EJ

0

EJ

f

B



1

3   2

EJ

c

2 d c M 0 

cos

tanh sin 









M d

2

2   

tanh cos  b

c

tanh ( 

)







2 kB h EJ

0

EJ

f

B



2

3   2

EJ

c

 d c

cos

tanh sin 









f kB M E A EJ

1

B

B

0,



 

( A2)

3

4

2

2 d



f

f

kB

2

M

M

h

f

2

2   ( 

2

0

B

h ]  b

[

)

tan







5

0

3 2  

E A

E

J

J E E J

f

f

B 6

1 6 1    A A B

M

C

C

0,



 

1

2

2 EJ C B c B c B c B c B C c C c C a c C a c C a c C 2 3 1 2 3 4 5 1 2 3 2 2  sin cos 3 2 3 2 ( ) ( ) ( )                

4

0

1

0

2

0

3

The integration constants for the solution in stage 3 are given again by Eqs. (A2), provided that the current lengths a and    d l a c are considered in place of 0 a and 0   d b c , respectively.

55