Issue 38

S. Bennati et alii, Frattura ed Integrità Strutturale, 38 (2016) 377-391; DOI: 10.3221/IGF-ESIS.38.47

we obtain





ql

ql

 



 

 



C

C

ql

0 and

(A12)

1

2

l 1 exp(2 )  

l 1 exp( 2 )   

where the approximations are justified by the values of the exponential functions in practical problems. Lastly, we obtain the following final expression for the interfacial shear stress: s q l s ql s ( ) ( ) exp( )         (A13) which is equivalent to Eq. (11) in the main text above. By substituting Eqs. (A8) and (A13) into (10) and integrating, we obtain

l

1

2

 

qb ls s (2 

)  



  

b Q N s ,

qb

s C )

( )

exp(

f

f

3



q 2 1 ( ) (1  

(A14)

h

h

l

2

b

b

b ls s )(2 



  

)  

b Q M s ,

qb

s C )

exp(

f

f

4



2

2

2

where C 3 and C 4 are integration constants. These are determined by imposing the continuity of the axial force and bending moment at the cross section of the anchor point:

(0) 0 

N M

  

b Q ,

(A15)

qa l a 1 (0) (2 ) 2 





b Q ,

Hence,

h

l

l

1 2

b

C qb  

C qa l a qb (2 )    

and

(A16)

f

f

3

4





2

The final expressions for the internal forces in the beam turn out to be

l

l

1 2

2





s 



ls    s )



b Q N s ,

qb

qb

( )

(

exp(

)

f

f





(A17)

l

l

1 2

1 2

1 2

1 2

2





s 

q a s l a s ( )(2      )

ls    s )



b Q M s ,

qb h

qb h

( )

(

exp(

)

f b

f b





It can be easily verified that Eqs. (A8) and (A17) are equivalent to Eqs. (12) in the main text above.

391