Issue 22

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

R EFERENCES

[1] L. Hollaway, M. Leeming, Strengthening of reinforced concrete structures, Woodhead Publishing, UK (1999). [2] V. Zerbo, A. Di Tommaso, L. Ceriolo, In: Proceedings of structural analysis of historical constructions, Balkema (2004). [3] L. C. Bank, Composites for Construction, John Wiley & Sons, New Jersey (2006). [4] CNR-DT 200/2004, Istruzioni per la Progettazione, l’Esecuzione ed il Controllo di Interventi di Consolidamento

Statico mediante l’utilizzo di Compositi Fibrorinforzati, rev. 7 (2008). [5] J. Yao, J. G. Teng, J. F. Chen, Compos. Part B-Eng., 36 (2005) 99. [6] C. Mazzotti, M. Savoia, B. Ferracuti, Constr. Build. Mater., 23 (2009) 1529. [7] A. Cottone, G. Giambanco, Eng. Fract. Mech., 76 (2009) 1957. [8] P. Cornetti, A. Carpinteri, Eng. Struct., 33 (2011) 1988. [9] A. Carpinteri, P. Cornetti, N. Pugno, Eng. Struct., 31 (2009) 2436. [10] L. De Lorenzis, G. Zavarise, Int. J. Solids Struct., 46 (2009) 4181.

A PPENDIX

Stage 1) Entirely elastic interface Imposing the boundary conditions given in Eqs. (26) yields the following expressions for the integration constants characterising the analytical solution in stage 1:

kB

kB

2 h M EJ EJ

2 h M EJ EJ

f

f

A

A

tanh ,  b

A

,

0

 





1

2

0

3

4

4





kB

kB b

M

M

1

f

f

A

A

,

 



0

4

5

2

2

E A EJ

E A EJ

2





f

f

f

f

kB

2 a a

a a

2

h

M

1

f

A

0 ( + )+ ( + b 0

tanh +  b

[

)]



0

0

0

6

0

2

2

EJ

E A

EJ

2

2







f

f

( A1)

M

C

C

0,



 

1

2

EJ

2

kB b

b

2

tanh

h

M



f

C

(

)





0

0

3

2

E A EJ

EJ





f

f

kB a a

2 2 0  a a h (

M b

f

C

b

[

(

)

tanh )] 







0

0

0

4

0

0

2

E A

EJ

EJ

2

2





f

f

Stages 2) Elastic−Damaged interface and 3) Elastic–Damaged–Debonded interface Imposing the boundary conditions given in Eqs. (30) yields the following expressions for the integration constants characterising the analytical solution in stage 2:

M

M

2   ( 

2

tanh sin b 

c

0

)







2 kB h EJ

0

EJ

f

A

 

1

4  

EJ

c

d c 

cos

tanh sin 









M

M

2   ( 

2

tanh sin b 

c

0

)







2 kB h EJ

0

EJ

f

A

d

tanh





2

4  

EJ

c

d c 

cos

tanh sin 









kB

kB

M

d

M

1

f

f

A

A

A

0,

,



 



3

4

5

2

2

E A EJ

E A EJ

2





f

f

f

f

54