PSI- Issue 9

Ernesto Grande et al. / Procedia Structural Integrity 9 (2018) 257–264 Author name / Structural Integrity Procedia 00 (2018) 000–000

261

5

         

2 d s K s dx d s d s    2 3 2 2 2 2 i e i

 

0

  

(8)

L a x L   

  

2 e

0

4 2   e K s



2

2 dx dx

2

i res e G 

where . The system of differential equations (7) and (8) has an analytical solution that depends on eight constants of integration determined by introducing suitable boundary conditions. In particular, the following conditions are indeed enforced:  

   

0 0 0 0  

c     c

1

P e

  L

0

e

c 



1

2



     





e

e

L a L a

L a 

c 

(9)

1

2







e p

e p

L a 



1

2

 

 













i s L a s L a    i

e s L a s L a   

2 e

1

2

1

i s L a s  

1

1

The solution is graphically reported in Fig. 2 by considering a length value of the part “2” equal to a =50 mm, a residual value of shear strength equal to zero and the data reported in Table 1.

a)

b)

c)

Fig. 2. Approach 1: a) shear stress developing at the interfaces; b) slip of the interfaces; c) normal stresses at the upper mortar layer.

Table 1. Data accounted for numerical analyses.

symbol [unit]

value

Young’s modulus of the reinforcement

E p [MPa] E c [MPa] t p [mm] t c [mm] b p [mm] b c [mm] L [mm]

206000

Young’s modulus of the mortar

7000 0.054

equivalent thickness of the reinforcement

thickness of the mortar width of the reinforcement

4

60 60

width of the mortar

bond length

1000