PSI- Issue 9

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

259

3

d



    

    e e i i s   

 

s b 

p

0

b t







p p

p

dx

(1)

e

d

c 

 

e

e e

0

b t

s b









p c

p

dx

where .. and e c  are the normal stresses in the reinforcement and in the upper mortar, respectively; p t and e c t are the thicknesses of the reinforcement and the upper mortar, respectively; i  and e  are the shear stresses at lower and upper interfaces, respectively, both depending on the corresponding slips i s and e s ; p b is the width of the reinforcement.

c 

c c d   

upper mortar

e 

P

upper interface

p 

strengthening

p p d   

e 

lower interface

lower mortar

i 

x

support

Fig. 1. Schematic of an infinitesimal portion of the strengthening system and the upper mortar component used for performing the equilibrium of the involved forces. The following hypotheses are introduced:  the support and the lower mortar layer are assumed to be rigid;  the (lower and upper) mortar/reinforcement interfaces are modeled as zero-thickness elements with only shear deformability;  the upper mortar layer and the reinforcement are assumed deformable only axially. These assumptions allow to write the displacements of both the reinforcement and the upper mortar layer (namely p u and e c u , respectively) as functions of the slip of the lower and upper interfaces:

i u s u s s    p e i

(2)

e

c

Then, considering a linear-elastic behavior for both the reinforcement and the mortar:

du

i

ds

p

E

E







p

p

p

dx

dx

(3)

e

i ds ds dx dx      e  

du

e

E

E

c 





c

c

c

dx

Taking into account relations (3), the system of differential equations (1) becomes: