Issue 57

K. Benyahi et alii, Frattura ed Integrità Strutturale, 57 (2021) 195-222; DOI: 10.3221/IGF-ESIS.57.16

  2

2

   x



sin

cos

(10)



1

2

(11)

  2

2

  



cos

sin



y

1

2

   1 2( ) sin cos  

 

(12)

The local equilibrium of the concrete layers can be expressed as follows:

      x x ax bx

(13)

       0 y y ay by

(14)

The overall equilibrium of the sections is expressed by the equality of the external loads N, M, V and the resultants of the internal loads int N , int M , int V , it is expressed by the following relation:

     xi axi i i bxi A b h int i i N     xi axi ai i i bxi i A y b h y int i i M   

(15)

(16)

For the shear force, only the shear stresses in the concrete are involved:

   i i bi b h int i

V

(17)

The principal stress  2 b is a function of the two principal strains 1  and 2  :   2 2 2 1 2 ( , ). b b E   

(18)

The stress-strain law of concrete in traction is linear before concrete cracking. Beyond that, the tensile stress decreases with increasing mean tensile strain, which includes the effect of crack opening (Fig. 5).

Figure 5: Behavior of tensile concrete according to Belarbi and Hsu [46].

201