Issue 64

H. Zine Laabidine et alii, Frattura ed Integrità Strutturale, 64 (2023) 186-203; DOI: 10.3221/IGF-ESIS.64.12

while:

E ii is modulus of elasticity in i direction. ν ij is poison‘s ratio of orthotropic material. G ij is shear modulus in plane with normal of i and in the j direction. σ ij is normal Stress in i direction. τ ij is shear stress in plane with normal of i and in the direction of j. ε ij is strain vector. For this numerical study, a realistic parameters of the orthotropic behaviour of the timber LVL are adopted and mentioned in Tab .2 [17]:

E 11

E 22 485

E 33 280

ν 12

ν 13

ν 23

G 12 600

G 13 600

G 23

12000

0.0464

0.365

0.309

24

Table 2: Timber LVL elastic orthotropic parameters [17]. The tensile strength is 33.4 MPa, and the shear strength is 5.3 MPa [18]. For the plastic behaviour, the option “potential” was added with the following parameters:

σ

0

11 R =

(2)

σ

eq

σ σ

90

22 33 R =R =

(3)

eq

3 σ

ν

12 13 23 R =R =R =

(4)

σ

eq

while

σ 0 is the yielding strength in the direction parallel to the grain. σ 90 is the yielding stress in the direction perpendicular to the grain. σ eq is the equivalent yielding strength for isotropic behaviour, and σ eq is taken as 33.4 MPa in the present paper and it is the reference yield. In this case, it equals σ 0 [9]. The OSB plate is simulated as an isotropic material with an elastic modulus equal to 3253 MPa [19] . The concrete grade adopted is the same in the experimental program with an average density ( ρ ) of 3405 Kg/m 3 . The calculated elastic modulus depends on the concrete compressive strength (f’c) and it is given by Eqn. 5 [11]

ρ

  

  

E =(3320 f' +6900)*

(5)

c

c

2300

Its values for each TCC beam is listed in Tab. 3.

N°

Beam

f’ c (MPa)

E c (MPa)

1

A1,B1,C2

58

34413.26

2

C1, D1,F1

54.4

33560.79

3

G1

48.2

32023.63

4

B2 29490.20 Table 3: The calculated concrete elastic modulus for each TCC beam. 38.8

192