Issue 47

E. Mele et alii, Frattura ed Integrità Strutturale, 47 (2019) 186-208; DOI: 10.3221/IGF-ESIS.47.15

Therefore the shear stiffnesses of the hexagrid, G * 12H

and G * 21H

, normalised to the shear modulus of the member solid

material, G s

, are given by:

     

      

5 I A h 1    h

  

11   



h 1 13





*

3

G 12I (1 ν) h dCosθ  

h



12,H

d

2 s 1 



 

(15)

6E

5

2

A h 24I (1 ν)χ  

G

bdh Senθ

s

h

h

h

       

                  

          

           

 

    

     

  

  

3 13



2Cos θ d I

d

2

5 A d 1 



d

4



d

11

2

2



 

6I Sen θ 6E

d

s 3

2

A d 24I (1 ν)χ  

d

d

d

*

21,H G 4(1 ν)Sen θ G b( h dCos θ)d   

(16)

       

5

s

 

     

     

 

 

2

3 13   

Sen θ d I

d

1 2

2

5



-A d Cos θ

Cos θ

d

4



d

11



where: I h is the inertia of the cross sectional area of the horizontal beam with respect to the flexural axis, and:

  

  

 I d 36E  h h 3 I

2

2

  

I

A d Sen θ

h

d d

d







1

2 s 11 12  





2

  

  

2

d 2h Cos θ d   h 3

d A Sen θ d







 

2

13

3

3 d I A d I Cosθ  d h



h d

d I

Cosθ 2A I



d h





d d

3

3

h

h Cosθ





3

2 s 11 12 2    

36E



2

2

d d 12A d I Cosθ

h h 12A h I Cosθ ,









h

d

2

2

A h 24I (1 ν) χ  

A d 24I (1 ν) χ  

h

h

h

d

d

d

2I Cos θ

2I Cos θ

I

I

d

d

h  

h  





,

11

12

3

3

2

2

h

d

h

d

2 8I 4I 2E d h   d s

 

h   





13

The Eqs. (13-15) and Eq. (16) only contains geometrical quantities, i.e. the geometrical characteristics of the grid (  , h, d), and the geometrical properties of the structural member cross sections (A h , A d , I h , I d , χ h , χ d ). Therefore E * 1H /E s , E * 2H /E s ,

196