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LES PORTIQUES 409

2.20. LE PORTIQUE VI4

N2(y) N1 N3(y) p1L p1L2 L
2 8 p1
N4 N5
N M x

p2H cosα p2 H cosα p2H 2 p2H 2 h1, Ω1, I1
2 2 8 8 h2 ,Ω2 , I 2

T p2 y Ω3 p2 H
Rh,E Rh,F Rh,D
Figure 2.20.2. Rh , A

nb = 5 ; nl = 8 ; nm = 6 ; nn = 6 ; nr = 10 : Dh = 1 . Rv, A Rv,E Rv,F Rv,D

Figure 2.20.1.

N1 = p1L (b H )(Ω1 Ω2 − Ω1 Ω3 )( H L )  2 ( Ω1 Ω2 + Ω1 Ω3 )(H L) + 4  ( H b+b H) 1+ H2 2   ,
   
b 



( ) 


− (1 k)(y L) 1+ H 2 b2 + (0,25 k ) 3 + H 2 b2 ( H L ) 1+ H2 b2

N2 ( y) = p1L   b2 3 / 2   ,
  
( ( )) ( ) − (Ω1 Ω3 )( H L)(b H ) 1+ H2 b2 +1 1+ H2 b2
2 (Ω1 Ω2 + Ω1 Ω3 )(H L) + 4(H b) 1+ H2

( ) 


(1 k)(y L) 1 + H 2 b2 − (0,25 k ) 3 + H 2 b2 ( H L ) 1+ H2 b2

N3 ( y) = p1L  
 − (Ω1 Ω3 )( H L )(b H ) 1+ H2 b2 +1 1+ H2 b2 
( ( )) ( )N  3 / 2  ,
 2 ( Ω1 Ω2 + Ω1 Ω3 )(H L) + 4(H b) 1+ H2 b2 

 (0, 25 k) 1+ H2 b2 (H L) 
 
= − p1L 
 +
( ( )) ( )N4 b2  3/2   ,
(Ω1 Ω3 )(H L)(b H) 1+ H2 b2 +1 1+ H2  2 ( Ω1 Ω2 + Ω1 Ω3 )(H L)+ 4(H b) 1+ H2 b2  

 − (0, 25 k) 1+ H2 b2 (H L) 
 
N5 = − p1L  
 3 / 2  
( ( )) ( )+  
(Ω1 Ω3 )(H L)(b H ) 1+ H2 b2 +1 1+ H2 b2 2 ( Ω1 Ω2 + Ω1 Ω3 )(H L) + 4(H b) 1+ H2 b2 .

T T1 ( x ) = p1 ( L 2 − x ) , T2 ( y) = T3 ( y) = p2 ( H 2 − y) 1+ b2 H 2 et T4 = T5 = 0 .

M M1 ( x) = p1x (L − x) , M2 ( y) = −M3 ( y) = p2 y ( H − y) et M4 = M5 =0 .

2 2

– si 1+ H2 b2 ≥ 1 (4ZH h2 ) :

( )   
 (b H ) Ω1 Ω2 − Ω1 Ω3  b2  1 + H2 1 + H 2 + 1 h2  H2
W = Z L +  Ω2 + Ω1 Ω3 ) H L + 4 ( H b) 1 + H 2 + 1 + H2   H + 1 b b2 + 2Z H b2 8Z H 1 .
h1 3/2  L k H h2 1+ H2 b2  L2
 2 (Ω1 b2
 

– si 1+ H2 b2 ≤ 1 (4ZH h2 ) :

( ) 
 (b H ) Ω1 Ω2 − Ω1 Ω3  b2   H2  H2
W = Z L +  Ω2 + Ω1 Ω3 ) H L + 4 ( H b) 1 + H 2 + 1 + H2   H + 1 b  2 + b2  L2 . 2.20.1.
h1 3/2  L k H
 2 (Ω1 b2
 