catalogo de elementos

ANEXO B

1

CATÁLOGO DE ELEMENTOS

1.- ELEMENTO RETICULADO PLANO
S1 , u 1

x

S1, u 1
z

i
x

S2, u 2

S2 , u 2







z


j
S3 , u 3
S4 , u 4

d

S3 , u 3
F1 , V 1

 1
 0
j
T  
 1
 
 0

f

j

j
LD

  
 
 EA 

s 2

F1 
j
kg 
 




0
c  s 0
s
c 0
0



0
0 c  s


0 s
c0

 EA 
k rj   
  

 sc  s 2
c

2

Sim.

sc 

sc  c 2 
s 2  sc 

c2 


c 2

EA 
j
k 
 




 c 
 s 
j T
(a )   
 c
 
 s
cs  c 2
s

2

sim

c = cos  = ( x d – x i ) / 
s = sen  = ( z d – z i ) / 

 cs 

 cs  s 2 
c2
cs 

s2 


S4 , u 4

ANEXO B

2

CATÁLOGO DE ELEMENTOS

2.-ELEMENTO DE RETICULADO ESPACIAL

F1 , V 1

S4, u 4

S5 , u 5

S5 , u 5

S4 , u 4

d
S6 , u 6

S6 , u 6


j
y
i

j

x

j

S2 , u 2

S2 , u 2

z

f

j

  
 
 EA 

2
c11



EA 
j
k 
 






y
x

S3 , u 3
S1, u 1

 1
 0
 
 0
Tj  
 1
 0
 
 0
 

S1, u 1

j
LD

c11
c
 12
c
 13






S3 , u 3

c 21

c31

c22

c32

c23

c33

0
c11
c12

c22

c13

0

c 21
c 23

  c11 
 c 
 12 
 c 
(a j )T   13 
 c11 
 c12 


 c13 








c31 
c32 

c33 


 EA 
k rj   
  

c11 c12

c11 c13

2
 c11

 c11 c12

2
c12

c12 c13

 c12 c11

2
 c12

2
c13

 c13c11

 c13 c12

2
11

c11 c12

c
Sim.

2
c12

 c11 c13 

 c12 c13 
2 
 c13 
c11 c13 

c12 c13 

2
c13 


cij = cos  ij

z

ANEXO B

3

CATÁLOGO DE ELEMENTOS

3.- ELEMENTO DE VIGA ESPACIAL
F4 , V 4

F5 , V 5

S 11 , u 11

S 10 , u 10
S 11 , u 11

F2 , V 2
d

F1 , V 1
F3 , V 3

S8 , u 8

S7, u 7

S 10 , u 10

S8 , u 8

S7, u 7

d

F6 , V 6

S9, u 9

S 12 , u 12

S9 , u 9


j
y
i

S5 , u 5

x

S2, u 2
i
S 1, u 1

z

j

j

S 12 , u 12

S5 , u 5
S4, u 4

S3 , u 3

y
x

S2 , u 2

S 1, u 1

S6 , u 6

S3 , u 3

z

S4, u 4
S6 , u 6

1 0 0 0 0 0


 0 1 0 0 0 0
 0 0 1 0 0 0


 0 0 0 1 0 0


 0 0  0 1 0


0  0 0 0 1

j 
T 
1




1
0




1


1




0
1




1



c11

c12
c
 13




j 
LD 











c21

c31

c22

c32

c23

c33

0
c11

c21

c31

c12

c22

c32

c13

c23

c33
c11

c22

c32

c13

cij = cos  ij

c31

c12
0

c21
c23

c33
c11

c21

c12

c22

c13

c23
















c31

c32
c33


ANEXO B

 c11  c21  c31

 c

 c22  c32
0
 12

 c13  c23  c33



 0  c31  c21  c11  c21  c31
 0  c32 c22  c12  c22  c32


j T
 0  c33 c23  c13  c23  c33
(a )  

c
c21
c31
 11

c22
c32
0
 c12

 c

c23
c33
 13


c11 c21 c31

0
c12 c22 c32


c13 c23 c33



kr

j

4

CATÁLOGO DE ELEMENTOS


EA





j 
f 









 EA

0
0 0
0
  0

 12EI
 6EI z 
z
0
0 0


3
2

 

12EI y
6EI y


0
0
3
2






GI t
0
0 




4EI y

sim
0 




4EI z 



 

0

0

0

0

3
3EIz

00

0

3
3EIy

0




GI
t

2
2EIy
0

EIy

Sim
.

j

j

T

j

k  (a ) * k r * a

j


0 

2 
2EIz 

0 


0 




 
EIz 


ANEXO B

5

CATÁLOGO DE ELEMENTOS

 EA
EA
0
0
0
0
0 
0
0
0


 
12EI z
6EI z
12EI z

0
0
0
0 
0
0
3
2



3

12EI y
6EI y
12EI y

0  2
0
0
0...