Resolución de Viga
February 13, 2023 | Author: Anonymous | Category: N/A
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MATRIZ DE RIGIDEZ
3
4
(Considerando Flexión
1
2
m= 1
m2= 1
6EI/L2
6EI/L2 2EI/L
4EI/L
6EI/L2
2EI/L
K 11 = 4EI/L K 21 =2EI/L K 31 = 6EI/L2 K 41 = -6EI/L2
K 12 = 2EI/L K 22 = 4EI/L K 32 = 6EI/L2 K 42 = -6EI/L2
m3= 1
m4= 1
12EI/L3 6EI/L2 12EI/L3 6EI/L2 K 13 = 6EI/L2 K 23 = 6EI/L2 K 33 = 12EI/L3 K 43 = -12EI/L3
12EI/L3
6EI/L2 K 14 = -6EI/L2 K 24 = -6EI/L2 K 34 = -12EI/L3 K 44 = 12EI/L3
y Corte)
4EI/L
6EI/L2
6EI/L2 12EI/L3
M!"#"$ M%!&ICI%LE$ E'E&CICI" 2 allar el #MF y #FC
3 1
A
EI=1
B
6*
EI=1 4*
%-+ EI = 1
3
4
1 1 1
1
L=6
A
1
K=
2
B 1 2
1
2
1
2
0.67 0.33 0.17 -0.17
0.33 0.67 0.17 -0.17
2
3
1
2
1 0.5 0.375 -0.375
0.5 1 0.375 -0.375
+-C EI = 1
3 2
4
1
1 1
B
L=4
1
K=
3 C 2
1
MATRIZ DE RIGIDEZ
K=
K11
K21
K31
K1 K 12 K13
K22 K23
K32 K33
K=
CÁLCULO DE FUERZAS DE LOS ELEMENTOS
TRAMO A-B
3
4
1 1
1 1
A
1
B 1 2
2
!
0
1
0 0 0
2 3 4
TRAMO B-C
1
3 2 1
1 1
4
B
3
!
C 1 2
MATRIZ DE FUERZA 3"#/$
0
1
0 0 0
2 3 4
1 2
3
CALCULO DE DESLAZAMIENTO -1
〖 = || 〗 ^(−1) x ||
0.667
0.333
0
0.333
1.667
0.5
0
0.5
1
x
1, 1,6 6. .31 3162 62 -,3 -,3 16 16 , ,1 1 . .46 461 1
〖 = || 〗 ^(−1) x ||
-, -,31 3162 62 ,0 ,023 23 -, -,3 3062 06264 64 % , ,1 1 . .46 46 -,3 -,3 06 063 3 1, 1,1 1. .. .13 132 2
CALCULO DE MOMENTO & FUERZA CORTANTE
ℱ_=|_ |+|_ | |_ |
ℱ_=
0 0 0 0
ℱ_=
0.67 0.33 0.17 -0.17
-,12
1,212 ,24
0.33 0.67 0.17 -0.17
0.17 0.17 0.06 --0 0.06
ℱ_=
ℱ_=
ℱ_=
-,24
-,12 M 1,212 M ,24 C -,24 C
0 0 0 0
1 0.5 0.375 -0.375
0 0 0 0
1.' 0 0.45 -0.45
0.5 1 0.375 -0.375
0.375 0.375 0.1'75 -0.1'75
1
ℱ_=
1.' 0 0.45 -0.45
M M
C
C
#MF
1 1
#FC
GDL 1
2
3
1
1
1
C
3
4
0.17 0.17 0.06 -0.06
-0.17 -0.17 -0.06 0.06
3
4
0.375 0.375 0. 0.1' 1'75 75 -0.1 -0.1'7 '75 5
-0.375 -0.375 0. 0.1' 1'75 75 0. 0.1' 1'75 75
1 2
1 2
2 3
3 4
1 2 3 4
K11= ,660 K12= ,333 K21= ,33 K22= ,60
K22= K23= K32= K33=
1 , , 1
0.667
0.333
0.333 0
1.667 0.5
, 1
1 2
K11= K12=
2
K12= K13=
3
GL1! GL1! GL1!
0 3 0
0
(!
3 0
0 3
!
0
3
-1.1)74' 1
!
2.3)'562
2
-1.1))2' 3
1
-0.17 -0.17 -0.06 0.06
-1,2 2,4
1 1 2 2
3
4
1
3 1
1 A 1
4
B 1 2
2
1
-0.375 -0.375 0.1'75 0.1'75
2,4 -1,2
3
B 1
12 2 3
3
4
4
1 C 2
M!"#"$ M%!&ICI%LE$ E'E&CICI" 2 allar el #MF y #FC
allar el #MF y #FC
A
1
4EI/L
2EI/L
A
2EI/L
B 11= 21= 31=
C
A
,660 ,333
,660 ,333
*
,333 1,6660 ,
, 1
MATRIZ DE RIGIDEZ 3 1
A
+ 2
CALCULO DE DESLAZAMI
,660
〖 = || 〗 ^(−1) x ||
,333
1,6.042
〖 = || 〗 ^(−1) x ||
-,3266.02 ,162.3436
CALCUL CALC ULO O DE MO MOME MEN N
M=|_0 |+|_ | |m| MF!
0
MF!
MF!
#MF
,660 ,333
,
, 1,2 1,. ,
1,2 1,. ,
#FC
3 1 EI=1
B
6*
4EI/L
K+
C
4*
4EI/L
B
12= 22= 32=
EI=1
2EI/L
C
,333 1,6660 ,
A
B
13= 23= 33=
,660
,333
,333
,660
, 1
1 ,
, 1
3 C
GL1! GL2! GL3!
0 3 0
ENTO
-1 ,333
1,6660
,
,
1
%
%
3
O & FUERZA CORTANTE
,333
,660
1 ,
, 1
!
-,32 -,3266. 66.0 0 ,162. ,162.3436 3436 ,00123 ,00 123434 434 -,3 -,3. .6 6102 102 -,3. -,3.610 6102 2 1,12. 1,12... ..
3
-1,10001
2,31303 -1,16.
-1.1)77701
!
2.3))13703 -1.1))56'5
GDL 1
2
3
1
1
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