Matriz de Rigidez Lateral
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7.35 tn/m
20.40tn
2.73
6.75tn 8.09tn
8.82 tn/m 10.29
16.20tn
3.35 3.556
3.045
3.234 5.335 5.525 2.7
1 2 3 4
1 2 3
4 5 6
5 6 7 8
7 8 9
10 11 12
9 10 11
Matriz de rigidez en coordenadas locales
0 0 0 0
0
0
[K]=0 0 I
M E
R I A
/
12/
^
3
-/
6
/
^24
/
-12
^/
3
6
/
^2-6
/
^2
2
/
12 ^/
3
/6
^2
4
/
6
/
^2
![Page 2: Matriz de Rigidez Lateral](https://reader031.fdocuments.in/reader031/viewer/2022020710/563dba6e550346aa9aa5929a/html5/thumbnails/2.jpg)
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BARRA 1 2 5
E 1.000 1 4
I 1.000 3 6
A 1.000 1 2 3 4 5 6
L 5.335
K´=
0.187 0.000 0.000 -0.187 0.000 0.000 1
n!"#$ 0.000 0.000 0.079 0.211 0.000 -0.079 0.211 2
%&n 0.000 0.000 0.211 0.750 0.000 -0.211 0.375 3
'$% 1.000 -0.187 0.000 0.000 0.187 0.000 0.000 4
EA/L 0.187 0.000 -0.079 -0.211 0.000 0.079 -0.211 5
EI 1.000 0.000 0.211 0.375 0.000 -0.211 0.750 6
T=
1.000 0.000 0.000 0.000 0.000 0.000
0.000 1.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 1.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
1 2 3 4 5 6
K=
0.187 0.000 0.000 -0.187 0.000 0.000 1
0.000 0.079 0.211 0.000 -0.079 0.211 2
0.000 0.211 0.750 0.000 -0.211 0.375 3
-0.187 0.000 0.000 0.187 0.000 0.000 4
0.000 -0.079 -0.211 0.000 0.079 -0.211 5
0.000 0.211 0.375 0.000 -0.211 0.750 6
BARRA 2 5 8
E 1.000 4 7
I 1.000 6 9
A 1.000 4 5 6 7 8 9
L 5.525
K´=
0.181 0.000 0.000 -0.181 0.000 0.000 4
n!"#$ 0.000 0.000 0.071 0.197 0.000 -0.071 0.197 5
%&n 0.000 0.000 0.197 0.724 0.000 -0.197 0.362 6
'$% 1.000 -0.181 0.000 0.000 0.181 0.000 0.000 7
EA/L 0.181 0.000 -0.071 -0.197 0.000 0.071 -0.197 8
EI 1.000 0.000 0.197 0.362 0.000 -0.197 0.724 9
T=
1.000 0.000 0.000 0.000 0.000 0.000
0.000 1.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 1.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
4 5 6 7 8 9
0.181 0.000 0.000 -0.181 0.000 0.000 40.000 0.071 0.197 0.000 -0.071 0.197 5
0.000 0.197 0.724 0.000 -0.197 0.362 6
![Page 3: Matriz de Rigidez Lateral](https://reader031.fdocuments.in/reader031/viewer/2022020710/563dba6e550346aa9aa5929a/html5/thumbnails/3.jpg)
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-0.181 0.000 0.000 0.181 0.000 0.000 7
0.000 -0.071 -0.197 0.000 0.071 -0.197 8
0.000 0.197 0.362 0.000 -0.197 0.724 9
BARRA 3 8 11
E 1.000 7 10
I 1.000 9 12
A 1.000 7 8 9 10 11 12
L 2.700
K´=
0.370 0.000 0.000 -0.370 0.000 0.000 7
n!"#$ 0.000 0.000 0.610 0.823 0.000 -0.610 0.823 8
%&n 0.000 0.000 0.823 1.481 0.000 -0.823 0.741 9
'$% 1.000 -0.370 0.000 0.000 0.370 0.000 0.000 10
EA/L 0.370 0.000 -0.610 -0.823 0.000 0.610 -0.823 11
EI 1.000 0.000 0.823 0.741 0.000 -0.823 1.481 12
T=
1.000 0.000 0.000 0.000 0.000 0.000
0.000 1.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 1.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
7 8 9 10 11 12
0.370 0.000 0.000 -0.370 0.000 0.000 7
0.000 0.610 0.823 0.000 -0.610 0.823 8
0.000 0.823 1.481 0.000 -0.823 0.741 9
-0.370 0.000 0.000 0.370 0.000 0.000 10
0.000 -0.610 -0.823 0.000 0.610 -0.823 11
0.000 0.823 0.741 0.000 -0.823 1.481 12
BARRA 4
E 1.000
I 1.000
A 1.000 16 17 18 1 2 3
L 2.730
K´=
0.366 0.000 0.000 -0.366 0.000 0.000 16
n!"#$ 90.000 0.000 0.590 0.805 0.000 -0.590 0.805 17
%&n 1.000 0.000 0.805 1.465 0.000 -0.805 0.733 18
'$% 0.000 -0.366 0.000 0.000 0.366 0.000 0.000 1
EA/L 0.366 0.000 -0.590 -0.805 0.000 0.590 -0.805 2
EI 1.000 0.000 0.805 0.733 0.000 -0.805 1.465 3
T=
0.000 1.000 0.000 0.000 0.000 0.000
-1.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.0000.000 0.000 0.000 -1.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
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16 17 18 1 2 3
0.590 0.000 -0.805 -0.590 0.000 -0.805 16
0.000 0.366 0.000 0.000 -0.366 0.000 17
-0.805 0.000 1.465 0.805 0.000 0.733 18
-0.590 0.000 0.805 0.590 0.000 0.805 1
0.000 -0.366 0.000 0.000 0.366 0.000 2
-0.805 0.000 0.733 0.805 0.000 1.465 3
BARRA 5
E 1.000
I 1.000
A 1.000 19 20 21 4 5 6
L 2.730
K´=
0.366 0.000 0.000 -0.366 0.000 0.000 19
n!"#$ 90.000 0.000 0.590 0.805 0.000 -0.590 0.805 20
%&n 1.000 0.000 0.805 1.465 0.000 -0.805 0.733 21
'$% 0.000 -0.366 0.000 0.000 0.366 0.000 0.000 4
EA/L 0.366 0.000 -0.590 -0.805 0.000 0.590 -0.805 5
EI 1.000 0.000 0.805 0.733 0.000 -0.805 1.465 6
T=
0.000 1.000 0.000 0.000 0.000 0.000
-1.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 -1.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
19 20 21 4 5 6
0.590 0.000 -0.805 -0.590 0.000 -0.805 19
0.000 0.366 0.000 0.000 -0.366 0.000 20
-0.805 0.000 1.465 0.805 0.000 0.733 21
-0.590 0.000 0.805 0.590 0.000 0.805 4
0.000 -0.366 0.000 0.000 0.366 0.000 5
-0.805 0.000 0.733 0.805 0.000 1.465 6
BARRA 6
E 1.000
I 1.000
A 1.000 22 23 24 7 8 9
L 2.730
K´=
0.366 0.000 0.000 -0.366 0.000 0.000 22
n!"#$ 90.000 0.000 0.590 0.805 0.000 -0.590 0.805 23
%&n 1.000 0.000 0.805 1.465 0.000 -0.805 0.733 24
'$% 0.000 -0.366 0.000 0.000 0.366 0.000 0.000 7
EA/L 0.366 0.000 -0.590 -0.805 0.000 0.590 -0.805 8
EI 1.000 0.000 0.805 0.733 0.000 -0.805 1.465 9
0.000 1.000 0.000 0.000 0.000 0.000
![Page 5: Matriz de Rigidez Lateral](https://reader031.fdocuments.in/reader031/viewer/2022020710/563dba6e550346aa9aa5929a/html5/thumbnails/5.jpg)
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T=
-1.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 -1.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
22 23 24 7 8 9
0.590 0.000 -0.805 -0.590 0.000 -0.805 22
0.000 0.366 0.000 0.000 -0.366 0.000 23
-0.805 0.000 1.465 0.805 0.000 0.733 24
-0.590 0.000 0.805 0.590 0.000 0.805 7
0.000 -0.366 0.000 0.000 0.366 0.000 8
-0.805 0.000 0.733 0.805 0.000 1.465 9
BARRA 7 14 17
E 1.000 13 16
I 1.000 15 18
A 1.000 13 14 15 16 17 18
L 3.234
K´=
0.309 0.000 0.000 -0.309 0.000 0.000 13
n!"#$ 0.000 0.000 0.355 0.574 0.000 -0.355 0.574 14
%&n 0.000 0.000 0.574 1.237 0.000 -0.574 0.618 15
'$% 1.000 -0.309 0.000 0.000 0.309 0.000 0.000 16
EA/L 0.309 0.000 -0.355 -0.574 0.000 0.355 -0.574 17
EI 1.000 0.000 0.574 0.618 0.000 -0.574 1.237 18
T=
1.000 0.000 0.000 0.000 0.000 0.000
0.000 1.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 1.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
13 14 15 16 17 18
0.309 0.000 0.000 -0.309 0.000 0.000 13
0.000 0.355 0.574 0.000 -0.355 0.574 14
0.000 0.574 1.237 0.000 -0.574 0.618 15
-0.309 0.000 0.000 0.309 0.000 0.000 16
0.000 -0.355 -0.574 0.000 0.355 -0.574 17
0.000 0.574 0.618 0.000 -0.574 1.237 18
BARRA 8 17 20
E 1.000 16 19
I 1.000 18 21
A 1.000 16 17 18 19 20 21
L 5.335
´
0.187 0.000 0.000 -0.187 0.000 0.000 16
n!"#$ 0.000 0.000 0.079 0.211 0.000 -0.079 0.211 17
%&n 0.000 0.000 0.211 0.750 0.000 -0.211 0.375 18
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'$% 1.000 -0.187 0.000 0.000 0.187 0.000 0.000 19
EA/L 0.187 0.000 -0.079 -0.211 0.000 0.079 -0.211 20
EI 1.000 0.000 0.211 0.375 0.000 -0.211 0.750 21
T=
1.000 0.000 0.000 0.000 0.000 0.000
0.000 1.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 1.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
16 17 18 19 20 21
0.187 0.000 0.000 -0.187 0.000 0.000 16
0.000 0.079 0.211 0.000 -0.079 0.211 17
0.000 0.211 0.750 0.000 -0.211 0.375 18
-0.187 0.000 0.000 0.187 0.000 0.000 190.000 -0.079 -0.211 0.000 0.079 -0.211 20
0.000 0.211 0.375 0.000 -0.211 0.750 21
BARRA 9 20 23
E 1.000 19 22
I 1.000 21 24
A 1.000 19 20 21 22 23 24
L 5.525
K´=
0.181 0.000 0.000 -0.181 0.000 0.000 19
n!"#$ 0.000 0.000 0.071 0.197 0.000 -0.071 0.197 20
%&n 0.000 0.000 0.197 0.724 0.000 -0.197 0.362 21
'$% 1.000 -0.181 0.000 0.000 0.181 0.000 0.000 22
EA/L 0.181 0.000 -0.071 -0.197 0.000 0.071 -0.197 23
EI 1.000 0.000 0.197 0.362 0.000 -0.197 0.724 24
T=
1.000 0.000 0.000 0.000 0.000 0.000
0.000 1.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 1.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
19 20 21 22 23 24
0.181 0.000 0.000 -0.181 0.000 0.000 19
0.000 0.071 0.197 0.000 -0.071 0.197 20
0.000 0.197 0.724 0.000 -0.197 0.362 21
-0.181 0.000 0.000 0.181 0.000 0.000 22
0.000 -0.071 -0.197 0.000 0.071 -0.197 23
0.000 0.197 0.362 0.000 -0.197 0.724 24
BARRA 10
E 1.000
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I 1.000
A 1.000 25 26 27 16 17 18
L 3.045
K´=
0.328 0.000 0.000 -0.328 0.000 0.000 25
n!"#$ 90.000 0.000 0.425 0.647 0.000 -0.425 0.647 26
%&n 1.000 0.000 0.647 1.314 0.000 -0.647 0.657 27
'$% 0.000 -0.328 0.000 0.000 0.328 0.000 0.000 16
EA/L 0.328 0.000 -0.425 -0.647 0.000 0.425 -0.647 17
EI 1.000 0.000 0.647 0.657 0.000 -0.647 1.314 18
T=
0.000 1.000 0.000 0.000 0.000 0.000
-1.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 -1.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
25 26 27 16 17 18
0.425 0.000 -0.647 -0.425 0.000 -0.647 25
0.000 0.328 0.000 0.000 -0.328 0.000 26
-0.647 0.000 1.314 0.647 0.000 0.657 27
-0.425 0.000 0.647 0.425 0.000 0.647 16
0.000 -0.328 0.000 0.000 0.328 0.000 17
-0.647 0.000 0.657 0.647 0.000 1.314 18
BARRA 11
E 1.000
I 1.000
A 1.000 28 29 30 19 20 21
L 3.045
K´=
0.328 0.000 0.000 -0.328 0.000 0.000 28
n!"#$ 90.000 0.000 0.425 0.647 0.000 -0.425 0.647 29
%&n 1.000 0.000 0.647 1.314 0.000 -0.647 0.657 30
'$% 0.000 -0.328 0.000 0.000 0.328 0.000 0.000 19
EA/L 0.328 0.000 -0.425 -0.647 0.000 0.425 -0.647 20
EI 1.000 0.000 0.647 0.657 0.000 -0.647 1.314 21
T=
0.000 1.000 0.000 0.000 0.000 0.000
-1.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 -1.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
28 29 30 19 20 21
0.425 0.000 -0.647 -0.425 0.000 -0.647 28
0.000 0.328 0.000 0.000 -0.328 0.000 29
-0.647 0.000 1.314 0.647 0.000 0.657 30
-0.425 0.000 0.647 0.425 0.000 0.647 19
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0.000 -0.328 0.000 0.000 0.328 0.000 20
-0.647 0.000 0.657 0.647 0.000 1.314 21
BARRA 12
E 1.000
I 1.000
A 1.000 31 32 33 22 23 24
L 3.045
K´=
0.328 0.000 0.000 -0.328 0.000 0.000 31
n!"#$ 90.000 0.000 0.425 0.647 0.000 -0.425 0.647 32
%&n 1.000 0.000 0.647 1.314 0.000 -0.647 0.657 33
'$% 0.000 -0.328 0.000 0.000 0.328 0.000 0.000 22
EA/L 0.328 0.000 -0.425 -0.647 0.000 0.425 -0.647 23
EI 1.000 0.000 0.647 0.657 0.000 -0.647 1.314 24
T=
0.000 1.000 0.000 0.000 0.000 0.000
-1.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 -1.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
31 32 33 22 23 24
0.425 0.000 -0.647 -0.425 0.000 -0.647 31
0.000 0.328 0.000 0.000 -0.328 0.000 32
-0.647 0.000 1.314 0.647 0.000 0.657 33
-0.425 0.000 0.647 0.425 0.000 0.647 22
0.000 -0.328 0.000 0.000 0.328 0.000 23
-0.647 0.000 0.657 0.647 0.000 1.314 24
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1 2 3 4 5 6 7 8 9
0.777 0.000 0.805 -0.187 0.000 0.000 0.000 0.000 0.00
0.000 0.445 0.211 0.000 -0.079 0.211 0.000 0.000 0.00
0.805 0.211 2.215 0.000 -0.211 0.375 0.000 0.000 0.00
-0.187 0.000 0.000 0.958 0.000 0.805 -0.181 0.000 0.00
0.000 -0.079 -0.211 0.000 0.516 -0.014 0.000 -0.071 0.19
0.000 0.211 0.375 0.805 -0.014 2.939 0.000 -0.197 0.36
0.000 0.000 0.000 -0.181 0.000 0.000 1.141 0.000 0.80
0.000 0.000 0.000 0.000 -0.071 -0.197 0.000 1.047 0.6
0.000 0.000 0.000 0.000 0.197 0.362 0.805 0.626 3.6
0.000 0.000 0.000 0.000 0.000 0.000 -0.370 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.610 -0.8
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.823 0.74
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
[K]= -0.590 0.000 -0.805 0.000 0.000 0.000 0.000 0.000 0.00
0.000 -0.366 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.805 0.000 0.733 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 -0.590 0.000 -0.805 0.000 0.000 0.00
0.000 0.000 0.000 0.000 -0.366 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.805 0.000 0.733 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 -0.590 0.000 -0.80
0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.366 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.805 0.000 0.7
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00
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[KLt&(#]= [K11] - [K12]
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