7/18/2019 matricial vigas

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5 6 3 1

900 0 -3.8 -900

S0= 900 E= 3 0 2.53 3.8 0

S1= 7.6 A= 0.09 K'1= -3.8 3.8 7.6 0

S2= 3.8 I= 1.9 -900 0 0 900

S3= 2.53 L= 3 0 -2.53 -3.8 0A= 900 -3.8 3.8 3.8 0

A'= 2.53

B= 0

C= 3.8

C'= 0

1 4 2 7

540 0 -1.368 -540

S0= 540 E= 3 0 0.55 1.368 0

S1= 4.56 A= 0.09 K'2= -1.368 1.368 4.56 0S2= 1.37 I= 1.9 -540 0 0 540

S3= 0.55 L= 5 0 -0.55 -1.368 0

A= 540 -1.368 1.368 2.28 0

A'= 0.55

B= 0

C= 1.37 1 0 0 0 0

C'= 0 0 1 0 0 0

 T1=T2= 0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

0 0 0 0 0

900 0 0 -900 0

0 2.53 3.8 0 -2.53

K1= 0 3.8 7.6 0 -3.8

-900 0 0 900 0

0 -2.53 -3.8 0 2.53

0 -3.8 3.8 0 3.8

540 0 0 540 0

0 0.55 1.4 0 -0.55

K2= 0 1.4 4.6 0 -1.4

540 0 0 540 0

0 -0.55 -1.4 0 0.55

0 -1.4 2.3 0 1.4

7/18/2019 matricial vigas

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4 2 1 2 3 4 5 6 7

0 -3.8   5   1440   -1 0 0 -900 0 -540

-2.53 3.8   6   -1.37   #   3.8 -2.43 -3.80 3.8 0

-3.8 3.8   3   0 4   7.6   -3.8 -3.8 3.8 0

0 0   1   0 -2 -3.8   3.08   0 -2.53 0

2.53 -3.8   4   K= -900 # -3.8 0   900   0 0-3.8 7.6   2   0 4 3.8 -2.53 0   2.53   0

-540 0 0 0 0 0   540

0 -1 0 -0.55 0 0 0

-1.37 2 0 1.368 0 0 0

8 9   0.001 # ###

0 -1.368   1   inv(K11)= ### 0 -0.05

-0.55 1.368   4   ### 0 0.156

-1.368 2.28   2

0 0   7

0.55 -1.368   8   0 D1

-1.368 4.56   9   Dd= -0.17 D2

-0.27 D3

0

0 !i1 900 0 0 -900 0

0 "i1 0 2.53 3.8 0 -2.53

0 i1 = 0 3.8 7.6 0 -3.8

0 !$1 -900 0 0 900 0

1 "$1 0 -2.53 -3.8 0 2.53

$1 0 -3.8 3.8 0 3.8

0

-3.8 !i2 540 0 0 540 0

3.8 "i2 0 0.55 1.4 0 -0.55

0 i2 = 0 1.4 4.6 0 -1.4

3.8 !$2 540 0 0 540 0

7.6 "$2 0 -0.55 -1.4 0 0.55

$2 0 -1.4 2.3 0 1.4

0

-1.4

2.3

0

1.4

4.6

7/18/2019 matricial vigas

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8 9

0 -1   1

-1.37 2   2

0 0   3

-0.55 1   4

0 0   5

0 0   6

0 0   7

0.55   -1   8

-1.37   5   9

0

%&= -3.06

-2.7

0 0 0

-3.8 0 -0.38

3.8 -0.3 = -3.04

0 0 0

3.8 0 0.38

7.6 -0.2 -2.66

0 0 0

-1.4 0 -0.28

2.3 -0.2 = -0.92

0 0 0

1.4 0 0.28

4.6 0 -0.46

7/18/2019 matricial vigas

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1 2

K= 7.6 3.8   1   inv(K11)= 0.156 -0.049

3.8 7.6   2   -0.049 0.097

2 3

K= 4.56 2.28   2%&=

  -2.7

2.28 4.56   3   -3.6

1 2 3

7.6 3.8   0 1   -0.246 D1

K= 3.8 12.16 2   2   Dd= -0.219 D2

0 2.28 5   3

-0.5

7.6 3.8 -0.25 -2.736

3.8 7.6 -0.22 -2.6221

4.56 2.28 -0.22 -1

2.28 4.56 0 -0.502

i1=

  7.6 3.8

  -0.25=

  -3.04

$1 3.8 7.6 -0.22 -2.66

i2=

  4.56 2.28

  -0.22=

  -0.92

$2 2.28 4.56 0 -0.46

7/18/2019 matricial vigas

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1.26 0.63

  1=

  2.7

0.63 2.02 2 3.06

0.9403 -0.2933 2.7

-0.2933 0.5865 3.06

1.6414

1.0029

-0.0018

4.5937

-4.9978

4.22