perhitungan truss dengan metode matriks

7/24/2019 Perhitungan Truss dengan Metode Matriks

1/45

B 3000 mm Pz 4,5 kN

H 4000 mm Px 1,35 kN

E 200000 Mpa Py 2,7 kN

4272

Koordinat titik-titik nodal

Nodal ! "

1 4500 0 0

2 4500 3000 0

3 0 3000 0

4 0 0 0

5 4500 0 4000

# 4500 3000 4000

7 0 3000 4000

$ 0 0 4000% 4500 1500 4000

10 2250 3000 4000 0,%3#3

11 0 1500 4000

12 2250 0 4000

Pan&an' (atan' dan )o*in+* *+d+t ara

Batan' Nodal

.mm/i & Px .N/

1 1 5 4174 4000 0 0 1 20$700

2 1 % 1150 4272 0 0,3511 0,%3#3 53$3%

3 2 % 1150 4272 0 -0,3511 0,%3#3 53$3%

4 2 # 4174 4000 0 0 1 20$700

5 2 10 1150 45$%,4 -0,4%03 0 0,$71# 5011#

# 3 10 1150 45$%,4 0,4%03 0 0,$71# 5011# 1350

7 3 7 4174 4000 0 0 1 20$700 1350

$ 3 11 1150 4272 0 -0,3511 0,%3#3 53$3% 1350

% 4 11 1150 4272 0 0,3511 0,%3#3 53$3%

10 4 $ 4174 4000 0 0 1 20$700

11 4 12 1150 45$%,4 0,4%03 0 0,$71# 5011#

12 1 12 1150 45$%,4 -0,4%03 0 0,$71# 5011#

13 5 % 4174 1500 0 1 0 55#53314 # % 4174 1500 0 -1 0 55#533

15 # 10 4174 2250 -1 0 0 371022

1# 7 10 4174 2250 1 0 0 371022

17 7 11 4174 1500 0 -1 0 55#533

1$ $ 11 4174 1500 0 1 0 55#533

1% $ 12 4174 2250 1 0 0 371022

20 5 12 4174 2250 -1 0 0 371022

21 % 12 1150 2704,2 -0,$321 -0,5547 0 $5054

22 % 10 1150 2704,2 -0,$321 0,5547 0 $5054

23 10 11 1150 2704,2 -0,$321 -0,5547 0 $5054

24 11 12 1150 2704,2 0,$321 -0,5547 0 $5054

Elemen 1 i = 1 j = 5

.mm2/ x

x

x

/L


2/45

AE/L

0 0 1 208700

1 1 1 5 5 5

1 20$700 0 0 -20$700 0 01 0 0 0 0 0 0

1 0 0 0 0 0 0

5 -20$700 0 0 20$700 0 0

5 0 0 0 0 0 0

5 0 0 0 0 0 0

1 1 1 5 5 5

1 0 0 1 0 0 0

1 0 0 0 0 0 0

1 0 0 0 0 0 0 x5 0 0 0 0 0 1

5 0 0 0 0 0 0

5 0 0 0 0 0 0

1 1 1 5 5 5

1 0 0 0 0 0 0

1 0 0 0 0 0 0

1 0 0 20$700 0 0 -20$700

5 0 0 0 0 0 0

5 0 0 0 0 0 0

5 0 0 -20$700 0 0 20$700

Elemen 2 i = 1 j = %

AE/L

0 0.351123 0.936329 53838.93

1 1 1 9 9 91 53$3% 0 0 -53$3% 0 0

1 0 0 0 0 0 0

1 0 0 0 0 0 0

9 -53$3% 0 0 53$3% 0 0

9 0 0 0 0 0 0

9 0 0 0 0 0 0

1 1 1 9 9 9

1 0 0,3511 0,%3#3 0 0 0

1 0 0 0 0 0 0

1 0 0 0 0 0 0

x9 0 0 0 0 0,3511 0,%3#3

x

x

x

kl.1/

k'

.1/

k'

.1/

x

x

x

Kl.2/

K'

.2/


3/45

9 0 0 0 0 0 0

9 0 0 0 0 0 0

1 1 1 9 9 9

1 0 0 0 0 0 0

1 0 ##37,7 17700 0 -##37,7 -17700

1 0 17700 47201 0 -17700 -47201

9 0 0 0 0 0 0

9 0 -##37,7 -17700 0 ##37,7 17700

9 0 -17700 -47201 0 17700 47201

Elemen 3 i = 2 j = %

AE/L

0 -0.351123 0.936329 53838.93

2 2 2 9 9 9

2 53$3% 0 0 -53$3% 0 0

2 0 0 0 0 0 0

2 0 0 0 0 0 0

9 -53$3% 0 0 53$3% 0 0

9 0 0 0 0 0 0

9 0 0 0 0 0 0

2 2 2 9 9 9

2 0 -0,3511 0,%3#3 0 0 0

2 0 0 0 0 0 0

2 0 0 0 0 0 0

x9 0 0 0 0 -0,3511 0,%3#3

9 0 0 0 0 0 0

9 0 0 0 0 0 0

2 2 2 9 9 9

2 0 0 0 0 0 02 0 ##37,7 -17700 0 -##37,7 17700

2 0 -17700 47201 0 17700 -47201

9 0 0 0 0 0 0

9 0 -##37,7 17700 0 ##37,7 -17700

9 0 17700 -47201 0 -17700 47201

Elemen 4 i = 2 j = #

AE/L

0 0 1 208700

2 2 2 6 6 6

K'

.2/

x

x

x

Kl.3/

K'

.3/

K'

.3/

x

x

x


4/45

2 20$700 0 0 -20$700 0 0

2 0 0 0 0 0 0

2 0 0 0 0 0 0

6 -20$700 0 0 20$700 0 0

6 0 0 0 0 0 0

6 0 0 0 0 0 0

2 2 2 6 6 6

2 0 0 1 0 0 0

2 0 0 0 0 0 0

2 0 0 0 0 0 0

x6 0 0 0 0 0 1

6 0 0 0 0 0 0

6 0 0 0 0 0 0

2 2 2 6 6 62 0 0 0 0 0 0

2 0 0 0 0 0 0

2 0 0 20$700 0 0 -20$700

6 0 0 0 0 0 0

6 0 0 0 0 0 0

6 0 0 -20$700 0 0 20$700

Elemen 5 i = 2 j = 10

AE/L

-0.490261 0 0.871576 50115.59

2 2 2 10 10 10

2 5011# 0 0 -5011# 0 0

2 0 0 0 0 0 0

2 0 0 0 0 0 0

10 -5011# 0 0 5011# 0 0

10 0 0 0 0 0 0

10 0 0 0 0 0 0

2 2 2 10 10 10

2 -0,4%03 0 0,$71# 0 0 0

2 0 0 0 0 0 0

2 0 0 0 0 0 0

x10 0 0 0 -0,4%03 0 0,$71#

10 0 0 0 0 0 0

10 0 0 0 0 0 0

2 2 2 10 10 10

2 1204# 0 -21414 -1204# 0 21414

Kl.4/

K'

.4/

K'

.4/

x

x

x

Kl.5/

K'

.5/


5/45

2 0 0 0 0 0 0

2 -21414 0 3$070 21414 0 -3$070

10 -1204# 0 21414 1204# 0 -21414

10 0 0 0 0 0 0

10 21414 0 -3$070 -21414 0 3$070

Elemen 6 i = 3 j = 10

AE/L

0.490261 0 0.871576 50115.59

3 3 3 10 10 10

3 5011# 0 0 -5011# 0 0

3 0 0 0 0 0 0

3 0 0 0 0 0 0

10 -5011# 0 0 5011# 0 010 0 0 0 0 0 0

10 0 0 0 0 0 0

3 3 3 10 10 10

3 0,4%03 0 0,$71# 0 0 0

3 0 0 0 0 0 0

3 0 0 0 0 0 0

x10 0 0 0 0,4%03 0 0,$71#

10 0 0 0 0 0 0

10 0 0 0 0 0 0

3 3 3 10 10 10

3 1204# 0 21414 -1204# 0 -21414

3 0 0 0 0 0 0

3 21414 0 3$070 -21414 0 -3$070

10 -1204# 0 -21414 1204# 0 21414

10 0 0 0 0 0 0

10 -21414 0 -3$070 21414 0 3$070

Elemen 7 i = 3 j = 7

AE/L

0 0 1 208700

3 3 3 7 7 7

3 20$700 0 0 -20$700 0 0

3 0 0 0 0 0 0

3 0 0 0 0 0 0

7 -20$700 0 0 20$700 0 0

7 0 0 0 0 0 0

K'

.5/

x

x

x

Kl.#/

K'

.#/

K'

.#/

x

x

x

Kl.7/


6/45

7 0 0 0 0 0 0

3 3 3 7 7 7

3 0 0 1 0 0 0

3 0 0 0 0 0 0

3 0 0 0 0 0 0 x7 0 0 0 0 0 1

7 0 0 0 0 0 0

7 0 0 0 0 0 0

3 3 3 7 7 7

3 0 0 0 0 0 0

3 0 0 0 0 0 0

3 0 0 20$700 0 0 -20$700

7 0 0 0 0 0 0

7 0 0 0 0 0 07 0 0 -20$700 0 0 20$700

Elemen 8 i = 3 j = 11

AE/L

0 -0.351123 0.936329 53838.93

3 3 3 11 11 11

3 53$3% 0 0 -53$3% 0 0

3 0 0 0 0 0 0

3 0 0 0 0 0 0

11 -53$3% 0 0 53$3% 0 0

11 0 0 0 0 0 0

11 0 0 0 0 0 0

3 3 3 11 11 11

3 0 -0,3511 0,%3#3 0 0 0

3 0 0 0 0 0 0

3 0 0 0 0 0 0

x11 0 0 0 0 -0,3511 0,%3#3

11 0 0 0 0 0 0

11 0 0 0 0 0 0

3 3 3 11 11 11

3 0 0 0 0 0 0

3 0 ##37,7 -17700 0 -##37,7 17700

3 0 -17700 47201 0 17700 -47201

11 0 0 0 0 0 0

11 0 -##37,7 17700 0 ##37,7 -17700

11 0 17700 -47201 0 -17700 47201

K'.7/

K'

.7/

x

x

x

Kl.$/

K'

.$/

K'.$/


7/45

ral *ti6n** Matrix

1 2

1

1

1204# 0 -21414 0 0 0 0

1 0 ##37,7 17700 0 0 0 0H1 -21414 17700 2%3%71 0 0 0 0

2

2

0 0 0 1204# 0 -21414 0

2 0 0 0 0 ##37,7 -17700 0

H2 0 0 0 -21414 -17700 2%3%71 0

3

3

0 0 0 0 0 0 1204#

3 0 0 0 0 0 0 0

H3 0 0 0 0 0 0 21414

4

4

0 0 0 0 0 0 0

4 0 0 0 0 0 0 0

H4 0 0 0 0 0 0 0

5 05

0 0 0 0 0 0 05 2700 0 0 0 0 0 0 0

H5 -4500 0 0 -20$700 0 0 0 0

# 1350

6

0 0 0 0 0 0 0

# 0 0 0 0 0 0 0 0

H# -4500 0 0 0 0 0 -20$700 0

7 1350

7

0 0 0 0 0 0 0

7 0 0 0 0 0 0 0 0

H7 -4500 0 0 0 0 0 0 0

$ 1350

8

0 0 0 0 0 0 0

$ 0 0 0 0 0 0 0 0

H$ -4500 0 0 0 0 0 0 0

% 0

9

0 0 0 0 0 0 0

% 0 0 -##37,7 -17700 0 -##37,7 17700 0

H% 0 0 -17700 -47201 0 17700 -47201 0

10 0

10

0 0 0 -1204# 0 21414 -1204#

10 0 0 0 0 0 0 0 0

H10 0 0 0 0 21414 0 -3$070 -21414

11 0

11

0 0 0 0 0 0 0

11 0 0 0 0 0 0 0 0

H11 0 0 0 0 0 0 0 0

12 012

-1204# 0 21414 0 0 0 012 0 0 0 0 0 0 0 0

H12 0 21414 0 -3$070 0 0 0 0

8arran'mnt

5 6

5 0

5

371022 0 0 0 0 0 0

5 2700 0 556533 0 0 0 0 0

H5 -4500 0 0 208700 0 0 0 0

# 1350

6

0 0 0 371022 0 0 0

# 0 0 0 0 0 556533 0 0

H# -4500 0 0 0 0 0 208700 0

7 1350 0 0 0 0 0 0 371022


8/45

7 0 7 0 0 0 0 0 0 0

H7 -4500 0 0 0 0 0 0 0

$ 1350

8

0 0 0 0 0 0 0

$ 0 0 0 0 0 0 0 0

H$ -4500 0 0 0 0 0 0 0

% 0

9

0 0 0 0 0 0 0

% 0 0 -55#533 0 0 -55#533 0 0H% 0 0 0 0 0 0 0 0

10 0

10

0 0 0 -371022 0 0 -371022

10 0 0 0 0 0 0 0 0

H10 0 0 0 0 0 0 0 0

11 0

11

0 0 0 0 0 0 0

11 0 0 0 0 0 0 0 0

H11 0 0 0 0 0 0 0 0

12 0

12

-371022 0 0 0 0 0 0

12 0 0 0 0 0 0 0 0

H12 0 0 0 0 0 0 0 0

11

0 0 0 0 0 0 01 0 0 0 0 0 0 0

H1 0 0 -20$700 0 0 0 0

2

2

0 0 0 0 0 0 0

2 0 0 0 0 0 0 0

H2 0 0 0 0 0 -20$700 0

3

3

0 0 0 0 0 0 0

3 0 0 0 0 0 0 0

H3 0 0 0 0 0 0 0

4

4

0 0 0 0 0 0 0

4 0 0 0 0 0 0 0

H4 0 0 0 0 0 0 0

5 6

95 #VALUE! 3.4E-005 1.2E-005 0 1.0E-005 1.2E-005 0 1.0E-005

:5 #VALUE! 1.2E-005 6.2E-005 0 -1E-005 6.0E-005 0 -1E-005

;5 #VALUE! 0 0 4.8E-006 0 0 0 0

9# #VALUE! 1.0E-005 -1E-005 0 3.4E-005 -1E-005 0 3.1E-005

:# #VALUE! 1.2E-005 6.0E-005 0 -1E-005 6.2E-005 0 -1E-005

;# #VALUE! 0 0 0 0 0 4.8E-006 0

97 #VALUE! 1.0E-005 -1E-005 0 3.1E-005 -1E-005 0 3.4E-005:7 #VALUE! -1E-005 1.5E-005 0 1.2E-005 1.5E-005 0 1.2E-005

;7 #VALUE! 0 0 0 0 0 0 0

9$ #VALUE! 3.1E-005 1.2E-005 0 1.0E-005 1.2E-005 0 1.0E-005

:$ #VALUE! -1E-005 1.5E-005 0 1.2E-005 1.5E-005 0 1.2E-005

;$ #VALUE! 0 0 0 0 0 0 0

9% #VALUE! 4.7E-005 1.1E-005 0 4.2E-005 1.1E-005 0 4.2E-005

:% #VALUE! 1.2E-005 6.0E-005 0 -1E-005 6.0E-005 0 -1E-005

;% #VALUE! 0 0 0 0 0 0 0

910 #VALUE! 1.0E-005 -1E-005 0 3.1E-005 -1E-005 0 3.1E-005

:10 #VALUE! -4E-005 2.2E-005 0 -3E-005 2.2E-005 0 -3E-005

;10 #VALUE! 0 0 0 0 0 0 0

911 #VALUE! -5E-006 -1E-005 0 -6E-007 -1E-005 0 -6E-007

:11 #VALUE! -1E-005 1.5E-005 0 1.2E-005 1.5E-005 0 1.2E-005


9/45

;11 #VALUE! 0 0 0 0 0 0 0

912 #VALUE! 3.1E-005 1.2E-005 0 1.0E-005 1.2E-005 0 1.0E-005

:12 #VALUE! 3.9E-005 5.4E-005 0 3.2E-005 5.4E-005 0 3.2E-005

;12 #VALUE! 0 0 0 0 0 0 0


10/45

0,%7#4

0,%##4

aya

Py .N/ Pz .N/

2700 -4500

-4500

-4500

-4500

Elemen 9 i = 4 j = 11


11/45

AE/L

0 0.351123 0.936329 53838.93

4 4 4 11 11

4 53$3% 0 0 -53$3% 04 0 0 0 0 0

4 0 0 0 0 0

11 -53$3% 0 0 53$3% 0

11 0 0 0 0 0

11 0 0 0 0 0

4 4 4 11 11

4 0 0,3511 0,%3#3 0 0

4 0 0 0 0 0

20$700 4 0 0 0 0 011 0 0 0 0 0,3511

11 0 0 0 0 0

11 0 0 0 0 0

4 4 4 11 11

4 0 0 0 0 0

4 0 ##37,7 17700 0 -##37,7

4 0 17700 47201 0 -17700

11 0 0 0 0 0

11 0 -##37,7 -17700 0 ##37,7

11 0 -17700 -47201 0 17700

Elemen 10 i = 4 j = $

AE/L

0 0 1 208700

4 4 4 8 84 20$700 0 0 -20$700 0

4 0 0 0 0 0

4 0 0 0 0 0

8 -20$700 0 0 20$700 0

8 0 0 0 0 0

8 0 0 0 0 0

4 4 4 8 8

4 0 0 1 0 0

4 0 0 0 0 0

53$3% 4 0 0 0 0 0

8 0 0 0 0 0

x

x

x

Kl.%/

K'

.%/

K'

.%/

x

x

x

Kl.10/

K'

.10/


12/45

8 0 0 0 0 0

8 0 0 0 0 0

4 4 4 8 8

4 0 0 0 0 0

4 0 0 0 0 0

4 0 0 20$700 0 0

8 0 0 0 0 0

8 0 0 0 0 0

8 0 0 -20$700 0 0

Elemen 11 i = 4 j = 12

AE/L

0.490261 0 0.871576 50115.59

4 4 4 12 12

4 5011# 0 0 -5011# 0

4 0 0 0 0 0

4 0 0 0 0 0

12 -5011# 0 0 5011# 0

12 0 0 0 0 0

12 0 0 0 0 0

4 4 4 12 12

4 0,4%03 0 0,$71# 0 0

4 0 0 0 0 0

53$3% 4 0 0 0 0 0

12 0 0 0 0,4%03 0

12 0 0 0 0 0

12 0 0 0 0 0

4 4 4 12 12

4 1204# 0 21414 -1204# 04 0 0 0 0 0

4 21414 0 3$070 -21414 0

12 -1204# 0 -21414 1204# 0

12 0 0 0 0 0

12 -21414 0 -3$070 21414 0

Elemen 12 i = 1 j = 12

AE/L

-0.490261 0 0.871576 50115.59

1 1 1 12 12

K'

.10/

x

x

x

Kl.11/

K'

.11/

K'

.11/

x

x

x


13/45

1 5011# 0 0 -5011# 0

1 0 0 0 0 0

1 0 0 0 0 0

12 -5011# 0 0 5011# 0

12 0 0 0 0 0

12 0 0 0 0 0

1 1 1 12 12

1 -0,4%03 0 0,$71# 0 0

1 0 0 0 0 0

20$700 1 0 0 0 0 0

12 0 0 0 -0,4%03 0

12 0 0 0 0 0

12 0 0 0 0 0

1 1 1 12 121 1204# 0 -21414 -1204# 0

1 0 0 0 0 0

1 -21414 0 3$070 21414 0

12 -1204# 0 21414 1204# 0

12 0 0 0 0 0

12 21414 0 -3$070 -21414 0

Elemen 13 i = 5 j = %

AE/L

0 1 0 556533.3

5 5 5 9 9

5 55#533 0 0 -55#533 0

5 0 0 0 0 0

5 0 0 0 0 0

9 -55#533 0 0 55#533 0

9 0 0 0 0 0

9 0 0 0 0 0

5 5 5 9 9

5 0 1 0 0 0

5 0 0 0 0 0

5011# 5 0 0 0 0 0

9 0 0 0 0 1

9 0 0 0 0 0

9 0 0 0 0 0

5 5 5 9 9

5 0 0 0 0 0

Kl.12/

K'

.12/

K'

.12/

x

x

x

Kl.13/

K'

.13/


14/45

5 0 55#533 0 0 -55#533

5 0 0 0 0 0

9 0 0 0 0 0

9 0 -55#533 0 0 55#533

9 0 0 0 0 0

Elemen 14 i = # j = %

AE/L

0 -1 0 556533.3

6 6 6 9 9

6 55#533 0 0 -55#533 0

6 0 0 0 0 0

6 0 0 0 0 0

9 -55#533 0 0 55#533 09 0 0 0 0 0

9 0 0 0 0 0

6 6 6 9 9

6 0 -1 0 0 0

6 0 0 0 0 0

5011# 6 0 0 0 0 0

9 0 0 0 0 -1

9 0 0 0 0 0

9 0 0 0 0 0

6 6 6 9 9

6 0 0 0 0 0

6 0 55#533 0 0 -55#533

6 0 0 0 0 0

9 0 0 0 0 0

9 0 -55#533 0 0 55#533

9 0 0 0 0 0

Elemen 15 i = # j = 10

AE/L

-1 0 0 371022.2

6 6 6 10 10

6 371022 0 0 -371022 0

6 0 0 0 0 0

6 0 0 0 0 0

10 -371022 0 0 371022 0

10 0 0 0 0 0

K'

.13/

x

x

x

Kl.14/

K'

.14/

K'

.14/

x

x

x

Kl.15/


15/45

10 0 0 0 0 0

6 6 6 10 10

6 -1 0 0 0 0

6 0 0 0 0 0

20$700 6 0 0 0 0 010 0 0 0 -1 0

10 0 0 0 0 0

10 0 0 0 0 0

6 6 6 10 10

6 371022 0 0 -371022 0

6 0 0 0 0 0

6 0 0 0 0 0

10 -371022 0 0 371022 0

10 0 0 0 0 010 0 0 0 0 0

Elemen 16 i = 7 j = 10

AE/L

1 0 0 371022.2

7 7 7 10 10

7 371022 0 0 -371022 0

7 0 0 0 0 0

7 0 0 0 0 0

10 -371022 0 0 371022 0

10 0 0 0 0 0

10 0 0 0 0 0

7 7 7 10 10

7 1 0 0 0 0

7 0 0 0 0 0

53$3% 7 0 0 0 0 0

10 0 0 0 1 0

10 0 0 0 0 0

10 0 0 0 0 0

7 7 7 10 10

7 371022 0 0 -371022 0

7 0 0 0 0 0

7 0 0 0 0 0

10 -371022 0 0 371022 0

10 0 0 0 0 0

10 0 0 0 0 0

K'.15/

K'

.15/

x

x

x

Kl.1#/

K'

.1#/

K'.1#/


16/45

3 4 5 6

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 -20$700 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 21414 0 0 0 0 0 0 0 0

##37,7 -17700 0 0 0 0 0 0 0 0

-17700 2%3%71 0 0 0 0 0 0 0 0

0 0 1204# 0 21414 0 0 0 0 0

0 0 0 ##37,7 17700 0 0 0 0 0

0 0 21414 17700 2%3%71 0 0 0 0 0

0 0 0 0 0 371022 0 0 0 00 0 0 0 0 0 55#533 0 0 0

0 0 0 0 0 0 0 20$700 0 0

0 0 0 0 0 0 0 0 371022 0

0 0 0 0 0 0 0 0 0 55#533

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 -20$700 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 -20$700 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 -55#533 0 0 -55#533

0 0 0 0 0 0 0 0 0 0

0 -21414 0 0 0 0 0 0 -371022 0

0 0 0 0 0 0 0 0 0 0

0 -3$070 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

-##37,7 17700 0 -##37,7 -17700 0 0 0 0 0

17700 -47201 0 -17700 -47201 0 0 0 0 0

0 0 -1204# 0 -21414 -371022 0 0 0 00 0 0 0 0 0 0 0 0 0

0 0 -21414 0 -3$070 0 0 0 0 0

7 8 9 10

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 -55#533 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 -371022 0

0 0 0 0 0 0 -55#533 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 -371022 0


17/45

556533 0 0 0 0 0 0 0 0 0

0 208700 0 0 0 0 0 0 0 0

0 0 371022 0 0 0 0 0 0 0

0 0 0 556533 0 0 0 0 0 0

0 0 0 0 208700 0 0 0 0 0

0 0 0 0 0 117767 0 0 -5$$$4 3%25#

0 0 0 0 0 0 ### 0 3%25# -2#1700 0 0 0 0 0 0 94403 0 0

0 0 0 0 0 -5$$$4 3%25# 0 883903 0

0 0 0 0 0 3%25# -2#170 0 0 52341

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 -5$$$4 -3%25#

-55#533 0 0 -55#533 0 0 0 0 -3%25# -2#170

0 0 0 0 0 0 0 0 0 0

0 0 -371022 0 0 -5$$$4 -3%25# 0 0 0

0 0 0 0 0 -3%25# -2#170 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 -##37,7 -17700 0 0

0 0 0 0 0 0 -17700 -47201 0 0

0 0 0 0 0 0 0 0 -1204# 0

0 0 0 0 0 0 -##37,7 17700 0 0

0 0 0 0 0 0 17700 -47201 21414 0

0 0 0 0 0 0 0 0 -1204# 0

0 0 0 0 0 0 0 0 0 0

0 -20$700 0 0 0 0 0 0 -21414 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 -20$700 0 0 0 0 0

7 8 9 10

-1E-005 0 3.1E-005 -1E-005 0 -2E-005 1.2E-005 0 1.0E-005 6.2E-005

1.5E-005 0 1.2E-005 1.5E-005 0 -4E-005 6.0E-005 0 -1E-005 0.00013

0 0 0 0 0 0 0 0 0 0

1.2E-005 0 1.0E-005 1.2E-005 0 -5E-006 -1E-005 0 3.1E-005 9.8E-006

1.5E-005 0 1.2E-005 1.5E-005 0 -4E-005 6.0E-005 0 -1E-005 0.00013

0 0 0 0 0 0 0 0 0 0

1.2E-005 0 1.0E-005 1.2E-005 0 -5E-006 -1E-005 0 3.1E-005 9.8E-006

6.2E-005 0 -1E-005 6.0E-005 0 -8E-006 1.5E-005 0 1.2E-005 5.0E-005

0 4.8E-006 0 0 0 0 0 0 0 0

-1E-005 0 3.4E-005 -1E-005 0 -2E-005 1.2E-005 0 1.0E-005 6.2E-005

6.0E-005 0 -1E-005 6.2E-005 0 -8E-006 1.5E-005 0 1.2E-005 5.0E-005

0 0 0 0 4.8E-006 0 0 0 0 0

1.5E-005 0 4.7E-005 1.5E-005 0 6.1E+010 1.1E-005 0 4.2E-005 -9E+010

1.5E-005 0 1.2E-005 1.5E-005 0 -4E-005 6.0E-005 0 -1E-005 0.00013

0 0 0 0 0 0 0 1.1E-005 0 0

1.2E-005 0 1.0E-005 1.2E-005 0 -5E-006 -1E-005 0 3.1E-005 9.8E-006

1.5E-005 0 -4E-005 1.5E-005 0 -9E+010 2.2E-005 0 -3E-005 1.4E+011

0 0 0 0 0 0 0 0 0 0

-2E-005 0 -5E-006 -2E-005 0 -6E+010 -1E-005 0 -6E-007 9.2E+010

6.0E-005 0 -1E-005 6.0E-005 0 -8E-006 1.5E-005 0 1.2E-005 5.0E-005


18/45

0 0 0 0 0 0 0 0 0 0

-1E-005 0 3.1E-005 -1E-005 0 -2E-005 1.2E-005 0 1.0E-005 6.2E-005

6.1E-005 0 3.9E-005 6.1E-005 0 9.2E+010 5.4E-005 0 3.2E-005 -1E+011

0 0 0 0 0 0 0 0 0 0


19/45

Elemen 1 7 i = 7 j = 11


20/45

AE/L

0 -1 0 556533.3

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0 7 55#533 0 00 7 0 0 0

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Elemen 18 i = $ j = 11

AE/L

0 1 0 556533.3

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21/45

0 11 0 0 0

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0 8 0 0 0

0 8 0 55#533 0-20$700

8 0 0 0

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20$700 11 0 0 0

Elemen 19 i = $ j = 12

AE/L

1 0 0 371022.2

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Elemen 20 i = 5 j = 12

AE/L

-1 0 0 371022.2

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22/45

0 5 371022 0 0

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Elemen 21 i = % j = 12

AE/L

-0.83205 -0.5547 0 85054.03

9 9 9 9

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23/45

0 9 3%25# 2#170 0

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0 12 -3%25# -2#170 0

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Elemen 22 i = % j = 10

AE/L

-0.83205 0.5547 0 85054.03

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0 9 $5054 0 0

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0 10 3%25# -2#170 0

0 10 0 0 0

Elemen 23 i = 10 j = 11

AE/L

-0.83205 -0.5547 0 85054.03

10 10 10 10

0 10 $5054 0 0

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24/45

0 11 0 0 0

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0 10 3%25# 2#170 0

0

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0 11 -5$$$4 -3%25# 0

0 11 -3%25# -2#170 00 11 0 0 0

Elemen 24 i = 11 j = 12

AE/L

0.83205 -0.5547 0 85054.03

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0 11 $5054 0 0

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0 12 0 0 0

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0 11 -3%25# 2#170 0

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25/45

7 8 9

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 -##37,7 -177000 0 0 0 0 0 0 0 -17700 -47201

0 0 0 0 0 0 0 0 0 0

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-20$700 0 0 0 0 0 0 0 17700 -47201

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 -20$700 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 -20$700 0 0 0

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 -55#533 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 -55#533 0

20$700 0 0 0 0 0 0 0 0 0

0 371022 0 0 0 0 0 0 0 0

0 0 55#533 0 0 0 0 0 0 0

0 0 0 20$700 0 0 0 0 0 0

0 0 0 0 371022 0 0 0 0 0

0 0 0 0 0 55#533 0 0 0 0

0 0 0 0 0 0 20$700 0 0 0

0 0 0 0 0 0 0 1177#7 0 0

0 0 0 0 0 0 0 0 1E


26/45

0 0 -55#533 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 -371022 0 0 0 0 0

0 0 -55#533 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 -5$$$4 -3%25# 0 0 0 0

0 0 0 0 -3%25# -2#170 0 0 -##37,7 -177000 0 0 0 0 0 0 0 -17700 -47201

0 -5$$$4 -3%25# 0 0 0 0 0 0 0

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0 0 ### 0 3%25# -2#170 0 0 0 0

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0 3%25# -2#170 0 0 52341 0 0 0 0

0 0 0 0 0 0 76140 21414 0 -3$070

0 0 0 0 -1204# 0 21414 12046 0 -214140 0 0 0 0 0 0 0 6637,7 17700

0 0 0 0 21414 0 -3$070 -21414 17700 293971

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0 0 0 0 -1204# 0 -21414 0 0 0

0 0 -##37,7 -17700 0 0 0 0 0 0

0 0 -17700 -47201 -21414 0 -3$070 0 0 0

11 12

0 6.2E-005 -1E-005 0 3.1E-005 -6E-005 0

0 6.1E-005 1.5E-005 0 1.2E-005 -8E-006 0

0 0 0 0 0 0 0

0 2.9E-005 1.2E-005 0 1.0E-005 -4E-005 0

0 6.1E-005 1.5E-005 0 1.2E-005 -8E-006 0

0 0 0 0 0 0 0

0 2.9E-005 1.2E-005 0 1.0E-005 -4E-005 0

0 8.5E-006 6.0E-005 0 -1E-005 2.5E-005 0

0 0 0 0 0 0 0

0 6.2E-005 -1E-005 0 3.1E-005 -6E-005 0

0 8.5E-006 6.0E-005 0 -1E-005 2.5E-005 0

0 0 0 0 0 0 0

0 -6E+010 1.5E-005 0 4.7E-005 9.2E+010 0

0 6.1E-005 1.5E-005 0 1.2E-005 -8E-006 0

0 0 0 0 0 0 0

0 2.9E-005 1.2E-005 0 1.0E-005 -4E-005 0

0 9.2E+010 1.5E-005 0 -4E-005 -1E+011 0

1.3E-005 0 0 0 0 0 0

0 6.1E+010 -2E-005 0 -5E-006 -9E+010 0

0 8.5E-006 6.0E-005 0 -1E-005 2.5E-005 0


27/45

0 0 0 1.1E-005 0 0 0

0 6.2E-005 -1E-005 0 3.1E-005 -6E-005 0

0 -9E+010 6.1E-005 0 3.9E-005 1.4E+011 0

0 0 0 0 0 0 1.3E-005


28/45


29/45

11 11 11

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30/45

0 0 0

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31/45

-371022 0 0

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32/45

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33/45

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34/45

10 11 12

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35/45

0 0 0 0 0 0 0 0 0

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36/45


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43/45

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44/45

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45/45

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