Statika konstrukcija 2 , programski zadatak

UNIVERZITET U SARAJEVU

GRAĐEVINSKI FAKULTET

INSTITUT ZA KONSTRUKCIJE I MATERIJALE - IMK

STATIKA KONSTRUKCIJA 2

PROGRAMSKI ZADATAK BROJ 2

Predmetni profesor: Prof. Dr. S. Dolarević

Predmetni asistent: dipl.ing. građ. J. Medić

Sarajevo, 1.6.2012. Student: Smiljan Tukić

Zadatak:

7

1 2

5

8

6

3

9 10

4

100 KN

2m 1m

4m

2m

2m

4m 3m

200 KN

I

II III

IV

V VI

VII

VIII IX X

q=10kN/m'

q=20kN/m'

20 kNm

Nepoznati uglovi:

φ1, φ3 , φ5 , φ6 , φ7 , φ8 , φ9−6 , φ9−3 , φ9−10 , φ10

Zglobna šema:

?1 ?1

?2?2?2

?2

SSK=2 ∙ n−( s+c+r )=2 ∙10−(10+8 )=2

u={φ1 , φ3 , φ5 , φ6 , φ7 , φ8 , φ10 , φ9−8 , φ9−10 , φ9−6 ,∆1 ,∆2 }={1,2,3,4,5,6,7,8,9,10,11,12 }

Identifikaciona matrica

ID=| 51120

30110

42110

72110

631211

1041211

3400

5600

6800

9700|

Vektor sila po štapovima

Štap 1 - Nema opterećenje

Štap 2 - Nema opterećenje

Štap 3

6

3

III

q=20kN/m' V(3-6)

M(6-3)

m6−3=−20 ∙ 22

30=−2,666m3−6=20 ∙

22

20=4,0

m6−3=−2,666−0,5 ∙4=−4,666m3−6=0

∑M 3=0V 6−3 ∙2+2 ∙202∙0,6666+4,6666=0

V 6−3 ∙2=−20 ∙0,666+4,666

V 6−3=−4,372V 3−6=−15,62

F3=[−4,6660−4,372−15,62]

Štap 4 - Nema opterećenja




Štap 8

7 8VIII

V(7-8) V(8-7)

200 KN

m7−8=200 ∙2 ∙12

32=44,44

m8−7=−200 ∙ 22 ∙19

=−88,88

∑M 8=0

V 7−8 ∙3−200 ∙1−44,44+88,88=0

V 7−8=200+44,44−88,88

3=51,58

V 8−7=200−51,58=148,14

F8=[ 44,44−88,8851,58148,14

]Štap 9

8 9IX

q=10kN/m'

V(8-9) V(9-8)

m8−9=−10 ∙ 42

12=−13,33m9−8=13,33

m8−9=−13,33−13,332

=−20m9,8=0

V 8−9=−20V 9−8=−20

F9=[−200−20−20 ]

-4,666

2m 1m 4m 3m

-4,666

100 KN

u={φ1φ3φ5φ6φ7φ8φ10φ9−8φ9−10φ9−6∆1∆2

}={123456789101112

} F={000

−4,66644,44

−108,8820000

−4,66−100

} Momenti inercije poprečnih presjeka:

40/40 = 0,002133

40/60 = 0,007200

40/50 = 0,004166

CODE IZ CAL2000 INPUT

slope k1 l=4 i=0.002133 e=30000000

slope k2 l=2 i=0.002133 e=30000000

slope k3 l=2 i=0.002133 e=30000000

slope k4 l=4 i=0.002133 e=30000000

slope k5 l=2 i=0.002133 e=30000000

slope k6 l=2 i=0.002133 e=30000000

slope k7 l=4 i=0.004166 e=30000000

slope k8 l=3 i=0.007200 e=30000000

slope k9 l=4 i=0.007200 e=30000000

slope k10 l=3 i=0.00720 e=30000000

loadi id r=4 c=10

5 3 4 7 6 10 3 5 6 9

1 0 2 0 3 4 4 6 8 7

12 11 11 12 12 12 0 0 0 0

0 0 0 0 11 11 0 0 0 0

zero k r=12 c=12

addk k k1 id n=1

addk k k2 id n=2

addk k k3 id n=3

addk k k4 id n=4

addk k k5 id n=5

addk k k6 id n=6

addk k k7 id n=7

addk k k8 id n=8

addk k k9 id n=9

addk k k10 id n=10

p k

load p r=12 c=1

0

0

0

4.666

-44.44

108.88

-20

0

0

0

4.66

100

solve k p

load p3 r=4 c=1

-4.666

0

-4.372

-15.62

load p8 r=4 c=1

44.44

-88.88

51.58

148.14

load p9 r=4 c=1

-20

0

-20

-20

memfrc k1 p id f1 n=1

p f1


p f2


add f3 p3

p f3


p f4


p f5


p f6


p f7


add f8 p8

p f8


add f9 p9

p f9


p f10

return

CODE IZ CAL2000 OUT

RUN

SLOPE K1 L=4 I=0.002133 E=30000000

SLOPE K2 L=2 I=0.002133 E=30000000

SLOPE K3 L=2 I=0.002133 E=30000000

SLOPE K4 L=4 I=0.002133 E=30000000

SLOPE K5 L=2 I=0.002133 E=30000000

SLOPE K6 L=2 I=0.002133 E=30000000

SLOPE K7 L=4 I=0.004166 E=30000000

SLOPE K8 L=3 I=0.007200 E=30000000

SLOPE K9 L=4 I=0.007200 E=30000000

SLOPE K10 L=3 I=0.00720 E=30000000

LOADI ID R=4 C=10

ARRAY NAME = ID NUMBER OF ROWS = 4 NUMBER OF COLUMNS = 10

ZERO K R=12 C=12

ADDK K K1 ID N=1

ADDK K K2 ID N=2

ADDK K K3 ID N=3

ADDK K K4 ID N=4

ADDK K K5 ID N=5

ADDK K K6 ID N=6

ADDK K K7 ID N=7

ADDK K K8 ID N=8

ADDK K K9 ID N=9

ADDK K K10 ID N=10

P K

COL# = 1 2 3 4 5 6

ROW 1 0.63990E+05 0.00000E+00 0.00000E+00 0.00000E+00 0.31995E+05 0.00000E+00

ROW 2 0.00000E+00 0.12798E+06 0.00000E+00 0.63990E+05 0.00000E+00 0.00000E+00

ROW 3 0.00000E+00 0.00000E+00 0.38094E+06 0.62490E+05 0.00000E+00 0.63990E+05

ROW 4 0.00000E+00 0.63990E+05 0.62490E+05 0.38094E+06 0.00000E+00 0.00000E+00

ROW 5 0.31995E+05 0.00000E+00 0.00000E+00 0.00000E+00 0.35199E+06 0.14400E+06

ROW 6 0.00000E+00 0.00000E+00 0.63990E+05 0.00000E+00 0.14400E+06 0.63198E+06

ROW 7 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00

ROW 8 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.10800E+06

ROW 9 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00

ROW 10 0.00000E+00 0.00000E+00 0.00000E+00 0.63990E+05 0.00000E+00 0.00000E+00

ROW 11 0.00000E+00 0.95985E+05 0.00000E+00 0.00000E+00 0.00000E+00-0.95985E+05

ROW 12 0.23996E+05 0.00000E+00 0.95985E+05 0.95985E+05 0.23996E+05 0.95985E+05

COL# = 7 8 9 10 11 12

ROW 1 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.23996E+05

ROW 2 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.95985E+05 0.00000E+00

ROW 3 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.95985E+05

ROW 4 0.00000E+00 0.00000E+00 0.00000E+00 0.63990E+05 0.00000E+00 0.95985E+05

ROW 5 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.23996E+05

ROW 6 0.00000E+00 0.10800E+06 0.00000E+00 0.00000E+00-0.95985E+05 0.95985E+05

ROW 7 0.35199E+06 0.00000E+00 0.14400E+06 0.00000E+00 0.00000E+00 0.23996E+05

ROW 8 0.00000E+00 0.21600E+06 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00

ROW 9 0.14400E+06 0.00000E+00 0.28800E+06 0.00000E+00 0.00000E+00 0.00000E+00

ROW 10 0.00000E+00 0.00000E+00 0.00000E+00 0.12798E+06-0.95985E+05 0.95985E+05

ROW 11 0.00000E+00 0.00000E+00 0.00000E+00-0.95985E+05 0.38394E+06-0.19197E+06

ROW 12 0.23996E+05 0.00000E+00 0.00000E+00 0.95985E+05-0.19197E+06 0.21597E+06

LOAD P R=12 C=1

ARRAY NAME = P NUMBER OF ROWS = 12 NUMBER OF COLUMNS = 1

SOLVE K P

TOTAL SOLUTION OF Ax = B

LOAD P3 R=4 C=1

ARRAY NAME = P3 NUMBER OF ROWS = 4 NUMBER OF COLUMNS = 1

LOAD P8 R=4 C=1


LOAD P9 R=4 C=1


MEMFRC K1 P ID F1 N=1

P F1

COL# = 1

ROW 1 13.835

ROW 2 0.00000E+00

ROW 3 3.4588

ROW 4 -3.4588


P F2

COL# = 1

ROW 1 44.288

ROW 2 79.857

ROW 3 62.072

ROW 4 -62.072


ADD F3 P3

P F3

COL# = 1

ROW 1 32.265

ROW 2-0.14211E-13

ROW 3 14.094

ROW 4 -34.086


P F4

COL# = 1

ROW 1 37.098

ROW 2 45.556

ROW 3 20.663

ROW 4 -20.663


P F5

COL# = 1

ROW 1 83.511

ROW 2 38.714

ROW 3 61.112

ROW 4 -61.112


P F6

COL# = 1

ROW 1 0.28422E-13

ROW 2 29.531

ROW 3 14.765

ROW 4 -14.765


P F7

COL# = 1

ROW 1 -83.002

ROW 2 -61.796

ROW 3 -36.199

ROW 4 36.199


ADD F8 P8

P F8

COL# = 1

ROW 1 -13.835

ROW 2 -86.871

ROW 3 32.825

ROW 4 166.90


ADD F9 P9

P F9

COL# = 1

ROW 1 3.3601

ROW 2 0.00000E+00

ROW 3 -14.160

ROW 4 -25.840


P F10

COL# = 1

ROW 1 0.71054E-14

ROW 2 -57.098

ROW 3 -19.033

ROW 4 19.033

Štap 1

3,45

3,45

-13,83 3,45

3,45

+

DijagramM

DijagramT

44,288

Štap 2

62,07

62,07

44,288 62,07

DijagramM

DijagramT

44,288

79,85 79,85 62,07

+

+

-

Štap 3

14,09

34,08

32,265 14,09

DijagramM

DijagramT

32,26

34,08

+

-

Štap 4

20,66

20,663

-37,09 20,66

20,66

+

DijagramM

DijagramT

37,09

45,5

+

-

45,5

Štap 5

61,12

61,12

-83,11 61,11

DijagramM

DijagramT

83,11

38,71 38,71 61,11

+

+

-

Štap 6

14,76

14,76

14,76

DijagramM

DijagramT

29,531 29,531 14,76

+

+

Štap 7

8361

DijagramM

DijagramT

-36 36

14,76

M T

14,76

+

83,0 61,00

3636

+

Štap 8

13,83

86,7Dijagram

M

DijagramT

32,82

166,9

200 kN

-

79,84

166,9

+

-

14,76

M T

29,531 14,76

+

+

13,8 86,87

32,825166,90

+

Štap 9

-21

25,84

3,36

14,1625,84

-3,36

0

DijagramM

DijagramT

-14,16

79,84

+

Štap 10

25,84

19,0319,03

DijagramM

DijagramT

-19,03

-57,09

57,09

-19,03

-

25,84

0M

T

79,84

+

M dijagram

13,93

-44,288

79,85

+

--32,265

-

-

+

-37,09

45,5

38,71

-83,11

-

+29,53 +

+

8361

+

-

-86,87

79,48

13,8-21,30

57,09

-

M

T dijagram

3,45

3,45

62,07

62,07

+

+34,08

14,09 +

20,66+

61,11

61,11

14,7

--36 -36

+

-

32,82 32,82

-166,90

-+

125,84

-14,16 -19,03

T

Dijagram N

-

-32,82

-32,82

-

-96 -96

-147

-147

-110

-

40,4

3,9

+

--36 -36 -21

-

-

-19,75

N

Statika konstrukcija 2 , programski zadatak

Documents

Transcript of Statika konstrukcija 2 , programski zadatak