hhawhr

7/23/2019 hhawhr

http://slidepdf.com/reader/full/hhawhr 1/26

TITIK KOORDINAT E = 200 GPa 200000000

X Z G = 76 GPa 76000000

1 0 0 I = 347*10^6 0.000347

2 8 0 J = 115*10^6 0.000115

3 0 6

4 8 6

Panjang Batang, dan Nilai Fungsi Cosinus dari Sudut yang Terbentuk

BATANG Tii! " #$% &' %i( &) E I' Z

1 1 0 0

10 0.8 0.6 200000000 0.0003474 8 6

2 2 8 0 6 0 1 200000000 0.0003474 8 6

3 3 0 6

8 1 0 200000000 0.0003474 8 6

!N+,

!N+,

++- +-

++- +-

Z

20 kN/m

Grid NAMA : WA NIM : 0903

x

Y

20 kN/m

6 m

8 m

E,G,I, ! "#$%&'$&

E ! 200 G('

G ! )6 G('

I ! 3*)+106.mm4

! 115+10 6.mm4

Grid

Z

20 kN/m

x

Y

21

3

12

3 4

13

2

4

6

5

79

8

1012

11

ERI10

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Z

20 kN/m

21

33 4

13

2

9

1012

11

A$'-&i"' M#d.

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6.4 12.5366

321.263 4.5337176

135.54688 8.05424

EI"3 GJ"2EI

NAMA : WATSIIQAH NIM : 0903120655

x

I, ! "#$%&'$&

200 G('

)6 G('

*)+106.mm4

15+10 6.mm4

x

/O/TI3120014

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Baa( I

1 0 0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 1 0 0

0 0 0 0 "#%/ %i$/

0 0 0 0

1 0 0 0 0 0

0 08 06 0 0 0

0 06 08 0 0 0

0 0 0 1 0 0

0 0 0 0 08 06

0 0 0 0 06 08

1 0 0 0 0 0

0 08 06 0 0 0

0 06 08 0 0 0

0 0 0 1 0 0

0 0 0 0 08 06

0 0 0 0 06 08

Matrix Kekakuan Elemen dalam Sistem Koordinat Lokal

k !

12 0 6" 12 0 6"

0 0 0 0

E" 6" 0 6" 0

12 0 6" 12 0 6"

0 0 0 0

6" 0 6" 0

k ! 6.4

12 0 60 12 0 600 12.5366 0 0 12.5366 0

60 0 400 60 0 200

12 0 60 12 0 60

0 12.5366 0 0 12.5366 0

60 0 200 60 0 400

k !

832.8 0 4164 832.8 0 4164

0 874 0 0 874 0

4164 0 27760 4164 0 13880

832.8 0 4164 832.8 0 41640 874 0 0 874 0

4164 0 13880 4164 0 27760

T₁ !

"#%& %i$&

%i$& "#%&

%i$& "#%&

T₁ !

TT !

GJ"2EI GJ"2EI

4"2 2"2

L#

GJ"2EI GJ"2EI

2"2 4"2

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Matrix Kekakuan Elemen dalam Koordinat $lobal

K !

1 0 0 0 0 0 832.8

0 0.8 0.6 0 0 0 0

0 0.6 0.8 0 0 0 ' 4164

0 0 0 1 0 0 832.8

0 0 0 0 0.8 0.6 0

0 0 0 0 0.6 0.8 4164

%K& ! %T

T

&%k&%T&

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K !

832.8 0 4164 832.8 0 4164 1

248.4 6.2 16656 248.4 6.2 8328 0

3331.2 524.4 22208 3331.2 524.4 11104 ' 0

832.8 0 4164 832.8 0 4164 0

248.4 6.2 8328 248.4 6.2 16656 0

3331.2 524.4 11104 3331.2 524.4 22208 0

K !

4 5 6 1 2 3

832.8 248.4 3331.2 832.8 248.4 3331.2 4

248.4 10552.6 1205.28 248.4 4437.44 7081.2 5

3331.2 1205.28 18081.04 3331.2 7081.2 8568.56 6

832.8 248.4 3331.2 832.8 248.4 3331.2 1

248.4 4437.44 7081.2 248.4 10552.6 1205.28 2

3331.2 7081.2 8568.56 3331.2 1205.28 18081.04 3

%= % = 2 = 0 !N

= + = 0 !N+

0

0

0

0

0

0

0 4

0 5

0 6

0 1

0 2

0 3

BATANG 2

1 0 0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 1 0 0

0 0 0 0 "#%/ %i$/

0 0 0 0

1 0 0 0 0 0

212 =

9: ; =

: = T T. 9

:

: ;=

T2 !

"#%& %i$&

%i$& "#%&

%i$& "#%&

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0 0 1 0 0 0

0 1 0 0 0 0

0 0 0 1 0 0

0 0 0 0 0 1

0 0 0 0 1 0

1 0 0 0 0 0

0 0 1 0 0 0

0 1 0 0 0 0

0 0 0 1 0 0

0 0 0 0 0 1

0 0 0 0 1 0

T2 !

T2

T !

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12 0 6" 12 0 6"

0 0 0 0E" 6" 0 6" 0

12 0 6" 12 0 6"

0 0 0 0

6" 0 6" 0

' 321.263

12 0 36 12 0 36

0 4.533718 0 0 4.533718 0

36 0 144 36 0 72

12 0 36 12 0 36

0 4.533718 0 0 4.5337176 0

36 0 72 36 144

'

3855.556 0 11566.67 3855.556 0 11566.667

0 1456.667 0 0 1456.667 0

11566.67 0 46266.67 11566.67 0 23133.333

3855.56 0 11566.67 3855.556 0 11566.67

0 1456.667 0 0 1456.667 0

11566.67 0 23133.33 11566.67 <A">E? 46266.667


'

1 0 0 0 0 0 3855.556

0 0 1 0 0 0 0

0 1 0 0 0 0 ' 11566.67

0 0 0 1 0 0 3855.556

0 0 0 0 0 1 0

0 0 0 0 1 0 11566.67

'

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 1

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? ' 0

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0

7 8 1 2 3

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 7<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 8

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E?

'

GJ"

2

EI GJ"

2

EI4"2 2"2

L#

GJ"2EI GJ"2EI

2"2 4"2

%TT&%k&%T&

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'<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 1

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 2

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 3

% 2 = 60 !N

60 !N+

60

0

60

60

0

60

212 =

9: 2 =

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60 7

60 8

0 60 1

60 2

0 3

B(T(N$ #

1 0 0 0 0 0

0 0 0 0

0 0 0 00 0 0 1 0 0

0 0 0 0 "#%/ %i$/

0 0 0 0

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1


12 0 6" 12 0 6"

0 0 0 0

E" 6" 0 6" 0

12 0 6" 12 0 6"

0 0 0 0

6" 0 6" 0

12 0 48 12 0 48

0 8 0542 0 0 8 0542 0

F* ! TT+

*

:2 =

"#%& %i$&

T) ! %i$& "#%&

%i$& "#%&

T ₃!

T ₃

T !

)

GJ"2EI GJ"2EI

4"2 2"2

L#

GJ"2EI GJ"2EI

2"2 4"2

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) 135.546 48 0 256 48 0 128

12 0 48 12 0 48

0 8.0542 0 0 8.05424 0

48 0 128 48 256

)

1626.6 0 6506.25 1626.563 0 6506.25

0 102.5 0 0 102.5 0

6506.3 0 34700 6506.25 0 17350

1626.56 0 6506.25 1626.563 0 6506.25

0 102.5 0 0 102.5 0

6506.25 0 17350 6506.25<A">E? 34700

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)

1 0 0 0 0 0 1626.5630 1 0 0 0 0 0

0 0 1 0 0 0 ' 6506.25

0 0 0 1 0 0 1626.563

0 0 0 0 1 0 0

0 0 0 0 0 1 6506.25

)

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 1

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? ' 0

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0

10 11 12 1 2 3

)

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 10

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 11

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 12

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 1

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 2

<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 3

%= % = 2 = 80 !N

= += 106.6667 !N+

80 10

0 11

106.6667 12

80 1

0 2

106.6667 3

%K& ! %TT&%k&%T&

212 =

:3 =9:3

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0 4164 832.8 0 4164

874 0 0 874 0

0 27760 4164 0 13880

0 4164 832.8 0 4164

874 0 0 874 0

0 13880 4164 0 27760

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0 0 0 0 0

0.8 0.6 0 0 0

0.6 0.8 0 0 0

0 0 1 0 0

0 0 0 0.8 0.6

0 0 0 0.6 0.8

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0 11566.67 3855.556 0 11566.67

1456.667 0 0 1456.667 0

0 46266.67 11566.67 0 23133.33

0 11566.67 3855.556 0 11566.67

1456.667 0 0 1456.667 0

0 23133.33 11566.67 <A">E? 46266.67

0 0 0 0 0

0 1 0 0 0

1 0 0 0 0

0 0 1 0 0

0 0 0 0 1

0 0 0 1 0

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0 6506.25 1626.563 0 6506.25102.5 0 0 102.5 0

0 34700 6506.25 0 17350

0 6506.25 1626.563 0 6506.25

102.5 0 0 102.5 0

0 17350 6506.25 <A">E? 34700

0 0 0 0 0

1 0 0 0 0

0 1 0 0 0

0 0 1 0 00 0 0 1 0

0 0 0 0 1

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ATRIK KEKAK>AN /TR>KT>R

Baa( 1

1 2 3

S1 !

832.8 248.4 3331.21

248.4 10552.6 1205.28 23331.2 1205.28 18081.043

Baa( 2

1 2 3

S2 !

<A">E? <A">E? <A">E?1

<A">E? <A">E? <A">E?2

<A">E? <A">E? <A">E?3

Baa( 3

1 2 3

S3 !

<A">E? <A">E? <A">E?1

<A">E? <A">E? <A">E?2

<A">E? <A">E? <A">E?3

GAB>NGAN ATRIK/ KEKAK>AN

1 2 3 1 2

S !

<A">E? <A">E? <A">E? 1 <A">E? <A">E?

<A">E? <A">E? <A">E? 2 <A">E? <A">E?

<A">E? <A">E? <A">E? 3 <A">E? <A">E?

!

1401

!

0 1

!

140

60 2 0 2 60

106.666667 3 0 3 106.667

PP: = /@

d !

<A">E? 1

<A">E? 2

<A">E? 3

S1 !

d! S1 + 4

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3

<A">E? 1

<A">E? 2

<A">E? 3

1

2

3

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-E(KS" $(.( B(T(N$

BATANG 1

1 = T1 . 1 91 = !1 . 1

1 =

0 4

>1

<A">E?4

91 =

<A">E?4

1 =

0 5 <A">E? 5 <A">E? 50 6 <A">E? 6 <A">E? 6

<A">E?1 <A">E? 1 <A">E? 1

<A">E?2 <A">E? 2 <A">E? 2

<A">E?3 <A">E? 3 <A">E? 3

BATANG 2

2 = T2 . 2 92 = !2 . >2 9:2

2 =

0 7

2 =

<A">E?7

!2 .>2 =

<A">E?7

92 =

0 8 <A">E? 8 <A">E? 80 <A">E? <A">E?

<A">E?1 <A">E? 1 <A">E? 1

<A">E?2 <A">E? 2 <A">E? 2

<A">E?3 <A">E? 3 <A">E? 3

BATANG 3

92 = !2 . >2 9:2

3 = 3

0 10

!3.3=

<A">E?100 11 <A">E? 11

0 12 <A">E? 12

<A">E?1 <A">E? 1

<A">E?2 <A">E? 2

<A">E?3 <A">E? 3

REAK/I GACA BATANG

= R4R7R10 = 91

R =

<A">E?4 0F0146857144F66845135F31686 = ."

<A">E?5 280= 20'6<A">E?6 280 = 280

<A">E?7

<A">E?8 '= 20 ' 8 = 160

<A">E?

<A">E?10 )= 20 X 6 = 120

<A">E?11

<A">E?12

1 =

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<A">E?4

<A">E?5<A">E?6

<A">E?1

<A">E?2

<A">E?3

<A">E?7

1 =

<A">E?7

<A">E?8 <A">E? 8<A">E? <A">E?

<A">E?1 <A">E? 1

<A">E?2 <A">E? 2

<A">E?3 <A">E? 3

93 = 3 =

<A">E?10<A">E?11

<A">E?12

<A">E?1

<A">E?2

<A">E?3

92

."

20'8

T T1 . 91

1 = T T1 . 91

hhawhr

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