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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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Matrix Kekakuan Elemen dalam Sistem Koordinat Lokal
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
Matrix Kekakuan Elemen dalam Koordinat $lobal
'
1 0 0 0 0 0 3855.556
0 0 1 0 0 0 0
0 1 0 0 0 0 ' 11566.67
0 0 0 1 0 0 3855.556
0 0 0 0 0 1 0
0 0 0 0 1 0 11566.67
'
<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 1
<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0
<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? ' 0
<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0
<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0
<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 0
7 8 1 2 3
<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 7<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 8
<A">E? <A">E? <A">E? <A">E? <A">E? <A">E?
'
GJ"
2
EI GJ"
2
EI4"2 2"2
L#
GJ"2EI GJ"2EI
2"2 4"2
%TT&%k&%T&
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'<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 1
<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 2
<A">E? <A">E? <A">E? <A">E? <A">E? <A">E? 3
% 2 = 60 !N
60 !N+
60
0
60
60
0
60
212 =
9: 2 =
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60 7
60 8
0 60 1
60 2
0 3
B(T(N$ #
1 0 0 0 0 0
0 0 0 0
0 0 0 00 0 0 1 0 0
0 0 0 0 "#%/ %i$/
0 0 0 0
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
Matrix Kekakuan Elemen dalam Sistem Koordinat Lokal
12 0 6" 12 0 6"
0 0 0 0
E" 6" 0 6" 0
12 0 6" 12 0 6"
0 0 0 0
6" 0 6" 0
12 0 48 12 0 48
0 8 0542 0 0 8 0542 0
F* ! TT+
*
:2 =
"#%& %i$&
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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Matrix Kekakuan Elemen dalam Koordinat $lobal
)
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