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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
1
Dik: E = 2.10E+06
Mutu baja BJ-34, Profl siku = !.!.
" = 10.10
P#$%#l#saia$:
& Bata$' a
( =
s =
s( =
)a =
)a =
*a = 1.06E+0!
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
1.06E+0! 0 -1.06E+0! 0
0 0 0 0
Suatu ko!t"uk!# "a$ka %a&a !''"t# t'"$a%a" *'$a #+a# o*u+u! '+a!t#!#ta! E , 2-1 . 10/ k$2 D#*#t'tuka !'*#"# %'"*a!a"ka ta%'+ "o3#+ %a&a Ha+ 4a+ a$ %'+u &'+a! *aat *#"'aaka !'*#"# Ko!
6aktu #!t#"a4at *# kau! H#tu$71 8'"#*a4a a*a !'t#a t#t#k !#u+
tuua 9 Gaa a!#
k'(2
(2
1
=
(2 =
s2 =
a % *
&
k
)
L
$
'3 4
#
1 2 9 ;8; , 9000 k$
/
<
=
81 , 1000 k$
82 , ;000 k$
85 , ;000 k$
89 , 2000
a1 2
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
2
-1.06E+0! 0 1.06E+0! 0
0 0 0 0
& Bata$' b
( =
s =
s( =
)b =
)b =
*b = 1.06E+0!
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
*b =
1060!0 0 -1060!0 0
0 0 0 0
-1060!0 0 1060!0 0
0 0 0 0
& Bata$' (
( =
s =
s( =
)( =
)( =
*( = 1.06E+0!
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
*( =
1.06E+0! 0 -1.06E+0! 0
0 0 0 0-1.06E+0! 0 1.06E+0! 0
0 0 0 0
2 =
(2 =
s2 =
3 =
(2 =
s
2
=
%
2 9
9 ;
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
3
& Bata$'
( =
s =
s( =) =
) =
* = 1.06E+0!
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
* =
1.06E+0! 0 -1.06E+0! 0
0 0 0 0
-1.06E+0! 0 1.06E+0! 00 0 0 0
& Bata$' #
( =
s =
s( =
)# =
)# =
*# = 1.41E+0!
3.!E-033 6.13E-01 -3./E-033 -6.126E-01
6.13E-01 1 -6.1E-01 -1
-3./E-033 -6.1E-01 3.!E-033 6.126E-01
-6.1E-01 -1 6.13E-01 1
*# =
!.31E-2/ /.66E-12 -!.31E-2/ -/.66E-12
/.66E-12 1.41E+0! -/.66E-12 -1.41E+0!
-!.31E-2/ -/.66E-12 !.31E-2/ /.66E-12
-/.66E-12 -1.41E+0! /.66E-12 1.41E+0!
4 =
(2 =
s2 =
! =
(2 =
s2 =
*
; 5
'
2
/
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
4
& Bata$'
( =
s =
s( =
) =
) =
* = /.4/E+04
0.64 -0.4/ -0.64 0.4/
-0.4/ 0.36 0.4/ -0.36
-0.64 0.4/ 0.64 -0.4/
0.4/ -0.36 -0.4/ 0.36
* =
!.43E+04 -4.0E+04 -!.43E+04 4.0E+04-4.0E+04 3.0!E+04 4.0E+04 -3.0!E+04
-!.43E+04 4.0E+04 !.43E+04 -4.0E+04
4.0E+04 -3.0!E+04 -4.0E+04 3.0!E+04
& Bata$' '
=
( =
s =
s( =
)' =
)' =
*' = .0E+04
3.!E-033 6.13E-01 -3./E-033 -6.126E-01
6.13E-01 1 -6.1E-01 -1
-3./E-033 -6.1E-01 3.!E-033 6.126E-01
-6.1E-01 -1 6.13E-01 1
*' =
2.6!E-2/ 4.33E-12 -2.6!E-2/ -4.33E-12
4.33E-12 .0E+04 -4.33E-12 -.0E+04
-2.6!E-2/ -4.33E-12 2.6!E-2/ 4.33E-12
6 = 0 + ar(ta$21.! =
(2
=
s2 =
(2 =
s2 =
9
<
$
3
9
/
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
!
-4.33E-12 -.0E+04 4.33E-12 .0E+04
& Bata$'
( =
s =
s( =
) =
) =
* = /.4/E+04
0.64 0.4/ -0.64 -0.4/
0.4/ 0.36 -0.4/ -0.36
-0.64 -0.4/ 0.64 0.4/-0.4/ -0.36 0.4/ 0.36
* =
!.43E+04 4.0E+04 -!.43E+04 -4.0E+04
4.0E+04 3.0!E+04 -4.0E+04 -3.0!E+04
-!.43E+04 -4.0E+04 !.43E+04 4.0E+04
-4.0E+04 -3.0!E+04 4.0E+04 3.0!E+04
& Bata$' i
( =
s =
s( =
)i =
)i =
*i = 1.41E+0!
3.!E-033 6.13E-01 -3./E-033 -6.126E-01
6.13E-01 1 -6.1E-01 -1
-3./E-033 -6.1E-01 3.!E-033 6.126E-01
-6.1E-01 -1 6.13E-01 1
/ = ar(ta$1.!2 =
(2 =
s2 =
=
(2 =
s2 =
#
;
=
4
9
=
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
6
*i =
!.31E-2/ /.66E-12 -!.31E-2/ -/.66E-12
/.66E-12 1.41E+0! -/.66E-12 -1.41E+0!
-!.31E-2/ -/.66E-12 !.31E-2/ /.66E-12
-/.66E-12 -1.41E+0! /.66E-12 1.41E+0!
5 Bata$' j
( =
s =
s( =
)j =
)j =
*j = /.4/E+04
0.64 0.4/ -0.64 -0.4/0.4/ 0.36 -0.4/ -0.36
-0.64 -0.4/ 0.64 0.4/
-0.4/ -0.36 0.4/ 0.36
*j =
!.43E+04 4.0E+04 -!.43E+04 -4.0E+04
4.0E+04 3.0!E+04 -4.0E+04 -3.0!E+04
-!.43E+04 -4.0E+04 !.43E+04 4.0E+04
-4.0E+04 -3.0!E+04 4.0E+04 3.0!E+04
5 Bata$' k
( =
s =
s( =
)k =
)k =
0.64 0.4/ -0.64 -0.4/
10 = ar(ta$1.!2 =
(2 =
s2 =
11 = ar(ta$1.!2 =
(2 =
s2
=
&
1
/
k
/
<
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
*k = /.4/E+040.4/ 0.36 -0.4/ -0.36
-0.64 -0.4/ 0.64 0.4/
-0.4/ -0.36 0.4/ 0.36
*k =
!.43E+04 4.0E+04 -!.43E+04 -4.0E+04
4.0E+04 3.0!E+04 -4.0E+04 -3.0!E+04
-!.43E+04 -4.0E+04 !.43E+04 4.0E+04
-4.0E+04 -3.0!E+04 4.0E+04 3.0!E+04
5 Bata$' )
( =
s =
s( =
)l =)l =
*l = /.4/E+04
0.64 -0.4/ -0.64 0.4/
-0.4/ 0.36 0.4/ -0.36
-0.64 0.4/ 0.64 -0.4/
0.4/ -0.36 -0.4/ 0.36
*l =
!.43E+04 -4.0E+04 -!.43E+04 4.0E+04
-4.0E+04 3.0!E+04 4.0E+04 -3.0!E+04
-!.43E+04 4.0E+04 !.43E+04 -4.0E+04
4.0E+04 -3.0!E+04 -4.0E+04 3.0!E+04
5 Bata$'
( =
s =
s( =
) =
12 = 20+ar(ta$21.! =
(2 =
s2 =
13 =0+ar(ta$21.! =
(2 =
s2 =
)
5
=
L
<
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
/
) =
* = /.4/E+04
0.64 -0.4/ -0.64 0.4/
-0.4/ 0.36 0.4/ -0.36
-0.64 0.4/ 0.64 -0.4/
0.4/ -0.36 -0.4/ 0.36
* =
!.43E+04 -4.0E+04 -!.43E+04 4.0E+04
-4.0E+04 3.0!E+04 4.0E+04 -3.0!E+04
-!.43E+04 4.0E+04 !.43E+04 -4.0E+04
4.0E+04 -3.0!E+04 -4.0E+04 3.0!E+04
Matrik k#kakua$ struktur:
1 = ka11.1+ka12.2+kj11.1+kj126
2 = ka21.1+ka22.2+kb11.2+kb12.3+k#11.2+k#12.6
3 = kb21.2+kb22.3+k(11.3+k(12.4+k11.3+k12.6+k'11.3+k'12.+k11.3+k
4 = k(21.3+k(22.4+k11.4+k12.!+ki11.4+ki12./
! = k21.4+k22.!+k11.!+k12./
6 = k#21.2+k#22.6+k21.3+k22.6+kj21.1+kj22.6+kk11.6+kk12.
= k'21.3+k'22.+kk21.6+kk22.+kl11.+kl12./
/ = k21.3+k22./+ki21.4+ki22./+kl21.+kl22./+k21.!+k22./
1
=
ka11+kj11 ka12 0
2 ka21 ka22+kb11+k#11 kb12
3 0 kb21 kb22+k(11+k11+k'11+k11 k(
40 0 k(21 k(22+k
! 0 0 0 k
6 kj21 k#21 k21
0 0 k'21
/ 0 0 k21 ki
s%arat batas :
u1 = 71 = u! = 7! = 0
u2 = 72 = u3 = 73 = u4= 74 = u6 = 76 = u = 7 = u/ = 7/ = b#r8i$a
91 1.60E+0! 4.0E+04 -1.06E+0! 0 0 0
9%1 4.0E+04 3.0!E+04 0 0 0 0
92 -1.06E+0! 0 2.12E+0! /.66E-12 -1.06E+0! 0
9%2 0 0 /.66E-12 1.41E+0! 0 0
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
93
=
0 0 -1.06E+0! 0 3.21E+0! .2/E-12
9%3 0 0 0 0 .2/E-12 1.32E+0!
94 0 0 0 0 -1.06E+0! 0
9%4 0 0 0 0 0 0
9! 0 0 0 0 0 0
9%! 0 0 0 0 0 0
96 -!.43E+04 -4.0E+04 -!.31E-2/ -/.66E-12 -!.43E+04 4.0E+04
9%6 -4.0E+04 -3.0!E+04 -/.66E-12 -1.41E+0! 4.0E+04 -3.0!E+04
9 0 0 0 0 -2.6!E-2/ -4.33E-12
9% 0 0 0 0 -4.33E-12 -.0E+04
9/ 0 0 0 0 -!.43E+04 -4.0E+04
9%/ 0 0 0 0 -4.0E+04 -3.0!E+04
atriks$%a #$jai :
92
=
2.12E+0! /.66E-12 -1.06E+0! 0 0 0
9%2 /.66E-12 1.41E+0! 0 0 0 0
93 -1.06E+0! 0 3.21E+0! .2/E-12 -1.06E+0! 0
9%3 0 0 .2/E-12 1.32E+0! 0 0
94 0 0 -1.06E+0! 0 2.12E+0! /.66E-12
9%4 0 0 0 0 /.66E-12 1.41E+0!
96 -!.31E-2/ -/.66E-12 -!.43E+04 4.0E+04 0 0
9%6 -/.66E-12 -1.41E+0! 4.0E+04 -3.0!E+04 0 0
9 0 0 -2.6!E-2/ -4.33E-12 0 0
9% 0 0 -4.33E-12 -.0E+04 0 0
9/ 0 0 -!.43E+04 -4.0E+04 -!.31E-2/ -/.66E-12
9%/ 0 0 -4.0E+04 -3.0!E+04 -/.66E-12 -1.41E+0!
u2
=
2.12E+0! /.66E-12 -1.06E+0! 0 0 0
72 /.66E-12 1.41E+0! 0 0 0 0
u3 -1.06E+0! 0 3.21E+0! .2/E-12 -1.06E+0! 0
73 0 0 .2/E-12 1.32E+0! 0 0
u4 0 0 -1.06E+0! 0 2.12E+0! /.66E-12
74 0 0 0 0 /.66E-12 1.41E+0!
u6 -!.31E-2/ -/.66E-12 -!.43E+04 4.0E+04 0 0
76 -/.66E-12 -1.41E+0! 4.0E+04 -3.0!E+04 0 0
u 0 0 -2.6!E-2/ -4.33E-12 0 0
7 0 0 -4.33E-12 -.0E+04 0 0u/ 0 0 -!.43E+04 -4.0E+04 -!.31E-2/ -/.66E-12
7/ 0 0 -4.0E+04 -3.0!E+04 -/.66E-12 -1.41E+0!
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
10
u2
=
.0E-06 -3.14E-06 4.1E-06 -/.30E-22 2.36E-06 3.14E-06
72 -3.14E-06 4.!E-0! -6.2E-06 3.16E-0! -3.14E-06 1.!E-0!
u3 4.1E-06 -6.2E-06 .43E-06 -1.66E-21 4.1E-06 6.2E-06
73 !.2E-22 3.16E-0! 1.0!E-21 4.6E-0! .3E-22 3.16E-0!
u4 2.36E-06 -3.14E-06 4.1E-06 -6.!3E-22 .0E-06 3.14E-06
74 3.14E-06 1.!E-0! 6.2E-06 3.16E-0! 3.14E-06 4.!E-0!
u6 2.36E-06 -1.1E-0! 4.1E-06 -1.14E-0! 2.36E-06 -!.6!E-06
76 -3.14E-06 4.0!E-0! -6.2E-06 3.16E-0! -3.14E-06 1.!E-0!
u -2.04E-21 6.14E-06 -4.0E-21 -1.64E-20 -2.04E-21 -6.14E-06
7 .3/E-22 2.46E-0! 1.4/E-21 3.2E-0! ./4E-22 2.46E-0!
u/ 2.36E-06 !.6!E-06 4.1E-06 1.14E-0! 2.36E-06 1.1E-0!
7/ 3.14E-06 1.!E-0! 6.2E-06 3.16E-0! 3.14E-06 4.0!E-0!
u2
=
-0.00314311
72 -0.2404!261
u3 -0.0062/6343
73 -0.366!06//
u4 -0.00314311
74 -0.31431146
u6 0.100!323!
76 -0.2404!261
u 0.0/00//
7 -0.302/!66
u/ -0.06/46
7/ -0.31431146
8#r8i$aa$ 8aa subu lokal :
& bata$' a
u1 lokal
=
0 0 u1 'lobal
71 lokal -si$ 0 0 71 'lobal
u2 lokal 0 0 u2 'lobal
72 loka) 0 0 -si$ 72 'lobal
u1 lokal
=
1 0 0 0 0
71 lokal 0 1 0 0 0
u2 lokal 0 0 1 0 -0.003143172 loka) 0 0 0 1 -0.2404!262
u1 lokal 0
71 lokal 0
(os si$
(os
(os si$
(os
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11
u2 lokal -0.003143
72 loka) -0.2404!3
& bata$' b
u2 lokal
=
1 0 0 0 u2 'lobal
72 lokal 0 1 0 0 72 'lobal
u3 lokal 0 0 1 0 u3 'lobal
73 loka) 0 0 0 1 73 'lobal
u2 lokal
=
1 0 0 0 -0.0031431
72 lokal 0 1 0 0 -0.2404!262
u3 lokal 0 0 1 0 -0.0062/634
73 loka) 0 0 0 1 -0.366!06/
u2 lokal
=
-0.003143
72 lokal -0.2404!3
u3 lokal -0.0062/6
73 loka) -0.366!0
& bata$' (
u3 lokal
=
1 0 0 0 u3 'lobal
73 lokal 0 1 0 0 73 'lobal
u4 lokal 0 0 1 0 u4 'lobal
74 loka) 0 0 0 1 74 'lobal
u3 lokal
=
1 0 0 0 -0.0062/634
73 lokal 0 1 0 0 -0.366!06/
u4 lokal 0 0 1 0 -0.0031431
74 loka) 0 0 0 1 -0.314311!
u3 lokal
=
-0.0062/6373 lokal -0.366!06
u4 lokal -0.0031432
74 loka) -0.314311
& bata$'
u4 lokal
=
1 0 0 0 u4 'lobal
74 lokal 0 1 0 0 u4 'lobal
u! lokal 0 0 1 0 u! 'lobal
7! loka) 0 0 0 1 7! 'lobal
u4 lokal
=
1 0 0 0 -0.0031431
74 lokal 0 1 0 0 -0.314311!
u! lokal 0 0 1 0 0
7! loka) 0 0 0 1 0
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
12
u4 lokal
=
-0.0031432
74 lokal -0.31431
u! lokal 0
7! loka) 0
& bata$' #
u2 lokal
=
6.126E-01 1 0 0 u2 'lobal
72 lokal -1 6.126E-01 0 0 72 'lobal
u6 lokal 0 0 6.126E-01 1 u6 'lobal
76 loka) 0 0 -1 6.126E-01 76 'lobal
u2 lokal
=
6.126E-01 1 0 0
72 lokal -1 6.126E-01 0 0
u6 lokal 0 0 6.126E-01 1
76 loka) 0 0 -1 6.126E-01
u2 lokal
=
-0.2404!26
72 lokal 0.0031432
u6 lokal -0.2404!3
76 loka) -0.100!32
& bata$'
u3 lokal
=
-0./ 0.6 0 0 u3 'lobal
73 lokal -0.6 -0./ 0 0 73 'lobal
u6 lokal 0 0 -0./ 0.6 u6 'lobal
76 loka) 0 0 -0.6 -0./ 76 'lobal
u3 lokal
=
-0./ 0.6 0 0 -0.0062/634
73 lokal -0.6 -0./ 0 0 -0.366!06/
u6 lokal 0 0 -0./ 0.6 0.100!323!
76 loka) 0 0 -0.6 -0./ -0.2404!262
u3 lokal
=
-0.214/!1
73 lokal 0.263
u6 lokal -0.2246
76 loka) 0.132042
& bata$' '
u3 lokal
=
6.126E-01 1 0 0
73 lokal -1 6.126E-01 0 0
u lokal 0 0 6.126E-01 17 loka) 0 0 -1 6.126E-01
u3 lokal 6.126E-01 1 0 0
73 lokal -1 6.126E-01 0 0
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13
u lokal 0 0 6.126E-01 1
7 loka) 0 0 -1 6.126E-01
u3 lokal
=
-0.366!06
73 lokal 0.0062/63
u lokal -0.302/!/
7 loka) -0.0/0
& bata$'
u3 lokal
=
0./ 0.6 0 0 u3 'lobal
73 lokal -0.6 0./ 0 0 73 'lobal
u/ lokal 0 0 0./ 0.6 u/ 'lobal
7/ loka) 0 0 -0.6 0./ 7/ 'lobal
u3 lokal
=
0./ 0.6 0 0 -0.0062/634
73 lokal -0.6 0./ 0 0 -0.366!06/
u/ lokal 0 0 0./ 0.6 -0.06/46/
7/ loka) 0 0 -0.6 0./ -0.314311!
u3 lokal
=
-0.224332
73 lokal -0.2/434
u/ lokal -0.244!/
7/ loka) -0.20463
& bata$' i
u4 lokal
=
6.126E-01 1 0 0
74 lokal -1 6.126E-01 0 0
u/ lokal 0 0 6.126E-01 1
7/ loka) 0 0 -1 6.126E-01
u4 lokal
=
6.126E-01 1 0 0
74 lokal -1 6.126E-01 0 0u/ lokal 0 0 6.126E-01 1
7/ loka) 0 0 -1 6.126E-01
u4 lokal
=
-0.314311
74 lokal 0.0031432
u/ lokal -0.31431
7/ loka) 0.06/4
& bata$' j
u1 lokal
=
0./ 0.6 0 0 u1 'lobal71 lokal -0.6 0./ 0 0 71 'lobal
u6 lokal 0 0 0./ 0.6 u6 'lobal
76 loka) 0 0 -0.6 0./ 76 'lobal
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
14
u1 lokal
=
0./ 0.6 0 0 0
71 lokal -0.6 0./ 0 0 0
u6 lokal 0 0 0./ 0.6 0.100!323!
76 loka) 0 0 -0.6 0./ -0.2404!262
u1 lokal
=
0
71 lokal 0
u6 lokal -0.063/46
76 loka) -0.2!26/2
& bata$' k
u6 lokal
=
0./ 0.6 0 0 u6 'lobal
76 loka) -0.6 0./ 0 0 76 'lobal
u lokal 0 0 0./ 0.6 u 'lobal
7 lokal 0 0 -0.6 0./ 7 'lobal
u6 lokal
=
0./ 0.6 0 0 0.100!323!
76 loka) -0.6 0./ 0 0 -0.2404!262
u lokal 0 0 0./ 0.6 0.0/00//
7 lokal 0 0 -0.6 0./ -0.302/!6
u6 lokal
=
-0.063/4!
76 loka) -0.2!26/1!
u lokal -0.11/6/
7 lokal -0.20104
& bata$' l
u lokal
=
0./ -0.6 0 0 u 'lobal
7 loka) 0.6 0./ 0 0 7 'lobal
u/ lokal 0 0 0./ -0.6 u/ 'lobal
7/ lokal 0 0 0.6 0./ 7/ 'lobal
u lokal
=
0./ -0.6 0 0 0.0/00//
7 loka) 0.6 0./ 0 0 -0.302/!6
u/ lokal 0 0 0./ -0.6 -0.06/46/
7/ lokal 0 0 0.6 0./ -0.314311!
u lokal
=
0.24!!602
7 loka) -0.14401
u/ lokal 0.132602!!
7/ lokal -0.23444!
& bata$'
u! lokal
=
-0./ 0.6 0 0 u! 'lobal
7! loka) -0.6 -0./ 0 0 7! 'lobal
u/ lokal 0 0 -0./ 0.6 u/ 'lobal
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
1!
7/ lokal 0 0 -0.6 -0./ 7/ 'lobal
u! lokal
=
-0./ 0.6 0 0 0
7! loka) -0.6 -0./ 0 0 0
u/ lokal 0 0 -0./ 0.6 -0.06/46/
7/ lokal 0 0 -0.6 -0./ -0.314311!
u! lokal
=
0
7! loka) 0
u/ lokal -0.132603
7/ lokal 0.23444!
;a%a ala 'a%a bata$'
'a%a bata$' a :
91= E")a
1 -1 u1 lokal
92 -1 1 u2 lokal
91= 1.06E+0!
1 -1 0
92 -1 1 -0.003143
91=
1.06E+0! -1.06E+0! 0
92 -1.06E+0! 1.06E+0! -0.003143
91=
333.33333 k'
92 -333.3333 k'
'a%a bata$' b :
92= 1.06E+0!
1 -1 -0.003143
93 -1 1 -0.0062/6
92=
1.06E+0! -1.06E+0! -0.003143
93 -1.06E+0! 1.06E+0! -0.0062/6
92=
333.33333 k'
93 -333.3333 k'
'a%a bata$' ( :
93= 1.06E+0!
1 -1 -0.0062/6
94 -1 1 -0.003143
93=
1.06E+0! -1.06E+0! -0.0062/6
94 -1.06E+0! 1.06E+0! -0.003143
93 -333.3333 k'
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
16
94 333.33333 k'
'a%a bata$' :
94= 1.06E+0!
1 -1 -0.003143
9! -1 1 0
94=
1.06E+0! -1.06E+0! -0.003143
9! -1.06E+0! 1.06E+0! 0
94=
-333.3333 k'
9! 333.33333 k'
'a%a bata$' # :
92= 1.41E+0!
1 -1 -0.2404!3
96 -1 1 -0.2404!3
92=
1.41E+0! -1.41E+0! -0.2404!3
96 -1.41E+0! 1.41E+0! -0.2404!3
92=
0 k'
96 0 k'
'a%a bata$' :
93 = /.4/E+04 1 -1 -0.214/!96 -1 1 -0.2246
93=
/.4/E+04 -/.4/E+04 -0.214/!
96 -/.4/E+04 /.4/E+04 -0.2246
93=
/33.33333 k'
96 -/33.3333 k'
'a%a bata$' ' :
93 = .0E+04 1 -1 -0.366!09 -1 1 -0.302/!/
93=
.0E+04 -.0E+04 -0.366!0
9 -.0E+04 .0E+04 -0.302/!/
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
1
93
=
-4!00 k'
9 4!00 k'
'a%a bata$' :
93= /.4/E+04
1 -1 -0.22433
9/ -1 1 -0.244!/
93=
/.4/E+04 -/.4/E+04 -0.22433
9/ -/.4/E+04 /.4/E+04 -0.244!/
93=
1666.666 k'
9/ -1666.66 k'
'a%a bata$' i :
94= 1.41E+0!
1 -1 -0.31431
9/ -1 1 -0.31431
94=
1.41E+0! -1.41E+0! -0.31431
9/ -1.41E+0! 1.41E+0! -0.31431
94=
0
9/ 0
'a%a bata$' j :
91= /.4/E+04
1 -1 0
96 -1 1 -0.063/46
91=
/.4/E+04 -/.4/E+04 0
96 -/.4/E+04 /.4/E+04 -0.063/46
91=
!416.666 k'
96 -!416.66 k'
'a%a bata$' k :
96= /.4/E+04
1 -1 -0.063/46
9 -1 1 -0.11/6
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
1/
96=
/.4/E+04 -/.4/E+04 -0.063/46
9 -/.4/E+04 /.4/E+04 -0.11/6
96=
4!/3.3333 k'
9 -4!/3.333 k'
'a%a bata$' l :
96= /.4/E+04
1 -1 0.24!!603
9 -1 1 0.132602!
96=
/.4/E+04 -/.4/E+04 0.24!!603
9 -/.4/E+04 /.4/E+04 0.132602!
96=
!/3.3333 k'
9 -!/3.333 k'
'a%a bata$' :
9!= /.4/E+04
1 -1 0
9/ -1 1 -0.132603
9!=
/.4/E+04 -/.4/E+04 0
9/ -/.4/E+04 /.4/E+04 -0.132603
9!=
112!0 k'
9/ -112!0 k'
<#aksi u8ua$ :
1
=
ka11+kj11 ka12 0
2 ka21 ka22+kb11+k#11 kb12
3 0 kb21 kb22+k(11+k11+k'11+k11 k(
4 0 0 k(21 k(22+k
! 0 0 0 k
6 kj21 k#21 k21
0 0 k'21/ 0 0 k21 ki
91 1.60E+0! 4.0E+04 -1.06E+0! 0 0 0
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
1
9%1
=
4.0E+04 3.0!E+04 0 0 0 0
92 -1.06E+0! 0 2.12E+0! /.66E-12 -1.06E+0! 0
9%2 0 0 /.66E-12 1.41E+0! 0 0
93 0 0 -1.06E+0! 0 3.21E+0! .2/E-12
9%3 0 0 0 0 .2/E-12 1.32E+0!
94 0 0 0 0 -1.06E+0! 0
9%4 0 0 0 0 0 0
9! 0 0 0 0 0 0
9%! 0 0 0 0 0 0
96 -!.43E+04 -4.0E+04 -!.31E-2/ -/.66E-12 -!.43E+04 4.0E+04
9%6 -4.0E+04 -3.0!E+04 -/.66E-12 -1.41E+0! 4.0E+04 -3.0!E+04
9 0 0 0 0 -2.6!E-2/ -4.33E-12
9% 0 0 0 0 -4.33E-12 -.0E+04
9/ 0 0 0 0 -!.43E+04 -4.0E+04
9%/ 0 0 0 0 -4.0E+04 -3.0!E+04
91
=
1.60E+0! 4.0E+04 -1.06E+0! 0 0 0
9%1 4.0E+04 3.0!E+04 0 0 0 0
92 -1.06E+0! 0 2.12E+0! /.66E-12 -1.06E+0! 0
9%2 0 0 /.66E-12 1.41E+0! 0 0
93 0 0 -1.06E+0! 0 3.21E+0! .2/E-12
9%3 0 0 0 0 .2/E-12 1.32E+0!
94 0 0 0 0 -1.06E+0! 0
9%4 0 0 0 0 0 0
9! 0 0 0 0 0 0
9%! 0 0 0 0 0 0
96 -!.43E+04 -4.0E+04 -!.31E-2/ -/.66E-12 -!.43E+04 4.0E+04
9%6 -4.0E+04 -3.0!E+04 -/.66E-12 -1.41E+0! 4.0E+04 -3.0!E+04
9 0 0 0 0 -2.6!E-2/ -4.33E-12
9% 0 0 0 0 -4.33E-12 -.0E+04
9/0 0 0 0 -!.43E+04 -4.0E+04
9%/ 0 0 0 0 -4.0E+04 -3.0!E+04
91
=
466
9%1 32!0
92 0
9%2 0
93 0
9%3 -300094 0
9%4 0
9! -/66
9%! 6!0 S.1 , ;//<
S1
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
20
96 0
9%6 -1000
9 4000
9% -4000
9/ 0 ko$trol :
9%/ -2000 %
0 0
<#ka8itulasi >asil P#ritu$'a$
Bata$' 9uut ?o. "@al ?o. "kir ;a%a Bata$' #ka$ arik
a 0 1 2 333.33
b 0 2 3 333.33
( 0 3 4 333.33
0 4 ! 333.33
# 0 2 6 0
143.13 3 6 /33.33
' 0 3 4!00
36./ 3 / 1666.6
i 0 4 / 0
j 36./ 1 6 !416.6
k 36./ 6 4!/3.33
l 323.13 / !/3.33
143.13 ! / 112!0
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
21
0
1
1
0
0
0
2
2.00E+02 (
'!# "o3#+ %a&a *aat+ta!# *aat *#+akuka a*a
2 R'ak!#$:a!#$ %ata$
5
$
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
22
0
1
1
0
0
0
2
2.00E+02 (
0
1
1
0
00
2
2.00E+02 (
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
23
0
1
1
0
0
02
2.00E+02 (
0
6.126E-01
3.!2E-033
1
1
6.126E-01
1.!
1.!0E+02 (
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
24
143.13
-0./
0.640.6
0.36
-0.4/
2.!
2.!0E+02 (
0
6.126E-01
3.!2E-033
1
1
6.126E-01
3
3.00E+02 (
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
2!
36./
0./
0.64
0.6
0.36
0.4/
2.!
2.!0E+02 (
0
0
0
1
1
6.126E-01
1.!
1.!0E+02 (
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
26
36./
0./
0.64
0.6
0.36
0.4/
2.!
2.!0E+02 (
36./
0./
0.64
0.6
0.360.4/
2.!
2.!0E+02 (
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
2
323.13
0./
0.64
-0.6
0.36
-0.4/
2.! 2.!0E+02 (
143.13
-0./
0.64
0.6
0.36
-0.4/
2.!
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
2/
2.!0E+02 (
12./
0 kj12 0 0
0 k#12 0 0
12 0 k12 k'12 k12
11+ki11 k12 0 0 ki12
21 k22+k11 0 0 k12
0 k#22+k22+kj22+kk11 kk12 0
0 kk21 k'22+kk22+kl11 kl12
1 k21 0 kl21 k22+ki22+kl22+k22
0 0 0 0 -!.43E+04 -4.0E+04 0 0
0 0 0 0 -4.0E+04 -3.0!E+04 0 0
0 0 0 0 -!.31E-2/ -/.66E-12 0 0
0 0 0 0 -/.66E-12 -1.41E+0! 0 0
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
2
-1.06E+0! 0 0 0 -!.43E+04 4.0E+04 -2.6!E-2/ -4.33E-12
0 0 0 0 4.0E+04 -3.0!E+04 -4.33E-12 -.0E+04
2.12E+0! /.66E-12 -1.06E+0! 0 0 0 0 0
/.66E-12 1.41E+0! 0 0 0 0 0 0
-1.06E+0! 0 1.60E+0! -4.0E+04 0 0 0 0
0 0 -4.0E+04 3.0!E+04 0 0 0 0
0 0 0 0 1.63E+0! 4.0E+04 -!.43E+04 -4.0E+04
0 0 0 0 4.0E+04 2.33E+0! -4.0E+04 -3.0!E+04
0 0 0 0 -!.43E+04 -4.0E+04 1.0E+0! 0.00E+00
0 0 0 0 -4.0E+04 -3.0!E+04 0.00E+00 1.32E+0!
-!.31E-2/ -/.66E-12 -!.43E+04 4.0E+04 0 0 -!.43E+04 4.0E+04
-/.66E-12 -1.41E+0! 4.0E+04 -3.0!E+04 0 0 4.0E+04 -3.0!E+04
-!.31E-2/ -/.66E-12 0 0 0 0 u2
-/.66E-12 -1.41E+0! 0 0 0 0 72
-!.43E+04 4.0E+04 -2.6!E-2/ -4.33E-12 -!.43E+04 -4.0E+04 u3
4.0E+04 -3.0!E+04 -4.33E-12 -.0E+04 -4.0E+04 -3.0!E+04 73
0 0 0 0 -!.31E-2/ -/.66E-12 u4
0 0 0 0 -/.66E-12 -1.41E+0! 74
1.63E+0! 4.0E+04 -!.43E+04 -4.0E+04 0 0 u6
4.0E+04 2.33E+0! -4.0E+04 -3.0!E+04 0 0 76
-!.43E+04 -4.0E+04 1.0E+0! 0.00E+00 -!.43E+04 4.0E+04 u
-4.0E+04 -3.0!E+04 0.00E+00 1.32E+0! 4.0E+04 -3.0!E+04 7
0 0 -!.43E+04 4.0E+04 1.63E+0! -4.0E+04 u/
0 0 4.0E+04 -3.0!E+04 -4.0E+04 2.33E+0! 7/
-!.31E-2/ -/.66E-12 0 0 0 0 -1 92
-/.66E-12 -1.41E+0! 0 0 0 0 9%2
-!.43E+04 4.0E+04 -2.6!E-2/ -4.33E-12 -!.43E+04 -4.0E+04 93
4.0E+04 -3.0!E+04 -4.33E-12 -.0E+04 -4.0E+04 -3.0!E+04 9%3
0 0 0 0 -!.31E-2/ -/.66E-12 94
0 0 0 0 -/.66E-12 -1.41E+0! 9%4
1.63E+0! 4.0E+04 -!.43E+04 -4.0E+04 0 0 96
4.0E+04 2.33E+0! -4.0E+04 -3.0!E+04 0 0 9%6
-!.43E+04 -4.0E+04 1.0E+0! 0.00E+00 -!.43E+04 4.0E+04 9
-4.0E+04 -3.0!E+04 0.00E+00 1.32E+0! 4.0E+04 -3.0!E+04 9%0 0 -!.43E+04 4.0E+04 1.63E+0! -4.0E+04 9/
0 0 4.0E+04 -3.0!E+04 -4.0E+04 2.33E+0! 9%/
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
30
2.36E-06 -3.14E-06 -1.66E-21 1.66E-21 2.36E-06 3.14E-06 0
-1.1E-0! 4.0!E-0! 6.14E-06 2.46E-0! !.6!E-06 1.!E-0! 0
4.1E-06 -6.2E-06 -3.32E-21 3.32E-21 4.1E-06 6.2E-06 0
-1.14E-0! 3.16E-0! -1./E-20 3.2E-0! 1.14E-0! 3.16E-0! -3000
2.36E-06 -3.14E-06 -1.63E-21 1.31E-21 2.36E-06 3.14E-06 0
-!.6!E-06 1.!E-0! -6.14E-06 2.46E-0! 1.1E-0! 4.0!E-0! 0
1.36E-0! -1.1E-0! 4.60E-06 -6.14E-06 3.6/E-0 -!.6!E-06 0
-1.1E-0! 4.0!E-0! 6.14E-06 2.46E-0! !.6!E-06 1.!E-0! -1000
4.60E-06 6.14E-06 1./4E-0! -1.36E-20 4.60E-06 -6.14E-06 4000
-6.14E-06 2.46E-0! -1.!E-20 3.2E-0! 6.14E-06 2.46E-0! -4000
3.6/E-0 !.6!E-06 4.60E-06 6.14E-06 1.36E-0! 1.1E-0! 0
-!.6!E-06 1.!E-0! -6.14E-06 2.46E-0! 1.1E-0! 4.0!E-0! -2000
ko$trol :
0.00
0.00
0.00
-3000.00
0.00
0.00
0.00
-1000.00
4000.00
-4000.00
0.00
-2000.00
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
31
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
32
-0.0031431
-0.2404!262
0.100!323!
-0.2404!262
u3 'lobal
73 'lobal
u 'lobal7 'lobal
-0.0062/634
-0.366!06/
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TUGAS BESAR (UJIAN FINAL)ANALISA STRUKTUR METODE MATRIK KELAS C2 TAHUN 2015
33
0.0/00//
-0.302/!6
u4 'lobal
74 'lobal
u/ 'lobal
7/ 'lobal
-0.0031431
-0.314311!-0.06/46/
-0.314311!
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