8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
1/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
2/345
() 1.2 = 0 = 0
() 2.2 = 12.EI/L*3 = 5+400
() 3.2 = +.EI / L*2 = ,0500
Akibat disla!ement arah 3 ""# $3 %r&tasi arah sb l&kal 3'
() 1.3 = 0 = 0
() 2.3 = +.EI / L*2 = ,0500
() 3.3 = 4 EI / L = 11,500
Akibat disla!ement arah 4 ""# $4 %translasi arah sb l&kal 4'
() 1.4 = " E.A / L = "1410000
() 2.4 = 0 = 0
() 3.4 = 0 = 0
Akibat disla!ement arah 5 ""# $5 %translasi arah sb l&kal 5'
() 1.5 = 0 = 0
() 2.5 = "12.EI/L*3 = "5+400
() 3.5 = "+.EI / L*2 = ",0500
Akibat disla!ement arah + ""# $+ %r&tasi arah sb l&kal +'
() 1.+ = 0 = 0
() 2.+ = +.EI / L*2 = ,0500
() 3.+ = 2 EI / L = 5-,50
(snan matriks kekakan batang 1 %()1' :
()11 ()12 ()13
()21 ()22 ()23
()1 = ()31 ()32 ()33
()41 ()42 ()43
()51 ()52 ()53
()+1 ()+2 ()+3
(dt batang 1 : =
)atriks trans&rmasi r&tasi :
α1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
3/345
0
= 0
0 0 1
0 0 0
0 0 0
0 0 0
rans&se matrik &tasi
1.00 0 0
= 0 1.00 0
0 0 1
0 0 0
0 0 0
0 0 0
)atriks kekakan strktr menadi :
1.00 0.00 0.00
0.00 1.00 0.00
0.00 0.00 1.00
()( 1 = 0.00 0.00 0.00
0.00 0.00 0.000.00 0.00 0.00
1410000 0 0
0 5+400 ,0500
0 ,0500 11,500
"1410000 0 0
0 "5+400 ",0500
0 ,0500 5-,50
Hitung matriks kekakuan batang 2 (SM2)
Akibat disla!ement arah 1 ""# $1 %translasi arah sb l&kal 1'
() 1.1 = E.A / L = ,05000
() 2.1 = 0 = 0
() 3.1 = 0 = 0
Akibat disla!ement arah 2 ""# $2 %translasi arah sb l&kal 2'
!&s α1
sin α1
" sin α1
!&s α1
()( = . () .
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
4/345
() 1.2 = 0 = 0
() 2.2 = 12.EI/L*3 = ,050
() 3.2 = +.EI / L*2 = 1,+25
Akibat disla!ement arah 3 ""# $3 %r&tasi arah sb l&kal 3'
() 1.3 = 0 = 0
() 2.3 = +.EI / L*2 = 1,+25
() 3.3 = 4 EI / L = 5-,50
Akibat disla!ement arah 4 ""# $4 %translasi arah sb l&kal 4'
() 1.4 = " E.A / L = ",05000
() 2.4 = 0 = 0
() 3.4 = 0 = 0
Akibat disla!ement arah 5 ""# $5 %translasi arah sb l&kal 5'
() 1.5 = 0 = 0
() 2.5 = "12.EI/L*3 = ",050
() 3.5 = "+.EI / L*2 = "1,+25
Akibat disla!ement arah + ""# $+ %r&tasi arah sb l&kal +'
() 1.+ = 0 = 0
() 2.+ = +.EI / L*2 = 1,+25
() 3.+ = 2 EI / L = 23,5
(snan matriks kekakan batang 2 %()2' :
()11 ()12 ()13
()21 ()22 ()23
()2 = ()31 ()32 ()33
()41 ()42 ()43
()51 ()52 ()53
()+1 ()+2 ()+3
(dt batang 2 : =
ata =
)atriks trans&rmasi r&tasi :
α2
α2
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
5/345
0
= 0
0 0 1
0 0 0
0 0 0
0 0 0
rans&se matrik &tasi
0.80 -0.6 0
= 0.6 0.80 0
0 0 1
0 0 0
0 0 0
0 0 0
)atriks kekakan strktr menadi :
0.-0 "0.+0 0.00
0.+0 0.-0 0.00
0.00 0.00 1.00
()( 2 = 0.00 0.00 0.00
0.00 0.00 0.000.00 0.00 0.00
5+4000 "4230 "105,5
423000 5+40 14100
0 1,+25 5-,50
"5+4000 4230 105,5
"423000 "5+40 "14100
0 1,+25 23,5
Hitung matriks kekakuan batang 3 (SM3)
Akibat disla!ement arah 1 ""# $1 %translasi arah sb l&kal 1'
() 1.1 = E.A / L = 1410000
() 2.1 = 0 = 0
() 3.1 = 0 = 0
Akibat disla!ement arah 2 ""# $2 %translasi arah sb l&kal 2'
() 1.2 = 0 = 0
!&s α1
sin α1
" sin α1
!&s α1
()( = . () .
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
6/345
() 2.2 = 12.EI/L*3 = 5+400
() 3.2 = +.EI / L*2 = ,0500
Akibat disla!ement arah 3 ""# $3 %r&tasi arah sb l&kal 3'
() 1.3 = 0 = 0
() 2.3 = +.EI / L*2 = ,0500
() 3.3 = 4 EI / L = 11,500
Akibat disla!ement arah 4 ""# $4 %translasi arah sb l&kal 4'
() 1.4 = " E.A / L = "1410000
() 2.4 = 0 = 0
() 3.4 = 0 = 0
Akibat disla!ement arah 5 ""# $5 %translasi arah sb l&kal 5'
() 1.5 = 0 = 0
() 2.5 = "12.EI/L*3 = "5+400
() 3.5 = "+.EI / L*2 = ",0500
Akibat disla!ement arah + ""# $+ %r&tasi arah sb l&kal +'
() 1.+ = 0 = 0
() 2.+ = +.EI / L*2 = ,0500
() 3.+ = 2 EI / L = 5-,50
(snan matriks kekakan batang 3 %()3' :
()11 ()12 ()13
()21 ()22 ()23
()3 = ()31 ()32 ()33
()41 ()42 ()43
()51 ()52 ()53
()+1 ()+2 ()+3
(dt batang 3 : =
ata =)atriks trans&rmasi r&tasi :
α3
α3
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
7/345
0
= 0
0 0 1
0 0 0
0 0 0
0 0 0
rans&se matrik &tasi
1.00 0 0
= 0 1.00 0
0 0 1
0 0 0
0 0 0
0 0 0
)atriks kekakan strktr menadi :
1.00 0.00 0.00
0.00 1.00 0.00
0.00 0.00 1.00
()( 3 = 0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
1410000 0 0
0 5+400 ,0500
0 ,0500 11,500
"1410000 0 0
0 "5+400 ",0500
0 ,0500 5-,50
Susun MAT!"S "#"A"$AN ST$"T$
0 0 0
1 2 3
164106000 0 0
0 5+6400 ,06500
()( 1 = 0 ,06500 11,6500
"164106000 0 0
0 "5+6400 ",06500
0 ,06500 5-6,50
$1 0 $2
4 5 +
!&s α1
sin α1
" sin α1
!&s α1
()( = . () .
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
8/345
4536,3- 335601+ "1065,5
335601+ 25-6312 146100
()( 2 = "1065,5 146100 5-6,50
"4536,3- "335601+ 1065,5
"335601+ "25-6312 "146100
"1065,5 146100 263,5
$3 0 $4
, -
164106000 0 0
0 5+6400 ,06500
()( 3 = 0 ,06500 11,6500
"164106000 0 0
0 "5+6400 ",06500
0 ,06500 5-6,50
MAT!"S "#"A"$AN ST$"T$
$1 $2 $3
4 + ,
16-+36,3- "1065,5 "4536,3-
()( = "1065,5 1,+6250 1065,5
"4536,3- 1065,5 16-+36,3-
"1065,5 263,5 1065,5
Batang 1
Gbr AM 1 =
Batang 2
Gbr AM 2 =
Hitung rekasi di ujung batang / freebody (AML) ---> Beban dimasukkan kecuai beban di joi
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
9/345
Batang !
Gbr AM 3 =
"ransformasi dari sumbu oka ke sumbu goba struktur
Batang 1
0 1 1
30 2 2
AM 1 = 12.5 3 3
0 4 4
30 5 5
-12.5 6 6
SB LOKAL SB GLOBAL
1.00 0.00 0.00
0.00 1.00 0.00
= 0.00 0.00 1.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0 1 1
30 2 2
= 12.53
3
0 4 4
30 5 5
-12.5 + 6
SB LOKAL SB GLOBAL
Batang 2
22.5 1
25.3125 2
AM 2 = 35.15625 3
37.5 4
RT
AMS
1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
10/345
54.6875 5
-58.59375 6
SB LOKAL
0.80 -0.60 0.000.60 0.80 0.00
= 0.00 0.00 1.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
2.8125 4
33.75 5
= 35.15625 6
-2.8125 7
66.25 8
-58.59375 9
SB GLOBAL
Batang !
0 1
60 2AM 3 = 25 3
0 4
60 5
-25 6
SB LOKAL
1.00 0.00 0.00
0.00 1.00 0.00
= 0.00 0.00 1.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0 7
60 8
= 25 9
0 10
60 11
-25 12
RT
AMS 2
RT
AMS 3
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
11/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
12/345
10 0 0
11 0 "+0
12 0 25
$1 "2.-125
$2 "22.+5+25
$3 2.-125
$4 33.53,5
#$%&'MA "'*+"*'
9itng erindahan
5.,05+5E"00, 2.22125E"00- 1.3-+5524+4-E"00,
= 2.22125E"00- 5.-3-15E"00+ "2.22124-1+3-E"00-
1.3-+55E"00, "2.22125E"00- 5.,05+4+11++,E"00,
2.22125E"00- ".,03+0E"00, "2.22124-1+3-E"00-
,AA-,AA #ALAM *.*, $L$M$
Batang 1
"(r#) *r*r +# #r# SUMBU GLOBAL &) b#*#$, 1 bb
0 1 0
0 2 0
0 0 3 0
-0.000001 4 1
0.000000 5 0
-0.000165 6 2
"(r#) *r*r +# #r# SUMBU LOKAL &) b#*#$, 1 bb
1 0 0
0 1 0
0 0 0 1
0 0 0
0 0 0
0 0 0
G## '$, b#*#$,
B"b#$ '()$* #$, "+#r# O: A:;
!
A%
0
: = S
::-1.A
:;S
::-1 = SMS -1
:
#M 1
∆M 1 = R . MS 1
M 1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
13/345
0 1410000
30 0
AM 1 0 12.5 0
0 -141000030 0
-12.5 0
Batang 2
"(r#) *r*r +# #r# SUMBU GLOBAL &) b#*#$, 2 bb
-9.7180E-07 4 1
0 5 0
0 -1.6499E-04 6 29.7180E-07 7 3
0 8 0
2.1799E-04 9 4
"(r#) *r*r +# #r# SUMBU LOKAL &) b#*#$, 2 bb
0.8 0.6 0-0.6 0.8 0
0 0 0 1
0 0 0
0 0 0
0 0 0
G## '$, b#*#$,
22.5 705000
25.3125 0
AM 2 0 35.15625 0
37.5 -705000
54.6875 0
-58.59375 0
Batang !"(r#) *r*r +# #r# SUMBU GLOBAL &) b#*#$, 3 bb
AM 1 = AML 1 SM 1 . ∆M 1
#M 2
∆M 2 = R . MS 2
M 2
AM 2 = AML 2 SM 2 . ∆M 2
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
14/345
9.7180E-07 7 3
0 8 0
0 2.1799E-04 9 4
0 10 0
0 11 0
0 12 0
"(r#) *r*r +# #r# SUMBU LOKAL &) b#*#$, 3 bb
1.0 0.0 0.0
0.0 1.0 0.0
0 0.0 0.0 1.0
0.0 0.0 0.00.0 0.0 0.0
0.0 0.0 0.0
G## '$, b#*#$,
0 1410000
60 0
AM 3 0 25 0
0 -1410000
60 0
-25 0
#M !
∆M 3 = R . MS 3
M !
AM 3 = AML 3 SM 3 . ∆M 3
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
15/345
%ata beban
= 100 kN
;1 = 24 kN/m
;2 = 4- kN/m
#&emen 'a&am matriks kekakuan batang
Batang EA / L 4.EI / L 2.EI / L +.EI / L*2
1 1410000 11,500 5-,50 ,0500
2 ,05000 5-,50 23,5 1,+25
3 1410000 11,500 5-,50 ,0500
9bngan antar batang
N(. B#*#$, U'$, ) U'$, '
1 1 2
2 2 3
3 3 4
(AL $AN (
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
16/345
() 4.2 = 0 =
() 5.2 = "12.EI/L*3 =
() +.2 = +.EI / L*2 =
() 4.3 = 0 =
() 5.3 = "+.EI / L*2 =
() +.3 = 2 EI / L =
() 4.4 = E.A / L =
() 5.4 = 0 =
() +.4 = 0 =
() 4.5 = 0 =
() 5.5 = 12.EI/L*3 =
() +.5 = "+.EI / L*2 =
() 4.+ = 0 =
() 5.+ = "+.EI / L*2 =
() +.+ = 4 EI / L =
""# !atatan matriks kekakan batang dalam arah smb l&kal %smb l&kal ata
1 2
()14 ()15 ()1+ 1410000 0
()24 ()25 ()2+ 0 5+400
()34 ()35 ()3+ = 0 ,0500
()44 ()45 ()4+ "1410000 0
()54 ()55 ()5+ 0 "5+400
()+4 ()+5 ()++ 0 ,0500
0deg
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
17/345
0 0 0
0 0 0 =
0 0 0
0
0
0 0 1
0 0 0
0 0 0
0 0 0
1.00 0 0
0 1.00 0
0 0 1
0.00 0.00 0.00 1410000 0
0.00 0.00 0.00 0 5+400
0.00 0.00 0.00 ? 0 ,0500
1.00 0.00 0.00 "1410000 0
0.00 1.00 0.00 0 "5+4000.00 0.00 1.00 0 ,0500
"1410000 0 0 1 0
0 "5+400 ,0500 0 1
0 ",0500 5-,50 ? 0 0
1410000 0 0 0 0
0 5+400 ",0500 0 0
0 ",0500 11,500 0 0
(AL $AN (
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
18/345
() 4.2 = 0 =
() 5.2 = "12.EI/L*3 =
() +.2 = +.EI / L*2 =
() 4.3 = 0 =
() 5.3 = "+.EI / L*2 =
() +.3 = 2 EI / L =
() 4.4 = E.A / L =
() 5.4 = 0 =
() +.4 = 0 =
() 4.5 = 0 =
() 5.5 = 12.EI/L*3 =
() +.5 = "+.EI / L*2 =
() 4.+ = 0 =
() 5.+ = "+.EI / L*2 =
() +.+ = 4 EI / L =
""# !atatan matriks kekakan batang dalam arah smb l&kal %smb l&kal ata
1 2
()14 ()15 ()1+ ,05000 0
()24 ()25 ()2+ 0 ,050
()34 ()35 ()3+ = 0 1,+25
()44 ()45 ()4+ ",05000 0
()54 ()55 ()5+ 0 ",050
()+4 ()+5 ()++ 0 1,+25
3+.-+-,+4+ deg 0.-
3+.-+-,+4+ deg 0.+
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
19/345
0 0 0
0 0 0 =
0 0 0
0
0
0 0 1
0 0 0
0 0 0
0 0 0
0.80 -0.6 0
0.6 0.80 0
0 0 1
0.00 0.00 0.00 ,05000 0
0.00 0.00 0.00 0 ,050
0.00 0.00 0.00 ? 0 1,+25
0.-0 "0.+0 0.00 ",05000 0
0.+0 0.-0 0.00 0 ",0500.00 0.00 1.00 0 1,+25
"5+4000 4230 "105,5 1 1
"423000 "5+40 14100 "1 1
0 "1,+25 23,5 ? 0 0
5+4000 "4230 105,5 0 0
423000 5+40 "14100 0 0
0 "1,+25 5-,50 0 0
(AL $AN (
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
20/345
() 5.2 = "12.EI/L*3 =
() +.2 = +.EI / L*2 =
() 4.3 = 0 =
() 5.3 = "+.EI / L*2 =
() +.3 = 2 EI / L =
() 4.4 = E.A / L =
() 5.4 = 0 =
() +.4 = 0 =
() 4.5 = 0 =
() 5.5 = 12.EI/L*3 =
() +.5 = "+.EI / L*2 =
() 4.+ = 0 =
() 5.+ = "+.EI / L*2 =
() +.+ = 4 EI / L =
""# !atatan matriks kekakan batang dalam arah smb l&kal %smb l&kal ata
1 2
()14 ()15 ()1+ 1410000 0
()24 ()25 ()2+ 0 5+400
()34 ()35 ()3+ = 0 ,0500
()44 ()45 ()4+ "1410000 0
()54 ()55 ()5+ 0 "5+400
()+4 ()+5 ()++ 0 ,0500
0 deg 1
0 deg 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
21/345
0 0 0
0 0 0 =
0 0 0
0
0
0 0 1
0 0 0
0 0 0
0 0 0
1.00 0 0
0 1.00 0
0 0 1
0.00 0.00 0.00 1410000 0
0.00 0.00 0.00 0 5+400
0.00 0.00 0.00 ? 0 ,0500
1.00 0.00 0.00 "1410000 0
0.00 1.00 0.00 0 "5+400
0.00 0.00 1.00 0 ,0500
"1410000 0 0 1 0
0 "5+400 ,0500 0 1
0 ",0500 5-,50 ? 0 0
1410000 0 0 0 0
0 5+400 ",0500 0 0
0 ",0500 11,500 0 0
$1 0 $2
4 5 + ==# EN)AN (B 7LBAL
"164106000 0 0 1 0
0 "5+6400 ,06500 2 0
0 ",06500 5-6,50 3 0
164106000 0 0 4 $1
0 5+6400 ",06500 5 0
0 ",06500 11,6500 + $2
$3 0 $4
, - ==# EN)AN (B 7LBAL
!&s α1
sin α1
" sin α1
!&s α1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
22/345
"4536,3- "335601+ "1065,5 4 $1
"335601+ "25-6312 146100 5 0
1065,5 "146100 263,5 + $2
4536,3- 335601+ 1065,5 , $3
335601+ 25-6312 "146100 - 0
1065,5 "146100 5-6,50 $4
0 0 0
10 11 12 ==# EN)AN (B 7LBAL
"164106000 0 0 , $3
0 "5+6400 ,06500 - 0
0 ",06500 5-6,50 $4
164106000 0 0 10 0
0 5+6400 ",06500 11 0
0 ",06500 11,6500 12 0
$4
"1065,5 4 $1
263,5 + $2 =
1065,5 , $3
1,+6250 $4
0 1
30 2 kN
= 12.5 3 kN.m
0 4
30 5 kN
"12.5 + kN.m
SB LOKAL
22.5 1
25.3125 2
= 35.15+25 3
3,.5 4 a =
54.+-,5 5 b =
"5-.53,5 + L =
()("1
t
AML 1
AML 2
AML 3
AML 4
AML 5
AML 6
AML 1 .!&s α =
AML 2 .sin α =
AML 3
AML 4
AML 5
AML 6
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
23/345
SB LOKAL
0 1
+0 2 kN
= 25 3 kN.m
0 4
+0 5 kN
"25 + kN.m
SB LOKAL
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
1.00 0.00 0.00
0.00 1.00 0.00
0.00 0.00 1.00
0
0
0
1
0
2
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
24/345
0.00 0.00 0.000.00 0.00 0.00
0.00 0.00 0.00
0.80 -0.60 0.00
0.60 0.80 0.00
0.00 0.00 1.00
1
0
2
3
0
4
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
1.00 0.00 0.00
0.00 1.00 0.00
0.00 0.00 1.00
3
0
4
0
0
0
AMS 2 = R
T
. AML 2
AMS 2
AMS 3 = RT . AM
L 3
AMS 3
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
25/345
B7 2 B7 3
0 0 0
0 0 30
0 0 12.5
2.-125 0 2.-125
33.,5 0 = +3.,5
35.15+25 8 0 22.+5+25
"2.-125 0 "2.-125
++.25 +0 12+.25
"5-.53,5 25 "33.53,5
0 0 0
0 +0 +0
0 "25 "25
0 0
"30 0
"12.5 0
"2.-125 $1
= "+3.,5 0
"22.+5+25 $2
2.-125 $3"12+.25 0
33.53,5 $4
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
26/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
27/345
0 0 -1410000 0 0
56400 70500 0 -56400 70500
70500 117500 0 -70500 58750 3
0 0 1410000 0 0
-56400 -70500 0 56400 -70500
70500 58750 0 -70500 117500
0 0 0 -9.7179607165E-0070 0 0 0
0 0 0 3 -0.0001649936 0
0.8 0.6 0 9.7179607165E-007
-0.6 0.8 0 0
0 0 1 0.0002179852
0 0 -705000 0 0
7050 17625 0 -7050 17625
17625 58750 0 -17625 29375 3
0 0 705000 0 0
-7050 -17625 0 7050 -17625
17625 29375 0 -17625 58750
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
28/345
0.0 0.0 0.0 9.7179607165E-007
0.0 0.0 0.0 0
0.0 0.0 0.0 3 0.0002179852 0
1.0 0.0 0.0 00.0 1.0 0.0 0
0.0 0.0 1.0 0
0 0 -1410000 0 0
56400 70500 0 -56400 70500
70500 117500 0 -70500 58750 3
0 0 1410000 0 0
-56400 -70500 0 56400 -70500
70500 58750 0 -70500 117500
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
29/345
12.EI / L*3
5+400
,050
5+400
N $AN AN$A %8' %"'
"1410000
0
0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
30/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
31/345
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
0 "1410000 0 0 1
,0500 0 "5+400 ,0500 0
11,500 0 ",0500 5-,50 ? 0
0 1410000 0 0 0
",0500 0 5+400 ",0500 05-,50 0 ",0500 11,500 0
1
0 0 0 0 164106000
0 0 0 0 0
1 0 0 0 = 0
0 1 0 0 "164106000
0 0 1 0 0
0 0 0 1 0
N $AN AN$A %8' %"'
",05000
0
0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
32/345
0
",050
1,+25
0
"1,+25
23,5
,05000
0
0
0
,050
"1,+25
0
"1,+25
5-,50
gl&bal menentkan en&m&ran dan tanda %8' %"'
3 4 5 + sb l&kal
0 ",05000 0 0 1
1,+25 0 ",050 1,+25 2
5-,50 0 "1,+25 23,5 3
0 ,05000 0 0 4
"1,+25 0 ,050 "1,+25 5
23,5 0 "1,+25 5-,50 +
sb l&kal
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
33/345
0.8 0.6 0 0 0 0
-0.6 0.8 0 0 0 0
0 0 1 0 0 0
0 0 0 0.8 0.6 0
0 0 0 -0.6 0.8 0
0 0 0 0 0 1
0 ",05000 0 0 0.-0
1,+25 0 ",050 1,+25 "0.+0
5-,50 0 "1,+25 23,5 ? 0.00
0 ,05000 0 0 0.00
"1,+25 0 ,050 "1,+25 0.0023,5 0 "1,+25 5-,50 0.00
4
0 0 0 0 4536,3-
0 0 0 0 335601+
1 0 0 0 = "1065,5
0 1 1 0 "4536,3-
0 "1 1 0 "335601+
0 0 0 1 "1065,5
N $AN AN$A %8' %"'
"1410000
0
0
0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
34/345
"5+400
,0500
0
",0500
5-,50
1410000
0
0
0
5+400
",0500
0
",0500
11,500
gl&bal menentkan en&m&ran dan tanda %8' %"'
3 4 5 + sb l&kal
0 "1410000 0 0 1
,0500 0 "5+400 ,0500 2
11,500 0 ",0500 5-,50 3
0 1410000 0 0 4
",0500 0 5+400 ",0500 5
5-,50 0 ",0500 11,500 +
sb l&kal
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
35/345
1.0 0.0 0 0 0 0
0.0 1.0 0 0 0 0
0 0 1 0 0 0
0 0 0 1.0 0.0 0
0 0 0 0.0 1.0 0
0 0 0 0 0 1
0 "1410000 0 0 1
,0500 0 "5+400 ,0500 0
11,500 0 ",0500 5-,50 ? 0
0 1410000 0 0 0
",0500 0 5+400 ",0500 0
5-,50 0 ",0500 11,500 0
,
0 0 0 0 164106000
0 0 0 0 0
1 0 0 0 = 0
0 1 0 0 "164106000
0 0 1 0 0
0 0 0 1 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
36/345
5.,05+E"00, 2.22124-1+E"00- 1.3-++E"00, 2.2212E"00-
2.2212E"00- 5.-3-150,E"00+ "2.221E"00- ".,04E"00,
1.3-++E"00, "2.22124-2E"00- 5.,05+E"00, "2.221E"00-
2.2212E"00- ".,035++E"00, "2.221E"00- 5.-3-2E"00+
-0 kN = b/L =
+0 kN =
=
3.125 m = a/L =
1.-,5 m =
5 m =
AML 1
AML 2 b2%3a8b'/L3 =
AML 3 ab2/L2 =
AML 4
AML 5 a2%a83b'/L3 =
AML 6 "a2b/L2 =
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
37/345
1.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00
= 0.00 0.00 0.00 1.00 0.00
0.00 0.00 0.00 0.00 1.00
0.00 0.00 0.00 0.00 0.00
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
38/345
0.80 -0.60 0.00 0.00 0.000.60 0.80 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00
= 0.00 0.00 0.00 0.80 -0.60
0.00 0.00 0.00 0.60 0.80
0.00 0.00 0.00 0.00 0.00
1.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00
= 0.00 0.00 0.00 1.00 0.00
0.00 0.00 0.00 0.00 1.00
0.00 0.00 0.00 0.00 0.00
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
39/345
0
"30
"12.5
"2.-125
AE = "+3.,5
"22.+5+25
2.-125
"12+.25
33.53,5
0
"+0
25
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
40/345
-9.71796E-07
-1.64994E-04
9.71796E-07
2.17985E-04
0 1
0 2
0 3
-9.717961E-007 4
0 5
-0.0001649936 6
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
41/345
0 0 1.370
0 30 -11.632
0 0 12.5 -9.693 0
-9.717961E-007 0 -1.3700 30 11.632
-0.0001649936 -12.5 -19.387
-7.774369E-007 4 15.830776E-007 5 0
-0.0001649936 6 2
7.774369E-007 7 3
-5.830776E-007 8 0
0.0002179852 9 4
-7.774369E-007 22.5 -1.096
5.830776E-007 25.3125 0.942
0.000 0 35.15625 -3.270 0
0.000 37.5 1.096
0.000 54.6875 -0.942
0.000 -58.59375 7.980
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
42/345
9.717961E-007 7 3
0 8 0
0.0002179852 9 4
0 10 00 11 0
0 12 0
9.717961E-007 0 1.370
0 60 15.368
0.0002179852 0 25 25.613 0
0 0 -1.370
0 60 -15.368
0 -25 12.807
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
43/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
44/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
45/345
0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 00 0 0 0 1
2 3 4 5 + sb gl&bal
0 0 "164106000 0 0 1
5+6400 ,06500 0 "5+6400 ,06500 2
,06500 11,6500 0 ",06500 5-6,50 3
0 0 164106000 0 0 4
"5+6400 ",06500 0 5+6400 ",06500 5
,06500 5-6,50 0 ",06500 11,6500 +
sb gl&bal
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
46/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
47/345
0.+0 0.00 0.00 0.00 0.00
0.-0 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00
0.00 0.00 0.-0 0.+0 0.00
0.00 0.00 "0.+0 0.-0 0.000.00 0.00 0.00 0.00 1.00
5 + , - sb gl&bal
335601+ "1065,5 "4536,3- "335601+ "1065,5 4
25-6312 146100 "335601+ "25-6312 146100 5
146100 5-6,50 1065,5 "146100 263,5 +
"335601+ 1065,5 4536,3- 335601+ 1065,5 ,
"25-6312 "146100 335601+ 25-6312 "146100 -
146100 263,5 1065,5 "146100 5-6,50
sb gl&bal
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
48/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
49/345
0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
- 10 11 12 sb gl&bal
0 0 "164106000 0 0 ,
5+6400 ,06500 0 "5+6400 ,06500 -
,06500 11,6500 0 ",06500 5-6,50
0 0 164106000 0 0 10
"5+6400 ",06500 0 5+6400 ",06500 11
,06500 5-6,50 0 ",06500 11,6500 12
sb gl&bal
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
50/345
30
22.5 kN
25.3125kN
35.15+25kN.m
3,.5 kN
54.+-,5kN
"5-.53,5 kN.m
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
51/345
0.00 0
0.00 30
0.00 > 12.5
0.00 0
0.00 30
1.00 -12.5
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
52/345
0.00 22.50.00 25.3125
0.00 > 35.15625
0.00 37.5
0.00 54.6875
1.00 -58.59375
0.00 0
0.00 60
0.00 > 25
0.00 0
0.00 60
1.00 -25
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
53/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
54/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
55/345
1.37 1 1.3,02kN
18.37 2 1-.3+-0kN
2.81 3 2.-0++ kN.m
-1.37 4 "1.3,02 kN41.63 5 41.+320kN
-31.89 6 "31.--+,kN.m
21.40 1 1 21.403-kN
26.25 2 0 2+.254,kN
31.89 3 2 31.--+,kN.m
38.60 4 3 3-.5+2kN
53.75 5 0 53.,453kN
-50.61 6 4 "50.+133kN.m
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
56/345
1.37 1 3 1.3,02kN
75.37 2 0 ,5.3+-0kN
50.61 3 4 50.+133kN.m
-1.37 4 0 "1.3,02 kN
44.63 5 0 44.+320kN
-12.19 6 0 "12.134kN.m
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
57/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
58/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
59/345
0
0
0
$1
0
$2
@E>
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
60/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
61/345
$1
0
$2
$3
0
$4
@E>
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
62/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
63/345
$3
0
$4
0
0
0
@E>
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
64/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
65/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
66/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
67/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
68/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
69/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
70/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
71/345
Beban ekialen
&int (b 7l&bal Element 1 Element 2 Element 3
1 1 0 0 0
1 2 30 0 0
1 3 12.5 0 0
"Ae = 2 4 0 2.-125 0
2 5 30 33.,5 0
2 + "12.5 8 35.15+25 8 0 =
3 , 0 "2.-125 0
3 - 0 ++.25 +0
3 0 "5-.53,5 254 10 0 0 0
4 11 0 0 +0
4 12 0 0 "25
eban *oint akibat beban &uar 'i *oint
&int (b 7l&bal $C
1 1 0
1 2 0
A = 1 3 0
2 4 0 d1
2 5 0
2 + 0 d2
3 , 0 d3
3 - 0
3 0 d4
4 10 0
4 11 0
4 12 0
eban kombinasi atau gabungan (Ae + A*)
A! = Ae 8 A
$C
1 0 0 1 0
A! = 2 "30 0 1 "30
3 "12.5 0 hi1 "12.5
4 "2.-125 0 2 "2.-125 d1
5 "+3.,5 0 2 "+3.,5+ "22.+5+25 8 0 = hi2 "22.+5+25 d2
, 2.-125 0 3 2.-125 d3
- "12+.25 0 3 "12+.25
33.53,5 0 hi3 33.53,5 d4
10 0 0 4 0
11 "+0 0 4 "+0
12 25 0 hi4 25
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
72/345
+0
sin 0.-++0254 +0
cos 0.5 +0
1.,32050-1 +0
tan theta 0.,5 3+.-+-,+
0.,5
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
73/345
M#"AN!"A #"A,ASA -
%ata beban
= 100 kN
;1 = 24 kN/m
;2 = 4- kN/m
versi lengka
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
74/345
ST#P 1 %is/reti0e an' &oba& %egrees o ree'om (%O)
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
75/345
P#N,##SA!AN
Properties penampang
Bahan / material :
E = 2.35E80, kN/m2
Batang 1 :
b = 0.30 m
h = 0.50 m
0.15 m2E = 2.35E80, kN/m2
3.13E"03m4
2.5m
Batang 3 :
b = 0.30 m
h = 0.50 m
0.15 m2
E = 2.35E80, kN/m2
3.13E"03m4
2.5m
ekap #&emen 'a&am Matriks "ekakuan atang
Batang EA ? L 4.EI ? L 2.EI ? L 6.EI ? L@2 12.EI ? L@3 S&* &",! D?
1 1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804 0 1
2 ,.05E805 5.--E804 2.4E804 1.,+E804 ,.05E803 3+.-+-,+4+ 0.-
3 1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804 0 1
4 $I@/0F $I@/0F $I@/0F $I@/0F $I@/0F 0 1
5 ECF ECF ECF ECF ECF ECF
%O sesuai sumbu g&oba& struktur 'an tentukan eban atau Momen pa'a Titik 5oint Struktur 'a&am Ara6 Sumbu &oba&7Su
A1 =
I1 =
L1 =
A3 =
I3 =
L3 =
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
76/345
DOF
1
1 1 0
2 2 0
3 3 0
2
4 d1 0
5 5 0
+ d2 0
3
, d3 0
- - 0
d4 0
410 10 011 11 0
12 12 0
Nomor *oint untuk setiap e&ement
#&ement (i)5oint
* k
1 1 22 2 3
3 3 4
%isp&a/ement titik sumbu g&oba& struktur pa'a tiap e&ement
#&ement * k
1 1 2 3 4 5 + ==> Global axis
2 4 5 + , - ==> Global axis
3 , - 10 11 12 ==> Global axis
No.titik!oint"
Dis.GlobalAxis
B#ban $%on
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
77/345
==> Global axis
==> Global axis
Meng6itung a8a 'an Momen $*ung (Akibat beban &uar 'i sepan*ang bentang 'engan u*ung 'ikekang7'i*epit) (%AAM AA
a8a 'an Momen $*ung pa'a #&ement 91
'a = 0 kN 'b = 0 kN
(a = 30 kN (b = 30 kN
%a = 12.5 kN.& %b = "12.5 kN.&
a8a 'an Momen $*ung pa'a #&ement 92'a = 22.5 kN 'b = 3,.5 kN
(a = 25.3125kN (b = 54.+-,5 kN
%a = 35.15+25 kN.& %b = "5-.53,5kN.&
a8a 'an Momen $*ung pa'a #&ement 93
'a = 0 kN 'b = 0 kN
(a = +0 kN (b = +0 kN
%a = 25 kN.& %b = "25 kN.&
ekap a8a $*ung atang (Sumbu oka&)
No. Btg)*+ng ki,i *" )*+ng kanan k"
B"b#$ :'! B"b#$ :'! B"b#$ MC'! B"b#$ :! B"b#$ :! B"b#$ MC!
1 0 30 12.5 0 30 "12.5
2 22.5 25.3125 35.15+25 3,.5 54.+-,5 "5-.53,5
3 0 +0 25 0 +0 "25
4 ECF ECF ECF ECF ECF ECF
5
Tentukan parameter 8ang 'ibutu6kan
a. (mb gl&bal strktr ada tia element
b. $C sesai smb gl&bal strktr
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
78/345
!. -#s#s+aian sb lokal #l#nt d#ngan DOF a,a global
d.
!.
Local Axis 1 2 3 4 5
/l#nt k# 1 1 2 3 d1 d2
/l#nt k# 2 &1.;>;&2;>; &1.;>;&2;>; d3 4 5
/l#nt k# 3 d1 d2 d3 , -
/l#nt 01
Local axis 1 2 3 4 5 +
Global axis 1 1 2 3 4 5
DOF 0 0 0 d1 0 d2
/l#nt 02
Local axis 1 2 3 4 5 +
Global axis 4 5 + , -
DOF d1 0 d2 0
d.
#&ement 1
0 0 0 0
0 0 0 0
= 0 0 1 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0 0 1
)atriks rans&rmasi dan tia element
-#s#s+aian S O"A #l#nt d#ngan S OA 'an %O ara6 g&oba&
)atriks rans&rmasi dan tia element
!&s α1
sin α1
" sin α1
!&s α1
!&s α1
sin α1
" sin α1
!&s α1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
79/345
#&ement 2
0 0 0 0
0 0 0 0
= 0 0 1 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0 0 1
#&ement 3
0 0 0 0
0 0 0 0
= 0 0 1 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0 0 1
!&s α1
sin α1
" sin α1
!&s α1
!&s α1
sin α1
" sin α1
!&s α1
!&s α1
sin α1
" sin α1
!&s α1
!&s α1
sin α1
" sin α1
!&s α1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
80/345
:::; %AAM S$M$ O"A
Batang = 1
/l#n dala& &at,iks k#kak+an batang :
EA / L 4.EI / L 2.EI / L +.EI / L*2 12.EI / L*3
1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804
D? = !&s theta = 1
DG = sin theta = 0
L&!al a?is 1 2 3 4 5 +
1 1410000 0 0 "1410000 0 0
2 0 5+400 ,0500 0 "5+400 ,0500
3 0 ,0500 11,500 0 ",0500 5-,50
4 "1410000 0 0 1410000 0 0
5 0 "5+400 ",0500 0 5+400 ",0500
+ 0 ,0500 5-,50 0 ",0500 11,500
:::; %AAM S$M$ O"A
Batang = 2
/l#n dala& &at,iks k#kak+an batang :
EA / L 4.EI / L 2.EI / L +.EI / L*2 12.EI / L*3,.05E805 5.--E804 2.4E804 1.,+E804 ,.05E803
D? = !&s theta = 0.-
DG = sin theta = 0.+
L&!al a?is 1 2 3 4 5 +
1 ,05000 0 0 ",05000 0 0
2 0 ,050 1,+25 0 ",050 1,+25
3 0 1,+25 5-,50 0 "1,+25 23,5
4 ",05000 0 0 ,05000 0 0
Hitung matriks kekakuan batang 1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
81/345
5 0 ",050 "1,+25 0 ,050 "1,+25
+ 0 1,+25 23,5 0 "1,+25 5-,50
:::; %AAM S$M$ O"A
Batang = 3
/l#n dala& &at,iks k#kak+an batang :
EA / L 4.EI / L 2.EI / L +.EI / L*2 12.EI / L*3
1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804
D? = !&s theta = 1DG = sin theta = 0
L&!al a?is 1 2 3 4 5 +
1 1410000 0 0 "1410000 0 0
2 0 5+400 ,0500 0 "5+400 ,0500
3 0 ,0500 11,500 0 ",0500 5-,50
4 "1410000 0 0 1410000 0 0
5 0 "5+400 ",0500 0 5+400 ",0500
+ 0 ,0500 5-,50 0 ",0500 11,500
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
82/345
, "453,3- 105,5 1-+3,3- 105,5 0 0
"105,5 23,5 105,5 1,+250 0 0
1 "1410000 0 0 0 1410000 0
2 0 ,0500 0 0 0 5+400
3 0 5-,50 0 0 0 ,0500
5 33501+ "5+400 "33501+ 14100 0 "5+400
- "33501+ "14100 33501+ 5+400 0 0
10 0 0 "1410000 0 0 0
11 0 0 0 ",0500 0 0
12 0 0 0 5-,50 0 0
0 0 0 0 0 0
0 0 0 0 0 00 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
Hitung Matriks eban 5oint7 No'a&
No'a& or/es
a. Akibat beban 'i sepan*ang bentang (ke'ua u*ung 'ikekang)
#&ement 1 rans&rmasi sb l&k
L&!al a?is
0 1
30 2
= 12.5 3
0 4
30 5
"12.5 +
()( =
A)L1
A)(1
A)(1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
83/345
#&ement 2 rans&rmasi sb l&k
L&!al a?is
22.5 1
25.3125 2
= 35.15+25 3
3,.5 4
54.+-,5 5
"5-.53,5 +
#&ement 3 rans&rmasi sb l&k
L&!al a?is
0 1
+0 2
= 25 3
0 4
+0 5
"25 +
A)L2
A)(2
A)(2
A%L3
A%(3
A%(3
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
84/345
Susun matriks beban eki>a&en
&int (b 7l&bal Element 1 Element 2
1 1 0 0
1 2 30 01 3 12.5 0
2 4 0 2.-125
"Ae = 2 5 30 8 33.,5 8
2 + "12.5 35.15+25
3 , 0 "2.-125
3 - 0 ++.25
3 0 "5-.53,5
4 10 0 0
4 11 0 0
4 12 0 0
5 13 0 0
5 14 0 0
5 15 0 0
+ 1+ 0 0
+ 1, 0 0+ 1- 0 0
b. Akibat eban 'i *oint (ke'ua u*ung 'ikekang)
&int (b 7l&bal $C
1 1 0 1
1 2 0 2
1 3 0 3
2 4 0 d1
A = 2 5 0 5
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
85/345
2 + 0 d2
3 , 0 d3
3 - 0 -
3 0 d4
4 10 0 10
4 11 0 11
4 12 0 12
5 13 N/A N/A
5 14 N/A N/A
5 15 N/A N/A
+ 1+ N/A N/A
+ 1, N/A N/A
+ 1- N/A N/A
/. eban kombinasi atau gabungan (Ae + A*)
&int (b 7l&bal $C
1 1 1 0 0
1 2 2 "30 0
1 3 3 "12.5 0
2 4 d1 "2.-125 0
A! = 2 5 5 "+3.,5 8 0
2 + d2 "22.+5+25 0
3 , d3 2.-125 0
3 - - "12+.25 0
3 d4 33.53,5 0
4 10 10 0 04 11 11 "+0 0
4 12 12 25 0
5 13 N/A 0 N/A
5 14 N/A 0 N/A
5 15 N/A 0 N/A
+ 1+ N/A 0 N/A
+ 1, N/A 0 N/A
+ 1- N/A 0 N/A
$isla!ement / $e&rmasi (trktr
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
86/345
d1 = ".,1,+0,1+E"00,
d2 = "0.0001+43+
d3 = .,1,+0,1+5E"00,
d4 = 0.00021,-52
=
=
=
=
=
=
=
=
=
ea!ti&ns:
7AHA"7AHA $ALA)
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
87/345
0 1410000 0 0 "1410000
30 0 5+400 ,0500 0
12.5 8 0 ,0500 11,500 0
0 "1410000 0 0 1410000
30 0 "5+400 ",0500 0
"12.5 0 ,0500 5-,50 0
atang 2
$e&rmasi strktr dalam arah (
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
88/345
10 10 0
11 11 0
12 12 0
7aGa ng batang
0 1410000 0 0 "1410000
+0 0 5+400 ,0500 0
25 8 0 ,0500 11,500 0
0 "1410000 0 0 1410000
+0 0 "5+400 ",0500 0
"25 0 ,0500 5-,50 0
S##SA!
AM ! 0 AML ! M ! 4 M !
A%3 =
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
89/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
90/345
Defined DOF
after boundary conditions
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
91/345
Batang 2 :
b = 0.30 m
h = 0.50 m
0.15 m2E = 2.35E80, kN/m2
3.13E"03m4
5 m
DG
0
0.+
0
0
mbu Struktur
A2 =
I2 =
L2 =
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
92/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
93/345
H S$M$ O"A)
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
94/345
+
d3 6=== DOF s#s+ai sb global
+ 6=== DOF s#s+ai sb global
6=== DOF s#s+ai sb global
),aian sb global :
),aian sb 4 = 1.7x 8 2.79
),aian sb = 1.79 8 2.7x
),aian sb ; = 4.7x 8 .79
),aian sb < = 4.79 8 .7x
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
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
95/345
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
"0.+ 0.- 0 0 0 0
= 0 0 1 0 0 0
0 0 0 0.- 0.+ 0
0 0 0 "0.+ 0.- 00 0 0 0 0 1
0.- "0.+ 0 0 0 0
0.+ 0.- 0 0 0 0
0 0 1 0 0 0
0 0 0 0.- "0.+ 0
0 0 0 0.+ 0.- 0
0 0 0 0 0 1
1 0 0 0 0 0
0 1 0 0 0 0
= 0 0 1 0 0 00 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
=
=
=
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
96/345
1 2 3 d1 5 d2
7l&bal a?is 1 2 3 4 5 +
1 1410000 0 0 "1410000 0 0 "
2 0 5+400 ,0500 0 "5+400 ,0500 "
3 0 ,0500 11,500 0 ",0500 5-,50 "
4 "1410000 0 0 1410000 0 0 "
5 0 "5+400 ",0500 0 5+400 ",0500 "
+ 0 ,0500 5-,50 0 ",0500 11,500 "
d1 5 d2 d3 - d4
7l&bal a?is 4 5 + , -
4 453,3- 33501+ "105,5 "453,3- "33501+ "105,5 "
5 33501+ 25-312 14100 "33501+ "25-312 14100 "
+ "105,5 14100 5-,50 105,5 "14100 23,5 "
, "453,3- "33501+ 105,5 453,3- 33501+ 105,5 "
()(1
=
()(2
=
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
97/345
- "33501+ "25-312 "14100 33501+ 25-312 "14100 "
"105,5 14100 23,5 105,5 "14100 5-,50 "
d3 - d4 10 11 12
7l&bal a?is , - 10 11 12
, 1410000 0 0 "1410000 0 0 "
- 0 5+400 ,0500 0 "5+400 ,0500 "
0 ,0500 11,500 0 ",0500 5-,50 "
10 "1410000 0 0 1410000 0 0 "
11 0 "5+400 ",0500 0 5+400 ",0500 "
12 0 ,0500 5-,50 0 ",0500 11,500 "
d3 - d4 10 11 12
, - 10 11 12
3 5 - 10 11 12 0 0 0 0 0
3 5 - 10 11 12
0 33501+ "33501+ 0 0 0 0 0 0 0 0
5-,50 "5+400 "14100 0 0 0 0 0 0 0 0
%(3
=
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
98/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
99/345
al ke gl&bal ==#
0.- "0.+ 0 0 0 0 22.5
0.+ 0.- 0 0 0 0 25.3125
= 0 0 1 0 0 0 ? 35.15+25
0 0 0 0.- "0.+ 0 3,.5
0 0 0 0.+ 0.- 0 54.+-,5
0 0 0 0 0 1 "5-.53,5
7l&bal a?is !ek
4 2.-125 "
5 33.,5 "
= + 35.15+25 "
, "2.-125 "
- ++.25 "
"5-.53,5 "
al ke gl&bal ==#
1 0 0 0 0 0 0
0 1 0 0 0 0 +0
= 0 0 1 0 0 0 ? 25
0 0 0 1 0 0 0
0 0 0 0 1 0 +0
0 0 0 0 0 1 "25
7l&bal a?is !ek
, 0 "
- +0 "
= 25 "
10 0 "
11 +0 "
AMS 2 = RT . AM
L 2
AMS 3 = RT . AM
L 3
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
100/345
12 "25 "
/l#nt 3 /l#nt 4 /l#nt
0 0 0 0 0 1
0 0 0 30 "30 20 0 0 12.5 "12.5 3
0 0 0 2.-125 "2.-125 4
0 8 0 8 0 = +3.,5 Ae = "+3.,5 5
0 0 0 22.+5+25 "22.+5+25 +
0 0 0 "2.-125 2.-125 ,
+0 0 0 12+.25 "12+.25 -
25 0 0 "33.53,5 33.53,5
0 0 0 0 0 10
+0 0 0 +0 "+0 11
"25 0 0 "25 25 12
0 0 0 0 0 13
0 0 0 0 0 14
0 0 0 0 0 15
0 0 0 0 0 1+
0 0 0 0 0 1,0 0 0 0 0 1-
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
101/345
ata lang A! :
0 d1 "2.-125 "
"30 d2 "22.+5+25 "
"12.5 d3 2.-125 "
"2.-125 d4 33.53,5 "
= "+3.,5 A! = 1 0 "
"22.+5+25 2 "30 "
2.-125 3 "12.5 "
"12+.25 5 "+3.,5 "
33.53,5 - "12+.25 "
0 10 0 ""+0 11 "+0 "
25 12 25 "
N/A 0 N/A
N/A 0 N/A
N/A 0 N/A
N/A 0 N/A
N/A 0 N/A
N/A 0 N/A
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
102/345
7#k: O-
"
"
"
"
$e&rmasi strktr dalam arah (AL di batang 16 sbb :
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 ? 0 = 0
0 0 0 1 0 0 ".,1-E"00, ".,1-E"00,
0 0 0 0 1 0 0 0
0 0 0 0 0 1 "0.0001+4 "0.0001+4
sb l&kal
M 1 0 ' 4 #M 1
∆M 1 =
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
103/345
0 0 0 0 1.3,02324+1 1.3,02324+1 1
"5+400 ,0500 0 30 "11.+3204+1 1-.3+,530 2
",0500 5-,50 ? 0 = 12.5 8 ".+33,2425 = 2.-0++2,5,52 3
0 0 ".,1-E"00, 0 "1.3,02324+1 "1.3,02324+1 4
5+400 ",0500 0 30 11.+3204+1 41.+3204+1 5
",0500 11,500 "0.0001+4 "12.5 "1.3-+,44-5 "31.--+,44-5 +
$e&rmasi strktr dalam arah (AL di batang 26 sbb :
0.- 0.+ 0 0 0 0 ".,1-E"00, ",.,,4E"00,
"0.+ 0.- 0 0 0 0 0 5.-31E"00,
0 0 1 0 0 0 ? "0.0001+4 = "0.0001+4
0 0 0 0.- 0.+ 0 .,1-E"00, ,.,,4E"00,
0 0 0 "0.+ 0.- 0 0 "5.-31E"00,
0 0 0 0 0 1 0.00021, 0.00021,
sb l&kal
0 0 ",.,,4E"00, 22.5 "1.0+1-5+ 21.403-14031 1
",050 1,+25 5.-31E"00, 25.3125 0.421,3 2+.254+,4 2
"1,+25 23,5 ? "0.0001+4 = 35.15+25 8 "3.2+50515 = 31.--+,44-5 3
0 0 ,.,,4E"00, 3,.5 1.0+1-5+-- 3-.5+1-5+ 4
,050 "1,+25 "5.-31E"00, 54.+-,5 "0.421,4 53.,453020+ 5
"1,+25 5-,50 0.00021, "5-.53,5 ,.-044-4, "50.+1325515 +
D#o,&asi st,+kt+, dala& a,a )%B) LO-AL di batang 35 sbb :
1 0 0 0 0 0 .,1-E"00, .,1-E"00,
0 1 0 0 0 0 0 0
0 0 1 0 0 0 ? 0.00021, = 0.00021,
M 2 0 ' 4 #M 2
∆M 2 =
M ! 0 ' 4 #M !
∆M 3 =
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
104/345
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
sb l&kal
0 0 .,1-E"00, 0 1.3,02324+1 1.3,02324+1 1
"5+400 ,0500 0 +0 15.3+,530 ,5.3+,530 2
",0500 5-,50 ? 0.00021, = 25 8 25.+1325515 = 50.+1325515 3
0 0 0 0 "1.3,02324+1 "1.3,02324+1 4
5+400 ",0500 0 +0 "15.3+,530 44.+3204+1 5
",0500 11,500 0 "25 12.-0++2,5,5 "12.133,2425 +
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
105/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
106/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
107/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
108/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
109/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
110/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
111/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
112/345
" " "
" " "
" " "
" " "
" " "
" " "
" " "
" " "
" " "
" " "
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
113/345
" " "
" " "
" " "
" " "
" " "
" " "
" " "
" " "
0 === $itata
0 4 d1
0 + d2
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
114/345
0 , d3
0 d4
0 1 1
0 2 2
0 3 3
0 5 5
0 - -
0 10 10
0 11 11
0 12 12
0 0 0
0 0 00 0 0
0 0 0
0 0 0
0 0 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
115/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
116/345
1
23
d1
5
d2
d3
-
d4
10
11
12
N/A
N/A
N/A
N/A
N/AN/A
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
117/345
"
"
"
"
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
118/345
sb l&kal DOF
1 1
2 2
3 3
4 d1
5 d2
+ d3
$C / sb gl&bal
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
119/345
1
2
3
d1
d2
d3
sb l&kal DOF
1 .D?DG8d2D?DG
2 .D?DG8d2D?DG
3 d3
4 4
5 5
+ +
$C / sb gl&bal
.D?DG8d2D?DG
.D?DG8d2D?DG
d3
4
5
+
sb l&kal DOF
1 d1
2 d2
3 d3
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
120/345
4 ,
5 -
+
$C / sb gl&bal
d1
d2
d3
,
-
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
121/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
122/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
123/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
124/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
125/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
126/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
127/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
128/345
%
" " 1 0 0 0 0 0 1410000 0
" " 0 1 0 0 0 0 0 5+400
" " 0 0 1 0 0 0 0 ,0500
" " 0 0 0 1 0 0 "1410000 0
" " 0 0 0 0 1 0 0 "5+400
" " 0 0 0 0 0 1 0 ,0500
" " %
" " 0.- "0.+ 0 0 0 0 ,05000 0
" " 0.+ 0.- 0 0 0 0 0 ,050
" " 0 0 1 0 0 0 0 1,+25
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
129/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
130/345
@ @ @ @
@ @ @ @
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
131/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
132/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
133/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
134/345
Dek
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
135/345
"
"
"
"
"
"
Dek
"
"
"
"
"
"
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
136/345
Dek
"
"
"
"
"
"
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
137/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
138/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
139/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
140/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
141/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
142/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
143/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
144/345
?
0 "1410000 0 0 1 0 0 0 0 0
,0500 0 "5+400 ,0500 0 1 0 0 0 0
11,500 0 ",0500 5-,50 0 0 1 0 0 0 =
0 1410000 0 0 0 0 0 1 0 0
",0500 0 5+400 ",0500 0 0 0 0 1 0
5-,50 0 ",0500 11,500 0 0 0 0 0 1
?
0 ",05000 0 0 1 1 0 0 0 0
1,+25 0 ",050 1,+25 "1 1 0 0 0 0
5-,50 0 "1,+25 23,5 0 0 1 0 0 0 =
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
145/345
0 ,05000 0 0 0 0 0 1 1 0
"1,+25 0 ,050 "1,+25 0 0 0 "1 1 0
23,5 0 "1,+25 5-,50 0 0 0 0 0 1
?
0 "1410000 0 0 1 0 0 0 0 0
,0500 0 "5+400 ,0500 0 1 0 0 0 0
11,500 0 ",0500 5-,50 0 0 1 0 0 0 =
0 1410000 0 0 0 0 0 1 0 0
",0500 0 5+400 ",0500 0 0 0 0 1 0
5-,50 0 ",0500 11,500 0 0 0 0 0 1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
146/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
147/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
148/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
149/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
150/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
151/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
152/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
153/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
154/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
155/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
156/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
157/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
158/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
159/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
160/345
1410000 0 0 "1410000 0 0 1 0 0 0 0
0 5+400 ,0500 0 "5+400 ,0500 0 1 0 0 0
0 ,0500 11,500 0 ",0500 5-,50 0 0 1 0 0
"1410000 0 0 1410000 0 0 0 0 0 1 0
0 "5+400 ",0500 0 5+400 ",0500 0 0 0 0 1
0 ,0500 5-,50 0 ",0500 11,500 0 0 0 0 0
5+4000 "4230 "105,5 "5+4000 4230 "105,5 0.- 0.+ 0 0 0
423000 5+40 14100 "423000 "5+40 14100 "0.+ 0.- 0 0 0
0 1,+25 5-,50 0 "1,+25 23,5 0 0 1 0 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
161/345
"5+4000 4230 105,5 5+4000 "4230 105,5 0 0 0 0.- 0.+
"423000 "5+40 "14100 423000 5+40 "14100 0 0 0 "0.+ 0.-
0 1,+25 23,5 0 "1,+25 5-,50 0 0 0 0 0
1410000 0 0 "1410000 0 0 1 0 0 0 0
0 5+400 ,0500 0 "5+400 ,0500 0 1 0 0 0
0 ,0500 11,500 0 ",0500 5-,50 0 0 1 0 0
"1410000 0 0 1410000 0 0 0 0 0 1 0
0 "5+400 ",0500 0 5+400 ",0500 0 0 0 0 1
0 ,0500 5-,50 0 ",0500 11,500 0 0 0 0 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
162/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
163/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
164/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
165/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
166/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
167/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
168/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
169/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
170/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
171/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
172/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
173/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
174/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
175/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
176/345
DE>
0 1410000 0 0 "1410000 0 0 " " "
0 0 5+400 ,0500 0 "5+400 ,0500 " " "
0 = 0 ,0500 11,500 0 ",0500 5-,50 " " "
0 "1410000 0 0 1410000 0 0 " " "
0 0 "5+400 ",0500 0 5+400 ",0500 " " "
1 0 ,0500 5-,50 0 ",0500 11,500 " " "
DE>
0 453,3- 33501+ "105,5 "453,3- "33501+ "105,5 " " "
0 33501+ 25-312 14100 "33501+ "25-312 14100 " " "
0 = "105,5 14100 5-,50 105,5 "14100 23,5 " " "
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
177/345
0 "453,3- "33501+ 105,5 453,3- 33501+ 105,5 " " "
0 "33501+ "25-312 "14100 33501+ 25-312 "14100 " " "
1 "105,5 14100 23,5 105,5 "14100 5-,50 " " "
DE>
0 1410000 0 0 "1410000 0 0 " " "
0 0 5+400 ,0500 0 "5+400 ,0500 " " "
0 = 0 ,0500 11,500 0 ",0500 5-,50 " " "
0 "1410000 0 0 1410000 0 0 " " "
0 0 "5+400 ",0500 0 5+400 ",0500 " " "
1 0 ,0500 5-,50 0 ",0500 11,500 " " "
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
178/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
179/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
180/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
181/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
182/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
183/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
184/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
185/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
186/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
187/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
188/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
189/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
190/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
191/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
192/345
" " "
" " "
" " "
" " "
" " "
" " "
" " "
" " "
" " "
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
193/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
194/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
195/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
196/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
197/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
198/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
199/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
200/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
201/345
M#"AN!"A #"A,ASA -
%ata beban
= 100 kN
;1 = 24 kN/m
;2 = 4- kN/m
versi lengkap
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
202/345
ST#P 1 %is/reti0e an' &oba& %egrees o ree'om (%O)
Defined DOF
after boundary
1
2
12
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
203/345
P#N,##SA!AN
Properties penampang
Bahan / material :
E = 2.35E80, kN/m2
Batang 1 : Batang 2 :
b = 0.30 m b =
h = 0.50 m h =
0.15 m2E = 2.35E80, kN/m2 E =
3.13E"03m4
2.5m
Batang 3 :
b = 0.30 m
h = 0.50 m
0.15 m2
E = 2.35E80, kN/m2
3.13E"03m4
2.5m
ekap #&emen 'a&am Matriks "ekakuan atang
Batang EA ? L 4.EI ? L 2.EI ? L 6.EI ? L@2 12.EI ? L@3 S&* &",! D? DG
1 1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804 1-0 "1 1.22515E"01+
2 ,.05E805 5.--E804 2.4E804 1.,+E804 ,.05E803 21+.-+-,+5 "0.- "0.+
3 1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804 1-0 "1 1.22515E"01+
4 $I@/0F $I@/0F $I@/0F $I@/0F $I@/0F 1 0
5 ECF ECF ECF ECF ECF 1 0
%O sesuai sumbu g&oba& struktur 'an tentukan eban atau Momen pa'a Titik 5oint Struktur 'a&am Ara6 Sumbu &oba&7Sumbu Struktur
A1 = A2 =
I1 = I
2 =
L1 = L
2 =
A3 =
I3 =
L3 =
3
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
204/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
205/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
206/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
207/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
208/345
:::; %AAM S$M$ O"A
Batang = 1
/l#n dala& &at,iks k#kak+an batang :
EA / L 4.EI / L 2.EI / L +.EI / L*2 12.EI / L*3
1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804
D? = !&s theta = "1DG = sin theta = 1.22515E"01+
L&!al a?is 1 2 3 4 5 +
1 1410000 0 0 "1410000 0 0
2 0 5+400 ,0500 0 "5+400 ,0500
3 0 ,0500 11,500 0 ",0500 5-,50
4 "1410000 0 0 1410000 0 0
5 0 "5+400 ",0500 0 5+400 ",0500
+ 0 ,0500 5-,50 0 ",0500 11,500
:::; %AAM S$M$ O"A
Batang = 2
/l#n dala& &at,iks k#kak+an batang :EA / L 4.EI / L 2.EI / L +.EI / L*2 12.EI / L*3
,.05E805 5.--E804 2.4E804 1.,+E804 ,.05E803
D? = !&s theta = "0.-
DG = sin theta = "0.+
L&!al a?is 1 2 3 4 5 +
1 ,05000 0 0 ",05000 0 0
2 0 ,050 1,+25 0 ",050 1,+25
3 0 1,+25 5-,50 0 "1,+25 23,5
Hitung matriks kekakuan batang 1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
209/345
4 ",05000 0 0 ,05000 0 0
5 0 ",050 "1,+25 0 ,050 "1,+25
+ 0 1,+25 23,5 0 "1,+25 5-,50
:::; %AAM S$M$ O"A
Batang = 3
/l#n dala& &at,iks k#kak+an batang :
EA / L 4.EI / L 2.EI / L +.EI / L*2 12.EI / L*3
1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804
D? = !&s theta = "1
DG = sin theta = 1.22515E"01+
L&!al a?is 1 2 3 4 5 +
1 1410000 0 0 "1410000 0 0
2 0 5+400 ,0500 0 "5+400 ,0500
3 0 ,0500 11,500 0 ",0500 5-,50
4 "1410000 0 0 1410000 0 0
5 0 "5+400 ",0500 0 5+400 ",0500
+ 0 ,0500 5-,50 0 ",0500 11,500
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
210/345
+ 105,5 1,+250 "105,5 23,5 "-.+3,3E"012 ",0500 5-,50 5+400
, "453,3- "105,5 1-+3,3- "105,5 0 0 0 "33501+
105,5 23,5 "105,5 1,+250 0 0 0 "14100
1 "1410000 "-.+3,3E"012 0 0 1410000 "1.+5-3+05E"010 "-.+3,3E"012 1.+5-E"010
2 1.+5-3+E"010 ",0500 0 0 "1.+5-4E"010 5+400 ",0500 "5+400
3 -.+3,30E"012 5-,50 0 0 "-.+3,3E"012 ",0500 11,500 ,0500
5 33501+ 5+400 "33501+ "14100 1.+5-3+E"010 "5+400 ,0500 314,12
- "33501+ 14100 33501+ "5+400 0 0 0 "25-312
10 0 0 "1410000 -.+3,2++0,1E"012 0 0 0 0
11 0 0 1.+5-3+E"010 ,0500 0 0 0 0
12 0 0 "-.+3,3E"012 5-,50 0 0 0 0
0 0 0 0 0 0 0 00 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 0 0 0 0 0 0
Hitung Matriks eban 5oint7 No'a&
No'a& or/es
a. Akibat beban 'i sepan*ang bentang (ke'ua u*ung 'ikekang)
#&ement 1 rans&rmasi sb l&kal ke gl&bal ==#
L&!al a?is
0 1 "1
"+0 2 1.225E"01+
= "25 3 = 0
0 4 0
"+0 5 0
25 + 0
7l&bal a?is
1
2
= 3
4
5
()( =
A)L1
A)(1
A)(1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
211/345
+
#&ement 2 rans&rmasi sb l&kal ke gl&bal ==#
L&!al a?is
"3,.5 1 "0.-
"54.+-,5 2 "0.+
= "5-.53,5 3 = 0
"22.5 4 0
"25.3125 5 0
35.15+25 + 0
7l&bal a?is
4
5
= +
,
-
#&ement 3 rans&rmasi sb l&kal ke gl&bal ==#
L&!al a?is
0 1 "1"30 2 1.225E"01+
= "12.5 3 = 0
0 4 0
"30 5 0
12.5 + 0
7l&bal a?is
,
-
=
10
A)L2
A)(2
A)(2
A%L3
A%(3
A%(3
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
212/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
213/345
A = 2 5 0 5
2 + 0 d2
3 , 0 d3
3 - 0 -
3 0 d4
4 10 0 10
4 11 0 11
4 12 0 12
5 13 N/A N/A
5 14 N/A N/A
5 15 N/A N/A
+ 1+ N/A N/A
+ 1, N/A N/A
+ 1- N/A N/A
/. eban kombinasi atau gabungan (Ae + A*)
&int (b 7l&bal $C
1 1 1 ",.350-0,2E"015 0 ",.351E"015
1 2 2 "+0 0 "+0
1 3 3 25 0 25
2 4 d1 2.-125 0 2.-125
A! = 2 5 5 "12+.25 8 0 = "12+.25
2 + d2 33.53,5 0 33.53,5
3 , d3 "2.-125 0 "2.-125
3 - - "+3.,5 0 "+3.,5
3 d4 "22.+5+25 0 "22.+5+254 10 10 "3.+,54453+5E"015 0 "3.+,5E"015
4 11 11 "30 0 "30
4 12 12 "12.5 0 "12.5
5 13 N/A 0 N/A N/A
5 14 N/A 0 N/A N/A
5 15 N/A 0 N/A N/A
+ 1+ N/A 0 N/A N/A
+ 1, N/A 0 N/A N/A
+ 1- N/A 0 N/A N/A
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
214/345
$isla!ement / $e&rmasi (trktr
d1 = .,1,+0,1+5E"00,
d2 = 0.00021,-52
d3 = ".,1,+0,1+E"00,
d4 = "0.0001+43+
=
=
=
=
=
=
=
=
=
ea!ti&ns:
7AHA"7AHA $ALA)
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
215/345
0 1410000 0 0 "1410000 0 0
"+0 0 5+400 ,0500 0 "5+400 ,0500
"25 8 0 ,0500 11,500 0 ",0500 5-,50
0 "1410000 0 0 1410000 0 0
"+0 0 "5+400 ",0500 0 5+400 ",0500
25 0 ,0500 5-,50 0 ",0500 11,500
atang 2 $e&rmasi strktr dalam ar
$e&rmasi strktr dalam arah (
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
216/345
d4 "0.0001+44 0
10 10 0 0
11 11 0 0
12 12 0 0
7aGa ng batang
0 1410000 0 0 "1410000 0 0
"30 0 5+400 ,0500 0 "5+400 ,0500
"12.5 8 0 ,0500 11,500 0 ",0500 5-,50
0 "1410000 0 0 1410000 0 0
"30 0 "5+400 ",0500 0 5+400 ",0500
12.5 0 ,0500 5-,50 0 ",0500 11,500
S##SA!
D%(3 = ∆M 3 =
AM ! 0 AML ! M ! 4 M !
A%3 =
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
217/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
218/345
3
3
4
3
1 2
3 4
1
2
4
;
<
12
1
11
C#,indaan titik st,+kt+, dislac#nt titik"
J
H
gl&bal a?is
2
;
<
4
02
;
<
12
03
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
219/345
0.30 m
0.50 m
0.15 m22.35E80,kN/m2
3.13E"03m4
5 m
1
4
01
C#,indaan titik tia ,##bod9
12
3
4
d1
d2
d4 d3
DOF = 4 b+a
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
220/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
221/345
a/L = 3,.5
54.+-,5
"5-.53,5
b/L = 22.5
25.3125
35.15+25
a2%a83b'/L3 =
"a2b/L2 =
b2%3a8b'/L3 =
ab2/L2 =
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
222/345
s#s+ai sb global
s#s+ai sb global
s#s+ai sb global
lobal :
= 1.7x 8 2.79
= 1.79 8 2.7x
= 4.7x 8 .79
= 4.79 8 .7x
"1 1.225E"01+ 0 0 0 0
"1.2251E"01+ "1 0 0 0 0
0 0 1 0 0 0
0 0 0 "1 1.225E"01+ 0
0 0 0 "1.22514-455E"01+ "1 0
0 0 0 0 0 1
"1 "1.225E"01+ 0 0 0 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
223/345
1.22515E"01+ "1 0 0 0 0
0 0 1 0 0 0
0 0 0 "1 "1.225E"01+ 0
0 0 0 1.22514-454E"01+ "1 0
0 0 0 0 0 1
"0.- "0.+ 0 0 0 0
0.+ "0.- 0 0 0 0
0 0 1 0 0 0
0 0 0 "0.- "0.+ 00 0 0 0.+ "0.- 0
0 0 0 0 0 1
"0.- 0.+ 0 0 0 0
"0.+ "0.- 0 0 0 0
0 0 1 0 0 0
0 0 0 "0.- 0.+ 0
0 0 0 "0.+ "0.- 0
0 0 0 0 0 1
"1 1.225E"01+ 0 0 0 0
"1.2251E"01+ "1 0 0 0 0
0 0 1 0 0 0
0 0 0 "1 1.225E"01+ 0
0 0 0 "1.22514-455E"01+ "1 0
0 0 0 0 0 1
"1 "1.225E"01+ 0 0 0 0
1.22515E"01+ "1 0 0 0 0
0 0 1 0 0 0
0 0 0 "1 "1.225E"01+ 0
0 0 0 1.22514-454E"01+ "1 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
224/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
225/345
, "453,3- "33501+ "105,5 453,3- 33501+ "105,5 " "
- "33501+ "25-312 14100 33501+ 25-312 14100 " "
105,5 "14100 23,5 "105,5 14100 5-,50 216150.00 %2-6200.00'
d3 - d4 10 11 12
7l&bal a?is , - 10 11 12
, 1410000 "1.+5-4E"010 "-.+3,2++0,E"012 "1410000 1.+5-3+E"010 "-.+3,E"012 " %0.00'
- "1.+5-E"010 5+400 ",0500 1.+5-E"010 "5+400 ",0500 %0.00' "
"-.+3,E"012 ",0500 11,500 -.+3,E"012 ,0500 5-,50 %0.00'
10 "1410000 1.+5-4E"010 -.+3,2++0,1E"012 1410000 "1.+5-4E"010 -.+3,E"012 " 0.00
11 1.+5-E"010 "5+400 ,0500 "1.+5-E"010 5+400 ,0500 0.00 "
12 "-.+3,E"012 ",0500 5-,50 -.+3,E"012 ,0500 11,500 %0.00'
d4 10 11 12
10 11 12
- 10 11 12 0 0 0 0 0 0
- 10 11 12
"33501+ 0 0 0 0 0 0 0 0 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
226/345
14100 0 0 0 0 0 0 0 0 0
33501+ "1410000 1.+5-4E"010 "-.+3,2++0,E"012 0 0 0 0 0 0
"5+400 -.+3,E"012 ,0500 5-,50 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 0 0 0
"25-312 0 0 0 0 0 0 0 0 0
314,12 1.+5-E"010 "5+400 ",0500 0 0 0 0 0 0
1.+5-3+E"010 1410000 "1.+5-4E"010 -.+3,2++0,1E"012 0 0 0 0 0 0
"5+400 "1.+5-E"010 5+400 ,0500 0 0 0 0 0 0
",0500 -.+3,E"012 ,0500 11,500 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 00 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 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
"1.2251E"01+ 0 0 0 0 0
"1 0 0 0 0 "+0
0 1 0 0 0 ? "25
0 0 "1 "1.22514-455E"01+ 0 0
0 0 1.2251E"01+ "1 0 "+0
0 0 0 0 1 25
,.350-E"015
+0
"25
,.350-E"015
+0
AMS 1 = RT . AM
L 1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
227/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
228/345
30
12.5
/l#nt 4 /l#nt
0 0 ,.351E"015 ",.350-0,2E"015 1 10 0 +0 "+0 2 2
0 0 "25 25 3 3
0 0 "2.-125 2.-125 4 d1
0 8 0 = 12+.25 Ae = "12+.25 5 5
0 0 "33.53,5 33.53,5 + d2
0 0 2.-125 "2.-125 , d3
0 0 +3.,5 "+3.,5 - -
0 0 22.+5+25 "22.+5+25 d4
0 0 3.+,5E"015 "3.+,54453+5E"015 10 10
0 0 30 "30 11 11
0 0 12.5 "12.5 12 12
0 0 0 0 13 N/A
0 0 0 0 14 N/A
0 0 0 0 15 N/A
0 0 0 0 1+ N/A0 0 0 0 1, N/A
0 0 0 0 1- N/A
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
229/345
ata lang A! :
d1 2.-125 "2.-125
d2 33.53,5 "22.+5+25
d3 "2.-125 2.-125
d4 "22.+5+25 33.53,5
A! = 1 ",.350E"015 0
2 "+0 "30
3 25 "12.5
5 "12+.25 "+3.,5
- "+3.,5 "12+.2510 "3.+,54E"015 0
11 "30 "+0
12 "12.5 25
0 N/A
0 N/A
0 N/A
0 N/A
0 N/A
0 N/A
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
230/345
7#k: O-
".,1,+0,1+E"00, "+.352,4,104E"021
"0.0001+43+ 0.0003-2,-,
.,1,+0,1+5E"00, "1.4352143E"00+
0.00021,-52 "0.0003-2,-,
ah (AL di batang 16 sbb :
sb l&kal
1.22515E"01+ 0 0 0 0 0 0 1
"1 0 0 0 0 0 0 2
0 1 0 0 0 ? 0 = 0 3
0 0 "1 1.22514-454E"01+ 0 .,1-E"00, ".,1-E"00, 4
0 0 "1.2251E"01+ "1 0 0 "1.11E"022 5
0 0 0 0 1 0.00021, 0.00021, +
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
231/345
sb l&kal $C / sb gl&
0 0 1.3,02324+1 1.3,02324+1 1 1
0 "+0 15.3+,530 "44.+3204+0- 2 2
? 0 = "25 8 12.-0++2,5,5 = "12.133,2424- 3 3
".,1-E"00, 0 "1.3,02324+1 "1.3,02324+1 4 d1
"1.11E"022 "+0 "15.3+,530 ",5.3+,53002 5 d2
0.00021, 25 25.+1325515 50.+132551503 + d3
ah (AL di batang 26 sbb :
sb l&kal"0.+ 0 0 0 0 .,1-E"00, ",.,,4E"00, 1
"0.- 0 0 0 0 0 5.-31E"00, 2
0 1 0 0 0 ? 0.00021, = 0.00021, 3
0 0 "0.- "0.+ 0 ".,1-E"00, ,.,,4E"00, 4
0 0 0.+ "0.- 0 0 "5.-31E"00, 5
0 0 0 0 1 "0.0001+4 "0.0001+4 +
sb l&kal $C / sb gl&
",.,,4E"00, "3,.5 "1.0+1-5+ "3-.5+1-5+-- 1 .D?DG8d2D?
5.-31E"00, "54.+-,5 0.421,3 "53.,453020+01 2 .D?DG8d2D?
? 0.00021, = "5-.53,5 8 ,.-044-4, = "50.+132551503 3 d3
,.,,4E"00, "22.5 1.0+1-5+-- "21.403-140312 4 .D?DG8d2D?
"5.-31E"00, "25.3125 "0.421,4 "2+.254+,3 5 .D?DG8d2D?
"0.0001+4 35.15+25 "3.2+50515 31.--+,44-4, + +
a,a )%B) LO-AL di batang 35 sbb :
sb l&kal
1.22515E"01+ 0 0 0 0 ".,1-E"00, .,1-E"00, 1
"1 0 0 0 0 0 1.11E"022 2
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
232/345
0 1 0 0 0 ? "0.0001+4 = "0.0001+4 3
0 0 "1 1.22514-454E"01+ 0 0 0 4
0 0 "1.2251E"01+ "1 0 0 0 5
0 0 0 0 1 0 0 +
sb l&kal $C / sb gl&
.,1-E"00, 0 1.3,02324+1 1.3,02324+1 1 d1
1.11E"022 "30 "11.+3204+1 "41.+3204+0- 2 d2
? "0.0001+4 = "12.5 8 "1.3-+,44-5 = "31.--+,44-4, 3 d3
0 0 "1.3,02324+1 "1.3,02324+1 4 ,
0 "30 11.+3204+1 "1-.3+,53002 5 -
0 12.5 ".+33,2425 2.-0++2,5,52 +
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
233/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
234/345
1
1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
235/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
236/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
237/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
238/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
239/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
240/345
%0.00' "
0.00
" 0.00
0.00 "
1416000.00 %0.00'
" 0.00
216150.00 "
%2-6200.00' "
" %216150.00'
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
241/345
%216150.00' "
2-6200.00 "
" %216150.00'
%0.00' "
0.00
" 0.00
0.00 "
1416000.00 %0.00'
" 0.00
=== $itata
4 d1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
242/345
+ d2
, d3
d4
1 1
2 2
3 3
5 5
- -
10 10
11 11
12 12
0 00 0
0 0
0 0
0 0
0 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
243/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
244/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
245/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
246/345
DOF1
2
3
d1
d2
d3
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
247/345
al
"1.3,02324+
44.+3204+
"12.133,24
1.3,02324+
,5.3+,531
50.+132552
DOF
.D?DG8d2D?DG
.D?DG8d2D?DG
d3
.D?DG8d2D?DG
.D?DG8d2D?DG
+
al
G 3-.5+1-+
G 53.,453021
"50.+132552
G 21.403-14
G 2+.254+,
31.--+,44-
DOF
d1
d2
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
248/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
249/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
250/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
251/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
252/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
253/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
254/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
255/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
256/345
%
0.00 %0.00' "1 "1.225E"01+ 0 0 0 0 1410000
" 1.22514-4540E"01+ "1 0 0 0 0 0
1416000.00 " 0 0 1 0 0 0 0
%0.00' 0.00 0 0 0 "1 "1.225E"01+ 0 "1410000
" 1416000.00 0 0 0 1.225E"01+ "1 0 0
1416000.00 " 0 0 0 0 0 1 0
" 216150.00 %
" %2-6200.00' "0.- 0.+ 0 0 0 0 ,05000
2-6200.00 " "0.+ "0.- 0 0 0 0 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
257/345
" %216150.00' 0 0 1 0 0 0 0
" 2-6200.00 0 0 0 "0.- 0.+ 0 ",05000
2-6200.00 " 0 0 0 "0.+ "0.- 0 0
0 0 0 0 0 1 0
0.00 %0.00' %
" "1 "1.225E"01+ 0 0 0 0 1410000
1416000.00 " 1.22514-4540E"01+ "1 0 0 0 0 0
%0.00' 0.00 0 0 1 0 0 0 0
" 1416000.00 0 0 0 "1 "1.225E"01+ 0 "1410000
1416000.00 " 0 0 0 1.225E"01+ "1 0 0
0 0 0 0 0 1 0
7#k:
lang manal
@ 000 @ 000
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
258/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
259/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
260/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
261/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
262/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
263/345
Dek
%0.00' ?.43@B4B?@1#D1
"
"
0.00 ?.43@B4B?@11#D1
"
"
Dek
"
"
"
"
"
"
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
264/345
Dek
0.00 .11112312#D1
"
"
%0.00' .11112313#D1
"
"
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
265/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
266/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
267/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
268/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
269/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
270/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
271/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
272/345
?
0 0 "1410000 0 0 "1 0 0 0 0 0
5+400 ,0500 0 "5+400 ,0500 0 "1 0 0 0 0
,0500 11,500 0 ",0500 5-,50 0 0 1 0 0 0
0 0 1410000 0 0 0 0 0 "1 0 0
"5+400 ",0500 0 5+400 ",0500 0 0 0 0 "1 0
,0500 5-,50 0 ",0500 11,500 0 0 0 0 0 1
?
0 0 ",05000 0 0 "1 "1 0 0 0 0
,050 1,+25 0 ",050 1,+25 1 "1 0 0 0 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
273/345
1,+25 5-,50 0 "1,+25 23,5 0 0 1 0 0 0
0 0 ,05000 0 0 0 0 0 "1 "1 0
",050 "1,+25 0 ,050 "1,+25 0 0 0 1 "1 0
1,+25 23,5 0 "1,+25 5-,50 0 0 0 0 0 1
?
0 0 "1410000 0 0 "1 0 0 0 0 0
5+400 ,0500 0 "5+400 ,0500 0 "1 0 0 0 0
,0500 11,500 0 ",0500 5-,50 0 0 1 0 0 0
0 0 1410000 0 0 0 0 0 "1 0 0
"5+400 ",0500 0 5+400 ",0500 0 0 0 0 "1 0
,0500 5-,50 0 ",0500 11,500 0 0 0 0 0 1
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
274/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
275/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
276/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
277/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
278/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
279/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
280/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
281/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
282/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
283/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
284/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
285/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
286/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
287/345
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
288/345
"1410000 "+.10E"012 "-.+3,E"012 1410000 +.10E"012 "-.+3,E"012 "1 1.225E"01+ 0 0
1.,2,E"010 "5+400 ",0500 "1.,2,E"010 5+400 ",0500 "1.225E"01+ "1 0 0
= 0 ,0500 11,500 0 ",0500 5-,50 0 0 1 0
1410000 +.10E"012 -.+3,E"012 "1410000 "+.10E"012 -.+3,E"012 0 0 0 "1
"1.,2,E"010 5+400 ,0500 1.,2,E"010 "5+400 ,0500 0 0 0 "1.225E"01+
0 ,0500 5-,50 0 ",0500 11,500 0 0 0 0
"5+4000 4230 105,5 5+4000 "4230 105,5 "0.- "0.+ 0 0
"423000 "5+40 "14100 423000 5+40 "14100 0.+ "0.- 0 0
8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah
289/345
= 0 1,+25 5-,50 0 "1,+25 23,5 0 0 1 0
5+4000 "4230 "105,5 "5+4000 4230 "105,5 0 0 0 "0.-
423000 5+40 14100 "423000 "5+40