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ANALISA PORTAL DENGAN METODE MATRIKSKEKAKUAN TINGKAT 1 ( Satu )
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= 0.5 T/M'10 T
4 M= 1.5 T/M'
8 T
4 M= 1.5 T/M'
6 T
4 M= 1.5 T/M'
4 T
4 M= 1.5 T/M'
2 T
4 M
4.5 M 4.5 M
SolusiLangkah - Langkah Penyelesaiannya adalah sebagai berikut :
1. Menentukan Sistem Koordinat Struktur (SKS )
q1
q2
q2
q2
q2
A
30/50 CM
30/50 CM
30/50 CM
30/50 CM 30/50 CM
30/50 CM
30/50 CM
30/50 CM
40/40 CM
30/50 CM 30/50 CM
D6D1
D2
D3
D4
D5
D7
D8
D9
D10
D11
D12
D13
D14
D15
D16
D17
D18
D19
D20
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
2. Menentukan Sistem Koordinat Element (SKE )
Ket :Reaksi PerletakanGaya Dalam
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.6826667 I
0.256 EI 0.256 EI = 6 E x 0.682667 I0.256 EI 0.256 EI 4
= 0.256 EI
Free Body ( Perpotongan )
0.256 EI
4 M
~" Berikan D1beban H sebesar 1 satuan
cm4
cm4
1 6
19 20 39 40
1
1
2
3
4
5
6
2
3
4
5
6
7
8
9
10
11
17
13
15
30
29
28
27
26
25
24
23
22
21
12
18
14
16
50
49
48
47
46
45
44
43
42
41
31
37
33
35
32
38
34
36
3
3
6 EL2 2
A
1 S/d 50
S/d
A
B
G
H
M
N
0.256 EI
Perletakan
= 0
x 4 - 0.256 - 0.256 = 0
= 0.512 EI4
= -0.128 EI
= 0
x 4 - 0.256 - 0.256 = 0
= 0.512 EI4
= 0.128 EI
Karena Kolomnya 3 batang, Maka EI perletakan dikalikan 3
A , G , M = 0.128 EI x 3 = 0.384 EIB , H , N = -0.128 EI x 3 = -0.384 EI
0.384 EI
0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
-0.384 EI
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
= 0.384 EI = -0.256 EI
= -0.384 EI = -0.256 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= -0.256 EI = -0.256 EI
= -0.256 EI = -0.256 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
ΣMA
-RBH
-RBH
RBH
ΣMB
RAH
RAH
RAH
S11 S61
S21 S71
S31 S81
S41 S91
S51 S101
S111 S161
S121 S171
S131 S181
S141 S191
S151 S201
B
A
B
G
H
M
N
» Matriks Reaksi Perletakan ( ASD )Maka Matriks ASD adalah = 0
» Matriks Momen ( AMD )
= -0.256 EI = -0.256 EI
= -0.256 EI = -0.256 EI
= -0.256 EI = -0.256 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.6826667 I
0.256 EI 0.256 EI = 6 E x 0.682667 I0.256 EI 0.256 EI 4
= 0.256 EI0.256 EI 0.256 EI 0.256 EI
0.256 EI 0.256 EI 0.256 EII O
Free Body ( Perpotongan )
0.256 EI
4 M
0.256 EIPerletakan
= 0
x 4 + 0.256 + 0.256 = 0
= -0.512 EI4
= -0.128 EI
= 0
x 4 + 0.256 + 0.256 = 0
= -0.512 EI
AMD91 AMD221
AMD101 AMD411
AMD211 AMD421
~" Berikan D2beban H sebesar 1 satuan
cm4
cm4
ΣMB
RAH
RAH
RAH
ΣMC
-RBH
-RBH
3
3
6 EL2 2
A
B
G
H
M
N
С
A
B
4
= 0.128 EI
Free Body ( Perpotongan )
0.256 EI
4 M
0.256 EIPerletakan
= 0
x 4 - 0.256 - 0.256 = 0
= 0.512 EI4
= 0.128 EI
= 0
x 4 - 0.256 - 0.256 = 0
= 0.512 EI4
= -0.128 EI
Karena Kolomnya 3 batang, Maka EI perletakan dikalikan 3A , G , M = -0.128 EI x 3 = -0.384 EIB , H , N = 0.256 EI x 3 = 0.768 EIC , I , O = -0.128 EI x 3 = -0.384 EI
-0.384 EI
0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI
0.768 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
-0.384 EI 0.256 EI 0.256 EI 0.256 EII O
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )Maka matriks kekakuannya ( S ) di atas adalah ;
= -0.384 EI = 0.256 EI
= 0.768 EI = 0.000 EI
RBH
ΣMC
RBH
RBH
RBH
ΣMB
-RCH
-RCH
RCH
S12 S62
S22 S72
B
C
A
B
G
H
M
N
C
= -0.384 EI = -0.256 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0.256 EI = 0.256 EI
= 0 EI = 0 EI
= -0.256 EI = -0.256 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
» Matriks Reaksi Perletakan ( ASD )Maka Matriks ASD adalah = 0
» Matriks Momen ( AMD )
= 0.256 EI = -0.256 EI
= 0.256 EI = -0.256 EI
= 0.256 EI = -0.256 EI
= 0.256 EI = -0.256 EI
= 0.256 EI = -0.256 EI
= 0.256 EI = -0.256 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.6826667 I
= 6 E x 0.682667 I4
= 0.256 EI0.256 EI 0.256 EI 0.256 EI
0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
D J P
Free Body ( Perpotongan )
S32 S82
S42 S92
S52 S102
S112 S162
S122 S172
S132 S182
S142 S192
S152 S202
AMD102 AMD82
AMD92 AMD72
AMD212 AMD232
AMD222 AMD242
AMD412 AMD432
AMD422 AMD442
~" Berikan D3beban H sebesar 1 satuan
cm4
cm4
3
3
6 EL2 2
B H N
СI O
0.256 EI
4 M
0.256 EI
Perletakan
= 0
x 4 + 0.256 + 0.256 = 0
= -0.512 EI4
= -0.128 EI
= 0
x 4 + 0.256 + 0.256 = 0
= -0.512 EI4
= 0.128 EI
Free Body ( Perpotongan )
0.256 EI
4 M
0.256 EI
Perletakan
= 0
x 4 - 0.256 - 0.256 = 0
= 0.512 EI4
= 0.128 EI
= 0
x 4 - 0.256 - 0.256 = 0
= 0.512 EI4
= -0.128 EI
Karena Kolomnya 3 batang, Maka EI perletakan dikalikan 3B , H , N = -0.128 EI x 3 = -0.384 EIC , I , O = 0.256 EI x 3 = 0.768 EID , J , P = -0.128 EI x 3 = -0.384 EI
-0.384 EI
0.256 EI 0.256 EI 0.256 EI
ΣMC
RBH
RBH
RBH
ΣMB
-RCH
-RCH
RCH
ΣMD
RCH
RCH
RCH
ΣMC
-RDH
-RDH
RDH
C
D
B
C
B H N
0.768 EI 0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
-0.384 EID J P
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )Maka matriks kekakuannya ( S ) di atas adalah ;
= 0 EI = 0 EI
= -0.384 EI = 0.256 EI
= 0.768 EI = 0 EI
= -0.384 EI = -0.256 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0.256 EI = 0.256 EI
= 0 EI = 0 EI
= -0.256 EI = -0.256 EI
= 0 EI = 0 EI
» Matriks Reaksi Perletakan ( ASD )Maka Matriks ASD adalah = 0
» Matriks Momen ( AMD )
= 0 EI = 0.256 EI
= 0 EI = 0.256 EI
= 0 EI = 0.256 EI
= 0 EI = 0.256 EI
= 0 EI = 0.256 EI
= 0 EI = 0.256 EI
= -0.256 EI
= -0.256 EI
= -0.256 EI
= -0.256 EI
= -0.256 EI
= -0.256 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
S13 S63
S23 S73
S33 S83
S43 S93
S53 S103
S113 S163
S123 S173
S133 S183
S143 S193
S153 S203
AMD103 AMD83
AMD93 AMD73
AMD213 AMD233
AMD223 AMD243
AMD413 AMD433
AMD423 AMD443
AMD63
AMD53
AMD253
AMD263
AMD453
AMD463
~" Berikan D4beban H sebesar 1 satuan
СI O
3
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.6826667 I
= 6 E x 0.682667 I4
= 0.256 EI
0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
D 0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
Free Body ( Perpotongan )
0.256 EI
4 M
0.256 EI
Perletakan
= 0
x 4 + 0.256 + 0.256 = 0
= -0.512 EI4
= -0.128 EI
= 0
x 4 + 0.256 + 0.256 = 0
= -0.512 EI4
= 0.128 EI
Free Body ( Perpotongan )
0.256 EI
cm4
cm4
ΣMD
RCH
RCH
RCH
ΣMC
-RDH
-RDH
RDH
3
6 EL2 2
D
СI O
C
D
PJ
4 M
0.256 EIPerletakan
= 0
x 4 - 0.256 - 0.256 = 0
= 0.512 EI4
= 0.128 EI
= 0
x 4 - 0.256 - 0.256 = 0
= 0.512 EI4
= -0.128 EI
Karena Kolomnya 3 batang, Maka EI perletakan dikalikan 3C , I , O = -0.128 EI x 3 = -0.384 EID , J , P = 0.256 EI x 3 = 0.768 EIE , K , Q = -0.128 EI x 3 = -0.384 EI
-0.384 EI
0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
0.768 EI0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
-0.384
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )Maka matriks kekakuannya ( S ) di atas adalah ;
= 0 EI = 0 EI
= 0 EI = 0 EI
= -0.384 EI = 0.256 EI
= 0.768 EI = 0 EI
= -0.384 EI = -0.256 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
ΣME
RDH
RDH
RDH
ΣMD
-REH
-REH
REH
S14 S64
S24 S74
S34 S84
S44 S94
S54 S104
S114 S164
S124 S174
D
E
СI O
D
E
J
K
P
Q
= 0.256 EI = 0.256 EI
= 0 EI = 0 EI
= -0.256 EI = -0.256 EI
» Matriks Reaksi Perletakan ( ASD )Maka Matriks ASD adalah = 0
» Matriks Momen ( AMD )
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0.256 EI = -0.256 EI
= 0.256 EI = -0.256 EI
= 0.256 EI = -0.256 EI
= 0.256 EI = -0.256 EI
= 0.256 EI = -0.256 EI
= 0.256 EI = -0.256 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.6826667 I
= 6 E x 0.682667 I4
D 0.256 EI 0.256 EI 0.256 EI = 0.256 EI0.256 EI 0.256 EI 0.256 EI
Free Body ( Perpotongan )E
0.256 EI 0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
S134 S184
S144 S194
S154 S204
AMD104 AMD84
AMD94 AMD74
AMD214 AMD234
AMD224 AMD244
AMD414 AMD434
AMD424 AMD444
AMD64 AMD44
AMD54 AMD34
AMD254 AMD274
AMD264 AMD284
AMD454 AMD474
AMD464 AMD484
~" Berikan D5beban H sebesar 1 satuan
cm4
cm4
3
3
6 EL2 2
PJ
K Q
L R
D
F 4 M
0.256 EI
Perletakan
= 0
x 4 + 0.256 + 0.256 = 0
= -0.512 EI4
= -0.128 EI
= 0
x 4 + 0.256 + 0.256 = 0
= -0.512 EI4
= 0.128 EI
Free Body ( Perpotongan )
0.256 EI
4 M
0.256 EIPerletakan
= 0
x 4 - 0.256 - 0.256 = 0
= 0.512 EI4
= 0.128 EI
= 0
x 4 - 0.256 - 0.256 = 0
= 0.512 EI4
= -0.128 EI
Karena Kolomnya 3 batang, Maka EI perletakan dikalikan 3D , J , P = -0.128 EI x 3 = -0.384 EIE , K , Q = 0.128 EI x 3 = 0.384 EIF , L , R = -0.128 EI x 3 = -0.384 EI
-0.384 EI0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
0.384 EI
ΣME
RDH
RDH
RDH
ΣMD
-REH
-REH
REH
ΣMF
REH
REH
REH
ΣME
-RFH
-RFH
RFH
E
F
D
E
J
K
P
Q
L R
E
0.256 EI 0.256 EI 0.256 EI0.256 EI 0.256 EI 0.256 EI
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= -0.384 EI = 0.256 EI
= 0.384 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0.256 EI = 0.256 EI
= 0 EI = 0 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = -0.128 EI
= = = 0
» Matriks Momen ( AMD )
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0.256 EI
= 0 EI = 0.256 EI
= 0 EI = 0.256 EI
= 0 EI = 0.256 EI
= 0 EI = 0.256 EI
= 0 EI = 0.256 EI
= -0.256 EI
= -0.256 EI
= -0.256 EI
= -0.256 EI
S15 S65
S25 S75
S35 S85
S45 S95
S55 S105
S115 S165
S125 S175
S135 S185
S145 S195
S155 S205
ASD25 ASD45 ASD65
ASD15 ASD35 ASD55
AMD105 AMD85
AMD95 AMD75
AMD215 AMD235
AMD225 AMD245
AMD415 AMD435
AMD425 AMD445
AMD65 AMD45
AMD55 AMD35
AMD255 AMD275
AMD265 AMD285
AMD455 AMD475
AMD465 AMD485
AMD25
AMD15
AMD295
AMD305
= -0.256 EI
= -0.256 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
0.8888889 0.4444444
0.683 = 4 E x 0.682667 I0.341 4
= 0.683 EI
= 2 E x 0.682667 I4
= 0.341 EI
= 4 EI = 0.889 EI4.5
= 2 EI = 0.444 EI4.5
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI = 0.256 EI4
= 0
AMD495
AMD505
~" Berikan D6 putaran sebesar 1 satuan
cm4
cm4
ΣMA
-RBH
-RBH
ΣMB
3
3
4 EL
A
B
A
B
2 EL
4 EIL
2 EIL
x 4 + 0.6826667 + 0.341333 = 0
= -1.024 EI = -0.256 EI4
Free Body ( Perpotongan )
1 EI0.444 EI
4.5Perletakan
= 0
x 4.5 + 0.4 + 0.9 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 1 + 0.444444 = 0
= -1.33333 EI4.5
= -0.2963 EI
0.8888889 0.4444444-0.256 EI
0.6830.341
0.256 EI
-0.2963 EI 0.2962963 EI
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
= -0.256 EI = 1.572 EI
= 0.256 EI = 0.341 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0.444 EI = 0 EI
= 0 EI = 0 EI
RAH
RAH
ΣMA
-RGV
-RGV
RGV
ΣMG
RAV
RAV
RAV
S16 S66
S26 S76
S36 S86
S46 S96
S56 S106
S116 S166
S126 S176
A G
A
B
G
= 0 EI = 0 EI
= 0 EI = 0 EI
= 0 EI = 0 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= -0.2963 EI
= 0.296296 EI
= 0 EI
» Matriks Momen ( AMD )
= 0.683 EI
= 0.341 EI
= 0.8888889 EI
= 0.4444444 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
0.341 = 4 E x 0.682667 I0.683 4
= 0.683 EI0.683 0.44444440.341 0.8888889 = 2 E x 0.682667 I
4= 0.341 EI
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
S136 S186
S146 S196
S156 S206
ASD26 ASD46 ASD66
ASD16
ASD36
ASD56
AMD106
AMD96
AMD196
AMD206
~" Berikan D7 putaran sebesar 1 satuan
cm4
cm4
3
3
4 EL
A
B
2 EL
4 EIL
2 EIL
H
C
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.341 + 0.682667 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.3413333 + 0.682667 = 0
= -1.024 EI4
= -0.256 EIFree Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.6826667 + 0.341333 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.89 EI0.444 EI
ΣMA
-RBH
-RBH
RBH
ΣMB
RAH
RAH
RAH
ΣMB
-RCH
-RCH
RCH
ΣMC
RBH
RBH
RBH
A
B
B H
B
C
4.5
Perletakan
= 0
x 4.5 + 0.4 + 0.9 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 1 + 0.444444 = 0
= -1.33333 EI4.5
= -0.2963 EI
-0.256
0.3410.683
0
0.683 0.44444440.341 0.8888889
0.256
-0.2963 0.2962963
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
= -0.256 EI = 0.341 EI
= 0.000 EI = 2.254 EI
= 0.256 EI = 0.341 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.444 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
ΣMB
-RHV
-RHV
RHV
ΣMH
RBV
RBV
RBV
S17 S67
S27 S77
S37 S87
S47 S97
S57 S107
S117 S167
S127 S177
S137 S187
S147 S197
A
B H
C
= 0.000 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= -0.2963 EI
= 0.296296 EI
= 0 EI
» Matriks Momen ( AMD )
= 0.341 EI
= 0.683 EI
= 0.8888889 EI
= 0.4444444 EI
= 0.683 EI
= 0.341 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
= 4 E x 0.682667 I4
= 0.683 EI0.3410.683 = 2 E x 0.682667 I
40.4444444 = 0.341 EI
0.683 0.88888890.341
S157 S207
ASD27 ASD47 ASD67
ASD17
ASD37
ASD57
AMD107
AMD97
AMD177
AMD187
AMD87
AMD77
~" Berikan D8 putaran sebesar 1 satuan
cm4
cm4
3
3
4 EL
B
2 EL
H
C
D
I
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.341 + 0.682667 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.3413333 + 0.682667 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.6826667 + 0.341333 = 0
ΣMB
-RCH
-RCH
RCH
ΣMC
RBH
RBH
RBH
ΣMC
-RDH
-RDH
RDH
ΣMD
RCH
B
C
4 EIL
2 EIL
C
D
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.89 EI0.4444444 EI
4.5
Perletakan
= 0
x 4.5 + 0.4 + 0.9 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 1 + 0.444444 = 0
= -1.33333 EI4.5
= -0.2963 EI
-0.256
0.3410.683
00.4444444
0.683 0.88888890.341
0.256
-0.296296 0.2962963
» Matriks Kekakuan ( S )Maka matriks kekakuannya ( S ) di atas adalah ;
= 0.000 EI = 0.000 EI
= -0.256 EI = 0.341 EI
= 0.000 EI = 2.254 EI
RCH
RCH
ΣMC
-RIV
-RIV
RIV
ΣMI
RCV
RCV
RCV
S18 S68
S28 S78
S38 S88
C I
B H
C
D
I
= 0.256 EI = 0.341 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.444 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= -0.2963 EI
= 0.296296 EI
= 0 EI
» Matriks Momen ( AMD )
= 0.341 EI
= 0.683 EI
= 0.683 EI
= 0.341 EI
= 0.889 EI
= 0.444 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
= 4 E x 0.682667 I4
= 0.683 EI0.3410.683 = 2 E x 0.682667 I
S48 S98
S58 S108
S118 S167
S128 S178
S138 S188
S148 S198
S158 S208
ASD28 ASD48 ASD68
ASD18
ASD38
ASD58
AMD88
AMD78
AMD68
AMD58
AMD158
AMD168
~" Berikan D9 putaran sebesar 1 satuan
cm4
cm4
3
3
4 EL
C
2 EL
40.4444444 = 0.341 EI
0.683 0.88888890.341
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.341 + 0.682667 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.3413333 + 0.682667 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI
ΣMC
-RDH
-RDH
RDH
ΣMD
RCH
RCH
RCH
ΣMD
-REH
-REH
C
D
2 EL
4 EIL
2 EIL
D
D
E
E
J
4
= 0.256 EI
= 0
x 4 + 0.6826667 + 0.341333 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.89 EI0.4444444 EI
4.5
Perletakan
= 0
x 4.5 + 0.4 + 0.9 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 1 + 0.444444 = 0
= -1.33333 EI4.5
= -0.2963 EI
-0.256
0.3410.683
00.4444444
0.683 0.88888890.341
0.256
REH
ΣME
RDH
RDH
RDH
ΣMD
-RJV
-RJV
RJV
ΣMJ
RDV
RDV
RDV
D J
C
D
E
J
-0.296296 0.2962963
» Matriks Kekakuan ( S )Maka matriks kekakuannya ( S ) di atas adalah ;
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= -0.256 EI = 0.341 EI
= 0.000 EI = 2.254 EI
= 0.256 EI = 0.341 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.444 EI = 0.000 EI
= 0.000 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= -0.2963 EI
= 0.296296 EI
= 0 EI
» Matriks Momen ( AMD )
= 0.341 EI Yang lainnya = 0
= 0.683 EI
= 0.683 EI
= 0.341 EI
= 0.889 EI
= 0.444 EI
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
S19 S69
S29 S79
S39 S89
S49 S99
S59 S109
S118 S169
S128 S179
S138 S189
S148 S199
S158 S209
ASD29 ASD49 ASD69
ASD19
ASD39
ASD59
AMD69
AMD59
AMD49
AMD39
AMD139
AMD149
~" Berikan D10 putaran sebesar 1 satuan
cm4
cm4
3
3
= 4 E x 0.682667 I4
= 0.683 EI0.3410.683 = 2 E x 0.682667 I
40.4444444 = 0.341 EI
0.683 0.88888890.341
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.341 + 0.682667 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.3413333 + 0.682667 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.683 EI
4 M
ΣMD
-REH
-REH
REH
ΣME
RDH
RDH
RDH
4 EL
D
E
D
2 EL
4 EIL
2 EIL
E
E
F
K
0.341 EI
Perletakan
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.6826667 + 0.341333 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.89 EI0.4444444 EI
4.5
Perletakan
= 0
x 4.5 + 0.4 + 0.9 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 1 + 0.444444 = 0
= -1.33333 EI4.5
= -0.2963 EI
-0.256
0.341 0.4444444
ΣME
-RFH
-RFH
RFH
ΣMF
REH
REH
REH
ΣME
-RKV
-RKV
RKV
ΣMK
REV
REV
REV
E K
F
D
0.6830
0.683 0.88888890.341
0.256
-0.296296 0.2962963
» Matriks Kekakuan ( S )Maka matriks kekakuannya ( S ) di atas adalah ;
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= -0.256 EI = 0.341 EI
= 0.000 EI = 2.254 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.444 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = 0.256 EI
= -0.2963 EI
= 0.296296 EI
= 0 EI
= = 0
» Matriks Momen ( AMD )
= 0.341 EI Yang lainnya = 0
= 0.683 EI
= 0.683 EI
= 0.341 EI
= 0.889 EI
= 0.444 EI
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33
S110 S610
S210 S710
S310 S810
S410 S910
S510 S1010
S1110 S1610
S1210 S1710
S1310 S1810
S1410 S1910
S1510 S2010
ASD210
ASD110
ASD310
ASD510
ASD410 ASD610
AMD410
AMD310
AMD210
AMD110
AMD1110
AMD1210
~" Berikan D11 putaran sebesar 1 satuan
cm4
cm4
E
F
K
3
3
= 0.683 I
0.4444444 0.88888890.8888889
0.683 0.444444 = 4 E x 0.682667 I0.341 4
= 0.683 EI
= 2 E x 0.682667 I4
= 0.341 EI
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.6826667 + 0.341333 = 0
= -1.024 EI4
= -0.256 EIFree Body ( Perpotongan )
0.444 EI0.8888889 EI
4.5Perletakan
= 0
ΣMG
-RHH
-RHH
RHH
ΣMH
RGH
RGH
RGH
ΣMA
4 EL
G
H
2 EL
4 EIL
2 EIL
A G
A GM
H
x 4.5 + 0.9 + 0.4 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 0 + 0.888889 = 0
= -1.33333 EI4.5
= -0.2963 EI
Free Body ( Perpotongan )
0.889 EI0.4444444 EI
4.5Perletakan
= 0
x 4.5 + 0.4 + 0.9 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 1 + 0.444444 = 0
= -1.33333 EI4.5
= -0.2963 EI
0.4444444 0.8888889-0.256 0.8888889
0.683 0.4444440.341
0.256
-0.2963 0 0.296296
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
= -0.256 EI = 0.444 EI
= 0.256 EI = 0.000 EI
-RGV
-RGV
RGV
ΣMG
RAV
RAV
RAV
ΣMG
-RMV
-RM
RMV
ΣMM
RGV
RGV
RGV
S111 S611
S211 S711
G M
A GM
H
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 2.460 EI = 0.444 EI
= 0.341 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= -0.2963 EI
= 0 EI
= 0.296296 EI
» Matriks Momen ( AMD )
= 0.444 EI = 0.683 EI
= 0.889 EI = 0.341 EI
= 0.889 EI
= 0.444 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
0.3410.683
0.4444444 0.890.8888889
0.683 0.444444 = 4 E x 0.682667 I0.341 4
S311 S811
S411 S911
S511 S1011
S1111 S1611
S1211 S1711
S1311 S1811
S1411 S1911
S1511 S2011
ASD211 ASD411 ASD611
ASD111
ASD311
ASD511
AMD1911 AMD2111
AMD2011 AMD2211
AMD3911
AMD4011
~" Berikan D12 putaran sebesar 1 satuan
cm4
cm4
3
3
4 EL
B
G
NH
= 0.683 EI
= 2 E x 0.682667 I4
= 0.341 EI
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.341 + 0.682667 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.3413333 + 0.682667 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI
ΣMG
-RHH
-RHH
RHH
ΣMH
RGH
RGH
RGH
ΣMH
-RIH
-RIH
4 EL
G
H
2 EL
4 EIL
2 EIL
I
H
I
4
= 0.256 EI
= 0
x 4 + 0.6826667 + 0.341333 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.444 EI0.8888889 EI
4.5Perletakan
= 0
x 4.5 + 0.9 + 0.4 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 0.4 + 0.888889 = 0
= -1.33333 EI4.5
= -0.2963 EI
Free Body ( Perpotongan )
0.889 EI0.4444444 EI
4.5Perletakan
= 0
x 4.5 + 0.4 + 0.9 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 1 + 0.444444 = 0
= -1.33333 EI4.5
= -0.2963 EI
-0.256 0.3410.683
RIH
ΣMI
RHH
RHH
RHH
ΣMB
-RHV
-RHV
RHV
ΣMH
RBV
RBV
RBV
ΣMH
-RNV
-RNV
RNV
ΣMN
RHV
RHV
RHV
B H
H N
G
0.4444444 0.890 0.8888889
0.683 0.4444440.341
0.256
-0.2963 0 0.296296
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
= -0.256 EI = 0.000 EI
= 0.000 EI = 0.444 EI
= 0.256 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.341 EI = 0.000 EI
= 3.143 EI = 0.444 EI
= 0.341 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= -0.2963 EI
= 0 EI
= 0.296296 EI
» Matriks Momen ( AMD )
= 0.341 EI = 0.444 EI
= 0.683 EI = 0.889 EI
= 0.683 EI = 0.889 EI
= 0.341 EI = 0.444 EIYang lainnya = 0
S112 S612
S212 S712
S312 S812
S412 S912
S512 S1012
S1112 S1612
S1212 S1712
S1312 S1812
S1412 S1912
S1512 S2012
ASD212 ASD412 ASD612
ASD112
ASD312
ASD512
AMD2112 AMD1712
AMD2212 AMD1812
AMD2312 AMD3712
AMD2412 AMD3812
~" Berikan D13 putaran sebesar 1 satuan
B N
I
H
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
0.3410.683
0.4444444 0.890.8888889
0.683 0.444444 = 4 E x 0.682667 I0.341 4
= 0.683 EI
= 2 E x 0.682667 I4
= 0.341 EI
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
= 0.256 EI
cm4
cm4
ΣMH
-RIH
-RIH
RIH
3
3
4 EL
H
I
2 EL
4 EIL
2 EIL
C
H
O
J
I
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.683 + 0.341 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.683 + 0.341 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.444 EI0.8888889 EI
4.5Perletakan
= 0
x 4.5 + 0.9 + 0.4 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 0.4 + 0.888889 = 0
= -1.33333 EI4.5
= -0.2963 EI
ΣMI
RHH
RHH
RHH
ΣMI
-RJH
-RJH
RJH
ΣMJ
RIH
RIH
RIH
ΣMC
-RIV
-RIV
RIV
ΣMI
RCV
RCV
RCV
I
J
C I
Free Body ( Perpotongan )
0.9 EI0.4444444 EI
4.5
Perletakan
= 0
x 4.5 + 0.4 + 0.9 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 1 + 0.444444 = 0
= -1.33333 EI4.5
= -0.2963 EI
-0.256 0.3410.683
0.4444444 0.890 0.8888889
0.683 0.4444440.341
0.256
-0.2963 0 0.296296
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )Maka matriks kekakuannya ( S ) di atas adalah ;
= 0.000 EI = 0.000 EI
= -0.256 EI = 0.000 EI
= 0.000 EI = 0.444 EI
= 0.256 EI = 0.000 EI
ΣMI
-ROV
-ROV
ROV
ΣMO
RIV
RIV
RIV
S113 S613
S213 S713
S313 S813
S413 S913
I O
C
H
O
J
I
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.341 EI = 0.000 EI
= 3.143 EI = 0.444 EI
= 0.341 EI = 0.000 EI
= 0.000 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= -0.2963 EI
= 0 EI
= 0.296296 EI
» Matriks Momen ( AMD )
= 0.341 EI = 0.444 EI
= 0.683 EI = 0.889 EI
= 0.683 EI = 0.889 EI
= 0.341 EI = 0.444 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
0.3410.683
0.4444444 0.890.8888889
0.683 0.444444 = 4 E x 0.682667 I0.341 4
= 0.683 EI
S513 S1013
S1113 S1613
S1213 S1713
S1313 S1813
S1413 S1913
S1513 S2013
ASD213 ASD413 ASD613
ASD113
ASD313
ASD513
AMD2313 AMD1513
AMD2413 AMD1613
AMD2513 AMD3513
AMD2613 AMD3613
~" Berikan D14 putaran sebesar 1 satuan
cm4
cm4
3
3
4 EL
D
I
P
K
J
= 2 E x 0.682667 I4
= 0.341 EI
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.683 + 0.341 = 0
= -1.024 EI4
= 0.256 EI
ΣMI
-RJH
-RJH
RJH
ΣMJ
RIH
RIH
RIH
ΣMJ
-RKH
-RKH
RKH
I
J
2 EL
4 EIL
2 EIL
K
J
K
= 0
x 4 + 0.683 + 0.341 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.444 EI0.8888889 EI
4.5Perletakan
= 0
x 4.5 + 0.9 + 0.4 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 0.4 + 0.888889 = 0
= -1.33333 EI4.5
= -0.2963 EI
Free Body ( Perpotongan )
0.9 EI0.4444444 EI
4.5Perletakan
= 0
x 4.5 + 0.4 + 0.9 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 1 + 0.444444 = 0
= -1.33333 EI4.5
= -0.2963 EI
ΣMK
RJH
RJH
RJH
ΣMD
-RJV
-RJV
RJV
ΣMJ
RDV
RDV
RDV
ΣMJ
-RPV
-RPV
RPV
ΣMP
RJV
RJV
RJV
D J
J P
-0.256 0.3410.683
0.4444444 0.890 0.8888889
0.683 0.4444440.341
0.256
-0.2963 0 0.296296
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )Maka matriks kekakuannya ( S ) di atas adalah ;
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= -0.256 EI = 0.000 EI
= 0.000 EI = 0.444 EI
= 0.256 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.341 EI = 0.000 EI
= 3.143 EI = 0.444 EI
= 0.341 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= -0.2963 EI
= 0 EI
S114 S614
S214 S714
S314 S814
S414 S914
S514 S1014
S1114 S1614
S1214 S1714
S1314 S1814
S1414 S1914
S1514 S2014
ASD214 ASD414 ASD614
ASD114
ASD314
D
I
P
K
J
= 0.296296 EI
» Matriks Momen ( AMD )
= 0.341 EI = 0.444 EI
= 0.683 EI = 0.889 EI
= 0.683 EI = 0.889 EI
= 0.341 EI = 0.444 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
0.3410.683
0.4444444 0.890.8888889
0.683 0.444444 = 4 E x 0.682667 I0.341 4
= 0.683 EI
= 2 E x 0.682667 I4
= 0.341 EI
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
ASD514
AMD2514 AMD1314
AMD2614 AMD1414
AMD2714 AMD3314
AMD2814 AMD3414
~" Berikan D15 putaran sebesar 1 satuan
cm4
cm4
3
3
4 EL
2 EL
4 EIL
2 EIL
E
J
Q
L
K
Free Body ( Perpotongan )
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.683 + 0.341 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.683 + 0.341 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
ΣMJ
-RKH
-RKH
RKH
ΣMK
RJH
RJH
RJH
ΣMK
-RLH
-RLH
RLH
ΣML
RKH
RKH
RKH
J
K
2 EIL
K
L
0.444 EI0.8888889 EI
4.5Perletakan
= 0
x 4.5 + 0.9 + 0.4 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 0.4 + 0.888889 = 0
= -1.33333 EI4.5
= -0.2963 EI
Free Body ( Perpotongan )
0.9 EI0.4 EI
4.5Perletakan
= 0
x 4.5 + 0.4 + 0.9 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 1 + 0.444444 = 0
= -1.33333 EI4.5
= -0.2963 EI
ΣME
-RKV
-RKV
RKV
ΣMK
REV
REV
REV
ΣMK
-RQV
-RQV
RQV
ΣMQ
RKV
RKV
RKV
E K
K Q
J
-0.256 0.3410.683
0.4444444 0.890 0.8888889
0.683 0.4444440.341
0.256
-0.2963 0 0.296296
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= -0.256 EI = 0.000 EI
= 0.000 EI = 0.444 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.341 EI = 0.000 EI
= 3.143 EI = 0.444 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = 0
= -0.2963 EI
= 0 EI
= 0.296296 EI
= 0.256 EI
» Matriks Momen ( AMD )
= 0.341 EI = 0.444 EI
= 0.683 EI = 0.889 EI
= 0.683 EI = 0.889 EI
= 0.341 EI = 0.444 EIYang lainnya = 0
S115 S615
S215 S715
S315 S815
S415 S915
S515 S1015
S1115 S1615
S1215 S1715
S1315 S1815
S1415 S1915
S1515 S2015
ASD215 ASD615
ASD115
ASD315
ASD515
ASD415
AMD2715 AMD1115
AMD2815 AMD1215
AMD2915 AMD3115
AMD3015 AMD3215
E
J
Q
L
K
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
0.444
0.889 0.683 = 4 E x 0.682667 I0.341 4
= 0.683 EI
= 2 E x 0.682667 I4
= 0.341 EI
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.683 + 0.341333 = 0
~" Berikan D16 putaran sebesar 1 satuan
cm4
cm4
ΣMM
-RNH
-RNH
RNH
ΣMN
RMH
3
3
4 EL
M
N
G
2 EL
4 EIL
2 EIL
M
N
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.444 EI0.889 EI
4.5Perletakan
= 0
x 4.5 + 0.9 + 0.4 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 0.4 + 0.888889 = 0
= -1.33333 EI4.5
= -0.2963 EI
0.444-0.256
0.889 0.6830.341
0.256
-0.296296 0.296296
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
= -0.256 EI = 0.000 EI
= 0.256 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.444 EI = 1.572 EI
= 0.000 EI = 0.341 EI
RMH
RMH
ΣMG
-RMV
-RMV
RMV
ΣMM
RGV
RGV
RGV
S116 S66
S216 S76
S316 S86
S416 S96
S516 S106
S1116 S1616
S1216 S1716
G M
G M
N
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= 0 EI
= -0.2963 EI
= 0.296296 EI
» Matriks Momen ( AMD )
= 0.444 EI
= 0.889 EI
= 0.683 EI
= 0.341 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
0.3410.444 0.683
0.889 0.683 = 4 E x 0.682667 I0.341 4
= 0.683 EI
= 2 E x 0.682667 I4
= 0.341 EI
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
S1316 S1816
S1416 S1916
S1516 S2016
ASD216 ASD416 ASD616
ASD116
ASD316
ASD516
AMD3916
AMD4016
AMD4116
AMD4216
~" Berikan D17 putaran sebesar 1 satuan
cm4
cm4
3
3
4 EL
H
2 EL
4 EIL
2 EIL
N
O
M
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.683 + 0.341 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.341 + 0.682667 = 0
= -1.024 EI4
= -0.256 EIFree Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.444 EI0.889 EI
4.5Perletakan
= 0
ΣMM
-RNH
-RNH
RNH
ΣMN
RMH
RMH
RMH
ΣMN
-ROH
-ROH
ROH
ΣMO
RNH
RNH
RNH
ΣMH
M
N
H N
N
O
x 4.5 + 0.9 + 0.4 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 0.4 + 0.888889 = 0
= -1.33333 EI4.5
= -0.2963 EI
-0.2560.341
0.444 0.6830
0.889 0.6830.341
0.256
-0.2963 0.296296
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
= -0.256 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.256 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.341 EI
= 0.444 EI = 2.254 EI
= 0.000 EI = 0.341 EI
-RNV
-RNV
RNV
ΣMN
RHV
RHV
RHV
S117 S617
S217 S717
S317 S817
S417 S917
S517 S106
S1117 S1617
S1217 S1717
S1317 S1817
H N
O
M
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= 0 EI
= -0.2963 EI
= 0.296296 EI
» Matriks Momen ( AMD )
= 0.341 EI = 0.444 EI
= 0.683 EI = 0.889 EI
= 0.683 EI
= 0.341 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
0.3410.444 0.683
0.889 0.683 = 4 E x 0.682667 I0.341 4
= 0.683 EI
= 2 E x 0.682667 I4
= 0.341 EI
S1417 S1917
S1517 S2017
ASD217 ASD417 ASD617
ASD117
ASD317
ASD517
AMD4117 AMD3717
AMD4217 AMD3817
AMD4317
AMD4417
~" Berikan D18 putaran sebesar 1 satuan
cm4
cm4
3
3
4 EL
I
2 EL
O
P
N
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.683 + 0.341 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.341 + 0.682667 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI
ΣMN
-ROH
-ROH
ROH
ΣMO
RNH
RNH
RNH
ΣMO
-RPH
-RPH
RPH
ΣMP
ROH
ROH
N
O
4 EIL
2 EIL
O
P
4
= -0.256 EI
Free Body ( Perpotongan )
0.444 EI0.889 EI
4.5Perletakan
= 0
x 4.5 + 0.9 + 0.4 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 0.4 + 0.888889 = 0
= -1.33333 EI4.5
= -0.2963 EI
-0.2560.341
0.444 0.6830
0.889 0.6830.341
0.256
-0.2963 0.296296
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
ROH
ΣMI
-ROV
-ROV
ROV
ΣMO
RIV
RIV
RIV
I O
I O
P
N
= 0.000 EI = 0.000 EI
= -0.256 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.256 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.341 EI
= 0.444 EI = 2.254 EI
= 0.000 EI = 0.341 EI
= 0.000 EI = 0.000 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= 0 EI
= -0.2963 EI
= 0.296296 EI
» Matriks Momen ( AMD )
= 0.341 EI = 0.444 EI
= 0.683 EI = 0.889 EI
= 0.683 EI
= 0.341 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
0.341
S118 S618
S218 S718
S318 S818
S418 S918
S518 S1018
S1118 S1618
S1218 S1718
S1318 S1818
S1418 S1918
S1518 S2018
ASD218 ASD418 ASD618
ASD118
ASD318
ASD518
AMD4318 AMD3518
AMD4418 AMD3618
AMD4518
AMD4618
~" Berikan D19 putaran sebesar 1 satuan
cm4
cm4
3
3
O
0.444 0.683
0.889 0.683 = 4 E x 0.682667 I0.341 4
= 0.683 EI
= 2 E x 0.682667 I4
= 0.341 EI
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.341 EI
4 M
0.683 EIPerletakan
= 0
x 4 + 0.683 + 0.341 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.341 + 0.682667 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
ΣMO
-RPH
-RPH
RPH
ΣMP
ROH
ROH
ROH
ΣMP
-RQH
-RQH
4 EL
O
P
J
2 EL
4 EIL
2 EIL
P
Q
P
Q
= 0.256 EI
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.444 EI0.9 EI
4.5
Perletakan
= 0
x 4.5 + 0.9 + 0.4 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 0.4 + 0.888889 = 0
= -1.33333 EI4.5
= -0.2963 EI
-0.2560.341
0.444 0.6830
0.889 0.6830.341
0.256
RQH
ΣMQ
RPH
RPH
RPH
ΣMJ
-RPV
-RPV
RPV
ΣMP
RJV
RJV
RJV
J P
J P
Q
O
-0.2963 0.296296
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) di atas adalah ;
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= -0.256 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.256 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.341 EI
= 0.444 EI = 2.254 EI
= 0.000 EI = 0.341 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = = 0
= 0 EI
= -0.2963 EI
= 0.296296 EI
» Matriks Momen ( AMD )
= 0.341 EI = 0.444 EI
= 0.683 EI = 0.889 EI
= 0.683 EI
= 0.341 EIYang lainnya = 0
Balok 30/50 = 1 x 30 x 5012
= 312500 = I
Kolom 40/40 = 1 x 40 x 4012
= 213333.33= 0.683 I
S119 S619
S219 S719
S319 S819
S419 S919
S519 S1019
S1119 S1619
S1219 S1719
S1319 S1819
S1419 S1919
S1519 S2019
ASD219 ASD419 ASD619
ASD119
ASD319
ASD519
AMD4519 AMD3319
AMD4619 AMD3419
AMD4719
AMD4819
~" Berikan D20 putaran sebesar 1 satuan
cm4
cm4
3
3
0.3410.444 0.683
0.889 0.683 = 4 E x 0.682667 I0.341 4
= 0.683 EI
= 2 E x 0.682667 I4
= 0.341 EI
= 4 EI = 0.888889 EI4.5
= 2 EI = 0.444444 EI4.5
Free Body ( Perpotongan )
0.341 EI
4 M
0.683 EI
Perletakan
= 0
x 4 + 0.683 + 0.341 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.341 + 0.682667 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
ΣMP
-RQH
-RQH
RQH
ΣMQ
RPH
RPH
RPH
4 EL
P
Q
K
2 EL
4 EIL
2 EIL
Q
R
P
0.683 EI
4 M
0.341 EI
Perletakan
= 0
x 4 + 0.341 + 0.683 = 0
= -1.024 EI4
= 0.256 EI
= 0
x 4 + 0.683 + 0.341333 = 0
= -1.024 EI4
= -0.256 EI
Free Body ( Perpotongan )
0.444 EI0.889 EI
4.5Perletakan
= 0
x 4.5 + 0.9 + 0.4 = 0
= -1.3 EI4.5
= 0.296296 EI
= 0
x 5 + 0.4 + 0.888889 = 0
= -1.33333 EI4.5
= -0.2963 EI
ΣMQ
-RRH
-RRH
RRH
ΣMR
RQH
RQH
RQH
ΣMK
-RQV
-RQV
RQV
ΣMQ
RKV
RKV
RKV
Q
R
K Q
-0.2560.341
0.444 0.6830
0.889 0.6830.341
0.256-0.2963 0.296296
Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
» Matriks Kekakuan ( S )Maka matriks kekakuannya ( S ) di atas adalah ;
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= -0.256 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.000 EI
= 0.000 EI = 0.341 EI
= 0.444 EI = 2.254 EI
» Matriks Reaksi Perletakan ( ASD )
Matriks ASD : = = 0
= 0 EI
= -0.2963 EI
= 0.296296 EI
= 0.256 EI» Matriks Momen ( AMD )
= 0.341 EI = 0.444 EI
= 0.683 EI = 0.889 EI
= 0.683 EI
= 0.341 EIYang lainnya = 0
S120 S620
S220 S720
S320 S820
S420 S920
S520 S1020
S1120 S1620
S1220 S1720
S1320 S1820
S1420 S1920
S1520 S2020
ASD220 ASD420
ASD120
ASD320
ASD520
ASD620
AMD4720 AMD3120
AMD4820 AMD3220
AMD4920
AMD5020
K Q
R
P
MATRIKS ( S )
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201 0.384 -0.384 0 0 0 -0.256 -0.256 0 0 0 -0.256 -0.256 0 0 0 -0.256 -0.256 0 0 02 -0.384 0.768 -0.384 0 0 0.256 0 -0.256 0 0 0.256 0 -0.256 0 0 0.256 0 -0.256 0 03 0 -0.384 0.768 -0.384 0 0 0.256 0 -0.256 0 0 0.256 0 -0.256 0 0 0.256 0 -0.256 04 0 0 -0.384 0.768 -0.384 0 0 0.256 0 -0.256 0 0 0.256 0 -0.256 0 0 0.256 0 -0.2565 0 0 0 -0.384 0.384 0 0 0 0.256 0 0 0 0 0.256 0 0 0 0 0.256 06 -0.256 0.256 0 0 0 1.5716 0.3413 0 0 0 0.4444 0 0 0 0 0 0 0 0 07 -0.256 0 0.256 0 0 0.3413 2.2542 0.3413 0 0 0 0.4444 0 0 0 0 0 0 0 08 0 -0.256 0 0.256 0 0 0.3413 2.2542 0.3413 0 0 0 0.4444 0 0 0 0 0 0 09 0 0 -0.256 0 0.256 0 0 0.3413 2.2542 0.3413 0 0 0 0.4444 0 0 0 0 0 0
10 0 0 0 -0.256 0 0 0 0 0.3413 2.2542 0 0 0 0 0.4444 0 0 0 0 011 -0.256 0.256 0 0 0 0.4444 0 0 0 0 2.460 0.3413 0 0 0 0.4444 0 0 0 012 -0.256 0 0.256 0 0 0 0.4444 0 0 0 0.3413 3.1431 0.3413 0 0 0 0.4444 0 0 013 0 -0.256 0 0.256 0 0 0 0.4444 0 0 0 0.3413 3.1431 0.3413 0 0 0 0.4444 0 014 0 0 -0.256 0 0.256 0 0 0 0.4444 0 0 0 0.3413 3.1431 0.3413 0 0 0 0.4444 015 0 0 0 -0.256 0 0 0 0 0 0.4444 0 0 0 0.3413 3.1431 0 0 0 0 0.444416 -0.256 0.256 0 0 0 0 0 0 0 0 0.4444 0 0 0 0 1.5716 0.3413 0 0 017 -0.256 0 0.256 0 0 0 0 0 0 0 0 0.4444 0 0 0 0.3413 2.2542 0.3413 0 018 0 -0.256 0 0.256 0 0 0 0 0 0 0 0 0.4444 0 0 0 0.3413 2.2542 0.3413 019 0 0 -0.256 0 0.256 0 0 0 0 0 0 0 0 0.4444 0 0 0 0.3413 2.2542 0.341320 0 0 0 -0.256 0 0 0 0 0 0 0 0 0 0 0.4444 0 0 0 0.3413 2.2542
MATRIK AMD
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201 0 0 0 0 -0.256 0 0 0 0 0.3413 0 0 0 0 0 0 0 0 0 02 0 0 0 0 -0.256 0 0 0 0 0.6827 0 0 0 0 0 0 0 0 0 03 0 0 0 -0.256 0.256 0 0 0 0.3413 0.6827 0 0 0 0 0 0 0 0 0 04 0 0 0 -0.256 0.256 0 0 0 0.6827 0.3413 0 0 0 0 0 0 0 0 0 05 0 0 -0.256 0.256 0 0 0 0.3413 0.6827 0 0 0 0 0 0 0 0 0 0 06 0 0 -0.256 0.256 0 0 0 0.6827 0.3413 0 0 0 0 0 0 0 0 0 0 07 0 -0.256 0.256 0 0 0 0.3413 0.6827 0 0 0 0 0 0 0 0 0 0 0 08 0 -0.256 0.256 0 0 0 0.6827 0.3413 0 0 0 0 0 0 0 0 0 0 0 09 -0.256 0.256 0 0 0 0.3413 0.6827 0 0 0 0 0 0 0 0 0 0 0 0 0
10 -0.256 0.256 0 0 0 0.6827 0.3413 0 0 0 0 0 0 0 0 0 0 0 0 011 0 0 0 0 0 0 0 0 0 0.8889 0 0 0 0 0.4444 0 0 0 0 012 0 0 0 0 0 0 0 0 0 0.4444 0 0 0 0 0.8889 0 0 0 0 013 0 0 0 0 0 0 0 0 0.8889 0 0 0 0 0.4444 0 0 0 0 0 014 0 0 0 0 0 0 0 0 0.4444 0 0 0 0 0.8889 0 0 0 0 0 015 0 0 0 0 0 0 0 0.8889 0 0 0 0 0.4444 0 0 0 0 0 0 016 0 0 0 0 0 0 0 0.4444 0 0 0 0 0.8889 0 0 0 0 0 0 017 0 0 0 0 0 0 0.8889 0 0 0 0 0.4444 0 0 0 0 0 0 0 018 0 0 0 0 0 0 0.4444 0 0 0 0 0.8889 0 0 0 0 0 0 0 019 0 0 0 0 0 0.8889 0 0 0 0 0.4444 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0.4444 0 0 0 0 0.8889 0 0 0 0 0 0 0 0 021 -0.256 0.256 0 0 0 0 0 0 0 0 0.6827 0.3413 0 0 0 0 0 0 0 022 -0.256 0.256 0 0 0 0 0 0 0 0 0.3413 0.6827 0 0 0 0 0 0 0 023 0 -0.256 0.256 0 0 0 0 0 0 0 0 0.6827 0.3413 0 0 0 0 0 0 024 0 -0.256 0.256 0 0 0 0 0 0 0 0 0.3413 0.6827 0 0 0 0 0 0 025 0 0 -0.256 0.256 0 0 0 0 0 0 0 0 0.6827 0.3413 0 0 0 0 0 026 0 0 -0.256 0.256 0 0 0 0 0 0 0 0 0.3413 0.6827 0 0 0 0 0 027 0 0 0 -0.256 0.256 0 0 0 0 0 0 0 0 0.6827 0.3413 0 0 0 0 028 0 0 0 -0.256 0.256 0 0 0 0 0 0 0 0 0.3413 0.6827 0 0 0 0 029 0 0 0 0 -0.256 0 0 0 0 0 0 0 0 0 0.6827 0 0 0 0 030 0 0 0 0 -0.256 0 0 0 0 0 0 0 0 0 0.3413 0 0 0 0 031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.8889 0 0 0 0 0.444432 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4444 0 0 0 0 0.8889
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0.8889 0 0 0 0 0.4444 034 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4444 0 0 0 0 0.8889 035 0 0 0 0 0 0 0 0 0 0 0 0 0.8889 0 0 0 0 0.4444 0 036 0 0 0 0 0 0 0 0 0 0 0 0 0.4444 0 0 0 0 0.8889 0 037 0 0 0 0 0 0 0 0 0 0 0 0.8889 0 0 0 0 0.4444 0 0 038 0 0 0 0 0 0 0 0 0 0 0 0.4444 0 0 0 0 0.8889 0 0 039 0 0 0 0 0 0 0 0 0 0 0.8889 0 0 0 0 0.4444 0 0 0 040 0 0 0 0 0 0 0 0 0 0 0.4444 0 0 0 0 0.8889 0 0 0 041 -0.256 0.256 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6827 0.3413 0 0 042 -0.256 0.256 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3413 0.6827 0 0 043 0 -0.256 0.256 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6827 0.3413 0 044 0 -0.256 0.256 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3413 0.6827 0 045 0 0 -0.256 0.256 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6827 0.3413 046 0 0 -0.256 0.256 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3413 0.6827 047 0 0 0 -0.256 0.256 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6827 0.341348 0 0 0 -0.256 0.256 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3413 0.682749 0 0 0 0 -0.256 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.682750 0 0 0 0 -0.256 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.3413
MATRIK ASD
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201 0 0 0 0 0 -0.296 -0.296 -0.296 -0.296 -0.296 -0.296 -0.296 -0.296 -0.296 -0.296 0 0 0 0 02 0 0 0 0 -0.128 0 0 0 0 0.256 0 0 0 0 0 0 0 0 0 03 0 0 0 0 0 0.2963 0.2963 0.2963 0.2963 0.2963 0 0 0 0 0 -0.296 -0.296 -0.296 -0.296 -0.304 0 0 0 0 -0.128 0 0 0 0 0 0 0 0 0 0.256 0 0 0 0 05 0 0 0 0 0 0 0 0 0 0 0.2963 0.2963 0.2963 0.2963 0.2963 0.2963 0.2963 0.2963 0.2963 0.29636 0 0 0 0 -0.128 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.256
4 Menentukan Matriks ADL ; ASL dan AML :
= 0.5 T/M'10 T
4 M= 1.5 T/M'
8 T
4 M= 1.5 T/M'
6 T
4 M= 1.5 T/M'
4 T
4 M= 1.5 T/M'
2 T
4 M
4.5 M 4.5 M
Lantai 5 (atap)q = 0.500 T/M'
R = q x L= 0.5 x 4.5
= 2.250 T4.5 M
= 1 q x12
= 1 0.500 x 4.512
= 0.844 TM
q1
q2
q2
q2
q2
RAV RGV
MF L2
2
A
30/50 CM
30/50 CM
30/50 CM
30/50 CM 30/50 CM
30/50 CM
30/50 CM
30/50 CM
40/40 CM
30/50 CM 30/50 CM
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
A G
= 0
x 4.5 - 0.844 - 2.250 x 2.25 + 0.844 = 0
4.5 + -5.063 = 0
= 5.063 = 1.125 T4.5
= 0
x 4.5 + 0.844 + 2.250 x 2.25 - 0.844 = 0
4.5 + 5.063 = 0
= -5.063 1.125 T4.5
q = 0.500 T/M'
R = q x L= 0.500 x 4.5
= 2.250 T4.5 M
= 1 q x12
= 1 0.500 x 4.512
= 0.844 TM
= 0
x 4.5 - 0.844 - 2.250 x 2.25 + 0.844 = 0
4.5 + -5.063 = 0
= 5.063 = 1.125 T4.5
= 0
x 4.5 + 0.844 + 2.250 x 2.25 - 0.844 = 0
4.5 + 5.063 = 0
= -5.063 = 1.125 T4.5
∑MG
RAV'
RAV'
RAV'
∑MA
-RGV'
-RGV'
-RGV'
RGV RMV
MF L2
2
∑MM
RGV'
RGV'
RGV'
∑MG
-RMV'
-RMV'
-RMV'
G M
Lantai 4q = 1.5 T/M'
R = q x L= 1.5 x 4.5
= 6.750 T4.5 M
= 1 q x12
= 1 1.5 x 4.512
= 2.531 TM
= 0
x 4.5 - 2.531 - 6.750 x 2.25 + 2.531 = 0
4.5 + -15.188 = 0
= ### = 3.375 T4.5
= 0
x 4.5 + 2.531 + 6.750 x 2.25 - 2.531 = 0
4.5 + 15.188 = 0
= -15.188 = 3.375 T4.5
q = 1.5 T/M'
R = q x L= 1.5 x 4.5
= 6.750 T4.5 M
RBV RHV
MF L2
2
∑MH
RBV'
RBV'
RBV'
∑MB
-RHV'
-RHV'
-RHV'
RHV RNV
B H
H N
= 1 q x12
= 1 1.5 x 4.512
= 2.53125 TM
= 0
x 4.5 - 2.531 - 6.750 x 2.25 + 2.531 = 0
4.5 + -15.188 = 0
= ### = 3.375 T4.5
= 0
x 4.5 + 2.531 + 6.750 x 2.25 - 2.531 = 0
4.5 + 15.188 = 0
= -15.188 = 3.375 T4.5
Lantai 3q = 1.5 T/M'
R = q x L= 1.5 x 4.5
= 6.750 T4.5 M
= 1 q x12
= 1 1.5 x 4.512
= 2.53125 TM
= 0
x 4.5 - 2.531 - 6.750 x 2.25 + 2.531 = 0
MF L2
2
∑MN
RHV'
RHV'
RHV'
∑MH
-RNV'
-RNV'
-RNV'
RCV RIV
MF L2
2
∑MI
RCV'
C I
4.5 + -15.188 = 0
= ### = 3.375 T4.5= 0
x 4.5 + 2.531 + 6.750 x 2.25 - 2.531 = 0
4.5 + 15.188 = 0
= -15.188 = 3.375 T4.5
q = 1.5 T/M'
R = q x L= 1.5 x 4.5
= 6.750 T4.5 M
= 1 q x12
= 1 1.5 x 4.512
= 2.53125 TM
= 0
x 4.5 - 2.531 - 6.750 x 2.25 + 2.531 = 0
4.5 + -15.188 = 0
= ### = 3.375 T4.5
= 0
x 4.5 + 2.531 + 6.750 x 2.25 - 2.531 = 0
4.5 + 15.188 = 0
= -15.188 3.375 T4.5
RCV'
RCV'
∑MC
-RIV'
-RIV'
-RIV'
RIV ROV
MF L2
2
∑MO
RIV'
RIV'
RIV'
∑MI
-ROV'
-ROV'
-ROV'
I O
Lantai 2q = 1.5 T/M'
R = q x L= 1.5 x 4.5
= 6.750 T4.5 M
= 1 q x12
= 1 1.5 x 4.512
= 2.53125 TM
= 0
x 4.5 - 2.531 - 6.750 x 2.25 + 2.531 = 0
4.5 + -15.188 = 0
= ### = 3.375 T4.5
= 0
x 4.5 + 2.531 + 6.750 x 2.25 - 2.531 = 0
4.5 + 15.188 = 0
= -15.188 = 3.375 T4.5
q = 1.5 T/M'
R = q x L= 1.5 x 4.5
= 6.750 T4.5 M
RDV RJV
MF L2
2
∑MJ
RDV'
RDV'
RDV'
∑MD
-RJV'
-RJV'
-RJV'
RJV RPV
D J
J P
= 1 q x12
= 1 1.5 x 4.512
= 2.53125 TM
= 0
x 4.5 - 2.531 - 6.750 x 2.25 + 2.531 = 0
4.5 + -15.188 = 0
= ### = 3.375 T4.5
= 0
x 4.5 + 2.531 + 6.750 x 2.25 - 2.531 = 0
4.5 + 15.188 = 0
= -15.188 = 3.375 T4.5
Lantai 1q = 1.5 T/M'
R = q x L= 1.5 x 4.5
= 6.750 T4.5 M
= 1 q x12
= 1 1.5 x 4.512
= 2.53125 TM
= 0
MF L2
2
∑MP
RJV'
RJV'
RJV'
∑MJ
-RPV'
-RPV'
-RPV'
REV RKV
MF L2
2
∑MK
E K
x 4.5 - 2.531 - 6.750 x 2.25 + 2.531 = 0
4.5 + -15.188 = 0
= ### = 3.375 T4.5= 0
x 4.5 + 2.531 + 6.750 x 2.25 - 2.531 = 0
4.5 + 15.188 = 0
= -15.188 = 3.375 T4.5
q = 1.5 T/M'
R = q x L= 1.5 x 4.5
= 6.750 T4.5 M
= 1 q x12
= 1 1.5 x 4.512
= 2.53125 TM
= 0
x 4.5 - 2.531 - 6.750 x 2.25 + 2.531 = 0
4.5 + -15.188 = 0
= ### = 3.375 T4.5= 0
x 4.5 + 2.531 + 6.750 x 2.25 - 2.531 = 0
4.5 + 15.188 = 0
= -15.188 = 3.375 T4.5
REV'
REV'
REV'
∑ME
-RKV'
-RKV'
-RKV'
RJV RPV
MF L2
2
∑MQ
RKV'
RKV'
RKV' RKV'
∑MK
-RQV'
-RQV'
-RQV'
K Q
0.844 0.844
0.844 0.844
2.53125 2.531252.53125 2.53125
2.53125 2.53125
2.53125 2.531252.53125 2.53125
2.53125 2.531252.53125 2.53125
2.53125 2.53125
14.625 29.250 14.6254 4
Menentukan Matriks Kekakuan ( ADL ), ( AML ), Dan ( ASL )
» Matriks Kekakuan ( ADL )
= 0 TM = -0.844 TM
= 0 TM = -2.531 TM
= 0 TM = -2.531 TM
= 0 TM = -2.531 TM
= 0 TM = -2.531 TM
= 0 TM = 0.844 TM
= 0 TM = 2.531 TM
= 0 TM = 2.531 TM
ADL1 ADL6
ADL2 ADL7
ADL3 ADL8
ADL4 ADL9
ADL5 ADL10
ADL11 ADL16
ADL12 ADL17
ADL13 ADL18
= 0 TM = 2.531 TM
= 0 TM = 2.531 TM
» Matriks Kekakuan ( ASL )
= 14.625 T
= 0 T
= 29.250 T
= 0 T
= 14.625 T
= 0 T
» Matriks Kekakuan ( AML )
= 0 TM = 0 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
= -2.531 TM = 2.531 TM
= 2.531 TM = -2.531 TM
= -2.531 TM = 2.531 TM
= 2.531 TM = -0.844 TM
= -2.531 TM = 0.844 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
= -2.531 TM = 2.531 TM
= 2.531 TM = -2.531 TM
ADL14 ADL19
ADL15 ADL20
ASL1
ASL2
ASL3
ASL4
ASL5
ASL6
AML1 AML6
AML2 AML7
AML3 AML8
AML4 AML9
AML5 AML10
AML11 AML16
AML12 AML17
AML13 AML18
AML14 AML19
AML15 AML20
AML21 AML26
AML22 AML27
AML23 AML28
AML24 AML29
AML25 AML30
AML31 AML36
AML32 AML37
= -2.531 TM = 2.531 TM
= 2.531 TM = -0.844 TM
= -2.531 TM = 0.844 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
= 0 TM = 0 TM
AML33 AML38
AML34 AML39
AML35 AML40
AML41 AML46
AML42 AML47
AML43 AML48
AML44 AML49
AML45 AML50
5. Menentukan Displacement (D)
AD = + S x D
AD = 0.00 Dikarenakan Struktur kita harus seimbang, tidak boleh bergoyang
D = - S x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### -0.84
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### -2.53
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### -2.53
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### x -2.53
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### -2.53
= #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 0.844
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 2.53
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 2.53
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 2.53
#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! ### ### ### ### ### ### ### ### ### ### ### ### ### ### 2.53
ADL
-1 ADL
D1
D2
D3
D4
D5
D6
D7
D8
D9
D10
D11
D12
D13
D14
D15
D16
D17
D18
D19
D20
-1 EI
### ###
### ###
### ###
### ###
### ###
### ###
### ###
### ###
### ###
### ###
= ### = = ###
### ###
### ###
### ###
### ###
### ###
### ###
### ###
### ###
### ###
D1
D2
D3
D4
D5
D6
D7
D8
D9
D10
D11
D12
D13
D14
D15
D16
D17
D18
D19
D20
-1 EI
1 EI
6. Menentukan Reaksi Perletakkan :
AS = + x D
14.625 ### ###
0 ### ###
= 29.25 + ### = ###
0 ### ###
14.625 ### ###
0 ### ###
7. Menentukan Gaya Dalam (AM) :
AM = + x D
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
-2.53125 ### ###
2.53125 ### ###
-2.53125 ### ###
2.53125 ### ###
= -2.53125 + ### = ###
2.53125 ### ###
-2.53125 ### ###
ASL ASD
AS1
AS2
AS3
AS4
AS5
AS6
AML AMD
AM1
AM2
AM3
AM4
AM5
AM6
AM7
AM8
AM9
AM10
AM11
AM12
AM13
AM14
AM15
AM16
AM17
2.53125 ### ###
-0.84375 ### ###
0.84375 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
-2.53125 ### ###
2.53125 ### ###
-2.53125 ### ###
2.53125 ### ###
-2.53125 ### ###
2.53125 ### ###
-2.53125 ### ###
2.53125 ### ###
-0.84375 ### ###
0.84375 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
0 ### ###
AM18
AM19
AM20
AM21
AM22
AM23
AM24
AM25
AM26
AM27
AM28
AM29
AM30
AM31
AM32
AM33
AM34
AM35
AM36
AM37
AM38
AM39
AM40
AM41
AM42
AM43
AM44
AM45
AM46
AM47
AM48
AM49
AM50
Hasil Momen
#VALUE! #VALUE!
### ### ### #VALUE! #VALUE!### ### #VALUE!
#VALUE! #VALUE!### ### #VALUE!
### #VALUE!### #VALUE! ### #VALUE! #VALUE!
### ###### #VALUE! #VALUE!### #VALUE! ### #VALUE! #VALUE!
### ### ### #VALUE! #VALUE!### #VALUE! ### #VALUE! #VALUE!
### ### ### #VALUE! #VALUE!### ### #VALUE!
### ####VALUE!
#VALUE! #VALUE! #VALUE!4 4
10 0.000 10.000
8 0.000 8.000
6 0.000 6.000
4 0.000 4.000
2 0.000 2.000
0 -0.844 0.844
0 -2.531 2.531
0 -2.531 2.531
0 -2.531 2.531
0 -2.531 2.531
0 0.000 0.000
0 0.000 0.000
0 0.000 0.000
0 0.000 0.000
0 0.000 0.000
0 0.844 -0.844
0 2.531 -2.531
0 2.531 -2.531
0 2.531 -2.531
0 2.531 -2.531
### ### ###### ### ###### ### ###### ### ###### ### ###
3100000
600000
ANALISA BALOK SEDERHANA DENGAN METODE MATRIKSKEKAKUAN TINGKAT 1 ( Satu )
dan jarak antara A-B adalah 2 m, B-C adalah 5 m.Tentukanlah nilai D (Displacement) nya?Lihatlah gambar dibawah ini...!!!
q = 0.2
2 m 5 m
SolusiLangkah - Langkah Penyelesaiannya adalah sebagai berikut :
1. Menentukan Sistem Koordinat Struktur (SKS )
2. Menentukan Sistem Koordinat Element (SKE )
Ket :Reaksi Perletakan
1, 2, 3, dan 4 Gaya Dalam
3. Menentukan Matriks Kekakuan ( S ), ( ASD ), Dan ( AMD )
3.1.
Diketahui balok sederhana, dimana nilai beban terbagi ratanya (q) adalah sebesar 20 t/m1
t/m1
Berikan D1 = 1 satuan
A B C
D1 D2 D3
A B C
1 2 3 4
1 2 3
1 2 3
A B
RAV
4 EIL
2 EIL
RBVL
C
A B CEI EI
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) adalah ;
= 2 EI
= EI
= 0
» Matriks Reaksi Perletakan ( ASD )
2 m
ΣMA = 0
x 2 + 2 EI + 4 EI = 02 2
-2 + 1 EI + 2 EI = 0
= -3 EI-2
= 1.5 EI
ΣMB = 0
x 2 + 4 EI + 2 EI = 02 2
2 + 2 EI + 1 EI = 0
= -3 EI2
= -1.5 EI
Maka Matriks ASD adalah ;
= -1.5 EI
= 1.5 EI
= 0
S11
S12
S13
- RBV
RBV
RBV
RBV
RAV
RAV
RAV
RAV
ASD11
ASD12
ASD13
A B
RAV
4 EIL
2 EIL
RBV
A B
RAV
4 EIL
2 EIL
RBV2
C
0 0
» Matriks Momen ( AMD )
= 2 EI
= EI
= 0
= 0
3.2.
» Matriks Kekakuan ( S )
= EI
= 2 + 0.8 = 2.8 EI
= 0.4 EI
AMD11
AMD12
AMD13
AMD14
Berikan D2 = 1 satuan
S21
S22
S23
A B
RAV
4 EIL
2 EIL
RBVL
C
4 EIL
2 EIL
RCVL
A B
RAV
4 EIL
2 EIL
RBV2
C
4 EIL
2 EIL
RCV3
A B
RAV RBV
C
0 02 EI EI
» Matriks Reaksi Perletakan ( ASD )
2 m
ΣMA = 0
x 2 + 4 EI + 2 EI = 02 2
-2 + 2 EI + 1 EI = 0
= -3 EI-2
= 1.5 EIΣMB = 0
x 2 + 2 EI + 4 EI = 02 2
2 + 1 EI + 2 EI = 0
= -3 EI2
= -1.5 EI
5 m
x 5 + 2 EI + 4 EI = 05 5
-5 + 0.4 EI + 0.8 EI = 0
= -1.2 EI-5
= 0.24 EIΣMC = 0
x 5 + 4 EI + 2 EI = 0
- RBV
RBV
RBV
RBV
RAV
RAV
RAV
RAV
ΣMB = 0
- RCV
RCV
RCV
RCV
RBV1
A B
RAV
4 EIL
RBV
2 EIL
B C
RBV1
4 EIL
RCV
2 EIL
5 5
5 + 0.8 EI + 0.4 EI = 0
= -1 EI5
= -0.24 EI
Maka Matriks ASD adalah ;
= -1.5 EI
= 1.5 + -0.24 = 1.3 EI
= 0.2 EI
» Matriks Momen ( AMD )
= EI
= 2 EI
= 0.8 EI
= 0.4 EI
3.3.
» Matriks Kekakuan ( S )
Maka matriks kekakuannya ( S ) adalah ;
= 0
RBV1
RBV1
RBV1
ASD21
ASD22
ASD23
AMD21
AMD22
AMD23
AMD24
Berikan D3 = 1 satuan
S31
A B
RAV RBV
C
RCV
EI 2 EI 1 , 33 EI 0 ,67 EI
A B
RBV
4 EIL
2 EIL
RCVL
C
A B
RCV
4 EIL
2 EIL
RBV5
C
0 0
= 0.4 EI
= 0.8 EI
» Matriks Reaksi Perletakan ( ASD )
5 m
ΣMA = 0
x 5 + 4 EI + 2 EI = 05 5
-5 + 0.8 EI + 0.4 EI = 0
= -1 EI-5
= 0.2 EI
ΣMC = 0
x 5 + 2 EI + 4 EI = 05 5
5 + 0.4 EI + 0.8 EI = 0
= -1 EI5
= -0.24 EI
Maka Matriks ASD adalah ;
= 0
= -0.24 EI
= 0.24 EI
» Matriks Momen ( AMD )
S32
S33
- RCV
RCV
RCV
RCV
RBV
RBV
RBV
RBV
ASD31
ASD32
ASD33
B C
RBV
4 EIL
2 EIL
RCV
A B
RAV RBV
C
0 0 0 , 67 EI 1 , 33 EI
= 0
= 0
= 0.4 EI
= 0.8 EI
4. Menentukan Matriks (ADL), ( ASL ), Dan ( AML )
q = 0.2
2 m 5 m
» Matriks Momen ( ADL )
q = 0.2
2 m 5 m
= - 1 x q x
12= - 1 x 0.2 x 2 = -0.07 EI
12
= 1 x q x - 1 x q x
12 12= 1 x 0.2 x 2 - 1 x 0.2 x 5
12 12= 0.1 EI - 0.4 EI= -0.35 EI
= 1 x q x
12= 1 x 0.2 x 5 = 0.4 EI
12
0.067 0.067 0.42 0.42
AMD31
AMD32
AMD33
AMD34
t/m1
t/m1
ADL1 L2
ADL2 L2 L2
ADL3 L2
A B CEI EI
A B CEI EI
2
2 2
2
A B C
» Matriks Reaksi Perletakan ( ASL )
q = 0.20.067 0.067
Dimana : R = q x L= 0.2 x 2
2 m = 0.4 T
ΣMA = 0
x 2 + R x 1 + 0.1 - 0.1 = 0
-2 + 0.4 + 0.1 - 0.1 = 0
= -0.4 T-2
= 0.2 T
x 2 - R x 1 - 0.1 + 0.1 = 0
2 - 0.4 - 0.1 + 0.1 = 0
= 0.4 T2
= 0.2 T
q = 0.20.42 0.42
Dimana : R = q x L= 0.2 x 5
5 m = 1 T
ΣMB = 0
x 5 + R x 2.5 + 0.4 - 0.4 = 0
-5 + 2.5 + 0.4 - 0.4 = 0
= -3 T-5
= 1 T
x 5 - R x 2.5 - 0.4 + 0.4 = 0
5 - 2.5 - 0.4 + 0.4 = 0
= 3 T5
= 1 TMaka Matriks ASL adalah ;
= 0 T
= 0 + 1 T = 1 T
t/m1
- RBV
RBV
RBV
RBV
ΣMB = 0
RAV
RAV
RAV
RAV
t/m1
- RCV
RCV
RCV
RCV
ΣMB = 0
RBV1
RBV1
RBV1
RBV1
ASL1
ASL2
A B
B C
= 1 T
» Matriks Momen ( AML )
0.067 0.067 0.42 0.42
= -0.067 TM
= 0.067 TM
= -0.42 TM
= 0.42 TM
5. Menentukan Joint Displacement
AD = ADL + S x D
AD =dan D3.
Jika matriks S & ADL, maka nilai D ( Displacement ) nya adalah sebagai berikut :2 1 0 -0.07
S = EI 1 2.80 0.40 ADL = EI -0.35
0 0.40 0.80 0.4
D = ADL
D1 0.62 -0.24 0.12 -0.07
= -0.24 0.48 -0.24 x -0.35
0.12 -0.24 1.37 0.42
D1 0.09 -0.09
= -0.25 = 0.25
0.65 -0.65
6. Menentukan Reaksi Perletakan
AS = ASL + ASD x D
Jika matriks ASL & ASD, maka nilai AS adalah sebagai berikut :0 -1.5 -1.5 0
ASL = 1 ASD = EI 1.5 1.26 -0.24
1 0 0.24 0.24
0 -1.50 -1.50 0 -0.09
= 1 + EI 1.50 1.26 -0.24 x 0.25
ASL3
AML1
AML2
AML3
AML4
0, Karena tidak ada momen luar yang bekerja pada Joint D1, D2,
-S-1
D2
D3
D2
D3
AS1
AS2
A B C
1EI
−1
EI
−1
EI1
EI
1 0 0.24 0.24 -0.65
0 -0.24 -0.04
= 1 + 0.33 = 1.03
1 -0.10 0.40
7. Menentukan Gaya Dalam AMAM = AML + AMD x D
Jika matriks AML & AMD, maka nilai AS adalah sebagai berikut :-0.07 2 1 0
AML =0.07
AMD = EI1 2 0
-0.42 0 0.80 0.4
0.42 0 0.40 0.8
-0.07 2 1 0
=0.07
+ EI1 2 0
x-0.09
-0.42 0 0.80 0.40 0.25
0.42 0 0.40 0.80 -0.65
-0.07 0.07 0
=0.07
+0.41
=0.48
-0.42 -0.06 -0.48
0.42 -0.42 0
8. Free Body
q = 0.2
2 m 5 m
0.000 0.48 -0.48 0.00
» Bentang A-B
q = 0.20 0.48
Dimana, R = q x L
AS3
AS1
AS2
AS3
AM1
AM2
AM3
AM4
AM1
AM2
AM3
AM4
t/m1
t/m1
1EI
1EI
A B CEI EI
A B C
A B
= 0.2 x 22 m = 0.4 T
Reaksi PerletakanΣMA = 0
x 2 + R x 1 + 0.48 - 0 = 0
-2 + 0.4 + 0.48 - 0 = 0
= -0.88 T-2
= 0.44 T
x 2 - R x 1 - 0 + 0.48 = 0
2 - 0.4 - 0 + 0.48 = 0
= -0.08 T2
= -0.04 T
MomenInterval 0 ≤ x ≤ 2
Mx = x X - 1 q - 02
= -0.04 X - 0.10
LintangInterval 0 ≤ x ≤ 2Dx = -0.2 X + -0.04
x Rumus Momen Rumus LintangNilai
Momen Lintang0 0 Tm -0.04 T1 -0.14 Tm -0.24 T2 -0.48 Tm -0.44 T
» Bentang B-C
q = 0.2-0.48 0
Dimana, R = q x L= 0.2 x 5
5 m = 1 T
Reaksi Perletakan
x 5 + R x 2.5 + 0 - 0.48 = 0
-5 + 2.5 + 0 - 0.48 = 0
- RBV
RBV
RBV
RBV
ΣMB = 0
RAV
RAV
RAV
RAV
RAV X2
X2
t/m1
ΣMB = 0
- RCV
RCV
A B
-0,04 x - 0,10X20,2 x +(-0,04)
B C
= -2.03 T-5
= 0.40 T
x 5 - R x 2.5 - 0.48 + 0 = 0
5 - 2.5 - 0.48 + 0 = 0
= 2.98 T5
= 0.60 TMomenInterval 0 ≤ x ≤ 2
Mx = x X - 1 q - 0.482
= ### X - 0.3 + ###
LintangInterval 0 ≤ x ≤ 5Dx = -0.5 X + ###
x Rumus Momen Rumus LintangNilai
Momen Lintang0 ### Tm ### T
2.5 ### Tm ### T4 ### Tm ### T
9. Gambar Momen dan Lintang
q = 0.2
2 m 5 m
-0.48 Tm
0 0
-0.14 Tm ### Tm
### T
0 0
RCV
RCV
ΣMC = 0
RBV1
RAV
RBV1
RBV1
RBV1 X2
X2
t/m1
0,60x -0,1X2 - 0,48 -0,2 x + 0,60
A B CEI EI
-0.04 T ### T
-0.44 T
Lantai RumusMomen Frimer
Reaksi Perletakan
SatuanGaya Vertikal
Batang Hasil Satuan Kolom 1 Kolom 2 Kolom 3
5
AG -0.844 TM 1.125 T
GA 0.844 TM 1.125 T
GM -0.844 TM 1.125 T
MG 0.844 TM 1.125 T
4
BH -2531 TM 3.375 T
HB 2531 TM 3.375 T
HN -2531 TM 3.375 T
NH 2531 TM 3.375 T
3
CI -2531 TM 3.375 T
IC 2531 TM 3.375 T
IO -2531 TM 3.375 T
OI 2531 TM 3.375 T
2
DJ -2531 TM 3.375 T
JD 2531 TM 3.375 T
JP -2531 TM 3.375 T
PJ 2531 TM 3.375 T
1
EK -2531 TM 3.375 T
KE 2531 TM 3.375 T
KQ -2531 TM 3.375 T
QK 2531 TM 3.375 T
Jumlah 14.625 29.250 14.625 T
5.0625
0.442
5.5045
1.2232222
2.752 1.266
1.487
16
Balok
q = 0.5#VALUE! ###
4.5 mDimana, R = q x L
= 0.5 x 4.5= 2.25 T
Reaksi Perletakan
x 4.5 + R x 2.25 + ### + ### = 0
-4.5 + 5.063 + ### + ### = 0
= ###-5
= ### T
x 4.5 - R x 2.25 + ### + ### = 0
4.5 - 5.063 + ### + ### = 0
= ###5
= ### TMomenInterval 0 ≤ x ≤ 2
Mx = x X - 1 q + #VALUE!2
= ### X - 0.25 + #VALUE!
LintangInterval 0 ≤ x ≤ 5
Dx = -0.50 X + ###
x Rumus Momen Rumus LintangNilai
Momen Lintang0 #VALUE! Tm #VALUE! T2 #VALUE! Tm #VALUE! T4 #VALUE! Tm #VALUE! T
t/m1
ΣMA = 0
- RGV
RGV
RGV
RGV
ΣMG = 0
RAV
RAV
RAV
RAV
RAV X2
X2
A G
0,48x -0,18X2 + 0,48 -0,36 x + 0,48
Balok
q = 0.5#VALUE! ###
Dimana, R = q x L= 0.5 x 4.5
4.5 m = 2.25 T
Reaksi Perletakan
x 4.5 + R x 2.25 + ### - ### = 0
-4.5 + 5.063 + ### - ### = 0
= ###-5
= ### T
x 4.5 - R x 2.25 - #VALUE! + ### = 0
4.5 - 5.063 - #VALUE! + ### = 0
= ###5
= ### TMomenInterval 0 ≤ x ≤ 2
Mx = x X - 1 q - #VALUE!2
= ### X - 0.25 - #VALUE!
LintangInterval 0 ≤ x ≤ 5
Dx = -0.50 X + ###
x Rumus Momen Rumus LintangNilai
Momen Lintang0 #VALUE! Tm #VALUE! T2 #VALUE! Tm #VALUE! T4 #VALUE! Tm #VALUE! T
t/m1
ΣMG = 0
- RMV
RMV
RMV
RMV
ΣMM = 0
RGV
RGV
RGV
RGV
RGV X2
X2
G M
0,673x -0,18X2 - 0,357 -0,36 x + 0,673
Kolom10 T ###
A
4 mB
###
Reaksi PerletakkanΣMB = 0
4.00 + ### - ### + 10 x 4 = 0
= ###4.00
= ###
Jarak (X)Momen(KN m) Lintang(KN)
#VALUE!0 #VALUE! #VALUE!1 #VALUE! #VALUE!2 #VALUE! #VALUE!4 #VALUE! #VALUE!
Kolom8 T ###
B
4 mC
###
Reaksi PerletakkanΣMC = 0
4.00 - ### - ### + 8 x 4 = 0
= ###4.00
= ###
Jarak (X)Momen(KN m) Lintang(KN)
#VALUE!0 #VALUE! #VALUE!
RAV
RAV
RAV
RAV (X) + 10 (X) - RAV+ 10
RBV
RBV
RBV
RBV (X) + 8 (X) - RBV+ 8
1 #VALUE! #VALUE!2 #VALUE! #VALUE!4 #VALUE! #VALUE!
Kolom2 T ###
E
4 mF
###
Reaksi PerletakkanΣMF = 0
4.00 + ### + ### + 2 x 4 = 0
= ###4.00
= ###
Jarak (X)Momen(KN m) Lintang(KN)
#VALUE!0 #VALUE! #VALUE!1 #VALUE! #VALUE!2 #VALUE! #VALUE!4 #VALUE! #VALUE!
REV
REV
REV
REV (X) + 2 (X) + REV+ 2