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Tugas Mekanika Teknik
1
Tugas
Mekanika Teknik 3 (Metode Distribusi Momen)
Dikerjakan oleh :
-Lionel ‘oneil’ Zakhy-
Jurusan Teknik Sipil - Fakultas Teknik
Universitas Tadulako
2010
TUGAS MEKANIKA TEKNIK 3
Diketahui seperti tergambar. Hitunglah menggunakan metode distribusi momen (Cross Method) :
a. momen yang terjadi di setiap titik kumpul b. gaya‐gaya geser yang terjadi c. gaya normal yang terjadi d. gambarkan bidang momen, lintang dan normal
Penyelesaian
A. Menghitung kekakuan relatif (k)
Rumus yang digunakan ⎛ ⎞= =⎜ ⎟⎝ ⎠
ii
EIk i elemen
L
‐ Batang AD : = =44AD
EIk EI
‐ Batang BE : = =5
1.254BE
EIk EI
‐ Batang CF : = =44CF
EIk EI
‐ Batang DG : = =2
0.666673DG
EIk EI
‐ Batang EH : = =2
0.666673EH
EIk EI
‐ Batang FI : = = 0.333333FI
EIk EI
‐ Batang DE : = =3
0.56DE
EIk EI
‐ Batang EF : = =3
0.428577EF
EIk EI
‐ Batang GH : = =2
0.333336GH
EIk EI
‐ Batang HI : = = 0.142867HI
EIk EI
B. Menghitung faktor distribusi (DF)
Rumus yang digunakan = = =Σ
; intii
j
kDF i elemen j jo
k
Joint A, B, C (tump. jepit) = = =0 0 0AD BE CFDF DF DF
Joint D
Σ = + += + +=
= = =Σ
= = =Σ
= = =Σ
0.66667 0.5
2.16667
0.461542.16667
0.666670.30769
2.16667
0.50.23077
2.16667
D DA DG DE
DADA
D
DGDG
D
DEDE
D
k k k kEI EI EI
EIk EI
DFk EIk EI
DFk EIk EI
DFk EI
Joint E
Σ = + + += + + +=
= = =Σ
= = =Σ
= = =Σ
= = =Σ
1.25 0.5 0.42857 0.66667
2.84524
1.250.43933
2.84524
0.50.17573
2.84524
0.428570.15063
2.84524
0.666672.84524
E BE DE EF EH
BEEB
E
DEED
E
EFEF
E
EHEH
E
k k k k kEI EI EI EI
EIk EI
DFk EIk EI
DFk EIk EI
DFk EIk EI
DFk EI
0.23431
Joint F
Σ = + += + +=
= = =Σ
= = =Σ
= = =Σ
0.42857 0.33333
1.76190
0.567571.76190
0.428570.24324
1.76190
0.333330.18919
1.76190
F CF EF FI
CFFC
F
EFFE
F
FIFI
F
k k k kEI EI EI
EIk EI
DFk EIk EI
DFk EIk EI
DFk EI
Joint G
Σ = += +=
= = =Σ
= = =Σ
0.66667 0.33333
0.666670.66667
0.333330.33333
G DG GH
DGGD
G
GHGH
G
k k kEI EI
EIk EI
DFk EIk EI
DFk EI
Joint H
Σ = + += + +=
= = =Σ
= = =Σ
= = =Σ
0.66667 0.33333 0.14286
1.14286
0.666670.58333
1.14286
0.333330.29167
1.14286
0.142860.125
1.14286
H EH GH HI
EHHE
G
GHHG
G
HIHI
G
k k k kEI EI EIEI
k EIDF
k EIk EI
DFk EIk EI
DFk EI
Joint I
kFI
F
IHkHI
Σ = += +=
= = =Σ
= = =Σ
0.14286 0.33333
0.47619
0.142860.7
0.47619
0.333330.3
0.47619
I HI FI
HIIH
G
FIIF
G
k k kEI EIEI
k EIDF
k EIk EI
DFk EI
C. Menghitung Momen Primer (Mo) Akibat Beban Luar
‐ Batang DE
( )( )( )( )
( )( ) ( )( )
= − = − = −
= + = + = +
22
22
22
22
6 2 45.33333
6
6 2 42.66667
6
DE
ED
PabMo tm
L
Pa bMo tm
L
‐ Batang EF
( )( )
( )( )
= − = − = −
= + = + = +
22
22
5 720.41667
12 12
5 720.41667
12 12
EF
FE
qLMo tm
qLMo tm
‐ Batang GH
q = 3 t/m
G H
Mo GH Mo HG
L = 6m
( )( )
( )( )
= − = − = −
= + = + = +
22
22
3 63.6
30 30
3 65.4
20 20
GH
HG
qLMo tm
qLMo tm
‐ Batang HI
q = 4 t/m
D E
Mo HI Mo IH
a = 2m b = 5m
L = 7m
( ) ( )( ) ( ){ }( ) ( ){ }
= − + + = − + = −
= + + = + =
+
+ +
2 22 2
2 2
3 3
2 2
22(4)(2)5 10 3.30884
30 30(7)
(4)(2)5 0.88163
2
2 5 2 5 10
0
5
20(2 5 5
7)
HI
IH
qaMo a ab b tm
L
qaMo a b tm
L
D. Menghitung Momen Primer (Mo) Akibat Pergoyangan Arah 1
( ) ( )Δ Δ= = − = − = − Δ
2 2
6 1 6 4 11.5 1
4AD
AD DA
EI EIMo Mo EI
L
( ) ( )Δ Δ= = − = − = − Δ2 2
6 1 6 5 11.875 1
4BE
BE EB
EI EIMo Mo EI
L
( ) ( )Δ Δ= = − = − = − Δ2 2
6 1 6 4 11.5 1
4CF
CF FC
EI EIMo Mo EI
L
( ) ( )Δ Δ= = + = + = + Δ
2 2
6 1 6 2 11.33333 1
3DG
DG GD
EI EIMo Mo EI
L
( ) ( )Δ Δ= = + = + = + Δ2 2
6 1 6 2 11.33333 1
3EH
EH HE
EI EIMo Mo EI
L
( ) ( )Δ Δ= = + = + = + Δ2 2
6 1 6 10.66667 1
3DG
FI IF
EI EIMo Mo EI
L
E. Menghitung Momen Primer (Mo) Akibat Pergoyangan Arah 2
( ) ( )Δ Δ= = − = − = − Δ2 2
6 2 6 2 21.33333 2
3DG
DG GD
EI EIMo Mo EI
L
( ) ( )Δ Δ= = − = − = − Δ2 2
6 2 6 2 21.33333 2
3EH
EH HE
EI EIMo Mo EI
L
( ) ( )Δ Δ= = − = − = − Δ2 2
6 2 6 20.66667 2
3DG
FI IF
EI EIMo Mo EI
L
DISTRIBUSI MOMEN AKIBAT BEBAN LUAR
A B CAD BE CF DA DE DG EB ED EF EH FC FE FI GD GH HE HG HI IF IH
1.0000 * EI 1.2500 * EI 1.0000 * EI 1.0000 * EI 0.5000 * EI 0.6667 * EI 1.2500 * EI 0.5000 * EI 0.4286 * EI 0.6667 * EI 1.0000 * EI 0.4286 * EI 0.3333 * EI 0.6667 * EI 0.3333 * EI 0.6667 * EI 0.3333 * EI 0.1429 * EI 0.3333 * EI 0.1429 * EISIKLUS DF 0.46154 0.23077 0.30769 0.43933 0.17573 0.15063 0.23431 0.56757 0.24324 0.18919 0.66667 0.33333 0.58333 0.29167 0.12500 0.70000 0.30000
Mo 0.00000 0.00000 0.00000 0.00000 ‐5.33333 0.00000 0.00000 2.66667 ‐20.41667 0.00000 0.00000 20.41667 0.00000 0.00000 ‐3.60000 0.00000 5.40000 ‐3.30884 0.00000 0.88163BALANCE 2.46154 1.23077 1.64103 7.79812 3.11925 2.67364 4.15900 ‐11.58784 ‐4.96622 ‐3.86261 2.40000 1.20000 ‐1.21984 ‐0.60992 ‐0.26139 ‐0.61714 ‐0.26449CARRY OVER 1.23077 3.89906 ‐5.79392 1.55962 1.20000 0.61538 ‐2.48311 ‐0.60992 1.33682 ‐0.30857 0.82051 ‐0.30496 2.07950 0.60000 ‐0.13224 ‐1.93131 ‐0.13070BALANCE ‐1.27367 ‐0.63684 ‐0.84911 1.08850 0.43540 0.37320 0.58054 ‐0.58360 ‐0.25011 ‐0.19453 ‐0.34370 ‐0.17185 ‐1.48590 ‐0.74295 ‐0.31841 1.44340 0.61860CARRY OVER ‐0.63684 0.54425 ‐0.29180 0.21770 ‐0.17185 ‐0.31842 ‐0.12506 ‐0.74295 0.18660 0.72170 ‐0.42456 ‐0.37147 0.29027 ‐0.08593 0.30930 ‐0.09727 ‐0.15920BALANCE ‐0.02116 ‐0.01058 ‐0.01411 0.52123 0.20849 0.17871 0.27799 ‐0.51552 ‐0.22094 ‐0.17184 0.53069 0.26534 ‐0.29963 ‐0.14981 ‐0.06421 0.17953 0.07694CARRY OVER ‐0.01058 0.26062 ‐0.25776 0.10425 0.26534 ‐0.00529 ‐0.11047 ‐0.14981 0.08935 0.08976 ‐0.00705 ‐0.07491 0.13900 0.13267 0.03847 ‐0.08592 ‐0.03210BALANCE ‐0.17058 ‐0.08529 ‐0.11372 0.11667 0.04667 0.04000 0.06223 ‐0.10166 ‐0.04357 ‐0.03389 0.05464 0.02732 ‐0.18091 ‐0.09046 ‐0.03877 0.08262 0.03541CARRY OVER ‐0.08529 0.05834 ‐0.05083 0.02333 0.02732 ‐0.04265 ‐0.02178 ‐0.09046 0.02000 0.04131 ‐0.05686 ‐0.04523 0.03111 0.01366 0.01770 ‐0.01694 ‐0.01938BALANCE ‐0.02338 ‐0.01169 ‐0.01559 0.06805 0.02722 0.02333 0.03629 ‐0.03480 ‐0.01491 ‐0.01160 0.06806 0.03403 ‐0.03644 ‐0.01822 ‐0.00781 0.02543 0.01090CARRY OVER ‐0.01169 0.03402 ‐0.01740 0.01361 0.03403 ‐0.00584 ‐0.00746 ‐0.01822 0.01167 0.01271 ‐0.00779 ‐0.00911 0.01815 0.01701 0.00545 ‐0.00580 ‐0.00390BALANCE ‐0.02199 ‐0.01099 ‐0.01466 0.01385 0.00554 0.00475 0.00739 ‐0.01384 ‐0.00593 ‐0.00461 0.01127 0.00563 ‐0.02369 ‐0.01184 ‐0.00508 0.00679 0.00291CARRY OVER ‐0.01099 0.00692 ‐0.00692 0.00277 0.00563 ‐0.00550 ‐0.00297 ‐0.01184 0.00237 0.00340 ‐0.00733 ‐0.00592 0.00369 0.00282 0.00146 ‐0.00231 ‐0.00254BALANCE ‐0.00388 ‐0.00194 ‐0.00259 0.00892 0.00357 0.00306 0.00476 ‐0.00328 ‐0.00140 ‐0.00109 0.00883 0.00442 ‐0.00465 ‐0.00232 ‐0.00100 0.00339 0.00145CARRY OVER ‐0.00194 0.00446 ‐0.00164 0.00178 0.00442 ‐0.00097 ‐0.00070 ‐0.00232 0.00153 0.00170 ‐0.00129 ‐0.00116 0.00238 0.00221 0.00073 ‐0.00055 ‐0.00050BALANCE ‐0.00286 ‐0.00143 ‐0.00191 0.00176 0.00070 0.00060 0.00094 ‐0.00183 ‐0.00078 ‐0.00061 0.00164 0.00082 ‐0.00310 ‐0.00155 ‐0.00066 0.00073 0.00031CARRY OVER ‐0.00143 0.00088 ‐0.00092 0.00035 0.00082 ‐0.00072 ‐0.00039 ‐0.00155 0.00030 0.00037 ‐0.00095 ‐0.00077 0.00047 0.00041 0.00016 ‐0.00031 ‐0.00033BALANCE ‐0.00054 ‐0.00027 ‐0.00036 0.00117 0.00047 0.00040 0.00062 ‐0.00038 ‐0.00016 ‐0.00013 0.00115 0.00058 ‐0.00060 ‐0.00030 ‐0.00013 0.00045 0.00019CARRY OVER ‐0.00027 0.00058 ‐0.00019 0.00023 0.00058 ‐0.00013 ‐0.00008 ‐0.00030 0.00020 0.00022 ‐0.00018 ‐0.00015 0.00031 0.00029 0.00010 ‐0.00006 ‐0.00006BALANCE ‐0.00037 ‐0.00019 ‐0.00025 0.00023 0.00009 0.00008 0.00012 ‐0.00024 ‐0.00010 ‐0.00008 0.00022 0.00011 ‐0.00041 ‐0.00020 ‐0.00009 0.00009 0.00004CARRY OVER ‐0.00019 0.00011 ‐0.00012 0.00005 0.00011 ‐0.00009 ‐0.00005 ‐0.00020 0.00004 0.00004 ‐0.00012 ‐0.00010 0.00006 0.00006 0.00002 ‐0.00004 ‐0.00004BALANCE ‐0.00007 ‐0.00004 ‐0.00005 0.00015 0.00006 0.00005 0.00008 ‐0.00005 ‐0.00002 ‐0.00002 0.00015 0.00008 ‐0.00008 ‐0.00004 ‐0.00002 0.00006 0.00003CARRY OVER ‐0.00004 0.00008 ‐0.00002 0.00003 0.00008 ‐0.00002 ‐0.00001 ‐0.00004 0.00003 0.00003 ‐0.00002 ‐0.00002 0.00004 0.00004 0.00001 ‐0.00001 ‐0.00001BALANCE ‐0.00005 ‐0.00002 ‐0.00003 0.00003 0.00001 0.00001 0.00002 ‐0.00003 ‐0.00001 ‐0.00001 0.00003 0.00001 ‐0.00005 ‐0.00003 ‐0.00001 0.00001 0.00000CARRY OVER ‐0.00002 0.00001 ‐0.00002 0.00001 0.00001 ‐0.00001 ‐0.00001 ‐0.00003 0.00001 0.00001 ‐0.00002 ‐0.00001 0.00001 0.00001 0.00000 ‐0.00001 ‐0.00001BALANCE ‐0.00001 0.00000 ‐0.00001 0.00002 0.00001 0.00001 0.00001 ‐0.00001 0.00000 0.00000 0.00002 0.00001 ‐0.00001 ‐0.00001 0.00000 0.00001 0.00000CARRY OVER 0.00000 0.00001 0.00000 0.00000 0.00001 0.00000 0.00000 ‐0.00001 0.00000 0.00000 0.00000 0.00000 0.00001 0.00000 0.00000 0.00000 0.00000BALANCE ‐0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 ‐0.00001 0.00000 0.00000 0.00000 0.00000CARRY OVER 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000BALANCE 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000CARRY OVER 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000BALANCE 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
0.47148 4.80935 ‐6.42154 0.94296 ‐2.93811 1.99515 9.61870 6.74989 ‐19.87091 3.50232 ‐12.84307 16.56141 ‐3.71834 3.04733 ‐3.04733 ‐0.69033 4.45559 ‐3.76526 ‐1.01515 1.01515
0.47148 4.80935 ‐6.42154 0.94296 2.39522 1.99515 9.61870 4.08322 0.54575 3.50232 ‐12.84307 ‐3.85525 ‐3.71834 3.04733 0.55267 ‐0.69033 ‐0.94441 ‐0.45642 ‐1.01515 0.13352‐0.47148 ‐4.80935 6.42154 ‐0.23574 ‐2.04161 ‐1.52366 ‐2.40468 ‐1.19761 1.92763 0.34517 ‐3.21077 ‐0.27288 0.50757 ‐0.99757 0.47220 ‐1.75116 ‐0.27634 ‐0.06676 1.85917 0.228210.00000 0.00000 0.00000 0.70722 0.35361 0.47148 7.21403 2.88561 2.47338 3.84748 ‐16.05384 ‐4.12813 ‐3.21077 2.04975 1.02488 ‐2.44149 ‐1.22074 ‐0.52318 0.84402 0.361720.000 /EI 0.000 /EI 0.000 /EI 0.236 /EI 0.236 /EI 0.236 /EI 1.924 /EI 1.924 /EI 1.924 /EI 1.924 /EI ‐5.351 /EI ‐3.211 /EI ‐3.211 /EI 1.025 /EI 1.025 /EI ‐1.221 /EI ‐1.221 /EI ‐1.221 /EI 0.844 /EI 0.844 /EIƟ = 0 Ɵ = 0 Ɵ = 0 Ɵ = sama
0.00000
CHECK DEFORMASI Ɵ = samaƟ = samaƟ = sama Ɵ = sama Ɵ = sama
‐ CO = ‐(1/2)(M‐Mo)jJUMLAH
JOINTELEMENK RELATIF (k = EI/L)
HD I
0.00000 0.00000 0.00000 0.00000 0.00000
E F G
TOTAL MOMEN (M)CHECK STATIK
ARAH MOMEN
PERUBAHAN (M‐Mo)i
Ɵ = JUMLAH /3k
11
12
7
8
9
10
13
14
15
16
6
1
2
3
4
5
DISTRIBUSI MOMEN AKIBAT PERGOYANGAN ARAH 1catatan : X1 = EIΔ1
A B CAD BE CF DA DE DG EB ED EF EH FC FE FI GD GH HE HG HI IF IH
1.0000 * EI 1.2500 * EI 1.0000 * EI 1.0000 * EI 0.5000 * EI 0.6667 * EI 1.2500 * EI 0.5000 * EI 0.4286 * EI 0.6667 * EI 1.0000 * EI 0.4286 * EI 0.3333 * EI 0.6667 * EI 0.3333 * EI 0.6667 * EI 0.3333 * EI 0.1429 * EI 0.3333 * EI 0.1429 * EISIKLUS DF 0.46154 0.23077 0.30769 0.43933 0.17573 0.15063 0.23431 0.56757 0.24324 0.18919 0.66667 0.33333 0.58333 0.29167 0.12500 0.70000 0.30000
Mo ‐1.50000 * X1 ‐1.87500 * X1 ‐1.50000 * X1 ‐1.50000 * X1 0.00000 * X1 1.33333 * X1 ‐1.87500 * X1 0.00000 * X1 0.00000 * X1 1.33333 * X1 ‐1.50000 * X1 0.00000 * X1 0.66667 * X1 1.33333 * X1 0.00000 * X1 1.33333 * X1 0.00000 * X1 0.00000 * X1 0.66667 * X1 0.00000 * X1BALANCE 0.07692 * X1 0.03846 * X1 0.05128 * X1 0.23797 * X1 0.09519 * X1 0.08159 * X1 0.12692 * X1 0.47297 * X1 0.20270 * X1 0.15766 * X1 ‐0.88889 * X1 ‐0.44444 * X1 ‐0.77778 * X1 ‐0.38889 * X1 ‐0.16667 * X1 ‐0.46667 * X1 ‐0.20000 * X1CARRY OVER 0.03846 * X1 0.11899 * X1 0.23649 * X1 0.04759 * X1 ‐0.44444 * X1 0.01923 * X1 0.10135 * X1 ‐0.38889 * X1 0.04079 * X1 ‐0.23333 * X1 0.02564 * X1 ‐0.19444 * X1 0.06346 * X1 ‐0.22222 * X1 ‐0.10000 * X1 0.07883 * X1 ‐0.08333 * X1BALANCE 0.18316 * X1 0.09158 * X1 0.12211 * X1 0.11788 * X1 0.04715 * X1 0.04041 * X1 0.06287 * X1 0.10928 * X1 0.04683 * X1 0.03643 * X1 0.11254 * X1 0.05627 * X1 0.15095 * X1 0.07547 * X1 0.03235 * X1 0.00315 * X1 0.00135 * X1CARRY OVER 0.09158 * X1 0.05894 * X1 0.05464 * X1 0.02358 * X1 0.05627 * X1 0.04579 * X1 0.02342 * X1 0.07547 * X1 0.02021 * X1 0.00158 * X1 0.06105 * X1 0.03774 * X1 0.03143 * X1 0.02813 * X1 0.00068 * X1 0.01821 * X1 0.01617 * X1BALANCE ‐0.03685 * X1 ‐0.01843 * X1 ‐0.02457 * X1 ‐0.06356 * X1 ‐0.02542 * X1 ‐0.02179 * X1 ‐0.03390 * X1 ‐0.01236 * X1 ‐0.00530 * X1 ‐0.00412 * X1 ‐0.06586 * X1 ‐0.03293 * X1 ‐0.03514 * X1 ‐0.01757 * X1 ‐0.00753 * X1 ‐0.02407 * X1 ‐0.01032 * X1CARRY OVER ‐0.01843 * X1 ‐0.03178 * X1 ‐0.00618 * X1 ‐0.01271 * X1 ‐0.03293 * X1 ‐0.00921 * X1 ‐0.00265 * X1 ‐0.01757 * X1 ‐0.01090 * X1 ‐0.01204 * X1 ‐0.01228 * X1 ‐0.00879 * X1 ‐0.01695 * X1 ‐0.01647 * X1 ‐0.00516 * X1 ‐0.00206 * X1 ‐0.00377 * X1BALANCE 0.02107 * X1 0.01053 * X1 0.01404 * X1 0.01293 * X1 0.00517 * X1 0.00443 * X1 0.00690 * X1 0.01302 * X1 0.00558 * X1 0.00434 * X1 0.01405 * X1 0.00702 * X1 0.02250 * X1 0.01125 * X1 0.00482 * X1 0.00408 * X1 0.00175 * X1CARRY OVER 0.01053 * X1 0.00647 * X1 0.00651 * X1 0.00259 * X1 0.00702 * X1 0.00527 * X1 0.00279 * X1 0.01125 * X1 0.00222 * X1 0.00204 * X1 0.00702 * X1 0.00563 * X1 0.00345 * X1 0.00351 * X1 0.00087 * X1 0.00217 * X1 0.00241 * X1BALANCE ‐0.00443 * X1 ‐0.00222 * X1 ‐0.00296 * X1 ‐0.00848 * X1 ‐0.00339 * X1 ‐0.00291 * X1 ‐0.00452 * X1 ‐0.00242 * X1 ‐0.00104 * X1 ‐0.00081 * X1 ‐0.00843 * X1 ‐0.00422 * X1 ‐0.00457 * X1 ‐0.00228 * X1 ‐0.00098 * X1 ‐0.00321 * X1 ‐0.00137 * X1CARRY OVER ‐0.00222 * X1 ‐0.00424 * X1 ‐0.00121 * X1 ‐0.00170 * X1 ‐0.00422 * X1 ‐0.00111 * X1 ‐0.00052 * X1 ‐0.00228 * X1 ‐0.00145 * X1 ‐0.00160 * X1 ‐0.00148 * X1 ‐0.00114 * X1 ‐0.00226 * X1 ‐0.00211 * X1 ‐0.00069 * X1 ‐0.00040 * X1 ‐0.00049 * X1BALANCE 0.00273 * X1 0.00136 * X1 0.00182 * X1 0.00172 * X1 0.00069 * X1 0.00059 * X1 0.00092 * X1 0.00174 * X1 0.00074 * X1 0.00058 * X1 0.00175 * X1 0.00087 * X1 0.00295 * X1 0.00147 * X1 0.00063 * X1 0.00062 * X1 0.00027 * X1CARRY OVER 0.00136 * X1 0.00086 * X1 0.00087 * X1 0.00034 * X1 0.00087 * X1 0.00068 * X1 0.00037 * X1 0.00147 * X1 0.00029 * X1 0.00031 * X1 0.00091 * X1 0.00074 * X1 0.00046 * X1 0.00044 * X1 0.00013 * X1 0.00029 * X1 0.00032 * X1BALANCE ‐0.00056 * X1 ‐0.00028 * X1 ‐0.00037 * X1 ‐0.00111 * X1 ‐0.00044 * X1 ‐0.00038 * X1 ‐0.00059 * X1 ‐0.00034 * X1 ‐0.00015 * X1 ‐0.00011 * X1 ‐0.00110 * X1 ‐0.00055 * X1 ‐0.00060 * X1 ‐0.00030 * X1 ‐0.00013 * X1 ‐0.00042 * X1 ‐0.00018 * X1CARRY OVER ‐0.00028 * X1 ‐0.00056 * X1 ‐0.00017 * X1 ‐0.00022 * X1 ‐0.00055 * X1 ‐0.00014 * X1 ‐0.00007 * X1 ‐0.00030 * X1 ‐0.00019 * X1 ‐0.00021 * X1 ‐0.00019 * X1 ‐0.00015 * X1 ‐0.00030 * X1 ‐0.00027 * X1 ‐0.00009 * X1 ‐0.00006 * X1 ‐0.00006 * X1BALANCE 0.00036 * X1 0.00018 * X1 0.00024 * X1 0.00023 * X1 0.00009 * X1 0.00008 * X1 0.00012 * X1 0.00023 * X1 0.00010 * X1 0.00008 * X1 0.00022 * X1 0.00011 * X1 0.00039 * X1 0.00019 * X1 0.00008 * X1 0.00009 * X1 0.00004 * X1CARRY OVER 0.00018 * X1 0.00011 * X1 0.00011 * X1 0.00005 * X1 0.00011 * X1 0.00009 * X1 0.00005 * X1 0.00019 * X1 0.00004 * X1 0.00004 * X1 0.00012 * X1 0.00010 * X1 0.00006 * X1 0.00006 * X1 0.00002 * X1 0.00004 * X1 0.00004 * X1BALANCE ‐0.00007 * X1 ‐0.00004 * X1 ‐0.00005 * X1 ‐0.00015 * X1 ‐0.00006 * X1 ‐0.00005 * X1 ‐0.00008 * X1 ‐0.00005 * X1 ‐0.00002 * X1 ‐0.00002 * X1 ‐0.00014 * X1 ‐0.00007 * X1 ‐0.00008 * X1 ‐0.00004 * X1 ‐0.00002 * X1 ‐0.00006 * X1 ‐0.00002 * X1CARRY OVER ‐0.00004 * X1 ‐0.00007 * X1 ‐0.00002 * X1 ‐0.00003 * X1 ‐0.00007 * X1 ‐0.00002 * X1 ‐0.00001 * X1 ‐0.00004 * X1 ‐0.00002 * X1 ‐0.00003 * X1 ‐0.00002 * X1 ‐0.00002 * X1 ‐0.00004 * X1 ‐0.00004 * X1 ‐0.00001 * X1 ‐0.00001 * X1 ‐0.00001 * X1BALANCE 0.00005 * X1 0.00002 * X1 0.00003 * X1 0.00003 * X1 0.00001 * X1 0.00001 * X1 0.00002 * X1 0.00003 * X1 0.00001 * X1 0.00001 * X1 0.00003 * X1 0.00001 * X1 0.00005 * X1 0.00003 * X1 0.00001 * X1 0.00001 * X1 0.00000 * X1CARRY OVER 0.00002 * X1 0.00001 * X1 0.00001 * X1 0.00001 * X1 0.00001 * X1 0.00001 * X1 0.00001 * X1 0.00003 * X1 0.00001 * X1 0.00001 * X1 0.00002 * X1 0.00001 * X1 0.00001 * X1 0.00001 * X1 0.00000 * X1 0.00000 * X1 0.00001 * X1BALANCE ‐0.00001 * X1 0.00000 * X1 ‐0.00001 * X1 ‐0.00002 * X1 ‐0.00001 * X1 ‐0.00001 * X1 ‐0.00001 * X1 ‐0.00001 * X1 0.00000 * X1 0.00000 * X1 ‐0.00002 * X1 ‐0.00001 * X1 ‐0.00001 * X1 ‐0.00001 * X1 0.00000 * X1 ‐0.00001 * X1 0.00000 * X1CARRY OVER 0.00000 * X1 ‐0.00001 * X1 0.00000 * X1 0.00000 * X1 ‐0.00001 * X1 0.00000 * X1 0.00000 * X1 ‐0.00001 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 ‐0.00001 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1BALANCE 0.00001 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00001 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1CARRY OVER 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1BALANCE 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1CARRY OVER 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1BALANCE 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1CARRY OVER 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1BALANCE 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1CARRY OVER 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1BALANCE 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1 0.00000 * X1
‐1.37882 * X1 ‐1.72628 * X1 ‐1.20896 * X1 ‐1.25764 * X1 0.18067 * X1 1.07698 * X1 ‐1.57757 * X1 0.17956 * X1 0.22671 * X1 1.17129 * X1 ‐0.91791 * X1 0.30045 * X1 0.61746 * X1 0.57826 * X1 ‐0.57826 * X1 0.77131 * X1 ‐0.52963 * X1 ‐0.24167 * X1 0.27720 * X1 ‐0.27720 * X1
0.12118 * X1 0.14872 * X1 0.29104 * X1 0.24236 * X1 0.18067 * X1 ‐0.25636 * X1 0.29743 * X1 0.17956 * X1 0.22671 * X1 ‐0.16204 * X1 0.58209 * X1 0.30045 * X1 ‐0.04921 * X1 ‐0.75507 * X1 ‐0.57826 * X1 ‐0.56202 * X1 ‐0.52963 * X1 ‐0.24167 * X1 ‐0.38946 * X1 ‐0.27720 * X1‐0.12118 * X1 ‐0.14872 * X1 ‐0.29104 * X1 ‐0.06059 * X1 ‐0.08978 * X1 0.37754 * X1 ‐0.07436 * X1 ‐0.09033 * X1 ‐0.15023 * X1 0.28101 * X1 0.14552 * X1 ‐0.11336 * X1 0.19473 * X1 0.12818 * X1 0.26482 * X1 0.08102 * X1 0.28913 * X1 0.13860 * X1 0.02460 * X1 0.12084 * X10.00000 * X1 0.00000 * X1 0.00000 * X1 0.18177 * X1 0.09088 * X1 0.12118 * X1 0.22307 * X1 0.08923 * X1 0.07648 * X1 0.11897 * X1 0.72761 * X1 0.18710 * X1 0.14552 * X1 ‐0.62689 * X1 ‐0.31345 * X1 ‐0.48100 * X1 ‐0.24050 * X1 ‐0.10307 * X1 ‐0.36486 * X1 ‐0.15637 * X10.000 * X1/EI 0.000 * X1/EI 0.000 * X1/EI 0.061 * X1/EI 0.061 * X1/EI 0.061 * X1/EI 0.059 * X1/EI 0.059 * X1/EI 0.059 * X1/EI 0.059 * X1/EI 0.243 * X1/EI 0.146 * X1/EI 0.146 * X1/EI ‐0.313 * X1/EI ‐0.313 * X1/EI ‐0.241 * X1/EI ‐0.241 * X1/EI ‐0.241 * X1/EI ‐0.365 * X1/EI ‐0.365 * X1/EI
Ɵ = 0 Ɵ = 0 Ɵ = 0 Ɵ = samaƟ = sama Ɵ = sama Ɵ = sama Ɵ = sama
JUMLAHƟ = JUMLAH /3k
CHECK DEFORMASI Ɵ = sama
0.00000
ARAH MOMEN
PERUBAHAN (M‐Mo)i‐ CO = ‐(1/2)(M‐Mo)j
0.00000 0.00000 0.00000 0.00000
16
TOTAL MOMEN (M)CHECK STATIK 0.00000
12
13
14
15
8
9
10
11
4
5
6
7
K RELATIF (k = EI/L)
1
2
3
G H IELEMENJOINT D E F
DISTRIBUSI MOMEN AKIBAT PERGOYANGAN ARAH 2catatan : X1 = EIΔ2
A B CAD BE CF DA DE DG EB ED EF EH FC FE FI GD GH HE HG HI IF IH
1.0000 * EI 1.2500 * EI 1.0000 * EI 1.0000 * EI 0.5000 * EI 0.6667 * EI 1.2500 * EI 0.5000 * EI 0.4286 * EI 0.6667 * EI 1.0000 * EI 0.4286 * EI 0.3333 * EI 0.6667 * EI 0.3333 * EI 0.6667 * EI 0.3333 * EI 0.1429 * EI 0.3333 * EI 0.1429 * EISIKLUS DF 0.46154 0.23077 0.30769 0.43933 0.17573 0.15063 0.23431 0.56757 0.24324 0.18919 0.66667 0.33333 0.58333 0.29167 0.12500 0.70000 0.30000
Mo 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 ‐1.33333 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 ‐1.33333 * X2 0.00000 * X2 0.00000 * X2 ‐0.66667 * X2 ‐1.33333 * X2 0.00000 * X2 ‐1.33333 * X2 0.00000 * X2 0.00000 * X2 ‐0.66667 * X2 0.00000 * X2BALANCE 0.61538 * X2 0.30769 * X2 0.41026 * X2 0.58577 * X2 0.23431 * X2 0.20084 * X2 0.31241 * X2 0.37838 * X2 0.16216 * X2 0.12613 * X2 0.88889 * X2 0.44444 * X2 0.77778 * X2 0.38889 * X2 0.16667 * X2 0.46667 * X2 0.20000 * X2CARRY OVER 0.30769 * X2 0.29289 * X2 0.18919 * X2 0.11715 * X2 0.44444 * X2 0.15385 * X2 0.08108 * X2 0.38889 * X2 0.10042 * X2 0.23333 * X2 0.20513 * X2 0.19444 * X2 0.15621 * X2 0.22222 * X2 0.10000 * X2 0.06306 * X2 0.08333 * X2BALANCE ‐0.25920 * X2 ‐0.12960 * X2 ‐0.17280 * X2 ‐0.27406 * X2 ‐0.10962 * X2 ‐0.09396 * X2 ‐0.14617 * X2 ‐0.18943 * X2 ‐0.08118 * X2 ‐0.06314 * X2 ‐0.26638 * X2 ‐0.13319 * X2 ‐0.27908 * X2 ‐0.13954 * X2 ‐0.05980 * X2 ‐0.10248 * X2 ‐0.04392 * X2CARRY OVER ‐0.12960 * X2 ‐0.13703 * X2 ‐0.09471 * X2 ‐0.05481 * X2 ‐0.13319 * X2 ‐0.06480 * X2 ‐0.04059 * X2 ‐0.13954 * X2 ‐0.04698 * X2 ‐0.05124 * X2 ‐0.08640 * X2 ‐0.06977 * X2 ‐0.07308 * X2 ‐0.06660 * X2 ‐0.02196 * X2 ‐0.03157 * X2 ‐0.02990 * X2BALANCE 0.08677 * X2 0.04339 * X2 0.05785 * X2 0.10761 * X2 0.04304 * X2 0.03689 * X2 0.05739 * X2 0.05575 * X2 0.02389 * X2 0.01858 * X2 0.10411 * X2 0.05206 * X2 0.09429 * X2 0.04714 * X2 0.02020 * X2 0.04303 * X2 0.01844 * X2CARRY OVER 0.04339 * X2 0.05380 * X2 0.02787 * X2 0.02152 * X2 0.05206 * X2 0.02169 * X2 0.01195 * X2 0.04714 * X2 0.01845 * X2 0.02152 * X2 0.02892 * X2 0.02357 * X2 0.02870 * X2 0.02603 * X2 0.00922 * X2 0.00929 * X2 0.01010 * X2BALANCE ‐0.03396 * X2 ‐0.01698 * X2 ‐0.02264 * X2 ‐0.03549 * X2 ‐0.01420 * X2 ‐0.01217 * X2 ‐0.01893 * X2 ‐0.02268 * X2 ‐0.00972 * X2 ‐0.00756 * X2 ‐0.03500 * X2 ‐0.01750 * X2 ‐0.03730 * X2 ‐0.01865 * X2 ‐0.00799 * X2 ‐0.01358 * X2 ‐0.00582 * X2CARRY OVER ‐0.01698 * X2 ‐0.01775 * X2 ‐0.01134 * X2 ‐0.00710 * X2 ‐0.01750 * X2 ‐0.00849 * X2 ‐0.00486 * X2 ‐0.01865 * X2 ‐0.00608 * X2 ‐0.00679 * X2 ‐0.01132 * X2 ‐0.00933 * X2 ‐0.00946 * X2 ‐0.00875 * X2 ‐0.00291 * X2 ‐0.00378 * X2 ‐0.00400 * X2BALANCE 0.01135 * X2 0.00568 * X2 0.00757 * X2 0.01406 * X2 0.00562 * X2 0.00482 * X2 0.00750 * X2 0.00731 * X2 0.00313 * X2 0.00244 * X2 0.01376 * X2 0.00688 * X2 0.01232 * X2 0.00616 * X2 0.00264 * X2 0.00544 * X2 0.00233 * X2CARRY OVER 0.00568 * X2 0.00703 * X2 0.00365 * X2 0.00281 * X2 0.00688 * X2 0.00284 * X2 0.00157 * X2 0.00616 * X2 0.00241 * X2 0.00272 * X2 0.00378 * X2 0.00308 * X2 0.00375 * X2 0.00344 * X2 0.00117 * X2 0.00122 * X2 0.00132 * X2BALANCE ‐0.00447 * X2 ‐0.00224 * X2 ‐0.00298 * X2 ‐0.00464 * X2 ‐0.00186 * X2 ‐0.00159 * X2 ‐0.00248 * X2 ‐0.00291 * X2 ‐0.00125 * X2 ‐0.00097 * X2 ‐0.00458 * X2 ‐0.00229 * X2 ‐0.00487 * X2 ‐0.00244 * X2 ‐0.00104 * X2 ‐0.00178 * X2 ‐0.00076 * X2CARRY OVER ‐0.00224 * X2 ‐0.00232 * X2 ‐0.00146 * X2 ‐0.00093 * X2 ‐0.00229 * X2 ‐0.00112 * X2 ‐0.00062 * X2 ‐0.00244 * X2 ‐0.00080 * X2 ‐0.00089 * X2 ‐0.00149 * X2 ‐0.00122 * X2 ‐0.00124 * X2 ‐0.00114 * X2 ‐0.00038 * X2 ‐0.00049 * X2 ‐0.00052 * X2BALANCE 0.00148 * X2 0.00074 * X2 0.00099 * X2 0.00184 * X2 0.00073 * X2 0.00063 * X2 0.00098 * X2 0.00096 * X2 0.00041 * X2 0.00032 * X2 0.00181 * X2 0.00090 * X2 0.00161 * X2 0.00081 * X2 0.00035 * X2 0.00071 * X2 0.00030 * X2CARRY OVER 0.00074 * X2 0.00092 * X2 0.00048 * X2 0.00037 * X2 0.00090 * X2 0.00037 * X2 0.00020 * X2 0.00081 * X2 0.00031 * X2 0.00035 * X2 0.00049 * X2 0.00040 * X2 0.00049 * X2 0.00045 * X2 0.00015 * X2 0.00016 * X2 0.00017 * X2BALANCE ‐0.00059 * X2 ‐0.00029 * X2 ‐0.00039 * X2 ‐0.00061 * X2 ‐0.00024 * X2 ‐0.00021 * X2 ‐0.00032 * X2 ‐0.00038 * X2 ‐0.00016 * X2 ‐0.00013 * X2 ‐0.00060 * X2 ‐0.00030 * X2 ‐0.00064 * X2 ‐0.00032 * X2 ‐0.00014 * X2 ‐0.00023 * X2 ‐0.00010 * X2CARRY OVER ‐0.00029 * X2 ‐0.00030 * X2 ‐0.00019 * X2 ‐0.00012 * X2 ‐0.00030 * X2 ‐0.00015 * X2 ‐0.00008 * X2 ‐0.00032 * X2 ‐0.00010 * X2 ‐0.00012 * X2 ‐0.00020 * X2 ‐0.00016 * X2 ‐0.00016 * X2 ‐0.00015 * X2 ‐0.00005 * X2 ‐0.00006 * X2 ‐0.00007 * X2BALANCE 0.00019 * X2 0.00010 * X2 0.00013 * X2 0.00024 * X2 0.00010 * X2 0.00008 * X2 0.00013 * X2 0.00012 * X2 0.00005 * X2 0.00004 * X2 0.00024 * X2 0.00012 * X2 0.00021 * X2 0.00011 * X2 0.00005 * X2 0.00009 * X2 0.00004 * X2CARRY OVER 0.00010 * X2 0.00012 * X2 0.00006 * X2 0.00005 * X2 0.00012 * X2 0.00005 * X2 0.00003 * X2 0.00011 * X2 0.00004 * X2 0.00005 * X2 0.00006 * X2 0.00005 * X2 0.00006 * X2 0.00006 * X2 0.00002 * X2 0.00002 * X2 0.00002 * X2BALANCE ‐0.00008 * X2 ‐0.00004 * X2 ‐0.00005 * X2 ‐0.00008 * X2 ‐0.00003 * X2 ‐0.00003 * X2 ‐0.00004 * X2 ‐0.00005 * X2 ‐0.00002 * X2 ‐0.00002 * X2 ‐0.00008 * X2 ‐0.00004 * X2 ‐0.00008 * X2 ‐0.00004 * X2 ‐0.00002 * X2 ‐0.00003 * X2 ‐0.00001 * X2CARRY OVER ‐0.00004 * X2 ‐0.00004 * X2 ‐0.00002 * X2 ‐0.00002 * X2 ‐0.00004 * X2 ‐0.00002 * X2 ‐0.00001 * X2 ‐0.00004 * X2 ‐0.00001 * X2 ‐0.00002 * X2 ‐0.00003 * X2 ‐0.00002 * X2 ‐0.00002 * X2 ‐0.00002 * X2 ‐0.00001 * X2 ‐0.00001 * X2 ‐0.00001 * X2BALANCE 0.00003 * X2 0.00001 * X2 0.00002 * X2 0.00003 * X2 0.00001 * X2 0.00001 * X2 0.00002 * X2 0.00002 * X2 0.00001 * X2 0.00001 * X2 0.00003 * X2 0.00002 * X2 0.00003 * X2 0.00001 * X2 0.00001 * X2 0.00001 * X2 0.00001 * X2CARRY OVER 0.00001 * X2 0.00002 * X2 0.00001 * X2 0.00001 * X2 0.00002 * X2 0.00001 * X2 0.00000 * X2 0.00001 * X2 0.00001 * X2 0.00001 * X2 0.00001 * X2 0.00001 * X2 0.00001 * X2 0.00001 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2BALANCE ‐0.00001 * X2 ‐0.00001 * X2 ‐0.00001 * X2 ‐0.00001 * X2 0.00000 * X2 0.00000 * X2 ‐0.00001 * X2 ‐0.00001 * X2 0.00000 * X2 0.00000 * X2 ‐0.00001 * X2 ‐0.00001 * X2 ‐0.00001 * X2 ‐0.00001 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2CARRY OVER ‐0.00001 * X2 ‐0.00001 * X2 0.00000 * X2 0.00000 * X2 ‐0.00001 * X2 0.00000 * X2 0.00000 * X2 ‐0.00001 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2BALANCE 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2CARRY OVER 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2BALANCE 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2CARRY OVER 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2BALANCE 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2CARRY OVER 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2BALANCE 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2 0.00000 * X2
0.20845 * X2 0.19733 * X2 0.11354 * X2 0.41691 * X2 0.28739 * X2 ‐0.70429 * X2 0.39466 * X2 0.26209 * X2 0.18397 * X2 ‐0.84072 * X2 0.22707 * X2 0.16497 * X2 ‐0.39205 * X2 ‐0.49216 * X2 0.49216 * X2 ‐0.66384 * X2 0.45768 * X2 0.20617 * X2 ‐0.23097 * X2 0.23097 * X2
0.20845 * X2 0.19733 * X2 0.11354 * X2 0.41691 * X2 0.28739 * X2 0.62904 * X2 0.39466 * X2 0.26209 * X2 0.18397 * X2 0.49261 * X2 0.22707 * X2 0.16497 * X2 0.27462 * X2 0.84117 * X2 0.49216 * X2 0.66949 * X2 0.45768 * X2 0.20617 * X2 0.43570 * X2 0.23097 * X2‐0.20845 * X2 ‐0.19733 * X2 ‐0.11354 * X2 ‐0.10423 * X2 ‐0.13105 * X2 ‐0.42059 * X2 ‐0.09867 * X2 ‐0.14369 * X2 ‐0.08249 * X2 ‐0.33475 * X2 0.05677 * X2 ‐0.09199 * X2 ‐0.21785 * X2 ‐0.31452 * X2 ‐0.22884 * X2 ‐0.24631 * X2 ‐0.24608 * X2 ‐0.11548 * X2 ‐0.13731 * X2 ‐0.10308 * X20.00000 * X2 0.00000 * X2 0.00000 * X2 0.31268 * X2 0.15634 * X2 0.20845 * X2 0.29600 * X2 0.11840 * X2 0.10148 * X2 0.15786 * X2 0.28384 * X2 0.07299 * X2 0.05677 * X2 0.52665 * X2 0.26333 * X2 0.42319 * X2 0.21159 * X2 0.09068 * X2 0.29839 * X2 0.12788 * X20.000 * X2/EI 0.000 * X2/EI 0.000 * X2/EI 0.104 * X2/EI 0.104 * X2/EI 0.104 * X2/EI 0.079 * X2/EI 0.079 * X2/EI 0.079 * X2/EI 0.079 * X2/EI 0.095 * X2/EI 0.057 * X2/EI 0.057 * X2/EI 0.263 * X2/EI 0.263 * X2/EI 0.212 * X2/EI 0.212 * X2/EI 0.212 * X2/EI 0.298 * X2/EI 0.298 * X2/EI
Ɵ = 0 Ɵ = 0 Ɵ = 0 Ɵ = samaƟ = sama Ɵ = sama Ɵ = sama Ɵ = sama
JUMLAHƟ = JUMLAH /3k
CHECK DEFORMASI Ɵ = sama
0.00000
ARAH MOMEN
PERUBAHAN (M‐Mo)i‐ CO = ‐(1/2)(M‐Mo)j
0.00000 0.00000 0.00000 0.00000
16
TOTAL MOMEN (M)CHECK STATIK 0.00000
12
13
14
15
8
9
10
11
4
5
6
7
K RELATIF (k = EI/L)
1
2
3
G H IELEMENJOINT D E F
G. Freebody Untuk Perhitungan Δ1 dan Δ2
Pergoyangan terjadi pada arah DEF (arah 1) dan arah GHI (arah 2), sehingga gaya‐gaya yang sepadan dengan arah pergoyangan tersebut diperhitungkan untuk nilai Δ1 dan Δ2. Gaya‐gaya horizontal sebagai reaksi yang terjadi akibat momen digambarkan sebagai berikut.
Total gaya‐gaya horizontal ARAH 1 adalah :
= − − − + + +
⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞+ ++ + + += − − − − + + +⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠+ ++ + ⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞= − − − − +⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜
⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝
1
6
64 4 4 3
beban DA EB FC DG EH FI
CF FC DG GDAD DA BE EB EH HE FI IF
AD BE CF DG EH FI
CF FC DG GDAD DA BE EB
H Rx H H H H H H
M M M MM M M M M M M ML L L L L L
M M M MM M M M + +⎛ ⎞ ⎛ ⎞+ +⎜ ⎟ ⎜ ⎟⎟⎝ ⎠ ⎝ ⎠⎠
+ + + + + + + + + +⎛ ⎞ ⎛ ⎞= − − + − − −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
3 3
6 (1)4 3
EH HE FI IF
AD DA BE EB CF FC DG GD EH HE FI IF
M M M M
M M M M M M M M M M M MPERS
Berdasarkan hasil yang diperoleh dari tabel distribusi momen maka : Momen Beban luar Pergoyangan 1 Pergoyangan 2
=ADM 0.47148 ‐1.37882 * X1 0.20845 * X2
=DAM 0.94296 ‐1.25764 * X1 0.41691 * X2
=BEM 4.80935 ‐1.72628 * X1 0.19733 * X2
=EBM 9.61870 ‐1.57757 * X1 0.39466 * X2
=CFM ‐6.42154 ‐1.20896 * X1 0.11354 * X2
=FCM ‐12.84307 ‐0.91791 * X1 0.22707 * X2JUMLAH ‐3.42212 ‐8.06718 * X1 1.55796 * X2Maka : ( ) ( )+ + + + + = − −3.42212 8.06718 X1 + 1.55796 X2AD DA BE EB CF FCM M M M M M
Momen Beban luar Pergoyangan 1 Pergoyangan 2 =DGM 1.99515 1.07698 * X1 ‐0.70429 * X2
=GDM 3.04733 0.57826 * X1 ‐0.49216 * X2
=EHM 3.50232 1.17129 * X1 ‐0.84072 * X2
=HEM ‐0.69033 0.77131 * X1 ‐0.66384 * X2
=FIM ‐3.71834 0.61746 * X1 ‐0.39205 * X2
=IFM ‐1.01515 0.27720 * X1 ‐0.23097 * X2 JUMLAH 3.12098 4.49250 * X1 ‐3.32403 * X2 Maka : ( ) ( )+ + + + + = −3.12098 + 4.49250 X1 3.32403 X2DG GD EH HE FI IFM M M M M M
Dengan demikian maka pers(1) menjadi
( ) ( ) ( ) ( )
( ) ( )( ) ( ) ( )( )( ) ( )
⎛ ⎞ ⎛ ⎞− − −= − − +⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠= − − − − + −
= − + − − − − −
3.42212 8.06718 X1 + 1.55796 X2 3.12098 + 4.49250 X1 3.32403 X21 6
4 3
6 0.85553 2.016795 X1 + 0.38949 X2 1.04033 + 1.49750 X1 1.10801 X2
4.10414 3.51430 X1 1.49750 X2 (1 )
H
pers a
Total gaya‐gaya horizontal ARAH 2 adalah :
( )
= − − −
⎛ ⎞ ⎛ ⎞ ⎛ ⎞+ + += − − − −⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠+ + +⎛ ⎞ ⎛ ⎞ ⎛ ⎞= − − − −⎜ ⎟ ⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠+ + + + +⎛ ⎞= − − − − −⎜ ⎟
⎝ ⎠−
= − −
2
4
43 3 3
4 (2)3
3.12098 + 4.49250 X1 3.32403 X4
beban GD HE IF
DG GD EH HE FI IF
DG EH FI
DG GD EH HE FI IF
DG GD EH HE FI IF
H Rx H H H
M M M M M ML L L
M M M M M M
M M M M M MPERS
( )
( ) ( )( )( ) ( )
⎛ ⎞⎜ ⎟⎝ ⎠
= − − −
= − − + −− −
2
3
4 1.04033 + 1.49750 X1 1.10801 X2
5.04033 1.49750 X1 1.10801 X2 (2 )pers a
Secara statika, jumlah gaya‐gaya pada arah pergoyangan harus sama dengan nol ( )= 0R sehingga :
= =1 0 2 0H dan H Dengan demikian persamaan (1a) dan persamaan (2a) dapat diselesaikan sebagai berikut :
( ) ( )( ) ( )
( ) ( )( ) ( )
( )( )
− + − =
− − + =
+ − =
− + =+
+ =
=
= Δ ⇒Δ =
4.10414 3.51430 X1 1.49750 X2 0
5.04033 1.49750 X1 1.10801 X2 0
3.51430 X1 1.49750 X2 4.10414 1.10801
1.49750 X1 1.10801 X2 5.04033 1.49750
1.65137 X1 12.09532
X1 7.32442
1 1 1 7.32442 /
x
x
karena X EI EI
Substitusi nilai X1 ke persamaan (1a) diperoleh :
( ) ( )( )
( )
− + − =
− =
=
= Δ ⇒Δ =
4.10414 3.51430 7.32442 1.49750 X2 0
21.63607 1.49750 X2 0
X2 14.44813
2 2 1 14.44813 /karena X EI EI
PERHITUNGAN X1 DAN X2
BEBAN PERGYG 1 PERGYG 2ARAH 1 (DEF) ‐4.104151 + 3.5142976 X1 + ‐1.497502 X2 = 0ARAH 2 (GHI) ‐5.040323 + ‐1.4975019 X1 + 1.108011 X2 = 0
PENYELESAIAN PERSAMAAN SIMULTAN DI ATAS MENGHASILKAN
3.5142976 ‐1.497502 X1 4.1041509‐1.497502 1.108011 X2 5.0403233
X1 3.5142976 ‐1.497502 4.1041509X2 ‐1.497502 1.108011 5.0403233
X1 = EI Δ1 = 7.32443X2 = EI Δ2 = 14.44812
DISTRIBUSI MOMEN AKHIR
A B CAD BE CF DA DE DG EB ED EF EH FC FE FI GD GH HE HG HI IF IH
1.0000 * EI 1.2500 * EI 1.0000 * EI 1.0000 * EI 0.5000 * EI 0.6667 * EI 1.2500 * EI 0.5000 * EI 0.4286 * EI 0.6667 * EI 1.0000 * EI 0.4286 * EI 0.3333 * EI 0.6667 * EI 0.3333 * EI 0.6667 * EI 0.3333 * EI 0.1429 * EI 0.3333 * EI 0.1429 * EI0.46154 0.23077 0.30769 0.43933 0.17573 0.15063 0.23431 0.56757 0.24324 0.18919 0.66667 0.33333 0.58333 0.29167 0.12500 0.70000 0.30000
Mo Beban Luar 0.00000 0.00000 0.00000 0.00000 ‐5.33333 0.00000 0.00000 2.66667 ‐20.41667 0.00000 0.00000 20.41667 0.00000 0.00000 ‐3.60000 0.00000 5.40000 ‐3.30884 0.00000 0.88163EI Δ1*Mo Pergyg arah 1 ‐10.98665 ‐13.73331 ‐10.98665 ‐10.98665 0.00000 9.76591 ‐13.73331 0.00000 0.00000 9.76591 ‐10.98665 0.00000 4.88296 9.76591 0.00000 9.76591 0.00000 0.00000 4.88296 0.00000EI Δ2*Mo Pergyg arah 2 0.00000 0.00000 0.00000 0.00000 0.00000 ‐19.26416 0.00000 0.00000 0.00000 ‐19.26416 0.00000 0.00000 ‐9.63208 ‐19.26416 0.00000 ‐19.26416 0.00000 0.00000 ‐9.63208 0.00000Jumlah Mo ‐10.98665 ‐13.73331 ‐10.98665 ‐10.98665 ‐5.33333 ‐9.49825 ‐13.73331 2.66667 ‐20.41667 ‐9.49825 ‐10.98665 20.41667 ‐4.74913 ‐9.49825 ‐3.60000 ‐9.49825 5.40000 ‐3.30884 ‐4.74913 0.88163
M Beban Luar 0.47148 4.80935 ‐6.42154 0.94296 ‐2.93811 1.99515 9.61870 6.74989 ‐19.87091 3.50232 ‐12.84307 16.56141 ‐3.71834 3.04733 ‐3.04733 ‐0.69033 4.45559 ‐3.76526 ‐1.01515 1.01515EI Δ1*M Pergyg arah 1 ‐10.09909 ‐12.64405 ‐8.85492 ‐9.21152 1.32327 7.88825 ‐11.55479 1.31519 1.66052 8.57907 ‐6.72319 2.20066 4.52253 4.23545 ‐4.23545 5.64940 ‐3.87927 ‐1.77013 2.03037 ‐2.03037EI Δ2*M Pergyg arah 2 3.01177 2.85105 1.64040 6.02354 4.15219 ‐10.17573 5.70210 3.78673 2.65803 ‐12.14686 3.28079 2.38356 ‐5.66435 ‐7.11083 7.11083 ‐9.59125 6.61255 2.97870 ‐3.33701 3.33701
Jumlah M ‐6.61583 ‐4.98364 ‐13.63606 ‐2.24502 2.53735 ‐0.29233 3.76602 11.85181 ‐15.55235 ‐0.06548 ‐16.28547 21.14563 ‐4.86016 0.17195 ‐0.17195 ‐4.63218 7.18887 ‐2.55669 ‐2.32179 2.32179
4.37082 8.74967 ‐2.64941 8.74163 7.87068 9.20592 17.49934 9.18514 4.86431 9.43277 ‐5.29882 0.72896 ‐0.11104 9.67020 3.42805 4.86607 1.78887 0.75215 2.42734 1.44016‐4.37082 ‐8.74967 2.64941 ‐2.18541 ‐4.59257 ‐4.83510 ‐4.37483 ‐3.93534 ‐0.36448 ‐2.43304 ‐1.32470 ‐2.43216 ‐1.21367 ‐4.60296 ‐0.89443 ‐4.71639 ‐1.71403 ‐0.72008 0.05552 ‐0.376080.00000 0.00000 0.00000 6.55623 3.27811 4.37082 13.12450 5.24980 4.49983 6.99974 ‐6.62352 ‐1.70319 ‐1.32470 5.06724 2.53362 0.14968 0.07484 0.03208 2.48285 1.064080.000 /EI 0.000 /EI 0.000 /EI 2.185 /EI 2.185 /EI 2.185 /EI 3.500 /EI 3.500 /EI 3.500 /EI 3.500 /EI ‐2.208 /EI ‐1.325 /EI ‐1.325 /EI 2.534 /EI 2.534 /EI 0.075 /EI 0.075 /EI 0.075 /EI 2.483 /EI 2.483 /EIƟ = 0 Ɵ = 0 Ɵ = 0 Ɵ = sama Ɵ = sama
DIST FACTOR
Ɵ = sama Ɵ = sama Ɵ = sama Ɵ = sama
‐ CO = ‐(1/2)(M‐Mo)jJUMLAH
Ɵ = JUMLAH /3kCHECK DEFORMASI
0.00000 0.00000
ARAH MOMEN
PERUBAHAN (M‐Mo)i
0.00000 0.00000 0.00000 0.00000CHECK STATIK
ELEMENK RELATIF (k = EI/L)
F G H I
=
JOINT D E
=‐1
I. Freebody Akhir
Batang AD
A
D
L = 4m
MDA
MAD
HDA
HAD
( )( )
( )( )
( )
( )
6.61583
2.24502
0
0
4 6.61583 2.24502 0
2.21521
0 2.21521
AD
DA
D
AD AD DA
AD
AD
DA
M tm
M tm
M
H L M M
H
H ton
H H ton
= −
= −
Σ =
⇒ − − =
⇒ − − =
⇒ = ←
Σ = ⇒ = →
Batang BE
B
E
L = 4m
MEB
MBE
HEB
HBE
( )( )
( )( )
( )
( )
4.98364
3.76602
0
0
4 4.98364 3.76602 0
0.30441
0 0.30441
BE
EB
E
BE BE EB
BE
BE
EB
M tm
M tm
M
H L M M
H
H ton
H H ton
= −
= +
Σ =
⇒ − + =
⇒ − + =
⇒ = ←
Σ = ⇒ = →
Batang CF
C
F
L = 4m
MFC
MCF
HFC
HCF
( )( )
( )( )
( )
( )
13.63606
16.28547
0
0
4 13.63606 16.28547 0
7.48038
0 7.48038
CF
FC
F
CF CF FC
CF
CF
FC
M tm
M tm
M
H L M M
H
H ton
H H ton
= −
= −
Σ =
⇒ − + =
⇒ − − =
⇒ = ←
Σ = ⇒ = →
Batang DG
L = 3m
D
G
MGD
MDG
HGD
HDG
( )( )
( )( )
( )
( )
0.29233
0.17195
0
0
3 0.29233 0.17195 0
0.04013
0 0.04013
DG
GD
G
DG DG GD
DG
DG
GD
M tm
M tm
M
H L M M
H
H ton
H H ton
= −
= +
Σ =
⇒ − + =
⇒ − + =
⇒ = ←
Σ = ⇒ = →
Batang EH
E
H
MHE
MEH
HHE
HEH
L = 3m
( )( )
( )( )
( )
( )
0.06548
4.63218
0
0
3 0.06548 4.63218 0
1.56589
0 1.56589
EH
HE
H
EH EH HE
EH
EH
HE
M tm
M tm
M
H L M M
H
H ton
H H ton
= −
= −
Σ =
⇒ − − =
⇒ − − =
⇒ = ←
Σ = ⇒ = →
Batang FI
F
I
MIF
MFI
HIF
HFI
L = 3m
( )( )
( )( )
( )
( )
4.86016
2.32179
0
0
3 4.86016 2.32179 0
2.39398
0 2.39398
FI
IF
I
FI FI IF
FI
FI
IF
M tm
M tm
M
H L M M
H
H ton
H H ton
= −
= −
Σ =
⇒ − − =
⇒ − − =
⇒ = ←
Σ = ⇒ = →
Batang DE
( )( )
( )( )
( )
( )
2.53735
11.85181
0
0
6 6(4) 2.53735 11.85181 0
1.60181
0
6 1.60181
4.39819
DE
ED
E
DE DE ED
DE
DE
ED DE
ED
ED
M tm
M tm
M
V L Pb M M
V
V ton
VV P VV
V ton
= +
= +
Σ =
⇒ − + + =
⇒ − + + =
⇒ = ↑
Σ =⇒ = −⇒ = −
⇒ = ↑
Batang EF
( )( )
( )( )
( )
( )
212
212
15.55235
21.14563
0
0
7 (5)(7) 15.55235 21.14563 0
16.70096
0
(5)(7) 16.70096
18.29904
EF
FE
F
EF EF FE
EF
EF
FE EF
FE
FE
M tm
M tm
M
V L qL M M
V
V ton
VV qL VV
V ton
= −
= +
Σ =
⇒ − − + =
⇒ − − + =
⇒ = ↑
Σ =⇒ = −⇒ = −
⇒ = ↑
Batang GH
q = 3 t/m
G H
MGH MHG
L = 6mVGH VHG
Q = (½)qL
( )( )
( )
( )
( )
( )
12
12
12
12
0.17195
7.18887
0
03
66 (3)(6) 0.17195 7.18887 0
3
1.83051
0
(3)(6) 1.83051
7.16949
GH
HG
H
GH GH HG
GH
GH
HG GH
HG
HG
M tm
M tm
M
LV L qL M M
V
V ton
V
V qL V
V
V ton
= −
= +
Σ =
⎛ ⎞⇒ − − + =⎜ ⎟⎝ ⎠
⎛ ⎞⇒ − − + =⎜ ⎟⎝ ⎠
⇒ = ↑
Σ =⇒ = −
⇒ = −
⇒ = ↑
Batang HI
q = 4 t/m
H I
MHI MIH
a = 2m b = 5m
L = 7mVHI VIH
Q = (½)qa
( )( )
( )
( )
( )
( )
12
12
12
12
2.55669
2.32179
0
03
27 (4)(2) 5 2.55669 2.32179 0
3
3.27165
0
(4)(2) 3.27165
0.72835
HI
IH
I
HI HI IH
HI
HI
IH HI
IH
IH
M tm
M tm
M
aV L qa b M M
V
V ton
V
V qa V
V
V ton
= −
= +
Σ =
⎛ ⎞⇒ − + − + =⎜ ⎟⎝ ⎠⎛ ⎞⇒ − + − + =⎜ ⎟⎝ ⎠
⇒ = ↑
Σ =⇒ = −
⇒ = −
⇒ = ↑
J. Pengecekan Statik
Dari hasil perhitungan gaya‐gaya pada ujung setiap elemen maka diperoleh Reaksi Perletakan sebagai berikut : Reaksi Vertikal :
( )( )
( )
1.60181 1.83051 3.43232
4.39819 16.70096 7.16949 3.27165 31.54029
18.29904 0.72835 19.02739
AV DE GH
BV ED EF HG HI
CV FE IH
R V V ton
R V V V V ton
R V V ton
= + = + = ↑
= + + + = + + + = ↑
= + = + = ↑
Reaksi Horizontal : ( )( )( )
2.21521
0.30441
7.48038
AH AD
BH BE
CH CF
R H ton
R H ton
R H ton
= = ←
= = ←
= = ←
Momen Tumpuan : ( )( )( )
6.61583
4.98364
13.63606
A AD
B BE
C CF
M M tm
M M tm
M M tm
= = −
= = −
= = −
Hasil perhitungan Reaksi Perletakan
3.43232AVR ton= 31.54029BVR ton= 19.02739CVR ton=
2.21521AHR ton= 0.30441BHR ton= 7.48038CHR ton=
6.61583AM tm=4.98364BM tm=
13.63606CM tm=
1
2
3
(5)(7) 35
1(3)(6) 9
21(4)(2) 4
2
Q ton
Q ton
Q ton
= =
= =
= =
KONTROL
1 2
0
0
6 4 2.21521 0.30441 7.48038 0
0.00000 0 .!
AH BH CH
HP P R R R
OK
Σ =+ − − − =+ − − − =
= − − − − − − − − − − − − − − − −
3 1 2 3
0
0
3.43232 31.54029 19.02739 6 35 9 4 0
0.00000 0 .!
AV BV CV
VR R R P Q Q Q
OK
Σ =+ + − − − − =
+ + − − − − == − − − − − − − − − − − − − − − −
( ) ( )
( ) ( ) ( ) ( )
1 2 3 1 2 3
0
7 6 213 7 (4) (7) (4 7) 7 5 0
2 3 3
23.43232 13 31.54029 7 6.61583 4.98364 13.63606 6(4) 4(7) 6(11) 35 3.5 9 9 4 5 0
3
44.62016 220.78203 6.61583 4.98364
C
AV BV A B C
M
R R M M M P P P Q Q Q
Σ =
⎛ ⎞ ⎛ ⎞ ⎛ ⎞+ − − − + + − + − − + − + =⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠
⎛ ⎞+ − − − + + − − − − + =⎜ ⎟⎝ ⎠
+ − − 13.63606 24 28 66 122.5 81 22.66667 0
0.00001 0 .!OK− + + − − − − =
− = − − − − − − − − − − − − − − − −
K. Perhitungan Bidang Momen, Gaya Geser dan Gaya Normal
1. Batang AD
( ) ( )( ) ( )
( )( )
6.61583 2.21521
2.24502 2.21521
2.21521 6.61583
2.21521
AD AD
DA DA
x AD AD
xx
M tm H ton
M tm H ton
M H x M
x
MD
x
= − = ←
= − = →
= −
= −
∂= =
∂
Tabel Hasil Perhitungan x (m) Mx (ton.m) Dx(ton) 0.000 ‐6.616 2.215 1.000 ‐4.401 2.215 2.000 ‐2.185 2.215 3.000 0.030 2.215 4.000 2.245 2.215
A
D
L = 4m
MDA
MAD
HDA
HAD
x
2. Batang BE ( ) ( )( ) ( )
( )( )
4.98364 0.30441
3.76602 0.30441
0.30441 4.98364
0.30441
BE BE
EB EB
x BE BE
xx
M tm H ton
M tm H ton
M H x M
x
MD
x
= − = ←
= + = →
= −
= −
∂= =
∂
Tabel Hasil Perhitungan x (m) Mx (ton.m) Dx(ton) 0.000 ‐4.984 0.304 1.000 ‐4.679 0.304 2.000 ‐4.375 0.304 3.000 ‐4.070 0.304 4.000 ‐3.766 0.304
3. Batang CF
( ) ( )( ) ( )
( )( )
13.63606 7.48038
16.28547 7.48038
7.48038 13.63606
7.48038
CF CF
FC FC
x CF CF
xx
M tm H ton
M tm H ton
M H x M
x
MD
x
= − = ←
= − = →
⎡ ⎤= − −⎣ ⎦⎡ ⎤= − −⎣ ⎦∂
= − =∂
Tabel Hasil Perhitungan x (m) Mx (ton.m) Dx(ton) 0.000 13.636 7.480 1.000 6.156 7.480 2.000 ‐1.325 7.480 3.000 ‐8.805 7.480 4.000 ‐16.285 7.480
4. Batang DG
( ) ( )( ) ( )
( )( )
0.29233 0.04013
0.17195 0.04013
0.04013 0.29233
0.04013
DG DG
GD GD
x DG DG
xx
M tm H ton
M tm H ton
M H x M
x
MD
x
= − = ←
= + = →
= −
= −
∂= =
∂
B
E
L = 4m
MEB
MBE
HEB
HBE
x
C
F
L = 4m
MFC
MCF
HFC
HCF
x
L = 3m
D
G
MGD
MDG
HGD
HDG
x
Tabel Hasil Perhitungan x (m) Mx (ton.m) Dx(ton) 0.000 ‐0.292 0.040 1.000 ‐0.252 0.040 2.000 ‐0.212 0.040 3.000 ‐0.172 0.040
5. Batang EH
( ) ( )( ) ( )
( )( )
0.06548 1.56589
4.63218 1.56589
1.56589 0.06548
1.56589
EH EH
HE HE
x EH EH
xx
M tm H ton
M tm H ton
M H x M
x
MD
x
= − = ←
= − = →
= −
= −
∂= =
∂
Tabel Hasil Perhitungan x (m) Mx (ton.m) Dx(ton) 0.000 ‐0.065 1.566 1.000 1.500 1.566 2.000 3.066 1.566 3.000 4.632 1.566
6. Batang FI
( ) ( )( ) ( )
( )( )
4.86016 2.39398
2.32179 2.39398
2.39398 4.86016
2.39398
FI FI
IF IF
x FI FI
xx
M tm H ton
M tm H ton
M H x M
x
MD
x
= − = ←
= − = →
⎡ ⎤= − −⎣ ⎦⎡ ⎤= − −⎣ ⎦∂
= − =∂
Tabel Hasil Perhitungan x (m) Mx (ton.m) Dx(ton) 0.000 4.860 2.394 1.000 2.466 2.394 2.000 0.072 2.394 3.000 ‐2.322 2.394
E
H
MHE
MEH
HHE
HEH
L = 3m
x
F
I
MIF
MFI
HIF
HFI
L = 3m
x
7. Batang DE
Tabel Hasil Perhitungan Interval 0 ≤x1≤2
x (m) Mx (ton.m) Dx(ton) 0.000 2.537 1.602 1.000 4.139 1.602 2.000 5.741 1.602
Interval 2 ≤x2≤6
x (m) Mx (ton.m) Dx(ton) 2.000 5.741 ‐4.398 3.000 1.343 ‐4.398 4.000 ‐3.055 ‐4.398 5.000 ‐7.454 ‐4.398 6.000 ‐11.852 ‐4.398
8. Batang EF
( ) ( )
( ) ( )
( ) ( )
( )
2
2
2
115.55235
21
21.14563 16.70096 (5) 15.552352
16.70096 15.55235 16.70096 2.5
18.29904 16.70096 5
EF x EF EF
FE
EF
xFE x
M tm M V x qx M
M tm x x
V ton x x
MV ton D x
x
= − = − −
= + = − −
= ↑ = − + −
∂= ↑ = = −
∂
( ) ( )( ) ( )
( )( )
( ) ( )( ) ( )( )
1
11
2
22
2.53735 1.60181
11.85181 4.39819
0 1 2
1.60181 2.53735
1.60181
2 2 6
2
1.60181 6 2 2.53735
4.39819 14.53735
DE DE
ED ED
x DE DE
xx
x DE DE
xx
M tm V ton
M tm V ton
INTERVAL x
M V x M
x
MD
x
INTERVAL x
M V x P x M
x x
x
MD
= + = ↑
= + = ↑
≤ ≤
= +
= +
∂= =
∂
≤ ≤
= − − +
= − − +
= − +
∂= 4.39819
x= −
∂
Tabel Hasil Perhitungan x (m) Mx (ton.m) Dx(ton) 0.000 ‐15.552 16.701 1.000 ‐1.351 11.701 2.000 7.850 6.701 3.000 12.051 1.701 3.34019 12.340 0.000 4.000 11.251 ‐3.299 5.000 5.452 ‐8.299 6.000 ‐5.347 ‐13.299 7.000 ‐21.146 ‐18.299
9. Batang GH
Tabel Hasil Perhitungan
x (m) Mx (ton.m) Dx(ton) 0.000 ‐0.172 1.831 1.000 1.575 1.581 2.000 2.822 0.831 2.70593 3.130 0.000 3.000 3.070 ‐0.419 4.000 1.817 ‐2.169 5.000 ‐1.436 ‐4.419 6.000 ‐7.189 ‐7.169
0
16.70096 5 0
3.34019 ( )
x
CHECK JARAKMOMENMAXSyaratD
xx m memenuhi
=− =
=
( ) ( )( ) ( )
( )
( )
( )
3
3
3
2
0.17195 1.83051
7.18887 7.16949
63
1.83051 0.171956(6)
0.17195 1.83051 0.08333
1.83051 0.25
GH GH
HG HG
x GH GH
xx
M tm V ton
M tm V ton
qxM V x M
Lx
x
x x
MD x
x
= − = ↑
= + = ↑
= − −
= − −
= − + −
∂= = −
∂
2
0
1.83051 0.25 0
1.830510.25
2.70593 ( )
x
CHECK JARAKMOMENMAXSyaratD
x
x
x m memenuhi
=
− =
=
=
10. Batang HI
Tabel Hasil Perhitungan Interval 0 ≤x1≤2
x (m) Mx (ton.m) Dx(ton) 0.000 ‐2.557 3.272 1.000 0.382 2.272 1.80877 1.388 0.000 2.000 1.320 ‐0.728
Interval 2 ≤x2≤6
x (m) Mx (ton.m) Dx(ton) 2.000 1.320 ‐0.728 3.000 0.592 ‐0.728 4.000 ‐0.137 ‐0.728 5.000 ‐0.865 ‐0.728 6.000 ‐1.593 ‐0.728 7.000 ‐2.322 ‐0.728
( ) ( )( ) ( )
( )
( )
( )
( )
3
1
3
3
211
2
2.55669 3.27165
2.32179 0.72835
0 1 2
64
3.27165 2.556696(2)
2.55669 3.27165 0.33333
3.27165
2 2 7
23
HI HI
IH IH
x HI HI
xx
x HI
M tm V ton
M tm V ton
INTERVAL x
qxM V x M
ax
x
x x
MD x
x
INTERVAL x
M V x Q x a
= − = ↑
= + = ↑
≤ ≤
= − −
= − −
= − + −
∂= = −
∂
≤ ≤
⎛ ⎞= − − −⎜ ⎟⎝ ⎠
( )
( ) ( )( )
22
23.27165 4 (2) 2.55669
3
3.27165 4 5.33333 2.55669
0.72835 2.77664
0.72835
HI
xx
M
x x
x x
x
MD
x
⎛ ⎞= − − −⎜ ⎟⎝ ⎠
= − + −
= − +
∂= = −
∂
1
2
0 1 2
0
3.27165 0
3.27165 1.80877 ( )
x
CHECK JARAKMOMENMAXPADA INTERVAL xSyaratD
x
x m memenuhi
≤ ≤=
− =
= =
Perhitungan Gaya Normal Dalam perhitungan gaya normal, harus memperhatikan keseimbangan statik pada setiap titik kumpul.
P = 6 ton
P2 = 4 ton
D
DAH
Q1
Q3Q2
P1 = 6 ton
A B C
F
I
E
HG
DEV
DEN
DGHGDH
DGN
DANEDV
GHVGDN
GHN
ADN
EDN
EBN
BEN
EFN
EHN
EFVEBH
HGN HIN
HENHGV HIV
EHHHEH
IHN
IFN
FIN
FCN
FEN
IHV
FEV
IFH
FIH
FCH
CFN
Arah D‐E‐F ( ) ( ) ( )1 6 2.21521 0.04013 3.82492DE DA DGN P H H ton= − − = − − = →
( )3.82492ED DEN N ton= − = ←
( ) ( ) ( )3.82492 0.30441 1.56589 5.08640EF ED EB EHN N H H ton= − − + − = − − + − = →
( )5.08640FE EFN N ton= − = ←
KONTROL :
0
5.08640 7.48038 2.39398 0
0.00000 0 .!
FE FC FIN H H
OK
− + − =− + − =
= − − − − − − − − − − − − −
Arah G‐H‐I
( )2 4 0.04013 3.95987GH GDN P H ton= − = − = →
( )3.95987HG GHN N ton= − = ←
( ) ( ) ( )3.95987 1.56589 2.39398HI HG HEN N H ton= − − + = − − + = →
( )2.39398IH HIN N ton= − = ←
KONTROL :
0
2.39398 2.39398 0
0.00000 0 .!
HI IFN H
OK
− + =− + =
= − − − − − − − − − − − − −
Arah G‐D‐A
( )1.83051GD GHN V ton= − = ↓
( )1.83051DG GDN N ton= − = ↑
( ) ( ) ( )1.83051 1.60181 3.43232DA DG DEN N V ton= − + = − + = ↓
( ) ( )3.43232AD DAN N ton= − − = ↑
Arah H‐E‐B
( ) ( ) ( )7.16949 3.27165 10.44144HE HG HIN V V ton= − + = − + = ↓
( ) ( )10.44144HE HEN N ton= − − = ↑
( ) ( ) ( )10.44144 4.39819 16.70096 31.54029EB EH ED EFN N V V ton= − + + = − + + = ↓
( ) ( )31.54029BE EBN N ton= − − = ↑
Arah I‐F‐C
( )0.72835IF IHN V ton= − = ↓
( ) ( )0.72835FI FIN N ton= − − = ↑
( ) ( ) ( )0.72835 18.29904 19.48038FC FI FEN N V ton= − + = − + = ↓
( ) ( )19.48038CF FCN N ton= − − = ↑
Tugas Mekanika Teknik
14
VERIFIKASI HASIL PERHITUNGAN MENGGUNAKAN PROGRAM SAP 2000
SAP2000
SAP2000 v7.40 - File:Lustriana - Frame Span Loads (LOAD1) - Ton-m Units
10/25/10 16:52:29
SAP2000 v7.40 File: LUSTRIANA Ton-m Units PAGE 1 10/25/10 16:43:23 [email protected] J O I N T D I S P L A C E M E N T S JOINT LOAD U1 U2 U3 R1 R2 R3 1 LOAD1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 LOAD1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3 LOAD1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 4 LOAD1 7.3244 0.0000 0.0000 0.0000 2.1854 0.0000 5 LOAD1 7.3244 0.0000 0.0000 0.0000 3.4999 0.0000 6 LOAD1 7.3244 0.0000 0.0000 0.0000 -1.3247 0.0000 7 LOAD1 14.4481 0.0000 0.0000 0.0000 2.5336 0.0000 8 LOAD1 14.4481 0.0000 0.0000 0.0000 0.0748 0.0000 9 LOAD1 14.4481 0.0000 0.0000 0.0000 2.4829 0.0000
SAP2000 v7.40 File: LUSTRIANA Ton-m Units PAGE 2 10/25/10 16:43:23 [email protected] J O I N T R E A C T I O N S JOINT LOAD F1 F2 F3 M1 M2 M3 1 LOAD1 -2.2152 0.0000 3.4323 0.0000 -6.6158 0.0000 2 LOAD1 -0.3044 0.0000 31.5403 0.0000 -4.9836 0.0000 3 LOAD1 -7.4804 0.0000 19.0274 0.0000 -13.6361 0.0000
SAP2000 v7.40 File: LUSTRIANA Ton-m Units PAGE 3 10/25/10 16:43:23 [email protected] F R A M E E L E M E N T F O R C E S FRAME LOAD LOC P V2 V3 T M2 M3 1 LOAD1 0.00 -3.43 2.22 0.00 0.00 0.00 6.62 2.00 -3.43 2.22 0.00 0.00 0.00 2.19 4.00 -3.43 2.22 0.00 0.00 0.00 -2.25 2 LOAD1 0.00 -31.54 3.044E-01 0.00 0.00 0.00 4.98 2.00 -31.54 3.044E-01 0.00 0.00 0.00 4.37 4.00 -31.54 3.044E-01 0.00 0.00 0.00 3.77 3 LOAD1 0.00 -19.03 7.48 0.00 0.00 0.00 13.64 2.00 -19.03 7.48 0.00 0.00 0.00 -1.32 4.00 -19.03 7.48 0.00 0.00 0.00 -16.29 4 LOAD1 0.00 -1.83 4.013E-02 0.00 0.00 0.00 2.923E-01 1.50 -1.83 4.013E-02 0.00 0.00 0.00 2.321E-01 3.00 -1.83 4.013E-02 0.00 0.00 0.00 1.719E-01 5 LOAD1 0.00 -10.44 1.57 0.00 0.00 0.00 6.548E-02 1.50 -10.44 1.57 0.00 0.00 0.00 -2.28 3.00 -10.44 1.57 0.00 0.00 0.00 -4.63 6 LOAD1 0.00 -7.283E-01 2.39 0.00 0.00 0.00 4.86 1.50 -7.283E-01 2.39 0.00 0.00 0.00 1.27 3.00 -7.283E-01 2.39 0.00 0.00 0.00 -2.32 7 LOAD1 0.00 -3.82 -1.60 0.00 0.00 0.00 2.54 1.50 -3.82 -1.60 0.00 0.00 0.00 4.94 3.00 -3.82 4.40 0.00 0.00 0.00 1.34 4.50 -3.82 4.40 0.00 0.00 0.00 -5.25 6.00 -3.82 4.40 0.00 0.00 0.00 -11.85 8 LOAD1 0.00 -5.09 -16.70 0.00 0.00 0.00 -15.55 1.75 -5.09 -7.95 0.00 0.00 0.00 6.02 3.50 -5.09 7.990E-01 0.00 0.00 0.00 12.28 5.25 -5.09 9.55 0.00 0.00 0.00 3.22 7.00 -5.09 18.30 0.00 0.00 0.00 -21.15 9 LOAD1 0.00 -3.96 -1.83 0.00 0.00 0.00 -1.719E-01 1.50 -3.96 -1.27 0.00 0.00 0.00 2.29 3.00 -3.96 4.195E-01 0.00 0.00 0.00 3.07 4.50 -3.96 3.23 0.00 0.00 0.00 4.716E-01 6.00 -3.96 7.17 0.00 0.00 0.00 -7.19 10 LOAD1 0.00 -2.39 -3.27 0.00 0.00 0.00 -2.56 1.75 -2.39 -2.092E-01 0.00 0.00 0.00 1.38 3.50 -2.39 7.283E-01 0.00 0.00 0.00 2.274E-01 5.25 -2.39 7.283E-01 0.00 0.00 0.00 -1.05 7.00 -2.39 7.283E-01 0.00 0.00 0.00 -2.32
SAP2000
SAP2000 v7.40 - File:Lustriana - Deformed Shape (LOAD1) - Ton-m Units
10/25/10 16:33:46
SAP2000
SAP2000 v7.40 - File:Lustriana - Moment 3-3 Diagram (LOAD1) - Ton-m Units
10/25/10 16:37:28
SAP2000
SAP2000 v7.40 - File:Lustriana - Shear Force 2-2 Diagram (LOAD1) - Ton-m Units
10/25/10 16:38:02
SAP2000
SAP2000 v7.40 - File:Lustriana - Axial Force Diagram (LOAD1) - Ton-m Units
10/25/10 16:38:29