mektek 3 metode distribusi momen

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



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



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


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

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SAP2000 v7.40 - File:Lustriana - Moment 3-3 Diagram (LOAD1) - Ton-m Units

10/25/10 16:37:28

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SAP2000 v7.40 - File:Lustriana - Shear Force 2-2 Diagram (LOAD1) - Ton-m Units

10/25/10 16:38:02

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SAP2000 v7.40 - File:Lustriana - Axial Force Diagram (LOAD1) - Ton-m Units

10/25/10 16:38:29

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