P1 q1 P2W1

Q R S T

q2 P1 q1W2

M N O P

P2 q2 P1W3

I J K L

q1 P2 q2W4

E F G H

C D

A B

L1 L2 L3

BALOK EI DIMENSI KOLOM EI DIMENSIQR 1 20/30 AE 2,5 40/50RS 1 20/30 EI 2 35/45

h1 ST 1 20/30 IM 1,5 25/35MN 1,5 25/35 MQ 1 20/20NO 1,5 25/35 BF 2,5 40/50OP 1,5 25/35 FJ 2 35/45IJ 2 35/45 JN 1,5 25/35JK 2 35/45 NR 1 20/20

h2 KL 2 35/45 CG 2,5 40/50EF 2,5 40/50 GK 2 35/45FG 2,5 40/50 KO 1,5 25/35GH 2,5 40/50 OS 1 20/20

DH 2,5 40/50HL 2 35/45

h3 LP 1,5 25/35PT 1 20/20

P1 = 1 ton L1 = 5mP2 = 1,5 ton L2 = 4,5 mq1 = 1t/m' L3 = 5,5 mq2 = 2t/m' h1 = 4m

h4 W1 = 5 ton h2 = 4mW2 = 4 ton h3 = 5mW3 = 3 ton h4 = 5mW4 = 2,5 ton h5 = 3m

h5

BALOK EI DIMENSIINERSIA

Jika 45000 = I KOLOM EI

QR 1 20/30 45000 1.00 AE 2,5RS 1 20/30 45000 1.00 EI 2ST 1 20/30 45000 1.00 IM 1,5MN 1,5 25/35 89322.917 1.98 MQ 1NO 1,5 25/35 89322.917 1.98 BF 2,5OP 1,5 25/35 89322.917 1.98 FJ 2IJ 2 35/45 265781.25 5.91 JN 1,5JK 2 35/45 265781.25 5.91 NR 1KL 2 35/45 265781.25 5.91 CG 2,5EF 2,5 40/50 416666.67 9.26 GK 2FG 2,5 40/50 416666.67 9.26 KO 1,5GH 2,5 40/50 416666.67 9.26 OS 1

DH 2,5HL 2LP 1,5PT 1

1/12 bh3

DIMENSIINERSIA

Jika 45000 = I

40/50 416666.67 9.2635/45 265781.25 5.9125/35 89322.917 1.9820/20 13333.333 0.3040/50 416666.67 9.2635/45 265781.25 5.9125/35 89322.917 1.9820/20 13333.333 0.3040/50 416666.67 9.2635/45 265781.25 5.9125/35 89322.917 1.9820/20 13333.333 0.3040/50 416666.67 9.2635/45 265781.25 5.9125/35 89322.917 1.9820/20 13333.333 0.30

1/12 bh3

TABEL MOMEN PRIMERQR P1 = 1 M°QR = 1/8 PL = 0.63

L1 = 5 M°RQ = -1/8 PL = -0.63

RS q1 = 1 M°RS = 1/12 ql2 = 1.69L2 = 4.5 -1.69

ST P2 = 1.5 M°ST = 1/8 PL = 1.03L3 = 5.5 M°TS = -1/8 PL = -1.03

MN q2 = 2 4.17L1 = 5 -4.17

NO P1 = 1 M°NO = 1/8 PL = 0.56L2 = 4.5 M°ON = -1/8 PL = -0.56

OP q1 = 1 2.52L3 = 5.5 -2.52

IJ P2 = 1.5 M°IJ = 1/8 PL = 0.94L1 = 5 M°JI = -1/8 PL = -0.94

JK q2 = 2 3.38L2 = 4.5 -3.38

KL P1 = 1 M°KL = 1/8 PL =- 0.69L3 = 5.5 M°LK = -1/8 PL = -0.69

EF q1 = 1 2.08L1 = 5 -2.08

FG P2 = 1.5 M°FG = 1/8 PL = 0.84L2 = 4.5 M°GF = -1/8 PL = -0.84

GH q2 = 2 5.04L3 = 5.5 -5.04

M°SR = - 1/12 qL2 =

M°MN = 1/12 qL2 =

M°NM = - 1/12 qL2 =

M°OP = 1/12 qL2 =

M°PO = - 1/12 qL2 =

M°JK = 1/12 qL2 =

M°KJ = - 1/12 qL2 =

M°EF = 1/12 qL2 =

M°FE = - 1/12 qL2 =

M°GH = 1/12 qL2 =

M°HG = - 1/12 qL2 =

1/2L1 1/2L1

P1

L2

q1

1/2L3

P2

1/2L2

P1

P2

P1

P2

L1

q2

L3

q1

L2

q2

L1

q1

L3

q2

1/2L3

1/2L2

1/2L1 1/2L1

1/2L3 1/2L3

1/2L2 1/2L2

L3

MOMEN KUMPUL

M°Q = M°QR+ M°QM = 0,63 + 0 = 0.625M°R = -0,63 + 0 + 1.69 = 1.063M°S = -1.69 +1,03 + 0 = -0.656M°T = M°TS+ M°TP = -1,03 + 0 = -1.031M°M = 0 + 4,17 + 0 = 4.167M°N = -4,17 + 0 + 0,56 + 0 = -3.604M°O = -0,56 + 0 + 2,52 + 0 = 1.958M°P = -2.52 + 0 + 0 = -2.521M°I = 0 + 0,94 + 0 = 0.938M°J = -0,94 + 0 + 3,38 + 0 = 2.438M°K =-3,38 + 0 + 0,69 + 0 = -2.688M°L = -0,69 + 0 + 0 = -0.688M°E = 0 + 2,08 + 0 = 2.083M°F = -2,08 + 0 + 0,84 + 0 = -1.240M°G = -0,84 + 0 + 5,04 + 0 = 4.198M°H = -0,54 +0 + 0 = -5.042

= M°RQ+ M°RN + M°RS = M°SR + M°SO + M°ST

= M°MQ+ M°MN + M°MI = M°NM + M°NR + M°NO + M°NJ = M°ON + M°OS + M°OP + M°OK = M°PO+ M°PT + M°PL = M°IM+ M°IJ + M°IE = M°JI + M°JN + M°JK + M°JF = M°KJ + M°KO + M°KL + M°KG = M°LK+ M°LP + M°LH = M°EI+ M°EF + M°EA = M°FE + M°FJ + M°FG + M°FB = M°GF + M°GK + M°GH + M°GC = M°HG+ M°HL + M°HD

k

JOIN BALOK EI L H Kij= ∑Kij αij = KLDIMENSI

Q QR 1 5 0.80 1.10 -0.365QM 0.30 4 0.30 -0.135 QR 20/30

RRQ 1 5 0.80

1.99-0.201 RS 20/30

RS 1 4.5 0.89 -0.224 ST 20/30RN 0.30 4 0.30 -0.075 MN 25/35

SSR 1 4.5 0.89

1.91-0.232 NO 25/35

ST 1 5.5 0.73 -0.191 OP 25/35SO 0.30 4 0.30 -0.077 IJ 35/45

TTS 1 5.5 0.73

1.02-0.355 JK 35/45

TP 0.30 4 0.30 -0.145 KL 35/45

MMN 1.98 5 1.59

3.87-0.205 EF 40/50

MQ 0.30 4 0.30 -0.038 FG 40/50MI 1.98 4 1.98 -0.257 GH 40/50

N

NM 1.98 5 1.59

5.63

-0.141NO 1.98 4.5 1.76 -0.157NR 0.30 4 0.30 -0.026NJ 1.98 4 1.98 -0.176

O

ON 1.98 4.5 1.76

5.49

-0.161OP 1.98 5.5 1.44 -0.131OS 0.30 4 0.30 -0.027OK 1.98 4 1.98 -0.181

PPO 1.98 5.5 1.44

3.72-0.194

PT 0.30 4 0.30 -0.040PL 1.98 4 1.98 -0.266

IIJ 5.91 5 4.73

11.43-0.207

IM 1.98 4 1.98 -0.086IE 5.91 5 4.73 -0.207

J

JI 5.91 5 4.73

16.68

-0.142JK 5.91 4.5 5.25 -0.157JN 1.98 4 1.98 -0.059JF 5.91 5 4.73 -0.142

K

KJ 5.91 4.5 5.25

16.26

-0.161KL 5.91 5.5 4.30 -0.132KO 1.98 4 1.98 -0.062KG 5.91 5 4.73 -0.095

LLK 5.91 5.5 4.30 11.01 -0.195LP 1.98 4 1.98 -0.090LH 5.91 5 4.73 -0.215

EEF 9.26 5 7.41

16.76-0.221

EI 5.91 5 4.73 -0.141EA 9.26 8 4.63 -0.138

F

FE 9.26 5 7.41

24.99

-0.147FG 9.26 4.5 8.23 -0.165FJ 5.91 5 4.73 -0.095

4 EIL

−12Kij

∑ Kij

F

FB 9.26 8 4.63

24.99

-0.093

G

GF 9.26 4.5 8.23

27.10

-0.152GH 9.26 5.5 6.73 -0.124GK 5.91 5 4.73 -0.087GC 9.26 5 7.41 -0.137

HHG 9.26 5.5 6.73

18.87-0.178

HL 5.91 5 4.73 -0.126HD 9.26 5 7.41 -0.196

Jika 45000 = I KOLOM EIJika 45000 = I

1.00 AE 2,5 9.261.00 EI ### 5.911.00 IM 1,5 1.981.98 MQ ### 0.301.98 BF 2,5 9.261.98 FJ ### 5.915.91 JN 1,5 1.985.91 NR ### 0.305.91 CG 2,5 9.269.26 GK ### 5.919.26 KO 1,5 1.989.26 OS ### 0.30

DH 2,5 9.26HL ### 5.91LP 1,5 1.98PT ### 0.30

KOEFISIEN PERGOYANGAN

DimanaC QM : C RN : C SO :C TP =1 W1C MI : C NJ : C OK :C PL = 1 QC IE : C JF : C KG : C LH = 1C EA : C FB =1C GC : C HD = 8/5 = 1,6

Tingkat ke I W2β EA = -3/2 1 x 4,63 M

1^2 x 4,63 + 1^2 x 4,63 + 1,6^2 x 7,41 + 1,6^2 x 7,41

-3/2 4.63 = -0.14747.1992

β FB = -3/2 4.63 = -0.147 W347.1992 I

β GC = -3/2 7.41 = -0.23547.1992

β HD = -3/2 7.41 = -0.235 W447.1992 E

Tingkat ke IIβ IE = -3/2 1 x 4,73

1^2 x 4,73 + 1^2 x 4,73 + 1^2 x 4,73 + 1^2 x 4,73

-3/2 4.73 = -0.37518.92

β JF = -3/2 4.73 = -0.37518.92

Aβ KG = -3/2 4.73 = -0.375

18.92

β LH = -3/2 4.73 = -0.37518.92

Tingkat ke IIIβ MI = -3/2 1 x 1,98

1^2 x 1,98 + 1^2 x 1,98 + 1^2 x 1,98 + 1^2 x 1,98

-3/2 1.98 = -0.3757.92

β ij=−32

CK∑ (C2K )

β NJ = -3/2 1.98 = -0.3757.92

β OK = -3/2 1.98 = -0.3757.92

β PL = -3/2 1.98 = -0.3757.92

β QM = -3/2 1 x 0,31^2 x 0,3 + 1^2 x 0,3 + 1^2 x 0,3 + 1^2 x 0,3

-3/2 0.3 = -0.3751.2

β RN = -3/2 0.3 = -0.3751.2

β SO = -3/2 0.3 = -0.3751.2

β TP = -3/2 0.3 = -0.3751.2

P1 q1 P2

R S T

q2 P1 q1

N O P

P2 q2 P1

J K L

q1 P2 q2

F G H

C D

B

L1 L2 L3

Momen tingkat

W1 = 5 Ton P1 = 1 ton L1 = 5mW2 = 4Ton + 5 Ton = 9 ton P2 = 1,5 ton L2 = 4,5 mW3 = 3 ton + 9 ton = 12 ton q1 = 1t/m' L3 = 5,5 mW4 = 2,5 Ton + 12 Ton = 14,5 Ton q2 = 2t/m' h1 = 4m

W1 = 5 ton h2 = 4mW2 = 4 ton h3 = 5m

MOMEN TINGKAT W3 = 3 ton h4 = 5mW4 = 2,5 ton h5 = 3m

1/3 x 4 x 5 = 6.6671/3 x 4 x 9 = 121/3 x 5 x 12= 201/3 x 8 x 14,5 = 38.667

Pº4 =Pº3 =Pº4 =Pº4 =

MºT = 1/3 x hc x Pº

Mº4 =Mº3 =Mº2 =Mº1 =

Q

0.625 -0.365 -0.201 1.063

-0.135 0.625 -0.625 -0.0750.253 0.684 0.152 0.0560.314 0.849 -2.325 0.055 0.0210.332 0.898 -2.459 0.073 0.0270.331 0.896 -2.455 0.081 0.0300.331 0.894 -2.450 0.082 0.0310.331 0.894 -2.448 -2.500 -2.500 0.083 0.0310.332 0.898 -2.460 -3.146 -3.146 8.389 0.083 0.031

-3.267 -3.267 8.711-3.308 -3.308 8.823-3.321 -3.321 8.856-3.325 -3.325 8.866

6.667-0.375 -3.321 -3.321 8.857 -0.375

6.667

0.045 0.2640.127 0.3380.155 0.3540.166 0.3580.169 0.3590.154 0.3490.169 0.360

-0.038 M -0.026

4.167 -0.205 -0.141 -3.604

-0.257 4.167 -4.167 -0.1760.298 0.239 1.418 1.7720.858 0.685 -3.339 1.832 2.2871.049 0.837 -4.083 1.918 2.3941.119 0.893 -4.356 1.942 2.4241.144 0.912 -4.450 1.948 2.4321.039 0.828 -4.041 -4.500 -4.500 1.895 2.3651.140 0.909 -4.436 -7.432 -7.432 19.819 1.954 2.440

-8.580 -8.580 22.881-8.969 -8.969 23.918-9.102 -9.102 24.273-8.651 -8.651 23.068

12.000-0.375 -9.081 -9.081 24.217 -0.375

12.000

12.000 12.000

0.926 0.3201.347 0.4671.482 0.5391.527 0.5691.542 0.5811.514 0.5651.537 0.581

-0.086 I -0.059

0.938 -0.207 -0.142 2.438

-0.207 0.938 -0.938 -0.1422.224 2.418 0.761 0.7613.241 3.241 -15.659 1.124 1.1243.566 3.566 -17.227 1.297 1.2973.675 3.675 -17.755 1.369 1.3693.711 3.711 -17.929 -7.500 -7.500 1.399 1.3993.644 3.644 -17.602 -11.777 -11.777 31.404 1.360 1.3603.700 3.700 -17.874 -13.223 -13.223 35.262 1.398 1.398

-13.756 -13.756 36.683-13.950 -13.950 37.200-14.019 -14.019 37.385-13.942 -13.942 37.179

20.000-0.375 -0.375

20.000

0.993 1.1831.465 1.4281.615 1.4651.672 1.4801.693 1.4851.711 1.4911.695 1.479

-0.141 E -0.095

2.083 -0.221 -0.147 -1.240

-0.138 2.083 -2.083 -0.0930.973 1.556 -7.043 1.839 1.1591.434 2.297 -10.393 2.210 1.3981.581 2.532 -11.457 2.268 1.4351.636 2.620 -11.857 2.291 1.4491.657 2.654 -12.008 2.298 1.4541.675 2.682 -12.135 2.308 1.460

1.659 2.657 -12.021 2.288 1.448-5.690 -5.690-6.150 -6.150 41.839-6.150 -6.150 42.809-6.150 -6.150 43.119

38.667-0.147 -6.150 -6.150 43.250 -0.147

38.667-6.150 -6.150 43.298-6.150 -6.150 43.331

=

A B

R S

-0.224 -0.232 -0.656 -0.191

1.688 -1.688 -0.077 1.0310.169 0.694 0.231 0.5710.062 -0.276 0.605 0.201 0.498 -2.6060.081 -0.363 0.594 0.197 0.489 -2.5610.090 -0.401 0.597 0.198 0.492 -2.5730.092 -0.409 0.598 0.198 0.492 -2.5760.092 -0.411 0.598 0.198 0.492 -2.5760.093 -0.413 0.601 0.199 0.494 -2.589

6.667-0.375

0.0820.1020.1130.1180.1200.1030.121

N -0.027 O

-0.157 -0.161 1.958 -0.131

0.563 -0.563 -0.181 2.5211.575 0.490 0.551 0.4012.040 -12.993 0.610 0.685 0.496 -3.7872.135 -13.601 0.671 0.755 0.546 -4.1702.162 -13.772 0.704 0.791 0.573 -4.3702.169 -13.818 0.717 0.806 0.583 -4.4542.110 -13.439 0.616 0.693 0.502 -3.8292.176 -13.861 0.721 0.811 0.587 -4.480

12.000-0.375

12.000

0.8241.0941.1861.2101.2161.1981.217

J -0.062 K

-0.157 -0.161 -2.688 -0.132

3.375 -3.375 -0.095 0.6880.845 2.146 1.256 1.7561.242 -7.913 2.841 1.676 2.329 -17.6441.434 -9.137 3.080 1.817 2.525 -19.1291.514 -9.643 3.141 1.853 2.575 -19.5091.546 -9.849 3.158 1.864 2.589 -19.6171.504 -9.580 3.112 1.836 2.551 -19.3271.545 -9.843 3.160 1.865 2.591 -19.629

20.000-0.375

0.6640.8320.9120.9510.9650.9710.965

F -0.087 G

-0.165 -0.152 4.198 -0.124

-0.844 -0.844 -0.137 5.0422.060 -12.512 1.156 1.041 0.9462.481 -15.034 1.453 1.310 1.185 -9.5592.545 -15.426 1.594 1.436 1.300 -10.4842.571 -15.584 1.661 1.497 1.355 -10.9272.580 -15.635 1.686 1.520 1.376 -11.0952.590 -15.699 1.697 1.529 1.384 -11.162

2.569 -15.568 1.685 1.519 1.375 -11.086

38.667-0.235

C

-0.355 -1.031 T

-1.031 -0.1451.052 0.4291.178 0.481 -3.3181.188 0.485 -3.3481.191 0.487 -3.3561.192 0.487 -3.359

-2.500 -2.500 1.193 0.487 -3.360-3.146 -3.146 1.179 0.482 -3.321-3.267 -3.267-3.308 -3.308-3.321 -3.321-3.325 -3.325-3.321 -3.321 -0.375

6.667

0.3620.4600.4920.5010.5030.5370.507

-0.040

-0.194 -2.521 P

-2.521 -0.2661.762 2.4232.233 3.062 -11.5122.387 3.273 -12.3062.430 3.332 -12.526

-4.500 -4.500 2.441 3.347 -12.583-7.432 -7.432 2.605 3.571 -13.426-8.580 -8.580 2.458 3.370 -12.669-8.969 -8.969-9.102 -9.102-8.651 -8.651-9.081 -9.081

-0.37512.000

12.000

0.7051.0811.2401.3010.0001.2721.316

-0.090

-0.195 -0.688 L

-0.688 -0.2151.661 1.8272.342 2.582 -12.0082.687 2.963 -13.7802.820 3.109 -14.460

-7.500 -7.500 2.869 3.163 -14.714-11.777 -11.777 2.756 3.038 -14.131-13.223 -13.223 2.852 3.144 -14.623-13.756 -13.756 -0.471 -0.520 2.417-13.950 -13.950-14.019 -14.019-13.942 -13.942

-0.37520.000

2.4972.9133.0463.0903.1043.1283.105

-0.126

-0.178 -5.042 H

-5.042 -0.1963.537 3.8914.116 4.578 -23.1234.304 4.787 -24.1774.365 4.855 -24.5224.385 4.878 -24.6374.418 4.915 -24.822

PerputaranM'ik = αij (Mi+ΣM'ji +ΣM''ij)

Pergoyanganβij (Mr+Σ(ij(Mij+M'ji)

PERPUTARANQ-R-S-T-P-O-N-M-I-J-K-L-H-G-F-E

4.386 4.879 -24.639-9.106 -9.106-9.832 -9.832

-10.060 -10.060-10.133 -10.133-10.164 -10.164 -0.235

38.667-10.175 -10.175-10.183 -10.183

D

PerputaranM'ik = αij (Mi+ΣM'ji +ΣM''ij)

Pergoyanganβij (Mr+Σ(ij(Mij+M'ji)

PERPUTARANQ-R-S-T-P-O-N-M-I-J-K-L-H-G-F-E

MOMEN AKHIR

Mij = Momen akhir

M'ij= momen akibat perputaran sudut i dan ujung terjepitM'ji= momen akibat perputaran sudut i pada simpul JM''ij= momen akibat pergoyangan

Mºij= momen jepit primer IJ

M IJ=M IJο +2M IJ

' +M JI' +M IJ

''

M IJ=M IJο +2M IJ

' +M JI' +M IJ

''