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Mekanika Rekayasa KANI

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P1 W1 Q R

q1 S

P2 T

q2 W2 M N

P1 O

q1 P

P2 W3 I J

q2 K

P1 L

q1 W4 E F

P2 G

q2 H

C

D

A L1

B L2 L3

h1

h2

BALOK QR RS ST MN NO OP IJ JK KL EF FG GH

h3

EI DIMENSI KOLOM 1 20/30 AE 1 20/30 EI 1 20/30 IM 1,5 25/35 MQ 1,5 25/35 BF 1,5 25/35 FJ 2 35/45 JN 2 35/45 NR 2 35/45 CG 2,5 40/50 GK 2,5 40/50 KO 2,5 40/50 OS DH HL LP PT = 1 ton = 1,5 ton = 1t/m' = 2t/m' = 5 ton = 4 ton = 3 ton = 2,5 ton L1 L2 L3 h1 h2 h3 h4 h5

EI DIMENSI 2,5 40/50 2 35/45 1,5 25/35 1 20/20 2,5 40/50 2 35/45 1,5 25/35 1 20/20 2,5 40/50 2 35/45 1,5 25/35 1 20/20 2,5 40/50 2 35/45 1,5 25/35 1 20/20 = 5m = 4,5 m = 5,5 m = 4m = 4m = 5m = 5m = 3m

h4

P1 P2 q1 q2 W1 W2 W3 W4

h5

BALOK QR RS ST MN NO OP IJ JK KL EF FG GH

EI 1 1 1 1,5 1,5 1,5 2 2 2 2,5 2,5 2,5

DIMENSI 20/30 20/30 20/30 25/35 25/35 25/35 35/45 35/45 35/45 40/50 40/50 40/50

INERSIA Jika 45000 = I 1/12 bh3 45000 1.00 45000 1.00 45000 1.00 89322.917 1.98 89322.917 1.98 89322.917 1.98 265781.25 5.91 265781.25 5.91 265781.25 5.91 416666.67 9.26 416666.67 9.26 416666.67 9.26

KOLOM AE EI IM MQ BF FJ JN NR CG GK KO OS DH HL LP PT

EI 2,5 2 1,5 1 2,5 2 1,5 1 2,5 2 1,5 1 2,5 2 1,5 1

DIMENSI 40/50 35/45 25/35 20/20 40/50 35/45 25/35 20/20 40/50 35/45 25/35 20/20 40/50 35/45 25/35 20/20

INERSIA Jika 45000 = I 1/12 bh3 416666.67 9.26 265781.25 5.91 89322.917 1.98 13333.333 0.30 416666.67 9.26 265781.25 5.91 89322.917 1.98 13333.333 0.30 416666.67 9.26 265781.25 5.91 89322.917 1.98 13333.333 0.30 416666.67 9.26 265781.25 5.91 89322.917 1.98 13333.333 0.30

QR1/2L1

TABEL MOMEN PRIMER P1 = 1 MQR = 1/8 PL = P1 L1 = 5 MRQ = -1/8 PL =1/2L1

0.63 -0.63

RS

q1 L2

q1 = L2 =

1 4.5

MRS = 1/12 ql2 = MSR = - 1/12 qL2=

1.69 -1.69

ST

P21/2L3 1/2L3

P2 = 1.5 L3 = 5.5

MST = 1/8 PL = MTS = -1/8 PL =

1.03 -1.03

MN

q2 L1

q2 = L1 =

2 5

MMN = 1/12 qL2 = MNM = - 1/12 qL2=

4.17 -4.17

NO1/2L2

P11/2L2

P1 = 1 L2 = 4.5

MNO = 1/8 PL = MON = -1/8 PL =

0.56 -0.56

OP

q1 L3

q1 =

1

MOP = 1/12 qL2 = MPO = - 1/12 qL2=

2.52 -2.52

L3 = 5.5

IJ1/2L1

P21/2L1

P2 = 1.5 L1 = 5

MIJ = 1/8 PL = MJI = -1/8 PL =

0.94 -0.94

JK

q2 L2

q2 =

2

MJK = 1/12 qL2 = MKJ = - 1/12 qL2 =

3.38 -3.38

L2 = 4.5

KL

P11/2L3 1/2L3

P1 = 1 L3 = 5.5

MKL = 1/8 PL =MLK = -1/8 PL =

0.69 -0.69

EF

q1 L1

q1 = L1 =

1 5

MEF = 1/12 qL2 = MFE = - 1/12 qL2=

2.08 -2.08

FG1/2L2

P21/2L2

P2 = 1.5 L2 = 4.5

MFG = 1/8 PL = MGF = -1/8 PL =

0.84 -0.84

GH

q2 L3

q2 =

2

MGH = 1/12 qL2 = MHG = - 1/12 qL2=

5.04 -5.04

L3 = 5.5

MOMEN KUMPUL MQ MR MS MT MM MN MO MP MI MJ MK ML ME MF MG MH = MQR+ MQM = MRQ+ MRN + MRS = MSR + MSO + MST = MTS+ MTP = MMQ+ MMN + MMI = MNM + MNR + MNO + MNJ = MON + MOS + MOP + MOK = MPO+ MPT + MPL = MIM+ MIJ + MIE = MJI + MJN + MJK + MJF = MKJ + MKO + MKL + MKG = MLK+ MLP + MLH = MEI+ MEF + MEA = MFE + MFJ + MFG + MFB = MGF + MGK + MGH + MGC = MHG+ MHL + MHD = 0,63 + 0 = = -0,63 + 0 + 1.69 = = -1.69 +1,03 + 0 = = -1,03 + 0 = 0.625 1.063 -0.656 -1.031

= 0 + 4,17 + 0 = 4.167 = -4,17 + 0 + 0,56 + 0 = -3.604 = -0,56 + 0 + 2,52 + 0 = 1.958 = -2.52 + 0 + 0 = -2.521 = 0 + 0,94 + 0 = 0.938 = -0,94 + 0 + 3,38 + 0 = 2.438 =-3,38 + 0 + 0,69 + 0 = -2.688 = -0,69 + 0 + 0 = -0.688 = 0 + 2,08 + 0 = 2.083 = -2,08 + 0 + 0,84 + 0 = -1.240 = -0,84 + 0 + 5,04 + 0 = 4.198 = -0,54 +0 + 0 = -5.042

k

JOIN Q R

BALOK QR QM RQ RS RN SR ST SO TS TP MN MQ MI NM NO NR NJ ON OP OS OK PO PT PL IJ IM IE JI JK JN JF KJ KL KO KG LK LP LH EF EI EA FE FG FJ FB

EI 1 0.30 1 1 0.30 1 1 0.30 1 0.30 1.98 0.30 1.98 1.98 1.98 0.30 1.98 1.98 1.98 0.30 1.98 1.98 0.30 1.98 5.91 1.98 5.91 5.91 5.91 1.98 5.91 5.91 5.91 1.98 5.91 5.91 1.98 5.91 9.26 5.91 9.26 9.26 9.26 5.91 9.26

L 5

H

Kij=

4 EI L

Kij 1.10 1.99

ij =

1 Kij 2 Kij

KL QR 20/30 RS 20/30 ST 20/30 MN 25/35 NO 25/35 OP 25/35 IJ 35/45 JK 35/45 KL 35/45 EF 40/50 FG 40/50 GH 40/50

4 5 4.5 4 4.5 5.5 4 5.5 4 5 4 4 5 4.5 4 4 4.5 5.5 4 4 5.5 4 4 5 4 5 5 4.5 4 5 4.5 5.5 4 5 5.5 4 5 5 5 8 5 4.5 5 8

S T M

N

O

P

I

J

K

L

E

F

0.80 0.30 0.80 0.89 0.30 0.89 0.73 0.30 0.73 0.30 1.59 0.30 1.98 1.59 1.76 0.30 1.98 1.76 1.44 0.30 1.98 1.44 0.30 1.98 4.73 1.98 4.73 4.73 5.25 1.98 4.73 5.25 4.30 1.98 4.73 4.30 1.98 4.73 7.41 4.73 4.63 7.41 8.23 4.73 4.63

1.91 1.02 3.87

5.63

5.49

3.72

11.43

16.68

16.26 11.01

16.76

24.99

-0.365 -0.135 -0.201 -0.224 -0.075 -0.232 -0.191 -0.077 -0.355 -0.145 -0.205 -0.038 -0.257 -0.141 -0.157 -0.026 -0.176 -0.161 -0.131 -0.027 -0.181 -0.194 -0.040 -0.266 -0.207 -0.086 -0.207 -0.142 -0.157 -0.059 -0.142 -0.161 -0.132 -0.062 -0.095 -0.195 -0.090 -0.215 -0.221 -0.141 -0.138 -0.147 -0.165 -0.095 -0.093

G

H

GF GH GK GC HG HL HD

9.26 9.26 5.91 9.26 9.26 5.91 9.26

4.5 5.5 5 5 5.5 5 5

8.23 6.73 4.73 7.41 6.73 4.73 7.41

27.10

18.87

-0.152 -0.124 -0.087 -0.137 -0.178 -0.126 -0.196

Jika 45000 = I 1.00 1.00 1.00 1.98 1.98 1.98 5.91 5.91 5.91 9.26 9.26 9.26

KOLOM Jika 45000 = I AE EI IM MQ BF FJ JN NR CG GK KO OS DH HL LP PT 2,5 1,5 2,5 1,5 2,5 1,5 2,5 1,5 9.26 5.91 1.98 0.30 9.26 5.91 1.98 0.30 9.26 5.91 1.98 0.30 9.26 5.91 1.98 0.30

KOEFISIEN PERGOYANGAN

ij

3 CK 2 (C 2 K )

Dimana C QM : C RN : C SO :C TP =1 C MI : C NJ : C OK :C PL = 1 C IE : C JF : C KG : C LH = 1 C EA : C FB =1 C GC : C HD = 8/5 = 1,6 Tingkat ke I EA = -3/2 1 x 4,63 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 47.1992 4.63 47.1992 7.41 47.1992 7.41 47.1992 = -0.147

W1 Q

W2 M

FB =

-3/2

=

-0.147

W3 I

GC =

-3/2

=

-0.235

HD =

-3/2

=

-0.235

W4 E

Tingkat ke II IE = -3/2 1 x 4,73 1^2 x 4,73 + 1^2 x 4,73 + 1^2 x 4,73 + -3/2 4.73 18.92 4.73 18.92 4.73 18.92 4.73 18.92 = -0.375

1^2 x 4,73

JF =

-3/2

=

-0.375 A

KG =

-3/2

=

-0.375

LH =

-3/2

=

-0.375

Tingkat ke III MI = -3/2 1 x 1,98 1^2 x 1,98 + 1^2 x 1,98 + 1^2 x 1,98 + -3/2 1.98 7.92 = -0.375

1^2 x 1,98

NJ =

-3/2

1.98 7.92 1.98 7.92 1.98 7.92

=

-0.375

OK =

-3/2

=

-0.375

PL =

-3/2

=

-0.375

QM =

-3/2 1 x 0,3 1^2 x 0,3 + -3/2 0.3 1.2 0.3 1.2 0.3 1.2 0.3 1.2

1^2 x 0,3 + =

1^2 x 0,3 + -0.375

1^2 x 0,3

RN =

-3/2

=

-0.375

SO =

-3/2

=

-0.375

TP =

-3/2

=

-0.375

P1 R

q1 S

P2 T

q2 N

P1 O

q1 P

P2

q2

P1

J

K

L

q1 F

P2 G

q2 H

C

D

B L1 L2 L3

Momen tingkat P4 = P3 = P4 = P4 = W1 = 5 Ton W2 = 4Ton + 5 Ton = 9 ton W3 = 3 ton + 9 ton = 12 ton W4 = 2,5 Ton + 12 Ton = 14,5 Ton P1 P2 q1 q2 W1 W2 W3 W4 = 1 ton = 1,5 ton = 1t/m' = 2t/m' = 5 ton = 4 ton = 3 ton = 2,5 ton L1 L2 L3 h1 h2 h3 h4 h5 = 5m = 4,5 m = 5,5 m = 4m = 4m = 5m = 5m = 3m

MOMEN TINGKAT MT = 1/3 x hc x P M4 = M3 = M2 = M1 = 1/3 x 4 x 5 = 1/3 x 4 x 9 = 1/3 x 5 x 12= 1/3 x 8 x 14,5 = 6.667 12 20 38.667

Q 0.625 -0.135 0.253 0.314 0.332 0.331 0.331 0.331 0.332 -0.365 0.625 0.684 0.849 0.898 0.896 0.894 0.894 0.898 -0.201 -0.625 0.152 0.055 0.073 0.081 0.082 0.083 0.083 1.063 -0.075 0.056 0.021 0.027 0.030 0.031 0.031 0.031

-2.325 -2.459 -2.455 -2.450 -2.448 -2.460

6.667 0.045 0.127 0.155 0.166 0.169 0.154 0.169

-0.375

-2.500 -3.146 -3.267 -3.308 -3.321 -3.325 -3.321

-2.500 -3.146 -3.267 -3.308 -3.321 -3.325 -3.321

8.389 8.711 8.823 8.856 8.866 8.857

-0.375

6.667 0.264 0.338 0.354 0.358 0.359 0.349 0.360

-0.038 4.167 -0.257 0.298 0.858 1.049 1.119 1.144 1.039 1.140

M -0.205 4.167 0.239 0.685 0.837 0.893 0.912 0.828 0.909 -0.141 -4.167 1.418 1.832 1.918 1.942 1.948 1.895 1.954

-0.026 -3.604 -0.176 1.772 2.287 2.394 2.424 2.432 2.365 2.440

-3.339 -4.083 -4.356 -4.450 -4.041 -4.436

12.000

-0.375

-4.500 -7.432 -8.580 -8.969 -9.102 -8.651 -9.081

-4.500 -7.432 -8.580 -8.969 -9.102 -8.651 -9.081

19.819 22.881 23.918 24.273 23.068 24.217

-0.375

12.000

0.926 1.347 1.482 1.527 1.542 1.514 1.537

0.320 0.467 0.539 0.569 0.581 0.565 0.581

-0.086 0.938 -0.207 2.224 3.241 3.566 3.675 3.711 3.644 3.700

I -0.207 0.938 2.418 3.241 3.566 3.675 3.711 3.644 3.700 -0.142 -0.938 0.761 1.124 1.297 1.369 1.399 1.360 1.398

-0.059 2.438 -0.142 0.761 1.124 1.297 1.369 1.399 1.360 1.398

-15.659 -17.227 -17.755 -17.929 -17.602 -17.874

-7.500 -11.777 -13.223 -13.756 -13.950 -14.019 -13.942

-7.500 -11.777 -13.223 -13.756 -13.950 -14.019 -13.942

31.404 35.262 36.683 37.200 37.385 37.179

20.000 0.993 1.465 1.615 1.672 1.693 1.711 1.695

-0.375

-0.3

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