Recoverd Xls File(515)

REKAP BERAT ATAP

Kuda-kuda Rangka Baja

TYPE L W n Σ

kgm kg/m titik kg

WF 300.150.6,5.9 17,892 114 7 14,277,816

WF 150.100.6.9 3.0 0.25 18 14

CANAL 160.65.7,5 34 0.25 18 153

Plat simpul 1,413

5 85,788 0.25 2 42,894

6 85,788 0.25 6 128,682

Total Berat 14,450,971 14,450,971

TYPE L W n Σ

m kg/m titik kg

7 28,500 0.25 2 14,250

8 27,156 0.25 1 6,789

9 23,904 0.25 1 5,976

10 14,314 0.25 1 3,579

11 6,367 0.25 2 3,184

Total Berat 33,777 33,777

Total Berat keseluruhan 14,484,748

Berat per m^2 P L Luasan Type

18,419.909 17.43 45.00 784.530 1&6

550 3.20 8.10 25.920 7

349 2.4 8.1 19.440 8

307 2.4 8.1 19.440 9

392 3.6 6 5.760

10 3.6 2 3.360

947 3.6 2 3.360

11 2 1 1 4.360

REKAP BERAT ATAP

Kuda-kuda

TYPE L W n Σ

kgm kg/m titik kg

1 85,788 0.25 10 214,470

2 85,788 0.25 8 171,576

3 85,788 0.25 8 171,576

4 85,788 0.25 4 85,788

5 85,788 0.25 2 42,894

6 85,788 0.25 6 128,682

Total Berat 814,986 814,986

TYPE L W n Σ

m kg/m titik kg

7 28,500 0.25 2 14,250

8 27,156 0.25 1 6,789

9 23,904 0.25 1 5,976

10 14,314 0.25 1 3,579

11 6,367 0.25 2 3,184

Total Berat 33,777 33,777

Total Berat keseluruhan 848,763

Berat per m^2 P L Luasan Type

1,038.821 17.43 45.00 784.530 1&6

550 3.20 8.10 25.920 7

349 2.4 8.1 19.440 8

307 2.4 8.1 19.440 9

392 3.6 6 5.760

10 3.6 2 3.360

947 3.6 2 3.360

11 2 1 1 4.360

PERHITUNGAN PEMBEBANAN PADA ATAP

A. Beban Mati

Kuda-kuda type 1-6

No. Jenis BahanWeight Dimensi Luas Total Berat

per Unit m m m^2 kg/m^2

1 Penutup atap 50.0 kg/m^2 32.000 19.700 630.400 31,520.000

36.000 17.890 644.040

2 Profil Kuda-kuda 160.65.7,5 1,038.8 kg/m^2 13.743 45.000 618.453 642,461.775

5,890.5 kg 8.950 28.000 250.600 0.043

3 Struktur Baja WF 300.150.6.5.9 8,457.4 kg 8.950 28.000 250.600 33.749

4 Struktur Baja WF 150.100.6.9 645.7 kg

5 Plat Simpul 1,412.8 kg

6 Gording

7 Reng 14.2 kg/m^2 13.743 45.000 618.453 8,782.033

8 Baut 0.05 kg/m^2 13.743 45.000 618.453 30.923

Total Wdk1-Wdk6 682,828.522

682.829

Kuda-kuda type 7

1 Penutup atap 50.0 kg/m^2 3.200 8.100 25.920 1,296.000

2 Profil Kuda-kuda 75.40.2 549.8 kg/m^2 3.200 8.100 25.920 14,250.000

3 Reng 14.2 kg/m^2 3.200 8.100 25.920 368.064

4 Baut 0.05 kg/m^2 3.200 8.100 25.920 1.296

Total Wdk7 15,915.360

15.915

Kuda-kuda type 8

1 Penutup atap 50.0 kg/m^2 2.400 8.100 19.440 972.000

2 Profil Kuda-kuda 75. 40. 2 349.2 kg/m^2 2.400 8.100 19.440 6,789.000

3 Reng 14.2 kg/m^2 2.400 8.100 19.440 276.048

4 Baut 0.05 kg/m^2 2.400 8.100 19.440 0.972

Total Wdk8 8,038.020

Kuda-kuda type 9

1 Penutup atap 50.0 kg/m^2 2.400 8.100 19.440 972.000

3 Reng 14.2 kg/m^2 2.400 8.100 19.440 276.048

4 Baut 0.05 kg/m^2 2.400 8.100 19.440 0.972

Total Wdk9 7,225.020

Kuda-kuda type 10

1 Penutup atap 50.0 kg/m^2 3.600 6.000 9.120 456.000

3.600 2.000

3 Reng 14.2 kg/m^2 3.600 6.000 9.120 129.504

3.600 2.000

4 Baut 0.05 kg/m^2 3.600 6.000 9.120 0.456

Total Wdk10 4,164.460

Kuda-kuda type 11

1 Penutup atap 50.0 kg/m^2 3.600 2.000 4.360 218.000

2.000 1.000

2 Profil Kuda-kuda 75. 40. 2 4.4 kg/m^2 3.600 2.000 4.360 19.010

2.000 1.000

3 Reng 14.2 kg/m^2 3.600 2.000 4.360 61.912

2.000 1.000

4 Baut 0.05 kg/m^2 3.600 2.000 4.360 0.218

2.000 1.000

Total Wdk11 299.140

B. BEBAN HIDUP

Beban Air Hujan = 100 kg/m^2

No. Luasan LL Luasan . LL ket

1&6 630.400 100 kg/m^2 63,040 kg/m^2 Wlk1-Wlk6

7 25.920 100 kg/m^2 2,592 kg/m^2 Wlk7

8 19.440 100 kg/m^2 1,944 kg/m^2 Wlk8

9 19.440 100 kg/m^2 1,944 kg/m^2 Wlk9

10 912 100 kg/m^2 91,200 kg/m^2 Wlk10

11 4.360 100 kg/m^2 436 kg/m^2 Wlk11

161,156.0 kg/m^2

161.156 ton/m^2

C. REKAPITULASI BEBAN ATAP

TypeBeban Mati Beban Hidup

Ketkg/m^2 kg/m^2

1s/d 6 682,828.522 63,040 Wk1-wk6

7 15,915.360 2,592 Wk7

8 8,038.020 1,944 Wk8

9 7,225.020 1,944 Wk9

10 4,164.460 91,200 Wk10

11 299.140 436 Wk11

Total 718,470.522 161,156

718.471 ton/m^2 161.16 ton/m^2

Jadi kombinasi beban hidup dan beban mati pada rangka atap adalah

Type 1 s/d 6

W tot Rangka Atap = 1,2*Wd + 1,6*WL

= 819,394 + 100,864.00 kg/m^2

= 920,258.23 kg/m^2

= 920.26 ton/m^2

Type 7 S/d 11

W tot Rangka Atap = 1,2*Wd + 1,6*WL

= 42,770 + 156,985.60 kg/m^2

= 199,756.00 kg/m^2

= 199.76 ton/m^2

Beban Segitiga Pada Atap

h y = 2/3 h

TipeL h y n Qu p

ketm m ton/m^2 ton

1 3.5 1.75 1.1667 1 920.26 1,073.63 Beban terpusat

2 6 3 2 1 920.26 1,840.52 Beban terpusat

3 3.6 7.2 4.8 1 199.76 958.83 Beban terpusat

4 2.4 1.2 0.8 1 199.76 159.80 Beban terpusat

Beban trapesium pada atap

h y = h - (4.h^3 / 3 .L^2)

TipeL h y n Qu q

ketm m ton/m^2 ton

1 45 1.75 1.7465 1 920.26 1,607.2 Beban merata

2 45 3 2.9822 1 920.26 2,744 Beban merata

3 6 1.8 1.584 1 199.76 316 Beban merata

4 6 1.2 1.136 1 199.76 227 Beban merata

PERHITUNGAN TAKABEYA ARAH X

Data -data struktur yang telah diketahui :

Type kolom K1 = 0.4 m x 0.4 m

Type kolom K2 = #REF! m x #REF! m

Tie Beam

Type TB 1 = 0.2 m x 0.4 m

Ring Balk

Dimensi RB1 = 0.2 m x 0.3 m

Type Balok 30/60 = 0.3 m x 0.6 m

Type Balok 30/40 = 0.3 m x 0.4 m

Type Balok 20/40 = 0.2 m x 0.4 m

Type Balok 20/30 = 0.2 m x 0.3 m

Gambar 4.1 Denah Portal Tinjauan

Gambar 4.2 Portal Tinjauan Arah Y

NB: Untuk mempermudah perhitungan maka portal tinjauan arah y akan dibagi menjadi 2 bagian, sehingga hasil perhitungan portal sisi kiri sama dengan hasil perhitungan pada sisi kanan.

Gambar 4.3 Skema Joint

Perhitungan inersia Kolom dan balok

Inersia

a. Inersia Kolom

No. Type kolom Dimensi Inersia

Kekakuanb x h

1 Type kolom K1 40.000 x 40 0.0833 213,333.333 0.5333

2 Type kolom K2 #REF! x #REF! 0.0833 #REF! #REF!

b. Inersia Tie Beam

No. Type Tie BeamDimensi Inersia

Kekakuanb x h

1 Type TB 1 20.000 x 40.00 0.0833 106,666.667 0.0762

c. Inersia Ring Balk

No. Type Ring BalkDimensi Inersia

Kekakuanb x h

1 Dimensi RB1 20.000 x 30 0.0833 45,000.000 0.0321

d. Inersia Balok

No. Type BalokDimensi Inersia

Kekakuanb x h

1 Type Balok 30/60 30.000 x 60 0.0833 540,000.000 0.3857

2 Type Balok 30/40 30.000 x 40 0.0833 160,000.000 0.1143

3 Type Balok 20/40 20.000 x 40 0.0833 106,666.667 0.0762

Perhitungan Momen Primer

== -0.0833333333 x 8188.432512 x 16.000 - 0.125 x 5,792.464 x= (10,917.9) - 2,896 = (13,814.1) kgm = (13.8) tm

== -0.0833333333 x 8188.432512 x 16.000 - 0.125 x 5,792.464 x= (10,917.9) - 2896.232= (13,814.1) kgm = (13.8) tm

== -0.0833333333 x 8188.432512 x 16.000 - 0.125 x 5,792.464 x= (10,917.9) - 2896.232= (13,814.1) kgm = (13.8) tm =

= -1/12 x qL2 - 1/8 PL= -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x= (3,643.2) - 2055.116= (5,698.4) kgm = (5.7) tm =

== -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x= (3,643.2) - 2055.116= (5,698.4) kgm = (5.7) tm

Mf1-2 -1/12 x qL2 - 1/8 PL

-Mf1-2

Mf2-3 -1/12 x qL2 - 1/8 PL

-Mf2-3

Mf3-4 -1/12 x qL2 - 1/8 PL

-Mf3-4

Mf4-5 -1/12 x qL2 - 1/8 PL

-Mf7-6

-Mf8-7

Mf9-8 -1/12 x qL2 - 1/8 PL

-Mf9-8

Mf9-10 -1/12 x qL2 - 1/8 PL

Mf10-9

-Mf9-10

Mf11-12 -1/12 x qL2 - 1/8 PL

Mf12-11

-Mf11-12

Mf12-13 -1/12 x qL2 - 1/8 PL

= -1/12 x qL2 - 1/8 PL= -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x= (3,643.2) - 2,055.12 = (5,698.4) kgm = (5.7) tm

= -1/12 x qL2 - 1/8 PL= -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x= (3,643.2) - 2055.12= (5.7) Tm

= -0.0833333333 x 523.26082177 x 16.000 = (697.7)= (0.698) kgm =

== -0.0833333333 x 523.26082177 x 16.000 = (697.7)= (0.698) tm =

= -1/12 x qL2 = -0.08333333 x 523.2608218 x 16.000 = (697.7)= (0.698) tm =

= -1/12 x qL2 = -0.0833333333 x 523.2608218 x 16.000 = -697.6810957= -0.698 tm

Mf13-12

-Mf12-13

Mf13-14

Mf14-13

-Mf13-14

Mf14-15

Mf15-14

-Mf14-15

Mf16-17 -1/12 x qL2

Mf17-16

-Mf16-17

Mf17-18 -1/12 x qL2

Mf18-17

-Mf17-18

Mf18--19

Mf19-18

-Mf18-19

Mf19-20

Mf20-19

Mf19-20

No. Batang Nilai Batang Nilai

1 -13.814 13.81

2 -13.814 13.81

3 -13.814 13.81

4 -13.814 13.81

5 -5.698 5.70

6 -5.698 5.70

7 -5.698 5.70

8 -5.698 5.70

9 -5.698 5.70

10 -5.698 5.70

11 -5.698 5.70

12 -5.698 5.70

13 -0.698 0.698

14 -0.698 0.698

15 -0.698 0.698

16 -0.698 0.698

T1 = +

T Nilai ρ Nilai

-13.814 1.219

0.000 1.371

8.116 0.152

0.000 0.152

0.000 2.438

-5.698 2.286

0.000 2.438

5.001 0.152

0.000 0.064

0.000 1.195

-5.698 1.131

Perhitungan nilai γ

Joint 1

= = 0.076 = 0.063 ρ1 1.219

= = 0.533 = 0.438 ρ1 1.219

0.500 oke!

Joint 2

= = 0.076 = 0.056 ρ2 1.371

= = 0.5333 = 0.389 ρ2 1.371

M11-12

M12-11

M12-13

M13-12

M13-14

M14-13

M14-15

M15-14

M16-17

M17-16

M17-18

M18-17

M18-19

M19-19

M19-20

M20-19

Perhitungan Nilai T,ρMf 1 - 2 Mf 1 - 6

T10 ρ

T11 ρ

T12 ρ

T13 ρ

T14 ρ

T15 ρ

T16 ρ

T17 ρ

T18 ρ18

T19 ρ

T20 ρ

γ1-10

γ2--1

γ2--9

0.500 oke!

Joint 3

= = 0.076 = 0.056 ρ3 1.371

= = 0.5333 = 0.389 ρ3 1.371

0.500 oke!

Joint 4

= = 0.076 = 0.056 oke!ρ4 1.371

= = 0.076 = 0.056 ρ4 1.371

= = 0.533 = 0.389 ρ4 1.371

0.500 oke!Joint 5

= = 0.076 = 0.500 oke!ρ5 0.152

Joint 6

= = 0.076 = 0.500 ρ6 0.152

0.500 oke!

Joint 7

= = 0.076 = 0.031 ρ7 2.438

= = 0.533 = 0.219 ρ7 2.438

0.500 oke!

Joint 8

= = 0.076 = 0.031 ρ8 2.438

= = 0.533 = 0.219 ρ8 2.438

0.500 oke!

K4-3γ

K4-7γ

K5-6γ

K6-5γ

γ7-14

γ8-13

Joint 9

= = 0.533 = 0.219 ρ9 2.438

= = 0.076 = 0.031 ρ9 2.438

0.500 oke!

Joint 10

= = 0.076 = 0.033 ρ10 2.286

= = 0.533 = 0.233 ρ10 2.286

0.500 oke!

Joint 11

= = 0.076 = 0.033 ρ11 2.286

= = 0.533 = 0.233 ρ11 2.286

0.500 oke!

Joint 12

= = 0.076 = 0.031 ρ12 2.438

= = 0.533 = 0.219 ρ12 2.438

= = 0.076 = 0.031 ρ12 2.438

= = 0.533 = 0.219 ρ12 2.438

0.500 oke!

Joint 13

= = 0.076 = 0.031 ρ13 2.438

= = 0.533 = 0.219 ρ13 2.438

0.500 oke!

γ9-12

γ9-10

γ10-9

γ10-11

K10-11

γ10-1

γ11-12

K11-12

γ11-10

K11-10

γ11-20

K11-16

γ12-11

K12-11

γ12-19

K12-19

γ12-13

K12-13

γ12-9

γ13-14

K13-14

γ13-12

K13-12

γ13-8

γ13-18 K13-14

Joint 14

= = 0.076 = 0.031ρ14 2.438

= = 0.533 = 0.219ρ14 2.438

0.500 oke!

Joint 15

= = 0.076 = 0.500 oke!ρ15 0.152

Joint 16

= = 0.032 = 0.500 oke!ρ16 0.064

Joint 17

= = 0.032 = 0.027 ρ17 1.195

= = 0.533 = 0.446 ρ17 1.195

= = 0.032 = 0.027 ρ17 1.195

0.500 oke!

Joint 18

= = 0.032 = 0.027 ρ18 1.195

= = 0.533 = 0.446 ρ18 1.195

= = 0.032 = 0.027 ρ18 1.195

0.500 oke!

Joint 19

= = 0.032 = 0.027

= = 0.533 = 0.446

= = 0.032 = 0.027

1.195 0.500 oke!

Joint 20

= = 0.533 = 0.472

= = 0.032 = 0.028

1.131 0.500 oke!

γ14-15

K14-15

γ14-13

K14-13

γ14-7

γ14-17

K14-11

γ15-14

K15-14

γ16-17

K16-17

γ17-16 K17-18

γ17-14

K17-14

γ17-18

K17-18

γ18-17

K17-18

γ18-13

K18-13

γ18-19

K18-19

γ18-17

K17-18

γ18-13

K18-13

γ18-19

K18-19

γ20-11

K20-11

γ20-19

K20-19

PERHITUNGAN MOMEN ROTASI

M1 = -Mf / ρ1

= 13.8141.219

= 11.332 ton

No. Momen Nilai

1 M1 11.332

2 M2 0.000

3 M3 0.000

4 M4 0.000

5 M5 -53.260

6 M6 0.000

7 M7 0.000

8 M8 0.000

9 M9 0.000

10 M10 2.493

11 M11 2.493

12 M12 0.000

13 M13 0.000

14 M14 0.000

15 M15 -32.817

16 M16 0.000

17 M17 0.000

18 M18 0.000

19 M19 0.000

20 M20 5.039

Menentukan nilai T

= 2 x ( 0.533 + 0.533 + 0.533 + 0.533 )

= 4.2667

T2 = 2 x ( 0.5 + 0.533 + 0.533 + 0.533 )

= 4.2667

T3 = 2 x ( 0.5 + 0.533 + 0.533 + 0.533 )

= 4.2667

2*(K1-10

2-9+ K

3-8+ K

2*(K10-11

+ K9-12

+ K6-13+

2*(K11-20

+ K12-19

+ K13-18+

K14+17

Perhitungan nilai t

= 0.375

No. t Nilai

1 0.375

2 0.375

3 0.375

4 0.375

5 0.375

6 0.375

7 0.375

8 0.375

9 0.375

10 0.375

11 0.375

12 0.375

13 0.375

14 0.375

15 0.375

16 0.375

Perhitungan Momen Displacment belum dihtungArah y

Combination Load (Beban Angin )

No. Lantai h Beban Angin Beban Gempa Beban Displacement1 3 3.600 0.80 0.802 2 4.000 0.70 0.703 1 3.500 0.70 0.70

Pemberesan Momen Displacement 3.500

Arah y =

M1 = -h1(∑W) =

T1 = = -3.500 x ( 2.20 )

4.2667= -1.805

M2 = -h2(∑W) =

= -4.000 x ( 1.50 ) = 4.2667

= -1.406

M3 = -h3(∑W) =

= -3.600 x ( 0.80 ) = 4.2667

= -0.675

3.(K1-10

MI (1) MI (0)

(-t1-8

) x (M1( I ) + M8(I) )

(-t2-7

) x (M2( I ) + M7(I) )

(-t3-6

) x (M3( I ) + M6(I) )

MII(1) MII (0)

(-t8-9

) x (M8( I ) + M9(I) )

(-t7-10

) x (M7( I )+ M10(I))

(-t6-11) x (M6( I )+ M11(I))

MIII(1) MIII (0)

(-t9-16

) x (M9( I ) + M16(I) )

(-t10-15

) x (M10( I )+ M15(I))

(-t6-11) x (M6( I )+ M11(I))

Perhitungan Momen parsil

Putaran 0

MI = MI(0) = 11.3 = 11.332 = γ 1 - 2 x M2 = (0.063) x 0.389 = (0.024)= γ 1 - 8 x MD 1+M8(0) = (0.438) x (1.805) = 0.790 +

MI 12.097

M2 = M2(0) = - = - = γ 2 - 1 x M1(1) = (0.056) x 12.097 = (0.672)= γ 2 - 3 x M3(0) = (0.056) x - = - = γ 2 - 7 x MD 1+M7(0) = (0.389) x (1.805) = 0.702 +

M2 0.030

M3 = M3(0) = - = - = γ 3-2 x M2(1) = (0.056) x 0.030 = (0.002)= γ 3-4 x M4(0) = (0.056) x - = - = γ 3-6 x MD 1+M6 = (0.389) x (1.805) = 0.702 +

M3 0.700

M4 = M4(0) = - = - = γ 4-3 x M4(1) = (0.056) x 0.700 = (0.039) +

M4 (0.039)

M5 = M4(0) = (53.3) = (53.260)= γ 5-6 x M5(1) = (0.500) x (0.039) = 0.019 +

M5 (53.240)

M6 = M6(0) = - = - = γ 6-7 x M7(1) = #REF! x - = #REF!= γ 6-5 x M5(1) = #REF! x (53.240) = #REF!= γ 6-11 x MD 2+M11 = #REF! x 1.087 = #REF!= γ 6-3 x MD 1+M3(1) = #REF! x (1.105) #REF! +

M6 #REF!

M7 = M7(0) = - = - = γ 7-6 x M6(1) = (0.031) x - = - = γ 7-8 x 8(1) = (0.031) x - = - = γ 7-11 x MD 2+M11 = (0.219) x #REF! = #REF!= γ7-2 x MD 1+M2(1) = (0.219) x (1.785) #REF! +

M7 #REF!

M8 = M8(0) = - = - = γ 8-7 x M7(1) = (0.031) x #REF! = #REF!= γ 8-1 x MD 1+ M1(1) = (0.031) x 10.292 = (0.322)= γ8-9 x MD 2+M1(1) = (0.219) x (1.376) = 0.301 +

M8 #REF!

M9 = M9(0) = - = - = γ 9-10 x M10(0) = (0.031) x 2.493 = (0.078)= γ 9-8 x MD 2+ M8(1) = (0.219) x #REF! = #REF!= γ9-16 x MD 3+M16(0) = (0.219) x (0.675) = 0.148 +

M9 #REF!

M10 = M10(0) = 2.5 = 2.493 = γ 10-9 x M9(1) = (0.033) x #REF! = #REF!= γ 10-11 x M11(0) = (0.233) x 2.493 = (0.582)= γ 10-7 x MD 2+M7(1) = #REF! x #REF! = #REF!= γ10-15 x MD 3+M15(0) = (0.219) x (33.492) #REF! +

M10 #REF!

M11 = M11(0) = 2.5 = 2.493 = γ 11-12 x M12(0) = (0.033) x - = - = γ 11-10 x M10(1) = (0.233) x #REF! = #REF!= γ 11-14 x MD 3+M14(0) = #REF! x (0.675) = #REF!= γ11-6 x MD 2+M6(1) = (0.233) x #REF! = #REF! +

M11 #REF!

M12 = M12(0) = - = - = γ 12-11 x M11(1) = (0.031) x #REF! = #REF! +

M12 #REF!

M13 = M13(0) = - = - = γ 13-14 x M14(0) = (0.031) x - = - +

M14 = M14(0) = - = - = γ 14-13 x M13(1) = (0.031) x - = - = γ 14-15 x M15(0) = (0.031) x (32.817) = 1.026 = γ 14-11 x MD 3+M11(1) = (0.219) x #REF! = #REF!= γ 14-19 x MD 4+M19(0) = (0.219) x #REF! #REF! +

M14 #REF!

M15 = M15(0) = (32.8) = (32.817)= γ 15-14 x M14(1) = (0.500) x #REF! = #REF!= γ 15-16 x M16(0) = #REF! x - = #REF!= γ 15-18 x MD 4+M18(0) = #REF! x #REF! = #REF!= γ 15-10 x MD 3+M10(1) = #REF! x #REF! #REF! +

M15 #REF!

M16 = M16(0) = - = - = γ 16-15 x M15(1) = #REF! x #REF! = #REF!= γ 16-9 x MD 3+ M9(1) = (0.500) x #REF! = #REF! +

M16 #REF!

M17 = M17(0) = - = - = γ 17-18 x M18(0) = (0.027) x - = - = γ 17-c x MD 3 + Mc(0) = (0.446) x (33.492) = 14.945 +

M17 14.945

M18 = M18(0) = - = - = γ 18-17 x M17(1) = (0.027) x 14.945 = (0.402)= γ 18-19 x M19(0) = (0.223) x - = - = γ18-15 x MD 4+M15(1) = (0.223) x #REF! = #REF! +

M18 #REF!

M19 = M19(0) = - = - = γ 19-18 x M18(1) = (0.027) x #REF! = #REF!= γ 19-20 x M20(0) = (0.223) x - = - = γ19-14 x MD 4+M14(1) = (0.223) x #REF! = #REF! +

M19 #REF!

M20 = M20(0) = 6.7 = 6.674 = γ 20-19 x M19(1) = (0.027) x #REF! = #REF!= γ20-13 x MD 4+M14(1) = (0.446) x #REF! = #REF! +

M20 #REF!

PERHITUNGAN MOMEN DESAIN

Joint 1

M1-2 = K 1-2 x + Mf1-2 = 0.076 x #REF! +

M1-8 = K 1-8 x + Mf1-8 = 0.533 x #REF! +

Joint 2

M2-1 = K 2-1 x + Mf2-1 = 0.076 x #REF! +

M2-3 = K 2-3 x + Mf2-3 = 0.076 x #REF! +

M2-7 = K 2-7 x + Mf2-7 = 0.533 x #REF! +

Joint 3

M3-2 = K 3-2 x + Mf3-2 = 0.076 x #REF! +

M3-4 = K 3-4 x + Mf3-4 = 0.076 x #REF! +

M3-6 = K 3-6 x + Mf3-6 = 0.533 x #REF! +

Joint 4

M4-3 = K 4-3 x + Mf4-3 = 0.076 x #REF! +

Joint 5

M5-6 = K 5-6 x + Mf5-6 = #REF! x #REF! +

Joint 6

M6-5 = K 6-5 x + Mf6-5 = #REF! x #REF! +

M6-7 = K 6-7 x + Mf6-7 = #REF! x #REF! +

M6-3 = K 6-3 x + Mf6-3 = 0.533 x #REF! +

M6-11 = K 6-11 x + Mf6-11 = #REF! x #REF! +

Joint 7

M7-6 = K 7-6 x + Mf7-6 = #REF! x #REF! +

M7-8 = K 7-8 x + Mf7-8 = #REF! x #REF! +

M7-2 = K 7-2 x + Mf7-2 = 0.533 x #REF! +

M7-11 = K 7-11 x + Mf7-11 = #REF! x #REF! +

Joint 8

M8-7 = K 8-7 x + Mf8-7 = #REF! x #REF! +

M8-9 = K 8-9 x + Mf8-9 = #REF! x #REF! +

M8-1 = K 8-1 x + Mf8-1 = 0.533 x #REF! +

Joint 9

M9-10 = K 9-10 x + Mf9-10 = #REF! x #REF! +

M9-8 = K 9-8 x + Mf9-8 = #REF! x #REF! +

M9-16 = K 9-16 x + Mf9-16 = #REF! x #REF! +

Joint 10

M10-11 = K 10-11 x + Mf10-11 = #REF! x #REF! +

M10-9 = K 10-9 x + Mf10-9 = #REF! x #REF! +

M10-7 = K 10-7 x + Mf10-7 = #REF! x #REF! +

M10-15 = K 10-15 x + Mf10-15 = #REF! x #REF! +

Joint 11

M11-10 = K 11-10 x + Mf11-10 = #REF! x #REF! +

M11-12 = K 11-12 x + Mf11-12 = #REF! x #REF! +

M11-6 = K 11-6 x + Mf11-6 = #REF! x #REF! +

M11-14 = K 11-14 x + Mf11-14 = #REF! x #REF! +

Joint 12

M12-11 = K 12-11 x + Mf12-11 = #REF! x #REF! +

Joint 13

M13-14 = K 13-14 x + Mf12-11 = #REF! x #REF! +

{ 2M1(k) + M2(k) }

{2M1(k) + M8(k) }

{ 2M2(k) + M1(k) }

{2M2(k) + M3(k) }

{2M2(k) + M7(k) }

{ 2M3(k) + M2(k) }

{2M3(k) + M4(k) }

{2M3(k) + M6(k) }

{ 2M4(k) + M3(k) }

{ 2M5(k) + M6(k) }

{ 2M6(k) + M5(k) }

{2M6(k) + M7(k) }

{2M6(k) + M3(k) }

{2M6(k) + M11(k) }

{ 2M7(k) + M6(k) }

{2M7(k) + M8(k) }

{2M7(k) + M2(k) }

{2M7(k) + M11(k) }

{ 2M8(k) + M7(k) }

{2M8(k) + M9(k) }

{2M8(k) + M1(k) }

{ 2M9(k) + M10(k) }

{2M9(k) + M8(k) }

{2M9(k) + M16(k) }

{ 2M10(k) + M11(k) }

{2M10(k) + M9(k) }

{2M10(k) + M7(k) }

{2M10(k) + M15(k) }

{ 2M11(k) + M10(k)}

{2M11(k) + M12(k) }

{2M11(k) + M6(k) }

{2M11(k) + M14(k) }

{ 2M12(k) + M11(k)}

{ 2M13(k) + M14(k)}

Joint 14

M14-13 = K 14-13 x + Mf14-13 = #REF! x #REF! +

M14-15 = K 14-15 x + Mf14-15 = #REF! x #REF! +

M14-19 = K 14-19 x + Mf114-19 = 0.076 x #REF! +

M14-11 = K 14-11 x + Mf14-11 = #REF! x #REF! +

Joint 15

M15-14 = K 15-14 x + Mf15-14 = #REF! x #REF! +

M15-16 = K 15-16 x + Mf15-16 = #REF! x #REF! +

M15-10 = K 15-10 x + Mf15-10 = 0.076 x #REF! +

M15-18 = K 15-19 x + Mf15-19 = #REF! x #REF! +

Joint 16

M16-15 = K 16-15 x + Mf1-2 = #REF! x #REF! +

M16-9 = K 16-9 x + Mf1-8 = #REF! x #REF! +

Joint 17

M17-18 = K 17-18 x + Mf17-18 = 0.032 x #REF! +

M17-c = K 17-c x + Mf17-c = #REF! x #REF! +

Joint 18

M18-17 = K 18-17 x + Mf18-17 = 0.032 x #REF! +

M18-19 = K 18-19 x + Mf18-19 = 0.032 x #REF! +

M18-15 = K 18-14 x + Mf18-14 = #REF! x #REF! +

Joint 19

M19-18 = K 19-18 x + Mf19-18 = 0.032 x #REF! +

M19-20 = K 19-20 x + Mf19-20 = 0.032 x #REF! +

M19-14 = K 19-13 x + Mf19-13 = #REF! x #REF! +

Joint 20

M20-19 = K 20-19 x + Mf20-19 = 0.032 x #REF! +

M20-13 = K 20-13 x + Mf20-13 = #REF! x #REF! +

KOREKSI MOMEN DESAIN

No. Joint Momen desain ∑M K ∑K K/∑ ∆M

1M1-2 #REF!

#REF!0.08

0.6100.125 #REF! ###

#REF!M1-8 #REF! 0.53 0.875 #REF! ###

M2-1 #REF!

0.08 0.111 #REF! ###

#REF!M2-3 #REF! 0.08 0.686 0.111 #REF! ###

M2-7 #REF! 0.53 0.778 #REF! ###

M3-2 #REF!

0.08 0.111 #REF! ###

#REF!M3-4 #REF! 0.08 0.686 0.111 #REF! ###

M3-6 #REF! 0.53 0.778 #REF! ###

4 #REF!M4-3 #REF! 0.08 0.076 1.000 #REF! ### #REF!

5 #REF!M5-6 #REF! #REF! ### #REF! #REF! ### #REF!

M6-5 #REF!

#REF! #REF! #REF! ###

#REF!M6-7 #REF! #REF! #REF! #REF! ###

M6-3 #REF! 0.53 ### #REF! #REF! ###

M6-11 #REF! #REF! #REF! #REF! ###

{ 2M14(k) + M13(k)}

{2M14(k) + M15(k) }

{2M14(k) + M19(k) }

{2M14(k) + M11(k) }

{ 2M15(k) + M14(k)}

{2M15(k) + M16(k) }

{2M15(k) + M110(k) }

{2M15(k) + M19(k) }

{ 2M16(k) + M15(k) }

{2M16(k) + M9(k) }

{ 2M17(k) + M18(k) }

{2M17(k) + Mc(k) }

{ 2M18(k) + M17(k) }

{2M18(k) + M19(k) }

{2M18(k) + M14(k) }

{ 2M19(k) + M18(k) }

{2M19(k) + M20(k) }

{2M19(k) + M13(k) }

{ 2M20(k) + M13(k) }

{2M20(k) + M13(k) }

K /∑K*∆M

Koreksi Mo

M7-6 #REF!

#REF! #REF! ###

M7-2 #REF! 0.53 #REF! #REF! ###

M7-11 #REF! #REF! #REF! #REF! ###

M8-7 #REF!

#REF!M8-9 #REF! #REF! ### #REF! #REF! ###

M8-1 #REF! 0.53 #REF! #REF! ###

M9-10 #REF!

M9-16 #REF! #REF! #REF! #REF! ###

M10-11 #REF!

#REF! #REF! ###

M10-7 #REF! #REF! #REF! #REF! ###

M10-15 #REF! #REF! #REF! #REF! ###

M11-10 #REF!

M11-6 #REF! #REF! ### #REF! #REF! ###

M11-14 #REF! #REF! #REF! #REF! ###

12 M12-11 #REF! #REF! #REF! ### #REF! #REF! ### #REF!

13 #REF!M13-14 #REF! #REF! ### #REF! #REF! ### #REF!

M14-13 #REF!

#REF! #REF! ###

M14-19 #REF! 0.08 #REF! #REF! ###

M14-11 #REF! #REF! #REF! #REF! ###

M15-14 #REF!

#REF! #REF! ###

M15-10 #REF! 0.08 #REF! #REF! ###

M15-18 #REF! #REF! #REF! #REF! ###

16M16-15 #REF!

#REF!#REF!

####REF! #REF! ###

17M17-18 #REF!

#REF!0.03

####REF! #REF! ###

#REF!M17-c #REF! #REF! #REF! #REF! ###

M18-17 #REF!

#REF! #REF! ###

#REF!M18-19 #REF! 0.03 #REF! #REF! ###

M18-15 #REF! #REF! #REF! #REF! ###

M19-18 #REF!

#REF! #REF! ###

#REF!M19-20 #REF! 0.03 #REF! #REF! ###

M19-14 #REF! #REF! #REF! #REF! ###

20M20-19 #REF!

#REF!0.03

####REF! #REF! ###

FREE BODY DIAGRAM BALOK

P1 P22 P1ba c d

∑`RA ∑`RB∑`RA ∑`RB

No. JointM.Desain

q p1 p2 L RA RB RM x-y RM y-x ∑R'AStlh Koreksi

1 M1-2 #REF! 8.188 #REF! #REF! 12 #REF! ### #REF! #REF! #REF!

2 M2-1 #REF! 8.188 #REF! #REF! 12 #REF! ### #REF! #REF! #REF!

3 M2-3 #REF! #REF! #REF! - 8 #REF! ### #REF! #REF! #REF!

5 M3-4 #REF! #REF! - - 4 #REF! ### #REF! #REF! #REF!

11 M7-8 #REF! 2.732 2.055 2.1 12 18.450 ### #REF! #REF! #REF!

12 M8-7 #REF! 2.732 2.055 2.1 12 18.450 ### #REF! #REF! #REF!

13 M9-10 #REF! 2.732 2.055 2.1 12 18.450 ### #REF! #REF! #REF!

15 M10-9 #REF! 2.732 2.055 2.1 12 18.450 ### #REF! #REF! #REF!

23 M15-16 #REF! 2.732 1.028 1.0 12 17.422 ### #REF! #REF! #REF!

24 M16-15 #REF! 2.732 1.028 1.0 12 17.422 ### #REF! #REF! #REF!

25 M17-18 #REF! 0.523 - - 8 2.093 ### #REF! #REF! #REF!

26 M18-17 #REF! 0.523 - - 8 2.093 ### #REF! #REF! #REF!

27 M18-19 #REF! 0.523 - - 4 1.047 ### #REF! #REF! #REF!

28 M19-18 #REF! 0.523 - - 4 1.047 ### #REF! #REF! #REF!

29 M19-20 #REF! 0.523 - - 4 1.047 ### #REF! #REF! #REF!

30 M20-19 #REF! 0.523 - - 4 1.047 ### #REF! #REF! #REF!

RA = P2/3 + 2P1/3 + 1/2qL

RA = P1/3 + 2P2/3 + 1/2qL

RM x-y = M x-y /L

RM y-x = - M y-x /L

RM y-x = -M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

ba c da b

RA = P2/3 + 2P1/3 + 1/2qL

RA = P1/3 + 2P2/3 + 1/2qL

RM x-y = M x-y /L

RM y-x = - M y-x /L

RM y-x = -M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

ba c da b

FREE BODY DIAGRAM KOLOM

RM x-y= Mx-y / L

RM y-x= Mx-y / L

RM x-y= Mx-y / L

No. Joint h M desain RMx-y/L RMy-x/L ∑RA ∑RB Da Kanan

1 M1-8 5 #REF! #REF! ### #REF! #REF! #REF!

(13.8)

0.0∑M

13.8 ∑M

5.7 ∑M

0.0∑M

-13.8∑M

∑`RB

∑R'B

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

Da kanan

= -1.8046875 = -1.80 -1.8046875

= (0.38) x #REF! = #REF! (0.38) x

= (0.38) x #REF! = #REF! (0.38) x#REF!

= -1.40625 = -1.41 -1.40625

= (0.38) x #REF! = #REF! (0.38) x

= (0.38) x (0.3) = 0.12 (0.38) x

= (0.38) x #REF! = #REF! (0.38) x#REF!

= -0.675 = -0.68 -0.675

= (0.38) x #REF! = #REF! (0.38) x

= (0.38) x #REF! = #REF! (0.38) x#REF!

Putaran 1 Putaran 2

11.3 = 11.332 11.3 (0.063) x 0.0 = (0.002) (0.063) x #REF! (0.438) x #REF! = #REF! (0.438) x #REF!

MI #REF! MI

- = - - (0.056) x #REF! = #REF! (0.056) x #REF! (0.056) x 0.7 = (0.039) (0.056) x #REF! (0.389) x #REF! = #REF! (0.389) x #REF!

M2 #REF! M2

- = - - (0.056) x #REF! = #REF! (0.056) x #REF! (0.056) x (0.0) = 0.002 (0.056) x #REF! (0.389) x #REF! = #REF! (0.389) x #REF!

M3 #REF! M3

- = - - (0.056) x #REF! = #REF! (0.056) x #REF!

M4 #REF! M4

(53.3) = (53.260) (53.3) (0.500) x #REF! = #REF! (0.500) x #REF!

M5 #REF! M5

- = - - #REF! x #REF! = #REF! #REF! x #REF!#REF! x #REF! = #REF! #REF! x #REF!#REF! x #REF! = #REF! #REF! x #REF!#REF! x #REF! #REF! #REF! x #REF!

M6 #REF! M6

- = - - (0.031) x #REF! = #REF! (0.031) x #REF! (0.031) x #REF! = #REF! (0.031) x #REF! (0.219) x #REF! = #REF! (0.219) x #REF! (0.219) x #REF! #REF! (0.219) x #REF!

M7 #REF! M7

- = - - (0.031) x #REF! = #REF! (0.031) x #REF! (0.031) x #REF! = #REF! (0.031) x #REF! (0.219) x #REF! = #REF! (0.219) x #REF!

M8 #REF! M8

- = - - 0.031 x #REF! = #REF! 0.031 x #REF! 0.219 x #REF! = #REF! 0.219 x #REF! 0.219 x #REF! = #REF! 0.219 x #REF!

M9 #REF! M9

2.5 = 2.493 2.5 (0.033) x #REF! = #REF! (0.033) x #REF! (0.233) x #REF! = #REF! (0.233) x #REF!

#REF! x #REF! = #REF! #REF! x #REF! (0.219) x #REF! #REF! (0.219) x #REF!

M10 #REF! M10

M11 #REF! M11

- = - - (0.031) x #REF! = #REF! (0.031) x #REF!

M12 #REF! #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x #REF!

M13 #REF! M13

M14 #REF! M14

(32.8) = (32.817) (32.8) (0.500) x #REF! = #REF! (0.500) x #REF!

#REF! x #REF! = #REF! #REF! x #REF!#REF! x #REF! = #REF! #REF! x #REF!#REF! x #REF! #REF! #REF! x #REF!

M15 #REF! M15

- = - - #REF! x #REF! = #REF! #REF! x #REF!

(0.500) x #REF! = #REF! (0.500) x #REF!M16 #REF! M16

- = - - (0.027) x #REF! = #REF! (0.027) x #REF! (0.446) x #REF! = #REF! (0.446) x #REF!

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

M20 #REF! M20

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! +

= #REF!= #REF!

= #REF!

= #REF! +

= #REF!= #REF!

= #REF! + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! +

= #REF!= #REF!

= #REF!

= #REF! +

= #REF!= #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! +

= #REF!= #REF!

= #REF!

= #REF! +

= #REF!= #REF!

= #REF!

= #REF! + = #REF!

∑`RB

R'A Da kanan Db kiri Db kanan Dc kiri Dc kanan Dd kiri Dd kanan

#REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

#REF! #REF! #REF! #REF! #REF! #REF!

= -1.80 -1.804688 = -1.80 -1.804688

#REF! = #REF! (0.38) x #REF! = #REF! (0.38)

#REF! = #REF! (0.38) x #REF! = #REF! (0.38)#REF! #REF!

= -1.41 -1.40625 = -1.41 -1.40625

#REF! = #REF! (0.38) x #REF! = #REF! (0.38)

= -0.68 -0.675 = -0.68 -0.675

#REF! = #REF! (0.38) x #REF! = #REF! (0.38)

Putaran 3 Putaran 4

= 11.3 11.3 = 11.3 11.3 = #REF! (0.063) x #REF! = #REF! (0.063) x = #REF! (0.438) x #REF! = #REF! (0.438) x

#REF! MI #REF!

= - - = - - = #REF! (0.056) x #REF! = #REF! (0.056) x = #REF! (0.056) x #REF! = #REF! (0.056) x= #REF! (0.389) x #REF! = #REF! (0.389) x

#REF! M2 #REF!

#REF! M3 #REF!

= - - = - - = #REF! (0.056) x #REF! = #REF! (0.056) x

#REF! M4 #REF!

= (53.3) (53.3) = (53.3) (53.3)= #REF! (0.500) x #REF! = #REF! (0.500) x

#REF! M5 #REF!

= - - = - - = #REF! #REF! x #REF! = #REF! #REF! x = #REF! #REF! x #REF! = #REF! #REF! x= #REF! #REF! x #REF! = #REF! #REF! x

#REF! #REF! x #REF! #REF! #REF! x#REF! M6 #REF!

#REF! (0.219) x #REF! #REF! (0.219) x#REF! M7 #REF!

#REF! M8 #REF!

= - - = - - = #REF! 0.031 x #REF! = #REF! 0.031 x = #REF! 0.219 x #REF! = #REF! 0.219 x= #REF! 0.219 x #REF! = #REF! 0.219 x

#REF! M9 #REF!

= 2.5 2.5 = 2.5 2.5 = #REF! (0.033) x #REF! = #REF! (0.033) x = #REF! (0.233) x #REF! = #REF! (0.233) x= #REF! #REF! x #REF! = #REF! #REF! x

= - - = - - = #REF! (0.031) x #REF! = #REF! (0.031) x

#REF! #REF! #REF!

= - - = - - = #REF! (0.031) x #REF! = #REF! (0.031) x

#REF! M13 #REF!

= (32.8) (32.8) = (32.8) (32.8)= #REF! (0.500) x #REF! = #REF! (0.500) x = #REF! #REF! x #REF! = #REF! #REF! x= #REF! #REF! x #REF! = #REF! #REF! x

#REF! #REF! x #REF! #REF! #REF! x#REF! M15 #REF!

= - - = - - = #REF! #REF! x #REF! = #REF! #REF! x = #REF! (0.500) x #REF! = #REF! (0.500) x

#REF! M16 #REF!

= - - = - - = #REF! (0.027) x #REF! = #REF! (0.027) x = #REF! (0.446) x #REF! = #REF! (0.446) x

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

= 6.7 6.7 = 6.7 6.7 = #REF! (0.027) x #REF! = #REF! (0.027) x = #REF! (0.446) x #REF! = #REF! (0.446) x

#REF! M20 #REF!

= -1.80 -1.804688 = -1.80

x #REF! = #REF! (0.38) x #REF! = #REF!

x #REF! = #REF! (0.38) x #REF! = #REF!#REF! #REF!

= -1.41 -1.40625 = -1.41

x #REF! = #REF! (0.38) x #REF! = #REF!

= -0.68 -0.675 = -0.68

x #REF! = #REF! (0.38) x #REF! = #REF!

Putaran 5 Putaran 6

= 11.3 11.3 = 11.3 11.3 #REF! = #REF! (0.063) x #REF! = #REF! (0.063)#REF! = #REF! (0.438) x #REF! = #REF! (0.438)

MI #REF! MI #REF!

= - - = - - #REF! = #REF! (0.056) x #REF! = #REF! (0.056)#REF! = #REF! (0.056) x #REF! = #REF! (0.056)#REF! = #REF! (0.389) x #REF! = #REF! (0.389)

M2 #REF! M2 #REF!

M3 #REF! M3 #REF!

= - - = - - #REF! = #REF! (0.056) x #REF! = #REF! (0.056)

M4 #REF! M4 #REF!

= (53.3) (53.3) = (53.3) (53.3)#REF! = #REF! (0.500) x #REF! = #REF! (0.500)

M5 #REF! M5 #REF!

= - - = - - #REF! = #REF! #REF! x #REF! = #REF! #REF!#REF! = #REF! #REF! x #REF! = #REF! #REF!#REF! = #REF! #REF! x #REF! = #REF! #REF!#REF! #REF! #REF! x #REF! #REF! #REF!

M6 #REF! M6 #REF!

= - - = - - #REF! = #REF! (0.031) x #REF! = #REF! (0.031)#REF! = #REF! (0.031) x #REF! = #REF! (0.031)#REF! = #REF! (0.219) x #REF! = #REF! (0.219)#REF! #REF! (0.219) x #REF! #REF! (0.219)

M7 #REF! M7 #REF!

M8 #REF! M8 #REF!

= - - = - - #REF! = #REF! 0.031 x #REF! = #REF! 0.031 #REF! = #REF! 0.219 x #REF! = #REF! 0.219 #REF! = #REF! 0.219 x #REF! = #REF! 0.219

M9 #REF! M9 #REF!

= 2.5 2.5 = 2.5 2.5 #REF! = #REF! (0.033) x #REF! = #REF! (0.033)#REF! = #REF! (0.233) x #REF! = #REF! (0.233)#REF! = #REF! #REF! x #REF! = #REF! #REF!#REF! #REF! (0.219) x #REF! #REF! (0.219)

M10 #REF! M10 #REF!

= 2.5 2.5 = 2.5 2.5 #REF! = #REF! (0.033) x #REF! = #REF! (0.033)#REF! = #REF! (0.233) x #REF! = #REF! (0.233)#REF! = #REF! #REF! x #REF! = #REF! #REF!#REF! #REF! (0.233) x #REF! #REF! (0.233)

M11 #REF! M11 #REF!

= - - = - - #REF! = #REF! (0.031) x #REF! = #REF! (0.031)

#REF! #REF! #REF! #REF!

= - - = - - #REF! = #REF! (0.031) x #REF! = #REF! (0.031)

M13 #REF! M13 #REF!

= - - = - - #REF! = #REF! (0.031) x #REF! = #REF! (0.031)#REF! = #REF! (0.031) x #REF! = #REF! (0.031)#REF! = #REF! (0.219) x #REF! = #REF! (0.219)#REF! #REF! (0.219) x #REF! #REF! (0.219)

M14 #REF! M14 #REF!

= (32.8) (32.8) = (32.8) (32.8)#REF! = #REF! (0.500) x #REF! = #REF! (0.500)#REF! = #REF! #REF! x #REF! = #REF! #REF!#REF! = #REF! #REF! x #REF! = #REF! #REF!#REF! #REF! #REF! x #REF! #REF! #REF!

M15 #REF! M15 #REF!

= - - = - - #REF! = #REF! #REF! x #REF! = #REF! #REF!#REF! = #REF! (0.500) x #REF! = #REF! (0.500)

M16 #REF! M16 #REF!

= - - = - - #REF! = #REF! (0.027) x #REF! = #REF! (0.027)#REF! = #REF! (0.446) x #REF! = #REF! (0.446)

M17 #REF! M17 #REF!

M18 #REF! M18 #REF!

M19 #REF! M19 #REF!

= 6.7 6.7 = 6.7 6.7 #REF! = #REF! (0.027) x #REF! = #REF! (0.027)#REF! = #REF! (0.446) x #REF! = #REF! (0.446)

M20 #REF! M20 #REF!

-1.804688 = -1.80 -1.804688 = -1.80

(0.38) x #REF! = #REF! (0.38) x #REF! = #REF!

(0.38) x #REF! = #REF! (0.38) x #REF! = #REF!#REF! #REF!

-1.40625 = -1.41 -1.40625 = -1.41

(0.38) x #REF! = #REF! (0.38) x #REF! = #REF!

-0.675 = -0.68 -0.675 = -0.68

(0.38) x #REF! = #REF! (0.38) x #REF! = #REF!

Putaran 7

= 11.3 11.3 = 11.3 x #REF! = #REF! (0.063) x #REF! = #REF!x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF! MI #REF!

= - - = - x #REF! = #REF! (0.056) x #REF! = #REF!x #REF! = #REF! (0.056) x #REF! = #REF!x #REF! = #REF! (0.389) x #REF! = #REF!

M2 #REF! M2 #REF!

M3 #REF! M3 #REF!

= - - = - x #REF! = #REF! (0.056) x #REF! = #REF!

M4 #REF! M4 #REF!

= (53.3) (53.3) = (53.3) x #REF! = #REF! (0.500) x #REF! = #REF!

M5 #REF! M5 #REF!

= - - = - x #REF! = #REF! #REF! x #REF! = #REF!x #REF! = #REF! #REF! x #REF! = #REF!x #REF! = #REF! #REF! x #REF! = #REF!x #REF! #REF! #REF! x #REF! #REF!

M6 #REF! M6 #REF!

= - - = - x #REF! = #REF! (0.031) x #REF! = #REF!x #REF! = #REF! (0.031) x #REF! = #REF!x #REF! = #REF! (0.219) x #REF! = #REF!x #REF! #REF! (0.219) x #REF! #REF!

M7 #REF! M7 #REF!

M8 #REF! M8 #REF!

= - - = - x #REF! = #REF! 0.031 x #REF! = #REF!x #REF! = #REF! 0.219 x #REF! = #REF!x #REF! = #REF! 0.219 x #REF! = #REF!

M9 #REF! M9 #REF!

= 2.5 2.5 = 2.5 x #REF! = #REF! (0.033) x #REF! = #REF!x #REF! = #REF! (0.233) x #REF! = #REF!x #REF! = #REF! #REF! x #REF! = #REF!x #REF! #REF! (0.219) x #REF! #REF!

M10 #REF! M10 #REF!

M11 #REF! M11 #REF!

= - - = - x #REF! = #REF! (0.031) x #REF! = #REF!

M13 #REF! M13 #REF!

M14 #REF! M14 #REF!

= (32.8) (32.8) = (32.8) x #REF! = #REF! (0.500) x #REF! = #REF!x #REF! = #REF! #REF! x #REF! = #REF!x #REF! = #REF! #REF! x #REF! = #REF!x #REF! #REF! #REF! x #REF! #REF!

M15 #REF! M15 #REF!

= - - = - x #REF! = #REF! #REF! x #REF! = #REF!x #REF! = #REF! (0.500) x #REF! = #REF!

M16 #REF! M16 #REF!

= - - = - x #REF! = #REF! (0.027) x #REF! = #REF!x #REF! = #REF! (0.446) x #REF! = #REF!

M17 #REF! M17 #REF!

M18 #REF! M18 #REF!

M19 #REF! M19 #REF!

M20 #REF! M20 #REF!

-1.804688 = -1.80 -1.804688 =

(0.38) x #REF! = #REF! (0.38) x #REF! =

(0.38) x #REF! = #REF! (0.38) x #REF! =#REF!

-1.40625 = -1.41 -1.40625 =

(0.38) x #REF! = #REF! (0.38) x #REF! =

(0.38) x #REF! = #REF! (0.38) x #REF! =#REF!

-0.675 = -0.68 -0.675 =

(0.38) x #REF! = #REF! (0.38) x #REF! =

(0.38) x #REF! = #REF! (0.38) x #REF! =#REF!

Putaran 8Putaran 9

11.3 = 11.3 11.3 = 11.3 (0.063) x #REF! = #REF! (0.063) x #REF! = #REF! (0.438) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF! MI #REF!

- = - - = - (0.056) x #REF! = #REF! (0.056) x #REF! = #REF! (0.056) x #REF! = #REF! (0.056) x #REF! = #REF! (0.389) x #REF! = #REF! (0.389) x #REF! = #REF!

M2 #REF! M2 #REF!

M3 #REF! M3 #REF!

- = - - = - (0.056) x #REF! = #REF! (0.056) x #REF! = #REF!

M4 #REF! M4 #REF!

(53.3) = (53.3) (53.3) = (53.3) (0.500) x #REF! = #REF! (0.500) x #REF! = #REF!

M5 #REF! M5 #REF!

- = - - = - #REF! x #REF! = #REF! #REF! x #REF! = #REF!#REF! x #REF! = #REF! #REF! x #REF! = #REF!#REF! x #REF! = #REF! #REF! x #REF! = #REF!#REF! x #REF! #REF! #REF! x #REF! #REF!

M6 #REF! M6 #REF!

- = - - = - (0.031) x #REF! = #REF! (0.031) x #REF! = #REF! (0.031) x #REF! = #REF! (0.031) x #REF! = #REF! (0.219) x #REF! = #REF! (0.219) x #REF! = #REF! (0.219) x #REF! #REF! (0.219) x #REF! #REF!

M7 #REF! M7 #REF!

M8 #REF! M8 #REF!

- = - - = - 0.031 x #REF! = #REF! 0.031 x #REF! = #REF! 0.219 x #REF! = #REF! 0.219 x #REF! = #REF! 0.219 x #REF! = #REF! 0.219 x #REF! = #REF!

M9 #REF! M9 #REF!

#REF! x #REF! = #REF! #REF! x #REF! = #REF! (0.219) x #REF! #REF! (0.219) x #REF! #REF!

M10 #REF! M10 #REF!

#REF! x #REF! = #REF! #REF! x #REF! = #REF! (0.233) x #REF! #REF! (0.233) x #REF! #REF!

M11 #REF! M11 #REF!

- = - - = - (0.031) x #REF! = #REF! (0.031) x #REF! = #REF!

M13 #REF! M13 #REF!

- = - - = - (0.031) x #REF! = #REF! (0.031) x #REF! = #REF! (0.031) x #REF! = #REF! (0.031) x #REF! = #REF! (0.219) x #REF! = #REF! (0.219) x #REF! = #REF! (0.219) x #REF! #REF! (0.219) x #REF! #REF!

M14 #REF! M14 #REF!

(32.8) = (32.8) (32.8) = (32.8) (0.500) x #REF! = #REF! (0.500) x #REF! = #REF!

#REF! x #REF! = #REF! #REF! x #REF! = #REF!#REF! x #REF! = #REF! #REF! x #REF! = #REF!#REF! x #REF! #REF! #REF! x #REF! #REF!

M15 #REF! M15 #REF!

- = - - = - #REF! x #REF! = #REF! #REF! x #REF! = #REF!

(0.500) x #REF! = #REF! (0.500) x #REF! = #REF!M16 #REF! M16 #REF!

- = - - = - (0.027) x #REF! = #REF! (0.027) x #REF! = #REF! (0.446) x #REF! = #REF! (0.446) x #REF! = #REF!

M17 #REF! M17 #REF!

M18 #REF! M18 #REF!

M19 #REF! M19 #REF!

M20 #REF! M20 #REF!

-1.80 -1.804688 = -1.80 -1.804688

#REF! (0.38) x #REF! = #REF! (0.38) x

#REF! (0.38) x #REF! = #REF! (0.38) x#REF! #REF!

-1.41 -1.40625 = -1.41 -1.40625

#REF! (0.38) x #REF! = #REF! (0.38) x

-0.68 -0.675 = -0.68 -0.675

#REF! (0.38) x #REF! = #REF! (0.38) x

Putaran 10

MI #REF! MI

M2 #REF! M2

M3 #REF! M3

- = - - (0.056) x #REF! = #REF! (0.056) x #REF!

M4 #REF! M4

(53.3) = (53.3) (53.3) (0.500) x #REF! = #REF! (0.500) x #REF!

M5 #REF! M5

M6 #REF! M6

M7 #REF! M7

M8 #REF! M8

M9 #REF! M9

M10 #REF! M10

M11 #REF! M11

- = - - (0.031) x #REF! = #REF! (0.031) x #REF!

#REF! #REF! #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x #REF!

M13 #REF! M13

M14 #REF! M14

(32.8) = (32.8) (32.8) (0.500) x #REF! = #REF! (0.500) x #REF!

M15 #REF! M15

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

M20 #REF! M20

= -1.80 -1.804688 = -1.80

#REF! = #REF! (0.38) x #REF! = #REF!

#REF! = #REF! (0.38) x #REF! = #REF!#REF! #REF!

= -1.41 -1.40625 = -1.41

#REF! = #REF! (0.38) x #REF! = #REF!

= -0.68 -0.675 = -0.68

#REF! = #REF! (0.38) x #REF! = #REF!

Putaran 12

= 11.3 11.3 = 11.3 = #REF! (0.063) x #REF! = #REF!= #REF! (0.438) x #REF! = #REF!

#REF! MI #REF!

= - - = - = #REF! (0.056) x #REF! = #REF!= #REF! (0.056) x #REF! = #REF!= #REF! (0.389) x #REF! = #REF!

#REF! M2 #REF!

#REF! M3 #REF!

= - - = - = #REF! (0.056) x #REF! = #REF!

#REF! M4 #REF!

= (53.3) (53.3) = (53.3)= #REF! (0.500) x #REF! = #REF!

#REF! M5 #REF!

= - - = - = #REF! #REF! x #REF! = #REF!= #REF! #REF! x #REF! = #REF!= #REF! #REF! x #REF! = #REF!

#REF! #REF! x #REF! #REF!#REF! M6 #REF!

#REF! (0.219) x #REF! #REF!#REF! M7 #REF!

#REF! M8 #REF!

= - - = - = #REF! 0.031 x #REF! = #REF!= #REF! 0.219 x #REF! = #REF!= #REF! 0.219 x #REF! = #REF!

#REF! M9 #REF!

= 2.5 2.5 = 2.5 = #REF! (0.033) x #REF! = #REF!= #REF! (0.233) x #REF! = #REF!= #REF! #REF! x #REF! = #REF!

= - - = - = #REF! (0.031) x #REF! = #REF!

#REF! #REF! #REF!

= - - = - = #REF! (0.031) x #REF! = #REF!

#REF! M13 #REF!

= (32.8) (32.8) = (32.8)= #REF! (0.500) x #REF! = #REF!= #REF! #REF! x #REF! = #REF!= #REF! #REF! x #REF! = #REF!

= - - = - = #REF! #REF! x #REF! = #REF!= #REF! (0.500) x #REF! = #REF!

#REF! M16 #REF!

= - - = - = #REF! (0.027) x #REF! = #REF!= #REF! (0.446) x #REF! = #REF!

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

#REF! M20 #REF!

-1.804688 = -1.80 -1.804688

(0.38) x #REF! = #REF! (0.38) x #REF!

(0.38) x #REF! = #REF! (0.38) x #REF!#REF!

-1.40625 = -1.41 -1.40625

(0.38) x #REF! = #REF! (0.38) x #REF!

(0.38) x #REF! = #REF! (0.38) x #REF!#REF!

-0.675 = -0.68 -0.675

(0.38) x #REF! = #REF! (0.38) x #REF!

(0.38) x #REF! = #REF! (0.38) x #REF!#REF!

Putaran 13 Putaran 14

11.3 = 11.3 11.3 = (0.063) x #REF! = #REF! (0.063) x #REF! = (0.438) x #REF! = #REF! (0.438) x #REF! =

MI #REF! MI

- = - - = (0.056) x #REF! = #REF! (0.056) x #REF! = (0.056) x #REF! = #REF! (0.056) x #REF! = (0.389) x #REF! = #REF! (0.389) x #REF! =

M2 #REF! M2

M3 #REF! M3

- = - - = (0.056) x #REF! = #REF! (0.056) x #REF! =

M4 #REF! M4

(53.3) = (53.3) (53.3) = (0.500) x #REF! = #REF! (0.500) x #REF! =

M5 #REF! M5

- = - - =#REF! x #REF! = #REF! #REF! x #REF! =#REF! x #REF! = #REF! #REF! x #REF! =#REF! x #REF! = #REF! #REF! x #REF! =#REF! x #REF! #REF! #REF! x #REF!

M6 #REF! M6

- = - - = (0.031) x #REF! = #REF! (0.031) x #REF! = (0.031) x #REF! = #REF! (0.031) x #REF! = (0.219) x #REF! = #REF! (0.219) x #REF! = (0.219) x #REF! #REF! (0.219) x #REF!

M7 #REF! M7

M8 #REF! M8

- = - - = 0.031 x #REF! = #REF! 0.031 x #REF! = 0.219 x #REF! = #REF! 0.219 x #REF! = 0.219 x #REF! = #REF! 0.219 x #REF! =

M9 #REF! M9

#REF! x #REF! = #REF! #REF! x #REF! = (0.219) x #REF! #REF! (0.219) x #REF!

M10 #REF! M10

#REF! x #REF! = #REF! #REF! x #REF! = (0.233) x #REF! #REF! (0.233) x #REF!

M11 #REF! M11

- = - - = (0.031) x #REF! = #REF! (0.031) x #REF! =

#REF! #REF! #REF!

- = - - = (0.031) x #REF! = #REF! (0.031) x #REF! =

M13 #REF! M13

M14 #REF! M14

(32.8) = (32.8) (32.8) = (0.500) x #REF! = #REF! (0.500) x #REF! =

#REF! x #REF! = #REF! #REF! x #REF! =#REF! x #REF! = #REF! #REF! x #REF! =#REF! x #REF! #REF! #REF! x #REF!

M15 #REF! M15

- = - - =#REF! x #REF! = #REF! #REF! x #REF! =

(0.500) x #REF! = #REF! (0.500) x #REF! =M16 #REF! M16

- = - - = (0.027) x #REF! = #REF! (0.027) x #REF! = (0.446) x #REF! = #REF! (0.446) x #REF! =

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

M20 #REF! M20

= -1.80 -1.804688 = -1.80

= #REF! (0.38) x #REF! = #REF!

= #REF! (0.38) x #REF! = #REF!#REF! #REF!

= -1.41 -1.40625 = -1.41

= #REF! (0.38) x #REF! = #REF!

= -0.68 -0.675 = -0.68

= #REF! (0.38) x #REF! = #REF!

Putaran 16

11.3 11.3 = 11.3 11.3 #REF! (0.063) x #REF! = #REF! (0.063)#REF! (0.438) x #REF! = #REF! (0.438)#REF! MI #REF!

- - = - - #REF! (0.056) x #REF! = #REF! (0.056)#REF! (0.056) x #REF! = #REF! (0.056)#REF! (0.389) x #REF! = #REF! (0.389)#REF! M2 #REF!

- - = - - #REF! (0.056) x #REF! = #REF! (0.056)#REF! M4 #REF!

(53.3) (53.3) = (53.3) (53.3)#REF! (0.500) x #REF! = #REF! (0.500)#REF! M5 #REF!

- - = - - #REF! #REF! x #REF! = #REF! #REF!#REF! #REF! x #REF! = #REF! #REF!#REF! #REF! x #REF! = #REF! #REF!#REF! #REF! x #REF! #REF! #REF!#REF! M6 #REF!

- - = - - #REF! (0.031) x #REF! = #REF! (0.031)#REF! (0.031) x #REF! = #REF! (0.031)#REF! (0.219) x #REF! = #REF! (0.219)#REF! (0.219) x #REF! #REF! (0.219)

#REF! M7 #REF!

- - = - - #REF! (0.031) x #REF! = #REF! (0.031)#REF! (0.031) x #REF! = #REF! (0.031)#REF! (0.219) x #REF! = #REF! (0.219)

#REF! M8 #REF!

- - = - - #REF! 0.031 x #REF! = #REF! 0.031 #REF! 0.219 x #REF! = #REF! 0.219 #REF! 0.219 x #REF! = #REF! 0.219

#REF! M9 #REF!

2.5 2.5 = 2.5 2.5 #REF! (0.033) x #REF! = #REF! (0.033)#REF! (0.233) x #REF! = #REF! (0.233)#REF! #REF! x #REF! = #REF! #REF!#REF! (0.219) x #REF! #REF! (0.219)

#REF! M10 #REF!

2.5 2.5 = 2.5 2.5 #REF! (0.033) x #REF! = #REF! (0.033)#REF! (0.233) x #REF! = #REF! (0.233)#REF! #REF! x #REF! = #REF! #REF!#REF! (0.233) x #REF! #REF! (0.233)

#REF! M11 #REF!

- - = - - #REF! (0.031) x #REF! = #REF! (0.031)

#REF! #REF! #REF!

- - = - - #REF! (0.031) x #REF! = #REF! (0.031)

#REF! M13 #REF!

#REF! M14 #REF!

(32.8) (32.8) = (32.8) (32.8)#REF! (0.500) x #REF! = #REF! (0.500)#REF! #REF! x #REF! = #REF! #REF!#REF! #REF! x #REF! = #REF! #REF!#REF! #REF! x #REF! #REF! #REF!

#REF! M15 #REF!

- - = - - #REF! #REF! x #REF! = #REF! #REF!#REF! (0.500) x #REF! = #REF! (0.500)

#REF! M16 #REF!

- - = - - #REF! (0.027) x #REF! = #REF! (0.027)#REF! (0.446) x #REF! = #REF! (0.446)

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

6.7 6.7 = 6.7 6.7 #REF! (0.027) x #REF! = #REF! (0.027)#REF! (0.446) x #REF! = #REF! (0.446)

#REF! M20 #REF!

-1.804688 = -1.80 -1.804688 =

(0.38) x #REF! = #REF! (0.38) x #REF! =

(0.38) x #REF! = #REF! (0.38) x #REF! =#REF!

-1.40625 = -1.41 -1.40625 =

(0.38) x #REF! = #REF! (0.38) x #REF! =

(0.38) x #REF! = #REF! (0.38) x #REF! =#REF!

-0.675 = -0.68 -0.675 =

(0.38) x #REF! = #REF! (0.38) x #REF! =

(0.38) x #REF! = #REF! (0.38) x #REF! =#REF!

Putaran 17

MI #REF! MI #REF!

M2 #REF! M2 #REF!

M3 #REF! M3 #REF!

= - - = - x #REF! = #REF! (0.056) x #REF! = #REF!

M4 #REF! M4 #REF!

= (53.3) (53.3) = (53.3) x #REF! = #REF! (0.500) x #REF! = #REF!

M5 #REF! M5 #REF!

= - - = - x #REF! = #REF! #REF! x #REF! = #REF!x #REF! = #REF! #REF! x #REF! = #REF!x #REF! = #REF! #REF! x #REF! = #REF!x #REF! #REF! #REF! x #REF! #REF!

M6 #REF! M6 #REF!

M7 #REF! M7 #REF!

M8 #REF! M8 #REF!

= - - = - x #REF! = #REF! 0.031 x #REF! = #REF!x #REF! = #REF! 0.219 x #REF! = #REF!x #REF! = #REF! 0.219 x #REF! = #REF!

M9 #REF! M9 #REF!

M10 #REF! M10 #REF!

M11 #REF! M11 #REF!

= - - = - x #REF! = #REF! (0.031) x #REF! = #REF!

M13 #REF! M13 #REF!

M14 #REF! M14 #REF!

= (32.8) (32.8) = (32.8) x #REF! = #REF! (0.500) x #REF! = #REF!x #REF! = #REF! #REF! x #REF! = #REF!x #REF! = #REF! #REF! x #REF! = #REF!x #REF! #REF! #REF! x #REF! #REF!

M15 #REF! M15 #REF!

= - - = - x #REF! = #REF! #REF! x #REF! = #REF!x #REF! = #REF! (0.500) x #REF! = #REF!

M16 #REF! M16 #REF!

= - - = - x #REF! = #REF! (0.027) x #REF! = #REF!x #REF! = #REF! (0.446) x #REF! = #REF!

M17 #REF! M17 #REF!

M18 #REF! M18 #REF!

M19 #REF! M19 #REF!

M20 #REF! M20 #REF!

-1.80 -1.8047 = -1.80 -1.8046875

#REF! (0.38) x #REF! = #REF! (0.38) x

-1.41 -1.4063 = -1.41 -1.40625

#REF! (0.38) x #REF! = #REF! (0.38) x

-0.68 -0.675 = -0.68 -0.675

#REF! (0.38) x #REF! = #REF! (0.38) x

MI #REF! MI

M2 #REF! M2

M3 #REF! M3

- = - - (0.056) x #REF! = #REF! (0.056) x #REF!

M4 #REF! M4

(53.3) = (53.3) (53.3) (0.500) x #REF! = #REF! (0.500) x #REF!

M5 #REF! M5

M6 #REF! M6

M7 #REF! M7

M8 #REF! M8

M9 #REF! M9

M10 #REF! M10

M11 #REF! M11

- = - - (0.031) x #REF! = #REF! (0.031) x #REF!

#REF! #REF! #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x #REF!

M13 #REF! M13

M14 #REF! M14

(32.8) = (32.8) (32.8) (0.500) x #REF! = #REF! (0.500) x #REF!

M15 #REF! M15

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

M20 #REF! M20

= -1.80 -1.804688 = -1.80

#REF! = #REF! (0.38) x #REF! = #REF!

= -1.41 -1.40625 = -1.41

#REF! = #REF! (0.38) x #REF! = #REF!

= -0.68 -0.675 = -0.68

#REF! = #REF! (0.38) x #REF! = #REF!

Putaran 19

#REF! MI #REF!

#REF! M2 #REF!

#REF! M3 #REF!

= - - = - = #REF! (0.056) x #REF! = #REF!

#REF! M4 #REF!

= (53.3) (53.3) = (53.3)= #REF! (0.500) x #REF! = #REF!

#REF! M5 #REF!

= - - = - = #REF! #REF! x #REF! = #REF!= #REF! #REF! x #REF! = #REF!= #REF! #REF! x #REF! = #REF!

#REF! M8 #REF!

= - - = - = #REF! 0.031 x #REF! = #REF!= #REF! 0.219 x #REF! = #REF!= #REF! 0.219 x #REF! = #REF!

#REF! M9 #REF!

= - - = - = #REF! (0.031) x #REF! = #REF!

#REF! #REF! #REF!

= - - = - = #REF! (0.031) x #REF! = #REF!

#REF! M13 #REF!

= (32.8) (32.8) = (32.8)= #REF! (0.500) x #REF! = #REF!= #REF! #REF! x #REF! = #REF!= #REF! #REF! x #REF! = #REF!

= - - = - = #REF! #REF! x #REF! = #REF!= #REF! (0.500) x #REF! = #REF!

#REF! M16 #REF!

= - - = - = #REF! (0.027) x #REF! = #REF!= #REF! (0.446) x #REF! = #REF!

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

#REF! M20 #REF!

-1.8046875 = -1.80 -1.8046875

(0.38) x #REF! = #REF! (0.38)

(0.38) x #REF! = #REF! (0.38)#REF!

-1.40625 = -1.41 -1.40625

(0.38) x #REF! = #REF! (0.38)

(0.38) x #REF! = #REF! (0.38)#REF!

-0.675 = -0.68 -0.675

(0.38) x #REF! = #REF! (0.38)

(0.38) x #REF! = #REF! (0.38)#REF!

11.3 = 11.3 11.3 (0.063) x #REF! = #REF! (0.063) x (0.438) x #REF! = #REF! (0.438) x

MI #REF!

- = - - (0.056) x #REF! = #REF! (0.056) x (0.056) x #REF! = #REF! (0.056) x (0.389) x #REF! = #REF! (0.389) x

M2 #REF!

M3 #REF!

- = - - (0.056) x #REF! = #REF! (0.056) x

M4 #REF!

(53.3) = (53.3) (53.3) (0.500) x #REF! = #REF! (0.500) x

M5 #REF!

- = - - #REF! x #REF! = #REF! #REF! x #REF! x #REF! = #REF! #REF! x#REF! x #REF! = #REF! #REF! x#REF! x #REF! #REF! #REF! x

M6 #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x (0.031) x #REF! = #REF! (0.031) x (0.219) x #REF! = #REF! (0.219) x (0.219) x #REF! #REF! (0.219) x

M7 #REF!

M8 #REF!

- = - - 0.031 x #REF! = #REF! 0.031 x 0.219 x #REF! = #REF! 0.219 x 0.219 x #REF! = #REF! 0.219 x

M9 #REF!

#REF! x #REF! = #REF! #REF! x (0.219) x #REF! #REF! (0.219) x

M10 #REF!

#REF! x #REF! = #REF! #REF! x (0.233) x #REF! #REF! (0.233) x

M11 #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x

#REF! #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x

M13 #REF!

M14 #REF!

(32.8) = (32.8) (32.8) (0.500) x #REF! = #REF! (0.500) x

#REF! x #REF! = #REF! #REF! x#REF! x #REF! = #REF! #REF! x#REF! x #REF! #REF! #REF! x

M15 #REF!

- = - - #REF! x #REF! = #REF! #REF! x

(0.500) x #REF! = #REF! (0.500) xM16 #REF!

- = - - (0.027) x #REF! = #REF! (0.027) x (0.446) x #REF! = #REF! (0.446) x

M17 #REF!

M18 #REF!

M19 #REF!

M20 #REF!

= -1.80 -1.8046875

x #REF! = #REF! (0.38) x #REF!

x #REF! = #REF! (0.38) x #REF!#REF!

= -1.41 -1.40625

x #REF! = #REF! (0.38) x #REF!

= -0.68 -0.675

x #REF! = #REF! (0.38) x #REF!

Putaran 22

= 11.3 11.3 =#REF! = #REF! (0.063) x #REF! =#REF! = #REF! (0.438) x #REF! =

MI #REF! MI

= - - =#REF! = #REF! (0.056) x #REF! =#REF! = #REF! (0.056) x #REF! =#REF! = #REF! (0.389) x #REF! =

M2 #REF! M2

M3 #REF! M3

= - - =#REF! = #REF! (0.056) x #REF! =

M4 #REF! M4

= (53.3) (53.3) =#REF! = #REF! (0.500) x #REF! =

M5 #REF! M5

= - - =#REF! = #REF! #REF! x #REF! =#REF! = #REF! #REF! x #REF! =#REF! = #REF! #REF! x #REF! =#REF! #REF! #REF! x #REF!

M6 #REF! M6

= - - =#REF! = #REF! (0.031) x #REF! =#REF! = #REF! (0.031) x #REF! =#REF! = #REF! (0.219) x #REF! =#REF! #REF! (0.219) x #REF!

M7 #REF! M7

M8 #REF! M8

= - - =#REF! = #REF! 0.031 x #REF! =#REF! = #REF! 0.219 x #REF! =#REF! = #REF! 0.219 x #REF! =

M9 #REF! M9

= 2.5 2.5 =#REF! = #REF! (0.033) x #REF! =#REF! = #REF! (0.233) x #REF! =#REF! = #REF! #REF! x #REF! =#REF! #REF! (0.219) x #REF!

M10 #REF! M10

= 2.5 2.5 =#REF! = #REF! (0.033) x #REF! =#REF! = #REF! (0.233) x #REF! =#REF! = #REF! #REF! x #REF! =#REF! #REF! (0.233) x #REF!

M11 #REF! M11

= - - =#REF! = #REF! (0.031) x #REF! =

#REF! #REF! #REF!

= - - =#REF! = #REF! (0.031) x #REF! =

M13 #REF! M13

= - - =#REF! = #REF! (0.031) x #REF! =#REF! = #REF! (0.031) x #REF! =#REF! = #REF! (0.219) x #REF! =#REF! #REF! (0.219) x #REF!

M14 #REF! M14

= (32.8) (32.8) =#REF! = #REF! (0.500) x #REF! =#REF! = #REF! #REF! x #REF! =#REF! = #REF! #REF! x #REF! =#REF! #REF! #REF! x #REF!

M15 #REF! M15

= - - =#REF! = #REF! #REF! x #REF! =#REF! = #REF! (0.500) x #REF! =

M16 #REF! M16

= - - =#REF! = #REF! (0.027) x #REF! =#REF! = #REF! (0.446) x #REF! =

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

= 6.7 6.7 =#REF! = #REF! (0.027) x #REF! =#REF! = #REF! (0.446) x #REF! =

M20 #REF! M20

= -1.80 -1.8046875 = -1.80

= #REF! (0.38) x #REF! = #REF!

= -1.41 -1.40625 = -1.41

= #REF! (0.38) x #REF! = #REF!

= -0.68 -0.675 = -0.68

= #REF! (0.38) x #REF! = #REF!

Putaran 23

11.3 11.3 = 11.3 #REF! (0.063) x #REF! = #REF!#REF! (0.438) x #REF! = #REF!#REF! MI #REF!

- - = - #REF! (0.056) x #REF! = #REF!#REF! (0.056) x #REF! = #REF!#REF! (0.389) x #REF! = #REF!#REF! M2 #REF!

- - = - #REF! (0.056) x #REF! = #REF!#REF! M4 #REF!

(53.3) (53.3) = (53.3)#REF! (0.500) x #REF! = #REF!#REF! M5 #REF!

- - = - #REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! #REF!#REF! M6 #REF!

- - = - #REF! (0.031) x #REF! = #REF!#REF! (0.031) x #REF! = #REF!#REF! (0.219) x #REF! = #REF!#REF! (0.219) x #REF! #REF!

#REF! M7 #REF!

- - = - #REF! (0.031) x #REF! = #REF!#REF! (0.031) x #REF! = #REF!#REF! (0.219) x #REF! = #REF!

#REF! M8 #REF!

- - = - #REF! 0.031 x #REF! = #REF!#REF! 0.219 x #REF! = #REF!#REF! 0.219 x #REF! = #REF!

#REF! M9 #REF!

2.5 2.5 = 2.5 #REF! (0.033) x #REF! = #REF!#REF! (0.233) x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! (0.219) x #REF! #REF!

#REF! M10 #REF!

#REF! M11 #REF!

- - = - #REF! (0.031) x #REF! = #REF!

#REF! #REF! #REF!

- - = - #REF! (0.031) x #REF! = #REF!

#REF! M13 #REF!

#REF! M14 #REF!

(32.8) (32.8) = (32.8)#REF! (0.500) x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! #REF!

#REF! M15 #REF!

- - = - #REF! #REF! x #REF! = #REF!#REF! (0.500) x #REF! = #REF!

#REF! M16 #REF!

- - = - #REF! (0.027) x #REF! = #REF!#REF! (0.446) x #REF! = #REF!

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

6.7 6.7 = 6.7 #REF! (0.027) x #REF! = #REF!#REF! (0.446) x #REF! = #REF!

#REF! M20 #REF!

-1.8046875 = -1.80

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

-1.40625 = -1.41

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

-0.675 = -0.68

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

11.3 = 11.3 11.3 (0.063) x #REF! = #REF! (0.063) (0.438) x #REF! = #REF! (0.438)

MI #REF!

- = - - (0.056) x #REF! = #REF! (0.056) (0.056) x #REF! = #REF! (0.056) (0.389) x #REF! = #REF! (0.389)

M2 #REF!

M3 #REF!

- = - - (0.056) x #REF! = #REF! (0.056)

M4 #REF!

(53.3) = (53.3) (53.3) (0.500) x #REF! = #REF! (0.500)

M5 #REF!

- = - - #REF! x #REF! = #REF! #REF!#REF! x #REF! = #REF! #REF!#REF! x #REF! = #REF! #REF!#REF! x #REF! #REF! #REF!

M6 #REF!

- = - - (0.031) x #REF! = #REF! (0.031) (0.031) x #REF! = #REF! (0.031) (0.219) x #REF! = #REF! (0.219) (0.219) x #REF! #REF! (0.219)

M7 #REF!

M8 #REF!

- = - - 0.031 x #REF! = #REF! 0.031 0.219 x #REF! = #REF! 0.219 0.219 x #REF! = #REF! 0.219

M9 #REF!

2.5 = 2.5 2.5 (0.033) x #REF! = #REF! (0.033) (0.233) x #REF! = #REF! (0.233)

#REF! x #REF! = #REF! #REF! (0.219) x #REF! #REF! (0.219)

M10 #REF!

2.5 = 2.5 2.5 (0.033) x #REF! = #REF! (0.033) (0.233) x #REF! = #REF! (0.233)

#REF! x #REF! = #REF! #REF! (0.233) x #REF! #REF! (0.233)

M11 #REF!

- = - - (0.031) x #REF! = #REF! (0.031)

#REF! #REF!

- = - - (0.031) x #REF! = #REF! (0.031)

M13 #REF!

M14 #REF!

(32.8) = (32.8) (32.8) (0.500) x #REF! = #REF! (0.500)

#REF! x #REF! = #REF! #REF!#REF! x #REF! = #REF! #REF!#REF! x #REF! #REF! #REF!

M15 #REF!

- = - - #REF! x #REF! = #REF! #REF!

(0.500) x #REF! = #REF! (0.500)M16 #REF!

- = - - (0.027) x #REF! = #REF! (0.027) (0.446) x #REF! = #REF! (0.446)

M17 #REF!

M18 #REF!

M19 #REF!

6.7 = 6.7 6.7 (0.027) x #REF! = #REF! (0.027) (0.446) x #REF! = #REF! (0.446)

M20 #REF!

-1.8046875 = -1.80 -1.8046875

(0.38) x #REF! = #REF! (0.38)

(0.38) x #REF! = #REF! (0.38)#REF!

-1.40625 = -1.41 -1.40625

(0.38) x #REF! = #REF! (0.38)

(0.38) x #REF! = #REF! (0.38)#REF!

-0.675 = -0.68 -0.675

(0.38) x #REF! = #REF! (0.38)

(0.38) x #REF! = #REF! (0.38)#REF!

Putaran 26

= 11.3 11.3 x #REF! = #REF! (0.063) x x #REF! = #REF! (0.438) x

MI #REF!

= - - x #REF! = #REF! (0.056) x x #REF! = #REF! (0.056) xx #REF! = #REF! (0.389) x

M2 #REF!

M3 #REF!

= - - x #REF! = #REF! (0.056) x

M4 #REF!

= (53.3) (53.3) x #REF! = #REF! (0.500) x

M5 #REF!

= - - x #REF! = #REF! #REF! x x #REF! = #REF! #REF! xx #REF! = #REF! #REF! xx #REF! #REF! #REF! x

M6 #REF!

= - - x #REF! = #REF! (0.031) x x #REF! = #REF! (0.031) xx #REF! = #REF! (0.219) xx #REF! #REF! (0.219) x

M7 #REF!

M8 #REF!

= - - x #REF! = #REF! 0.031 x x #REF! = #REF! 0.219 xx #REF! = #REF! 0.219 x

M9 #REF!

= 2.5 2.5 x #REF! = #REF! (0.033) x x #REF! = #REF! (0.233) xx #REF! = #REF! #REF! xx #REF! #REF! (0.219) x

M10 #REF!

= 2.5 2.5 x #REF! = #REF! (0.033) x x #REF! = #REF! (0.233) xx #REF! = #REF! #REF! xx #REF! #REF! (0.233) x

M11 #REF!

= - - x #REF! = #REF! (0.031) x

#REF! #REF!

= - - x #REF! = #REF! (0.031) x

M13 #REF!

= - - x #REF! = #REF! (0.031) x x #REF! = #REF! (0.031) xx #REF! = #REF! (0.219) xx #REF! #REF! (0.219) x

M14 #REF!

= (32.8) (32.8) x #REF! = #REF! (0.500) x x #REF! = #REF! #REF! xx #REF! = #REF! #REF! xx #REF! #REF! #REF! x

M15 #REF!

= - - x #REF! = #REF! #REF! x x #REF! = #REF! (0.500) x

M16 #REF!

= - - x #REF! = #REF! (0.027) x x #REF! = #REF! (0.446) x

M17 #REF!

M18 #REF!

M19 #REF!

M20 #REF!

= -1.80 -1.8046875

x #REF! = #REF! (0.38) x

x #REF! = #REF! (0.38) x#REF!

= -1.41 -1.40625

x #REF! = #REF! (0.38) x

x #REF! = #REF! (0.38) x#REF!

= -0.68 -0.675

x #REF! = #REF! (0.38) x

x #REF! = #REF! (0.38) x#REF!

Putaran 27

= 11.3 11.3 #REF! = #REF! (0.063) x #REF!#REF! = #REF! (0.438) x #REF!

MI #REF! MI

= - - #REF! = #REF! (0.056) x #REF!#REF! = #REF! (0.056) x #REF!#REF! = #REF! (0.389) x #REF!

M2 #REF! M2

M3 #REF! M3

= - - #REF! = #REF! (0.056) x #REF!

M4 #REF! M4

= (53.3) (53.3)#REF! = #REF! (0.500) x #REF!

M5 #REF! M5

= - - #REF! = #REF! #REF! x #REF!#REF! = #REF! #REF! x #REF!#REF! = #REF! #REF! x #REF!#REF! #REF! #REF! x #REF!

M6 #REF! M6

= - - #REF! = #REF! (0.031) x #REF!#REF! = #REF! (0.031) x #REF!#REF! = #REF! (0.219) x #REF!#REF! #REF! (0.219) x #REF!

M7 #REF! M7

M8 #REF! M8

= - - #REF! = #REF! 0.031 x #REF!#REF! = #REF! 0.219 x #REF!#REF! = #REF! 0.219 x #REF!

M9 #REF! M9

= 2.5 2.5 #REF! = #REF! (0.033) x #REF!#REF! = #REF! (0.233) x #REF!#REF! = #REF! #REF! x #REF!#REF! #REF! (0.219) x #REF!

M10 #REF! M10

= 2.5 2.5 #REF! = #REF! (0.033) x #REF!#REF! = #REF! (0.233) x #REF!#REF! = #REF! #REF! x #REF!#REF! #REF! (0.233) x #REF!

M11 #REF! M11

= - - #REF! = #REF! (0.031) x #REF!

#REF! #REF! #REF!

= - - #REF! = #REF! (0.031) x #REF!

M13 #REF! M13

M14 #REF! M14

= (32.8) (32.8)#REF! = #REF! (0.500) x #REF!#REF! = #REF! #REF! x #REF!#REF! = #REF! #REF! x #REF!#REF! #REF! #REF! x #REF!

M15 #REF! M15

= - - #REF! = #REF! #REF! x #REF!#REF! = #REF! (0.500) x #REF!

M16 #REF! M16

= - - #REF! = #REF! (0.027) x #REF!#REF! = #REF! (0.446) x #REF!

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

M20 #REF! M20

= -1.80 -1.8046875

#REF! = #REF! (0.38) x #REF!

#REF! = #REF! (0.38) x #REF!#REF!

= -1.41 -1.40625

#REF! = #REF! (0.38) x #REF!

#REF! = #REF! (0.38) x #REF!#REF!

= -0.68 -0.675

#REF! = #REF! (0.38) x #REF!

#REF! = #REF! (0.38) x #REF!#REF!

Putaran 28

= 11.3 11.3 == #REF! (0.063) x #REF! == #REF! (0.438) x #REF! =

#REF! MI

= - - == #REF! (0.056) x #REF! == #REF! (0.056) x #REF! == #REF! (0.389) x #REF! =

#REF! M2

#REF! M3

= - - == #REF! (0.056) x #REF! =

#REF! M4

= (53.3) (53.3) == #REF! (0.500) x #REF! =

#REF! M5

= - - == #REF! #REF! x #REF! == #REF! #REF! x #REF! == #REF! #REF! x #REF! =

#REF! #REF! x #REF!#REF! M6

#REF! (0.219) x #REF!#REF! M7

#REF! M8

= - - == #REF! 0.031 x #REF! == #REF! 0.219 x #REF! == #REF! 0.219 x #REF! =

#REF! M9

= 2.5 2.5 == #REF! (0.033) x #REF! == #REF! (0.233) x #REF! == #REF! #REF! x #REF! =

#REF! (0.219) x #REF!#REF! M10

#REF! (0.233) x #REF!#REF! M11

= - - == #REF! (0.031) x #REF! =

#REF! #REF!

= - - == #REF! (0.031) x #REF! =

#REF! M13

#REF! (0.219) x #REF!#REF! M14

= (32.8) (32.8) == #REF! (0.500) x #REF! == #REF! #REF! x #REF! == #REF! #REF! x #REF! =

= - - == #REF! #REF! x #REF! == #REF! (0.500) x #REF! =

#REF! M16

= - - == #REF! (0.027) x #REF! == #REF! (0.446) x #REF! =

#REF! M17

#REF! M18

#REF! M19

= 6.7 6.7 == #REF! (0.027) x #REF! == #REF! (0.446) x #REF! =

#REF! M20

= -1.80 -1.8046875 =

= #REF! (0.38) x #REF! =

= #REF! (0.38) x #REF! =#REF!

= -1.41 -1.40625 =

= #REF! (0.38) x #REF! =

= #REF! (0.38) x #REF! =#REF!

= -0.68 -0.675 =

= #REF! (0.38) x #REF! =

= #REF! (0.38) x #REF! =#REF!

Putaran 29

- - = - #REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! #REF!#REF! M6 #REF!

#REF! M7 #REF!

#REF! M8 #REF!

#REF! M9 #REF!

#REF! M10 #REF!

#REF! M11 #REF!

- - = - #REF! (0.031) x #REF! = #REF!

#REF! #REF! #REF!

- - = - #REF! (0.031) x #REF! = #REF!

#REF! M13 #REF!

#REF! M14 #REF!

(32.8) (32.8) = (32.8)#REF! (0.500) x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! #REF!

#REF! M15 #REF!

- - = - #REF! #REF! x #REF! = #REF!#REF! (0.500) x #REF! = #REF!

#REF! M16 #REF!

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

#REF! M20 #REF!

-1.80 -1.8046875 = -1.80

#REF! (0.38) x #REF! = #REF!

#REF! (0.38) x #REF! = #REF!#REF! #REF!

-1.41 -1.40625 = -1.41

#REF! (0.38) x #REF! = #REF!

-0.68 -0.675 = -0.68

#REF! (0.38) x #REF! = #REF!

Putaran 30

11.3 = 11.3 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

- = - (0.056) x #REF! = #REF! (0.056) x #REF! = #REF! (0.389) x #REF! = #REF!

M2 #REF!

M3 #REF!

- = - (0.056) x #REF! = #REF!

M4 #REF!

(53.3) = (53.3) (0.500) x #REF! = #REF!

M5 #REF!

- = - #REF! x #REF! = #REF!#REF! x #REF! = #REF!#REF! x #REF! = #REF!#REF! x #REF! #REF!

M6 #REF!

- = - (0.031) x #REF! = #REF! (0.031) x #REF! = #REF! (0.219) x #REF! = #REF! (0.219) x #REF! #REF!

M7 #REF!

M8 #REF!

- = - 0.031 x #REF! = #REF! 0.219 x #REF! = #REF! 0.219 x #REF! = #REF!

M9 #REF!

2.5 = 2.5 (0.033) x #REF! = #REF! (0.233) x #REF! = #REF!

#REF! x #REF! = #REF! (0.219) x #REF! #REF!

M10 #REF!

2.5 = 2.5 (0.033) x #REF! = #REF! (0.233) x #REF! = #REF!

M11 #REF!

- = - (0.031) x #REF! = #REF!

#REF! #REF!

- = - (0.031) x #REF! = #REF!

M13 #REF!

M14 #REF!

(32.8) = (32.8) (0.500) x #REF! = #REF!

#REF! x #REF! = #REF!#REF! x #REF! = #REF!#REF! x #REF! #REF!

M15 #REF!

- = - #REF! x #REF! = #REF!

(0.500) x #REF! = #REF!M16 #REF!

- = - (0.027) x #REF! = #REF! (0.446) x #REF! = #REF!

M17 #REF!

M18 #REF!

M19 #REF!

6.7 = 6.7 (0.027) x #REF! = #REF! (0.446) x #REF! = #REF!

M20 #REF!

-1.8046875 = -1.80

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

-1.40625 = -1.41

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

-0.675 = -0.68

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

Putaran 31

11.3 = 11.3 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

- = - (0.056) x #REF! = #REF!

M4 #REF!

(53.3) = (53.3) (0.500) x #REF! = #REF!

M5 #REF!

M6 #REF!

M7 #REF!

M8 #REF!

M9 #REF!

2.5 = 2.5 (0.033) x #REF! = #REF! (0.233) x #REF! = #REF!

M10 #REF!

2.5 = 2.5 (0.033) x #REF! = #REF! (0.233) x #REF! = #REF!

M11 #REF!

- = - (0.031) x #REF! = #REF!

#REF! #REF!

- = - (0.031) x #REF! = #REF!

M13 #REF!

M14 #REF!

(32.8) = (32.8) (0.500) x #REF! = #REF!

M15 #REF!

- = - #REF! x #REF! = #REF!

(0.500) x #REF! = #REF!M16 #REF!

- = - (0.027) x #REF! = #REF! (0.446) x #REF! = #REF!

M17 #REF!

M18 #REF!

M19 #REF!

6.7 = 6.7 (0.027) x #REF! = #REF! (0.446) x #REF! = #REF!

M20 #REF!

-1.8046875 = -1.80

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

-1.40625 = -1.41

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

-0.675 = -0.68

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

Putaran 32

11.3 = 11.3 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

- = - (0.056) x #REF! = #REF!

M4 #REF!

(53.3) = (53.3) (0.500) x #REF! = #REF!

M5 #REF!

M6 #REF!

M7 #REF!

M8 #REF!

M9 #REF!

2.5 = 2.5 (0.033) x #REF! = #REF! (0.233) x #REF! = #REF!

M10 #REF!

2.5 = 2.5 (0.033) x #REF! = #REF! (0.233) x #REF! = #REF!

M11 #REF!

- = - (0.031) x #REF! = #REF!

#REF! #REF!

- = - (0.031) x #REF! = #REF!

M13 #REF!

M14 #REF!

(32.8) = (32.8) (0.500) x #REF! = #REF!

M15 #REF!

- = - #REF! x #REF! = #REF!

(0.500) x #REF! = #REF!M16 #REF!

- = - (0.027) x #REF! = #REF! (0.446) x #REF! = #REF!

M17 #REF!

M18 #REF!

M19 #REF!

6.7 = 6.7 (0.027) x #REF! = #REF! (0.446) x #REF! = #REF!

M20 #REF!

-1.8046875 = -1.80

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

-1.40625 = -1.41

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

-0.675 = -0.68

(0.38) x #REF! = #REF!

(0.38) x #REF! = #REF!#REF!

Putaran 33

11.3 = 11.3 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

- = - (0.056) x #REF! = #REF!

M4 #REF!

(53.3) = (53.3) (0.500) x #REF! = #REF!

M5 #REF!

M6 #REF!

M7 #REF!

M8 #REF!

M9 #REF!

2.5 = 2.5 (0.033) x #REF! = #REF! (0.233) x #REF! = #REF!

M10 #REF!

2.5 = 2.5 (0.033) x #REF! = #REF! (0.233) x #REF! = #REF!

M11 #REF!

- = - (0.031) x #REF! = #REF!

#REF! #REF!

- = - (0.031) x #REF! = #REF!

M13 #REF!

M14 #REF!

(32.8) = (32.8) (0.500) x #REF! = #REF!

M15 #REF!

- = - #REF! x #REF! = #REF!

(0.500) x #REF! = #REF!M16 #REF!

- = - (0.027) x #REF! = #REF! (0.446) x #REF! = #REF!

M17 #REF!

M18 #REF!

M19 #REF!

6.7 = 6.7 (0.027) x #REF! = #REF! (0.446) x #REF! = #REF!

M20 #REF!

Tie Beam

Type TB 1 = 0.2 m x 0.4 m

Ring Balk

Type Balok 30/60 = 0.3 m x 0.6 m

Type Balok 30/40 = 0.3 m x 0.4 m

Type Balok 20/40 = 0.2 m x 0.4 m

Type Balok 20/30 = 0.2 m x 0.3 m

Gambar 4.2 Portal Tinjauan Arah X

NB: Untuk mempermudah perhitungan maka portal tinjauan arah X akan dibagi menjadi 2 bagian, sehingga hasil perhitungan portal sisi kiri sama dengan hasil perhitungan pada sisi kanan.

Inersia

a. Inersia Kolom

1 Type kolom K1 40.000 x 40 0.0833 213,333.333

b. Inersia Tie Beam

1 Type TB 1 20.000 x 40 0.0833 106,666.667

1 Dimensi RB1 30.000 x 40 0.0833 160,000.000

d. Inersia Balok

1 Type Balok 30/60 30.000 x 60 0.0833 540,000.000

2 Type Balok 30/40 30.000 x 40 0.0833 160,000.000

3 Type Balok 20/40 20.000 x 40 0.0833 106,666.667

4 Type Balok 20/30 20.000 x 30 0.0833 45,000.000

== -0.0833333333 x 8536.632512 x 64.000 = (45,528.7) - 7,998 = (53,526.8) kgm = (53.5) tm

Mf2-1 =

== -0.0833333333 x 8536.632512 x 6.250 = (4,446.2)= (4,446.2) kgm = (4.4) tm

== -0.0833333333 x 6,190.03 x 64.000 = (33,013.5) - 7459.064= (40,472.6) kgm = (40.5) tm

== -0.0833333333 x 6190.03 x 6.250 = (3,224.0)= (3,224.0) kgm = (3.2) tm

== -0.0833333333 x 6,190.03 x 64.000 = (33,013.5) - 7459.064= (40,472.6) kgm = (40.5) tm =

== -0.0833333333 x 6190.03 x 6.250 = (3,224.0)= (3,224.0) kgm = (3.2) tm =

Mf1-2 -1/12 x qL2 - (P1.a.b2/L2)

-Mf2-1

Mf2-2" -1/12 x qL2 - 1/8 PL

Mf2"-2

-Mf2-2"

Mf4-3 -1/12 x qL2 - 1/8 PL

-Mf4-3

Mf3-3" -1/12 x qL2

Mf3"-3

-Mf4-3

Mf5-6 -1/12 x qL2 - 1/8 PL

-Mf5-6

Mf6-6" -1/12 x qL2

Mf6"-6

-Mf6-6"

== -0.0833333333 x 6,190.03 x 64.000 = (33,013.5) - 7459.064= (40,472.6) kgm = (40.5) tm =

== -0.0833333333 x 6190.032512 x 6.250 = (3,224.0)= (3,224.0) kgm = (3.2) tm =

1 -53.527 53.53

2 -53.527 53.53

3 -4.446 4.45

4 40.473 (40.47)

5 -3.224 3.22

6 40.473 (40.47)

7 -3.224 3.22

8 -40.473 40.47

9 40.473 (40.47)

T1 = +

T Nilai ρ Nilai

-53.527 1.219

4.446 1.371

-4.446 0.229

37.249 3.133

-3.224 0.771

-40.473 2.905

37.249 3.133

-3.224 0.771

-80.945 2.067

-3.224 0.771

-40.473 1.838

Mf7-8 -1/12 x qL2 - 1/8 PL

Mf 8-7

-Mf7-8

Mf7-7" -1/12 x qL2

Mf 7"-7

-Mf7"-7

" M3"-3

M8-7 M7-8

T2" ρ

T3 ρ3

T3" ρ

T5 ρ5

T6" ρ

T7 ρ7

T7" ρ7'

Joint 1

= = 0.076 = 0.063 ρ1 1.219

= = 0.533 = 0.438 ρ1 1.219

Joint 2

= = 0.076 = 0.056 ρ2 1.371

= = 0.5333 = 0.389 ρ2 1.371

Joint 3

= = 0.533 = 0.170 ρ3 3.133

= = 0.386 = 0.123 ρ3 3.133

= = 0.114 = 0.036 ρ3 3.133

= = 0.5333 = 0.170 ρ3 3.133

Joint 4

= = 0.386 = 0.133 ρ4 2.905

= = 0.533 = 0.184 ρ4 2.905

Joint 5

γ2-2"

γ2--1

K2-3γ

γ3-3"

K4-3γ4-3

= = 0.386 = 0.133 ρ5 2.905

= = 0.533 = 0.184 ρ5 2.905

0.500 Joint 6

= = 0.386 = 0.123 ρ6 3.133

= = 0.114 = 0.036 ρ6 3.133

= = 0.533 = 0.170 ρ6 3.133

Joint 7

= = 0.114 = 0.055 ρ7 2.067

= = 0.386 = 0.187 ρ7 2.067

= = 0.533 = 0.258 ρ7 2.067

= = 0.386 = 0.210 ρ8 1.838

= = 0.533 = 0.290 ρ8 1.838

K5-8γ

γ6-6"

γ7-7"

M1 = -Mf / ρ1

= 53.5271.219

= 43.909 ton

No. Momen Nilai

1 M1 43.909

2 M2 -3.242

3 M2" 19.452

4 M3 -11.888

5 M3" 4.179

6 M4 13.933

7 M5 13.933

8 M6 -11.888

9 M6" 4.179

10 M7 39.167

11 M7" 4.179

= 2 x ( 0.5333 + 0.533

= 2.1333

T2 = 2 x ( 0.5333 + 0.53

= 2.1333

T3 = 2 x ( 0.53 + 0.53

= 2.1333

Perhitungan nilai t

Menentukan nilai T (Thou)

2*(K1-2

2*(K4-5

+ K3-6

2*(K5-8

+ K6-7

3.(K1-8

T1= 0.750

No. t Nilai

1 0.750

2 0.750

3 0.750

4 0.750

5 0.750

6 0.750

7 0.750

Perhitungan Momen Displacment Belum dihitungArah y

Combination Load (Beban Angin + Beban Gempa)

Arah y

M1 = -h1(∑W)

= -3.500 x ( 2.20 )2.1333

= -3.609

M2 = -h2(∑W)

= -4.000 x ( 1.50 )2.1333

= -2.813

M3 = -h3(∑W)

= -3.600 x ( 0.80 )2.1333

= -1.350

Putaran 0

MI = MI(0) = 43.9 = γ 1 - 2 x M2(0) = (0.063)

= γ 1 - 4 x MD 1+M4(0) = (0.438)

M2 = M2(0) = (3.2)= γ 2 - 1 x M1(1) = (0.056)= γ 2 - 2" x M2"(0) = (0.056)= γ 2 - 3 x MD 1+M3(0) = (0.389)

M3 = M3(0) = (11.9)= γ 3-4 x M4(0) = (0.123)= y 3-3" x M3"(0) = 0.036 = γ 3-2 x MD2+M2(0) = 0.170 = γ 3-6 x MD 1+M6 = (0.170)

M4 = M4(0) = 13.9 = γ 4-3 x M3(1) = (0.133)= γ 4-5 x MD(2)+M5(0) = 0.184 = γ 4-1 x MD(1)+M1(0) = 0.184

M5 = M5(0) = 13.9 = γ 5-6 x M6(1) = (0.133)= γ 5-8 x MD3 + M8(0) = 0.184 = γ 5-4 x MD 1 + M4(1) = 0.184

M6 = M6(0) = (11.9)= γ 6-5 x M5(1) = 0.123 = γ 6-6" x M6"(0) = 0.036 = γ 6-7 x MD 3+M7(0) = 0.170 = γ 6-3 x MD 2+M3(1) = 0.170

M7 = M7(0) = 39.2 = γ 7-7" x M7"(0) = 0.055 = γ 7-8 x M8(0) = 0.187 = γ 7-9 x MD 4+M9(0) = #REF!= γ7-6 x MD 3+M6(1) = 0.258

M8 = M8(0) = #REF!= γ 8-7 x M7(1) = #REF!= γ8-5 x MD 3+M5(1) = #REF!

M9 = M9(0) = #REF!= γ 9-9" x M9"(0) = #REF!= γ 9-9' x M9'(0) = #REF!= γ9-7 x MD 4+M7(1) = #REF!

Joint 1

M1-2 = K 1-2 x + Mf1-2

M1-4 = K 1-4 x + Mf1-4

Joint 2

M2-1 = K 2-1 x + Mf2-1

M2-3 = K 2-3 x + Mf2-3

M2-2" = K 2-2" x + Mf2-2"

Joint 3

M3-2 = K 3-2 x + Mf3-2

M3-4 = K 3-4 x + Mf3-4

M3-6 = K 3-6 x + Mf3-6

M3-3" = K 3-2" x + Mf3-3" Joint 4

M4-3 = K 4-3 x + Mf4-3

M4-1 = K 4-1 x + Mf4-1

M4-5 = K 4-5 x + Mf4-5

Joint 5

M5-6 = K 5-6 x + Mf5-6

M5-4 = K 5-4 x + Mf5-4

M5-8 = K 5-8 x + Mf5-8

Joint 6

M6-5 = K 6-5 x + Mf6-5

M6-7 = K 6-7 x + Mf6-7

M6-3 = K 6-3 x + Mf6-3

M6-6' = K 6-6' x + Mf6-6

Joint 7

M7-6 = K 7-6 x + Mf7-6

M7-8 = K 7-8 x + Mf7-8

M7-9 = K 7-2 x + Mf7-9

M7-7" = K 7-7' x + Mf7-7'

Joint 8

M8-7 = K 8-7 x + Mf8-7

M8-5 = K 8-5 x + Mf8-5

Joint 9

M9-9" = K 9-9" x + Mf9-9"

{ 2M1(k) + M2(k) }

{2M1(k) + M4(k) }

{ 2M2(k) + M1(k) }

{2M2(k) + M3(k) }

{2M2(k) + M2"(k) }

{ 2M3(k) + M2(k) }

{2M3(k) + M4(k) }

{2M3(k) + M6(k) }

{2M3(k) + M3"(k) }

{ 2M4(k) + M3(k) }

{ 2M4(k) + M1(k) }

{ 2M4(k) + M3(k) }

{ 2M5(k) + M6(k) }

{ 2M5(k) + M4(k) }

{ 2M5(k) + M8(k) }

{ 2M6(k) + M5(k) }

{2M6(k) + M7(k) }

{2M6(k) + M3(k) }

{2M6(k) + M6"(k) }

{ 2M7(k) + M6(k) }

{2M7(k) + M8(k) }

{2M7(k) + M2(k) }

{2M7(k) + M7'(k) }

{ 2M8(k) + M7(k) }

{2M8(k) + M5(k) }

{ 2M9(k) + M9"(k) }

M9-9' = K 9-9' x + Mf9-9'

M9-7 = K 9-7 x + Mf9-7

No. Joint ∑M K ∑K K/∑

1M1-2 #REF!

#REF!0.08

0.6100.125 #REF!

M1-4 #REF! 0.53 0.875 #REF!

M2-1 #REF!

0.111 #REF!

M2-3 #REF! 0.53 0.778 #REF!

M2-2" #REF! 0.08 0.111 #REF!

M3-2 #REF!

0.111 #REF!

M3-4 #REF! 0.08 0.111 #REF!

M3-6 #REF! 0.53 0.778 #REF!

M4-5 #REF!

#REF! #REF!

M4-3 #REF! 0.08 #REF! #REF!

M4-1 #REF! 0.53 #REF! #REF!

M5-4 #REF!

#REF! #REF!

M5-6 #REF! 0.03 #REF! #REF!

M5-8 #REF! #REF! #REF! #REF!

M6-5 #REF!

#REF! #REF!

M6-6' #REF! 0.03 #REF! #REF!

M7-6 #REF!

#REF! #REF!

M7-8 #REF! 0.03 #REF! #REF!

M7-7" #REF! 0.03 #REF! #REF!

8M8-7 #REF!

#REF!0.03

####REF! #REF!

M9-9" #REF!

#REF! #REF!

M9-9' #REF! 0.11 #REF! #REF!

{2M9(k) + M9'(k) }

{2M9(k) + M7(k) }

Momen desain

K /∑K*∆M

M9-7 #REF!

#REF! #REF!

∑`RA

No. JointM.Desain

q p1 p2 L RA Stlh Koreksi

1 M1-2 #REF! #REF! #REF! - 8 #REF!

2 M2-1 #REF! #REF! #REF! - 8 #REF!

5 M3-4 #REF! #REF! #REF! - 8 #REF!

6 M4-3 #REF! #REF! #REF! - 8 #REF!

7 M5-6 #REF! #REF! #REF! - 8 #REF!

8 M6-5 #REF! #REF! #REF! - 8 #REF!

11 M7-8 #REF! #REF! 2.055 - 8 #REF!

12 M8-7 #REF! #REF! 2.055 - 8 #REF!

13 M9-9" #REF! 0.523 - - 4 1.047

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RM x-y= Mx-y / L

RM y-x= Mx-y / L

RM x-y= Mx-y / L

No. Joint h M desain RMx-y/L

1 M1-4 5 #REF! #REF!

M4-1 5 #REF! #REF!

2 M2-3 5 #REF! #REF!

M3-2 5 #REF! #REF!

3 M3-6 4 #REF! #REF!

M6-3 4 #REF! #REF!

4 M4-5 4 #REF! #REF!

M5-4 4 #REF! #REF!

5 M5-8 4 #REF! #REF!

M8-5 4 #REF! #REF!

6 M6-7 4 #REF! #REF!

M7-6 4 #REF! #REF!

M9-7 5 #REF! #REF!

7 M7-9 5 #REF! #REF!

……………………………………………..FINISH……………………………………..

Kekakuan

0.5333

Kekakuan

0.0762

Kekakuan

0.1143

Kekakuan

0.3857

0.1143

0.0762

0.0321

- ( 7,998.081 )

- 0.125 x 7,459.064 x 8

Pemberesan Momen Displacement

= = -3.609

= = (0.75) x

= = -2.813

= = (0.75) x

= = -1.350

= = (0.75) x

Putaran 1

= 43.909 43.9 x (3.242) = 0.203 (0.063) x (0.5)

MI (1) MI (0)

(-t1-4) x (M1( I ) + M4(I) )

(-t2-3

) x (M2( I ) + M3(I) )

MII(1) MII (0)

(-t4-5) x (M4( I ) + M5(I) )

(-t3-6) x (M3( I )+ M6(I))

MIII(1) MIII (0)

(-t5-8) x (M5 ( I ) + M8 (I) )

(-t6-7) x (M6 ( I )+ M7 (I))

x 10.324 = (4.517) + (0.438) x (18.4) MI 39.595 MI

= (3.242) (3.2) x 39.595 = (2.200) (0.056) x 52.0 x 19.452 = (1.081) (0.056) x 19.5 x (15.497) = 6.027 + (0.389) x (53.85)

M2 (0.496) M2

= (11.888) (11.9) x 13.933 = (1.715) (0.123) x 24.1 x 4.179 = 0.152 0.036 x 4.2 x (3.308) = (0.563) (0.123) x #REF!x (15.497) = 2.638 + (0.170) x #REF!

M3 (11.376) M3

= 13.933 13.9 x (11.376) = 1.511 + (0.133) x 24.1 x 11.121 = 2.042 0.184 x #REF! x 35.985 = 6.607 0.184 x 9.5

M4 24.093 M4

= 13.933 13.9 x (11.888) = 1.579 (0.133) x #REF! x #REF! = #REF! 0.184 x #REF! x 20.483 = 3.761 + 0.184 x #REF!

M5 #REF! M5

= (11.888) (11.9) x #REF! = #REF! 0.123 x #REF!x 4.179 = 0.152 0.036 x 4.2 x 37.817 = 6.437 0.170 x #REF!x (14.188) 6.437 + 0.170 x #REF!

M6 #REF! M6

= 39.167 39.2 x 4.179 = 0.231 0.055 x 4.2 x #REF! = #REF! 0.187 x #REF!x #REF! = #REF! #REF! x #REF!x #REF! #REF! + 0.258 x #REF!

M7 #REF! M7

= #REF! #REF! x #REF! = #REF! #REF! x #REF!x #REF! = #REF! + #REF! x #REF!

M8 #REF! M8

= #REF! #REF! x #REF! = #REF! #REF! x #REF!x #REF! = #REF! #REF! x #REF!x #REF! = #REF! + #REF! x #REF!

M9 #REF! M9

= 0.076 x #REF! + # = #REF!

= 0.533 x #REF! + ### = #REF! + ∑M = #REF!

= 0.076 x #REF! + # = #REF!

= 0.533 x #REF! + ### = #REF! +

= 0.076 x #REF! + ## = #REF!∑M = #REF!

= 0.076 x #REF! + - = #REF!

= 0.076 x #REF! + ## = #REF! +

= 0.533 x #REF! + 0 = #REF!

0.076 x #REF! + ### = #REF!

= 0.076 x #REF! + # = #REF!

= 0.533 x #REF! + - = #REF!

= #REF! x #REF! + - = #REF!

∑M = #REF!

= 0.032 x #REF! + # = #REF!

= #REF! x #REF! + - = #REF!

= #REF! x #REF! + - = #REF! + ∑M = #REF!

= 0.032 x #REF! + # = #REF!

= #REF! x #REF! + ### = #REF!

= #REF! x #REF! + 0 = #REF!

= 0.032 x #REF! + # = #REF! + ∑M = #REF!

= #REF! x #REF! + - = #REF!

= 0.032 x #REF! + ## = #REF!

= #REF! x #REF! + 0 = #REF!

= 0.032 x #REF! + ### = #REF! + ∑M = #REF!

= 0.032 x #REF! + # = #REF!

= #REF! x #REF! + ### = #REF! + ∑M = #REF!

= 0.114 x #REF! + # = #REF!

= 0.114 x #REF! + # = #REF! +

= #REF! x #REF! + 0 = #REF!∑M = #REF!

#REF!#REF!

Koreksi Momen

∑`RA ∑`RB

RB RM x-y RM y-x ∑R'A∑R'B R'A Da kanan Db kiri

#REF! #REF! #REF! ### # #REF! #REF! #REF!

1.047 #REF! #REF! ### # #REF! #REF! #REF!

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RMy-x/L ∑RA ∑RB Da Da kanan

#REF! #REF! #REF! ### #

……………………………………………..FINISH……………………………………..

= -3.61 -3.609

63.7 = -47.77 (0.75) x

(11.9) = 8.90 (0.75) x-42.47

= -2.81 -2.813

#REF! = #REF! (0.75) x

= -1.35 -1.350

#REF! = #REF! (0.75) x

Putaran 2

= 43.909 43.9 = 0.031 (0.063) x 13.7

= 8.041 (0.438) x #REF! 51.980 MI

= (3.242) (3.2)= (2.888) (0.056) x #REF!= (1.081) (0.056) x 19.5 = 20.941 (0.389) x #REF!

13.730 M2

= (11.888) (11.9)= (2.966) (0.123) x #REF!

0.152 0.036 x 4.2 = #REF! (0.123) x #REF!= #REF! (0.170) x #REF!

#REF! M3

= 13.933 13.9 = (3.199) (0.133) x #REF!= #REF! 0.184 x #REF!= 1.746 0.184 x #REF!

#REF! M4

= 13.933 13.9 = #REF! (0.133) x #REF!= #REF! 0.184 x #REF!= #REF! 0.184 x #REF!

#REF! M5

= (11.888) (11.9)= #REF! 0.123 x #REF!= 0.152 0.036 x 4.2 = #REF! 0.170 x #REF!

#REF! 0.170 x #REF!#REF! M6

= 39.167 39.2 = 0.231 0.055 x 4.2 = #REF! 0.187 x #REF!= #REF! #REF! x #REF!

= #REF! #REF!= #REF! #REF! x #REF!= #REF! #REF! x #REF!

#REF! M8

= #REF! #REF!= #REF! #REF! x #REF!= #REF! #REF! x #REF!= #REF! #REF! x #REF!

#REF! M9

Db kanan Dc kiri Dc kanan Dd kiri Dd kanan

#REF! #REF! #REF!

= -3.61 -3.609 =

#REF! = #REF! (0.75) x #REF! =

#REF! = #REF! (0.75) x #REF! =#REF!

= -2.81 -2.813 =

#REF! = #REF! (0.75) x #REF! =

= -1.35 -1.350 =

#REF! = #REF! (0.75) x #REF! =

Putaran 3

= 43.909 43.9 = 43.909 = (0.858) (0.063) x #REF! = #REF!

= #REF! (0.438) x #REF! = #REF!#REF! MI #REF!

= (3.242) (3.2) = (3.242)= #REF! (0.056) x #REF! = #REF!= (1.081) (0.056) x 19.5 = (1.081)= #REF! (0.389) x #REF! = #REF!

#REF! M2 #REF!

= (11.888) (11.9) = (11.888)= #REF! (0.123) x #REF! = #REF!

0.152 0.036 x 4.2 0.152 = #REF! (0.123) x #REF! = #REF!= #REF! (0.170) x #REF! = #REF!

#REF! M3 #REF!

= 13.933 13.9 = 13.933 = #REF! (0.133) x #REF! = #REF!= #REF! 0.184 x #REF! = #REF!= #REF! 0.184 x #REF! = #REF!

#REF! M4 #REF!

#REF! M5 #REF!

= (11.888) (11.9) = (11.888)= #REF! 0.123 x #REF! = #REF!= 0.152 0.036 x 4.2 = 0.152 = #REF! 0.170 x #REF! = #REF!

#REF! 0.170 x #REF! #REF!#REF! M6 #REF!

= 39.167 39.2 = 39.167 = 0.231 0.055 x 4.2 = 0.231 = #REF! 0.187 x #REF! = #REF!= #REF! #REF! x #REF! = #REF!

= #REF! #REF! = #REF!= #REF! #REF! x #REF! = #REF!= #REF! #REF! x #REF! = #REF!

#REF! M8 #REF!

= #REF! #REF! = #REF!= #REF! #REF! x #REF! = #REF!= #REF! #REF! x #REF! = #REF!= #REF! #REF! x #REF! = #REF!

#REF! M9 #REF!

-3.61 -3.609 = -3.61

#REF! (0.75) x #REF! = #REF!

-2.81 -2.813 = -2.81

#REF! (0.75) x #REF! = #REF!

#REF! #REF!

-1.35 -1.350 = -1.35

#REF! (0.75) x #REF! = #REF!

#REF! #REF!

Putaran 4

43.9 = 43.909 (0.063) x #REF! = #REF!

(0.438) x #REF! = #REF!MI #REF!

(3.2) = (3.242) (0.056) x #REF! = #REF! (0.056) x 19.5 = (1.081) (0.389) x #REF! = #REF!

M2 #REF!

(11.9) = (11.888) (0.123) x #REF! = #REF! 0.036 x 4.2 0.152 (0.123) x #REF! = #REF! (0.170) x #REF! = #REF!

M3 #REF!

13.9 = 13.933 (0.133) x #REF! = #REF! 0.184 x #REF! = #REF! 0.184 x #REF! = #REF!

M4 #REF!

M5 #REF!

(11.9) = (11.888) 0.123 x #REF! = #REF! 0.036 x 4.2 = 0.152 0.170 x #REF! = #REF! 0.170 x #REF! #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

#REF! x #REF! = #REF! 0.258 x #REF! #REF!

M7 #REF!

#REF! = #REF!#REF! x #REF! = #REF!#REF! x #REF! = #REF!

M8 #REF!

#REF! = #REF!#REF! x #REF! = #REF!#REF! x #REF! = #REF!#REF! x #REF! = #REF!

M9 #REF!

-3.609 = -3.61 -3.609

(0.75) x #REF! = #REF! (0.75)

(0.75) x #REF! = #REF! (0.75)#REF!

-2.813 = -2.81 -2.813

(0.75) x #REF! = #REF! (0.75)

-1.350 = -1.35 -1.350

(0.75) x #REF! = #REF! (0.75)

Putaran 5 Putaran 6

43.9 = 43.909 43.9 (0.063) x #REF! = #REF! (0.063) x

(0.438) x #REF! = #REF! (0.438) xMI #REF!

(3.2) = (3.242) (3.2) (0.056) x #REF! = #REF! (0.056) x (0.056) x 19.5 = (1.081) (0.056) x (0.389) x #REF! = #REF! (0.389) x

M2 #REF!

(11.9) = (11.888) (11.9) (0.123) x #REF! = #REF! (0.123) x 0.036 x 4.2 0.152 0.036 x (0.123) x #REF! = #REF! (0.123) x (0.170) x #REF! = #REF! (0.170) x

M3 #REF!

13.9 = 13.933 13.9 (0.133) x #REF! = #REF! (0.133) x 0.184 x #REF! = #REF! 0.184 x 0.184 x #REF! = #REF! 0.184 x

M4 #REF!

M5 #REF!

(11.9) = (11.888) (11.9) 0.123 x #REF! = #REF! 0.123 x 0.036 x 4.2 = 0.152 0.036 x 0.170 x #REF! = #REF! 0.170 x 0.170 x #REF! #REF! 0.170 x

M6 #REF!

39.2 = 39.167 39.2 0.055 x 4.2 = 0.231 0.055 x 0.187 x #REF! = #REF! 0.187 x

#REF! x #REF! = #REF! #REF! x 0.258 x #REF! #REF! 0.258 x

M7 #REF!

#REF! = #REF! #REF!#REF! x #REF! = #REF! #REF! x #REF! x #REF! = #REF! #REF! x

M8 #REF!

#REF! = #REF! #REF!#REF! x #REF! = #REF! #REF! x #REF! x #REF! = #REF! #REF! x#REF! x #REF! = #REF! #REF! x

M9 #REF!

= -3.61 -3.609

x #REF! = #REF! (0.75) x

x #REF! = #REF! (0.75) x#REF!

= -2.81 -2.813

x #REF! = #REF! (0.75) x

= -1.35 -1.350

x #REF! = #REF! (0.75) x

Putaran 7

= 43.909 43.9 #REF! = #REF! (0.063) x #REF!

#REF! = #REF! (0.438) x #REF!MI #REF! MI

= (3.242) (3.2)#REF! = #REF! (0.056) x #REF!

19.5 = (1.081) (0.056) x 19.5 #REF! = #REF! (0.389) x #REF!

M2 #REF! M2

= (11.888) (11.9)#REF! = #REF! (0.123) x #REF!

4.2 0.152 0.036 x 4.2 #REF! = #REF! (0.123) x #REF!#REF! = #REF! (0.170) x #REF!

M3 #REF! M3

= 13.933 13.9 #REF! = #REF! (0.133) x #REF!#REF! = #REF! 0.184 x #REF!#REF! = #REF! 0.184 x #REF!

M4 #REF! M4

M5 #REF! M5

= (11.888) (11.9)#REF! = #REF! 0.123 x #REF!

4.2 = 0.152 0.036 x 4.2 #REF! = #REF! 0.170 x #REF!#REF! #REF! 0.170 x #REF!

M6 #REF! M6

= 39.167 39.2 4.2 = 0.231 0.055 x 4.2

#REF! = #REF! 0.187 x #REF!#REF! = #REF! #REF! x #REF!#REF! #REF! 0.258 x #REF!

M7 #REF! M7

= #REF! #REF!#REF! = #REF! #REF! x #REF!#REF! = #REF! #REF! x #REF!

M8 #REF! M8

= #REF! #REF!#REF! = #REF! #REF! x #REF!#REF! = #REF! #REF! x #REF!#REF! = #REF! #REF! x #REF!

M9 #REF! M9

= -3.61 -3.609

#REF! = #REF! (0.75) x #REF!

#REF! = #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

#REF! = #REF! (0.75) x #REF!

= -1.35 -1.350

#REF! = #REF! (0.75) x #REF!

Putaran 8

= 43.909 43.9 == #REF! (0.063) x #REF! =

= #REF! (0.438) x #REF! =#REF! MI

= (3.242) (3.2) == #REF! (0.056) x #REF! == (1.081) (0.056) x 19.5 == #REF! (0.389) x #REF! =

#REF! M2

= (11.888) (11.9) == #REF! (0.123) x #REF! =

0.152 0.036 x 4.2 = #REF! (0.123) x #REF! == #REF! (0.170) x #REF! =

#REF! M3

= 13.933 13.9 == #REF! (0.133) x #REF! == #REF! 0.184 x #REF! == #REF! 0.184 x #REF! =

#REF! M4

#REF! M5

= (11.888) (11.9) == #REF! 0.123 x #REF! == 0.152 0.036 x 4.2 == #REF! 0.170 x #REF! =

= 39.167 39.2 == 0.231 0.055 x 4.2 == #REF! 0.187 x #REF! == #REF! #REF! x #REF! =

= #REF! #REF! == #REF! #REF! x #REF! == #REF! #REF! x #REF! =

#REF! M8

= #REF! #REF! == #REF! #REF! x #REF! == #REF! #REF! x #REF! == #REF! #REF! x #REF! =

#REF! M9

= -3.61 -3.609 =

= #REF! (0.75) x #REF! =

= #REF! (0.75) x #REF! =#REF!

= -2.81 -2.813 =

= #REF! (0.75) x #REF! =

= -1.35 -1.350 =

= #REF! (0.75) x #REF! =

Putaran 9

43.909 43.9 = 43.909 #REF! (0.063) x #REF! = #REF!

#REF! (0.438) x #REF! = #REF!#REF! MI #REF!

(3.242) (3.2) = (3.242)#REF! (0.056) x #REF! = #REF!

(1.081) (0.056) x 19.5 = (1.081)#REF! (0.389) x #REF! = #REF!#REF! M2 #REF!

(11.888) (11.9) = (11.888)#REF! (0.123) x #REF! = #REF!

0.152 0.036 x 4.2 0.152 #REF! (0.123) x #REF! = #REF!#REF! (0.170) x #REF! = #REF!#REF! M3 #REF!

13.933 13.9 = 13.933 #REF! (0.133) x #REF! = #REF!#REF! 0.184 x #REF! = #REF!#REF! 0.184 x #REF! = #REF!

#REF! M4 #REF!

#REF! M5 #REF!

(11.888) (11.9) = (11.888)#REF! 0.123 x #REF! = #REF!

0.152 0.036 x 4.2 = 0.152 #REF! 0.170 x #REF! = #REF!#REF! 0.170 x #REF! #REF!#REF! M6 #REF!

39.167 39.2 = 39.167 0.231 0.055 x 4.2 = 0.231

#REF! 0.187 x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! 0.258 x #REF! #REF!#REF! M7 #REF!

#REF! #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! M8 #REF!

#REF! #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! M9 #REF!

-3.61 -3.609 = -3.61

#REF! (0.75) x #REF! = #REF!

-2.81 -2.813 = -2.81

#REF! (0.75) x #REF! = #REF!

#REF! #REF!

-1.35 -1.350 = -1.35

#REF! (0.75) x #REF! = #REF!

#REF! #REF!

Putaran 10

43.9 = 43.909 (0.063) x #REF! = #REF!

(0.438) x #REF! = #REF!MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

M9 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

43.9 = 43.909 (0.063) x #REF! = #REF!

(0.438) x #REF! = #REF!MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

M9 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

43.9 = 43.909 43.9 (0.063) x #REF! = #REF! (0.063)

(0.438) x #REF! = #REF! (0.438)MI #REF!

(3.2) = (3.242) (3.2) (0.056) x #REF! = #REF! (0.056) (0.056) x 19.5 = (1.081) (0.056) (0.389) x #REF! = #REF! (0.389)

M2 #REF!

(11.9) = (11.888) (11.9) (0.123) x #REF! = #REF! (0.123) 0.036 x 4.2 0.152 0.036 (0.123) x #REF! = #REF! (0.123) (0.170) x #REF! = #REF! (0.170)

M3 #REF!

13.9 = 13.933 13.9 (0.133) x #REF! = #REF! (0.133) 0.184 x #REF! = #REF! 0.184 0.184 x #REF! = #REF! 0.184

M4 #REF!

M5 #REF!

(11.9) = (11.888) (11.9) 0.123 x #REF! = #REF! 0.123 0.036 x 4.2 = 0.152 0.036 0.170 x #REF! = #REF! 0.170 0.170 x #REF! #REF! 0.170

M6 #REF!

39.2 = 39.167 39.2 0.055 x 4.2 = 0.231 0.055 0.187 x #REF! = #REF! 0.187

#REF! x #REF! = #REF! #REF! 0.258 x #REF! #REF! 0.258

M7 #REF!

#REF! = #REF! #REF!#REF! x #REF! = #REF! #REF!#REF! x #REF! = #REF! #REF!

M8 #REF!

#REF! = #REF! #REF!#REF! x #REF! = #REF! #REF!#REF! x #REF! = #REF! #REF!#REF! x #REF! = #REF! #REF!

M9 #REF!

-3.609 = -3.61 -3.609

(0.75) x #REF! = #REF! (0.75)

(0.75) x #REF! = #REF! (0.75)#REF!

-2.813 = -2.81 -2.813

(0.75) x #REF! = #REF! (0.75)

-1.350 = -1.35 -1.350

(0.75) x #REF! = #REF! (0.75)

Putaran 14

= 43.909 43.9 x #REF! = #REF! (0.063) x

x #REF! = #REF! (0.438) xMI #REF!

= (3.242) (3.2) x #REF! = #REF! (0.056) x x 19.5 = (1.081) (0.056) xx #REF! = #REF! (0.389) x

M2 #REF!

= (11.888) (11.9) x #REF! = #REF! (0.123) x x 4.2 0.152 0.036 x x #REF! = #REF! (0.123) xx #REF! = #REF! (0.170) x

M3 #REF!

= 13.933 13.9 x #REF! = #REF! (0.133) x x #REF! = #REF! 0.184 x x #REF! = #REF! 0.184 x

M4 #REF!

M5 #REF!

= (11.888) (11.9) x #REF! = #REF! 0.123 x x 4.2 = 0.152 0.036 xx #REF! = #REF! 0.170 xx #REF! #REF! 0.170 x

M6 #REF!

= 39.167 39.2 x 4.2 = 0.231 0.055 x x #REF! = #REF! 0.187 xx #REF! = #REF! #REF! xx #REF! #REF! 0.258 x

M7 #REF!

= #REF! #REF! x #REF! = #REF! #REF! x x #REF! = #REF! #REF! x

M8 #REF!

= #REF! #REF! x #REF! = #REF! #REF! x x #REF! = #REF! #REF! xx #REF! = #REF! #REF! x

M9 #REF!

= -3.61 -3.609

x #REF! = #REF! (0.75)

x #REF! = #REF! (0.75)#REF!

= -2.81 -2.813

x #REF! = #REF! (0.75)

= -1.35 -1.350

x #REF! = #REF! (0.75)

= 43.909 43.9 #REF! = #REF! (0.063) x

#REF! = #REF! (0.438) xMI #REF!

= (3.242) (3.2)#REF! = #REF! (0.056) x

19.5 = (1.081) (0.056) x#REF! = #REF! (0.389) x

M2 #REF!

= (11.888) (11.9)#REF! = #REF! (0.123) x

4.2 0.152 0.036 x #REF! = #REF! (0.123) x#REF! = #REF! (0.170) x

M3 #REF!

= 13.933 13.9 #REF! = #REF! (0.133) x #REF! = #REF! 0.184 x #REF! = #REF! 0.184 x

M4 #REF!

M5 #REF!

= (11.888) (11.9)#REF! = #REF! 0.123 x

4.2 = 0.152 0.036 x#REF! = #REF! 0.170 x#REF! #REF! 0.170 x

M6 #REF!

= 39.167 39.2 4.2 = 0.231 0.055 x

#REF! = #REF! 0.187 x#REF! = #REF! #REF! x#REF! #REF! 0.258 x

M7 #REF!

= #REF! #REF!#REF! = #REF! #REF! x #REF! = #REF! #REF! x

M8 #REF!

= #REF! #REF!#REF! = #REF! #REF! x #REF! = #REF! #REF! x#REF! = #REF! #REF! x

M9 #REF!

= -3.61 -3.609

x #REF! = #REF! (0.75) x

x #REF! = #REF! (0.75) x#REF!

= -2.81 -2.813

x #REF! = #REF! (0.75) x

= -1.35 -1.350

x #REF! = #REF! (0.75) x

Putaran 16

= 43.909 43.9 #REF! = #REF! (0.063) x #REF!

#REF! = #REF! (0.438) x #REF!MI #REF! MI

= (3.242) (3.2)#REF! = #REF! (0.056) x #REF!

19.5 = (1.081) (0.056) x 19.5 #REF! = #REF! (0.389) x #REF!

M2 #REF! M2

= (11.888) (11.9)#REF! = #REF! (0.123) x #REF!

M3 #REF! M3

M4 #REF! M4

M5 #REF! M5

= (11.888) (11.9)#REF! = #REF! 0.123 x #REF!

M6 #REF! M6

= 39.167 39.2 4.2 = 0.231 0.055 x 4.2

M7 #REF! M7

M8 #REF! M8

= #REF! #REF!#REF! = #REF! #REF! x #REF!#REF! = #REF! #REF! x #REF!#REF! = #REF! #REF! x #REF!

M9 #REF! M9

= -3.61 -3.609

#REF! = #REF! (0.75) x

#REF! = #REF! (0.75) x#REF!

= -2.81 -2.813

#REF! = #REF! (0.75) x

= -1.35 -1.350

#REF! = #REF! (0.75) x

Putaran 17

= 43.909 43.9 = #REF! (0.063) x #REF!

= #REF! (0.438) x #REF!#REF! MI

= (3.242) (3.2)= #REF! (0.056) x #REF!= (1.081) (0.056) x 19.5 = #REF! (0.389) x #REF!

#REF! M2

= (11.888) (11.9)= #REF! (0.123) x #REF!

#REF! M3

#REF! M4

#REF! M5

#REF! M8

= #REF! #REF!= #REF! #REF! x #REF!= #REF! #REF! x #REF!= #REF! #REF! x #REF!

#REF! M9

= -3.61 -3.609

#REF! = #REF! (0.75) x #REF!

#REF! = #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

#REF! = #REF! (0.75) x #REF!

= -1.35 -1.350

#REF! = #REF! (0.75) x #REF!

Putaran 17

= 43.909 43.9 == #REF! (0.063) x #REF! =

= #REF! (0.438) x #REF! =#REF! MI

#REF! M2

= (11.888) (11.9) == #REF! (0.123) x #REF! =

#REF! M3

#REF! M4

#REF! M5

#REF! M8

= #REF! #REF! == #REF! #REF! x #REF! == #REF! #REF! x #REF! == #REF! #REF! x #REF! =

#REF! M9

= -3.61 -3.609

= #REF! (0.75) x #REF!

= #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

= #REF! (0.75) x #REF!

= -1.35 -1.350

= #REF! (0.75) x #REF!

Putaran 18

43.909 43.9 =#REF! (0.063) x #REF! =

#REF! (0.438) x #REF! =#REF! MI

(3.242) (3.2) =#REF! (0.056) x #REF! =

(1.081) (0.056) x 19.5 =#REF! (0.389) x #REF! =#REF! M2

(11.888) (11.9) =#REF! (0.123) x #REF! =

0.152 0.036 x 4.2 #REF! (0.123) x #REF! =#REF! (0.170) x #REF! =#REF! M3

13.933 13.9 =#REF! (0.133) x #REF! =#REF! 0.184 x #REF! =#REF! 0.184 x #REF! =

#REF! M4

#REF! M5

(11.888) (11.9) =#REF! 0.123 x #REF! =

0.152 0.036 x 4.2 =#REF! 0.170 x #REF! =#REF! 0.170 x #REF!#REF! M6

39.167 39.2 = 0.231 0.055 x 4.2 =

#REF! 0.187 x #REF! =#REF! #REF! x #REF! =#REF! 0.258 x #REF!#REF! M7

#REF! #REF! =#REF! #REF! x #REF! =#REF! #REF! x #REF! =#REF! M8

#REF! #REF! =#REF! #REF! x #REF! =#REF! #REF! x #REF! =#REF! #REF! x #REF! =#REF! M9

= -3.61 -3.609

= #REF! (0.75) x #REF!

= #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

= #REF! (0.75) x #REF!

= -1.35 -1.350

= #REF! (0.75) x #REF!

Putaran 19

43.909 43.9 =#REF! (0.063) x #REF! =

#REF! (0.438) x #REF! =#REF! MI

(3.242) (3.2) =#REF! (0.056) x #REF! =

(1.081) (0.056) x 19.5 =#REF! (0.389) x #REF! =#REF! M2

(11.888) (11.9) =#REF! (0.123) x #REF! =

#REF! M4

#REF! M5

(11.888) (11.9) =#REF! 0.123 x #REF! =

39.167 39.2 = 0.231 0.055 x 4.2 =

= -3.61 -3.609

= #REF! (0.75) x #REF!

= #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

= #REF! (0.75) x #REF!

= -1.35 -1.350

= #REF! (0.75) x #REF!

Putaran 20

43.909 43.9 =#REF! (0.063) x #REF! =

#REF! (0.438) x #REF! =#REF! MI

(3.242) (3.2) =#REF! (0.056) x #REF! =

(1.081) (0.056) x 19.5 =#REF! (0.389) x #REF! =#REF! M2

(11.888) (11.9) =#REF! (0.123) x #REF! =

#REF! M4

#REF! M5

(11.888) (11.9) =#REF! 0.123 x #REF! =

39.167 39.2 = 0.231 0.055 x 4.2 =

= -3.61 -3.609

= #REF! (0.75) x

= #REF! (0.75) x#REF!

= -2.81 -2.813

= #REF! (0.75) x

= -1.35 -1.350

= #REF! (0.75) x

Putaran 21

43.909 43.9 #REF! (0.063) x #REF!

#REF! (0.438) x #REF!#REF! MI

(3.242) (3.2)#REF! (0.056) x #REF!

(1.081) (0.056) x 19.5 #REF! (0.389) x #REF!#REF! M2

(11.888) (11.9)#REF! (0.123) x #REF!

0.152 0.036 x 4.2 #REF! (0.123) x #REF!#REF! (0.170) x #REF!#REF! M3

13.933 13.9 #REF! (0.133) x #REF!#REF! 0.184 x #REF!#REF! 0.184 x #REF!

#REF! M4

#REF! M5

(11.888) (11.9)#REF! 0.123 x #REF!

0.152 0.036 x 4.2 #REF! 0.170 x #REF!#REF! 0.170 x #REF!#REF! M6

39.167 39.2 0.231 0.055 x 4.2

#REF! 0.187 x #REF!#REF! #REF! x #REF!#REF! 0.258 x #REF!#REF! M7

#REF! #REF!#REF! #REF! x #REF!#REF! #REF! x #REF!#REF! M8

#REF! #REF!#REF! #REF! x #REF!#REF! #REF! x #REF!#REF! #REF! x #REF!#REF! M9

= -3.61 -3.609

#REF! = #REF! (0.75)

#REF! = #REF! (0.75)#REF!

= -2.81 -2.813

#REF! = #REF! (0.75)

= -1.35 -1.350

#REF! = #REF! (0.75)

Putaran 22

= 43.909 43.9 = #REF! (0.063) x

= #REF! (0.438) x#REF!

= (3.242) (3.2)= #REF! (0.056) x = (1.081) (0.056) x= #REF! (0.389) x

= (11.888) (11.9)= #REF! (0.123) x

0.152 0.036 x = #REF! (0.123) x= #REF! (0.170) x

= 13.933 13.9 = #REF! (0.133) x = #REF! 0.184 x = #REF! 0.184 x

= (11.888) (11.9)= #REF! 0.123 x = 0.152 0.036 x= #REF! 0.170 x

#REF! 0.170 x#REF!

= 39.167 39.2 = 0.231 0.055 x = #REF! 0.187 x= #REF! #REF! x

#REF! 0.258 x#REF!

= #REF! #REF!= #REF! #REF! x = #REF! #REF! x

= #REF! #REF!= #REF! #REF! x = #REF! #REF! x= #REF! #REF! x

= -3.61

x #REF! = #REF!

x #REF! = #REF!#REF!

= -2.81

x #REF! = #REF!

= -1.35

x #REF! = #REF!

Putaran 23

= 43.909 43.9 #REF! = #REF! (0.063)

#REF! = #REF! (0.438)MI #REF!

= (3.242) (3.2)#REF! = #REF! (0.056)

19.5 = (1.081) (0.056)#REF! = #REF! (0.389)

M2 #REF!

= (11.888) (11.9)#REF! = #REF! (0.123)

4.2 0.152 0.036 #REF! = #REF! (0.123)#REF! = #REF! (0.170)

M3 #REF!

= 13.933 13.9 #REF! = #REF! (0.133)#REF! = #REF! 0.184 #REF! = #REF! 0.184

M4 #REF!

M5 #REF!

= (11.888) (11.9)#REF! = #REF! 0.123

4.2 = 0.152 0.036 #REF! = #REF! 0.170 #REF! #REF! 0.170

M6 #REF!

= 39.167 39.2 4.2 = 0.231 0.055

#REF! = #REF! 0.187 #REF! = #REF! #REF!#REF! #REF! 0.258

M7 #REF!

= #REF! #REF!#REF! = #REF! #REF!#REF! = #REF! #REF!

M8 #REF!

= #REF! #REF!#REF! = #REF! #REF!#REF! = #REF! #REF!#REF! = #REF! #REF!

M9 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

= 43.909 x #REF! = #REF!

x #REF! = #REF!MI #REF!

= (3.242) x #REF! = #REF!x 19.5 = (1.081)x #REF! = #REF!

M2 #REF!

= (11.888) x #REF! = #REF! x 4.2 0.152 x #REF! = #REF!x #REF! = #REF!

M3 #REF!

= 13.933 x #REF! = #REF! x #REF! = #REF! x #REF! = #REF!

M4 #REF!

M5 #REF!

= (11.888) x #REF! = #REF!x 4.2 = 0.152 x #REF! = #REF!x #REF! #REF!

M6 #REF!

= 39.167 x 4.2 = 0.231 x #REF! = #REF!x #REF! = #REF!x #REF! #REF!

M7 #REF!

= #REF! x #REF! = #REF!x #REF! = #REF!

M8 #REF!

= #REF! x #REF! = #REF!x #REF! = #REF!x #REF! = #REF!

M9 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

Putaran 24

43.9 = 43.909 (0.063) x #REF! = #REF!

(0.438) x #REF! = #REF!MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

M9 #REF!

-3.609 =

(0.75) x #REF! =

-2.813 =

(0.75) x #REF! =

-1.350 =

(0.75) x #REF! =

Putaran 25

43.9 = 43.909 (0.063) x #REF! = #REF!

(0.438) x #REF! = #REF!MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

M9 #REF!

-3.61 -3.609

#REF! (0.75) x #REF!

#REF! (0.75) x #REF!#REF!

-2.81 -2.813

#REF! (0.75) x #REF!

-1.35 -1.350

#REF! (0.75) x #REF!

Putaran 26

43.9 = (0.063) x #REF! =

(0.438) x #REF! =MI

(3.2) = (0.056) x #REF! = (0.056) x 19.5 = (0.389) x #REF! =

(11.9) = (0.123) x #REF! = 0.036 x 4.2 (0.123) x #REF! = (0.170) x #REF! =

13.9 = (0.133) x #REF! = 0.184 x #REF! = 0.184 x #REF! =

(11.9) = 0.123 x #REF! = 0.036 x 4.2 = 0.170 x #REF! = 0.170 x #REF!

39.2 = 0.055 x 4.2 = 0.187 x #REF! =

#REF! x #REF! = 0.258 x #REF!

#REF! =#REF! x #REF! =#REF! x #REF! =

#REF! =#REF! x #REF! =#REF! x #REF! =#REF! x #REF! =

= -3.61 -3.609

= #REF! (0.75) x

= #REF! (0.75) x#REF!

= -2.81 -2.813

= #REF! (0.75) x

= -1.35 -1.350

= #REF! (0.75) x

Putaran 27

43.909 43.9 #REF! (0.063) x #REF!

#REF! (0.438) x #REF!#REF! MI

(3.242) (3.2)#REF! (0.056) x #REF!

(1.081) (0.056) x 19.5 #REF! (0.389) x #REF!#REF! M2

(11.888) (11.9)#REF! (0.123) x #REF!

#REF! M4

#REF! M5

(11.888) (11.9)#REF! 0.123 x #REF!

39.167 39.2 0.231 0.055 x 4.2

#REF! #REF!#REF! #REF! x #REF!#REF! #REF! x #REF!#REF! #REF! x #REF!#REF! M9

= -3.61 -3.609

#REF! = #REF! (0.75)

#REF! = #REF! (0.75)#REF!

= -2.81 -2.813

#REF! = #REF! (0.75)

= -1.35 -1.350

#REF! = #REF! (0.75)

Putaran 28

= 43.909 43.9 = #REF! (0.063) x

= #REF! (0.438) x#REF!

= (3.242) (3.2)= #REF! (0.056) x = (1.081) (0.056) x= #REF! (0.389) x

= (11.888) (11.9)= #REF! (0.123) x

0.152 0.036 x = #REF! (0.123) x= #REF! (0.170) x

= 13.933 13.9 = #REF! (0.133) x = #REF! 0.184 x = #REF! 0.184 x

= (11.888) (11.9)= #REF! 0.123 x = 0.152 0.036 x= #REF! 0.170 x

#REF! 0.170 x#REF!

= 39.167 39.2 = 0.231 0.055 x = #REF! 0.187 x= #REF! #REF! x

#REF! 0.258 x#REF!

= #REF! #REF!= #REF! #REF! x = #REF! #REF! x= #REF! #REF! x

= -3.61

x #REF! = #REF!

= -2.81

x #REF! = #REF!

= -1.35

x #REF! = #REF!

= 43.909 #REF! = #REF!

#REF! = #REF!MI #REF!

= (3.242)#REF! = #REF!

19.5 = (1.081)#REF! = #REF!

M2 #REF!

= (11.888)#REF! = #REF!

4.2 0.152 #REF! = #REF!#REF! = #REF!

M3 #REF!

= 13.933 #REF! = #REF!#REF! = #REF!#REF! = #REF!

M4 #REF!

M5 #REF!

= (11.888)#REF! = #REF!

4.2 = 0.152 #REF! = #REF!#REF! #REF!

M6 #REF!

= 39.167 4.2 = 0.231

#REF! = #REF!#REF! = #REF!#REF! #REF!

M7 #REF!

= #REF!#REF! = #REF!#REF! = #REF!

M8 #REF!

= #REF!#REF! = #REF!#REF! = #REF!#REF! = #REF!

M9 #REF!

-3.609 =

(0.75) x #REF! =

-2.813 =

(0.75) x #REF! =

-1.350 =

(0.75) x #REF! =

Putaran 29

43.9 = 43.909 (0.063) x #REF! = #REF!

(0.438) x #REF! = #REF!MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

M9 #REF!

-3.61 -3.609

#REF! (0.75) x

#REF! (0.75) x#REF!

-2.81 -2.813

#REF! (0.75) x

-1.35 -1.350

#REF! (0.75) x

Putaran 30

43.9 (0.063) x #REF!

(0.438) x #REF!MI

(3.2) (0.056) x #REF! (0.056) x 19.5 (0.389) x #REF!

(11.9) (0.123) x #REF! 0.036 x 4.2 (0.123) x #REF! (0.170) x #REF!

13.9 (0.133) x #REF! 0.184 x #REF! 0.184 x #REF!

(11.9) 0.123 x #REF! 0.036 x 4.2 0.170 x #REF! 0.170 x #REF!

39.2 0.055 x 4.2 0.187 x #REF!

#REF! x #REF! 0.258 x #REF!

#REF!#REF! x #REF!#REF! x #REF!

#REF!#REF! x #REF!#REF! x #REF!#REF! x #REF!

= -3.61

#REF! = #REF!

#REF! = #REF!#REF!

= -2.81

#REF! = #REF!

= -1.35

#REF! = #REF!

Putaran 31

= 43.909 43.9 = #REF! (0.063)

= #REF! (0.438)#REF!

= (3.242) (3.2)= #REF! (0.056)= (1.081) (0.056)= #REF! (0.389)

= (11.888) (11.9)= #REF! (0.123)

0.152 0.036 = #REF! (0.123)= #REF! (0.170)

= 13.933 13.9 = #REF! (0.133)= #REF! 0.184 = #REF! 0.184

= (11.888) (11.9)= #REF! 0.123 = 0.152 0.036 = #REF! 0.170

#REF! 0.170 #REF!

= 39.167 39.2 = 0.231 0.055 = #REF! 0.187 = #REF! #REF!

#REF! 0.258 #REF!

= #REF! #REF!= #REF! #REF!= #REF! #REF!

= #REF! #REF!= #REF! #REF!= #REF! #REF!= #REF! #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

= 43.909 x #REF! = #REF!

x #REF! = #REF!MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

M7 #REF!

M8 #REF!

= #REF! x #REF! = #REF!x #REF! = #REF!x #REF! = #REF!

M9 #REF!

-3.609

(0.75) x #REF!

-2.813

(0.75) x #REF!

-1.350

(0.75) x #REF!

Putaran 32

43.9 = (0.063) x #REF! =

(0.438) x #REF! =MI

(3.2) = (0.056) x #REF! = (0.056) x 19.5 = (0.389) x #REF! =

(11.9) = (0.123) x #REF! = 0.036 x 4.2 (0.123) x #REF! = (0.170) x #REF! =

13.9 = (0.133) x #REF! = 0.184 x #REF! = 0.184 x #REF! =

(11.9) = 0.123 x #REF! = 0.036 x 4.2 = 0.170 x #REF! = 0.170 x #REF!

39.2 = 0.055 x 4.2 = 0.187 x #REF! =

#REF! x #REF! = 0.258 x #REF!

#REF! =#REF! x #REF! =#REF! x #REF! =#REF! x #REF! =

= -3.61 -3.609375

= #REF! (0.75)

= #REF! (0.75)#REF!

= -2.81 -2.8125

= #REF! (0.75)

= #REF! (0.75) (0.75)

= -1.35 -1.35

= #REF! (0.75)

= #REF! (0.75) (0.75)

Putaran 33

43.909 43.9 #REF! (0.063) x

#REF! (0.438) x#REF!

(3.242) (3.2)#REF! (0.056) x

(1.081) (0.056) x#REF! (0.389) x#REF!

(11.888) (11.9)#REF! (0.123) x

0.152 #REF! (0.123) x#REF! (0.170) x#REF!

13.933 13.9 #REF! (0.133) x #REF!#REF!

(11.888) (11.9)#REF! 0.123 x

0.152 0.036 x#REF! 0.170 x#REF! 0.170 x#REF!

39.167 39.2 0.231 0.055 x

#REF! 0.187 x#REF! #REF! x#REF! 0.258 x#REF!

#REF! #REF!#REF! #REF! x #REF! #REF! x#REF!

#REF! #REF!#REF! #REF! x #REF! #REF! x#REF! #REF! x#REF!

= -3.61

x #REF! = #REF!

= -2.81

x #REF! = #REF!

x #REF! = #REF!x #REF! = #REF!

= -1.35

x #REF! = #REF!

= 43.9 #REF! = #REF!

#REF! = #REF!MI #REF!

= (3.2)#REF! = #REF!#REF! = #REF!#REF! = #REF!

M2 #REF!

= (11.9)#REF! = #REF!

#REF! = #REF!#REF! = #REF!

M3 #REF!

= 13.9 #REF! = #REF!

M4 #REF!

= 13.9 #REF! = #REF!

M5 #REF!

= (11.9)#REF! = #REF!#REF! = #REF!#REF! = #REF!#REF! #REF!

M6 #REF!

= 39.2 #REF! = #REF!#REF! = #REF!#REF! = #REF!#REF! #REF!

M7 #REF!

M8 #REF!

= #REF!#REF! = #REF!#REF! = #REF!#REF! = #REF!

M9 #REF!

Tie Beam

Type TB 1 = 0.2 m x 0.4 m

Ring Balk

Type Balok 30/60 = 0.3 m x 0.6 m

Type Balok 30/40 = 0.3 m x 0.4 m

Type Balok 20/40 = 0.2 m x 0.4 m

Type Balok 20/30 = 0.2 m x 0.3 m

Inersia

a. Inersia Kolom

Kekakuanb x h

1 Type kolom K1 40.000 x 40 0.0833 213,333.333 0.5333

2 Type kolom K2 #REF! x #REF! 0.0833 #REF! #REF!

b. Inersia Tie Beam

Kekakuanb x h

1 Type TB 1 20.000 x 40.00 0.0833 106,666.667 0.0762

Kekakuanb x h

1 Dimensi RB1 20.000 x 30 0.0833 45,000.000 0.0321

d. Inersia Balok

Kekakuanb x h

1 Type Balok 30/60 30.000 x 60 0.0833 540,000.000 0.3857

2 Type Balok 30/40 30.000 x 40 0.0833 160,000.000 0.1143

3 Type Balok 20/40 20.000 x 40 0.0833 106,666.667 0.0762

== -0.0833333333 x 8188.432512 x 16.000 - 0.125 x 5,792.464 x 4= (10,917.9) - 2,896 = (13,814.1) kgm = (13.8) tm

== -0.0833333333 x 8188.432512 x 16.000 - 0.125 x 5,792.464 x 4= (10,917.9) - 2896.232= (13,814.1) kgm = (13.8) tm

== -0.0833333333 x 8188.432512 x 16.000 - 0.125 x 5,792.464 x 4= (10,917.9) - 2896.232= (13,814.1) kgm = (13.8) tm =

= -1/12 x qL2 - 1/8 PL= -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x 4= (3,643.2) - 2055.116= (5,698.4) kgm = (5.7) tm =

== -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x 4= (3,643.2) - 2055.116= (5,698.4) kgm = (5.7) tm

= -1/12 x qL2 - 1/8 PL= -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x 4= (3,643.2) - 2,055.12

Mf1-2 -1/12 x qL2 - 1/8 PL

-Mf1-2

Mf2-3 -1/12 x qL2 - 1/8 PL

-Mf2-3

Mf3-4 -1/12 x qL2 - 1/8 PL

-Mf3-4

Mf4-5 -1/12 x qL2 - 1/8 PL

-Mf7-6

-Mf8-7

Mf9-8 -1/12 x qL2 - 1/8 PL

-Mf9-8

Mf9-10 -1/12 x qL2 - 1/8 PL

Mf10-9

-Mf9-10

Mf11-12 -1/12 x qL2 - 1/8 PL

Mf12-11

-Mf11-12

Mf12-13 -1/12 x qL2 - 1/8 PL

Mf13-12

-Mf12-13

Mf13-14

= (5,698.4) kgm = (5.7) tm

= -1/12 x qL2 - 1/8 PL= -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x 4= (3,643.2) - 2055.12= (5.7) Tm

= -0.0833333333 x 523.26082177 x 16.000 = (697.7)= (0.698) kgm =

== -0.0833333333 x 523.26082177 x 16.000 = (697.7)= (0.698) tm =

= -1/12 x qL2 = -0.08333333 x 523.2608218 x 16.000 = (697.7)= (0.698) tm =

= -1/12 x qL2 = -0.0833333333 x 523.2608218 x 16.000 = -697.6810957= -0.698 tm

Mf14-13

-Mf13-14

Mf14-15

Mf15-14

-Mf14-15

Mf16-17 -1/12 x qL2

Mf17-16

-Mf16-17

Mf17-18 -1/12 x qL2

Mf18-17

-Mf17-18

Mf18--19

Mf19-18

-Mf18-19

Mf19-20

Mf20-19

Mf19-20

1 -13.814 13.81

2 -13.814 13.81

3 -13.814 13.81

4 -13.814 13.81

5 -5.698 5.70

6 -5.698 5.70

7 -5.698 5.70

8 -5.698 5.70

9 -5.698 5.70

10 -5.698 5.70

11 -5.698 5.70

12 -5.698 5.70

13 -0.698 0.698

14 -0.698 0.698

15 -0.698 0.698

16 -0.698 0.698

T1 = +

T Nilai ρ Nilai

-13.814 1.219

0.000 1.371

8.116 0.152

0.000 0.152

0.000 2.438

-5.698 2.286

0.000 2.438

5.001 0.152

0.000 0.064

0.000 1.195

-5.698 1.131

Joint 1

= = 0.076 = 0.063 ρ1 1.219

= = 0.533 = 0.438 ρ1 1.219

0.500 oke!

Joint 2

= = 0.076 = 0.056 ρ2 1.371

= = 0.5333 = 0.389 ρ2 1.371

0.500 oke!

M11-12

M12-11

M12-13

M13-12

M13-14

M14-13

M14-15

M15-14

M16-17

M17-16

M17-18

M18-17

M18-19

M19-19

M19-20

M20-19

T10 ρ

T11 ρ

T12 ρ

T13 ρ

T14 ρ

T15 ρ

T16 ρ

T17 ρ

T18 ρ

T19 ρ

T20 ρ

γ1-10

γ2--1

γ2--9

Joint 3

= = 0.076 = 0.056 ρ3 1.371

= = 0.5333 = 0.389 ρ3 1.371

0.500 oke!

Joint 4

= = 0.076 = 0.056 oke!ρ4 1.371

= = 0.076 = 0.056 ρ4 1.371

= = 0.533 = 0.389 ρ4 1.371

0.500 oke!Joint 5

= = 0.076 = 0.500 oke!ρ5 0.152

Joint 6

= = 0.076 = 0.500 ρ6 0.152

0.500 oke!

Joint 7

= = 0.076 = 0.031 ρ7 2.438

= = 0.533 = 0.219 ρ7 2.438

0.500 oke!

Joint 8

= = 0.076 = 0.031 ρ8 2.438

= = 0.533 = 0.219 ρ8 2.438

0.500 oke!

γ7-14

γ8-13

Joint 9

= = 0.533 = 0.219 ρ9 2.438

= = 0.076 = 0.031 ρ9 2.438

0.500 oke!

Joint 10

= = 0.076 = 0.033 ρ10 2.286

= = 0.533 = 0.233 ρ10 2.286

0.500 oke!

Joint 11

= = 0.076 = 0.033 ρ11 2.286

= = 0.533 = 0.233 ρ11 2.286

0.500 oke!

Joint 12

= = 0.076 = 0.031 ρ12 2.438

= = 0.533 = 0.219 ρ12 2.438

= = 0.076 = 0.031 ρ12 2.438

= = 0.533 = 0.219 ρ12 2.438

0.500 oke!

Joint 13

= = 0.076 = 0.031 ρ13 2.438

= = 0.533 = 0.219 ρ13 2.438

0.500 oke!

γ9-12

γ9-10

γ10-9

γ10-11

K10-11

γ10-1

γ11-12

K11-12

γ11-10

K11-10

γ11-20

K11-16

γ12-11

K12-11

γ12-19

K12-19

γ12-13

K12-13

γ12-9

γ13-14

K13-14

γ13-12

K13-12

γ13-8

γ13-18

K13-14

Joint 14

= = 0.076 = 0.031ρ14 2.438

= = 0.533 = 0.219ρ14 2.438

0.500 oke!

Joint 15

= = 0.076 = 0.500 oke!ρ15 0.152

Joint 16

= = 0.032 = 0.500 oke!ρ16 0.064

Joint 17

= = 0.032 = 0.027 ρ17 1.195

= = 0.533 = 0.446 ρ17 1.195

= = 0.032 = 0.027 ρ17 1.195

0.500 oke!

Joint 18

= = 0.032 = 0.027 ρ18 1.195

= = 0.533 = 0.446 ρ18 1.195

= = 0.032 = 0.027 ρ18 1.195

0.500 oke!

Joint 19

= = 0.032 = 0.027

= = 0.533 = 0.446

= = 0.032 = 0.027

1.195 0.500 oke!

Joint 20

= = 0.533 = 0.472

= = 0.032 = 0.028

1.131 0.500 oke!

γ14-15

K14-15

γ14-13

K14-13

γ14-7

γ14-17

K14-11

γ15-14

K15-14

γ16-17

K16-17

γ17-16

K17-18

γ17-14

K17-14

γ17-18

K17-18

γ18-17

K17-18

γ18-13

K18-13

γ18-19

K18-19

γ19-18

K19-18

γ19-12

K19-12

γ19-20

K19-20

γ20-11

K20-11

γ20-19

K20-19

M1 = -Mf / ρ1

= 13.8141.219

= 11.332 ton

No. Momen Nilai

1 M1 11.332

2 M2 0.000

3 M3 0.000

4 M4 0.000

5 M5 -53.260

6 M6 0.000

7 M7 0.000

8 M8 0.000

9 M9 0.000

10 M10 2.493

11 M11 2.493

12 M12 0.000

13 M13 0.000

14 M14 0.000

15 M15 -32.817

16 M16 0.000

17 M17 0.000

18 M18 0.000

19 M19 0.000

20 M20 5.039

Menentukan nilai T

= 2 x ( 0.533 + 0.533 + 0.533 + 0.533 )

= 4.2667

T2 = 2 x ( 0.5 + 0.533 + 0.533 + 0.533 )

= 4.2667

T3 = 2 x ( 0.5 + 0.533 + 0.533 + 0.533 )

= 4.2667

2*(K1-10

2-9+ K

3-8+ K

2*(K10-11

+ K9-12

+ K6-13+

2*(K11-20

+ K12-19

+ K13-18+

K14+17

Perhitungan nilai t

= 0.375

No. t Nilai

1 0.375

2 0.375

3 0.375

4 0.375

5 0.375

6 0.375

7 0.375

8 0.375

9 0.375

10 0.375

11 0.375

12 0.375

13 0.375

14 0.375

15 0.375

16 0.375

Perhitungan Momen Displacment Arah y

Arah y =

M1 = -h1(∑W) =

= -3.500 x ( 2.20 ) = 4.2667

= -1.805

M2 = -h2(∑W) =

= -4.000 x ( 1.50 ) =

4.2667 = = -1.406 `

M3 = -h3(∑W) =

= -3.600 x ( 0.80 ) =

4.2667 = = -0.675

3.(K1-10

MI (1) MI (0)

(-t1-10

) x (M1( I ) + M10(I) )

(-t2-9

) x (M2( I ) + M9(I) )

(-t3-8

) x (M3( I ) + M8(I) )

(-t4-7

) x (M4( I ) + M7(I) )

MII(1) MII (0)

(-t7-14) x (M7( I ) + M14(I) )

(-t8-13) x (M8( I )+ M13(I))

(-t9-12) x (M9( I )+ M12(I))

(-t10-11) x (M10( I )+ M11(I))

MIII(1) MIII (0)

(-t14-17

) x (M14( I ) + M17(I) )

(-t13-18

) x (M13( I )+ M18(I))

(-t12-19) x (M12( I )+ M19(I))

(-11-20) x (M11( I )+ M20(I))

Putaran 0

MI = MI(0) = 11.3 = 11.332 = γ 1 - 2 x M2 = (0.063) x - = - = γ 1 - 10 x MD 1+M10(0) = (0.438) x 0.688 = (0.301) +

MI = 11.031

M2 = 0.089

M3 = 0.697

M4 = M4(0) = - = - = γ 4-3 x M3(1) = (0.056) x 0.697 = (0.039)= γ 4-5 x M5(0) = (0.056) x -53.260 = 2.959 = γ 4-7 x MD 1+M7 = (0.389) x (1.805) = 0.702 +

M4 = 3.622

M5 = M5(0) = (53.3) = (53.260)= γ 5-4 x M4(1) = (0.500) x 3.622 = (1.811) +

M5 = (55.071)

M6 = M6(0) = - = - = γ 6-7 x M7(0) = (0.031) x - = - +

M6 = -

M7 = M7(0) = - = - = γ 7-6 x M6(1) = (0.031) x - = - = γ 7-8 x M8(0) = (0.031) x - = - = γ 7-14 x MD 2+M14 = (0.219) x (1.406) = 0.308 = γ7-4 x MD 1+M4(1) = (0.219) x 1.817 = 0.308 +

M7 = 0.615

M8 = M8(0) = - = - = γ 8-7 x M7(1) = (0.031) x 0.615 = (0.019)= γ 8-3 x MD 1+ M3(1) = (0.219) x (1.108) = 0.242 = γ8-9 x M9(0) = (0.031) x - = - = γ8-13 x MD 2+M13 = (0.219) x -1.406 = +

M8 = 0.223

M9 = M9(0) = - = - = γ 9-10 x M10(0) = (0.031) x 2.493 = (0.078)= γ 9-8 x M8(1) = (0.031) x 0.223 = (0.007)= γ9-12 x MD 2+M12(0) = (0.219) x (1.406) = 0.308 = γ9-2 x MD 1+M2(1) = (0.219) x (1.317) = 0.288 +

M9 = 0.511

M10 = M10(0) = 2.5 = 2.493 = γ 10-9 x M9(1) = (0.033) x 0.511 = (0.017)= γ 10-11 x MD 2 +M11(0) = (0.233) x 1.087 = (0.254)= γ 10-1 x MD 1+M1(1) = (0.233) x 9.226 = (2.153) +

M10 0.070

M11 = M11(0) = 2.5 = 2.493 = γ 11-12 x M12(0) = (0.033) x - = - = γ 11-10 x MD 2 + M10(1) = (0.233) x (1.337) = 0.312 = γ 11-20 x MD 3+M20(0) = (0.233) x 4.364 = (1.018) +

M11 1.787

M12 = M12(0) = - = - = γ 12-11 x M11(1) = (0.031) x 1.787 = (0.056)= γ 12-13 x M13(0) = (0.031) x - = - = γ 12-9 x MD2+ M9(1) = (0.219) x (0.895) = 0.196 = γ 12-19 x MD3+M19(0) = (0.219) x (0.675) = 0.148 +

M12 = 0.288

M13 = M13(0) = - = - = γ 13-14 x M14(0) = (0.031) x - = - = γ 13-12 x M12(1) = (0.031) x 0.288 = (0.009)= γ 13-18 x MD3+M18(0) = (0.219) x (0.675) = 0.148 = γ 13-8 x MD2+M8(1) = (0.219) x (1.183) = 0.259 +

M13 = 0.397

M14 = M14(0) = - = - = γ 14-13 x M13(1) = (0.031) x 0.397 = (0.012)= γ 14-15 x M15(0) = (0.031) x (32.817) = 1.026 = γ 14-17 x MD 3+M17(0) = (0.219) x (0.675) = 0.148 = γ 14-7 x MD 2+M7(1) = (0.219) x (0.791) = 0.173 +

M14 = 1.334

M15 = M15(0) = (32.8) = (32.817)= γ 15-14 x M14(1) = (0.500) x 1.334 = (0.667) +

M15 = (33.484)

M16 = M16(0) = - = - = γ 16-17 x M17(0) = (0.500) x - = - +

M16 = -

M17 = M17(0) = - = - = γ 17-18 x M18(0) = (0.027) x - = - = γ 17-16 x M16(1) = (0.027) x - = - = γ 17-14 x MD 3+ M14(1) = (0.446) x 0.659 = (0.294) +

M17 = (0.294)

M18 = M18(0) = - = - = γ 18-17 x M17(1) = (0.027) x (0.294) = 0.008 = γ 18-19 x M19(0) = (0.027) x - = - = γ18-13 x MD 3+M13(1) = (0.446) x (0.278) = 0.124 +

M18 = 0.132

M19 = M19(0) = - = - = γ 19-18 x M18(1) = (0.027) x 0.132 = (0.004)= γ 19-20 x M20(0) = (0.027) x 5.039 = (0.135)= γ19-12 x MD 3+M12(1) = (0.446) x (0.387) = 0.173 +

M19 = 0.034

M20 = M20(0) = 5.0 = 5.039 = γ 20-19 x M19(1) = (0.028) x 0.034 = (0.001)= γ20-11 x MD 3+M11(1) = (0.472) x 1.112 = (0.524) +

M20 = 4.513

Joint 1

M1-2 = K 1-2 x + Mf1-2 = 0.076 x #REF! + (13.8)

M1-10 = K 1-10 x + Mf1-10 = 0.533 x #REF! + 0.0∑M

Joint 2

M2-1 = K 2-1 x + Mf2-1 = 0.076 x #REF! + 13.8

M2-3 = K 2-3 x + Mf2-3 = 0.076 x #REF! + -13.8

M2-9 = K 2-9 x + Mf2-9 = 0.533 x #REF! + 0∑M

Joint 3

M3-2 = K 3-2 x + Mf3-2 = 0.076 x #REF! + 13.8

M3-4 = K 3-4 x + Mf3-4 = 0.076 x #REF! + -13.8

M3-8 = K 3-8 x + Mf3-8 = 0.533 x #REF! + 0∑M

Joint 4

M4-3 = K 4-3 x + Mf4-3 = 0.076 x #REF! + 13.8

M4-5 = K 4-5 x + Mf4-5 = 0.076 x +

M4-7 = K 4-7 x + Mf4-7 = 0.533 x + ∑M

Joint 5

M5-4 = K 5-4 x + Mf5-4 = 0.076 x #REF! + 13.8 ∑M

Joint 6

M6-7 = K 6-7 x + Mf6-7 = 0.076 x #REF! + #REF!∑M

Joint 7

M7-6 = K 7-6 x + Mf7-6 = 0.076 x #REF! + (5.7)

M7-8 = K 7-8 x + Mf7-8 = 0.076 x #REF! + 5.7

M7-4 = K 7-4 x + Mf7-4 = 0.533 x #REF! + 0

M7-14 = K 7-14 x + Mf7-14 = 0.533 x #REF! + 0∑M

Joint 8

M8-7 = K 8-7 x + Mf8-7 = 0.076 x #REF! + -

M8-9 = K 8-9 x + Mf8-9 = #REF! x #REF! + 0.0

M8-3 = K 8-3 x + Mf8-3 = 0.533 x #REF! + 0

M8-13 = K 8-13 x + Mf8-13 = 0.533 x + ∑M

Joint 9

M9-10 = K 9-10 x + Mf9-10 = 0.076 x #REF! + (5.7)

M9-8 = K 9-8 x + Mf9-8 = 0.076 x #REF! + 0.0

M9-2 = K 9-2 x + Mf9-2 = 0.533 x #REF! + 0

M9-12 = K 9-12 x + Mf9-13 = 0.533 x + ∑M

Joint 10

M10-11 = K 10-11 x + Mf10-11 = 0.533 x #REF! + (5.7)

M10-9 = K 10-9 x + Mf10-9 = 0.076 x #REF! + 5.7

M10-1 = K 10-7 x + Mf10-7 = 0.533 x #REF! + 0

M10-20 = K 10-15 x + Mf10-15 = 0.533 x #REF! + 0∑M

Joint 11

M11-10 = K 11-10 x + Mf11-10 = 0.533 x #REF! + #REF!

M11-12 = K 11-12 x + Mf11-12 = 0.076 x #REF! + 0.7

M11-20 = K 11-6 x + Mf11-6 = 0.533 x #REF! + 0∑M

Joint 12

M12-11 = K 12-11 x + Mf12-11 = 0.076 x #REF! + 5.7

M12-9 = K 12-9 x + Mf12-19 = 0.533 x +

M12-19 = K 12-19 x + Mf12-19 = 0.533 x +

M12-13 = K 12-13 x + Mf12-13 = 0.076 x + ∑M

Joint 13

M13-14 = K 13-14 x + Mf12-11 = 0.076 x #REF! + 5.7

M13-12 = K 13-12 x + Mf12-11 = 0.076 x +

M13-18 = K 13-18 x + Mf12-11 = 0.533 x +

M13-8 = K 13-8 x + Mf12-11 = 0.533 x + ∑M

{ 2M1(k) + M2(k) }

{2M1(k) + M10(k) }

{ 2M2(k) + M1(k) }

{2M2(k) + M3(k) }

{2M2(k) + M9(k) }

{ 2M3(k) + M2(k) }

{2M3(k) + M4(k) }

{2M3(k) + M8(k) }

{ 2M4(k) + M3(k) }

{ 2M4(k) + M5(k) }

{ 2M4(k) + M7(k) }

{ 2M5(k) + M4(k) }

{2M6(k) + M7(k) }

{ 2M7(k) + M6(k) }

{2M7(k) + M8(k) }

{2M7(k) + M4(k) }

{2M7(k) + M14(k) }

{ 2M8(k) + M7(k) }

{2M8(k) + M9(k) }

{2M8(k) + M3(k) }

{2M8(k) + M13(k) }

{ 2M9(k) + M10(k) }

{2M9(k) + M8(k) }

{2M9(k) + M2(k) }

{2M9(k) + M12(k) }

{ 2M10(k) + M11(k) }

{2M10(k) + M9(k) }

{2M10(k) + M7(k) }

{2M10(k) + M15(k) }

{ 2M11(k) + M10(k)}

{2M11(k) + M12(k) }

{2M11(k) + M6(k) }

{ 2M12(k) + M11(k)}

{ 2M12(k) + M9(k)}

{ 2M12(k) + M19(k)}

{ 2M12(k) + M13(k)}

{ 2M13(k) + M14(k)}

{ 2M13(k) + M12(k)}

{ 2M13(k) + M18(k)}

{ 2M13(k) + M8(k)}

Joint 14

M14-13 = K 14-13 x + Mf14-13 = 0.076 x #REF! + (5.7)

M14-15 = K 14-15 x + Mf14-15 = 0.076 x #REF! + 5.7

M14-17 = K 14-17 x + Mf114-17 = 0.533 x #REF! + 0

M14-7 = K 14-7 x + Mf14-7 = 0.533 x #REF! + 0∑M

Joint 15

M15-14 = K 15-14 x + Mf15-14 = 0.076 x #REF! + (5.7)∑M

Joint 16

M16-17 = K 16-17 x + Mf16-17 = 0.032 x #REF! + (5.7)∑M

Joint 17

M17-18 = K 17-18 x + Mf17-18 = 0.032 x #REF! + (0.7)

M17-16 = K 17-16 x + Mf17-16 = 0.032 x +

M17-14 = K 17-14 x + Mf17-14 = 0.533 x + ∑M

Joint 18

M18-17 = K 18-17 x + Mf18-17 = 0.032 x #REF! + 0.7

M18-19 = K 18-19 x + Mf18-19 = 0.032 x #REF! + -0.7

M18-13 = K 18-13 x + Mf18-13 = 0.533 x #REF! + 0∑M

Joint 19

M19-18 = K 19-18 x + Mf19-18 = 0.032 x #REF! + 0.7

M19-20 = K 19-20 x + Mf19-20 = 0.032 x #REF! + #REF!

M19-12 = K 19-12 x + Mf19-12 = 0.533 x #REF! + 0∑M

Joint 20

M20-19 = K 20-19 x + Mf20-19 = 0.032 x #REF! + -

M20-11 = K 20-11 x + Mf20-11 = 0.533 x #REF! + -13.8∑M

No. Joint ∑M K ∑K K/∑ ∆M

1M1-2 #REF!

#REF!0.08

0.6100.125 #REF! ###

#REF!M1-10 #REF! 0.53 0.875 #REF! ###

M2-1 #REF!

0.08 0.111 #REF! ###

#REF!M2-3 #REF! 0.08 0.686 0.111 #REF! ###

M2-9 #REF! 0.53 0.778 #REF! ###

M3-2 #REF!

0.08 0.111 #REF! ###

#REF!M3-4 #REF! 0.08 0.686 0.111 #REF! ###

M3-8 #REF! 0.53 0.778 #REF! ###

4 #VALUE!M4-3 #REF! 0.08 0.076 1.000 #VALUE! ### #VALUE!

5 #REF!M5-4 #REF! 0.08 0.076 1.000 #REF! ### #REF!

#REF! #REF!

#REF!M6-7 #REF! 0.08 #REF! #REF! ###

#REF! #REF! #REF! ### #REF! #REF! ###

#REF! #REF! #REF! #REF! #REF! ###

{ 2M14(k) + M13(k)}

{2M14(k) + M15(k) }

{2M14(k) + M17(k) }

{2M14(k) + M7(k) }

{ 2M15(k) + M14(k)}

{ 2M16(k) + M17(k) }

{ 2M17(k) + M18(k) }

{ 2M17(k) + M16(k) }

{ 2M17(k) + M14(k) }

{ 2M18(k) + M17(k) }

{2M18(k) + M19(k) }

{2M18(k) + M13(k) }

{ 2M19(k) + M18(k) }

{2M19(k) + M20(k) }

{2M19(k) + M12(k) }

{ 2M20(k) + M13(k) }

{2M20(k) + M11(k) }

Momen desain K /∑K*∆M

Koreksi Mo

M7-6 #REF!

0.063 #REF! ###

#REF!M7-8 #REF! 0.08 0.063 #REF! ###

M7-4 #REF! 0.53 0.438 #REF! ###

M7-14 #REF! 0.53 0.438 #REF! ###

M8-7 #REF!

0.08 #REF! #REF! ###

M8-3 #REF! 0.53 #REF! #REF! ###

M9-10 #REF!

0.08 0.111 #REF! ###

#REF!M9-8 #REF! 0.08 0.686 0.111 #REF! ###

M9-2 #REF! 0.53 0.778 #REF! ###

M10-11 #REF!

0.318 #REF! ###

#REF!M10-9 #REF! 0.08 0.045 #REF! ###

M10-1 #REF! 0.53 0.318 #REF! ###

M10-20 #REF! 0.53 0.318 #REF! ###

M11-10 #REF!

0.53 #REF! #REF! ###

#REF!M11-12 #REF! 0.08 #REF! #REF! ###

M11-20 #REF! 0.53 ### #REF! #REF! ###

12 M12-11 #REF! #REF! 0.08 0.076 1.000 #REF! ### #REF!

13 #REF!M13-14 #REF! 0.08 0.076 1.000 #REF! ### #REF!

M14-13 #REF!

0.063 #REF! ###

#REF!M14-15 #REF! 0.08 0.063 #REF! ###

M14-17 #REF! 0.53 0.438 #REF! ###

M14-7 #REF! 0.53 0.438 #REF! ###

M15-14 #REF!

#REF! #REF! ###

#REF!#REF! #REF! #REF! #REF! #REF! ###

16M16-17 #REF!

#REF!0.03

####REF! #REF! ###

17M17-18 #REF!

#REF!0.03

####REF! #REF! ###

M18-17 #REF!

0.054 #REF! ###

#REF!M18-19 #REF! 0.03 0.054 #REF! ###

M18-13 #REF! 0.53 0.892 #REF! ###

M19-18 #REF!

0.054 #REF! ###

#REF!M19-20 #REF! 0.03 0.054 #REF! ###

M19-12 #REF! 0.53 0.892 #REF! ###

20M20-19 #REF!

#REF!0.03

0.5650.057 #REF! ###

#REF!M20-11 #REF! 0.53 0.943 #REF! ###

P1 P22

RA = P2/3 + 2P1/3 + 1/2qL

RA = P1/3 + 2P2/3 + 1/2qL

RA = 1/2P+ 1/2qL

ba c da b

P1 P22

RA = P2/3 + 2P1/3 + 1/2qL

RA = P1/3 + 2P2/3 + 1/2qL

RA = 1/2P+ 1/2qL

ba c da b

No. JointM.Desain

q p1 p2 L RA RB RM x-y RM y-x ∑R'A ∑R'BStlh Koreksi

1 M1-2 #REF! 8.188 #REF! #REF! 12 #REF! ### #REF! #REF! #REF! #REF!

2 M2-1 #REF! 8.188 #REF! #REF! 12 #REF! ### #REF! #REF! #REF! #REF!

3 M2-3 #REF! #REF! #REF! - 8 #REF! ### #REF! #REF! #REF! #REF!

5 M3-4 #REF! #REF! - - 4 #REF! ### #REF! #VALUE! #REF! #VALUE!

6 M4-3 #VALUE! #REF! - - 4 #REF! ### #REF! #VALUE! #REF! #VALUE!

7 M5-4 #REF! #REF! - - 4 #REF! ### #REF! #REF! #REF! #REF!

8 #REF! #REF! #REF! - - 4 #REF! ### #REF! #REF! #REF! #REF!

11 M7-8 #REF! 2.732 2.055 2.1 12 18.450 ### #REF! #REF! #REF! #REF!

23 #REF! #REF! 2.732 1.028 1.0 12 17.422 ### #REF! #REF! #REF! #REF!

25 M17-18 #REF! 0.523 - - 8 2.093 ### #REF! #REF! #REF! #REF!

RM x-y = M x-y /L

RM y-x = - M y-x /L

RM y-x = -M y-x /L

RM x-y = M x-y /L

RM y-x = M y-x /L

RM x-y = M x-y /L

RM y-x = - M y-x /L

RM y-x = -M y-x /L

RM x-y = M x-y /L

RM y-x = M y-x /L

RM x-y= Mx-y / L

RM y-x= Mx-y / L

RM x-y= Mx-y / L

No. Joint h M desain RMx-y/L RMy-x/L ∑RA ∑RB Da KanDa kanan

1 M1-10 5 #REF! #REF! ### #REF! #REF! #REF! #REF!

4 #REF! 5 #REF! #REF! ### #REF! #REF! #REF! #REF!

Dari put 0 Ke Put 1 Dari put 1 Ke Put 2

= -1.8046875 = -1.80 -1.8046875 =

= (0.38) x 11.1 = -4.16 (0.38) x 12.1 =

= (0.38) x 0.6 = -0.22 (0.38) x 0.5 =

= (0.38) x 0.9 = -0.34 (0.38) x 0.9 =

= (0.38) x 4.237 = -1.59 (0.38) 3.524 =-8.13 =

= -1.40625 = -1.41 -1.40625 =

= (0.38) x 1.9 = 1.57 (0.38) x 1.6 =

= (0.38) x 0.9 = -0.34 (0.38) x 0.8 =

= (0.38) x 0.8 = -0.30 (0.38) x 0.9 =

= (0.38) x 1.856 = -0.70 (0.38) 1.903 =-1.17 =

= -0.675 = -0.68 -0.675 =

= (0.38) x 1.0 = 0.66 (0.38) x 1.1 =

= (0.38) x 0.5 = -0.20 (0.38) x 0.3 =

= (0.38) x 0.3 = -0.12 (0.38) x 0.3 =

= (0.38) x 6.300 = -2.36 (0.38) 6.9 =-2.69 =

Putaran 1 Putaran 2

11.3 = 11.332 11.3 = 11.3 (0.063) x 0.1 = (0.006) (0.063) x (0.207) = 0.0129364 (0.438) x (1.7) = 0.759 + (0.438) x (1.8) = 0.796906

MI 12.09 MI = 12.14

- = - - = - (0.056) x 12.1 = (0.671) (0.056) x 12.1 = -0.674542 (0.056) x 0.7 = (0.039) (0.056) x 0.4 = -0.02363 (0.389) x (1.29) = 0.503 + (0.389) x (1.14) = 0.4425269

M2 (0.207) M2 = (0.3)

- = - - = - (0.056) x (0.207) = 0.011 (0.056) x (0.3) = 0.0142025 (0.056) x 3.6 = (0.201) (0.056) x 3.5 = -0.194357 (0.389) x (1.58) = 0.615 + (0.389) x (1.30) = 0.5051831

M3 = 0.425 M3 = 0.3

- = - - = - (0.056) x 0.4 = (0.024) (0.056) x 0.3 = -0.018057 (0.056) x (55.071) = 3.059 (0.056) x (55.009) = 3.0560576 (0.389) x (1.189) = 0.463 + (0.389) x (1.779) = 0.691974

M4 = 3.498 M4 = 3.7

(53.3) = (53.260) (53.3) = (53.3) (0.500) x 3.498 = (1.749) + (0.500) x 3.7 = -1.864987

M5 = (55.009) M5 = (55.1)

- = - - = - (0.031) x 0.6 = (0.019) + (0.031) x 0.025 = -0.000791

M6 = (0.019) M6 = (0.001)

- = - - = - (0.031) x (0.019) = 0.001 (0.031) x (0.0) = 2.47E-005 (0.031) x 0.2 = (0.007) (0.031) x 0.51 = -0.015801 (0.219) x (0.07) = 0.016 (0.219) x 0.15 = -0.031897 (0.219) x 1.69 = 0.016 + (0.219) x 1.93 = -0.031897

M7 = 0.025 M7 = (0.080)

- = - - = - (0.031) x 0.025 = (0.001) (0.031) x (0.080) = 0.0024866 (0.219) x (1.4) = 0.302 (0.219) x (1.5) = 0.3236754 (0.031) x 0.51 = (0.016) (0.031) x 0.67 = -0.020836 (0.219) x (1.009) = 0.221 + (0.219) x (1.139) = 0.2492134

M8 = 0.506 M8 = 0.6

- = - - = - (0.031) x 0.070 = (0.002) (0.031) x (0.0) = 0.0005254 (0.031) x 0.506 = (0.016) (0.031) x 0.6 = -0.017329 (0.219) x (1.12) = 0.245 (0.219) x (1.18) = 0.2573897 (0.219) x (2.01) = 0.440 + (0.219) x (2.06) = 0.4506977

M9 = 0.67 M9 = 0.7

2.5 = 2.493 2.5 = 2.5 (0.033) x 0.667 = (0.022) (0.033) x 0.7 = -0.023043 (0.233) x 0.4 = (0.089) (0.233) x 0.5 = -0.119848 (0.233) x 10.28 = (2.399) + (0.233) x 10.34 = -2.411983

M10 = (0.017) M10 (0.062)

2.5 = 2.493 2.5 = 2.5 (0.033) x 0.3 = (0.010) (0.033) x 0.230 = -0.007654 (0.233) x (1.4) = 0.332 (0.233) x (1.47) = 0.3425546 (0.233) x 3.84 = (0.896) + (0.233) x 4.33 = -1.009867

M11 = 1.920 M11 = 1.8

- = - - = - (0.031) x 1.9 = (0.060) (0.031) x 1.8 = -0.056815 (0.031) x 0.4 = (0.012) (0.031) x 0.3 = -0.008343 (0.219) x (0.7) = 0.162 (0.219) x (0.7) = 0.1563989 (0.219) x (0.6) = 0.140 + (0.219) x (0.6) = 0.1308257

M12 = 0.230 M12 = 0.2

- = - - = - (0.031) x 1.3 = (0.042) (0.031) x 1.6 = -0.048502 (0.031) x 0.23 = (0.007) (0.031) x 0.2 = -0.00694 (0.219) x (0.5) = 0.119 (0.219) x (0.7) = 0.144196 (0.219) x (0.9) = 0.197 + (0.219) x (0.9) = 0.1863118

M13 = 0.267 M13 = 0.3

- = - - = - (0.031) x 0.3 = (0.008) (0.031) x 0.3 = -0.008596 (0.031) x (33.48) = 1.046 (0.031) x (33.6) = 1.0497807 (0.219) x (0.97) = 0.212 (0.219) x (1.14) = 0.2483882 (0.219) x (1.38) = 0.302 + (0.219) x (1.49) 0.3250233

M14 = 1.552 M14 1.6

(32.8) x = (32.817) (32.8) = (32.8) (0.500) x 1.6 = (0.776) + (0.500) x 1.61 = -0.807298

M15 (33.593) M15 (33.6)

- = - - = - (0.500) x (0.29) = 0.147 + (0.500) x (0.5) = 0.2302444

M16 0.147 M16 0.2

- = - - = - (0.027) x 0.1 = (0.004) (0.027) x 0.016 = -4E-04 (0.446) x 0.1 = (0.066) (0.446) x 0.2 = -0.102739 (0.446) x 0.9 = (0.391) + (0.446) x 0.9 = -0.419262

M17 = (0.460) M17 = (0.5)

- = - - = - (0.027) x (0.5) = 0.012 (0.027) x (0.5) = 0.0140493 (0.223) x 0.0 = (0.008) (0.223) x 0.08 = -0.017166 (0.027) x (0.41) = 0.011 + (0.027) x (0.40) = 0.0107552

M18 = 0.016 M18 0.0

- = - - = - (0.027) x 0.016 = (0.000) (0.027) x 0.0 = -0.000205 (0.027) x 4.5 = (0.121) (0.027) x 5.0 = -0.134543 (0.446) x (0.45) = 0.199 + (0.027) x (0.45) = 0.0121805

M19 = 0.077 M19 (0.1)

5.0 = 5.039 5.0 = 5.0 (0.027) x 0.077 = (0.002) (0.027) x (0.1) = 0.0032961 (0.027) x 1.24 = (0.033) + (0.027) x 1.14 = -0.03074

M20 5.003 M20 5.0

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! +

= #REF!= #REF!

= #REF!

= #REF! +

= #REF!= #REF!

= #REF! +

= 0.000000

= 0.000000= #VALUE!

= #REF! + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= - + = #REF!

= #REF!

= - + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= 0.000000

= 0.000000 + = #VALUE!

= #REF!

= 0.000000

= 0.000000 + = #REF!

= #REF!

= #REF! + = #REF!

= #REF!

= - + = #REF!

= #REF!

= #REF! +

= #REF!= #REF!

= #REF!

= #REF! +

= #REF!= #REF!

= #REF!

= #REF! + = #REF!

∑`RB

-1.80 -1.804688 = -1.80 -1.804688 =

-4.53 (0.38) x 12.1 = -4.53 (0.38) x 12.1 =

-0.17 (0.38) x 0.4 = -0.16 (0.38) x 0.4 =

-0.35 (0.38) x 0.9 = -0.33 (0.38) x 0.9 =

-1.32 (0.38) x 3.650 = -1.37 (0.38) x 3.7 =-8.17 = -8.20 =

-1.41 -1.40625 = -1.41 -1.40625 =

-0.59 (0.38) x 1.5 = -0.58 (0.38) x 1.5 =

-0.29 (0.38) x 0.8 = -0.31 (0.38) x 0.8 =

-0.34 (0.38) x 0.9 = -0.34 (0.38) x 1.0 =

-0.71 (0.38) x 1.756 = -0.66 (0.38) x 1.8 =-3.34 = -3.29 =

-0.68 -0.675 = -0.68 -0.675 =

-0.41 (0.38) x 1.1 = -0.41 (0.38) x 1.1 =

-0.11 (0.38) x 0.3 = -0.11 (0.38) x 0.3 =

-0.11 (0.38) x 0.1 = -0.04 (0.38) x 0.1 =

-2.60 (0.38) x 7 = -2.56 (0.38) x 6.8 =-3.90 = -3.79 =

Putaran 3 Putaran 4

11.3 = 11.3 11.3 = 11.3 (0.063) x (0.3) = 0.015978 (0.063) x (0.3) = 0.016305 (0.438) x (1.9) = 0.816606 (0.438) x (1.8) = 0.808593

MI 12.2 MI 12.2

- = - - = - (0.056) x 12.2 = -0.675805 (0.056) x 12.2 = -0.675378 (0.056) x 0.3 = -0.018057 (0.056) x 0.3 = -0.016302 (0.389) x (1.11) = 0.43299 (0.389) x (1.11) = 0.431421

M2 (0.3) M2 (0.3)

- = - - = - (0.056) x (0.3) = 0.014493 (0.056) x (0.3) = 0.014459 (0.056) x 3.7 = -0.207221 (0.056) x 3.8 = -0.209942 (0.389) x (1.25) = 0.486169 (0.389) x (1.24) = 0.484115

M3 0.3 M3 0.3

- = - - = - (0.056) x 0.3 = -0.016302 (0.056) x 0.3 = -0.016035 (0.056) x (55.1) = 3.062489 (0.056) x (55.1) = 3.06385 (0.389) x (1.884) = 0.732767 (0.389) x -1.913 = 0.74404

M4 = 3.8 M4 = 3.8

(53.3) = (53.3) (53.3) = (53.3) (0.500) x 3.8 = -1.889477 (0.500) x 3.8 = -1.895928

M5 (55.1) M5 (55.2)

- = - - = - (0.031) x (0.1) = 0.002487 (0.031) x (0.1) = 0.003392

M6 0.0 M6 0.0

- = - - = - (0.031) x 0.0 = -8E-005 (0.031) x 0.0 = -0.000106 (0.031) x 0.6 = -0.017329 (0.031) x 0.6 = -0.017494 (0.219) x 0.21 = -0.045576 (0.219) x 0.23 = -0.050159 (0.219) x 1.97 = -0.045576 (0.219) x 1.99 = -0.050159

M7 = (0.1) M7 = (0.1)

- = - - = - (0.031) x (0.1) = 0.003392 (0.031) x (0.1) = 0.003685 (0.219) x (1.5) = 0.330585 (0.219) x (1.5) = 0.331637 (0.031) x 0.7 = -0.021603 (0.031) x 0.7 = -0.021729 (0.219) x (1.131) = 0.247446 (0.219) x -1.134 = 0.248027

M8 = 0.6 M8 = 0.6

- = - - = - (0.031) x (0.1) = 0.001933 (0.031) x (0.0) = 0.00136 (0.031) x 0.6 = -0.017494 (0.031) x 0.6 = -0.017551 (0.219) x (1.18) = 0.25904 (0.219) x (1.14) = 0.249701 (0.219) x (2.07) = 0.451841 (0.219) x (2.06) = 0.451707

M9 = 0.7 M9 = 0.7

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.7 = -0.023177 (0.033) x 0.7 = -0.022841 (0.233) x 0.4 = -0.09609 (0.233) x 0.4 = -0.094711 (0.233) x 10.36 = -2.417289 (0.233) x 10.35 = -2.415495

M10 (0.0) M10 (0.0)

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.2 = -0.007402 (0.033) x 0.3 = -0.008825 (0.233) x (1.4) = 0.338281 (0.233) x (1.4) = 0.337462 (0.233) x 4.34 = -1.011758 (0.233) x 4.34 = -1.011811

M11 1.8 M11 = 2

- = - - = - (0.031) x 1.8 = -0.05663 (0.031) x 1.8 = -0.056558 (0.031) x 0.3 = -0.008596 (0.031) x 0.3 = -0.008513 (0.219) x (0.7) = 0.155516 (0.219) x (0.7) = 0.157726 (0.219) x (0.8) = 0.174468 (0.219) x (0.8) = 0.175033

M12 = 0.3 M12 = 0.3

- = - - = - (0.031) x 1.6 = -0.050456 (0.031) x 1.6 = -0.051111 (0.031) x 0.3 = -0.008274 (0.031) x 0.3 = -0.008365 (0.219) x (0.7) = 0.145985 (0.219) x (0.6) = 0.136098 (0.219) x (0.8) = 0.185156 (0.219) x (0.8) = 0.184763

M13 = 0.3 M13 = 0.3

- = - - = - (0.031) x 0.3 = -0.008513 (0.031) x 0.3 = -0.008168 (0.031) x (33.6) = 1.050758 (0.031) x (33.6) = 1.051085 (0.219) x (1.20) = 0.261937 (0.219) x (1.2) = 0.266957 (0.219) x (1.51) 0.331364 (0.219) x (1.52) 0.333412

M14 1.6 M14 1.6

(32.8) = (32.8) (32.8) = (32.8) (0.500) x 1.6 = -0.817773 (0.500) x 1.6 = -0.821643

M15 (33.6) M15 (33.6)

- = - - = - (0.500) x (0.5) = 0.261213 (0.500) x (0.5) = 0.272686

M16 = 0.3 M16 = 0.3

- = - - = - (0.027) x 0.0 = -0.000205 (0.027) x 0.1 = -0.001421 (0.446) x 0.3 = -0.116557 (0.446) x 0.3 = -0.121677 (0.446) x 1.0 = -0.42861 (0.446) x 1.0 = -0.432063

M17 = (0.5) M17 = (0.6)

- = - - = - (0.027) x (0.5) = 0.014666 (0.027) x (0.6) = 0.01493 (0.223) x (0.1) = 0.027346 (0.223) x (0.1) = 0.027922 (0.027) x (0.40) = 0.010827 (0.027) x (0.41) = 0.011123

M18 = 0.1 M18 0.1

- = - - = - (0.027) x 0.1 = -0.001421 (0.027) x 0.1 = -0.001452 (0.027) x 5.0 = -0.134761 (0.027) x 5.0 = -0.134767 (0.027) x (0.41) = 0.011032 (0.027) x (0.41) = 0.010954

M19 = (0.1) M19 (0.1)

5.0 = 5.0 5.0 = 5.0 (0.027) x (0.1) = 0.003366 (0.027) x (0.1) = 0.003369 (0.027) x 1.14 = -0.030581 (0.027) x 1.13 = -0.030519

M20 = 5.0 M20 = 5.0

Dari put 4 Ke Put 5Dari put 5 Ke Put 6

-1.80 -1.804688 = -1.80 -1.804688 =

-4.55 (0.38) x 12.1 = -4.54 (0.38) x 12.1 =

-0.16 (0.38) x 0.4 = -0.16 (0.38) x 0.4 =

-0.32 (0.38) x 0.9 = -0.32 (0.38) x 0.9 =

-1.38 (0.38) x 3.7 = -1.38 (0.38) x 3.8 =-8.2 = -8.2 =

-1.41 -1.40625 = -1.41 -1.40625 =

-0.57 (0.38) x 1.5 = -0.57 (0.38) x 1.2 =

-0.31 (0.38) x 0.8 = -0.31 (0.38) x 0.8 =

-0.36 (0.38) x 1.0 = -0.36 (0.38) x 1.0 =

-0.66 (0.38) x 1.8 = -0.66 (0.38) x 1.8 =-3.3 = -3.3 =

-0.68 -0.675 = -0.68 -0.675 =

-0.41 (0.38) x 1.1 = -0.43 (0.38) x 1.1 =

-0.12 (0.38) x 0.3 = -0.12 (0.38) x 0.3 =

-0.05 (0.38) x 0.1 = -0.05 (0.38) x 0.1 =

-2.56 (0.38) x 6.8 = -2.56 (0.38) x 6.8 =-3.8 = -3.8 =

Putaran 5 Putaran 6

11.3 = 11.3 11.3 = 11.3 (0.063) x (0.3) = 0.016266 (0.063) x (0.3) = 0.015999 (0.438) x (1.8) = 0.807057 (0.438) x (1.8) = 0.806631

MI 12.2 MI 12.2

- = - - = - (0.056) x 12.2 = -0.675291 (0.056) x 12.2 = -0.675252 (0.056) x 0.3 = -0.016035 (0.056) x 0.287 = -0.015943 (0.389) x (1.12) = 0.435349 (0.389) x (1.12) = 0.43619

M2 = (0.256) M2 = (0.3)

- = - - = - (0.056) x (0.3) = 0.014221 (0.056) x (0.3) = 0.014167 (0.056) x 3.8 = -0.210659 (0.056) x 3.8 = -0.210886 (0.389) x (1.24) = 0.483415 (0.389) x (1.23) = 0.477508

M3 = 0.3 M3 = 0.3

- = - - = - (0.056) x 0.287 = -0.015943 (0.056) x 0.3 = -0.015599 (0.056) x (55.2) = 3.064208 (0.056) x (55.2) = 3.064322 (0.389) x (1.923) = 0.74768 (0.389) x (2.310) = 0.898253

M4 = 3.8 M4 = 3.9

(53.3) = (53.3) (53.3) = (53.3) (0.500) x 3.8 = -1.897972 (0.500) x 3.9 = -1.973488

M5 (55.2) M5 = (55.2)

- = - - = - (0.031) x (0.1) = 0.003685 (0.031) x (0.5) = 0.015785

M6 0.0 M6 = 0.0

- = - - = - (0.031) x 0.0 = -0.000115 (0.031) x 0.0 = -0.000493 (0.031) x 0.6 = -0.017551 (0.031) x 0.6 = -0.018025 (0.219) x 0.24 = -0.051851 (0.219) x 0.32 = -0.0709 (0.219) x 1.99 = -0.435588 (0.219) x 2.14 = -0.0709

M7 = (0.5) M7 = (0.2)

- = - - = - (0.031) x (0.5) = 0.015785 (0.031) x (0.2) = 0.00501 (0.219) x (1.5) = 0.331999 (0.219) x (1.5) = 0.333353 (0.031) x 0.7 = -0.021413 (0.031) x 0.68 = -0.021345 (0.219) x (1.145) = 0.250439 (0.219) x (1.149) = 0.251279

M8 = 0.6 M8 = 0.6

- = - - = - (0.031) x (0.0) = 0.00125 (0.031) x (0.0) = 0.00122 (0.031) x 0.6 = -0.018025 (0.031) x 0.6 = -0.017759 (0.219) x (1.14) = 0.249061 (0.219) x (1.14) = 0.248874 (0.219) x (2.06) = 0.45077 (0.219) x (2.06) = 0.450558

M9 = 0.7 M9 = 0.7

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.7 = -0.022769 (0.033) x 0.7 = -0.022763 (0.233) x 0.4 = -0.094175 (0.233) x 0.4 = -0.094096 (0.233) x 10.35 = -2.415128 (0.233) x 10.35 = -2.414966

M10 = (0.0) M10 = (0.0)

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.3 = -0.008923 (0.033) x 0.3 = -0.008951 (0.233) x (1.4) = 0.337234 (0.233) x (1.4) = 0.337177 (0.233) x 4.34 = -1.011826 (0.233) x 4.34 = -1.011829

M11 = 1.8 M11 = 1.8

- = - - = - (0.031) x 1.8 = -0.056547 (0.031) x 1.8 = -0.056545 (0.031) x 0.3 = -0.008168 (0.031) x 0.3 = -0.008048 (0.219) x (0.7) = 0.158199 (0.219) x (0.7) = 0.158234 (0.219) x (0.8) = 0.175058 (0.219) x (0.8) = 0.175071

M12 = 0.3 M12 = 0.3

- = - - = - (0.031) x 1.6 = -0.051353 (0.031) x 1.7 = -0.054074 (0.031) x 0.3 = -0.008392 (0.031) x 0.3 = -0.008397 (0.219) x (0.6) = 0.135849 (0.219) x (0.6) = 0.135579 (0.219) x (0.8) = 0.18144 (0.219) x (0.8) = 0.183302

M13 = 0.3 M13 = 0.3

- = - - = - (0.031) x 0.3 = -0.008048 (0.031) x 0.3 = -0.008013 (0.031) x (34) = 1.051206 (0.031) x (34) = 1.052567 (0.219) x (1.23) = 0.269098 (0.219) x (1.27) = 0.278082 (0.219) x (1.91) = 0.418109 (0.219) x (1.57) 0.342687

M14 = 1.7 M14 1.7

(32.8) = (32.8) (32.8) = (32.8) (0.500) x 1.7 = -0.865182 (0.500) x 1.7 = -0.832661

M15 = (33.7) M15 = (33.6)

- = - - = - (0.500) x (0.6) = 0.277581 (0.500) x (0.6) = 0.298116

M16 = 0.3 M16 = 0.3

- = - - = - (0.027) x 0.1 = -0.001452 (0.027) x 0.1 = -0.001485 (0.446) x 0.3 = -0.123861 (0.446) x 0.3 = -0.133024 (0.446) x 1.1 = -0.47092 (0.446) x 1.0 = -0.441897

M17 = (0.6) M17 = (0.6)

- = - - = - (0.027) x (0.6) = 0.016034 (0.027) x (0.6) = 0.015501 (0.223) x (0.1) = 0.027948 (0.223) x (0.1) = 0.02796 (0.027) x (0.42) = 0.011226 (0.027) x (0.42) = 0.011257

M18 0.1 M18 0.1

- = - - = - (0.027) x 0.1 = -0.001485 (0.027) x 0.1 = -0.001472 (0.027) x 5.0 = -0.134769 (0.027) x 5.0 = -0.134769 (0.027) x (0.41) = 0.010931 (0.027) x (0.41) = 0.010926

M19 = (0.1) M19 = (0.1)

5.0 = 5.0 5.0 = 5.0 (0.027) x (0.1) = 0.00337 (0.027) x (0.1) = 0.00337 (0.027) x 1.13 = -0.03051 (0.027) x 1.13 = -0.030508

M20 = 5.0 M20 = 5.0

-1.80 -1.804688 = -1.80 -1.804688 =

-4.54 (0.38) x 12.1 = -4.54 (0.38) x 12.1 =

-0.16 (0.38) x 0.4 = -0.16 (0.38) x 0.4 =

-0.32 (0.38) x 0.8 = -0.32 (0.38) x 0.8 =

-1.42 (0.38) x 3.8 = -1.42 (0.38) x 3.7 =-8.3 = -8.2 =

-1.41 -1.40625 = -1.41 -1.40625 =

-0.46 (0.38) x 1.5 = -0.56 (0.38) x 1.5 =

-0.31 (0.38) x 0.8 = -0.31 (0.38) x 0.8 =

-0.36 (0.38) x 1.0 = -0.36 (0.38) x 1.0 =

-0.66 (0.38) x 1.8 = -0.66 (0.38) x 1.8 =-3.2 = -3.3 =

-0.68 -0.675 = -0.68 -0.675 =

-0.43 (0.38) x 1.1 = -0.41 (0.38) x 1.1 =

-0.12 (0.38) x 0.3 = -0.12 (0.38) x 0.3 =

-0.05 (0.38) x 0.1 = -0.05 (0.38) x 0.1 =

-2.56 (0.38) x 6.8 = -2.56 (0.38) x 6.8 =-3.8 = -3.8 =

Putaran 7 Putaran 8

11.3 = 11.3 11.3 = 11.3 (0.063) x (0.3) = 0.015938 (0.063) x (0.3) = 0.015912 (0.438) x (1.8) = 0.806523 (0.438) x (1.8) = 0.806494

MI = 12.2 MI 12.2

- = - - = - (0.056) x 12.2 = -0.675243 (0.056) x 12.2 = -0.67524 (0.056) x 0.3 = -0.015599 (0.056) x 0.3 = -0.015316 (0.389) x (1.12) = 0.436254 (0.389) x (1.12) = 0.436312

M2 = (0.3) M2 (0.3)

- = - - = - (0.056) x (0.3) = 0.014144 (0.056) x (0.3) = 0.014125 (0.056) x 3.9 = -0.219276 (0.056) x 3.8 = -0.212076 (0.389) x (1.24) = 0.480819 (0.389) x (1.24) = 0.480639

M3 = 0.3 M3 = 0.3

- = - - = - (0.056) x 0.3 = -0.015316 (0.056) x 0.3 = -0.015705 (0.056) x (55.2) = 3.068517 (0.056) x (55.2) = 3.064917 (0.389) x (1.965) = 0.764169 (0.389) x (1.936) = 0.752869

M4 = 3.8 M4 = 3.8

(53.3) = (53.3) (53.3) = (53.3) (0.500) x 3.8 = -1.908685 (0.500) x 3.8 = -1.90104

M5 (55.2) M5 (55.2)

- = - - = - (0.031) x (0.2) = 0.00501 (0.031) x (0.1) = 0.004102

M6 0.0 M6 0.0

- = - - = - (0.031) x 0.0 = -0.000157 (0.031) x 0.0 = -0.000128 (0.031) x 0.6 = -0.017759 (0.031) x 0.6 = -0.017774 (0.219) x 0.26 = -0.056672 (0.219) x 0.25 = -0.054097 (0.219) x 2.01 = -0.056672 (0.219) x 2.00 = -0.054097

M7 = (0.1) M7 = (0.1)

- = - - = - (0.031) x (0.1) = 0.004102 (0.031) x (0.1) = 0.00394 (0.219) x (1.5) = 0.334469 (0.219) x (1.5) = 0.332937 (0.031) x 0.68 = -0.02134 (0.031) x 0.68 = -0.021336 (0.219) x (1.150) = 0.251527 (0.219) x (1.148) = 0.251082

M8 = 0.6 M8 = 0.6

- = - - = - (0.031) x (0.0) = 0.001212 (0.031) x (0.0) = 0.00121 (0.031) x 0.6 = -0.017774 (0.031) x 0.6 = -0.017707 (0.219) x (1.14) = 0.248836 (0.219) x (1.14) = 0.248822 (0.219) x (2.06) = 0.450467 (0.219) x (2.06) = 0.450391

M9 = 0.7 M9 = 0.7

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.7 = -0.022758 (0.033) x 0.7 = -0.022757 (0.233) x 0.4 = -0.094075 (0.233) x 0.4 = -0.09407 (0.233) x 10.35 = -2.414927 (0.233) x 10.35 = -2.414914

M10 = (0.0) M10 = (0.0)

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.3 = -0.008957 (0.033) x 0.3 = -0.008959 (0.233) x (1.4) = 0.337161 (0.233) x (1.4) = 0.337157 (0.233) x 4.34 = -1.011829 (0.233) x 4.34 = -1.01183

M11 = 1.8 M11 = 1.8

- = - - = - (0.031) x 1.8 = -0.056544 (0.031) x 1.8 = -0.056544 (0.031) x 0.3 = -0.008013 (0.031) x 0.3 = -0.008076 (0.219) x (0.7) = 0.158267 (0.219) x (0.7) = 0.158273 (0.219) x (0.8) = 0.175069 (0.219) x (0.8) = 0.175067

M12 = 0.3 M12 = 0.3

- = - - = - (0.031) x 1.7 = -0.052041 (0.031) x 1.7 = -0.051673 (0.031) x 0.3 = -0.008399 (0.031) x 0.3 = -0.008398 (0.219) x (0.6) = 0.135687 (0.219) x (0.6) = 0.135756 (0.219) x (0.8) = 0.183201 (0.219) x (0.8) = 0.183668

M13 0.3 M13 = 0.3

- = - - = - (0.031) x 0.3 = -0.008076 (0.031) x 0.3 = -0.008105 (0.031) x (34) = 1.05155 (0.031) x (34) = 1.051366 (0.219) x (1.25) = 0.273745 (0.219) x (1.24) = 0.271625 (0.219) x (1.54) 0.33633 (0.219) x (1.53) 0.335201

M14 1.7 M14 1.7

(32.8) = (32.8) (32.8) = (32.8) (0.500) x 1.7 = -0.826775 (0.500) x 1.7 = -0.825044

M15 (33.6) M15 (33.6)

- = - - = - (0.500) x (0.6) = 0.288203 (0.500) x (0.6) = 0.283358

M16 0.3 M16 0.3

- = - - = - (0.027) x 0.1 = -0.001472 (0.027) x 0.1 = -0.001463 (0.446) x 0.3 = -0.1286 (0.446) x 0.3 = -0.126438 (0.446) x 1.0 = -0.436643 (0.446) x 1.0 = -0.435099

M17 = (0.6) M17 = (0.6)

- = - - = - (0.027) x (0.6) = 0.01524 (0.027) x (0.6) = 0.01514 (0.223) x (0.1) = 0.027959 (0.223) x (0.1) = 0.027957 (0.027) x (0.42) = 0.011202 (0.027) x (0.42) = 0.011178

M18 0.1 M18 = 0.1

- = - - = - (0.027) x 0.1 = -0.001463 (0.027) x 0.1 = -0.00146 (0.027) x 5.0 = -0.134769 (0.027) x 5.0 = -0.134769 (0.027) x (0.41) = 0.010924 (0.027) x (0.41) = 0.010926

M19 (0.1) M19 = (0.1)

5.0 = 5.0 5.0 = 5.0 (0.027) x (0.1) = 0.00337 (0.027) x (0.1) = 0.00337 (0.027) x 1.13 = -0.030507 (0.027) x 1.13 = -0.030507

M20 5.0 M20 = 5.0

-1.80 -1.804688 = -1.80 -1.804688

-4.54 (0.38) x 12.1 = -4.54 (0.38) x 12.1

-0.16 (0.38) x 0.4 = -0.16 (0.38) x 0.4

-0.32 (0.38) x 0.8 = -0.32 (0.38) x 0.9

-1.38 (0.38) x 3.7 = -1.38 (0.38) x 3.7 -8.2 = -8.2

-1.41 -1.40625 = -1.41 -1.40625

-0.57 (0.38) x 1.5 = -0.57 (0.38) x 1.5

-0.31 (0.38) x 0.8 = -0.31 (0.38) x 0.8

-0.36 (0.38) x 1.0 = -0.36 (0.38) x 1.0

-0.66 (0.38) x 1.8 = -0.66 (0.38) x 1.8 -3.3 = -3.3

-0.68 -0.675 = -0.68 -0.675

-0.41 (0.38) x 1.1 = -0.41 (0.38) x 1.1

-0.12 (0.38) x 0.3 = -0.12 (0.38) x 0.3

-0.05 (0.38) x 0.1 = -0.05 (0.38) x 0.1

-2.56 (0.38) x 6.8 = -2.56 (0.38) x 6.8 -3.8 = -3.8

11.3 = 11.3 11.3 = (0.063) x (0.3) = 0.01589 (0.063) x (0.3) = (0.438) x (1.8) = 0.806486 (0.438) x (1.8) =

MI 12.2 MI

- = - - = (0.056) x 12.2 = -0.675238 (0.056) x 12.2 = (0.056) x 0.3 = -0.015705 (0.056) x 0.3 = (0.389) x (1.12) = 0.436322 (0.389) x (1.12) =

M2 (0.3) M2

- = - - = (0.056) x (0.3) = 0.014146 (0.056) x (0.3) = (0.056) x 3.8 = -0.211227 (0.056) x 3.8 = (0.389) x (1.24) = 0.481469 (0.389) x (1.24) =

M3 0.3 M3

- = - - = (0.056) x 0.3 = -0.015799 (0.056) x 0.3 = (0.056) x (55.2) = 3.064492 (0.056) x (55.2) = (0.389) x (1.931) = 0.75086 (0.389) x (1.929) =

M4 = 3.8 M4 =

(53.3) = (53.3) (53.3) = (0.500) x 3.8 = -1.899777 (0.500) x 3.8 =

M5 (55.2) M5 =

- = - - = (0.031) x (0.1) = 0.00394 (0.031) x (0.1) =

M6 0.0 M6 =

- = - - = (0.031) x 0.0 = -0.000123 (0.031) x 0.0 = (0.031) x 0.6 = -0.017707 (0.031) x 0.6 = (0.219) x 0.24 = -0.053339 (0.219) x 0.24 = (0.219) x 1.99 -0.053339 (0.219) x 1.99

M7 (0.1) M7

- = - - = (0.031) x (0.1) = 0.003891 (0.031) x (0.1) = (0.219) x (1.5) = 0.332566 (0.219) x (1.5) = (0.031) x 0.68 = -0.021335 (0.031) x 0.68 = (0.219) x (1.147) = 0.250884 (0.219) x (1.147) =

M8 = 0.6 M8 =

- = - - = (0.031) x (0.0) = 0.00121 (0.031) x (0.0) = (0.031) x 0.6 = -0.017688 (0.031) x 0.6 = (0.219) x (1.14) = 0.248835 (0.219) x (1.14) = (0.219) x (2.06) = 0.450474 (0.219) x (2.06) =

M9 = 0.7 M9 =

2.5 = 2.5 2.5 = (0.033) x 0.7 = -0.022761 (0.033) x 0.7 = (0.233) x 0.4 = -0.094068 (0.233) x 0.4 = (0.233) x 10.35 = -2.414907 (0.233) x 10.35 =

M10 = (0.0) M10 =

2.5 = 2.5 2.5 = (0.033) x 0.3 = -0.008957 (0.033) x 0.3 = (0.233) x (1.4) = 0.337156 (0.233) x (1.4) = (0.233) x 4.34 = -1.01183 (0.233) x 4.34 =

M11 = 1.8 M11 =

- = - - = (0.031) x 1.8 = -0.056544 (0.031) x 1.8 = (0.031) x 0.3 = -0.008105 (0.031) x 0.3 = (0.219) x (0.7) = 0.158248 (0.219) x (0.7) = (0.219) x (0.8) = 0.175066 (0.219) x (0.8) =

M12 = 0.3 M12 =

- = - - = (0.031) x 1.7 = -0.051565 (0.031) x 1.6 = (0.031) x 0.3 = -0.008396 (0.031) x 0.3 = (0.219) x (0.6) = 0.135784 (0.219) x (0.6) = (0.219) x (0.8) = 0.183804 (0.219) x (0.8) =

M13 = 0.3 M13 =

- = - - = (0.031) x 0.3 = -0.008113 (0.031) x 0.3 = (0.031) x (34) = 1.051312 (0.031) x (34) = (0.219) x (1.24) = 0.270813 (0.219) x (1.24) = (0.219) x (1.53) = 0.334854 (0.219) x (1.53)

M14 = 1.6 M14

(32.8) = (32.8) (32.8) = (0.500) x 1.6 = -0.824433 (0.500) x 1.6 =

M15 (33.6) M15

- = - - = (0.500) x (0.6) = 0.2815 (0.500) x (0.6) =

M16 0.3 M16

- = - - = (0.027) x 0.1 = -0.00146 (0.027) x 0.1 = (0.446) x 0.3 = -0.12561 (0.446) x 0.3 = (0.446) x 1.0 = -0.434553 (0.446) x 1.0 =

M17 = (0.6) M17 =

- = - - = (0.027) x (0.6) = 0.015103 (0.027) x (0.6) = (0.223) x (0.1) = 0.027956 (0.223) x (0.1) = (0.027) x (0.42) = 0.01117 (0.027) x (0.42) =

M18 0.1 M18

- = - - = (0.027) x 0.1 = -0.001458 (0.027) x 0.1 = (0.027) x 5.0 = -0.134769 (0.027) x 5.0 = (0.027) x (0.41) = 0.010927 (0.027) x (0.41) =

M19 (0.1) M19

5.0 = 5.0 5.0 = (0.027) x (0.1) = 0.00337 (0.027) x (0.1) = (0.027) x 1.13 = -0.030507 (0.027) x 1.13 =

M20 5.0 M20

= -1.80 -1.804688 = -1.80 -1.804688

= -4.54 (0.38) x 12.1 = -4.54 (0.38)

= -0.16 (0.38) x 0.4 = -0.16 (0.38)

= -0.32 (0.38) x 0.9 = -0.32 (0.38)

= -1.38 (0.38) 3.7 = -1.38 (0.38)= -8.2 = -8.2

= -1.41 -1.40625 = -1.41 -1.40625

= -0.57 (0.38) x 1.5 = -0.57 (0.38)

= -0.31 (0.38) x 0.8 = -0.31 (0.38)

= -0.36 (0.38) x 1.0 = -0.36 (0.38)

= -0.66 (0.38) 1.8 = -0.66 (0.38)= -3.3 = -3.3

= -0.68 -0.675 = -0.68 -0.675

= -0.41 (0.38) x 1.1 = -0.41 (0.38)

= -0.12 (0.38) x 0.3 = -0.12 (0.38)

= -0.05 (0.38) x 0.1 = -0.05 (0.38)

= -2.56 (0.38) x 6.8 = -2.56 (0.38)= -3.8 = -3.8

11.3 11.3 = 11.3 11.3 0.015914 (0.063) x (0.3) = 0.015922567 (0.063) x 0.806484 (0.438) x (1.8) = 0.806486942 (0.438) x 12.2 MI 12.2

- - = - - -0.67524 (0.056) x 12.2 = -0.67524016 (0.056) x

-0.015799 (0.056) x 0.3 = -0.015820939 (0.056) x0.436278 (0.389) x (1.12) = 0.436259261 (0.389) x

(0.3) M2 (0.3)

- - = - - 0.014153 (0.056) x (0.3) = 0.014155658 (0.056) x -0.211086 (0.056) x 3.8 = -0.21104691 (0.056) x

0.48171 (0.389) x (1.24) = 0.4817742111 (0.389) x 0.3 M3 = 0.3

- - = - - -0.015821 (0.056) x 0.3 = -0.015826831 (0.056) x 3.064422 (0.056) x (55.2) = 3.064402552 (0.056) x 0.750243 (0.389) x (1.929) = 0.750027002 (0.389) x 3.8 M4 = 3.8

(53.3) (53.3) = (53.3) (53.3)-1.899422 (0.500) x 3.8 = -1.899301362 (0.500) x (55.2) M5 (55.2)

- - = - - 0.003891 (0.031) x (0.1) = 0.003873543 (0.031) x 0.0 M6 0.0

- - = - - -0.000122 (0.031) x 0.0 = -0.000121 (0.031) x -0.017688 (0.031) x 0.6 = -0.017682 (0.031) x-0.053072 (0.219) x 0.24 = -0.052975 (0.219) x-0.053072 (0.219) x 1.99 -0.052975 (0.219) x (0.1) M7 (0.1)

- - = - - 0.003874 (0.031) x (0.1) = 0.003867 (0.031) x

0.33248 (0.219) x (1.5) = 0.332457 (0.219) x-0.021338 (0.031) x 0.68 = -0.021340 (0.031) x0.250824 (0.219) x (1.147) = 0.250805 (0.219) x

0.6 M8 = 0.6

- - = - - 0.00121 (0.031) x (0.0) = 0.001210 (0.031) x

-0.017682 (0.031) x 0.6 = -0.017681 (0.031) x0.248847 (0.219) x (1.14) = 0.248851 (0.219) x0.450504 (0.219) x (2.06) = 0.450513 (0.219) x

0.7 M9 = 0.7

2.5 2.5 = 2.5 2.5 -0.022763 (0.033) x 0.7 = -0.022763 (0.033) x -0.094069 (0.233) x 0.4 = -0.094069 (0.233) x-2.414912 (0.233) x 10.35 = -2.414915 (0.233) x (0.0) M10 (0.0)

2.5 2.5 = 2.5 2.5 -0.008956 (0.033) x 0.3 = -0.008955 (0.033) x 0.337158 (0.233) x (1.4) = 0.337159 (0.233) x-1.011829 (0.233) x 4.34 = -1.011829 (0.233) x 1.8 M11 = 1.8

- - = - - -0.056544 (0.031) x 1.8 = -0.056544 (0.031) x -0.008113 (0.031) x 0.3 = -0.008116 (0.031) x 0.158238 (0.219) x (0.7) = 0.158238 (0.219) x 0.175066 (0.219) x (0.8) = 0.175065 (0.219) x

0.3 M12 = 0.3

- - = - - -0.051527 (0.031) x 1.6 = -0.051513 (0.031) x -0.008395 (0.031) x 0.3 = -0.008395 (0.031) x 0.135793 (0.219) x (0.6) = 0.135797 (0.219) x

0.18384 (0.219) x (0.8) = 0.183851 (0.219) x 0.3 M13 = 0.3

- - = - - -0.008116 (0.031) x 0.3 = -0.008117 (0.031) x 1.051293 (0.031) x (34) = 1.051286 (0.031) x0.270511 (0.219) x (1.24) = 0.270400277 (0.219) x0.334732 (0.219) x (1.53) 0.334688178 (0.219) x

1.6 M14 1.6

(32.8) (32.8) = (32.8) (32.8)-0.82421 (0.500) x 1.6 = -0.824128943 (0.500) x

(33.6) M15 (33.6)

- - = - - 0.280811 (0.500) x (0.6) = 0.280557777 (0.500) x

0.3 M16 0.3

- - = - - -0.001458 (0.027) x 0.1 = -0.001457927 (0.027) x -0.125302 (0.446) x 0.3 = -0.125189127 (0.446) x-0.434355 (0.446) x 1.0 = -0.434354937 (0.446) x (0.6) M17 = (0.6)

- - = - - 0.01509 (0.027) x (0.6) = 0.015086707 (0.027) x

0.027955 (0.223) x (0.1) = 0.027955185 (0.223) x0.011168 (0.027) x (0.42) = 0.0111673645 (0.027) x

0.1 M18 0.1

- - = - - -0.001458 (0.027) x 0.1 = -0.001457819 (0.027) x -0.134769 (0.027) x 5.0 = -0.134769048 (0.027) x0.010928 (0.027) x (0.41) = 0.010927923 (0.027) x

(0.1) M19 (0.1)

5.0 5.0 = 5.0 5.0 0.00337 (0.027) x (0.1) = 0.003369593 (0.027) x

-0.030507 (0.027) x 1.13 = -0.030506946 (0.027) x 5.0 M20 5.0

= -1.80 -1.804688 = -1.80

x 12.1 = -4.54 (0.38) x 12.1 = -4.54

x 0.4 = -0.16 (0.38) x 0.4 = -0.16

x 0.9 = -0.32 (0.38) x 0.9 = -0.32

x 3.7 = -1.38 (0.38) x 3.7 = -1.38= -8.2 = -8.2

= -1.41 -1.40625 = -1.41

x 1.5 = -0.57 (0.38) x 1.5 = -0.57

x 0.8 = -0.31 (0.38) x 0.8 = -0.31

x 1.0 = -0.36 (0.38) x 1.0 = -0.36

x 1.8 = -0.66 (0.38) x 1.8 = -0.66= -3.3 = -3.3

= -0.68 -0.675 = -0.68

x 1.1 = -0.41 (0.38) x 1.1 = -0.41

x 0.3 = -0.12 (0.38) x 0.3 = -0.12

x 0.1 = -0.05 (0.38) x 0.1 = -0.05

x 6.8 = -2.56 (0.38) x 6.8 = -2.56= -3.8 = -3.8

Putaran 13

= 11.3 11.3 = 11.3 (0.3) = 0.015925115 (0.063) x (0.3) = 0.015925862 (1.8) = 0.806488708 (0.438) x (1.8) = 0.806489371MI 12.2 MI 12.2

= - - = - 12.2 = -0.6752404 (0.056) x 12.2 = -0.675240478 0.3 = -0.015826831 (0.056) x 0.3 = -0.015828684 (1.12) = 0.436253439 (0.389) x (1.12) = 0.4362519273M2 (0.3) M2 (0.3)

= - - = - (0.3) = 0.014156322 (0.056) x (0.3) = 0.0141565131 3.8 = -0.211033485 (0.056) x 3.8 = -0.2110286821 (1.24) = 0.481793477 (0.389) x (1.24) = 0.4817998012M3 0.3 M3 0.3

= - - = - 0.3 = -0.015829 (0.056) x 0.3 = -0.015829313 (55.2) = 3.064396 (0.056) x (55.2) = 3.0643934383 (1.928) = 0.749949 (0.389) x (1.928) = 0.7499207877M4 3.8 M4 = 3.8

= (53.3) (53.3) = (53.3) 3.8 = -1.899258139 (0.500) x 3.8 = -1.899242457M5 (55.2) M5 (55.2)

= - - = - (0.1) = 0.003867284 (0.031) x (0.1) = 0.0038650075

M6 0.0 M6 0.0

= - - = - 0.0 = -0.000121 (0.031) x 0.0 = -0.000120781 0.6 = -0.017681 (0.031) x 0.6 = -0.017680429 0.24 = -0.052939 (0.219) x 0.24 = -0.052929683 1.99 -0.052939 (0.219) x 1.99 -0.052929683

M7 (0.1) M7 (0.1)

= - - = - (0.1) = 0.003865 (0.031) x (0.1) = 0.0038644 (1.5) = 0.332450 (0.219) x (1.5) = 0.3324475 0.68 = -0.021340 (0.031) x 0.68 = -0.0213405 (1.147) = 0.250799 (0.219) x (1.147) = 0.2507971

M8 = 0.6 M8 0.6

= - - = - (0.0) = 0.001210 (0.031) x (0.0) = 0.001210 0.6 = -0.017680 (0.031) x 0.6 = -0.017680 (1.14) = 0.248851 (0.219) x (1.14) = 0.248853 (2.06) = 0.450516 (0.219) x (2.06) = 0.450517

M9 = 0.7 M9 = 0.7

= 2.5 2.5 = 2.5 0.7 = -0.022763 (0.033) x 0.7 = -0.0227633 0.4 = -0.094070 (0.233) x 0.4 = -0.0940699 10.35 = -2.414916 (0.233) x 10.35 = -2.4149163

M10 (0.0) M10 (0.0)

= 2.5 2.5 = 2.5 0.3 = -0.008955 (0.033) x 0.3 = -0.008954603 (1.4) = 0.337159 (0.233) x (1.4) = 0.3371590326 4.34 = -1.011829 (0.233) x 4.34 = -1.0118294545

M11 1.8 M11 1.8

= - - = - 1.8 = -0.056544 (0.031) x 1.8 = -0.056543975 0.3 = -0.008117 (0.031) x 0.3 = -0.0081171613 (0.7) = 0.158234 (0.219) x (0.7) = 0.1582330518 (0.8) = 0.175065 (0.219) x (0.8) = 0.1750653434

M12 = 0.3 M12 = 0.3

= - - = - 1.6 = -0.051508 (0.031) x 1.6 = -0.051506696 0.3 = -0.008395 (0.031) x 0.3 = -0.008394914 (0.6) = 0.135798 (0.219) x (0.6) = 0.1357987322 (0.8) = 0.183854 (0.219) x (0.8) = 0.1838553507

M13 = 0.3 M13 = 0.3

= - - = - 0.3 = -0.008117 (0.031) x 0.3 = -0.0081172648 (34) = 1.051284 (0.031) x (34) = 1.0512830679 (1.24) = 0.270375 (0.219) x (1.24) = 0.2703497448 (1.53) 0.334672 (0.219) x (1.53) 0.3346679384

M14 1.6 M14 1.6

= (32.8) (32.8) = (32.8) 1.6 = -0.824107 (0.500) x 1.6 = -0.824091743

M15 (33.6) M15 (33.6)

= - - = - (0.6) = 0.280501 (0.500) x (0.6) = 0.2804422739

M16 0.3 M16 0.3

= - - = - 0.1 = -0.001458 (0.027) x 0.1 = -0.001457726 0.3 = -0.125164 (0.446) x 0.3 = -0.125137588 1.0 = -0.434263 (0.446) x 1.0 = -0.434249205

M17 = (0.6) M17 = (0.6)

= - - = - (0.6) = 0.015083549 (0.027) x (0.6) = 0.0150824721 (0.1) = 0.027955143 (0.223) x (0.1) = 0.0279550913 (0.42) = 0.011167104 (0.027) x (0.42) = 0.0111670152

M18 0.1 M18 0.1

= - - = - 0.1 = -0.001457726 (0.027) x 0.1 = -0.001457693 5.0 = -0.134769047 (0.027) x 5.0 = -0.134769046 (0.41) = 0.01092806 (0.027) x (0.41) = 0.0109280817

M19 (0.1) M19 (0.1)

= 5.0 5.0 = 5.0 (0.1) = 0.003369587 (0.027) x (0.1) = 0.0033695854 1.13 = -0.030506958 (0.027) x 1.13 = -0.030506966

M20 5.0 M20 5.0

-1.804688 = -1.80 -1.804688 =

(0.38) x 12.1 = -4.54 (0.38) x 12.1 =

(0.38) x 0.4 = -0.16 (0.38) x 0.4 =

(0.38) x 0.9 = -0.32 (0.38) x 0.9 =

(0.38) x 3.7 = -1.38 (0.38) x 3.7 == -8.2 =

-1.40625 = -1.41 -1.40625 =

(0.38) x 1.5 = -0.57 (0.38) x 1.5 =

(0.38) x 0.8 = -0.31 (0.38) x 0.8 =

(0.38) x 1.0 = -0.36 (0.38) x 1.0 =

(0.38) x 1.8 = -0.66 (0.38) x 1.8 == -3.3 =

-0.675 = -0.68 -0.675 =

(0.38) x 1.1 = -0.41 (0.38) x 1.1 =

(0.38) x 0.3 = -0.12 (0.38) x 0.3 =

(0.38) x 0.1 = -0.05 (0.38) x 0.1 =

(0.38) x 6.8 = -2.56 (0.38) x 6.8 == -3.8 =

11.3 = 11.3 11.3 = 11.3 (0.063) x (0.3) = 0.0159260772 (0.063) x (0.3) = 0.0159261685 (0.438) x (1.8) = 0.8064895924 (0.438) x (1.8) = 0.8064896752

MI 12.2 MI 12.2

- = - - = - (0.056) x 12.2 = -0.6752405023 (0.056) x 12.2 = -0.675240512 (0.056) x 0.3 = -0.0158293129 (0.056) x 0.3 = -0.0158295293 (0.389) x (1.12) = 0.4362511198 (0.389) x (1.12) = 0.4362508949

M2 (0.3) M2 (0.3)

- = - - = - (0.056) x (0.3) = 0.0141565942 (0.056) x (0.3) = 0.0141566192 (0.056) x 3.8 = -0.2110269396 (0.056) x 3.8 = -0.2110264543 (0.389) x (1.24) = 0.4818018735 (0.389) x (1.24) = 0.4818026778

M3 0.3 M3 0.3

- = - - = - (0.056) x 0.3 = -0.0158295293 (0.056) x 0.3 = -0.0158296024 (0.056) x (55.2) = 3.064392567 (0.056) x (55.2) = 3.0643923244 (0.389) x (1.928) = 0.7499131406 (0.389) x (1.928) = 0.7499078319

M4 = 3.8 M4 = 3.8

(53.3) = (53.3) (53.3) = (53.3) (0.500) x 3.8 = -1.8992380891 (0.500) x 3.8 = -1.899235277

M5 (55.2) M5 (55.2)

- = - - = - (0.031) x (0.1) = 0.003864393 (0.031) x (0.1) = 0.0038639664

M6 0.0 M6 0.0

- = - - = - (0.031) x 0.0 = -0.0001207623 (0.031) x 0.0 = -0.000120749 (0.031) x 0.6 = -0.0176802624 (0.031) x 0.6 = -0.0176801978 (0.219) x 0.24 = -0.0529229501 (0.219) x 0.24 = -0.0529202648 (0.219) x 1.99 -0.0529229501 (0.219) x 1.99 -0.0529202648

M7 (0.1) M7 (0.1)

- = - - = - (0.031) x (0.1) = 0.0038639664 (0.031) x (0.1) = 0.0038637961 (0.219) x (1.5) = 0.3324466189 (0.219) x (1.5) = 0.3324463313 (0.031) x 0.68 = -0.0213405908 (0.031) x 0.68 = -0.0213406089 (0.219) x (1.146) = 0.2507963341 (0.219) (1.146) = 0.2507959648

M8 = 0.6 M8 = 0.6

- = - - = - (0.031) x (0.0) = 0.0012099151 (0.031) x (0.0) = 0.001209921 (0.031) x 0.6 = -0.0176801978 (0.031) x 0.6 = -0.0176801714 (0.219) x (1.14) = 0.2488527871 (0.219) x (1.14) = 0.2488527871 (0.219) x (2.06) = 0.4505169802 (0.219) x (2.06) = 0.4505170789

M9 = 0.7 M9 = 0.7

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.7 = -0.0227633162 (0.033) x 0.7 = -0.0227633205 (0.233) x 0.4 = -0.0940700112 (0.233) x 0.4 = -0.0940700284 (0.233) x 10.35 = -2.4149163598 (0.233) x 10.35 = -2.4149164004

M10 (0.0) M10 = (0.0)

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.3 = -0.0089545753 (0.033) x 0.3 = -0.0089545672 (0.233) x (1.4) = 0.3371590768 (0.233) x (1.4) = 0.3371590913 (0.233) x 4.34 = -1.0118294523 (0.233) x 4.34 = -1.0118294517

M11 1.8 M11 = 1.8

- = - - = - (0.031) x 1.8 = -0.056543977 (0.031) x 1.8 = -0.0565439777 (0.031) x 0.3 = -0.0081172648 (0.031) x 0.3 = -0.0081173175 (0.219) x (0.7) = 0.1582329252 (0.219) x (0.7) = 0.1582328966 (0.219) x (0.8) = 0.1750653313 (0.219) x (0.8) = 0.1750653272

M12 = 0.3 M12 = 0.3

- = - - = - (0.031) x 1.6 = -0.0515057339 (0.031) x 1.6 = -0.0515053503 (0.031) x 0.3 = -0.0083949067 (0.031) x 0.3 = -0.008394904 (0.219) x (0.6) = 0.1357989984 (0.219) x (0.6) = 0.135799096 (0.219) x (0.8) = 0.1838558031 (0.219) x (0.8) = 0.183855988

M13 = 0.3 M13 = 0.3

- = - - = - (0.031) x 0.3 = -0.0081173175 (0.031) x 0.3 = -0.0081173384 (0.031) x (34) = 1.051282587 (0.031) x (34) = 1.0512823951 (0.219) x (1.24) = 0.2703409885 (0.219) x (1.24) = 0.2703378295 (0.219) x (1.53) = 0.3346649523 (0.219) x (1.53) 0.3346637604

M14 1.6 M14 1.6

(32.8) = (32.8) (32.8) = (32.8) (0.500) x 1.6 = -0.8240856052 (0.500) x 1.6 = -0.8240833233

M15 (33.6) M15 (33.6)

- = - - = - (0.500) x (0.6) = 0.2804222595 (0.500) x (0.6) = 0.2804150389

M16 0.3 M16 0.3

- = - - = - (0.027) x 0.1 = -0.0014576929 (0.027) x 0.1 = -0.0014576809 (0.446) x 0.3 = -0.1251286576 (0.446) x 0.3 = -0.1251254357 (0.446) x 1.0 = -0.4342437273 (0.446) x 1.0 = -0.4342416909

M17 (0.6) M17 (0.6)

- = - - = - (0.027) x (0.6) = 0.0150820838 (0.027) x (0.6) = 0.015081942 (0.223) x (0.1) = 0.027955079 (0.223) x (0.1) = 0.0279550748 (0.027) x (0.42) = 0.0111669698 (0.027) x (0.42) = 0.0111669518

M18 0.1 M18 0.1

- = - - = - (0.027) x 0.1 = -0.0014576809 (0.027) x 0.1 = -0.0014576764 (0.027) x 5.0 = -0.1347690462 (0.027) x 5.0 = -0.1347690461 (0.027) x (0.41) = 0.0109280882 (0.027) x (0.41) = 0.0109280906

M19 (0.1) M19 (0.1)

5.0 = 5.0 5.0 = 5.0 (0.027) x (0.1) = 0.0033695849 (0.027) x (0.1) = 0.0033695847 (0.027) x 1.13 = -0.0305069683 (0.027) x 1.13 = -0.0305069689

M20 5.0 M20 5.0

-1.80 -1.804688 = -1.80 -1.804688

-4.54 (0.38) x 12.1 = -4.54 (0.38) x

-0.16 (0.38) x 0.4 = -0.16 (0.38) x

-0.32 (0.38) x 0.9 = -0.32 (0.38) x

-1.38 (0.38) x 3.7 = -1.38 (0.38) x-8.2 = -8.2

-1.41 -1.40625 = -1.41 -1.40625

-0.57 (0.38) x 1.5 = -0.57 (0.38) x

-0.31 (0.38) x 0.8 = -0.31 (0.38) x

-0.36 (0.38) x 1.0 = -0.36 (0.38) x

-0.66 (0.38) x 1.8 = -0.66 (0.38) x-3.3 = -3.3

-0.68 -0.675 = -0.68 -0.675

-0.41 (0.38) x 1.1 = -0.41 (0.38) x

-0.12 (0.38) x 0.3 = -0.12 (0.38) x

-0.05 (0.38) x 0.1 = -0.05 (0.38) x

-2.56 (0.38) x 6.8 = -2.56 (0.38) x-3.8 = -3.8

11.3 = 11.3 11.3 (0.063) x (0.3) = 0.015926197 (0.063) x (0.3) (0.438) x (1.8) = 0.806489702 (0.438) x (1.8)

MI 12.2 MI

- = - - (0.056) x 12.2 = -0.675240515 (0.056) x 12.2 (0.056) x 0.3 = -0.015829602 (0.056) x 0.3 (0.389) x (1.12) = 0.436250844 (0.389) x (1.12)

M2 (0.3) M2

- = - - (0.056) x (0.3) = 0.014156626 (0.056) x (0.3) (0.056) x 3.8 = -0.211026142 (0.056) x 3.8 (0.389) x (1.24) = 0.481803006 (0.389) x (1.24)

M3 0.3 M3

- = - - (0.056) x 0.3 = -0.015829638 (0.056) x 0.3 (0.056) x (55.2) = 3.064392168 (0.056) x (55.2) (0.389) x (1.928) = 0.749905713 (0.389) x (1.928)

M4 = 3.8 M4

(53.3) = (53.3) (53.3) (0.500) x 3.8 = -1.899234121 (0.500) x 3.8

M5 (55.2) M5

- = - - (0.031) x (0.1) = 0.003863796 (0.031) x (0.1)

M6 0.0 M6

- = - - (0.031) x 0.0 = -0.000120744 (0.031) x 0.0 (0.031) x 0.6 = -0.017680171 (0.031) x 0.6 (0.219) x 0.24 = -0.052919266 (0.219) x 0.24 (0.219) x 1.99 -0.052919266 (0.219) x 1.99

M7 (0.1) M7

- = - - (0.031) x (0.1) = 0.0038637 (0.031) x (0.1) (0.219) x (1.5) = 0.3324462 (0.219) x (1.5) (0.031) x 0.68 = -0.0213406 (0.031) x 0.68 (0.219) x (1.146) = 0.2507958 (0.219) x (1.146)

M8 0.6 M8

- = - - (0.031) x (0.0) = 0.001209923 (0.031) x (0.0) (0.031) x 0.6 = -0.01768016 (0.031) x 0.6 (0.219) x (1.14) = 0.248852859 (0.219) x (1.14) (0.219) x (2.06) = 0.450517107 (0.219) x (2.06)

M9 = 0.7 M9

2.5 = 2.5 2.5 (0.033) x 0.7 = -0.022763324 (0.033) x 0.7 (0.233) x 0.4 = -0.094070034 (0.233) x 0.4 (0.233) x 10.35 = -2.414916413 (0.233) x 10.35

M10 = (0.0) M10

2.5 = 2.5 2.5 (0.033) x 0.3 = -0.008954564 (0.033) x 0.3 (0.233) x (1.4) = 0.337159096 (0.233) x (1.4) (0.233) x 4.34 = -1.011829452 (0.233) x 4.34

M11 = 1.8 M11

- = - - (0.031) x 1.8 = -0.056543978 (0.031) x 1.8 (0.031) x 0.3 = -0.008117338 (0.031) x 0.3 (0.219) x (0.7) = 0.158232872 (0.219) x (0.7) (0.219) x (0.8) = 0.175065326 (0.219) x (0.8)

M12 = 0.3 M12

- = - - (0.031) x 1.6 = -0.051505208 (0.031) x 1.6 (0.031) x 0.3 = -0.008394903 (0.031) x 0.3 (0.219) x (0.6) = 0.135799132 (0.219) x (0.6) (0.219) x (0.8) = 0.183856066 (0.219) x (0.8)

M13 = 0.3 M13

- = - - (0.031) x 0.3 = -0.008117346 (0.031) x 0.3 (0.031) x (34) = 1.051282324 (0.031) x (34) (0.219) x (1.24) = 0.270336677 (0.219) x (1.24) (0.219) x (1.53) = 0.334663317 (0.219) x (1.53)

M14 1.6 M14

(32.8) = (32.8) (32.8) (0.500) x 1.6 = -0.824082485 (0.500) x 1.6

M15 (33.6) M15

- = - - (0.500) x (0.6) = 0.280412404 (0.500) x (0.6)

M16 0.3 M16

- = - - (0.027) x 0.1 = -0.001457676 (0.027) x 0.1 (0.446) x 0.3 = -0.12512426 (0.446) x 0.3 (0.446) x 1.0 = -0.434240943 (0.446) 1.0

M17 (0.6) M17

- = - - (0.027) x (0.6) = 0.01508189 (0.027) x (0.6) (0.223) x (0.1) = 0.027955073 (0.223) x (0.1) (0.027) x (0.42) = 0.0111669449 (0.027) x (0.42)

M18 0.1 M18

- = - - (0.027) x 0.1 = -0.001457675 (0.027) x 0.1 (0.027) x 5.0 = -0.134769046 (0.027) x 5.0 (0.027) x (0.41) = 0.010928092 (0.027) x (0.41)

M19 (0.1) M19

5.0 = 5.0 5.0 (0.027) x (0.1) = 0.003369585 (0.027) x (0.1) (0.027) x 1.13 = -0.030506969 (0.027) x 1.13

M20 5.0 M20

= -1.80 -1.8047 = -1.80 -1.8046875

12.1 = -4.54 (0.38) x 12.1 = -4.54 (0.38)

0.4 = -0.16 (0.38) x 0.4 = -0.16 (0.38)

0.9 = -0.32 (0.38) x 0.9 = -0.32 (0.38)

3.7 = -1.38 (0.38) x 3.7 = -1.38 (0.38)= -8.2 = -8.2

= -1.41 -1.4063 = -1.41 -1.40625

1.5 = -0.57 (0.38) x 1.5 = -0.57 (0.38)

0.8 = -0.31 (0.38) x 0.8 = -0.31 (0.38)

1.0 = -0.36 (0.38) x 1.0 = -0.36 (0.38)

1.8 = -0.66 (0.38) x 1.8 = -0.66 (0.38)= -3.3 = -3.3

= -0.68 -0.675 = -0.68 -0.675

1.1 = -0.41 (0.38) x 1.1 = -0.41 (0.38)

0.3 = -0.12 (0.38) x 0.3 = -0.12 (0.38)

0.1 = -0.05 (0.38) x 0.1 = -0.05 (0.38)

6.8 = -2.56 (0.38) x 6.8 = -2.56 (0.38)= -3.8 = -3.8

= 11.3 11.3 = 11.3 11.3 = 0.015926205 (0.063) x (0.3) = 0.0159262097 (0.063) x = 0.806489712 (0.438) x (1.8) = 0.8064897152 (0.438) x

12.2 MI 12.2

= - - = - - = -0.675240516 (0.056) x 12.2 = -0.675240517 (0.056) x = -0.015829638 (0.056) x 0.3 = -0.015829653 (0.056) x= 0.4362508 (0.389) x (1.12) = 0.436250787 (0.389) x

(0.3) M2 (0.3)

= - - = - - = 0.014156631 (0.056) x (0.3) = 0.0141566324 (0.056) x = -0.211026013 (0.056) x 3.8 = -0.211025965 (0.056) x= 0.481803145 (0.389) x (1.24) = 0.4818032002 (0.389) x

0.3 M3 0.3

= - - = - - = -0.015829653 (0.056) x 0.3 = -0.015829659 (0.056) x = 3.064392104 (0.056) x (55.2) = 3.0643920799 (0.056) x = 0.749904924 (0.389) x (1.928) = 0.7499046339 (0.389) x = 3.8 M4 = 3.8

= (53.3) (53.3) = (53.3) (53.3)= -1.899233687 (0.500) x 3.8 = -1.899233527 (0.500) x

(55.2) M5 (55.2)

= - - = - - = 0.003863733 (0.031) x (0.1) = 0.0038637094 (0.031) x

0.0 M6 0.0

= - - = - - = -0.000120742 (0.031) x 0.0 = -0.000120741 (0.031) x = -0.01768016 (0.031) x 0.6 = -0.017680156 (0.031) x= -0.0529189 (0.219) x 0.24 = -0.052918765 (0.219) x

-0.0529189 (0.219) x 1.99 = -0.052918765 (0.219) x (0.1) - M7 = (0.1) -

= - - = - - = 0.003863709 (0.031) x (0.1) = 0.0038637009 (0.031) x = 0.33244613 (0.219) x (1.5) = 0.3324461071 (0.219) x= -0.021340617 (0.031) x 0.68 = -0.021340618 (0.031) x= 0.250795762 (0.219) x (1.146) = 0.2507957409 (0.219) x= 0.6 M8 = 0.6

= - - = - - = 0.001209924 (0.031) x (0.0) = 0.0012099239 (0.031) x = -0.017680156 (0.031) x 0.6 = -0.017680154 (0.031) x= 0.24885287 (0.219) x (1.14) = 0.2488528733 (0.219) x= 0.450517124 (0.219) x (2.06) = 0.4505171307 (0.219) x= 0.7 M9 = 0.7

= 2.5 2.5 = 2.5 2.5 = -0.022763325 (0.033) x 0.7 = -0.022763326 (0.033) x = -0.094070036 (0.233) x 0.4 = -0.094070036 (0.233) x= -2.414916417 (0.233) x 10.35 = -2.414916419 (0.233) x

(0.0) M10 = (0.0)

= 2.5 2.5 = 2.5 2.5 = -0.008954563 (0.033) x 0.3 = -0.008954562 (0.033) x = 0.337159098 (0.233) x (1.4) = 0.3371590988 (0.233) x= -1.011829451 (0.233) x 4.34 = -1.011829451 (0.233) x

1.8 M11 = 1.8

= - - = - - = -0.056543978 (0.031) x 1.8 = -0.056543978 (0.031) x = -0.008117346 (0.031) x 0.3 = -0.00811735 (0.031) x = 0.158232865 (0.219) x (0.7) = 0.158232862 (0.219) x = 0.175065325 (0.219) x (0.8) = 0.1750653249 (0.219) x = 0.3 M12 = 0.3

= - - = - - = -0.051505155 (0.031) x 1.6 = -0.051505136 (0.031) x = -0.008394902 (0.031) x 0.3 = -0.008394902 (0.031) x = 0.135799145 (0.219) x (0.6) = 0.1357991499 (0.219) x = 0.183856097 (0.219) x (0.8) = 0.1838561088 (0.219) x = 0.3 M13 = 0.3

= - - = - - = -0.00811735 (0.031) x 0.3 = -0.008117351 (0.031) x = 1.051282298 (0.031) x (34) = 1.0512822881 (0.031) x= 0.270336255 (0.219) x (1.24) = 0.2703361005 (0.219) x= 0.334663153 (0.219) x (1.53) 0.3346630936 (0.219) x

1.6 M14 1.6

= (32.8) (32.8) = (32.8) (32.8)= -0.824082178 (0.500) x 1.6 = -0.824082066 (0.500) x

(33.6) M15 (33.6)

= - - = - - = 0.28041144 (0.500) x (0.6) = 0.2804110868 (0.500) x

0.3 M16 0.3

= - - = - - = -0.001457675 (0.027) x 0.1 = -0.001457674 (0.027) x = -0.12512383 (0.446) x 0.3 = -0.125123672 (0.446) x

-0.434240669 (0.446) x 1.0 = -0.434240569 (0.446) x (0.6) M17 = (0.6)

= - - = - - = 0.015081871 (0.027) x (0.6) = 0.0150818642 (0.027) x = 0.027955073 (0.223) x (0.1) = 0.0279550724 (0.223) x= 0.0111669422 (0.027) x (0.42) = 0.0111669413 (0.027) x

0.1 M18 0.1

= - - = - - = -0.001457674 (0.027) x 0.1 = -0.001457674 (0.027) x = -0.134769046 (0.027) x 5.0 = -0.134769046 (0.027) x= 0.010928092 (0.027) x (0.41) = 0.0109280924 (0.027) x

(0.1) M19 (0.1)

= 5.0 5.0 = 5.0 5.0 = 0.003369585 (0.027) x (0.1) = 0.0033695846 (0.027) x = -0.030506969 (0.027) x 1.13 = -0.030506969 (0.027) x

5.0 M20 5.0

= -1.80 -1.804688 = -1.80

x 12.1 = -4.54 (0.38) x 12.1 = -4.54

x 0.4 = -0.16 (0.38) x 0.4 = -0.16

x 0.9 = -0.32 (0.38) x 0.9 = -0.32

x 3.7 = -1.38 (0.38) x 3.7 = -1.38= -8.2 = -8.2

= -1.41 -1.40625 = -1.41

x 1.5 = -0.57 (0.38) x 1.5 = -0.57

x 0.8 = -0.31 (0.38) x 0.8 = -0.31

x 1.0 = -0.36 (0.38) x 1.0 = -0.36

x 1.8 = -0.66 (0.38) x 1.8 = -0.66= -3.3 = -3.3

= -0.68 -0.675 = -0.68

x 1.1 = -0.41 (0.38) x 1.1 = -0.41

x 0.3 = -0.12 (0.38) x 0.3 = -0.12

x 0.1 = -0.05 (0.38) x 0.1 = -0.05

x 6.8 = -2.56 (0.38) x 6.8 = -2.56= -3.8 = -3.8

Putaran 20

= 11.3 11.3 = 11.3 (0.3) = 0.0159262114 (0.063) x (0.3) = 0.0159262121 (1.8) = 0.8064897165 (0.438) x (1.8) = 0.806489717MI 12.2 MI 12.2

= - - = - 12.2 = -0.675240517 (0.056) x 12.2 = -0.6752405168 0.3 = -0.015829659 (0.056) x 0.3 = -0.0158296615 (1.12) = 0.4362507825 (0.389) x (1.1) = 0.4362507808M2 (0.3) M2 (0.3)

= - - = - (0.3) = 0.014156633 (0.056) x (0.3) = 0.0141566332 3.8 = -0.2110259475 (0.056) x 3.8 = -0.2110259409 (1.24) = 0.4818032212 (0.389) x (1.24) = 0.4818032289M3 0.3 M3 0.3

= - - = - 0.3 = -0.015829661 (0.056) x 0.3 = -0.0158296623 (55.2) = 3.064392071 (0.056) x (55.2) = 3.0643920677 (1.928) = 0.7499045274 (0.389) x (1.928) = 0.7499044884M4 = 3.8 M4 = 3.8

= (53.3) (53.3) = (53.3) 3.8 = -1.899233468 (0.500) x 3.8 = -1.8992334469M5 (55.2) M5 (55.2)

= - - = - (0.1) = 0.0038637009 (0.031) x (0.1) = 0.0038636977

M6 0.0 M6 0.0

= - - = - 0.0 = -0.000120741 (0.031) x 0.0 = -0.0001207406 0.6 = -0.017680154 (0.031) x 0.6 = -0.0176801535 0.24 = -0.052918716 (0.219) x 0.24 = -0.0529186982 1.99 = -0.052918716 (0.219) x 1.99 = -0.0529186982

M7 = (0.1) - M7 = (0.1)

= - - = - (0.1) = 0.0038636977 (0.031) x (0.1) = 0.0038636966 (1.5) = 0.3324460985 (0.219) x (1.5) = 0.3324460985 0.68 = -0.021340618 (0.031) x 0.68 = -0.0213406181 (1.146) = 0.250795733 (0.219) x (1.146) = 0.2507957301

M8 = 0.6 M8 = 0.6

= - - = - (0.0) = 0.0012099239 (0.031) x (0.0) = 0.001209924 0.6 = -0.017680153 (0.031) x 0.6 = -0.0176801533 (1.14) = 0.2488528745 (0.219) x (1.14) = 0.248852875 (2.06) = 0.450517133 (0.219) x (2.06) = 0.4505171338

M9 = 0.7 M9 = 0.7

= 2.5 2.5 = 2.5 0.7 = -0.022763326 (0.033) x 0.7 = -0.022763326 0.4 = -0.094070037 (0.233) x 0.4 = -0.0940700369 10.35 = -2.41491642 (0.233) x 10.35 = -2.4149164204

M10 = (0.0) M10 (0.0)

= 2.5 2.5 = 2.5 0.3 = -0.008954562 (0.033) x 0.3 = -0.0089545619 (1.4) = 0.3371590991 (0.233) x (1.4) = 0.3371590992 4.34 = -1.0118294514 (0.233) x 4.34 = -1.0118294514

M11 = 1.8 M11 = 1.8

= - - = - 1.8 = -0.056543978 (0.031) x 1.8 = -0.0565439782 0.3 = -0.0081173506 (0.031) x 0.3 = -0.0081173511 (0.7) = 0.1582328611 (0.219) x (0.7) = 0.1582328607 (0.8) = 0.1750653248 (0.219) x (0.8) = 0.1750653248

M12 0.3 M12 = 0.3

= - - = - 1.6 = -0.051505129 (0.031) x 1.6 = -0.0515051265 0.3 = -0.008394902 (0.031) x 0.3 = -0.0083949018 (0.6) = 0.1357991517 (0.219) x (0.6) = 0.1357991524 (0.8) = 0.1838561132 (0.219) x (0.8) = 0.1838561141

M13 = 0.3 M13 = 0.3

= - - = - 0.3 = -0.0081173511 (0.031) x 0.3 = -0.0081173512 (34) = 1.0512822845 (0.031) x (34) = 1.0512822833 (1.24) = 0.2703360439 (0.219) x (1.24) = 0.2703360232 (1.53) 0.3346630716 (0.219) x (1.53) = 0.3346630635

M14 1.6 M14 = 1.6

= (32.8) (32.8) = (32.8) 1.6 = -0.824082024 (0.500) x 1.6 = -0.8240820094

M15 (33.6) M15 (33.6)

= - - = - (0.6) = 0.2804109575 (0.500) x (0.6) = 0.2804109102

M16 0.3 M16 0.3

= - - = - 0.1 = -0.001457674 (0.027) x 0.1 = -0.0014576739 0.3 = -0.125123615 (0.446) x 0.3 = -0.1251235934 1.0 = -0.434240532 (0.446) x 1.0 = -0.4342405183

M17 = (0.6) M17 = (0.6)

= - - = - (0.6) = 0.0150818617 (0.027) x (0.6) = 0.0150818608 (0.1) = 0.0279550723 (0.223) x (0.1) = 0.0279550723 (0.42) = 0.0111669409 (0.027) x (0.42) = 0.0111669408

M18 0.1 M18 0.1

= - - = - 0.1 = -0.001457674 (0.027) x 0.1 = -0.0014576739 5.0 = -0.134769046 (0.027) x 5.0 = -0.1347690461 (0.41) = 0.0109280925 (0.027) x (0.41) = 0.0109280925

M19 (0.1) M19 (0.1)

= 5.0 5.0 = 5.0 (0.1) = 0.0033695846 (0.027) x (0.1) = 0.0033695846 1.13 = -0.030506969 (0.027) x 1.13 = -0.0305069693

M20 5.0 M20 5.0

Dari put 20 Ke Put 20

-1.8046875 = -1.80 -1.8046875

(0.38) x 12.1 = -4.54 (0.38)

(0.38) x 0.4 = -0.16 (0.38)

(0.38) x 0.9 = -0.32 (0.38)

(0.38) x 3.7 = -1.38= -8.21

-1.40625 = -1.41 -1.40625

(0.38) x 1.5 = -0.57 (0.38)

(0.38) x 0.8 = -0.31 (0.38)

(0.38) x 1.0 = -0.36 (0.38)

(0.38) x 1.8 = -0.66= -3.31

-0.675 = -0.68 -0.675

(0.38) x 1.1 = -0.41 (0.38)

(0.38) x 0.3 = -0.12 (0.38)

(0.38) x 0.1 = -0.05 (0.38)

(0.38) x 6.8 = -2.56= -3.81

11.3 = 11.3 11.3 (0.063) x (0.3) = 0.0159262123 (0.063) x (0.438) x (7.6) = 3.3424474664 (0.438) x

MI 14.7

- = - - (0.056) x 14.7 = -0.8161270584 (0.056) x (0.056) x 0.3 = -0.0158296623 (0.056) x (0.389) x (8.33) = 3.2391656581 (0.389) x

M2 2.4

- = - - (0.056) x 2.4 = -0.1337338299 (0.056) x (0.056) x 3.8 = -0.2110259385 (0.056) x (0.389) x (8.20) = 3.1895815515 (0.389) x

M3 2.8

- = - - (0.056) x 2.8 = -0.1580456546 (0.056) x

M4 (0.2)

(53.3) = (53.3) (53.3) (0.500) x (0.2) = 0.0790228273 (0.500) x

M5 (53.2)

- = - - (0.031) x (0.1) = 0.0038636966 (0.031) x

M6 0.0

- = - - (0.031) x 0.0 = -0.0001207405 (0.031) x (0.031) x 0.6 = -0.0176801533 (0.031) x (0.219) x (1.50) = 0.3278941728 (0.219) x (0.219) x (5.80) 0.3278941728 (0.219) x - M7 0.6 -

- = - - (0.031) x 0.6 = -0.0199371079 (0.031) x (0.219) x 6.5 = -1.4185154858 (0.219) x (0.031) x (2.63) = 0.0820453847 (0.031) x

M8 (1.4)

- = - - 0.031 x (0.0) = -0.001209924 0.031 x 0.219 x (4.7) = -1.0204160969 0.219 x 0.219 x (3.53) = -0.7725454064 0.219 x

M9 (1.8)

2.5 = 2.5 2.5 (0.033) x (1.8) = 0.0598057142 (0.033) x (0.233) x 1.8 = -0.4221950369 (0.233) x (0.233) x (2.67) = 0.6230850825 (0.233) x

M10 2.8

2.5 = 2.5 2.5 (0.033) x 2.8 = -0.0917909325 (0.033) x (0.233) x 3 = -0.6425365275 (0.233) x

#REF! x (2.16) = #REF! #REF! xM11 #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x

0.3 #REF!

- = - - (0.031) x 1.6 = -0.0515051256 (0.031) x

M13 (0.1)

- = - - (0.031) x (0.1) = 0.0016095352 (0.031) x (0.031) x (34) = 1.0512822828 (0.031) x (0.219) x #REF! = #REF! (0.219) x (0.219) x #REF! #REF! (0.219) x

M14 #REF!

(32.8) = (32.8) (32.8) (0.500) x #REF! = #REF! (0.500) x

M15 #REF!

- = - - (0.500) x #REF! = #REF! (0.500) x

M16 #REF!

- = - - (0.027) x 0.1 = -0.0014576739 (0.027) x (0.446) x (4.4) = 1.9512402789 (0.446) x

M17 1.9

- = - - (0.027) x 1.9 = -0.0524343928 (0.027) x (0.223) x (0.1) = 0.0279550723 (0.223) x (0.027) x #REF! = #REF! (0.027) x

M18 #REF!

- = - - (0.027) x #REF! = #REF! (0.027) x (0.027) x 5.0 = -0.1347690461 (0.027) x (0.027) x #REF! = #REF! (0.027) x

M19 #REF!

M20 #REF!

= -1.80 -1.8046875 =

x 13.3 = 12.96 (0.38) x #REF! =

x 3.0 = -1.14 (0.38) x #REF! =

x 2.8 = -1.07 (0.38) x (3.3) =

= -1.41 -1.40625 =

x (3.2) = -3.53 (0.38) x #REF! =

x (1.6) = 0.61 (0.38) x (3.7) =

x #REF! = #REF! (0.38) x #REF! =

= -0.68 -0.675 =

x (1.8) = -2.17 (0.38) x #REF! =

x (1.2) = 0.44 (0.38) x #REF! =

x 0.3 = -0.12 (0.38) x #REF! =

Putaran 22

= 11.3 11.3 = 11.3 2.4 = -0.1504505586 (0.063) x (4.3) = 0.2700713099 7.6 = -3.3195660017 (0.438) x #REF! = #REF!MI 7.9 MI #REF!

= - - = - 7.9 = -0.4367720451 (0.056) x #REF! = #REF! 2.8 = -0.1580456546 (0.056) x (3.2) = 0.1794931042 9.58 = -3.7263232584 (0.389) x #REF! = #REF!M2 (4.3) M2 #REF!

= - - = - (4.3) = 0.2400633866 (0.056) x #REF! = #REF! (0.2) = 0.0087803141 (0.056) x 0.2 = -0.0099718391 8.95 = -3.4797195759 (0.389) x #REF! = #REF!M3 (3.2) M3 #REF!

= - - = - (3.2) = 0.1794931042 (0.056) x #REF! = #REF!

M4 0.2 M4 #REF!

= (53.3) (53.3) = (53.3) 0.2 = -0.0897465521 (0.500) x #REF! = #REF!M5 (53.3) M5 #REF!

= - - = - 0.6 = -0.0199371079 (0.031) x #REF! = #REF!

M6 (0.0) M6 #REF!

= - - = - (0.0) = 0.0006230346 (0.031) x #REF! = #REF! (1.4) = 0.0423877253 (0.031) x #REF! = #REF!

#REF! = #REF! (0.219) x #REF! = #REF! 4.62 #REF! (0.219) x #REF! #REF!

M7 #REF! - M7 #REF!

= - - = - #REF! = #REF! (0.031) x #REF! = #REF!

16.8 = -3.6762870055 (0.219) x #REF! = #REF!#REF! = #REF! (0.031) x #REF! = #REF!

M8 #REF! M8 #REF!

= - - = - 2.8 = 0.0860539992 0.031 x #REF! = #REF!

#REF! = #REF! 0.219 x #REF! = #REF!#REF! = #REF! 0.219 x #REF! = #REF!

M9 #REF! M9 #REF!

= 2.5 2.5 = 2.5 #REF! = #REF! (0.033) x #REF! = #REF!#REF! = #REF! (0.233) x #REF! = #REF!#REF! = #REF! (0.233) x #REF! = #REF!

M10 #REF! M10 #REF!

= 2.5 2.5 = 2.5 #REF! = #REF! (0.033) x #REF! = #REF!#REF! = #REF! (0.233) x #REF! = #REF!#REF! = #REF! #REF! x #REF! = #REF!

M11 #REF! M11 #REF!

= - - = - #REF! = #REF! (0.031) x #REF! = #REF!

0.3 #REF! 0.3 #REF!

= - - = - #REF! = #REF! (0.031) x #REF! = #REF!

M13 #REF! M13 #REF!

= - - = - #REF! = #REF! (0.031) x #REF! = #REF!#REF! = #REF! (0.031) x #REF! = #REF!#REF! = #REF! (0.219) x #REF! = #REF!#REF! #REF! (0.219) x #REF! #REF!

M14 #REF! M14 #REF!

= (32.8) (32.8) = (32.8)#REF! = #REF! (0.500) x #REF! = #REF!

M15 #REF! M15 #REF!

= - - = - #REF! = #REF! (0.500) x #REF! = #REF!

M16 #REF! M16 #REF!

= - - = - #REF! = #REF! (0.027) x #REF! = #REF!

(0.6) = 0.2550397441 (0.446) x #REF! = #REF!

M17 #REF! M17 #REF!

= - - = - #REF! = #REF! (0.027) x #REF! = #REF!#REF! = #REF! (0.223) x #REF! = #REF!#REF! = #REF! (0.027) x #REF! = #REF!

M18 #REF! M18 #REF!

= - - = - #REF! = #REF! (0.027) x #REF! = #REF!#REF! = #REF! (0.027) x #REF! = #REF!#REF! = #REF! (0.027) x #REF! = #REF!

M19 #REF! M19 #REF!

= 5.0 5.0 = 5.0 #REF! = #REF! (0.027) x #REF! = #REF!#REF! = #REF! (0.027) x #REF! = #REF!

M20 #REF! M20 #REF!

-1.80 -1.8046875 = -1.80

#REF! (0.38) x #REF! = #REF!

1.22 (0.38) x #REF! = #REF!

#REF! #REF!

-1.41 -1.40625 = -1.41

#REF! (0.38) x #REF! = #REF!

1.38 (0.38) x #REF! = #REF!

#REF! (0.38) x #REF! = #REF!

#REF! #REF!

-0.68 -0.675 = -0.68

#REF! (0.38) x #REF! = #REF!

#REF! #REF!

11.3 = 11.3 11.3 (0.063) x #REF! = #REF! (0.063) (0.438) x #REF! = #REF! (0.438)

MI #REF!

M2 #REF!

M3 #REF!

- = - - (0.056) x #REF! = #REF! (0.056)

M4 #REF!

(53.3) = (53.3) (53.3) (0.500) x #REF! = #REF! (0.500)

M5 #REF!

- = - - (0.031) x #REF! = #REF! (0.031)

M6 #REF!

- = - - (0.031) x #REF! = #REF! (0.031) (0.031) x #REF! = #REF! (0.031) (0.219) x #REF! = #REF! (0.219) (0.219) x #REF! #REF! (0.219) - M7 #REF! -

M8 #REF!

M9 #REF!

2.5 = 2.5 2.5 (0.033) x #REF! = #REF! (0.033) (0.233) x #REF! = #REF! (0.233) (0.233) x #REF! = #REF! (0.233)

M10 #REF!

2.5 = 2.5 2.5 (0.033) x #REF! = #REF! (0.033) (0.233) x #REF! = #REF! (0.233)

#REF! x #REF! = #REF! #REF!M11 #REF!

- = - - (0.031) x #REF! = #REF! (0.031)

0.3 #REF!

- = - - (0.031) x #REF! = #REF! (0.031)

M13 #REF!

M14 #REF!

(32.8) = (32.8) (32.8) (0.500) x #REF! = #REF! (0.500)

M15 #REF!

- = - - (0.500) x #REF! = #REF! (0.500)

M16 #REF!

- = - - (0.027) x #REF! = #REF! (0.027) (0.446) x #REF! = #REF! (0.446)

M17 #REF!

M18 #REF!

M19 #REF!

5.0 = 5.0 5.0 (0.027) x #REF! = #REF! (0.027) (0.027) x #REF! = #REF! (0.027)

M20 #REF!

-1.8046875 = -1.80 -1.8046875

(0.38) x #REF! = #REF! (0.38) x #REF!

-1.40625 = -1.41 -1.40625

(0.38) x #REF! = #REF! (0.38) x #REF!

-0.675 = -0.68 -0.675

(0.38) x #REF! = #REF! (0.38) x #REF!

Putaran 25

= 11.3 11.3 = x #REF! = #REF! (0.063) x #REF! =x #REF! = #REF! (0.438) x #REF! =

MI #REF! MI

= - - = x #REF! = #REF! (0.056) x #REF! =x #REF! = #REF! (0.056) x #REF! =x #REF! = #REF! (0.389) x #REF! =

M2 #REF! M2

M3 #REF! M3

= - - = x #REF! = #REF! (0.056) x #REF! =

M4 #REF! M4

= (53.3) (53.3) = x #REF! = #REF! (0.500) x #REF! =

M5 #REF! M5

= - - = x #REF! = #REF! (0.031) x #REF! =

M6 #REF! M6

= - - = x #REF! = #REF! (0.031) x #REF! =x #REF! = #REF! (0.031) x #REF! =x #REF! = #REF! (0.219) x #REF! =x #REF! #REF! (0.219) x #REF!

M7 #REF! - M7

M8 #REF! M8

= - - = x #REF! = #REF! 0.031 x #REF! =x #REF! = #REF! 0.219 x #REF! =x #REF! = #REF! 0.219 x #REF! =

M9 #REF! M9

= 2.5 2.5 = x #REF! = #REF! (0.033) x #REF! =x #REF! = #REF! (0.233) x #REF! =x #REF! = #REF! (0.233) x #REF! =

M10 #REF! M10

= 2.5 2.5 = x #REF! = #REF! (0.033) x #REF! =x #REF! = #REF! (0.233) x #REF! =x #REF! = #REF! #REF! x #REF! =

M11 #REF! M11

= - - = x #REF! = #REF! (0.031) x #REF! =

0.3 #REF! 0.3

= - - = x #REF! = #REF! (0.031) x #REF! =

M13 #REF! M13

M14 #REF! M14

= (32.8) (32.8) = x #REF! = #REF! (0.500) x #REF! =

M15 #REF! M15

= - - = x #REF! = #REF! (0.500) x #REF! =

M16 #REF! M16

= - - = x #REF! = #REF! (0.027) x #REF! =x #REF! = #REF! (0.446) x #REF! =

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

M20 #REF! M20

= -1.80 -1.8046875 = -1.80

= #REF! (0.38) x #REF! = #REF!

#REF! #REF!

= -1.41 -1.40625 = -1.41

= #REF! (0.38) x #REF! = #REF!

#REF! #REF!

= -0.68 -0.675 = -0.68

= #REF! (0.38) x #REF! = #REF!

#REF! #REF!

Putaran 26

- - = - #REF! (0.056) x #REF! = #REF!

#REF! M4 #REF!

#REF! - M7 #REF!

#REF! M8 #REF!

#REF! M9 #REF!

2.5 2.5 = 2.5 #REF! (0.033) x #REF! = #REF!#REF! (0.233) x #REF! = #REF!#REF! (0.233) x #REF! = #REF!

#REF! M10 #REF!

2.5 2.5 = 2.5 #REF! (0.033) x #REF! = #REF!#REF! (0.233) x #REF! = #REF!#REF! #REF! x #REF! = #REF!

#REF! M11 #REF!

- - = - #REF! (0.031) x #REF! = #REF!

#REF! 0.3 #REF!

- - = - #REF! (0.031) x #REF! = #REF!

#REF! M13 #REF!

#REF! M14 #REF!

(32.8) (32.8) = (32.8)#REF! (0.500) x #REF! = #REF!

#REF! M15 #REF!

- - = - #REF! (0.500) x #REF! = #REF!

#REF! M16 #REF!

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

#REF! M20 #REF!

-1.8046875 = -1.80

(0.38) x #REF! = #REF!

-1.40625 = -1.41

(0.38) x #REF! = #REF!

-0.675 = -0.68

(0.38) x #REF! = #REF!

11.3 = 11.3 11.3 (0.063) x #REF! = #REF! (0.063) (0.438) x #REF! = #REF! (0.438)

MI #REF!

M2 #REF!

M3 #REF!

- = - - (0.056) x #REF! = #REF! (0.056)

M4 #REF!

(53.3) = (53.3) (53.3) (0.500) x #REF! = #REF! (0.500)

M5 #REF!

- = - - (0.031) x #REF! = #REF! (0.031)

M6 #REF!

- = - - (0.031) x #REF! = #REF! (0.031) (0.031) x #REF! = #REF! (0.031) (0.219) x #REF! = #REF! (0.219) (0.219) x #REF! #REF! (0.219) - M7 #REF! -

M8 #REF!

M9 #REF!

2.5 = 2.5 2.5 (0.033) x #REF! = #REF! (0.033) (0.233) x #REF! = #REF! (0.233) (0.233) x #REF! = #REF! (0.233)

M10 #REF!

2.5 = 2.5 2.5 (0.033) x #REF! = #REF! (0.033) (0.233) x #REF! = #REF! (0.233)

- = - - (0.031) x #REF! = #REF! (0.031)

0.3 #REF!

- = - - (0.031) x #REF! = #REF! (0.031)

M13 #REF!

M14 #REF!

(32.8) = (32.8) (32.8) (0.500) x #REF! = #REF! (0.500)

M15 #REF!

- = - - (0.500) x #REF! = #REF! (0.500)

M16 #REF!

- = - - (0.027) x #REF! = #REF! (0.027) (0.446) x #REF! = #REF! (0.446)

M17 #REF!

M18 #REF!

M19 #REF!

5.0 = 5.0 5.0 (0.027) x #REF! = #REF! (0.027) (0.027) x #REF! = #REF! (0.027)

M20 #REF!

-1.8046875 = -1.80 -1.8046875

(0.38) x #REF! = #REF! (0.38) x

-1.40625 = -1.41 -1.40625

(0.38) x #REF! = #REF! (0.38) x

-0.675 = -0.68 -0.675

(0.38) x #REF! = #REF! (0.38) x

Putaran 29

= 11.3 11.3 x #REF! = #REF! (0.063) x #REF!x #REF! = #REF! (0.438) x #REF!

MI #REF! MI

= - - x #REF! = #REF! (0.056) x #REF!x #REF! = #REF! (0.056) x #REF!x #REF! = #REF! (0.389) x #REF!

M2 #REF! M2

M3 #REF! M3

= - - x #REF! = #REF! (0.056) x #REF!

M4 #REF! M4

= (53.3) (53.3) x #REF! = #REF! (0.500) x #REF!

M5 #REF! M5

= - - x #REF! = #REF! (0.031) x #REF!

M6 #REF! M6

= - - x #REF! = #REF! (0.031) x #REF!x #REF! = #REF! (0.031) x #REF!x #REF! = #REF! (0.219) x #REF!x #REF! #REF! (0.219) x #REF!

M7 #REF! - M7

M8 #REF! M8

= - - x #REF! = #REF! 0.031 x #REF!x #REF! = #REF! 0.219 x #REF!x #REF! = #REF! 0.219 x #REF!

M9 #REF! M9

= 2.5 2.5 x #REF! = #REF! (0.033) x #REF!x #REF! = #REF! (0.233) x #REF!x #REF! = #REF! (0.233) x #REF!

M10 #REF! M10

= 2.5 2.5 x #REF! = #REF! (0.033) x #REF!x #REF! = #REF! (0.233) x #REF!x #REF! = #REF! #REF! x #REF!

M11 #REF! M11

= - - x #REF! = #REF! (0.031) x #REF!

0.3 #REF! 0.3

= - - x #REF! = #REF! (0.031) x #REF!

M13 #REF! M13

= - - x #REF! = #REF! (0.031) x #REF!x #REF! = #REF! (0.031) x #REF!x #REF! = #REF! (0.219) x #REF!x #REF! #REF! (0.219) x #REF!

M14 #REF! M14

= (32.8) (32.8) x #REF! = #REF! (0.500) x #REF!

M15 #REF! M15

= - - x #REF! = #REF! (0.500) x #REF!

M16 #REF! M16

= - - x #REF! = #REF! (0.027) x #REF!x #REF! = #REF! (0.446) x #REF!

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

= 5.0 5.0 x #REF! = #REF! (0.027) x #REF!x #REF! = #REF! (0.027) x #REF!

M20 #REF! M20

= -1.80 -1.8046875

#REF! = #REF! (0.38) x #REF!

= -1.41 -1.40625

#REF! = #REF! (0.38) x #REF!

= -0.68 -0.675

#REF! = #REF! (0.38) x #REF!

Putaran 30

= 11.3 11.3 == #REF! (0.063) x #REF! == #REF! (0.438) x #REF! =

#REF! MI

#REF! M2

#REF! M3

= - - == #REF! (0.056) x #REF! =

#REF! M4

= (53.3) (53.3) == #REF! (0.500) x #REF! =

#REF! M5

= - - == #REF! (0.031) x #REF! =

#REF! M6

#REF! (0.219) x #REF!#REF! - M7

#REF! M8

#REF! M9

= 2.5 2.5 == #REF! (0.033) x #REF! == #REF! (0.233) x #REF! == #REF! (0.233) x #REF! =

#REF! M10

#REF! M11

= - - == #REF! (0.031) x #REF! =

#REF! 0.3

= - - == #REF! (0.031) x #REF! =

#REF! M13

#REF! (0.219) x #REF!#REF! M14

= (32.8) (32.8) == #REF! (0.500) x #REF! =

#REF! M15

= - - == #REF! (0.500) x #REF! =

#REF! M16

= - - == #REF! (0.027) x #REF! == #REF! (0.446) x #REF! =

#REF! M17

#REF! M18

#REF! M19

= 5.0 5.0 == #REF! (0.027) x #REF! == #REF! (0.027) x #REF! =

#REF! M20

= -1.80 -1.8046875

= #REF! (0.38) x #REF!

= -1.41 -1.40625

= #REF! (0.38) x #REF!

= -0.68 -0.675

= #REF! (0.38) x #REF!

Putaran 31

11.3 11.3 =#REF! (0.063) x #REF! =#REF! (0.438) x #REF! =#REF! MI

- - =#REF! (0.056) x #REF! =#REF! (0.056) x #REF! =#REF! (0.389) x #REF! =#REF! M2

- - =#REF! (0.056) x #REF! =

#REF! M4

(53.3) (53.3) =#REF! (0.500) x #REF! =#REF! M5

- - =#REF! (0.031) x #REF! =#REF! M6

- - =#REF! (0.031) x #REF! =#REF! (0.031) x #REF! =#REF! (0.219) x #REF! =#REF! (0.219) x #REF!

#REF! - M7

- - =#REF! (0.031) x #REF! =#REF! (0.219) x #REF! =#REF! (0.031) x #REF! =

#REF! M8

- - =#REF! 0.031 x #REF! =#REF! 0.219 x #REF! =#REF! 0.219 x #REF! =

#REF! M9

2.5 2.5 =#REF! (0.033) x #REF! =#REF! (0.233) x #REF! =#REF! (0.233) x #REF! =

#REF! M10

2.5 2.5 =#REF! (0.033) x #REF! =#REF! (0.233) x #REF! =#REF! #REF! x #REF! =

#REF! M11

- - =#REF! (0.031) x #REF! =

#REF! 0.3

- - =#REF! (0.031) x #REF! =

#REF! M13

#REF! M14

(32.8) (32.8) =#REF! (0.500) x #REF! =

#REF! M15

- - =#REF! (0.500) x #REF! =

#REF! M16

- - =#REF! (0.027) x #REF! =#REF! (0.446) x #REF! =

#REF! M17

#REF! M18

#REF! M19

5.0 5.0 =#REF! (0.027) x #REF! =#REF! (0.027) x #REF! =

#REF! M20

= -1.80 -1.8046875

= #REF! (0.38) x #REF!

= -1.41 -1.40625

= #REF! (0.38) x #REF!

= -0.68 -0.675

= #REF! (0.38) x #REF!

Putaran 32

- - =#REF! (0.056) x #REF! =

#REF! M4

(53.3) (53.3) =#REF! (0.500) x #REF! =#REF! M5

- - =#REF! (0.031) x #REF! =#REF! M6

#REF! - M7

#REF! M8

#REF! M9

#REF! M10

#REF! M11

- - =#REF! (0.031) x #REF! =

#REF! 0.3

- - =#REF! (0.031) x #REF! =

#REF! M13

#REF! M14

(32.8) (32.8) =#REF! (0.500) x #REF! =

#REF! M15

- - =#REF! (0.500) x #REF! =

#REF! M16

- - =#REF! (0.027) x #REF! =#REF! (0.446) x #REF! =

#REF! M17

#REF! M18

#REF! M19

5.0 5.0 =#REF! (0.027) x #REF! =#REF! (0.027) x #REF! =

#REF! M20

= -1.80 -1.8046875

= #REF! (0.38) x #REF!

= -1.41 -1.40625

= #REF! (0.38) x #REF!

= -0.68 -0.675

= #REF! (0.38) x #REF!

Putaran 33

- - =#REF! (0.056) x #REF! =

#REF! M4

(53.3) (53.3) =#REF! (0.500) x #REF! =#REF! M5

- - =#REF! (0.031) x #REF! =#REF! M6

#REF! - M7

#REF! M8

#REF! M9

#REF! M10

#REF! M11

- - =#REF! (0.031) x #REF! =

#REF! 0.3

- - =#REF! (0.031) x #REF! =

#REF! M13

#REF! M14

(32.8) (32.8) =#REF! (0.500) x #REF! =

#REF! M15

- - =#REF! (0.500) x #REF! =

#REF! M16

- - =#REF! (0.027) x #REF! =#REF! (0.446) x #REF! =

#REF! M17

#REF! M18

#REF! M19

5.0 5.0 =#REF! (0.027) x #REF! =#REF! (0.027) x #REF! =

#REF! M20

= -1.80

= #REF!

= -1.41

= #REF!

= -0.68

= #REF!

11.3 #REF!#REF!#REF!

- #REF!#REF!#REF!#REF!

- #REF!

(53.3)#REF!#REF!

- #REF!#REF!

- #REF!#REF!#REF!

2.5 #REF!#REF!#REF!

- #REF!

(32.8)#REF!

- #REF!

- #REF!#REF!

- #REF!#REF!#REF!

5.0 #REF!#REF!

Tie Beam

Type TB 1 = 0.2 m x 0.4 m

Ring Balk

Type Balok 30/60 = 0.3 m x 0.6 m

Type Balok 30/40 = 0.3 m x 0.4 m

Type Balok 20/40 = 0.2 m x 0.4 m

Type Balok 20/30 = 0.2 m x 0.3 m

Inersia

a. Inersia Kolom

1 Type kolom K1 40.000 x 40 0.0833 213,333.333

2 Type kolom K2 #REF! x #REF! 0.0833 #REF!

b. Inersia Tie Beam

1 Type TB 1 20.000 x 40 0.0833 106,666.667

1 Dimensi RB1 30.000 x 40 0.0833 160,000.000

d. Inersia Balok

1 Type Balok 30/60 30.000 x 60 0.0833 540,000.000

2 Type Balok 30/40 30.000 x 40 0.0833 160,000.000

3 Type Balok 20/40 20.000 x 40 0.0833 106,666.667

4 Type Balok 20/30 20.000 x 30 0.0833 45,000.000

== -0.0833333333 x 8536.632512 x 64.000 = (45,528.7) - 7,998 = (53,526.8) kgm = (53.5) tm

Mf2-1 =

== -0.0833333333 x 8536.632512 x 6.250 = (4,446.2)= (4,446.2) kgm = (4.4) tm

== -0.0833333333 x 6,190.03 x 64.000 = (33,013.5) - 7459.064= (40,472.6) kgm = (40.5) tm

== -0.0833333333 x 6190.03 x 6.250 = (3,224.0)= (3,224.0) kgm = (3.2) tm

== -0.0833333333 x 6,190.03 x 64.000 = (33,013.5) - 7459.064= (40,472.6) kgm = (40.5) tm =

== -0.0833333333 x 6190.03 x 6.250 = (3,224.0)= (3,224.0) kgm = (3.2) tm =

Mf1-2 -1/12 x qL2 - (P1.a.b2/L2)

-Mf2-1

Mf2-2" -1/12 x qL2 - 1/8 PL

Mf2"-2

-Mf2-2"

Mf4-3 -1/12 x qL2 - 1/8 PL

-Mf4-3

Mf3-3" -1/12 x qL2

Mf3"-3

-Mf4-3

Mf5-6 -1/12 x qL2 - 1/8 PL

-Mf5-6

Mf6-6" -1/12 x qL2

Mf6"-6

-Mf6-6"

== -0.0833333333 x 6,190.03 x 64.000 = (33,013.5) - 7459.064= (40,472.6) kgm = (40.5) tm =

== -0.0833333333 x 6190.032512 x 6.250 = (3,224.0)= (3,224.0) kgm = (3.2) tm =

1 -53.527 53.53

2 -53.527 53.53

3 -4.446 4.45

4 40.473 (40.47)

5 -3.224 3.22

6 40.473 (40.47)

7 -3.224 3.22

8 -40.473 40.47

9 40.473 (40.47)

T1 = +

T Nilai ρ Nilai

-53.527 1.219

4.446 1.371

-4.446 0.229

37.249 3.133

-3.224 0.771

-40.473 2.905

37.249 3.133

-3.224 0.771

-80.945 2.067

Mf7-8 -1/12 x qL2 - 1/8 PL

Mf 8-7

-Mf7-8

Mf7-7" -1/12 x qL2

Mf 7"-7

-Mf7"-7

" M3"-3

T2" ρ2"

T3 ρ3

T3" ρ

T4 ρ4

T5 ρ5

T6 ρ6

T6" ρ

T7 ρ7

-3.224 0.771

-40.473 1.838

Joint 1

= = 0.076 = 0.063 ρ1 1.219

= = 0.533 = 0.438 ρ1 1.219

Joint 2

= = 0.076 = 0.056 ρ2 1.371

= = 0.5333 = 0.389 ρ2 1.371

Joint 3

= = 0.533 = 0.170 ρ3 3.133

= = 0.386 = 0.123 ρ3 3.133

= = 0.114 = 0.036 ρ3 3.133

= = 0.5333 = 0.170 ρ3 3.133

Joint 4

= = 0.386 = 0.133 ρ4 2.905

= = 0.533 = 0.184 ρ4 2.905

T7" ρ

T8 ρ8

γ2-2"

γ2--1

γ3-3"

Joint 5

= = 0.386 = 0.133 ρ5 2.905

= = 0.533 = 0.184 ρ5 2.905

0.500 Joint 6

= = 0.386 = 0.123 ρ6 3.133

= = 0.114 = 0.036 ρ6 3.133

= = 0.533 = 0.170 ρ6 3.133

Joint 7

= = 0.114 = 0.055 ρ7 2.067

= = 0.386 = 0.187 ρ7 2.067

= = 0.533 = 0.258 ρ7 2.067

= = 0.386 = 0.210 ρ8 1.838

= = 0.533 = 0.290 ρ8 1.838

K6-5γ6-6"

K7-8γ7-7"

M1 = -Mf / ρ1

= 53.5271.219

= 43.909 ton

No. Momen Nilai

1 M1 43.909

2 M2 -3.242

3 M2" 19.452

4 M3 -11.888

5 M3" 4.179

6 M4 13.933

7 M5 13.933

8 M6 -11.888

9 M6" 4.179

10 M7 39.167

11 M7" 4.179

= 2 x ( 0.5333 + 0.533

= 2.1333

T2 = 2 x ( 0.5333 + 0.53

= 2.1333

T3 = 2 x ( 0.53 + 0.53

= 2.1333

Perhitungan nilai t

2*(K1-2

2*(K4-5

+ K3-6

2*(K5-8

+ K6-7

= 0.750

No. t Nilai

1 0.750

2 0.750

3 0.750

4 0.750

5 0.750

6 0.750

7 0.750

Perhitungan Momen Displacment Belum dihitungArah y

Arah y

M1 = -h1(∑W)

= -3.500 x ( 2.20 )2.1333

= -3.609

M2 = -h2(∑W)

= -4.000 x ( 1.50 )2.1333

= -2.813

M3 = -h3(∑W)

= -3.600 x ( 0.80 )2.1333

= -1.350

Putaran 0

3.(K1-8

MI = MI(0) = 43.9 = γ 1 - 2 x M2(0) = (0.063)= γ 1 - 4 x MD 1+M4(0) = (0.438)

M2 = M2(0) = (3.2)= γ 2 - 1 x M1(1) = (0.056)= γ 2 - 2" x M2"(0) = (0.056)= γ 2 - 3 x MD 1+M3(0) = (0.389)

M3 = M3(0) = (11.9)= γ 3-4 x M4(0) = (0.123)= y 3-3" x M3"(0) = 0.036 = γ 3-2 x MD2+M2(0) = 0.170 = γ 3-6 x MD 1+M6 = (0.170)

M4 = M4(0) = 13.9 = γ 4-3 x M3(1) = (0.133)= γ 4-5 x MD(2)+M5(0) = 0.184 = γ 4-1 x MD(1)+M1(0) = 0.184

M5 = M5(0) = 13.9 = γ 5-6 x M6(1) = (0.133)= γ 5-8 x MD3 + M8(0) = 0.184 = γ 5-4 x MD 1 + M4(1) = 0.184

M6 = M6(0) = (11.9)= γ 6-5 x M5(1) = 0.123 = γ 6-6" x M6"(0) = 0.036 = γ 6-7 x MD 3+M7(0) = 0.170 = γ 6-3 x MD 2+M3(1) = 0.170

M7 = M7(0) = 39.2 = γ 7-7" x M7"(0) = 0.055 = γ 7-8 x M8(0) = 0.187 = γ 7-9 x MD 4+M9(0) = #REF!= γ7-6 x MD 3+M6(1) = 0.258

M8 = M8(0) = #REF!= γ 8-7 x M7(1) = #REF!= γ8-5 x MD 3+M5(1) = #REF!

M9 = M9(0) = #REF!= γ 9-9" x M9"(0) = #REF!= γ 9-9' x M9'(0) = #REF!

= γ9-7 x MD 4+M7(1) = #REF!

Joint 1

M1-2 = K 1-2 x + Mf1-2

M1-4 = K 1-4 x + Mf1-4

Joint 2

M2-1 = K 2-1 x + Mf2-1

M2-3 = K 2-3 x + Mf2-3

M2-2" = K 2-2" x + Mf2-2"

Joint 3

M3-2 = K 3-2 x + Mf3-2

M3-4 = K 3-4 x + Mf3-4

M3-6 = K 3-6 x + Mf3-6

M3-3" = K 3-2" x + Mf3-3" Joint 4

M4-3 = K 4-3 x + Mf4-3

M4-1 = K 4-1 x + Mf4-1

M4-5 = K 4-5 x + Mf4-5

Joint 5

M5-6 = K 5-6 x + Mf5-6

M5-4 = K 5-4 x + Mf5-4

M5-8 = K 5-8 x + Mf5-8

Joint 6

M6-5 = K 6-5 x + Mf6-5

M6-7 = K 6-7 x + Mf6-7

M6-3 = K 6-3 x + Mf6-3

M6-6' = K 6-6' x + Mf6-6

Joint 7

M7-6 = K 7-6 x + Mf7-6

M7-8 = K 7-8 x + Mf7-8

M7-9 = K 7-2 x + Mf7-9

M7-7" = K 7-7' x + Mf7-7'

Joint 8

M8-7 = K 8-7 x + Mf8-7

M8-5 = K 8-5 x + Mf8-5

{ 2M1(k) + M2(k) }

{2M1(k) + M4(k) }

{ 2M2(k) + M1(k) }

{2M2(k) + M3(k) }

{2M2(k) + M2"(k) }

{ 2M3(k) + M2(k) }

{2M3(k) + M4(k) }

{2M3(k) + M6(k) }

{2M3(k) + M3"(k) }

{ 2M4(k) + M3(k) }

{ 2M4(k) + M1(k) }

{ 2M4(k) + M3(k) }

{ 2M5(k) + M6(k) }

{ 2M5(k) + M4(k) }

{ 2M5(k) + M8(k) }

{ 2M6(k) + M5(k) }

{2M6(k) + M7(k) }

{2M6(k) + M3(k) }

{2M6(k) + M6"(k) }

{ 2M7(k) + M6(k) }

{2M7(k) + M8(k) }

{2M7(k) + M2(k) }

{2M7(k) + M7'(k) }

{ 2M8(k) + M7(k) }

{2M8(k) + M5(k) }

Joint 9

M9-9" = K 9-9" x + Mf9-9"

M9-9' = K 9-9' x + Mf9-9'

M9-7 = K 9-7 x + Mf9-7

1M1-2 #REF!

#REF!0.08

0.6100.125 #REF!

M1-4 #REF! 0.53 0.875 #REF!

M2-1 #REF!

0.111 #REF!

M2-3 #REF! 0.53 0.778 #REF!

M2-2" #REF! 0.08 0.111 #REF!

M3-2 #REF!

0.111 #REF!

M3-4 #REF! 0.08 0.111 #REF!

M3-6 #REF! 0.53 0.778 #REF!

M4-5 #REF!

#REF! #REF!

M4-3 #REF! 0.08 #REF! #REF!

M4-1 #REF! 0.53 #REF! #REF!

M5-4 #REF!

#REF! #REF!

M5-6 #REF! 0.03 #REF! #REF!

M6-5 #REF!

#REF! #REF!

M6-6' #REF! 0.03 #REF! #REF!

M7-6 #REF!

#REF! #REF!

M7-8 #REF! 0.03 #REF! #REF!

M7-7" #REF! 0.03 #REF! #REF!

8M8-7 #REF!

#REF!0.03

#REF!#REF! #REF!

{ 2M9(k) + M9"(k) }

{2M9(k) + M9'(k) }

{2M9(k) + M7(k) }

Momen desain

K /∑K*∆M

M9-9" #REF!

#REF! #REF!

M9-9' #REF! 0.11 #REF! #REF!

∑`RA

No. JointM.Desain

1 M1-2 #REF! #REF! #REF! - 8 #REF!

2 M2-1 #REF! #REF! #REF! - 8 #REF!

5 M3-4 #REF! #REF! #REF! - 8 #REF!

6 M4-3 #REF! #REF! #REF! - 8 #REF!

7 M5-6 #REF! #REF! #REF! - 8 #REF!

8 M6-5 #REF! #REF! #REF! - 8 #REF!

11 M7-8 #REF! #REF! 2.055 - 8 #REF!

12 M8-7 #REF! #REF! 2.055 - 8 #REF!

13 M9-9" #REF! 0.523 - - 4 1.047

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RM x-y= Mx-y / L

RM y-x= Mx-y / L

RM x-y= Mx-y / L

1 M1-4 5 #REF! #REF!

M4-1 5 #REF! #REF!

2 M2-3 5 #REF! #REF!

M3-2 5 #REF! #REF!

3 M3-6 4 #REF! #REF!

M6-3 4 #REF! #REF!

4 M4-5 4 #REF! #REF!

M5-4 4 #REF! #REF!

5 M5-8 4 #REF! #REF!

M8-5 4 #REF! #REF!

6 M6-7 4 #REF! #REF!

M7-6 4 #REF! #REF!

M9-7 5 #REF! #REF!

7 M7-9 5 #REF! #REF!

……………………………………………..FINISH……………………………………..

Kekakuan

0.5333

Kekakuan

0.0762

Kekakuan

0.1143

Kekakuan

0.3857

0.1143

0.0762

0.0321

- ( 7,998.081 )

- 0.125 x 7,459.064 x 8

= = -3.609

= = (0.75) x

= = -2.813

= = (0.75) x

= = -1.350

= = (0.75) x

Putaran 1

MI (1) MI (0)

(-t1-4

) x (M1( I ) + M4(I) )

(-t2-3

) x (M2( I ) + M3(I) )

MII(1) MII (0)

(-t4-5) x (M4( I ) + M5(I) )

(-t3-6) x (M3( I )+ M6(I))

MIII(1) MIII (0)

(-t5-8) x (M5 ( I ) + M8 (I) )

(-t6-7) x (M6 ( I )+ M7 (I))

= 43.909 43.9 x (3.242) = 0.203 (0.063) x (0.5)x 10.324 = (4.517) + (0.438) x (18.4)

MI 39.595 MI

= (3.242) (3.2) x 39.595 = (2.200) (0.056) x 52.0 x 19.452 = (1.081) (0.056) x 19.5 x (15.497) = 6.027 + (0.389) x (53.85)

M2 (0.496) M2

= (11.888) (11.9) x 13.933 = (1.715) (0.123) x 24.1 x 4.179 = 0.152 0.036 x 4.2 x (3.308) = (0.563) (0.123) x #REF!x (15.497) = 2.638 + (0.170) x #REF!

M3 (11.376) M3

= 13.933 13.9 x (11.376) = 1.511 + (0.133) x 24.1 x 11.121 = 2.042 0.184 x #REF! x 35.985 = 6.607 0.184 x 9.5

M4 24.093 M4

= 13.933 13.9 x (11.888) = 1.579 (0.133) x #REF! x #REF! = #REF! 0.184 x #REF! x 20.483 = 3.761 + 0.184 x #REF!

M5 #REF! M5

= (11.888) (11.9) x #REF! = #REF! 0.123 x #REF!x 4.179 = 0.152 0.036 x 4.2 x 37.817 = 6.437 0.170 x #REF!x (14.188) 6.437 + 0.170 x #REF!

M6 #REF! M6

= 39.167 39.2 x 4.179 = 0.231 0.055 x 4.2 x #REF! = #REF! 0.187 x #REF!x #REF! = #REF! #REF! x #REF!x #REF! #REF! + 0.258 x #REF!

M7 #REF! M7

= #REF! #REF! x #REF! = #REF! #REF! x #REF!x #REF! = #REF! + #REF! x #REF!

M8 #REF! M8

= #REF! #REF! x #REF! = #REF! #REF! x #REF!x #REF! = #REF! #REF! x #REF!

x #REF! = #REF! + #REF! x #REF! M9 #REF! M9

= 0.076 x #REF! + # = #REF!

= 0.533 x #REF! + ### = #REF! + ∑M = #REF!

= 0.076 x #REF! + # = #REF!

= 0.533 x #REF! + ### = #REF! +

= 0.076 x #REF! + ## = #REF!∑M = #REF!

= 0.076 x #REF! + - = #REF!

= 0.076 x #REF! + ## = #REF! +

= 0.533 x #REF! + 0 = #REF!

0.076 x #REF! + ### = #REF!

= 0.076 x #REF! + # = #REF!

= 0.533 x #REF! + - = #REF!

= #REF! x #REF! + - = #REF!

∑M = #REF!

= 0.032 x #REF! + # = #REF!

= #REF! x #REF! + - = #REF!

= #REF! x #REF! + - = #REF! + ∑M = #REF!

= 0.032 x #REF! + # = #REF!

= #REF! x #REF! + ### = #REF!

= #REF! x #REF! + 0 = #REF!

= 0.032 x #REF! + # = #REF! + ∑M = #REF!

= #REF! x #REF! + - = #REF!

= 0.032 x #REF! + ## = #REF!

= #REF! x #REF! + 0 = #REF!

= 0.032 x #REF! + ### = #REF! + ∑M = #REF!

= 0.032 x #REF! + # = #REF!

= #REF! x #REF! + ### = #REF! + ∑M = #REF!

= 0.114 x #REF! + # = #REF!

= 0.114 x #REF! + # = #REF! +

= #REF! x #REF! + 0 = #REF!∑M = #REF!

#REF!#REF!

Koreksi Momen

#REF!#REF!

∑`RA ∑`RB

RB RM x-y RM y-x ∑R'A∑R'B R'A Da kanan Db kiri

#REF! #REF! #REF! ### # #REF! #REF! #REF!

1.047 #REF! #REF! ### # #REF! #REF! #REF!

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RMy-x/L ∑RA ∑RB Da Da kanan

#REF! #REF! #REF! ### #

……………………………………………..FINISH……………………………………..

= -3.61 -3.609

63.7 = -47.77 (0.75) x

(11.9) = 8.90 (0.75) x-42.47

= -2.81 -2.813

#REF! = #REF! (0.75) x

= -1.35 -1.350

#REF! = #REF! (0.75) x

Putaran 2

= 43.909 43.9 = 0.031 (0.063) x 13.7 = 8.041 (0.438) x #REF!

51.980 MI

= (3.242) (3.2)= (2.888) (0.056) x #REF!= (1.081) (0.056) x 19.5 = 20.941 (0.389) x #REF!

13.730 M2

= (11.888) (11.9)= (2.966) (0.123) x #REF!

#REF! M3

= 13.933 13.9 = (3.199) (0.133) x #REF!= #REF! 0.184 x #REF!= 1.746 0.184 x #REF!

#REF! M4

#REF! M5

#REF! M8

= #REF! #REF! x #REF!#REF! M9

Db kanan Dc kiri Dc kanan Dd kiri Dd kanan

#REF! #REF! #REF!

= -3.61 -3.609 =

#REF! = #REF! (0.75) x #REF! =

#REF! = #REF! (0.75) x #REF! =#REF!

= -2.81 -2.813 =

#REF! = #REF! (0.75) x #REF! =

= -1.35 -1.350 =

#REF! = #REF! (0.75) x #REF! =

Putaran 3

= 43.909 43.9 = 43.909 = (0.858) (0.063) x #REF! = #REF!= #REF! (0.438) x #REF! = #REF!

#REF! MI #REF!

= (3.242) (3.2) = (3.242)= #REF! (0.056) x #REF! = #REF!= (1.081) (0.056) x 19.5 = (1.081)= #REF! (0.389) x #REF! = #REF!

#REF! M2 #REF!

= (11.888) (11.9) = (11.888)= #REF! (0.123) x #REF! = #REF!

0.152 0.036 x 4.2 0.152 = #REF! (0.123) x #REF! = #REF!= #REF! (0.170) x #REF! = #REF!

#REF! M3 #REF!

#REF! M4 #REF!

#REF! M5 #REF!

= (11.888) (11.9) = (11.888)= #REF! 0.123 x #REF! = #REF!= 0.152 0.036 x 4.2 = 0.152 = #REF! 0.170 x #REF! = #REF!

= 39.167 39.2 = 39.167 = 0.231 0.055 x 4.2 = 0.231 = #REF! 0.187 x #REF! = #REF!= #REF! #REF! x #REF! = #REF!

#REF! M8 #REF!

= #REF! #REF! x #REF! = #REF!#REF! M9 #REF!

-3.61 -3.609 = -3.61

#REF! (0.75) x #REF! = #REF!

-2.81 -2.813 = -2.81

#REF! (0.75) x #REF! = #REF!

#REF! #REF!

-1.35 -1.350 = -1.35

#REF! (0.75) x #REF! = #REF!

#REF! #REF!

Putaran 4

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

#REF! x #REF! = #REF!M9 #REF!

-3.609 = -3.61 -3.609

(0.75) x #REF! = #REF! (0.75)

(0.75) x #REF! = #REF! (0.75)#REF!

-2.813 = -2.81 -2.813

(0.75) x #REF! = #REF! (0.75)

-1.350 = -1.35 -1.350

(0.75) x #REF! = #REF! (0.75)

Putaran 5 Putaran 6

MI #REF!

(3.2) = (3.242) (3.2) (0.056) x #REF! = #REF! (0.056) x (0.056) x 19.5 = (1.081) (0.056) x (0.389) x #REF! = #REF! (0.389) x

M2 #REF!

(11.9) = (11.888) (11.9) (0.123) x #REF! = #REF! (0.123) x 0.036 x 4.2 0.152 0.036 x (0.123) x #REF! = #REF! (0.123) x (0.170) x #REF! = #REF! (0.170) x

M3 #REF!

M4 #REF!

M5 #REF!

(11.9) = (11.888) (11.9) 0.123 x #REF! = #REF! 0.123 x 0.036 x 4.2 = 0.152 0.036 x 0.170 x #REF! = #REF! 0.170 x 0.170 x #REF! #REF! 0.170 x

M6 #REF!

39.2 = 39.167 39.2 0.055 x 4.2 = 0.231 0.055 x 0.187 x #REF! = #REF! 0.187 x

#REF! x #REF! = #REF! #REF! x 0.258 x #REF! #REF! 0.258 x

M7 #REF!

M8 #REF!

#REF! x #REF! = #REF! #REF! xM9 #REF!

= -3.61 -3.609

x #REF! = #REF! (0.75) x

x #REF! = #REF! (0.75) x#REF!

= -2.81 -2.813

x #REF! = #REF! (0.75) x

= -1.35 -1.350

x #REF! = #REF! (0.75) x

Putaran 7

MI #REF! MI

= (3.242) (3.2)#REF! = #REF! (0.056) x #REF!

19.5 = (1.081) (0.056) x 19.5 #REF! = #REF! (0.389) x #REF!

M2 #REF! M2

= (11.888) (11.9)#REF! = #REF! (0.123) x #REF!

M3 #REF! M3

M4 #REF! M4

M5 #REF! M5

= (11.888) (11.9)#REF! = #REF! 0.123 x #REF!

M6 #REF! M6

= 39.167 39.2 4.2 = 0.231 0.055 x 4.2

M7 #REF! M7

M8 #REF! M8

#REF! = #REF! #REF! x #REF!M9 #REF! M9

= -3.61 -3.609

#REF! = #REF! (0.75) x #REF!

#REF! = #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

#REF! = #REF! (0.75) x #REF!

= -1.35 -1.350

#REF! = #REF! (0.75) x #REF!

Putaran 8

= 43.909 43.9 == #REF! (0.063) x #REF! == #REF! (0.438) x #REF! =

#REF! MI

#REF! M2

= (11.888) (11.9) == #REF! (0.123) x #REF! =

#REF! M3

#REF! M4

#REF! M5

#REF! M8

= #REF! #REF! x #REF! =#REF! M9

= -3.61 -3.609 =

= #REF! (0.75) x #REF! =

= #REF! (0.75) x #REF! =#REF!

= -2.81 -2.813 =

= #REF! (0.75) x #REF! =

= -1.35 -1.350 =

= #REF! (0.75) x #REF! =

Putaran 9

(3.242) (3.2) = (3.242)#REF! (0.056) x #REF! = #REF!

(11.888) (11.9) = (11.888)#REF! (0.123) x #REF! = #REF!

0.152 0.036 x 4.2 0.152 #REF! (0.123) x #REF! = #REF!#REF! (0.170) x #REF! = #REF!#REF! M3 #REF!

#REF! M4 #REF!

#REF! M5 #REF!

(11.888) (11.9) = (11.888)#REF! 0.123 x #REF! = #REF!

0.152 0.036 x 4.2 = 0.152 #REF! 0.170 x #REF! = #REF!#REF! 0.170 x #REF! #REF!#REF! M6 #REF!

39.167 39.2 = 39.167 0.231 0.055 x 4.2 = 0.231

#REF! 0.187 x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! 0.258 x #REF! #REF!#REF! M7 #REF!

#REF! #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! M8 #REF!

#REF! #REF! = #REF!#REF! #REF! x #REF! = #REF!#REF! #REF! x #REF! = #REF!

#REF! #REF! x #REF! = #REF!#REF! M9 #REF!

-3.61 -3.609 = -3.61

#REF! (0.75) x #REF! = #REF!

-2.81 -2.813 = -2.81

#REF! (0.75) x #REF! = #REF!

#REF! #REF!

-1.35 -1.350 = -1.35

#REF! (0.75) x #REF! = #REF!

#REF! #REF!

Putaran 10

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

43.9 = 43.909 43.9 (0.063) x #REF! = #REF! (0.063) (0.438) x #REF! = #REF! (0.438)

MI #REF!

(3.2) = (3.242) (3.2) (0.056) x #REF! = #REF! (0.056) (0.056) x 19.5 = (1.081) (0.056) (0.389) x #REF! = #REF! (0.389)

M2 #REF!

(11.9) = (11.888) (11.9) (0.123) x #REF! = #REF! (0.123) 0.036 x 4.2 0.152 0.036 (0.123) x #REF! = #REF! (0.123) (0.170) x #REF! = #REF! (0.170)

M3 #REF!

M4 #REF!

M5 #REF!

(11.9) = (11.888) (11.9) 0.123 x #REF! = #REF! 0.123 0.036 x 4.2 = 0.152 0.036 0.170 x #REF! = #REF! 0.170 0.170 x #REF! #REF! 0.170

M6 #REF!

39.2 = 39.167 39.2 0.055 x 4.2 = 0.231 0.055 0.187 x #REF! = #REF! 0.187

#REF! x #REF! = #REF! #REF! 0.258 x #REF! #REF! 0.258

M7 #REF!

M8 #REF!

-3.609 = -3.61 -3.609

(0.75) x #REF! = #REF! (0.75)

(0.75) x #REF! = #REF! (0.75)#REF!

-2.813 = -2.81 -2.813

(0.75) x #REF! = #REF! (0.75)

-1.350 = -1.35 -1.350

(0.75) x #REF! = #REF! (0.75)

Putaran 14

MI #REF!

= (3.242) (3.2) x #REF! = #REF! (0.056) x x 19.5 = (1.081) (0.056) xx #REF! = #REF! (0.389) x

M2 #REF!

= (11.888) (11.9) x #REF! = #REF! (0.123) x x 4.2 0.152 0.036 x x #REF! = #REF! (0.123) xx #REF! = #REF! (0.170) x

M3 #REF!

M4 #REF!

M5 #REF!

= (11.888) (11.9) x #REF! = #REF! 0.123 x x 4.2 = 0.152 0.036 xx #REF! = #REF! 0.170 xx #REF! #REF! 0.170 x

M6 #REF!

= 39.167 39.2 x 4.2 = 0.231 0.055 x x #REF! = #REF! 0.187 xx #REF! = #REF! #REF! xx #REF! #REF! 0.258 x

M7 #REF!

M8 #REF!

x #REF! = #REF! #REF! xM9 #REF!

= -3.61 -3.609

x #REF! = #REF! (0.75)

x #REF! = #REF! (0.75)#REF!

= -2.81 -2.813

x #REF! = #REF! (0.75)

= -1.35 -1.350

x #REF! = #REF! (0.75)

= 43.909 43.9 #REF! = #REF! (0.063) x #REF! = #REF! (0.438) x

MI #REF!

= (3.242) (3.2)#REF! = #REF! (0.056) x

19.5 = (1.081) (0.056) x#REF! = #REF! (0.389) x

M2 #REF!

= (11.888) (11.9)#REF! = #REF! (0.123) x

4.2 0.152 0.036 x #REF! = #REF! (0.123) x#REF! = #REF! (0.170) x

M3 #REF!

M4 #REF!

M5 #REF!

= (11.888) (11.9)#REF! = #REF! 0.123 x

4.2 = 0.152 0.036 x#REF! = #REF! 0.170 x#REF! #REF! 0.170 x

M6 #REF!

= 39.167 39.2 4.2 = 0.231 0.055 x

#REF! = #REF! 0.187 x#REF! = #REF! #REF! x#REF! #REF! 0.258 x

M7 #REF!

M8 #REF!

#REF! = #REF! #REF! xM9 #REF!

= -3.61 -3.609

x #REF! = #REF! (0.75) x

x #REF! = #REF! (0.75) x#REF!

= -2.81 -2.813

x #REF! = #REF! (0.75) x

= -1.35 -1.350

x #REF! = #REF! (0.75) x

Putaran 16

MI #REF! MI

= (3.242) (3.2)#REF! = #REF! (0.056) x #REF!

19.5 = (1.081) (0.056) x 19.5 #REF! = #REF! (0.389) x #REF!

M2 #REF! M2

= (11.888) (11.9)#REF! = #REF! (0.123) x #REF!

M3 #REF! M3

M4 #REF! M4

M5 #REF! M5

= (11.888) (11.9)#REF! = #REF! 0.123 x #REF!

M6 #REF! M6

= 39.167 39.2 4.2 = 0.231 0.055 x 4.2

M7 #REF! M7

M8 #REF! M8

#REF! = #REF! #REF! x #REF!M9 #REF! M9

= -3.61 -3.609

#REF! = #REF! (0.75) x

#REF! = #REF! (0.75) x#REF!

= -2.81 -2.813

#REF! = #REF! (0.75) x

= -1.35 -1.350

#REF! = #REF! (0.75) x

Putaran 17

= 43.909 43.9 = #REF! (0.063) x #REF!= #REF! (0.438) x #REF!

#REF! MI

= (3.242) (3.2)= #REF! (0.056) x #REF!= (1.081) (0.056) x 19.5 = #REF! (0.389) x #REF!

#REF! M2

= (11.888) (11.9)= #REF! (0.123) x #REF!

#REF! M3

#REF! M4

#REF! M5

#REF! M8

= #REF! #REF! x #REF!#REF! M9

= -3.61 -3.609

#REF! = #REF! (0.75) x #REF!

#REF! = #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

#REF! = #REF! (0.75) x #REF!

= -1.35 -1.350

#REF! = #REF! (0.75) x #REF!

Putaran 17

= 43.909 43.9 == #REF! (0.063) x #REF! == #REF! (0.438) x #REF! =

#REF! MI

#REF! M2

= (11.888) (11.9) == #REF! (0.123) x #REF! =

#REF! M3

#REF! M4

#REF! M5

#REF! M8

= #REF! #REF! x #REF! =#REF! M9

= -3.61 -3.609

= #REF! (0.75) x #REF!

= #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

= #REF! (0.75) x #REF!

= -1.35 -1.350

= #REF! (0.75) x #REF!

Putaran 18

(3.242) (3.2) =#REF! (0.056) x #REF! =

(1.081) (0.056) x 19.5 =#REF! (0.389) x #REF! =#REF! M2

(11.888) (11.9) =#REF! (0.123) x #REF! =

#REF! M4

#REF! M5

(11.888) (11.9) =#REF! 0.123 x #REF! =

39.167 39.2 = 0.231 0.055 x 4.2 =

#REF! #REF! =#REF! #REF! x #REF! =#REF! #REF! x #REF! =

#REF! #REF! x #REF! =#REF! M9

= -3.61 -3.609

= #REF! (0.75) x #REF!

= #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

= #REF! (0.75) x #REF!

= -1.35 -1.350

= #REF! (0.75) x #REF!

Putaran 19

(3.242) (3.2) =#REF! (0.056) x #REF! =

(1.081) (0.056) x 19.5 =#REF! (0.389) x #REF! =#REF! M2

(11.888) (11.9) =#REF! (0.123) x #REF! =

#REF! M4

#REF! M5

(11.888) (11.9) =#REF! 0.123 x #REF! =

39.167 39.2 = 0.231 0.055 x 4.2 =

= -3.61 -3.609

= #REF! (0.75) x #REF!

= #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

= #REF! (0.75) x #REF!

= -1.35 -1.350

= #REF! (0.75) x #REF!

Putaran 20

(3.242) (3.2) =#REF! (0.056) x #REF! =

(1.081) (0.056) x 19.5 =#REF! (0.389) x #REF! =#REF! M2

(11.888) (11.9) =#REF! (0.123) x #REF! =

#REF! M4

#REF! M5

(11.888) (11.9) =#REF! 0.123 x #REF! =

39.167 39.2 = 0.231 0.055 x 4.2 =

= -3.61 -3.609

= #REF! (0.75) x

= #REF! (0.75) x#REF!

= -2.81 -2.813

= #REF! (0.75) x

= -1.35 -1.350

= #REF! (0.75) x

Putaran 21

43.909 43.9 #REF! (0.063) x #REF!#REF! (0.438) x #REF!#REF! MI

(3.242) (3.2)#REF! (0.056) x #REF!

(1.081) (0.056) x 19.5 #REF! (0.389) x #REF!#REF! M2

(11.888) (11.9)#REF! (0.123) x #REF!

#REF! M4

#REF! M5

(11.888) (11.9)#REF! 0.123 x #REF!

39.167 39.2 0.231 0.055 x 4.2

#REF! #REF!#REF! #REF! x #REF!#REF! #REF! x #REF!

= -3.61 -3.609

#REF! = #REF! (0.75)

#REF! = #REF! (0.75)#REF!

= -2.81 -2.813

#REF! = #REF! (0.75)

= -1.35 -1.350

#REF! = #REF! (0.75)

Putaran 22

= 43.909 43.9 = #REF! (0.063) x = #REF! (0.438) x

= (3.242) (3.2)= #REF! (0.056) x = (1.081) (0.056) x= #REF! (0.389) x

= (11.888) (11.9)= #REF! (0.123) x

0.152 0.036 x = #REF! (0.123) x= #REF! (0.170) x

= 13.933 13.9 = #REF! (0.133) x = #REF! 0.184 x = #REF! 0.184 x

= (11.888) (11.9)= #REF! 0.123 x = 0.152 0.036 x= #REF! 0.170 x

#REF! 0.170 x#REF!

= 39.167 39.2 = 0.231 0.055 x = #REF! 0.187 x= #REF! #REF! x

#REF! 0.258 x#REF!

= #REF! #REF! x#REF!

= -3.61

x #REF! = #REF!

= -2.81

x #REF! = #REF!

= -1.35

x #REF! = #REF!

Putaran 23

= 43.909 43.9 #REF! = #REF! (0.063)#REF! = #REF! (0.438)

MI #REF!

= (3.242) (3.2)#REF! = #REF! (0.056)

19.5 = (1.081) (0.056)#REF! = #REF! (0.389)

M2 #REF!

= (11.888) (11.9)#REF! = #REF! (0.123)

4.2 0.152 0.036 #REF! = #REF! (0.123)#REF! = #REF! (0.170)

M3 #REF!

M4 #REF!

M5 #REF!

= (11.888) (11.9)#REF! = #REF! 0.123

4.2 = 0.152 0.036 #REF! = #REF! 0.170 #REF! #REF! 0.170

M6 #REF!

= 39.167 39.2 4.2 = 0.231 0.055

#REF! = #REF! 0.187 #REF! = #REF! #REF!#REF! #REF! 0.258

M7 #REF!

M8 #REF!

#REF! = #REF! #REF!M9 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

= 43.909 x #REF! = #REF!x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

M7 #REF!

M8 #REF!

x #REF! = #REF!M9 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

Putaran 24

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

-3.609 =

(0.75) x #REF! =

-2.813 =

(0.75) x #REF! =

-1.350 =

(0.75) x #REF! =

Putaran 25

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

-3.61 -3.609

#REF! (0.75) x #REF!

-2.81 -2.813

#REF! (0.75) x #REF!

-1.35 -1.350

#REF! (0.75) x #REF!

Putaran 26

43.9 = (0.063) x #REF! = (0.438) x #REF! =

(3.2) = (0.056) x #REF! = (0.056) x 19.5 = (0.389) x #REF! =

(11.9) = (0.123) x #REF! = 0.036 x 4.2 (0.123) x #REF! = (0.170) x #REF! =

13.9 = (0.133) x #REF! = 0.184 x #REF! = 0.184 x #REF! =

(11.9) = 0.123 x #REF! = 0.036 x 4.2 = 0.170 x #REF! = 0.170 x #REF!

39.2 = 0.055 x 4.2 = 0.187 x #REF! =

#REF! x #REF! = 0.258 x #REF!

#REF! x #REF! =M9

= -3.61 -3.609

= #REF! (0.75) x

= #REF! (0.75) x#REF!

= -2.81 -2.813

= #REF! (0.75) x

= -1.35 -1.350

= #REF! (0.75) x

Putaran 27

(3.242) (3.2)#REF! (0.056) x #REF!

(1.081) (0.056) x 19.5 #REF! (0.389) x #REF!#REF! M2

(11.888) (11.9)#REF! (0.123) x #REF!

#REF! M4

#REF! M5

(11.888) (11.9)#REF! 0.123 x #REF!

39.167 39.2 0.231 0.055 x 4.2

#REF! #REF!#REF! #REF! x #REF!#REF! #REF! x #REF!

= -3.61 -3.609

#REF! = #REF! (0.75)

#REF! = #REF! (0.75)#REF!

= -2.81 -2.813

#REF! = #REF! (0.75)

= -1.35 -1.350

#REF! = #REF! (0.75)

Putaran 28

= 43.909 43.9 = #REF! (0.063) x = #REF! (0.438) x

= (3.242) (3.2)= #REF! (0.056) x = (1.081) (0.056) x= #REF! (0.389) x

= (11.888) (11.9)= #REF! (0.123) x

0.152 0.036 x = #REF! (0.123) x= #REF! (0.170) x

= 13.933 13.9 = #REF! (0.133) x = #REF! 0.184 x = #REF! 0.184 x

= (11.888) (11.9)= #REF! 0.123 x = 0.152 0.036 x= #REF! 0.170 x

#REF! 0.170 x#REF!

= 39.167 39.2 = 0.231 0.055 x = #REF! 0.187 x= #REF! #REF! x

#REF! 0.258 x#REF!

= #REF! #REF! x#REF!

= -3.61

x #REF! = #REF!

= -2.81

x #REF! = #REF!

= -1.35

x #REF! = #REF!

= 43.909 #REF! = #REF!#REF! = #REF!

MI #REF!

= (3.242)#REF! = #REF!

19.5 = (1.081)#REF! = #REF!

M2 #REF!

= (11.888)#REF! = #REF!

4.2 0.152 #REF! = #REF!#REF! = #REF!

M3 #REF!

M4 #REF!

M5 #REF!

= (11.888)#REF! = #REF!

4.2 = 0.152 #REF! = #REF!#REF! #REF!

M6 #REF!

= 39.167 4.2 = 0.231

#REF! = #REF!#REF! = #REF!#REF! #REF!

M7 #REF!

M8 #REF!

#REF! = #REF!M9 #REF!

-3.609 =

(0.75) x #REF! =

-2.813 =

(0.75) x #REF! =

-1.350 =

(0.75) x #REF! =

Putaran 29

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

39.2 = 39.167 0.055 x 4.2 = 0.231 0.187 x #REF! = #REF!

M7 #REF!

M8 #REF!

-3.61 -3.609

#REF! (0.75) x

#REF! (0.75) x#REF!

-2.81 -2.813

#REF! (0.75) x

-1.35 -1.350

#REF! (0.75) x

Putaran 30

43.9 (0.063) x #REF! (0.438) x #REF!

(3.2) (0.056) x #REF! (0.056) x 19.5 (0.389) x #REF!

(11.9) (0.123) x #REF! 0.036 x 4.2 (0.123) x #REF! (0.170) x #REF!

13.9 (0.133) x #REF! 0.184 x #REF! 0.184 x #REF!

(11.9) 0.123 x #REF! 0.036 x 4.2 0.170 x #REF! 0.170 x #REF!

39.2 0.055 x 4.2 0.187 x #REF!

#REF! x #REF! 0.258 x #REF!

#REF!#REF! x #REF!#REF! x #REF!

#REF! x #REF!M9

= -3.61

#REF! = #REF!

#REF! = #REF!#REF!

= -2.81

#REF! = #REF!

= -1.35

#REF! = #REF!

Putaran 31

= 43.909 43.9 = #REF! (0.063)= #REF! (0.438)

= (3.242) (3.2)= #REF! (0.056)= (1.081) (0.056)= #REF! (0.389)

= (11.888) (11.9)= #REF! (0.123)

0.152 0.036 = #REF! (0.123)= #REF! (0.170)

= 13.933 13.9 = #REF! (0.133)= #REF! 0.184 = #REF! 0.184

= (11.888) (11.9)= #REF! 0.123 = 0.152 0.036 = #REF! 0.170

#REF! 0.170 #REF!

= 39.167 39.2 = 0.231 0.055 = #REF! 0.187 = #REF! #REF!

#REF! 0.258 #REF!

= #REF! #REF!= #REF! #REF!= #REF! #REF!

= #REF! #REF!#REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

= 43.909 x #REF! = #REF!x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

M7 #REF!

M8 #REF!

x #REF! = #REF!M9 #REF!

-3.609

(0.75) x #REF!

-2.813

(0.75) x #REF!

-1.350

(0.75) x #REF!

Putaran 32

43.9 = (0.063) x #REF! = (0.438) x #REF! =

(3.2) = (0.056) x #REF! = (0.056) x 19.5 = (0.389) x #REF! =

(11.9) = (0.123) x #REF! = 0.036 x 4.2 (0.123) x #REF! = (0.170) x #REF! =

13.9 = (0.133) x #REF! = 0.184 x #REF! = 0.184 x #REF! =

(11.9) = 0.123 x #REF! = 0.036 x 4.2 = 0.170 x #REF! = 0.170 x #REF!

39.2 = 0.055 x 4.2 = 0.187 x #REF! =

#REF! x #REF! = 0.258 x #REF!

#REF! x #REF! =M9

= -3.61 -3.609375

= #REF! (0.75)

= #REF! (0.75)#REF!

= -2.81 -2.8125

= #REF! (0.75)

= #REF! (0.75) (0.75)

= -1.35 -1.35

= #REF! (0.75)

= #REF! (0.75) (0.75)

Putaran 33

43.909 43.9 #REF! (0.063) x #REF! (0.438) x#REF!

(3.242) (3.2)#REF! (0.056) x

(1.081) (0.056) x#REF! (0.389) x#REF!

(11.888) (11.9)#REF! (0.123) x

0.152 #REF! (0.123) x#REF! (0.170) x#REF!

13.933 13.9 #REF! (0.133) x #REF!#REF!

(11.888) (11.9)#REF! 0.123 x

0.152 0.036 x#REF! 0.170 x#REF! 0.170 x#REF!

39.167 39.2 0.231 0.055 x

#REF! 0.187 x#REF! #REF! x#REF! 0.258 x#REF!

#REF! #REF!#REF! #REF! x #REF! #REF! x#REF!

#REF! #REF!#REF! #REF! x #REF! #REF! x

#REF! #REF! x#REF!

= -3.61

x #REF! = #REF!

= -2.81

x #REF! = #REF!

= -1.35

x #REF! = #REF!

= 43.9 #REF! = #REF!#REF! = #REF!

MI #REF!

= (3.2)#REF! = #REF!#REF! = #REF!#REF! = #REF!

M2 #REF!

= (11.9)#REF! = #REF!

#REF! = #REF!#REF! = #REF!

M3 #REF!

= 13.9 #REF! = #REF!

M4 #REF!

= 13.9 #REF! = #REF!

M5 #REF!

= (11.9)#REF! = #REF!#REF! = #REF!#REF! = #REF!#REF! #REF!

M6 #REF!

= 39.2 #REF! = #REF!#REF! = #REF!#REF! = #REF!#REF! #REF!

M7 #REF!

M8 #REF!

#REF! = #REF!M9 #REF!

DIKETAHUI : DATA - DATA KONSTRUKSI

1 . Luasan Atap 32 m x 20,7 m = 662.40 m2

23 . Berat Struktur kuda - kuda WF 300.150.6,5.9 = 8547.43 Kg = 12.90371 . Berat Struktur kuda - kuda WF 150.100.6.9 = 645.66 Kg = 0.974731 . Berat Baja 160.6,5.7 = 589.50 Kg = 0.889951 . Berat Plat Simpul = 1412.76 Kg = 2.13279

1 . Berat Atap Genteng Keramik = =

kg/cm^2kg/cm^2kg/cm^2kg/cm^2

PERHITUNGAN PEMBEBANAN PADA ATAP

Diketahui Data - data Konstruksi :1 Berat Struktur Kuda - kuda WF 300.150. = 8,547.43 Kg/m22 Berat Struktur Kuda - kuda WF 150.100. = 645.66 Kg/m23 Berat Baja 160.6,5 7 = 589.5 Kg/m24 Berat Plat Simpul = 1412.76 Kg/m25 Berat Genteng = 50 Kg/m26 Luasan Atap Kuda - kuda WF 300.150.6, = 666 Kg/m27 luasan Atap Kuda - kuda WF 150.100.6,5 = 115.2 m2

A. BEBAN MATI

Kuda-kuda WF 300.150.6,5.9

No. Jenis BahanWeight Luas Total Berat

Ketper Unit m^2 kg/m^2

1 Penutup atap 50.0 kg/m^2 666.00 33300.00 kg/m^2

2 Kuda-kuda WF 300.150.6,5.9 8,547.4 kg/m^2 666.00 12.83 kg/m^2

3 Baja 160.7,5.6 589.5 kg/m^2 666.00 0.89 kg/m^2

4 Berat Plat Simpul 1,412.8 kg/m^2 666.00 2.12 kg/m^2

6 Reng 14.2 kg/m^2 666.00 0.02 kg/m^2

7 Baut 0.05 kg/m^2 666.00 33.30 kg/m^2

Total Beban Mati 33,349.162 kg/m^2 33.349 Ton/m^2

Kuda-kuda WF 150.100.6,5.9

No. Jenis BahanWeight Luas Total Berat

Ketper Unit m^2 kg/m^2

1 Penutup atap 50.0 kg/m^2 115.200 5,760.000 kg/m^2

2 Kuda-kuda WF 150.100.6,5.9 645.7 kg/m^2 115.200 5.605 kg/m^2

3 Baja 160.7,5.6 589.5 kg/m^2 115.200 5.117 kg/m^2

5 Reng 14.2 kg/m^2 115.200 0.123 kg/m^2

6 Baut 0.05 kg/m^2 115.200 5.760 kg/m^2

Total Beban Mati 5,776.605 kg/m^2 5.777 Ton/m^2

B. BEBAN HIDUP

Beban Air Hujan = 50 kg/m^2

No. Luasan Luasan LL Luasan . LL

1 Kuda-kuda WF 300.150.6,5.9 666.000 50 kg/m^2 33,300 kg/m^2

2 Kuda-kuda WF 150.100.6,5.9 115.200 50 kg/m^2 5,760 kg/m^2

39,060.0 kg/m^2

39.1 Ton/m^2

C. REKAPITULASI BEBAN ATAP

No.Beban Mati Beban Hidup

Ketkg/m^2 kg/m^2

1 33,349.162 33,300 kg/m^22 5,776.605 5,760 kg/m^2

Total 39,125.767 39,060.00 kg/m^2

39.126 ton/m^2 39.06 ton/m^2Jadi kombinasi beban hidup dan beban mati pada rangka atap adalah

Kuda-kuda WF 300.150.6,5.9W tot Rangka Atap = 1,2*Wd + 1,6*WL

= 40,019 + 53,280 kg/m^2= 93,298.99 kg/m^2= 93.30 ton/m^2

Kuda-kuda WF 150.100.6,5.9W tot Rangka Atap = 1,2*Wd + 1,6*WL

= 6,932 + 9,216.00 kg/m^2= 16,147.93 kg/m^2= 16.15 ton/m^2

Beban Segitiga Pada Atap

h y = 2/3 h

TipeL h y n Qu p

ketm m ton/m^2 ton1 18.5 5.45 3.6333333 1 93.30 338.99 Beban terpusat2 4 1.83 1.22 1 93.30 113.82 Beban terpusat

Beban trapesium pada atap

h y = h - (4.h^3 / 3 .L^2)

TipeL h y n Qu q

ketm m ton/m^2 ton1 28 5.95 5.5917604 1 93.30 521.7 Beban merata2 18.5 1.8 1.7772798 1 93.30 166 Beban merata

PEMBEBANAN PADA PLAT ATAP y = 2/3 h

Beban Segitiga

TipeL h y

LL WD p Ketm m

S9 3.5 1.78 1.187 250 408 889.6 1,055.7 Beban terpusath

Beban mati pada plat atap

- Berat pelat atap = 0.12 x 2400 = 288kg/m^2- Berat plafond = 50kg/m^2- Berat Spesi = 21kg/m^3- Berat Keramik = 24kg/m^4- Ornamen = 25kg/m^2

∑ 408kg/m^2

Beban trapesium

hy = h - (4.h^3 / 3 .L^2)

TipeL h t

y LL WD QKOM Qm m m

T10 4.5 1.78 1.41 250 408 889.6 1253.1

PEMBEBANAN PADA PLAT LANTAI ,2 DAN 3y = 2/3 h

Beban Segitiga

TipeL h y

LL WD p Ketm m

S4 4 1.8 1.200 100 408 649.6 779.520 Beban terpusath

Beban trapesium

hy = h - (4.h^3 / 3 .L^2)

TipeL h t

y LL WD QKOM Wpltm m mT6 4 1.12 1.00 100 408 649.6 651.5

L T8 4 1.36 1.15 100 408 649.6 747.3

Beban merata dan terpusat pada Lt 1. pada portal tinjauan 1. Berat plat

Wplt (trapesium) = 747.3 kgWplt (segitiga) = 779.5 kg

Berat sendiri balok induk ( TB 200 X 400)Wbalok = ( hblok - t plat) x b balok x p blok x ρ beton

= 0.4 - 0.12 x 0.2 x 28 x 2400= 3763.2 kg

Berat dinding Wdin = 250 x 28

= 7000 kg

Beban Merata ( q ) = 11,510.5 Beban terpusat ( p ) = 4,542.7

Beban merata dan terpusat pada Lt 1. pada portal tinjauan Berat sendiri balok induk ( TB 200 X 400)

Wbalok = ( hblok - t plat) x b balok x p blok x ρ beton

= 0.4 - 0.12 x 0.2 x 18.5 x 2400= 2486.4 kg

Berat dinding Wdin = 250 x 18.5

= 4625 kg

Beban merata dan terpusat pada portal tinjauan pada Lt. 2 & Lt. 3 arah X1. Berat plat

Wplt (trapesium) = 747.29 Wplt (segitiga) = 779.52

Berat sendiri balok induk ( BL 300 X 600)Wbalok = ( hblok - t plat ) x b balok x p blok x ρ beton

= 0.6 - 0.12 x 0.3 x 8 x 2400= 2,764.80 kg

Berat sendiri balok anak ( BL 300 X 400)Wbalok = ( hblok - t plat ) x b balok x p blok x ρ beton

= 0.4 - 0.12 x 0.3 x 2.5 x 2400= 504 kg

= 2000Wdin' = 250 x 2.5

Berat Sendiri kolom ( KL 400 x 400)= h kolom x b kolom x p kolom x ρ beton= 0.4 x 0.4 x 4 x 2400= 1536 kg

Beban merata dan terpusat pada portal tinjauan pada Lt. 2 & Lt. 3 arah YBerat sendiri balok anak ( BL 200 X 400)

Wbalok = ( hblok - t plat ) x b balok x p blok x ρ beton

= 0.2 - 0.12 x 0.4 x 4 x 2400= 307.2 kg

Berat DindingWdin = 250 x 4

= 1000

Pembebanan pada lantai atap1. Berat atap

Wplt (trapesium) = 521.7

Berat sendiri balok induk ( RB1 200 x 300)Wbalok = ( hblok - t plat ) x b balok x p blok x ρ beton

= 0.3 - 0.12 x 0.2 x 18.5 x 2400= 1,598.40 kg

Beban Merata ( q ) = 2,120.1 kgbeban terpusat ( p ) = 1,598.4 kg

∑`RA ∑`RB

No. JointM.Desain

q p1 p2 L RA RB RM x-y RM y-x ∑R'A ∑R'B R'A Da kanan Db kiriStlh Koreksi

1 M1-2 -11.568 11.510 4.543 4 25.292 25.292 (2.892) 3.489 31.674 18.911 31.674 31.674 (14.368)2 M2-1 13.957 11.510 4.543 4 25.292 25.292 (2.892) 3.489 31.674 18.911 31.674 31.674 (14.368)3 M2-3 -13.345 11.510 4.543 - 4 25.292 25.292 (3.336) 3.269 31.898 18.687 31.898 31.898 (14.144)4 M3-2 13.077 11.510 4.543 - 4 25.292 25.292 (3.336) 3.269 31.898 18.687 31.898 31.898 (14.144)5 M3-4 -12.971 11.510 4.543 - 4 25.292 25.292 (3.243) 0.127 28.662 21.923 28.662 28.662 (17.380)6 M4-3 0.507 11.510 4.543 - 4 25.292 25.292 (3.243) 0.127 28.662 21.923 28.662 28.662 (17.380)7 M5-4 0.000 11.510 4.543 - 4 25.292 25.292 - - 25.292 25.292 25.292 25.292 (20.750)8 M4-5 -4.245 11.510 4.543 - 4 25.292 25.292 (1.061) (1.061) 25.292 25.292 25.292 25.292 (20.750)9 M6-7 0.000 2.054 2.316 - 4 5.267 5.267 (1.061) - 6.328 4.205 6.328 6.328 (1.890)10 M7-6 -5.127 2.732 2.316 - 4 6.623 6.623 (1.282) (1.176) 6.728 6.517 6.728 6.728 (4.201)11 M8-7 -4.704 2.732 2.316 - 4 6.623 6.623 (1.282) (1.176) 6.728 6.517 6.728 6.728 (4.201)12 M7-8 4.815 2.732 2.316 - 4 6.623 6.623 1.204 (1.029) 4.390 8.856 4.390 4.390 (6.540)13 M8-9 4.939 2.054 2.316 - 4 5.267 5.267 1.235 (1.013) 3.019 7.514 3.019 3.019 (5.198)14 M9-10 -4.117 2.732 2.316 - 4 6.623 6.623 1.204 (1.029) 4.390 8.856 4.390 4.390 (6.540)15 M9-8 -4.050 2.732 2.316 - 4 6.623 6.623 1.235 (1.013) 4.375 8.870 4.375 4.375 (6.554)16 M10-9 4.107 2.732 2.316 - 4 6.623 6.623 1.027 (1.087) 4.508 8.737 4.508 4.508 (6.421)17 M11-12 -4.350 2.732 2.316 - 4 6.623 6.623 1.027 (1.087) 4.508 8.737 4.508 4.508 (6.421)18 M12-11 4.779 2.732 2.316 - 4 6.623 6.623 1.027 1.195 6.790 6.455 6.790 6.790 (4.139)19 M12-13 -5.009 2.732 2.316 - 4 6.623 6.623 1.027 1.195 6.790 6.455 6.790 6.790 (4.139)20 M14-13 4.663 2.732 2.316 - 4 6.623 6.623 1.027 1.166 6.761 6.484 6.761 6.761 (4.168)21 M14-15 -5.099 2.732 2.316 - 4 6.623 6.623 1.027 1.166 6.761 6.484 6.761 6.761 (4.168)22 M15-14 0.000 2.732 2.316 - 4 6.623 6.623 1.027 1.166 6.761 6.484 6.761 6.761 (4.168)

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

Db kanan Dc kiri Dc kanan

-14.368 (18.911) 0.000 (14.368) (18.911) 0.000

-14.144 (18.687) 0.000-14.144 (18.687) 0.000-17.380 (21.923) 0.000-17.380 (21.923) 0.000-20.750 (25.292) 0.000-20.750 (25.292) 0.000-1.890 (4.205) 0.000

(4.201) (6.517) 0.000 (4.201) (6.517) 0.000 (6.540) (8.856) 0.000

-5.198 (7.514) 0.000 (6.540) (8.856) 0.000

-6.554 (8.870) 0.000-6.421 (8.737) 0.000-6.421 (8.737) 0.000-4.139 (6.455) 0.000-4.139 (6.455) 0.000-4.168 (6.484) 0.000-4.168 (6.484) 0.000

(4.168) (6.484) 0.000

RM x-y= Mx-y / L

RM y-x= Mx-y / L

RM x-y= Mx-y / L

No. Joint h M desain RMx-y/L RMy-x/L ∑RA ∑RB Da KananDa kanan

1 M1-A 4.00 2.188 0.547 0.273 0.820 (0.820) 0.820 0.000 2 MA-1 4.00 1.094 0.547 0.273 0.820 (0.820) 0.820 0.000 3 M2-B 4.00 1.734 0.433 0.217 0.650 (0.650) 0.650 0.000 4 MB-2 4.00 0.867 0.433 0.217 0.650 (0.650) 0.650 0.000 5 M3-C 4.00 (0.105) (0.026) (0.013) (0.039) 0.039 (0.039) 0.000 6 MC-3 4.00 (0.052) (0.026) (0.013) (0.039) 0.039 (0.039) 0.000 7 M4-D 4.00 0.001 0.000 0.000 0.000 (0.000) 0.000 0.000 8 MD-4 4.00 0.000 0.000 0.000 0.000 (0.000) 0.000 0.000 9 M5-E 4.00 (0.340) (0.085) (0.042) (0.127) 0.127 (0.127) 0.000 10 ME-5 4.00 (0.170) (0.085) (0.042) (0.127) 0.127 (0.127) 0.000 11 M6-F 4.00 (0.010) (0.003) (0.001) (0.004) 0.004 (0.004) 0.000 12 MF-6 4.00 (0.005) (0.003) (0.001) (0.004) 0.004 (0.004) 0.000 13 M7-G 4.00 0.007 0.002 0.001 0.003 (0.003) 0.003 0.000 14 MG-7 4.00 0.004 0.002 0.001 0.003 (0.003) 0.003 0.000 15 M8-H 4.00 (1.623) (0.406) (0.203) (0.609) 0.609 (0.609) 0.000 16 MH-8 4.00 (0.811) (0.406) (0.203) (0.609) 0.609 (0.609) 0.000 17 M1-16 4.00 (0.341) (0.085) (0.474) (0.559) 0.559 (0.559) 0.000 18 M16-1 4.00 (1.895) (0.085) (0.474) (0.559) 0.559 (0.559) 0.000 19 M2-15 4.00 0.353 0.088 (0.065) 0.023 (0.023) 0.023 0.000 20 M15-2 4.00 (0.261) 0.088 (0.065) 0.023 (0.023) 0.023 0.000 21 M3-14 4.00 (0.022) (0.006) 0.008 0.003 (0.003) 0.003 0.000 22 M14-3 4.00 0.033 (0.006) 0.008 0.003 (0.003) 0.003 0.000 23 M4-13 4.00 0.027 0.007 0.090 0.097 (0.097) 0.097 0.000 24 M13-4 4.00 0.360 0.007 0.090 0.097 (0.097) 0.097 0.000 25 M5-12 4.00 (0.268) (0.067) (0.016) (0.083) 0.083 (0.083) 0.000 26 M12-5 4.00 (0.063) (0.067) (0.016) (0.083) 0.083 (0.083) 0.000 27 M6-11 4.00 0.031 0.008 (0.005) 0.003 (0.003) 0.003 0.000 28 M11-6 4.00 (0.021) 0.008 (0.005) 0.003 (0.003) 0.003 0.000 29 M7-10 4.00 0.119 0.030 0.036 0.066 (0.066) 0.066 0.000 30 M10-7 4.00 0.144 0.030 0.036 0.066 (0.066) 0.066 0.000 31 M8-9 4.00 (2.670) (0.667) (0.619) (1.287) 1.287 (1.287) 0.000 32 M9-8 4.00 (2.477) (0.667) (0.619) (1.287) 1.287 (1.287) 0.000

33 M9-24 4.00 (2.477) (0.619) (0.582) (1.201) 1.201 (1.201) 0.000 34 M24-9 4.00 (2.327) (0.619) (0.582) (1.201) 1.201 (1.201) 0.000 35 M10-23 4.00 0.128 0.032 0.026 0.058 (0.058) 0.058 0.000 36 M23-10 4.00 0.103 0.032 0.026 0.058 (0.058) 0.058 0.000 37 M11-22 4.00 (0.014) (0.004) 0.001 (0.003) 0.003 (0.003) 0.000 38 M22-11 4.00 0.003 (0.004) 0.001 (0.003) 0.003 (0.003) 0.000 39 M12-21 4.00 0.026 0.006 0.002 0.009 (0.009) 0.009 0.000 40 M21-12 4.00 0.009 0.006 0.002 0.009 (0.009) 0.009 0.000 41 M13-20 4.00 0.239 0.060 0.002 0.061 (0.061) 0.061 0.000 42 M20-13 4.00 0.006 0.060 0.002 0.061 (0.061) 0.061 0.000 43 M14-19 4.00 0.015 0.004 (0.022) (0.018) 0.018 (0.018) 0.000 44 M19-14 4.00 (0.088) 0.004 (0.022) (0.018) 0.018 (0.018) 0.000 45 M15-18 4.00 0.197 0.049 0.286 0.336 (0.336) 0.336 0.000 46 M18-15 4.00 1.145 0.049 0.286 0.336 (0.336) 0.336 0.000 47 M16-17 4.00 (1.252) (0.313) 0.123 (0.190) 0.190 (0.190) 0.000 48 M17-16 4.00 0.493 (0.313) 0.123 (0.190) 0.190 (0.190) 0.000

Perhitungan Aksial Kolom

Perhitungan Aksial Kolom Pada Batang 1-A Arah XGaya Aksial Kolom 1-A = Ra 1 - A + Ra 16 - 1 + Ra17 - 16

= 5.877 + 0.5824 + 0.5824= 7.0418

ElemenGaya Aksial

KolomKolom 1-A 7.0418Kolom 2-B 10.3121Kolom 3-C 10.9797Kolom 4-D 10.1934kolom 5-E 10.0411Kolom 6-F 10.2139Kolom 7-G 10.0404Kolom 8-H 5.0175Kolom 8-9 1.1228

Kolom 7-10 2.2456Kolom 6-11 2.1172Kolom 5-12 2.3636Kolom 4-13 2.486Kolom 3-14 2.8046Kolom 2-15 2.5226Kolom 1-16 1.1648

Kolom 16-17 0.5824Kolom 15-18 1.2613Kolom 14-19 1.4023Kolom 13-20 1.243Kolom 12-21 1.1818Kolom 11-22 1.0586Kolom 10-23 1.1228Kolom 9-24 0.5614

Elemen Gaya Aksial

KolomKolom 1-A 53.38Kolom 2-B 76.896Kolom 3-C 48.983Kolom 3-4 30.403Kolom 2-5 71.802Kolom 1-6 33.659Kolom 6-7 11.348Kolom 5-8 33.207Kolom 4-9 14.119

PERHITUNGAN TAKABEYA ARAH Y

Kolom Type kolom K1 = 0.5 m 0.4 mType kolom K1 = 0.4 m 0.3 mType kolom K1 = 0.35 m 0.30 m

Tie Beam

Type TB 1 = 0.3 m 0.40 m

Ring Balk

Dimensi RB1 = 0.2 m 0.4 m

Type Balok B1 25/60 = 0.25 m 0.6 m

Type Balok B2 20/40 = 0.2 m 0.4 m

Gambar 4.1 Denah Portal Tinjauan Arah Y

Inersia

a. Inersia Kolom

Kekakuanb x h

1 Type kolom K1 40.000 x 50 0.0833 416,666.667 1.0417

2 Type kolom K1 30.000 x 40 0.0833 160,000.000 0.4000

3 Type kolom K1 30.000 x 35 0.0833 107,187.500 0.2680

b. Inersia Tie Beam

Kekakuanb x h

1 Type TB 1 30.000 x 40 0.0833 160,000.000 0.1143

Kekakuanb x h

1 Dimensi RB1 20.000 x 30 0.0833 45,000.000 0.0321

d. Inersia Balok

Kekakuanb x h

1 Type Balok B1 25.000 x 60 0.0833 450,000.00 0.3214

2 Type Balok B2 20.000 x 40 0.0833 106,666.67 0.0762

Mf1-2 == -0.0833333333 x 4215.0133 x 45.563 - 2,454.544 = (18,458.4)= (18,458.4) kgm = (18.5) tm

Mf2-1 = Mf5-6

Mf2-3 == -0.0833333333 x 4215.0133 x 36.240 - 6,829.349 + 724.633 = (20,283.5)= (20,283.5) kgm = (20.3) tm

Mf3-2 = -Mf7-8

Mf4-5 == -0.0833333333 x 4031.163 x 36.240 - 736.074 + 1,385.904 = (14,296.2) kgm = (14.3) tm

Mf5-4 =

Mf5-6 = -1/12xqL2-P1.a.b2/L2= -0.0833333333 x 4215.0133 x 45.563 - 1,630.591 = (17,634.5) kgm = (17.6) tm =

Mf6-5 = -Mf10-11

Mf7-8 == -0.0833333333 x 2734.9333 x 45.563 - 1,519.175 = (11,903.4)= (11,903.4) kgm = (11.9) tm

Mf8-7 = Mf11-12

Mf8-9 == -0.0833333333 x 2553.3867 x 36.240 - 434.780 + 732.284 = (8,878.4) kgm = (8.9) tm

1 -18.458 18.46

2 -20.283 20.28

3 -14.296 14.30

4 -17.634 17.63

5 M7-8 -11.903 M8-7 11.90

6 M 8-9 -8.878 M9-8 8.88

T1 = Mf 1 - 2 + Mf 1 - 6

T Nilai ρ Nilai

-18.458 3.036

-1.825 3.188

20.283 3.036

-14.296 1.488

-3.338 1.641

17.634 1.488

-11.903 0.688

3.025 0.841

8.878 0.688

-1/12xqL2-P1.a.b2/L2

-1/12xqL2-(P1.a.b2/L2+P2.a.b2/L2)

-Mf8-9

-1/12xqL2-P1.a.b2/L2

-1/12xqL2-(P1.a.b2/L2+P2.a.b2/L2)

Perhitungan Nilai T,ρ

Perhitungan nilai γJoint 1

= = 0.076 = 0.025 ρ1 3.036

= = 0.400 = 0.132 ρ1 3.036

= = 1.042 = 0.343 ρ1 3.036

= 0.500

Joint 2

= = 0.076 = 0.024 ρ2 3.188

= = 0.4000 = 0.125 ρ2 3.188

= = 1.0417 = 0.327 ρ2 3.188

= 0.500

Joint 3

= = 0.076 = 0.025 ρ3 3.036

= = 0.400 = 0.132 ρ3 3.036

= = 1.042 = 0.343 ρ3 3.036

= 0.500

Joint 4

= = 0.268 = 0.180 ρ4 1.488

= = 0.076 = 0.051 ρ4 1.488

= = 0.400 = 0.269 ρ4 1.488

= 0.500

Joint 5

= = 0.076 = 0.046 ρ5 1.641

= = 0.268 = 0.163 ρ5 1.641

= = 0.076 = 0.046 ρ5 1.641

= = 0.400 = 0.244 ρ5 1.641

= 0.500

Joint 6

= = 0.400 = 0.269 ρ6 1.488

= = 0.076 = 0.051 ρ6 1.488

== 0.268 = 0.180

ρ6 1.488= 0.500 oke!

Joint 7

= = 0.268 = 0.389 ρ7 0.688

= = 0.076 = 0.111 ρ7 0.688

= 0.500 oke!

Joint 8

= = 0.076 = 0.091 ρ8 0.841

= = 0.268 = 0.319 ρ8 0.841

= 0.500 oke!

Joint 9

= = 0.268 = 0.389 ρ9 0.688

= = 0.076 = 0.111 ρ9 0.688

= 0.500 oke!

M1 = -Mf / ρ1

= -18.4583.036

= 6.080 ton

No. Momen Nilai

1 M1 6.080

2 M2 0.572

3 M3 -6.682

4 M4 9.606

5 M5 2.035

6 M6 -11.849

7 M7 17.293

8 M8 3.598

9 M9 12.899

Menentukan nilai T

= 2 x 1.042 + 1.042 + 1.042 )

= 6.250

T2 = 2 x 0.4 + 0.400 + 0.400 )

= 2.400

T3 = 2 x 0.3 + 0.268 + 0.268 )

= 1.608

Perhitungan nilai t

2*(KA-1+ KB-2+ KC

2*(K1-6+ K2-5+ K3

2*(K7-12 + K8-11+ K9

3.(K1-6

= 0.500

No. t Nilai

1 0.500

2 0.500

3 0.500

4 2.880

5 2.880

6 2.880

7 0.500

8 0.500

9 0.500

Perhitungan Momen Displacment Arah Y

No. Lantai h Beban Angin1 3 4.000 0.391 2 4.000 0.45

2 1 4.000 0.41

Arah y =

M1 = -h1(∑W) =

T1 = = -4.000 x ( 1.25 )

6.2500= -0.799

M2 = -h2(∑W) =

= -4.000 x ( 0.84 ) = 2.4000

= -1.406

M3 = -h3(∑W) =

= -4.000 x ( 0.39 ) =

1.6078 = = -0.980

MI (1) MI (0)

(-t1-A) x (M1( I )

(-t2-B

) x (M2( I )

(-t3-C

) x (M3( I )

MII(1) MII (0)

(-t1-6) x (M1( I ) + M6(I) )

(-t2-5) x (M2( I )+ M5(I))

(-t3-4) x (M3( I )+ M4(I))

MIII(1) MII (0)

(-t6-7) x (M6( I ) + M7(I) )

(-t5-8) x (M5( I )+ M8(I))

(-t4-9) x (M4( I )+ M9(I))

Putaran 0

MI = MI(0) = 6.1 = 6.080 = γ 1 - 2 x M2 = (0.025) x 0.572 = (0.014)= γ 1 - 6 x MD 1+M6(0) = (0.132) x (12.648) = 1.667 = γ 1 - A x MD 1 = (0.343) x (0.799) = 0.274 +

M1 = 8.0068

M2 = M2(0) = 0.6 = 0.572 = γ 2 - 1 x M1(1) = (0.024) x 8.007 = (0.191)= γ 2 - 3 x M3(0) = (0.024) x (6.682) = 0.160 = γ 2 - 5 x MD 1+M5(0) = (0.125) x 1.235 = (0.155) += γ 2 - B x MD 1 = (0.327) x (0.799) = 0.261

M2 = 0.647

M3 = M3(0) = (6.7) = (6.682)= γ 3-2 x M2(1) = (0.025) x 0.647 = (0.016)= γ 3-4 x MD 1+M4(0) = (0.132) x 8.806 = (1.160)= γ 3-C x MD 1 = (0.343) x (0.799) = 0.274

M3 = (7.584)

M4 = M4(0) = 9.6 = 9.606 = γ 4-3 x M3(1) = (0.269) x (7.584) = 2.038 = γ 4-5 x M5(0) = (0.051) x 2.035 = (0.104)= γ 4-9 x MD 1+M9 = (0.180) x 12.099 = (2.178) +

M4 = 9.361

M5 = M5(0) = 2.0 = 2.035 = γ 5-4 x M4(1) = (0.046) x 9.361 = (0.435)= γ 5-2 x MD 2+ M2 (1) = (0.244) x (0.759) = 0.185 = γ 5-6 x M 6 (0) = (0.046) x (11.849) = 0.550 = γ 5-8 x MD 3+ M8(0) = (0.163) x 2.619 = (0.428)

M5 = 1.908

M6 = M6 (0) = (11.8) = (11.849)= γ 6-7 x MD 3+ M7(0) = (0.180) x 16.314 = (2.937)= γ 6-5 x M5 (1) = (0.051) x 1.907595481 = (0.098)= γ 6-1 x MD 2+ M1 (1) = (0.269) x 6.601 = (1.774)

M6 = (16.657)

M7 = M7(0) = 17.3 = 17.293 = γ 7-6 x MD3+M6(1) = (0.389) x (17.637) = 6.866 = γ 7-8 x M8(0) = (0.111) x 3.598 = (0.398)

M7 = 23.761

M8 = M8(0) = 3.6 = 3.598 = γ 8-7 x M7(1) = (0.091) x 23.76140063 = (2.153)= γ 8-5 x MD 3+ M5(1) = (0.319) x 0.93 = (0.296)= γ8-9 x M9(0) = (0.091) x 12.899 = (1.169)

M8 = (0.020)

M9 = M9(0) = 12.9 = 12.899 = γ 9-8 x M8(1) = (0.111) x -0.02001233 = 0.002 = γ9-4 x MD 3+M4(1) = (0.389) x 8.38 = (3.263)

M9 9.638

Joint 1

M1-2 = K 1-2 x + Mf1-2 = 0.032 x 18.300 + (18.5)

M1-6 = K 1-6 x + Mf1-6 = 1.042 x (0.547) + 0.0

M1-A = K 1-A x + Mf1-A = 1.042 x 17.698 + 0.0

Joint 2

M2-1 = K 2-1 x + Mf2-1 = 0.076 x 10.054 + 18.5

M2-3 = K 2-3 x + Mf2-3 = 0.076 x (5.918) + -20.3

M2-5 = K 2-5 x + Mf2-5 = 0.400 x 3.518 + 0

M2-B = K 2-B x + Mf2-B = 0.076 x 1.205 + 0

Joint 3

M3-2 = K 3-2 x + Mf3-2 = 0.400 x (13.642) + 20.3

M3-4 = K 3-4 x + Mf3-4 = 0.076 x 4.312 + 0.0

M3-C = K 3-C x + Mf3-C = 1.042 x (14.245) + 0.0

Joint 4

M4-9 = K 4-9 x + Mf4-9 = 1.042 x (31.101) + -

M4-5 = K 4-5 x + Mf4-5 = 0.400 x 39.427 + (14.3)

M4-3 = K 4-3 x + Mf4-3 = 1.042 x 29.992 + - ∑M

Joint 5

M5-4 = K 5-4 x + Mf5-4 = 0.076 x 23.183 + 14.3

M5-2 = K 5-2 x + Mf5-2 = 1.042 x 5.228 + -

M5-6 = K 5-6 x + Mf5-6 = 0.400 x (13.618) + (17.6)

M5-8 = K 5-8 x + Mf5-8 = 0.400 x 5.013 + - ∑M

Joint 6

M6-7 = K 6-7 x + Mf6-7 = 0.400 x (11.754) + 0.0

M6-5 = K 6-5 x + Mf6-5 = 0.076 x (34.176) + 17.6

M6-1 = K 6-1 x + Mf6-1 = 0.400 x (27.640) + 0.0∑M

Joint 7

M7-6 = K 7-6 x + Mf7-6 = 0.321 x 31.225 + -

M7-8 = K 7-8 x + Mf7-8 = 0.032 x 49.856 + -11.9∑M

Joint 8

M8-7 = K 8-7 x + Mf8-7 = 0.076 x 25.508 + (11.9)

M8-9 = K 8-9 x + Mf8-9 = 0.076 x 6.786 + 8.9

M8-5 = K 8-5 x + Mf8-5 = 0.032 x 3.086 + 0∑M

Joint 9

M9-8 = K 9-8 x + Mf9-8 = 0.076 x 12.412 + -8.9

M9-4 = K 9-4 x + Mf9-4 = 0.268 x 30.583 + 0∑M

{ 2M1(k) + M2(k) }

{2M1(k) + M6(k) }

{2M1(k) + MA(k) }

{ 2M2(k) + M1(k) }

{2M2(k) + M3(k) }

{2M2(k) + M5(k) }

{2M2(k) + MB(k) }

{ 2M3(k) + M2(k) }

{2M3(k) + M4(k) }

{2M3(k) + MC(k) }

{ 2M4(k) + M9(k) }

{ 2M4(k) + M5(k) }

{ 2M4(k) + M3(k) }

{ 2M5(k) + M4(k) }

{ 2M5(k) + M2(k) }

{ 2M5(k) + M6(k) }

{ 2M5(k) + M8(k) }

{2M6(k) + M7(k) }

{2M6(k) + M5(k) }

{2M6(k) + M1(k) }

{ 2M7(k) + M6(k) }

{2M7(k) + M8(k) }

{ 2M8(k) + M7(k) }

{2M8(k) + M9(k) }

{2M8(k) + M5(k) }

{2M9(k) + M8(k) }

{2M9(k) + M4(k) }

No. Joint ∑M K ∑K K/∑ ∆M

1M1-2 -17.870

-0.0050.03

2.1150.015 0.000 -17.870

0.000M1-6 -0.569 1.04 0.492 0.002 -0.567M1-A 18.435 1.04 0.492 0.002 18.437

M2-1 19.224

-0.011

0.121 0.001 19.226

0.000M2-3 -20.734 0.08 0.121 0.001 -20.733M2-5 1.407 0.40 0.636 0.007 1.414M2-B 0.092 0.08 0.121 0.001 0.093

3M3-2 14.827

0.3170.40

1.5180.264 -0.083 14.743

0.000M3-4 0.329 0.08 0.050 -0.016 0.313M3-C -14.838 1.04 0.686 -0.217 -15.056

4M4-9 -32.397

0.3191.04

2.4830.419 -0.134 -32.531

0.000M4-5 1.475 0.40 0.161 -0.051 1.423M4-3 31.242 1.04 0.419 -0.134 31.108

M5-4 16.063

0.040 -0.017 16.045

0.000M5-2 5.446 1.04 0.543 -0.235 5.212M5-6 -23.082 0.40 0.209 -0.090 -23.172M5-8 2.005 0.40 0.209 -0.090 1.915

6M6-7 -4.702

-0.7270.40

0.8760.457 0.332 -4.370

0.000M6-5 15.031 0.08 0.087 0.063 15.094M6-1 -11.056 0.40 0.457 0.332 -10.724

7M7-6 10.037

-0.2640.32

0.3540.909 0.240 10.277

0.000M7-8 -10.301 0.03 0.091 0.024 -10.277

8M8-7 -9.960

-0.4440.08

0.1850.413 0.183 -9.777

0.000M8-9 9.417 0.08 0.413 0.183 9.600M8-5 0.099 0.032 0.17 0.08 0.176

9M9-8 -7.954

0.241 0.076

0.344 0.22 (0.05) (8.008)

0.000M9-4 8.195 0.268 0.78 (0.19) 8.008

∑`RA -1.438 ∑`RB ∑`RA

No. Joint Koreksi M.Desain q p1 p2 L RA RB RM x-y RM y-x ∑R'A ∑R'B

1 M1-2 -17.870 4.215 2.608 - 6.75 15.530 15.530 (2.647) 2.848 21.026 10.034 2 M2-1 19.226 4.215 2.608 - 6.75 15.530 15.530 (2.647) 2.848 21.026 10.034 3 M2-3 -20.733 4.215 1.719 1.7 6.02 14.412 14.412 (3.444) 2.449 20.305 8.519 4 M3-2 14.743 4.215 1.728 1.7 6.02 14.409 14.409 (3.444) 2.449 20.302 8.516 5 M4-5 1.423 4.031 1.728 1.7 6.02 13.856 13.856 0.236 2.665 16.284 11.427 6 M5-4 16.045 4.031 1.719 1.7 6.02 13.859 13.859 0.236 2.665 16.287 11.430 7 M5-6 -23.172 4.215 4.832 6.75 16.642 16.642 (3.433) 2.236 22.311 10.973 8 M6-5 15.094 4.215 4.832 6.75 16.642 16.642 (3.433) 2.236 22.311 10.973 9 M7-8 -10.277 4.215 1.614 6.75 15.033 15.033 (1.522) (1.448) 15.107 14.959 10 M8-7 -9.777 4.215 1.614 6.75 15.033 15.033 (1.522) (1.448) 15.107 14.959 11 M 8-9 9.600 4.031 1.733 2.5 6.02 14.372 14.372 1.595 (1.330) 11.447 17.297 12 M9-8 -8.008 4.031 2.491 1.7 6.02 14.119 14.119 1.595 (1.330) 11.194 17.044

Momen desain K /∑K*∆M

Koreksi Momen

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RA = P2/3 + 2P1/3 + 1/2qL

RM x-y = M x-y /L

RM y-x = - M y-x /L

RM x-y= Mx-y / L

RM y-x= Mx-y / L

RM x-y= Mx-y / L

No. Joint h M desain RMx-y/L RMy-x/L ∑RA ∑RB Da Kanan Db kanan

1 M1-A 4.00 18.437 4.609 4.609 9.219 (9.219) 9.219 0.000 2 MA-1 4.00 9.219 4.609 4.609 9.219 (9.219) 9.219 0.000 3 M2-B 4.00 0.093 0.023 0.023 0.047 (0.047) 0.047 0.000 4 MB-2 4.00 0.047 0.023 0.023 0.047 (0.047) 0.047 0.000 5 M3-C 4.00 (15.056) (3.764) (3.764) (7.528) 7.528 (7.528) 0.000 6 MC-3 4.00 (7.528) (3.764) (3.764) (7.528) 7.528 (7.528) 0.000 7 M1-6 4.00 (0.567) (0.142) (2.681) (2.823) 2.823 (2.823) 0.000 8 M6-1 4.00 (10.724) (0.142) (2.681) (2.823) 2.823 (2.823) 0.000 9 M2-5 4.00 1.414 0.354 1.303 1.656 (1.656) 1.656 0.000 10 M5-2 4.00 5.212 0.354 1.303 1.656 (1.656) 1.656 0.000 11 M3-4 4.00 0.313 0.078 7.777 7.855 (7.855) 7.855 0.000 12 M4-3 4.00 31.108 0.078 7.777 7.855 (7.855) 7.855 0.000 13 M4-9 4.00 (32.531) (8.133) 2.002 (6.131) 6.131 (6.131) 0.000 14 M9-4 4.00 8.008 (8.133) 2.002 (6.131) 6.131 (6.131) 0.000 15 M5-8 4.00 1.915 0.479 0.044 0.523 (0.523) 0.523 0.000 16 M8-5 4.00 0.176 0.479 0.044 0.523 (0.523) 0.523 0.000 17 M6-7 4.00 (4.370) (1.092) 2.569 1.477 (1.477) 1.477 0.000 18 M7-6 4.00 10.277 (1.092) 2.569 1.477 (1.477) 1.477 0.000

Dari put 0 Ke Put 1

= -0.799 = -0.80

= (0.50) x 8.0 = -4.00

= (0.50) x 0.6 = -0.32

= (0.50) x (7.6) = 3.79-1.3341

= -1.40625 = -1.41

= (2.88) x (8.7) = 24.91

= (2.88) x 2.6 = -7.36

= (2.88) x 1.8 = -5.1211.0322

= -0.980 = -0.98

= (0.50) x 7.1 = -3.55

= (0.50) x 1.9 = -0.94

= (0.50) x 19.0 = -9.50-14.9749

Putaran 1 Putaran 2

6.1 = 6.080 6.1 (0.025) x 0.647 = (0.016) (0.025) (0.132) x (17.457) = 2.300 + (0.132) (0.343) x (0.799) = 0.274 (0.343)

M1 = 8.6386

0.6 = 0.572 0.6 (0.024) x 8.639 = (0.206) (0.024) (0.024) x (7.584) = 0.181 (0.024) (0.125) x 1.108 = (0.139) + (0.125) (0.327) x (0.799) = 0.261 (0.327)

M2 = 0.6693

(6.7) = (6.682) (6.7) (0.025) x 0.669 = (0.017) (0.025) (0.025) x 8.562 = (0.215) (0.025) (0.025) x (0.799) = 0.020 (0.025)

M3 = -6.8932

17.7 = 17.700 17.7 (0.269) x (6.893) = 1.853 (0.269) (0.051) x 1.908 = (0.098) (0.051) (0.180) x 8.839 = (1.591) + (0.180)

M4 = 17.8636

2.0 = 2.035 2.0 (0.046) x 17.864 = (0.830) (0.046) (0.244) x (0.737) = 0.180 (0.244) (0.046) x (16.657) = 0.774 (0.046) (0.163) x (1.000) = 0.163 (0.163)

M5 = 2.3216

(11.8) = (11.849) (11.8) (0.180) x 22.782 = (4.102) (0.180) (0.051) x 2.321563 = (0.119) (0.051) (0.269) x 7.232 = (1.944) (0.269)

M6 = -18.0130

17.3 = 17.293 17.3 (0.389) x (18.993) = 7.394 (0.389) (0.111) x -0.020 = 0.002 (0.111)

M7 = 24.6896

3.6 = 3.598 3.6 (0.091) x 24.68962 = (2.238) (0.091) (0.319) x 1.34 = (0.428) (0.319) (0.091) x 9.638 = (0.873) (0.091)

M8 = 0.0594

12.9 = 12.899 12.9 (0.111) x 0.059437 = (0.007) (0.111) (0.389) x 16.88 = (6.573) (0.389)

M9 6.3190

= (17.87)

= (0.57)

= 18.43 + = (0.0047)

= 19.22

= (20.73) +

= 1.41

= 0.09-0.0110

= 14.83

= 0.33

= (14.84)= 0.32

= -32.397

= 1.474638

= ###= 0.3

= 16.0625

= 5.4461

= -23.0818

= 2.0050= 0.4319

= (4.70)

= 15.03

= (11.06)= (0.73)

= 10.04

= (10.30)= (0.3)

= (9.96)

= 9.42

= 0.10 = (0.4)

= (7.95)

= 8.20 = 0.2

∑`RB

R'A Da kanan Db kiri Db kanan Dc kiri Dc kanan Dd kanan

21.026 15.530 1.304 -1.304 (15.530) 0.000 -

20.305 14.412 4.127 2.408 (4.251) -5.979 0.00

20.302 14.409 4.124 2.397 (4.263) -5.982 (0.00)

16.284 13.856 4.020 2.292 (4.077) -5.796 (0.00)

16.287 13.859 4.022 2.304 (4.066) -5.793 0.00

22.311 16.642 2.416 -2.416 (16.642) 0.000 -

15.107 15.033 0.807 -0.807 (15.033) 0.000 -

11.447 14.372 4.536 2.803 (3.566) -6.057 0.00

11.194 14.119 4.283 1.793 (4.577) -6.309 0.00

RA = P1/3 + 2P2/3 + 1/2qL

RM x-y = M x-y /L

RM y-x = - M y-x /L

-0.7992 = -0.80 -0.7992 = -0.80

(0.50) x 8.6 = -4.32 (0.50) x 8.8 = -4.41

(0.50) x 0.7 = -0.33 (0.50) x 0.6 = -0.30

(0.50) x (6.9) = 3.45 (0.50) x (7.1) = 3.55-2.0065 -1.9534

-1.4063 = -1.41 -1.4063 = -1.41

(2.88) x (9.4) = 27.00 (2.88) x (9.4) = 27.11

(2.88) x 3.0 = -8.61 (2.88) x 3.0 = -8.51

(2.88) x 11.0 = -31.59 (2.88) x 11.4 = -32.81-14.6163 -15.6195

-0.980 = -0.98 -0.980 = -0.98

(0.50) x 6.7 = -3.34 (0.50) x 6.5 = -3.27

(0.50) x 2.4 = -1.19 (0.50) x 2.7 = -1.35

(0.50) x 24.2 = -12.09 (0.50) x 24.5 = -12.27-17.5997 -17.8668

Putaran 2 Putaran 3 Putaran 4

= 6.080 6.1 = 6.080 6.1 x 0.669 = (0.017) ### x 0.597 = (0.015) (0.025)x (18.812) = 2.479 ### x (19.029) = 2.507 (0.132)x (0.799) = 0.274 ### x (0.799) = 0.274 (0.343)

M1 = 8.8166 M1 = 8.8471

= 0.572 0.6 = 0.572 0.6 x 8.817 = (0.211) ### x 8.847 = (0.211) (0.024)x (6.893) = 0.165 ### x (7.105) = 0.170 (0.024)x 1.522 = (0.191) ### x 1.561 = (0.196) (0.125)x (0.799) = 0.261 ### x (0.799) = 0.261 (0.327)

M2 = 0.5966 M2 = 0.5961

= (6.682) ### = (6.682) (6.7) x 0.597 = (0.015) ### x 0.596 = (0.015) (0.025)x 17.064 = (0.428) ### x 17.698 = (0.444) (0.025)x (0.799) = 0.020 ### x (0.799) = 0.020 (0.025)

M3 = -7.1048 M3 = -7.1207

= 17.700 ### = 17.700 17.7 x (7.105) = 1.909 ### x (7.121) = 1.914 (0.269) x 2.322 = (0.119) ### x 2.360 = (0.121) (0.051) x 5.520 = (0.994) ### x 5.242 = (0.944) (0.180)

M4 = 18.4968 M4 = 18.5491

= 2.035 2.0 = 2.035 2.0 x 18.497 = (0.859) ### x 18.549 = (0.861) (0.046) x (0.810) = 0.197 ### x (0.810) = 0.198 (0.244) x (18.013) = 0.836 ### x (18.230) = 0.847 (0.046)x (0.920) = 0.150 ### x (0.638) = 0.104 (0.163)

M5 = 2.3599 M5 = 2.3216

= (11.849) ### = (11.849) (11.8) x 23.710 = (4.269) ### x 23.786 = (4.283) (0.180) x 2.3598546 = (0.121) ### x 2.32160401 = (0.119) (0.051) x 7.410 = (1.992) ### x 7.441 = (2.000) (0.269)

M6 = -18.2300 M6 = -18.2498

= 17.293 ### = 17.293 17.3 x (19.210) = 7.478 ### x (19.229) = 7.486 (0.389)x 0.059 = (0.007) ### x 0.341 = (0.038) (0.111)

M7 = 24.7653 M7 = 24.7418

= 3.598 3.6 = 3.598 3.6 x 24.765286 = (2.244) ### x 24.741826 = (2.242) (0.091)x 1.38 = (0.440) ### x 1.34 = (0.428) (0.319)x 6.319 = (0.573) ### x 6.041 = (0.548) (0.091)

M8 = 0.3412 M8 = 0.3806

= 12.899 ### = 12.899 12.9 x 0.3411525 = (0.038) ### x 0.38063819 = (0.042) (0.111)x 17.52 = (6.820) ### x 17.57 = (6.840) (0.389)

M9 6.0413 M9 6.0165

-0.7992 = -0.80 -0.7992 = -0.80

(0.50) x 8.8 = -4.42 (0.50) x 8.8 = -4.42

(0.50) x 0.6 = -0.30 (0.50) x 0.6 = -0.30

(0.50) x (7.1) = 3.56 (0.50) x (7.1) = 3.56-1.9604 -1.9636

-1.4063 = -1.41 -1.40625 = -1.41

(2.88) x (9.4) = 27.08 (2.88) x (9.4) = 27.06

(2.88) x 2.9 = -8.40 (2.88) x 2.9 = -8.40

(2.88) x 11.4 = -32.91 (2.88) x 11.4 = -32.93-15.6434 -15.6718

-0.980 = -0.98 -0.980 = -0.98

(0.50) x 6.5 = -3.25 (0.50) x 6.5 = -3.25

(0.50) x 2.7 = -1.35 (0.50) x 2.7 = -1.35

(0.50) x 24.6 = -12.28 (0.50) x 24.6 = -12.28-17.8596 -17.8593

= 6.080 ## = 6.080 6.1 x 0.596 = (0.015) ### x 0.601 = (0.015) (0.025)x (19.049) = 2.510 ### x (19.045) = 2.509 (0.132)x (0.799) = 0.274 ### x (0.799) = 0.274 (0.343)

M1 = 8.8497 M1 = 8.8490

= 0.572 ## = 0.572 0.6 x 8.850 = (0.211) ### x 8.849 = (0.211) (0.024)x (7.121) = 0.170 ### x (7.122) = 0.170 (0.024)x 1.522 = (0.191) ### x 1.515 = (0.190) (0.125)x (0.799) = 0.261 ### x (0.799) = 0.261 (0.327)

M2 = 0.6013 M2 = 0.6022

= (6.682) # = (6.682) (6.7) x 0.601 = (0.015) ### x 0.602 = (0.015) (0.025)x 17.750 = (0.445) ### x 17.757 = (0.446) (0.025)x (0.799) = 0.020 ### x (0.799) = 0.020 (0.025)

M3 = -7.1221 M3 = -7.1223

= 17.700 # = 17.700 17.7 x (7.122) = 1.914 ### x (7.122) = 1.914 (0.269) x 2.322 = (0.119) ### x 2.315 = (0.118) (0.051) x 5.217 = (0.939) ### x 5.214 = (0.939) (0.180)

M4 = 18.5559 M4 = 18.5569

= 2.035 ## = 2.035 2.0 x 18.556 = (0.862) ### x 18.557 = (0.862) (0.046) x (0.805) = 0.196 ### x (0.804) = 0.196 (0.244) x (18.250) = 0.847 ### x (18.246) = 0.847 (0.046)x (0.599) = 0.098 ### x (0.594) = 0.097 (0.163)

M5 = 2.3145 M5 = 2.3132

= (11.849) ### = (11.849) (11.8) x 23.762 = (4.278) ### x 23.756 = (4.277) (0.180) x 2.3145132 = (0.118) ### x 2.3132355 = (0.118) (0.051) x 7.443 = (2.000) ### x 7.443 = (2.000) (0.269)

M6 = -18.2459 M6 = -18.2446

= 17.293 # = 17.293 17.3 x (19.225) = 7.485 ### x (19.224) = 7.484 (0.389)x 0.381 = (0.042) ### x 0.386 = (0.043) (0.111)

M7 = 24.7359 M7 = 24.7349

= 3.598 ## = 3.598 3.6 x 24.735944 = (2.242) ### x 24.7349 = (2.242) (0.091)x 1.33 = (0.425) ### x 1.33 = (0.425) (0.319)x 6.017 = (0.545) ### x 6.013 = (0.545) (0.091)

M8 = 0.3857 M8 = 0.3865

= 12.899 # = 12.899 12.9 x 0.385673 = (0.043) ### x 0.3864669 = (0.043) (0.111)x 17.58 = (6.843) ### x 17.58 = (6.843) (0.389)

M9 6.0133 M9 6.0129

Dari put 5 Ke Put 6 Dari put 6 Ke Put 7 Dari put 7 Ke Put 8

-0.7992 = -0.80 -0.7992 = -0.80 -0.7992 = -0.80

(0.50) x 8.8 = -4.42 (0.50) x 8.8 = -4.42 (0.50) x 8.8 = -4.42

(0.50) x 0.6 = -0.30 (0.50) x 0.6 = -0.30 (0.50) x 0.6 = -0.30

(0.50) x (7.1) = 3.56 (0.50) x (7.1) = 3.56 (0.50) x (7.1) = 3.56-1.9637 -1.9636 -1.9636

-1.4063 = -1.41 -1.4063 = -1.41 -1.40625 = -1.41

(2.88) x (9.4) = 27.06 (2.88) x (9.4) = 27.06 (2.88) x (9.4) = 27.06

(2.88) x 2.9 = -8.40 (2.88) x 2.9 = -8.40 (2.88) x 2.9 = -8.40

(2.88) x 11.4 = -32.93 (2.88) x 11.4 = -32.93 (2.88) x 11.4 = -32.93-15.6750 -15.6754 -15.6755

-0.980 = -0.98 -0.980 = -0.98 -0.980 = -0.98

(0.50) x 6.5 = -3.25 (0.50) x 6.5 = -3.25 (0.50) x 6.5 = -3.25

(0.50) x 2.7 = -1.35 (0.50) x 2.7 = -1.35 (0.50) x 2.7 = -1.35

(0.50) x 24.6 = -12.28 (0.50) x 24.6 = -12.28 (0.50) x 24.6 = -12.28-17.8595 -17.8595 -17.8595

Putaran 6 Putaran 7 Putaran 8Putaran 9

= ### ## = ### ### = ### 6.1 x ### = ### ### x ### = ### ### x ### = ### (0.025)x ### = ### ### x ### = ### ### x ### = ### (0.132)x ### = ### ### x ### = ### ### x ### = ### (0.343)

M1 = ### M1 = ### M1 = ###

= ### ## = ### ### = ### 0.6 x ### = ### ### x ### = ### ### x ### = ### (0.024)x ### = ### ### x ### = ### ### x ### = ### (0.024)x ### = ### ### x ### = ### ### x ### = ### (0.125)x ### = ### ### x ### = ### ### x ### = ### (0.327)

M2 = ### M2 = ### M2 = ###

= ### # = ### ### = ### (6.7) x ### = ### ### x ### = ### ### x ### = ### (0.025)x ### = ### ### x ### = ### ### x ### = ### (0.025)x ### = ### ### x ### = ### ### x ### = ### (0.025)

M3 = ### M3 = ### M3 = ###

= ### # = ### ### = ### 17.7 x ### = ### ### x ### = ### ### x ### = ### (0.269) x ### = ### ### x ### = ### ### x ### = ### (0.051) x ### = ### ### x ### = ### ### x ### = ### (0.180)

M4 = ### M4 = ### M4 = ###

= ### ## = ### ### = ### 2.0 x ### = ### ### x ### = ### ### x ### = ### (0.046) x ### = ### ### x ### = ### ### x ### = ### (0.244) x ### = ### ### x ### = ### ### x ### = ### (0.046)x ### = ### ### x ### = ### ### x ### = ### (0.163)

M5 = ### M5 = ### M5 = ###

= ### ### = ### ### = ### (11.8) x ### = ### ### x ### = ### ### x ### = ### (0.180) x 2.31 = ### ### x 2.31 = ### ### x 2.31 = ### (0.051) x ### = ### ### x ### = ### ### x ### = ### (0.269)

M6 = ### M6 = ### M6 = ###

= ### # = ### ### = ### 17.3 x ### = ### ### x ### = ### ### x ### = ### (0.389)x ### = ### ### x ### = ### ### x ### = ### (0.111)

M7 = ### M7 = ### M7 = ###

= ### ## = ### ### = ### 3.6 x ### = ### ### x ### = ### ### x ### = ### (0.091)x ### = ### ### x ### = ### ### x ### = ### (0.319)x ### = ### ### x ### = ### ### x ### = ### (0.091)

M8 = ### M8 = ### M8 = ###

= ### # = ### ### = ### 12.9 x 0.39 = ### ### x 0.39 = ### ### x 0.39 = ### (0.111)x ### = ### ### x ### = ### ### x ### = ### (0.389)

M9 ### M9 ### M9 ###

-0.7992 = -0.80 -0.7992 = -0.80

(0.50) x 8.8 = -4.42 (0.50) x 8.8 = -4.42

(0.50) x 0.6 = -0.30 (0.50) x 0.6 = -0.30

(0.50) x (7.1) = 3.56 (0.50) x (7.1) = 3.56-1.9636 -1.9636

-1.40625 = -1.41 -1.40625 = -1.41

(2.88) x (9.4) = 27.06 (2.88) x (9.4) = 27.06

(2.88) x 2.9 = -8.40 (2.88) x 2.9 = -8.40

(2.88) x 11.4 = -32.93 (2.88) x 11.4 = -32.93-15.6755 -15.6755

-0.980 = -0.98 -0.980 = -0.98

(0.50) x 6.5 = -3.25 (0.50) x 6.5 = -3.25

(0.50) x 2.7 = -1.35 (0.50) x 2.7 = -1.35

(0.50) x 24.6 = -12.28 (0.50) x 24.6 = -12.28-17.8595 -17.8595

= 6.080 # = 6.080 x 0.602 = (0.015) ### x 0.602 = (0.015)x (19.044) = 2.509 ### x (19.044) = 2.509 x (0.799) = 0.274 ### x (0.799) = 0.274

M1 = 8.8488 M1 = 8.8488

= 0.572 # = 0.572 x 8.849 = (0.211) ### x 8.849 = (0.211)x (7.122) = 0.170 ### x (7.122) = 0.170 x 1.514 = (0.190) ### x 1.514 = (0.190)x (0.799) = 0.261 ### x (0.799) = 0.261

M2 = 0.6024 M2 = 0.6024

= (6.682) ### = (6.682) x 0.602 = (0.015) ### x 0.602 = (0.015)x 17.758 = (0.446) ### x 17.758 = (0.446)x (0.799) = 0.020 ### x (0.799) = 0.020

M3 = -7.1224 M3 = -7.1224

= 17.700 ### = 17.700 x (7.122) = 1.914 ### x (7.122) = 1.914 x 2.313 = (0.118) ### x 2.313 = (0.118) x 5.214 = (0.939) ### x 5.214 = (0.939)

M4 = 18.5571 M4 = 18.5571

= 2.035 # = 2.035 x 18.557 = (0.862) ### x 18.557 = (0.862) x (0.804) = 0.196 ### x (0.804) = 0.196 x (18.244) = 0.847 ### x (18.244) = 0.847 x (0.593) = 0.097 ### x (0.593) = 0.097

M5 = 2.3129 M5 = 2.3129

= (11.849) ### = (11.849) x 23.755 = (4.277) ### x 23.755 = (4.277) x 2.312945 = (0.118) ### x 2.312944723 = (0.118) x 7.443 = (2.000) ### x 7.443 = (2.000)

M6 = -18.2443 M6 = -18.2443

= 17.293 ### = 17.293 x (19.224) = 7.484 ### x (19.224) = 7.484 x 0.387 = (0.043) ### x 0.387 = (0.043)

M7 = 24.7347 M7 = 24.7347

= 3.598 # = 3.598 x 24.7347 = (2.242) ### x 24.7347 = (2.242)x 1.33 = (0.425) ### x 1.33 = (0.425)x 6.013 = (0.545) ### x 6.013 = (0.545)

M8 = 0.3866 M8 = 0.3866

= 12.899 ### = 12.899 x 0.3866315 = (0.043) ### x 0.386631585 = (0.043)x 17.58 = (6.843) ### x 17.58 = (6.843)

M9 6.0128 M9 6.0128

PERHITUNGAN BEBAN ANGIN

Lantai Dimensi Luasan Kecepatan Angin

h(m) b(m)1 3.5 4.5 15.75 252 4 4.5 18 253 3.6 4.5 16.2 25

m2 kg/m2

Kg393.75

450405

Perhitungan Momen Maksimal :

Perhitungan Momen Maksimal pada Batang 1-2 Arah Y

== 52.4133113 - -17.87014 - 24.0058 - 0= 46.28

Perhitungan Momen Maksimal pada Batang 4 - 5 Arah Y

== 53.7318844 - 6.7000051 - 30.31 - 1.42329= 15.30

Perhitungan Momen Maksimal pada Batang 1-2 Arah X

= R1.x-1/2qx2-M1-2= 6.620595 - 3.3102975 - -1.85= 5

Tabel Momen Maksimal Portal Y

Batang q p1 p2

Ral Jarak (X)

( ton.m) (ton) (ton) (m) (m) ( ton.m)1 - 2 4.215 2.6084 15.5299 6.75 3.375 46.28 2 - 3 4.215 1.7188 1.727696 14.4119 6.02 1.438 38.264 - 5 4.031 1.727696 1.7188 13.8556 6.02 1.438 15.305 - 6 4.215 4.8324 16.6419 6.75 3.375 55.337 - 8 4.215 1.6144 15.0329 6.75 3.375 37.018 - 9 4.031 1.7328 2.49056 14.3718 6.02 1.438 13.33

Tabel Momen Maksimal Portal X

Batang q p1

Dal Jarak (X)

( ton.m) (ton) (m) (m) ( ton.m)1 - 2 2.942 4.41373 3 1.5 5.16 2 - 3 2.861 6.4365306672 4.5 2.25 11.073 - 4 2.861 6.43653 4.5 2.25 6.444 - 5 3.329 7.490706 4.5 2.25 7.525 - 6 2.861 6.44 4.5 2.25 11.376 - 7 2.861 6.44 4.5 2.25 11.257 - 8 2.938 1.008 7.11 4.5 3.375 12.249 - 10 3.329 7.49 4.5 2.25 2.54

10 -11 3.329 7.490706 4.5 2.25 13.0611 - 12 3.329 7.490706 4.5 2.25 13.1012 - 13 3.329 7.490706 4.5 2.25 13.0913 - 14 2.861 6.4365306672 4.5 2.25 6.0814 - 15 2.861 6.4365306672 4.5 2.25 11.3315 - 16 2.373 3.559496 3 1.5 7.2417 - 18 1.125 1.68752 3 1.5 1.7618 - 19 1.512 3.40152 4.5 2.25 5.7319 - 20 1.512 3.40152 4.5 2.25 5.9620 -21 1.512 3.40152 4.5 2.25 5.9521 - 22 1.512 3.40152 4.5 2.25 3.3922 - 23 1.512 3.40152 4.5 2.25 5.9523 - 24 1.512 3.40152 4.5 2.25 6.06

Mmaks R1.L - M1-2 - 1/2.ql2-p.l

Mmaks R1.(l+x)-P1.x-1/2.qx2-M4-5

RM x-y= Mx-y / L

RM y-x= Mx-y / L

RM x-y= Mx-y / L

No. Joint h M desain RMx-y/L RMy-x/L ∑RA ∑RB Da Kanan Da kanan

1 M1-4 3.5 42.974 12.278 7.250 19.528 (19.528) 19.528 0.000

M4-1 3.5 25.374 7.250 12.278 19.528 (19.528) 19.528 0.000

2 M2-3 3.5 (37.949) (10.842) (2.109) (12.951) 12.951 (12.951) 0.000

M3-2 3.5 (7.381) (10.842) (2.109) (12.951) 12.951 (12.951) 0.000

3 M3-6 4.0 (19.460) (4.865) (4.761) (9.626) 9.626 (9.626) 0.000

M6-3 4.0 (19.046) (4.761) (4.761) (9.523) 9.523 (9.523) 0.000

4 M4-5 4.0 11.335 2.834 5.373 8.206 (8.206) 8.206 0.000

M5-4 4.0 21.491 5.373 2.834 8.206 (8.206) 8.206 0.000

5 M5-8 3.6 8.803 (10.842) (2.109) (12.951) 12.951 (12.951) 0.000

M8-5 3.6 (7.749) (2.109) (10.842) (12.951) 12.951 (12.951) 0.000

6 M6-7 3.6 (5.569) (1.547) 1.555 0.008 (0.008) 0.008 0.000

M7-6 3.6 5.598 1.555 (1.547) 0.008 (0.008) 0.008 0.000

Fi = Wi . Zi x Vjumlah Wi * Zi

Percepatan Garvitasi (g) 9.80

Simpangan pada struktur pada arah x (Sx) 0.06

Simpangan pada struktur arah y (Sy) 0.04

Tingkat Zi Wi Rotasi Mi Mi * L * Uix

3 4.00 227747.600 1.0000 23,239.55 23,239.55 23239.551 0.022

2 4.00 512420.400 1.0000 52,287.80 52,287.80 52287.796 0.022

1 4.00 520945.600 1.0000 53,157.71 53,157.71 53157.714 0.022

Jumlah 1261113.600 128,685.06 128685.06

g = 9,8100Mi = Wi / g R=1,6 Mi * = Mi . Rotasi ^2 I= 1 L* = Mi* . RotasiUi = Li* x Ʃ 1 x Sai

Mi*Ʃ ωi²simpangan pada struktur arah X (Sax) Sax = Cx . I . G / R

Sax = 0,049 . 1 . 9,8100/ 1,60.30043125

Simpangan pada struktur arah Y(Say)Sax = 0,059 . 1 . 9,8100/ 1,6

0.36174375

Tinggi total struktur 4.00 Rasio struktur terhadap denah arah x(H/Bx) 0.31 < 3 Rasio struktur terhadap denah arah y(H/By) 0.13 < 3

Tingkat Zi Wi WiZi Fix Fiy dix diy

4 4 227747.600 910990.40 1,383.08 902.36 0.0225 0.0345

3 4 512420.400 2049681.60 3,111.85 2,030.27 0.0225 0.0345

2 4 520945.600 2083782.40 3,163.62 2,064.05 0.0225 0.03450.000 0.00 - - 0.0000 0.0000

Jumlah 1261113.6 5044454.4 7,658.55 4,996.68 0

- Waktu getar alami berdasarkan persamaan Rayleigh (Tx) 3.87 - Waktu getar alami berdasarkan persamaan Rayleigh (Ty) 5.93 - Jumlah lantai (n) 4.00 - Faktor waktu getar alami 0.19 - Pembatasan waktu getar alami fundamental 1.52 - nilai respon struktur terhadap gempa dengan nilai T baru (Cx) 0.04 - nilai respon struktur terhadap gempa dengan nilai T baru (Cy) 0.03 - Gaya geser dasar nominal statik ekivalen baru arah x 7,634.23 > 7,821.27 - Gaya geser dasar nominal statik ekivalen baru arah y 4,980.81 > 5,102.84

Tabel Distribusi Beban Gempa pada tiap lantai

Tingkat Zi Wi WiZi Vx Vy Fix Fiy

3 4 227747.600 910990.4 7,634.23 16,176.53 1378.68479 2921.3591

2 4 512420.400 2049681.6 7,634.23 16,176.53 3101.96995 6572.9080

1 4 520945.600 2083782.4 7,634.23 16,176.53 3153.57780 6682.2622

12 1261113.6 5044454.4 7634.2325 16176.5293

Frekwensi Alami gedung (ώx)Frekwensi Alami gedung (ώy)

Vx = Cx . R . Wt

RVx = 0,048 . 1 . 1055885

1.639106.3674 kg / KN

391.063674 KN

Vy = 0,059 .1 . 1055885

38935.7594 kg / KN389.357594 KN

Uiy Fix Fiy

0.03 1,383.08 902.36

0.03 3,111.85 2,030.27

0.03 3,163.62 2,064.05

7658.545 4996.6751

Widix^2 Widiy^2 Fix*di Fiy*di

115.061058 270.3078893 31.0873117 31.087

258.88147 608.1788645 69.9448542 69.945

263.188512 618.2972096 71.1085352 71.1090 0 0 0

637.13104 1496.783963 172.140701 172.14

3.87168584

7,821.27 5,102.84

Fi = Wi . Zi x V

jumlah Wi * Zi

Perhitungan Momen Maksimal :

Perhitungan Momen Maksimal pada Batang 1-2

= x q x

= 0.125 x 11,510.49 x 4= 23,020.97 Kg

Perhitungan Momen Maksimal pada Batang 2 - 2"

= x q x + p

= 0.125 x 7,858.69 x 2.5 += 14,031 Kg

Tabel Momen Maksimal Portal Y

Batang q p l Jarak

( ton.m) (ton) (m) (m)1 - 2 4.215 4.00 2

2 - 3 4.215 4.00 23 - 4 4.031 4.00 24 - 5 4.215 4.00 26 - 7 4.215 4.00 27 - 8 4.215 4.00 28 - 9 4.215 4.00 2

9 - 10 4.215 4.00 211 - 12 4.215 4.00 212 - 13 4.215 4.00 213 - 14 4.215 4.00 214 - 15 4.215 4.00 2

Tabel Momen Maksimal Portal X

Batang q p l Jarak

( ton.m) (ton) (m) (m)1 - 2 7.859 8 43 - 4 5.512 8 45 - 6 5.512 8 47 - 8 2.120 8 4

1/8 l 2

1/8 L 2

2 - 2" 3.929 7.89 2.5 1.253 - 3" 1.102 6.21 2.5 1.256 - 6" 1.102 6.21 2.5 1.257 - 7" 1.060 1.60 2.5 1.25

( ton.m)8.438.438.068.438.438.438.438.438.438.438.438.43

( ton.m)62.8744.1044.1016.96

24.225.355.351.32

Lantai Dimensi Luasan Kecepatan Angin

h(m) b(m)1 3.5 8 28 252 4 8 32 253 3.6 8 28.8 25

m2 kg/m2

Kg700800720

Fi = Wi . Zi x Vjumlah Wi * Zi

Percepatan Garvitasi (g) 9.80

Simpangan pada struktur pada arah x (Sx) 0.05

Simpangan pada struktur arah y (Sy) 0.03

Tingkat Zi Wi Rotasi Mi Mi * L * Uix

3 3.60 408997.767 1.0000 41,734.47 41,734.47 41734.466 0.025

2 4.00 881654.000 1.1111 89,964.69 111,067.52 123408.359 0.028

1 3.50 880206.000 0.8750 89,816.94 68,766.09 60170.332 0.022

Jumlah 2170857.767 221,568.08 225313.16

g = 9,8100Mi = Wi / g R=1,6 Mi * = Mi . Rotasi ^2 I= 1 L* = Mi* . RotasiUi = Li* x Ʃ 1 x Sai

Mi*Ʃ ωi²simpangan pada struktur arah X (Sax) Sax = Cx . I . G / R

Sax = 0,049 . 1 . 9,8100/ 1,60.30043125

0.36174375

Tingkat Zi Wi WiZi Fix Fiy dix diy

4 3.6 408997.767 1472391.96 2,268.61 1,393.95 0.0250 0.0407

3 4 881654.000 3526616.00 5,433.69 3,338.74 0.0278 0.0453

2 3.5 880206.000 3080721.00 4,272.00 2,624.94 0.0219 0.03560.000 0.00 - - 0.0000 0.0000

Jumlah 2170857.766836 8079728.96061 11,974.31 7,357.63 0

- Waktu getar alami berdasarkan persamaan Rayleigh (Tx) 4.27 - Waktu getar alami berdasarkan persamaan Rayleigh (Ty) 6.96 - Jumlah lantai (n) 4.00 - Faktor waktu getar alami 0.19 - Pembatasan waktu getar alami fundamental 1.52 - nilai respon struktur terhadap gempa dengan nilai T baru (Cx) 0.04 - nilai respon struktur terhadap gempa dengan nilai T baru (Cy) 0.02 - Gaya geser dasar nominal statik ekivalen baru arah x 11,902.83 > 12,323.55 - Gaya geser dasar nominal statik ekivalen baru arah y 7,313.71 > 7,572.23

Tabel Distribusi Beban Gempa pada tiap lantai

Tingkat Zi Wi WiZi Vx Vy Fix Fiy

3 3.6 408997.767 1472391.96061 11,902.83 16,176.53 2169.08574 2947.8949

2 4 881654.000 3526616 11,902.83 16,176.53 5195.30985 7060.6833

1 3.5 880206.000 3080721 11,902.83 16,176.53 4538.43009 6167.9511

11.1 2170857.766836 8079728.96061 11902.8257 16176.5293

Frekwensi Alami gedung (ώx)Frekwensi Alami gedung (ώy)

Vx = Cx . R . Wt

RVx = 0,048 . 1 . 1055885

1.661617.7453 kg / KN

616.177453 KN

Vy = 0,059 .1 . 1055885

38935.7594 kg / KN389.357594 KN

Uiy Fix Fiy

0.04 2,268.61 1,393.95

0.05 5,433.69 3,338.74

0.04 4,272.00 2,624.94

11974.307 7357.63477

Widix^2 Widiy^2 Fix*di Fiy*di

256.12961 678.3973453 56.7714057 56.771

681.635208 1805.412173 151.085183 151.09

422.026072 1117.798786 93.5425365 93.5430 0 0 0

1359.79089 3601.608305 301.399125 301.4

4.27457146

12,323.55 7,572.23

Fi = Wi . Zi x V

jumlah Wi * Zi

BEBAN TANGGA

Tangga Tipe 1

No. Uraian Dimensi

L Volume Berat

n p l t m^3 kg/m^3

1 Plat Tangga 1.92 3.50 0.19 6.72 1.2923 2400 2

2 Anak Tangga 0.45 0.30 0.19 0.07 0.1385 2400 25

3 Spesi 0.30 1.92 0.01 0.58 0.0058 2100 25

5 Penutup Lantai 0.30 1.92 0.01 0.58 0.0058 2400 25

Total Berat Sendiri Tangga Tipe1……………………

Tangga Tipe 2

No. Uraian Dimensi

L Volume Berat

n p l t m^3 kg/m^3

1 Plat Tangga 0.80 0.80 0.19 0.64 0.1231 2400 1

2 Anak Tangga 0.45 0.30 0.19 0.07 0.0577 2400 25

3 Spesi 0.30 0.80 0.01 0.24 0.0024 2100 25

4 Penutup Lantai 0.30 0.80 0.01 0.24 0.0024 2400 25

Total Berat Sendiri Tangga Tipe 2……………………

Total Berat

6202.83

8307.36

302.40

345.60

15158.1888

60632.7552

Total Berat

295.37

3461.40

126.00

144.00

4026.7728

PEMBEBANAN PADA PLAT ATAP y = 2/3 h

Beban Segitiga

TipeL h y

LL WD p Ketm m

S9 3.5 1.78 1.187 100 265.5 478.6 567.939 Beban terpusat

Beban mati pada plat atap

- Berat pelat atap = 0.1 x 2400 = 240 kg/m^2

- Berat plafond = 0.5 kg/m^2

- Ornamen = 25 kg/m^2

∑ 265.5 kg/m^2

Beban trapesium

hy = h - (4.h^3 / 3 .L^2)

TipeL h t

y LL WD QKOM Qm m m

T10 4.5 1.78 1.41 100 265.5 478.6 674.2

PEMBEBANAN PADA PLAT LANTAI ,2 DAN 3y = 2/3 h

Beban Segitiga

TipeL h y

LL WD p Ketm m

S6 2.5 1.14 0.760 100 265.5 478.6 363.736 Beban terpusat

h S8 3 1.38 0.920 100 265.5 478.6 440.312 Beban terpusat

S4 4 1.8 1.200 100 265.5 478.6 574.320 Beban terpusat

S7 4 1.8 1.200 100 265.5 478.6 574.320 S9 3.5 1.66 1.107 100 265.5 478.6 529.651 Beban terpusat

Beban trapesium

hy = h - (4.h^3 / 3 .L^2)

TipeL h t

y LL WD QKOM Wpltm m m

T4 4 1.8 1.31 100 265.5 478.6 628.9

L T7 5 1.8 1.49 100 265.5 478.6 712.6

Beban merata dan terpusat pada Lt 1. pada portal tinjauan 1. Berat plat

Wplt (trapesium) = 1,425.2 kg

Wplt (segitiga) = 1,148.6 kg

Wplt (segitiga) = 880.6 kg

Berat sendiri balok induk ( TB 200 X 400)Wbalok = ( hblok - t plat) x b balok x p blok x ρ beton

= 0.4 - 0.12 x 0.2 x 28 x 2400

= 3763.2 kg

= 3000 kg

Beban merata dan terpusat pada Lt 1. pada portal tinjauan Berat sendiri balok induk ( TB 200 X 400)

Wbalok = ( hblok - t plat) x b balok x p blok x ρ beton

= 0.4 - 0.12 x 0.2 x 18.5 x 2400= 2486.4 kg

Berat dinding Wdin = 250 x 18.5

= 4625 kg

Beban merata dan terpusat pada portal tinjauan pada Lt. 2 & Lt. 31. Berat plat

Wplt (trapesium) = 1,425.23

Wplt (segitiga) = 1,148.64

Wplt (segitiga) = 880.62

Berat sendiri balok induk ( BL 300 X 600)Wbalok = ( hblok - t plat ) x b balok x p blok x ρ beton

= 0.6 - 0.12 x 0.3 x 8 x 2400= 2,764.80 kg

= 0.4 - 0.12 x 0.3 x 2.5 x 2400

= 504 kg

= 2000

Wdin' = 250 x 2.5

Beban merata dan terpusat pada portal tinjauan pada Lt. 2 & Lt. 3Berat sendiri balok anak ( BL 200 X 400)

Wbalok = ( hblok - t plat ) x b balok x p blok x ρ beton

= 0.2 - 0.12 x 0.4 x 4 x 2400

= 307.2 kg

= 0.3 - 0.12 x 0.2 x 1.62 x 2400

= 139.968 kg

Berat DindingWdin = 250 x 4

= 1000Wdin' = 250 x 1.62

Pembebanan pada lantai atap1. Berat atap

Wplt (trapesium) = 521.7

Berat sendiri balok induk ( RB1 200 x 300)Wbalok = ( hblok - t plat ) x b balok x p blok x ρ beton

= 0.3 - 0.12 x 0.2 x 18 x 2400

= 1555.2 kg

Beban Merata ( q ) = 523.3 ton

Tie Beam

Type TB 1 = 0.2 m x 0.4 m

Ring Balk

Type Balok 30/60 = 0.3 m x 0.6 m

Type Balok 30/40 = 0.3 m x 0.4 m

Type Balok 20/40 = 0.2 m x 0.4 m

Type Balok 20/30 = 0.2 m x 0.3 m

Gambar 4.1 Denah Portal Tinjauan Arah Y

Inersia

a. Inersia Kolom

Kekakuanb x h

1 Type kolom K1 40.000 x 40 0.0833 213,333.333 0.5333

b. Inersia Tie Beam

Kekakuanb x h

1 Type TB 1 20.000 x 40.00 0.0833 106,666.667 0.0762

Kekakuanb x h

1 Dimensi RB1 20.000 x 30 0.0833 45,000.000 0.0321

d. Inersia Balok

Kekakuanb x h

1 Type Balok 30/60 30.000 x 60 0.0833 540,000.000 0.3857

2 Type Balok 30/40 30.000 x 40 0.0833 160,000.000 0.1143

3 Type Balok 20/40 20.000 x 40 0.0833 106,666.667 0.0762

== -0.0833333333 x 8188.432512 x 16.000 - 0.125 x 5,792.464 x 4= (10,917.9) - 2,896 = (13,814.1) kgm = (13.8) tm

== -0.0833333333 x 8188.432512 x 16.000 - 0.125 x 5,792.464 x 4= (10,917.9) - 2896.232= (13,814.1) kgm = (13.8) tm

== -0.0833333333 x 8188.432512 x 16.000 - 0.125 x 5,792.464 x 4= (10,917.9) - 2896.232= (13,814.1) kgm = (13.8) tm =

= -1/12 x qL2 - 1/8 PL= -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x 4= (3,643.2) - 2055.116= (5,698.4) kgm = (5.7) tm =

== -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x 4= (3,643.2) - 2055.116= (5,698.4) kgm = (5.7) tm

= -1/12 x qL2 - 1/8 PL= -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x 4= (3,643.2) - 2,055.12 = (5,698.4) kgm = (5.7) tm

= -1/12 x qL2 - 1/8 PL= -0.0833333333 x 2732.432512 x 16.000 - 0.125 x 4,110.232 x 4

Mf1-2 -1/12 x qL2 - 1/8 PL

-Mf1-2

Mf2-3 -1/12 x qL2 - 1/8 PL

-Mf2-3

Mf3-4 -1/12 x qL2 - 1/8 PL

-Mf3-4

Mf4-5 -1/12 x qL2 - 1/8 PL

-Mf7-6

-Mf8-7

Mf9-8 -1/12 x qL2 - 1/8 PL

-Mf9-8

Mf9-10 -1/12 x qL2 - 1/8 PL

Mf10-9

-Mf9-10

Mf11-12 -1/12 x qL2 - 1/8 PL

Mf12-11

-Mf11-12

Mf12-13 -1/12 x qL2 - 1/8 PL

Mf13-12

-Mf12-13

Mf13-14

Mf14-13

-Mf13-14

Mf14-15

= (3,643.2) - 2055.12= (5.7) Tm

= -0.0833333333 x 523.2608217655 x 16.000 = (697.7)= (0.698) kgm =

== -0.0833333333 x 523.2608217655 x 16.000 = (697.7)= (0.698) tm =

= -1/12 x qL2 = -0.08333333 x 523.2608218 x 16.000 = (697.7)= (0.698) tm =

= -1/12 x qL2 = -0.0833333333 x 523.2608218 x 16.000 = -697.68109569= -0.698 tm

Mf15-14

-Mf14-15

Mf16-17 -1/12 x qL2

Mf17-16

-Mf16-17

Mf17-18 -1/12 x qL2

Mf18-17

-Mf17-18

Mf18--19

Mf19-18

-Mf18-19

Mf19-20

Mf20-19

Mf19-20

1 -13.814 13.81

2 -13.814 13.81

3 -13.814 13.81

4 -13.814 13.81

5 -5.698 5.70

6 -5.698 5.70

7 -5.698 5.70

8 -5.698 5.70

9 -5.698 5.70

10 -5.698 5.70

11 -5.698 5.70

12 -5.698 5.70

13 -0.698 0.698

14 -0.698 0.698

15 -0.698 0.698

16 -0.698 0.698

T1 = +

T Nilai ρ Nilai

-13.814 1.219

0.000 1.371

8.116 0.152

0.000 0.152

0.000 2.438

-5.698 2.286

0.000 2.438

5.001 0.152

0.000 0.064

0.000 1.195

-5.698 1.131

Joint 1

= = 0.076 = 0.063 ρ1 1.219

= = 0.533 = 0.438 ρ1 1.219

0.500 oke!

Joint 2

= = 0.076 = 0.056 ρ2 1.371

= = 0.5333 = 0.389 ρ2 1.371

0.500 oke!

M11-12

M12-11

M12-13

M13-12

M13-14

M14-13

M14-15

M15-14

M16-17

M17-16

M17-18

M18-17

M18-19

M19-19

M19-20

M20-19

T10 ρ

T11 ρ

T12 ρ

T13 ρ

T14 ρ

T15 ρ

T16 ρ

T17 ρ

T18 ρ

T19 ρ

T20 ρ

γ1-10

γ2--1

γ2--9

Joint 3

= = 0.076 = 0.056 ρ3 1.371

= = 0.5333 = 0.389 ρ3 1.371

0.500 oke!

Joint 4

= = 0.076 = 0.056 oke!ρ4 1.371

= = 0.076 = 0.056 ρ4 1.371

= = 0.533 = 0.389 ρ4 1.371

0.500 oke!

Joint 5

= = 0.076 = 0.500 oke!ρ5 0.152

Joint 6

= = 0.076 = 0.500 ρ6 0.152

0.500 oke!

Joint 7

= = 0.076 = 0.031 ρ7 2.438

= = 0.533 = 0.219 ρ7 2.438

0.500 oke!

Joint 8

= = 0.076 = 0.031 ρ8 2.438

= = 0.533 = 0.219 ρ8 2.438

0.500 oke!

K6-5γ

K7-6γ

γ7-14

γ8-13

Joint 9

= = 0.533 = 0.219 ρ9 2.438

= = 0.076 = 0.031 ρ9 2.438

0.500 oke!

Joint 10

= = 0.076 = 0.033 ρ10 2.286

= = 0.533 = 0.233 ρ10 2.286

0.500 oke!

Joint 11

= = 0.076 = 0.033 ρ11 2.286

= = 0.533 = 0.233 ρ11 2.286

0.500 oke!

Joint 12

= = 0.076 = 0.031 ρ12 2.438

= = 0.533 = 0.219 ρ12 2.438

= = 0.076 = 0.031 ρ12 2.438

= = 0.533 = 0.219 ρ12 2.438

0.500 oke!

Joint 13

= = 0.076 = 0.031 ρ13 2.438

= = 0.533 = 0.219 ρ13 2.438

0.500 oke!

γ9-12

γ9-10

γ10-9

γ10-11

K10-11

γ10-1

γ11-12

K11-12

γ11-10

K11-10

γ11-20

K11-16

γ12-11

K12-11

γ12-19

K12-19

γ12-13

K12-13

γ12-9

γ13-14

K13-14

γ13-12

K13-12

γ13-8

γ13-18

K13-14

Joint 14

= = 0.076 = 0.031ρ14 2.438

= = 0.533 = 0.219ρ14 2.438

0.500 oke!

Joint 15

= = 0.076 = 0.500 oke!ρ15 0.152

Joint 16

= = 0.032 = 0.500 oke!ρ16 0.064

Joint 17

= = 0.032 = 0.027 ρ17 1.195

= = 0.533 = 0.446 ρ17 1.195

= = 0.032 = 0.027 ρ17 1.195

0.500 oke!

Joint 18

= = 0.032 = 0.027 ρ18 1.195

= = 0.533 = 0.446 ρ18 1.195

= = 0.032 = 0.027 ρ18 1.195

0.500 oke!

Joint 19

= = 0.032 = 0.027

= = 0.533 = 0.446

= = 0.032 = 0.027

1.195 0.500 oke!

Joint 20

= = 0.533 = 0.472

= = 0.032 = 0.028

1.131 0.500 oke!

γ14-15

K14-15

γ14-13

K14-13

γ14-7

γ14-17

K14-11

γ15-14

K15-14

γ16-17

K16-17

γ17-16

K17-16

γ17-14

K17-14

γ17-18

K17-18

γ18-17

K17-18

γ18-13

K18-13

γ18-19

K18-19

γ19-18

K19-18

γ19-12

K19-12

γ19-20

K19-20

γ20-11

K20-11

γ20-19

K20-19

M1 = -Mf / ρ1

= 13.8141.219

= 11.332 ton

No. Momen Nilai

1 M1 11.332

2 M2 0.000

3 M3 0.000

4 M4 0.000

5 M5 -53.260

6 M6 0.000

7 M7 0.000

8 M8 0.000

9 M9 0.000

10 M10 2.493

11 M11 2.493

12 M12 0.000

13 M13 0.000

14 M14 0.000

15 M15 -32.817

16 M16 0.000

17 M17 0.000

18 M18 0.000

19 M19 0.000

20 M20 5.039

Menentukan nilai T

= 2 x ( 0.533 + 0.533 + 0.533 + 0.533 )

= 4.2667

T2 = 2 x ( 0.5 + 0.533 + 0.533 + 0.533 )

= 4.2667

T3 = 2 x ( 0.5 + 0.533 + 0.533 + 0.533 )

= 4.2667

2*(K1-10

2-9+ K

3-8+ K

2*(K10-11

+ K9-12

+ K6-13+

2*(K11-20

+ K12-19

+ K13-18+

K14+17

Perhitungan nilai t

= 0.375

No. t Nilai

1 0.375

2 0.375

3 0.375

4 0.375

5 0.375

6 0.375

7 0.375

8 0.375

9 0.375

10 0.375

11 0.375

12 0.375

13 0.375

14 0.375

15 0.375

16 0.375

Arah y =

M1 = -h1(∑W) =

= -3.500 x ( 2.20 ) = 4.2667

= -1.805

M2 = -h2(∑W) =

= -4.000 x ( 1.50 ) =

4.2667 = = -1.406 `

M3 = -h3(∑W) =

= -3.600 x ( 0.80 ) =

4.2667 = = -0.675

3.(K1-10

MI (1) MI (0)

(-t1-10

) x (M1( I ) + M10(I) )

(-t2-9

) x (M2( I ) + M9(I) )

(-t3-8

) x (M3( I ) + M8(I) )

(-t4-7

) x (M4( I ) + M7(I) )

MII(1) MII (0)

(-t7-14) x (M7( I ) + M14(I) )

(-t8-13) x (M8( I )+ M13(I))

(-t9-12) x (M9( I )+ M12(I))

(-t10-11) x (M10( I )+ M11(I))

MIII(1) MIII (0)

(-t14-17

) x (M14( I ) + M17(I) )

(-t13-18

) x (M13( I )+ M18(I))

(-t12-19) x (M12( I )+ M19(I))

(-11-20) x (M11( I )+ M20(I))

Putaran 0

MI = MI(0) = 11.3 = 11.332 = γ 1 - 2 x M2 = (0.063) x - = - = γ 1 - 10 x MD 1+M10(0) = (0.438) x 0.688 = (0.301) +

MI = 11.031

M2 = 0.089

M3 = 0.697

M4 = M4(0) = - = - = γ 4-3 x M3(1) = (0.056) x 0.697 = (0.039)= γ 4-5 x M5(0) = (0.056) x -53.260 = 2.959 = γ 4-7 x MD 1+M7 = (0.389) x (1.805) = 0.702 +

M4 = 3.622

M5 = M5(0) = (53.3) = (53.260)= γ 5-4 x M4(1) = (0.500) x 3.622 = (1.811) +

M5 = (55.071)

M6 = M6(0) = - = - = γ 6-7 x M7(0) = (0.031) x - = - +

M6 = -

M7 = M7(0) = - = - = γ 7-6 x M6(1) = (0.031) x - = - = γ 7-8 x M8(0) = (0.031) x - = - = γ 7-14 x MD 2+M14 = (0.219) x (1.406) = 0.308 = γ7-4 x MD 1+M4(1) = (0.219) x 1.817 = 0.308 +

M7 = 0.615

M8 = M8(0) = - = - = γ 8-7 x M7(1) = (0.031) x 0.615 = (0.019)= γ 8-3 x MD 1+ M3(1) = (0.219) x (1.108) = 0.242 = γ8-9 x M9(0) = (0.031) x - = - = γ8-13 x MD 2+M13 = (0.219) x -1.406 = +

M8 = 0.223

M9 = M9(0) = - = - = γ 9-10 x M10(0) = (0.031) x 2.493 = (0.078)= γ 9-8 x M8(1) = (0.031) x 0.223 = (0.007)= γ9-12 x MD 2+M12(0) = (0.219) x (1.406) = 0.308 = γ9-2 x MD 1+M2(1) = (0.219) x (1.317) = 0.288 +

M9 = 0.511

M10 = M10(0) = 2.5 = 2.493 = γ 10-9 x M9(1) = (0.033) x 0.511 = (0.017)= γ 10-11 x MD 2 +M11(0) = (0.233) x 1.087 = (0.254)= γ 10-1 x MD 1+M1(1) = (0.233) x 9.226 = (2.153) +

M10 0.070

M11 = M11(0) = 2.5 = 2.493 = γ 11-12 x M12(0) = (0.033) x - = - = γ 11-10 x MD 2 + M10(1) = (0.233) x (1.337) = 0.312 = γ 11-20 x MD 3+M20(0) = (0.233) x 4.364 = (1.018) +

M11 1.787

M12 = M12(0) = - = - = γ 12-11 x M11(1) = (0.031) x 1.787 = (0.056)= γ 12-13 x M13(0) = (0.031) x - = - = γ 12-9 x MD2+ M9(1) = (0.219) x (0.895) = 0.196 = γ 12-19 x MD3+M19(0) = (0.219) x (0.675) = 0.148 +

M12 = 0.288

M13 = M13(0) = - = - = γ 13-14 x M14(0) = (0.031) x - = - = γ 13-12 x M12(1) = (0.031) x 0.288 = (0.009)= γ 13-18 x MD3+M18(0) = (0.219) x (0.675) = 0.148 = γ 13-8 x MD2+M8(1) = (0.219) x (1.183) = 0.259 +

M13 = 0.397

M14 = M14(0) = - = - = γ 14-13 x M13(1) = (0.031) x 0.397 = (0.012)= γ 14-15 x M15(0) = (0.031) x (32.817) = 1.026 = γ 14-17 x MD 3+M17(0) = (0.219) x (0.675) = 0.148 = γ 14-7 x MD 2+M7(1) = (0.219) x (0.791) = 0.173 +

M14 = 1.334

M15 = M15(0) = (32.8) = (32.817)= γ 15-14 x M14(1) = (0.500) x 1.334 = (0.667) +

M15 = (33.484)

M16 = M16(0) = - = - = γ 16-17 x M17(0) = (0.500) x - = - +

M16 = -

M17 = M17(0) = - = - = γ 17-18 x M18(0) = (0.027) x - = - = γ 17-16 x M16(1) = (0.027) x - = - = γ 17-14 x MD 3+ M14(1) = (0.446) x 0.659 = (0.294) +

M17 = (0.294)

M18 = M18(0) = - = - = γ 18-17 x M17(1) = (0.027) x (0.294) = 0.008 = γ 18-19 x M19(0) = (0.027) x - = - = γ18-13 x MD 3+M13(1) = (0.446) x (0.278) = 0.124 +

M18 = 0.132

M19 = M19(0) = - = - = γ 19-18 x M18(1) = (0.027) x 0.132 = (0.004)= γ 19-20 x M20(0) = (0.027) x 5.039 = (0.135)= γ19-12 x MD 3+M12(1) = (0.446) x (0.387) = 0.173 +

M19 = 0.034

M20 = M20(0) = 5.0 = 5.039 = γ 20-19 x M19(1) = (0.028) x 0.034 = (0.001)= γ20-11 x MD 3+M11(1) = (0.472) x 1.112 = (0.524) +

M20 = 4.513

Joint 1

M1-2 = K 1-2 x + Mf1-2 = 0.076 x 24.054 + (13.8)

M1-10 = K 1-10 x + Mf1-10 = 0.533 x 24.270 + 0.0∑M

Joint 2

M2-1 = K 2-1 x + Mf2-1 = 0.076 x 11.645 + 13.8

M2-3 = K 2-3 x + Mf2-3 = 0.076 x (0.225) + -13.8

M2-9 = K 2-9 x + Mf2-9 = 0.533 x 0.173 + 0∑M

Joint 3

M3-2 = K 3-2 x + Mf3-2 = 0.076 x 0.315 + 13.8

M3-4 = K 3-4 x + Mf3-4 = 0.076 x 4.368 + -13.8

M3-8 = K 3-8 x + Mf3-8 = 0.533 x 1.136 + 0∑M

Joint 4

M4-3 = K 4-3 x + Mf4-3 = 0.076 x 7.882 + 13.8

M4-5 = K 4-5 x + Mf4-5 = 0.076 x (47.562) + (13.8)

M4-7 = K 4-7 x + Mf4-7 = 0.533 x 7.473 + 0∑M

Joint 5

M5-4 = K 5-4 x + Mf5-4 = 0.076 x (106.520) + 13.8 ∑M

Joint 6

M6-7 = K 6-7 x + Mf6-7 = 0.076 x (0.116) + 5.7∑M

Joint 7

M7-6 = K 7-6 x + Mf7-6 = 0.076 x (0.243) + (5.7)

M7-8 = K 7-8 x + Mf7-8 = 0.076 x 0.318 + 5.7

M7-4 = K 7-4 x + Mf7-4 = 0.533 x 3.551 + 0

M7-14 = K 7-14 x + Mf7-14 = 0.533 x 1.401 + 0∑M

Joint 8

M8-7 = K 8-7 x + Mf8-7 = 0.076 x 1.008 + (5.7)

M8-9 = K 8-9 x + Mf8-9 = 0.076 x 1.814 + 5.7

M8-3 = K 8-3 x + Mf8-3 = 0.533 x 1.416 + 0

M8-13 = K 8-13 x + Mf8-13 = 0.533 x 1.391 + 0∑M

Joint 9

M9-10 = K 9-10 x + Mf9-10 = 0.076 x 1.327 + (5.7)

M9-8 = K 9-8 x + Mf9-8 = 0.076 x 1.932 + -5.7

M9-2 = K 9-2 x + Mf9-2 = 0.533 x 1.111 + 0

M9-12 = K 9-12 x + Mf9-12 = 0.533 x 1.634 + 0∑M

Joint 10

M10-11 = K 10-11 x + Mf10-11 = 0.533 x 1.732 + 0

M10-9 = K 10-9 x + Mf10-9 = 0.076 x 0.605 + 5.7

M10-1 = K 10-7 x + Mf10-1 = 0.533 x 12.077 + 0∑M

Joint 11

M11-10 = K 11-10 x + Mf11-10 = 0.533 x 3.580 + 0

M11-12 = K 11-12 x + Mf11-12 = 0.076 x 3.887 + -5.7

M11-20 = K 11-6 x + Mf11-20 = 0.533 x 8.630 + 0∑M

Joint 12

M12-11 = K 12-11 x + Mf12-11 = 0.076 x 2.347 + 5.7

M12-9 = K 12-9 x + Mf12-9 = 0.533 x 1.220 + 0

M12-19 = K 12-19 x + Mf12-19 = 0.533 x 0.412 + 0

M12-13 = K 12-13 x + Mf12-13 = 0.076 x 0.797 + (5.7)∑M

Joint 13

M13-14 = K 13-14 x + Mf13-14 = 0.076 x 2.168 + (5.7)

M13-12 = K 13-12 x + Mf13-12 = 0.076 x 0.788 + 5.7

M13-18 = K 13-18 x + Mf13-18 = 0.533 x 0.574 + 0

M13-8 = K 13-8 x + Mf13-8 = 0.533 x 1.085 + 0∑M

{ 2M1(k) + M2(k) }

{2M1(k) + M10(k) }

{ 2M2(k) + M1(k) }

{2M2(k) + M3(k) }

{2M2(k) + M9(k) }

{ 2M3(k) + M2(k) }

{2M3(k) + M4(k) }

{2M3(k) + M8(k) }

{ 2M4(k) + M3(k) }

{ 2M4(k) + M5(k) }

{ 2M4(k) + M7(k) }

{ 2M5(k) + M4(k) }

{2M6(k) + M7(k) }

{ 2M7(k) + M6(k) }

{2M7(k) + M8(k) }

{2M7(k) + M4(k) }

{2M7(k) + M14(k) }

{ 2M8(k) + M7(k) }

{2M8(k) + M9(k) }

{2M8(k) + M3(k) }

{2M8(k) + M13(k) }

{ 2M9(k) + M10(k) }

{2M9(k) + M8(k) }

{2M9(k) + M2(k) }

{2M9(k) + M12(k) }

{ 2M10(k) + M11(k) }

{2M10(k) + M9(k) }

{2M10(k) + M1(k) }

{ 2M11(k) + M10(k)}

{2M11(k) + M12(k) }

{2M11(k) + M20(k) }

{ 2M12(k) + M11(k)}

{ 2M12(k) + M9(k)}

{ 2M12(k) + M19(k)}

{ 2M12(k) + M13(k)}

{ 2M13(k) + M14(k)}

{ 2M13(k) + M12(k)}

{ 2M13(k) + M18(k)}

{ 2M13(k) + M8(k)}

Joint 14

M14-13 = K 14-13 x + Mf14-13 = 0.076 x 3.556 + 5.7

M14-15 = K 14-15 x + Mf14-15 = 0.076 x (30.345) + -5.7

M14-17 = K 14-17 x + Mf114-17 = 0.533 x 2.736 + 0

M14-7 = K 14-7 x + Mf14-7 = 0.533 x 3.173 + 0∑M

Joint 15

M15-14 = K 15-14 x + Mf15-14 = 0.076 x (65.634) + 5.7 ∑M

Joint 16

M16-17 = K 16-17 x + Mf16-17 = 0.032 x 0.000 + (0.7)∑M

Joint 17

M17-18 = K 17-18 x + Mf17-18 = 0.032 x (1.067) + (0.698)

M17-16 = K 17-16 x + Mf17-16 = 0.032 x (0.841) + 0.698

M17-14 = K 17-14 x + Mf17-14 = 0.533 x 0.527 + 0∑M

Joint 18

M18-17 = K 18-17 x + Mf18-17 = 0.032 x (0.452) + 0.698

M18-19 = K 18-19 x + Mf18-19 = 0.032 x (0.017) + (0.698)

M18-13 = K 18-13 x + Mf18-13 = 0.533 x 0.368 + 0∑M

Joint 19

M19-18 = K 19-18 x + Mf19-18 = 0.032 x (0.196) + 0.698

M19-20 = K 19-20 x + Mf19-20 = 0.032 x 4.761 + (0.698)

M19-12 = K 19-12 x + Mf19-12 = 0.533 x 0.018 + 0∑M

Joint 20

M20-19 = K 20-19 x + Mf20-19 = 0.032 x 10.023 + 0.698

M20-11 = K 20-11 x + Mf20-11 = 0.533 x 11.832 + 0∑M

No. Joint Momen desain ∑M K ∑K K/∑ ∆M

1M1-2 -11.981

0.9620.08

0.6100.125 -0.120 -12.102

0.0M1-10 12.944 0.53 0.875 -0.842 12.102

M2-1 14.701

0.08 0.111 -0.107 14.594

0.0M2-3 -13.831 0.08 0.686 0.111 -0.107 -13.938

M2-9 0.092 0.53 0.778 -0.749 -0.656

M3-2 13.838

0.08 0.111 -0.107 13.731

0.0M3-4 -13.481 0.08 0.686 0.111 -0.107 -13.588

M3-8 0.606 0.53 0.778 -0.749 -0.143

M4-3 0.601

0.08 0.111 -0.107 0.494

0.0M4-5 -3.624 0.08 0.686 0.111 -0.107 -3.731

M4-7 3.986 0.53 0.778 -0.749 3.237

5 M5-4 5.698 5.698 0.08 0.076 1.000 -5.698 0.000 0.0

6 M6-7 5.690 5.690 0.08 0.076 1.000 -5.690 0.000 0.0

{ 2M14(k) + M13(k)}

{2M14(k) + M15(k) }

{2M14(k) + M17(k) }

{2M14(k) + M7(k) }

{ 2M15(k) + M14(k)}

{ 2M16(k) + M17(k) }

{ 2M17(k) + M18(k) }

{ 2M17(k) + M16(k) }

{ 2M17(k) + M14(k) }

{ 2M18(k) + M17(k) }

{2M18(k) + M19(k) }

{2M18(k) + M13(k) }

{ 2M19(k) + M18(k) }

{2M19(k) + M20(k) }

{2M19(k) + M12(k) }

{ 2M20(k) + M13(k) }

{2M20(k) + M11(k) }

K /∑K*∆M Koreksi Momen

M7-6 -5.717

0.063 -0.165 -5.882

0.0M7-8 5.723 0.08 0.063 -0.165 5.557

M7-4 1.894 0.53 0.438 -1.158 0.736

M7-14 0.747 0.53 0.438 -1.158 -0.411

M8-7 -5.622

0.063 -0.107 -5.729

0.0M8-9 5.837 0.08 0.063 -0.107 5.730

M8-3 0.755 0.53 0.438 -0.749 0.006

M8-13 0.742 0.53 0.438 -0.749 -0.007

M9-10 -5.597

-9.684

0.063 0.605 -4.992

0.0M9-8 -5.551 0.08 0.063 0.605 -4.946

M9-2 0.593 0.53 0.438 4.237 4.829

M9-12 0.872 0.53 0.438 4.237 5.109

M10-11 0.924

13.109

0.467 -6.118 -5.194

0.0M10-9 5.744 0.08 0.067 -0.874 4.871

M10-1 6.441 0.53 0.467 -6.118 0.323

M11-10 1.909

0.467 -0.518 1.391

0.0M11-12 -5.402 0.08 0.067 -0.074 -5.476

M11-20 4.603 0.53 0.467 -0.518 4.085

M12-11 5.877

0.063 -0.069 5.808

0.0M12-9 0.651 0.53 0.438 -0.486 0.165

M12-19 0.220 0.53 0.438 -0.486 -0.266

M12-13 -5.638 0.08 0.063 -0.069 -5.707

M13-14 -5.533

0.063 -0.069 -5.603

0.0M13-12 5.758 0.08 0.0625 -0.069 5.689

M13-18 0.306 0.53 0.438 -0.486 -0.180

M13-8 0.579 0.53 0.438 -0.486 0.093

M14-13 5.969

0.063 -0.069 5.900

0.0M14-15 -8.010 0.08 0.063 -0.069 -8.080

M14-17 1.459 0.53 0.438 -0.486 0.973

M14-7 1.692 0.53 0.438 -0.486 1.206

15 M15-14 0.698 0.698 0.08 0.076 1.000 -0.698 0.000 0.0

16 M16-17 -0.698 -0.698 0.03 0.032 1.000 0.698 0.000 0.0

M17-18 -0.732

0.057 -0.012 -0.744

0.0M17-16 0.671 0.03 0.057 -0.012 0.658

M17-14 0.281 0.53 0.943 -0.207 0.074

M18-17 0.683

0.054 -0.010 0.673

0.0M18-19 -0.698 0.03 0.054 -0.010 -0.708

M18-13 0.196 0.53 0.892 -0.162 0.035

M19-18 0.691

0.054 -0.008 0.683

0.0M19-20 -0.545 0.03 0.054 -0.008 -0.553

M19-12 0.010 0.53 0.892 -0.140 -0.130

20M20-19 1.020

7.3300.03

0.5650.057 -0.417 0.603

0.0M20-11 6.311 0.53 0.943 -6.914 -0.603

P1 P22

RA = P2/3 + 2P1/3 + 1/2qL

RA = P1/3 + 2P2/3 + 1/2qL

RM x-y = M x-y /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RA = 1/2P+ 1/2qL

ba c da b

P1 P22

RA = P2/3 + 2P1/3 + 1/2qL

RA = P1/3 + 2P2/3 + 1/2qL

RM x-y = M x-y /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RA = 1/2P+ 1/2qL

ba c da b

No. JointM.Desain

q p1 p2 L RA RB RM x-y RM y-x ∑R'A ∑R'BStlh Koreksi

1 M1-2 -12.102 8.188 #REF! #REF! 12 #REF! #REF! (1.008) 1.216 #REF! #REF!

2 M2-1 14.594 8.188 #REF! #REF! 12 #REF! #REF! (1.008) 1.216 #REF! #REF!

3 M2-3 -13.938 8.188 #REF! - 8 #REF! #REF! (1.742) 1.716 #REF! #REF!

4 M3-2 13.731 8.188 #REF! - 8 #REF! #REF! (1.742) 1.716 #REF! #REF!

5 M3-4 -13.588 8.188 - - 4 16.377 16.377 (3.397) 0.123 19.897 12.856

6 M4-3 0.494 8.188 - - 4 16.377 16.377 (3.397) 0.123 19.897 12.856

7 M5-4 0.000 8.188 - - 4 16.377 16.377 - #REF! #REF! #REF!

8 M4-5 -3.731 2.732 #REF! - 8 #REF! #REF! (0.466) - #REF! #REF!

9 M6-7 0.000 2.732 #REF! - 8 #REF! #REF! (0.466) - #REF! #REF!

10 M7-6 -5.882 2.732 2.055 2.1 12 18.450 18.450 (0.490) (0.477) 18.463 18.437

11 M8-7 -5.729 2.732 2.055 2.1 12 18.450 18.450 (0.490) (0.477) 18.463 18.437

12 M7-8 5.557 2.732 2.055 2.1 12 18.450 18.450 0.463 (0.416) 17.571 19.329

13 M8-9 5.730 2.732 #REF! - 8 #REF! #REF! 0.716 (0.618) #REF! #REF!

14 M9-10 -4.992 2.732 2.055 2.1 12 18.450 18.450 0.463 (0.416) 17.571 19.329

15 M9-8 -4.946 #REF! #REF! - 8 #REF! #REF! 0.716 (0.618) #REF! #REF!

16 M10-9 4.871 #REF! - - 4 #REF! #REF! 1.218 (1.369) #REF! #REF!

17 M11-12 -5.476 #REF! - - 4 #REF! #REF! 1.218 (1.369) #REF! #REF!

18 M12-11 5.808 #REF! - - 4 #REF! #REF! (1.427) 1.452 #REF! #REF!

19 M12-13 -5.707 #REF! - - 4 #REF! #REF! (1.427) 1.452 #REF! #REF!

20 M14-13 5.900 #REF! #REF! - 8 #REF! #REF! (1.010) 0.737 #REF! #REF!

21 M14-15 -8.080 #REF! #REF! - 8 #REF! #REF! (1.010) 0.737 #REF! #REF!

22 M15-14 0.000 #REF! #REF! #REF! 12 #REF! #REF! - #REF! #REF! #REF!

23 M16-17 0.000 0.523 - - 8 2.093 2.093 (0.093) - 2.186 2.000

24 M17-18 -0.744 0.523 - - 8 2.093 2.093 (0.093) - 2.186 2.000

25 M17-16 0.658 0.523 - - 4 1.047 1.047 0.165 0.168 1.050 1.043

26 M18-17 0.673 0.523 - - 4 1.047 1.047 0.165 0.168 1.050 1.043

27 M18-19 -0.708 0.523 - - 4 1.047 1.047 (0.177) 0.171 1.394 0.699

28 M19-18 0.683 0.523 - - 4 1.047 1.047 (0.177) 0.171 1.394 0.699

29 M19-20 -0.553

30 M20-19 0.603

RM y-x = - M y-x /L

RM y-x = -M y-x /L

RM y-x = M y-x /L

RM y-x = - M y-x /L

RM y-x = -M y-x /L

RM y-x = M y-x /L

RM x-y= Mx-y / L

RM y-x= Mx-y / L

RM x-y= Mx-y / L

No. Joint h M desain RMx-y/L RMy-x/L ∑RA ∑RB Da Kanan Da kanan

1 M1-10 3.50 12.102 3.458 0.002 3.459 (3.459) 3.459 0.000

2 M2-9 3.50 (0.656) (0.187) 0.210 0.023 (0.023) 0.023 0.000

3 M3-8 3.50 (0.143) (0.041) 0.925 0.884 (0.884) 0.884 0.000

4 M4-7 3.50 3.237 (0.041) 0.925 0.884 (0.884) 0.884 0.000

5 M7-4 3.50 0.736 (0.187) 0.210 0.023 (0.023) 0.023 0.000

6 M7-14 4.00 (0.411) (0.103) 0.348 0.245 (0.245) 0.245 0.000

7 M8-3 3.50 0.006 3.458 0.002 3.459 (3.459) 3.459 0.000

8 M8-13 4.00 (0.007) (0.002) 1.380 1.378 (1.378) 1.378 0.000

9 M9-2 3.50 4.829 (0.002) 1.380 1.378 (1.378) 1.378 0.000

10 M9-12 4.00 5.109 1.277 0.270 1.548 (1.548) 1.548 0.000

11 M10-11 4.00 (5.194) (1.298) (0.050) (1.348) 1.348 (1.348) 0.000

12 M10-1 3.50 0.323 0.092 (0.103) (0.010) 0.010 (0.010) 0.000

13 M11-10 4.00 1.391 0.348 (0.103) 0.245 (0.245) 0.245 0.000

14 M11-20 3.60 4.085 1.135 (0.074) 1.061 (1.061) 1.061 0.000

15 M12-9 4.00 0.165 0.041 0.021 0.062 (0.062) 0.062 0.000

16 M12-19 3.60 (0.266) 1.135 (0.074) 1.061 (1.061) 1.061 0.000

17 M13-18 3.60 (0.180) (1.298) (0.050) (1.348) 1.348 (1.348) 0.000

18 M13-8 4.00 0.093 0.023 0.302 0.325 (0.325) 0.325 0.000

19 M14-17 3.60 0.973 1.277 0.270 1.548 (1.548) 1.548 0.000

20 M14-7 4.00 1.206 0.302 0.023 0.325 (0.325) 0.325 0.000

21 M17-14 3.60 0.074 0.041 0.021 0.062 (0.062) 0.062 0.000

22 M18-13 3.60 0.035 1.135 (0.074) 1.061 (1.061) 1.061 0.000

23 M19-12 3.60 (0.130) (1.298) (0.050) (1.348) 1.348 (1.348) 0.000

24 M20-11 3.60 (0.603) 0.023 0.302 0.325 (0.325) 0.325 0.000

= -1.8046875 = -1.80 -1.8046875 =

= (0.38) x 11.1 = -4.16 (0.38) x 12.1 =

= (0.38) x 0.6 = -0.22 (0.38) x 0.5 =

= (0.38) x 0.9 = -0.34 (0.38) x 0.9 =

= (0.38) x 4.237 = -1.59 (0.38) 3.524 =-8.13 =

= -1.40625 = -1.41 -1.40625 =

= (0.38) x 1.9 = 1.57 (0.38) x 1.6 =

= (0.38) x 0.9 = -0.34 (0.38) x 0.8 =

= (0.38) x 0.8 = -0.30 (0.38) x 0.9 =

= (0.38) x 1.856 = -0.70 (0.38) 1.903 =-1.17 =

= -0.675 = -0.68 -0.675 =

= (0.38) x 1.0 = 0.66 (0.38) x 1.1 =

= (0.38) x 0.5 = -0.20 (0.38) x 0.3 =

= (0.38) x 0.3 = -0.12 (0.38) x 0.3 =

= (0.38) x 6.300 = -2.36 (0.38) 6.9 =-2.69 =

Putaran 1 Putaran 2

11.3 = 11.332 11.3 = 11.3 (0.063) x 0.1 = (0.006) (0.063) x (0.207) = 0.0129364 (0.438) x (1.7) = 0.759 + (0.438) x (1.8) = 0.796906

MI 12.09 MI = 12.14

- = - - = - (0.056) x 12.1 = (0.671) (0.056) x 12.1 = -0.674542 (0.056) x 0.7 = (0.039) (0.056) x 0.4 = -0.02363 (0.389) x (1.29) = 0.503 + (0.389) x (1.14) = 0.4425269

M2 (0.207) M2 = (0.3)

- = - - = - (0.056) x (0.207) = 0.011 (0.056) x (0.3) = 0.0142025 (0.056) x 3.6 = (0.201) (0.056) x 3.5 = -0.194357 (0.389) x (1.58) = 0.615 + (0.389) x (1.30) = 0.5051831

M3 = 0.425 M3 = 0.3

- = - - = - (0.056) x 0.4 = (0.024) (0.056) x 0.3 = -0.018057 (0.056) x (55.071) = 3.059 (0.056) x (55.009) = 3.0560576 (0.389) x (1.189) = 0.463 + (0.389) x (1.779) = 0.691974

M4 = 3.498 M4 = 3.7

(53.3) = (53.260) (53.3) = (53.3) (0.500) x 3.498 = (1.749) + (0.500) x 3.7 = -1.864987

M5 = (55.009) M5 = (55.1)

- = - - = - (0.031) x 0.6 = (0.019) + (0.031) x 0.025 = -0.000791

M6 = (0.019) M6 = (0.001)

- = - - = - (0.031) x (0.019) = 0.001 (0.031) x (0.0) = 2.47E-005 (0.031) x 0.2 = (0.007) (0.031) x 0.51 = -0.015801 (0.219) x (0.07) = 0.016 (0.219) x 0.15 = -0.031897 (0.219) x 1.69 = 0.016 + (0.219) x 1.93 = -0.031897

M7 = 0.025 M7 = (0.080)

- = - - = - (0.031) x 0.025 = (0.001) (0.031) x (0.080) = 0.0024866 (0.219) x (1.4) = 0.302 (0.219) x (1.5) = 0.3236754 (0.031) x 0.51 = (0.016) (0.031) x 0.67 = -0.020836 (0.219) x (1.009) = 0.221 + (0.219) x (1.139) = 0.2492134

M8 = 0.506 M8 = 0.6

- = - - = - (0.031) x 0.070 = (0.002) (0.031) x (0.0) = 0.0005254 (0.031) x 0.506 = (0.016) (0.031) x 0.6 = -0.017329 (0.219) x (1.12) = 0.245 (0.219) x (1.18) = 0.2573897 (0.219) x (2.01) = 0.440 + (0.219) x (2.06) = 0.4506977

M9 = 0.67 M9 = 0.7

2.5 = 2.493 2.5 = 2.5 (0.033) x 0.667 = (0.022) (0.033) x 0.7 = -0.023043 (0.233) x 0.4 = (0.089) (0.233) x 0.5 = -0.119848 (0.233) x 10.28 = (2.399) + (0.233) x 10.34 = -2.411983

M10 = (0.017) M10 (0.062)

2.5 = 2.493 2.5 = 2.5 (0.033) x 0.3 = (0.010) (0.033) x 0.230 = -0.007654 (0.233) x (1.4) = 0.332 (0.233) x (1.47) = 0.3425546 (0.233) x 3.84 = (0.896) + (0.233) x 4.33 = -1.009867

M11 = 1.920 M11 = 1.8

- = - - = - (0.031) x 1.9 = (0.060) (0.031) x 1.8 = -0.056815 (0.031) x 0.4 = (0.012) (0.031) x 0.3 = -0.008343 (0.219) x (0.7) = 0.162 (0.219) x (0.7) = 0.1563989 (0.219) x (0.6) = 0.140 + (0.219) x (0.6) = 0.1308257

M12 = 0.230 M12 = 0.2

- = - - = - (0.031) x 1.3 = (0.042) (0.031) x 1.6 = -0.048502 (0.031) x 0.23 = (0.007) (0.031) x 0.2 = -0.00694 (0.219) x (0.5) = 0.119 (0.219) x (0.7) = 0.144196 (0.219) x (0.9) = 0.197 + (0.219) x (0.9) = 0.1863118

M13 = 0.267 M13 = 0.3

- = - - = - (0.031) x 0.3 = (0.008) (0.031) x 0.3 = -0.008596 (0.031) x (33.48) = 1.046 (0.031) x (33.6) = 1.0497807 (0.219) x (0.97) = 0.212 (0.219) x (1.14) = 0.2483882 (0.219) x (1.38) = 0.302 + (0.219) x (1.49) 0.3250233

M14 = 1.552 M14 1.6

(32.8) x = (32.817) (32.8) = (32.8) (0.500) x 1.6 = (0.776) + (0.500) x 1.61 = -0.807298

M15 (33.593) M15 (33.6)

- = - - = - (0.500) x (0.29) = 0.147 + (0.500) x (0.5) = 0.2302444

M16 0.147 M16 0.2

- = - - = - (0.027) x 0.1 = (0.004) (0.027) x 0.016 = -4E-04 (0.446) x 0.1 = (0.066) (0.446) x 0.2 = -0.102739 (0.446) x 0.9 = (0.391) + (0.446) x 0.9 = -0.419262

M17 = (0.460) M17 = (0.5)

- = - - = - (0.027) x (0.5) = 0.012 (0.027) x (0.5) = 0.0140493 (0.223) x 0.0 = (0.008) (0.223) x 0.08 = -0.017166 (0.027) x (0.41) = 0.011 + (0.027) x (0.40) = 0.0107552

M18 = 0.016 M18 0.0

- = - - = - (0.027) x 0.016 = (0.000) (0.027) x 0.0 = -0.000205 (0.027) x 4.5 = (0.121) (0.027) x 5.0 = -0.134543 (0.446) x (0.45) = 0.199 + (0.027) x (0.45) = 0.0121805

M19 = 0.077 M19 (0.1)

5.0 = 5.039 5.0 = 5.0 (0.027) x 0.077 = (0.002) (0.027) x (0.1) = 0.0032961 (0.027) x 1.24 = (0.033) + (0.027) x 1.14 = -0.03074

M20 5.003 M20 5.0

= (11.98)

= 12.94 + = 1.0

= 14.70

= (13.83) +

= 0.09= 1.0

= 13.84

= (13.48) +

= 0.61= 1.0

= 0.600523

= -3.623781

= 3.985758 + = 1.0

= 5.698359 + = 5.7

= 5.69 + = 5.7

= (5.72)

= 5.72

= 1.89

= 0.75 + = 2.6

= (5.62)

= 5.84

= 0.76

= 0.74 + = 1.7

= (5.60)

= (5.55)

= 0.59

= 0.87 + = (9.7)

= 0.92

= 5.74

= 6.44 + = 13.1

= 1.91

= (5.40)

= 4.60 + = 1.1

= 5.877154

= 0.650759

= 0.219720

= -5.637633 + = 1.1

= -5.533203

= 5.758409

= 0.305981

= 0.578814 + = 1.1

= 5.97

= (8.01)

= 1.46

= 1.69 + = 1.1

= 0.70 + = 0.7

= (0.70) + = (0.7)

= (0.73)

= 0.67

= 0.28 + = 0.2

= 0.68

= (0.70) +

= 0.20= 0.2

= 0.69

= (0.54) +

= 0.01= 0.2

= 1.02

= 6.31 + = 7.3

∑`RB

19.897 19.897 (12.856) -12.856 (12.856) 0.000

18.463 18.463 (3.397) (3.397) (8.862) (10.917) (12.972) 0.000

17.571 17.571 (4.289) (4.289) (9.754) (11.809) (13.864) 0.000

2.186 2.186 (2.000) -2.000 (2.000) 0.000

1.050 1.050 (1.043) -1.043 (1.043) 0.000

1.394 1.394 (0.699) -0.699 (0.699) 0.000

-1.80 -1.804688 = -1.80 -1.804688 = -1.80

-4.53 (0.38) x 12.1 = -4.53 (0.38) x 12.1 = -4.55

-0.17 (0.38) x 0.4 = -0.16 (0.38) x 0.4 = -0.16

-0.35 (0.38) x 0.9 = -0.33 (0.38) x 0.9 = -0.32

-1.32 (0.38) x 3.650 = -1.37 (0.38) x 3.7 = -1.38-8.17 = -8.20 = -8.2

-1.41 -1.40625 = -1.41 -1.40625 = -1.41

-0.59 (0.38) x 1.5 = -0.58 (0.38) x 1.5 = -0.57

-0.29 (0.38) x 0.8 = -0.31 (0.38) x 0.8 = -0.31

-0.34 (0.38) x 0.9 = -0.34 (0.38) x 1.0 = -0.36

-0.71 (0.38) x 1.756 = -0.66 (0.38) x 1.8 = -0.66-3.34 = -3.29 = -3.3

-0.68 -0.675 = -0.68 -0.675 = -0.68

-0.41 (0.38) x 1.1 = -0.41 (0.38) x 1.1 = -0.41

-0.11 (0.38) x 0.3 = -0.11 (0.38) x 0.3 = -0.12

-0.11 (0.38) x 0.1 = -0.04 (0.38) x 0.1 = -0.05

-2.60 (0.38) x 7 = -2.56 (0.38) x 6.8 = -2.56-3.90 = -3.79 = -3.8

Putaran 3 Putaran 4

11.3 = 11.3 11.3 = 11.3 (0.063) x (0.3) = 0.015978 (0.063) x (0.3) = 0.016305 (0.438) x (1.9) = 0.816606 (0.438) x (1.8) = 0.808593

MI 12.2 MI 12.2

- = - - = - (0.056) x 12.2 = -0.675805 (0.056) x 12.2 = -0.675378 (0.056) x 0.3 = -0.018057 (0.056) x 0.3 = -0.016302 (0.389) x (1.11) = 0.43299 (0.389) x (1.11) = 0.431421

M2 (0.3) M2 (0.3)

- = - - = - (0.056) x (0.3) = 0.014493 (0.056) x (0.3) = 0.014459 (0.056) x 3.7 = -0.207221 (0.056) x 3.8 = -0.209942 (0.389) x (1.25) = 0.486169 (0.389) x (1.24) = 0.484115

M3 0.3 M3 0.3

- = - - = - (0.056) x 0.3 = -0.016302 (0.056) x 0.3 = -0.016035 (0.056) x (55.1) = 3.062489 (0.056) x (55.1) = 3.06385 (0.389) x (1.884) = 0.732767 (0.389) x -1.913 = 0.74404

M4 = 3.8 M4 = 3.8

(53.3) = (53.3) (53.3) = (53.3) (0.500) x 3.8 = -1.889477 (0.500) x 3.8 = -1.895928

M5 (55.1) M5 (55.2)

- = - - = - (0.031) x (0.1) = 0.002487 (0.031) x (0.1) = 0.003392

M6 0.0 M6 0.0

- = - - = - (0.031) x 0.0 = -7.8E-005 (0.031) x 0.0 = -0.000106 (0.031) x 0.6 = -0.017329 (0.031) x 0.6 = -0.017494 (0.219) x 0.21 = -0.045576 (0.219) x 0.23 = -0.050159 (0.219) x 1.97 = -0.045576 (0.219) x 1.99 = -0.050159

M7 = (0.1) M7 = (0.1)

- = - - = - (0.031) x (0.1) = 0.003392 (0.031) x (0.1) = 0.003685 (0.219) x (1.5) = 0.330585 (0.219) x (1.5) = 0.331637 (0.031) x 0.7 = -0.021603 (0.031) x 0.7 = -0.021729 (0.219) x (1.131) = 0.247446 (0.219) x -1.134 = 0.248027

M8 = 0.6 M8 = 0.6

- = - - = - (0.031) x (0.1) = 0.001933 (0.031) x (0.0) = 0.00136 (0.031) x 0.6 = -0.017494 (0.031) x 0.6 = -0.017551 (0.219) x (1.18) = 0.25904 (0.219) x (1.14) = 0.249701 (0.219) x (2.07) = 0.451841 (0.219) x (2.06) = 0.451707

M9 = 0.7 M9 = 0.7

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.7 = -0.023177 (0.033) x 0.7 = -0.022841 (0.233) x 0.4 = -0.09609 (0.233) x 0.4 = -0.094711 (0.233) x 10.36 = -2.417289 (0.233) x 10.35 = -2.415495

M10 (0.0) M10 (0.0)

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.2 = -0.007402 (0.033) x 0.3 = -0.008825 (0.233) x (1.4) = 0.338281 (0.233) x (1.4) = 0.337462 (0.233) x 4.34 = -1.011758 (0.233) x 4.34 = -1.011811

M11 1.8 M11 = 2

- = - - = - (0.031) x 1.8 = -0.05663 (0.031) x 1.8 = -0.056558 (0.031) x 0.3 = -0.008596 (0.031) x 0.3 = -0.008513 (0.219) x (0.7) = 0.155516 (0.219) x (0.7) = 0.157726 (0.219) x (0.8) = 0.174468 (0.219) x (0.8) = 0.175033

M12 = 0.3 M12 = 0.3

- = - - = - (0.031) x 1.6 = -0.050456 (0.031) x 1.6 = -0.051111 (0.031) x 0.3 = -0.008274 (0.031) x 0.3 = -0.008365 (0.219) x (0.7) = 0.145985 (0.219) x (0.6) = 0.136098 (0.219) x (0.8) = 0.185156 (0.219) x (0.8) = 0.184763

M13 = 0.3 M13 = 0.3

- = - - = - (0.031) x 0.3 = -0.008513 (0.031) x 0.3 = -0.008168 (0.031) x (33.6) = 1.050758 (0.031) x (33.6) = 1.051085 (0.219) x (1.20) = 0.261937 (0.219) x (1.2) = 0.266957 (0.219) x (1.51) 0.331364 (0.219) x (1.52) 0.333412

M14 1.6 M14 1.6

(32.8) = (32.8) (32.8) = (32.8) (0.500) x 1.6 = -0.817773 (0.500) x 1.6 = -0.821643

M15 (33.6) M15 (33.6)

- = - - = - (0.500) x (0.5) = 0.261213 (0.500) x (0.5) = 0.272686

M16 = 0.3 M16 = 0.3

- = - - = - (0.027) x 0.0 = -0.000205 (0.027) x 0.1 = -0.001421 (0.446) x 0.3 = -0.116557 (0.446) x 0.3 = -0.121677 (0.446) x 1.0 = -0.42861 (0.446) x 1.0 = -0.432063

M17 = (0.5) M17 = (0.6)

- = - - = - (0.027) x (0.5) = 0.014666 (0.027) x (0.6) = 0.01493 (0.223) x (0.1) = 0.027346 (0.223) x (0.1) = 0.027922 (0.027) x (0.40) = 0.010827 (0.027) x (0.41) = 0.011123

M18 = 0.1 M18 0.1

- = - - = - (0.027) x 0.1 = -0.001421 (0.027) x 0.1 = -0.001452 (0.027) x 5.0 = -0.134761 (0.027) x 5.0 = -0.134767 (0.027) x (0.41) = 0.011032 (0.027) x (0.41) = 0.010954

M19 = (0.1) M19 (0.1)

5.0 = 5.0 5.0 = 5.0 (0.027) x (0.1) = 0.003366 (0.027) x (0.1) = 0.003369 (0.027) x 1.14 = -0.030581 (0.027) x 1.13 = -0.030519

M20 = 5.0 M20 = 5.0

Dari put 4 Ke Put 5Dari put 5 Ke Put 6

-1.804688 = -1.80 -1.804688 = -1.80

(0.38) x 12.1 = -4.54 (0.38) x 12.1 = -4.54

(0.38) x 0.4 = -0.16 (0.38) x 0.4 = -0.16

(0.38) x 0.9 = -0.32 (0.38) x 0.9 = -0.32

(0.38) x 3.7 = -1.38 (0.38) x 3.8 = -1.42= -8.2 = -8.3

-1.40625 = -1.41 -1.40625 = -1.41

(0.38) x 1.5 = -0.57 (0.38) x 1.2 = -0.46

(0.38) x 0.8 = -0.31 (0.38) x 0.8 = -0.31

(0.38) x 1.0 = -0.36 (0.38) x 1.0 = -0.36

(0.38) x 1.8 = -0.66 (0.38) x 1.8 = -0.66= -3.3 = -3.2

-0.675 = -0.68 -0.675 = -0.68

(0.38) x 1.1 = -0.43 (0.38) x 1.1 = -0.43

(0.38) x 0.3 = -0.12 (0.38) x 0.3 = -0.12

(0.38) x 0.1 = -0.05 (0.38) x 0.1 = -0.05

(0.38) x 6.8 = -2.56 (0.38) x 6.8 = -2.56= -3.8 = -3.8

11.3 = 11.3 11.3 = 11.3 11.3 (0.063) x (0.3) = 0.016266 (0.063) x (0.3) = 0.015999 (0.063) (0.438) x (1.8) = 0.807057 (0.438) x (1.8) = 0.806631 (0.438)

MI 12.2 MI 12.2

- = - - = - - (0.056) x 12.2 = -0.675291 (0.056) x 12.2 = -0.675252 (0.056) (0.056) x 0.3 = -0.016035 (0.056) x 0.287 = -0.015943 (0.056) (0.389) x (1.12) = 0.435349 (0.389) x (1.12) = 0.43619 (0.389)

M2 = (0.256) M2 = (0.3)

- = - - = - - (0.056) x (0.3) = 0.014221 (0.056) x (0.3) = 0.014167 (0.056) (0.056) x 3.8 = -0.210659 (0.056) x 3.8 = -0.210886 (0.056) (0.389) x (1.24) = 0.483415 (0.389) x (1.23) = 0.477508 (0.389)

M3 = 0.3 M3 = 0.3

- = - - = - - (0.056) x 0.287 = -0.015943 (0.056) x 0.3 = -0.015599 (0.056) (0.056) x (55.2) = 3.064208 (0.056) x (55.2) = 3.064322 (0.056) (0.389) x (1.923) = 0.74768 (0.389) x (2.310) = 0.898253 (0.389)

M4 = 3.8 M4 = 3.9

(53.3) = (53.3) (53.3) = (53.3) (53.3) (0.500) x 3.8 = -1.897972 (0.500) x 3.9 = -1.973488 (0.500)

M5 (55.2) M5 = (55.2)

- = - - = - - (0.031) x (0.1) = 0.003685 (0.031) x (0.5) = 0.015785 (0.031)

M6 0.0 M6 = 0.0

- = - - = - - (0.031) x 0.0 = -0.000115 (0.031) x 0.0 = -0.000493 (0.031) (0.031) x 0.6 = -0.017551 (0.031) x 0.6 = -0.018025 (0.031) (0.219) x 0.24 = -0.051851 (0.219) x 0.32 = -0.0709 (0.219) (0.219) x 1.99 = -0.435588 (0.219) x 2.14 = -0.0709 (0.219)

M7 = (0.5) M7 = (0.2)

- = - - = - - (0.031) x (0.5) = 0.015785 (0.031) x (0.2) = 0.00501 (0.031) (0.219) x (1.5) = 0.331999 (0.219) x (1.5) = 0.333353 (0.219) (0.031) x 0.7 = -0.021413 (0.031) x 0.68 = -0.021345 (0.031) (0.219) x (1.145) = 0.250439 (0.219) x (1.149) = 0.251279 (0.219)

M8 = 0.6 M8 = 0.6

- = - - = - - (0.031) x (0.0) = 0.00125 (0.031) x (0.0) = 0.00122 (0.031) (0.031) x 0.6 = -0.018025 (0.031) x 0.6 = -0.017759 (0.031) (0.219) x (1.14) = 0.249061 (0.219) x (1.14) = 0.248874 (0.219) (0.219) x (2.06) = 0.45077 (0.219) x (2.06) = 0.450558 (0.219)

M9 = 0.7 M9 = 0.7

2.5 = 2.5 2.5 = 2.5 2.5 (0.033) x 0.7 = -0.022769 (0.033) x 0.7 = -0.022763 (0.033) (0.233) x 0.4 = -0.094175 (0.233) x 0.4 = -0.094096 (0.233) (0.233) x 10.35 = -2.415128 (0.233) x 10.35 = -2.414966 (0.233)

M10 = (0.0) M10 = (0.0)

2.5 = 2.5 2.5 = 2.5 2.5 (0.033) x 0.3 = -0.008923 (0.033) x 0.3 = -0.008951 (0.033) (0.233) x (1.4) = 0.337234 (0.233) x (1.4) = 0.337177 (0.233) (0.233) x 4.34 = -1.011826 (0.233) x 4.34 = -1.011829 (0.233)

M11 = 1.8 M11 = 1.8

- = - - = - - (0.031) x 1.8 = -0.056547 (0.031) x 1.8 = -0.056545 (0.031) (0.031) x 0.3 = -0.008168 (0.031) x 0.3 = -0.008048 (0.031) (0.219) x (0.7) = 0.158199 (0.219) x (0.7) = 0.158234 (0.219) (0.219) x (0.8) = 0.175058 (0.219) x (0.8) = 0.175071 (0.219)

M12 = 0.3 M12 = 0.3

- = - - = - - (0.031) x 1.6 = -0.051353 (0.031) x 1.7 = -0.054074 (0.031) (0.031) x 0.3 = -0.008392 (0.031) x 0.3 = -0.008397 (0.031) (0.219) x (0.6) = 0.135849 (0.219) x (0.6) = 0.135579 (0.219) (0.219) x (0.8) = 0.18144 (0.219) x (0.8) = 0.183302 (0.219)

M13 = 0.3 M13 = 0.3

- = - - = - - (0.031) x 0.3 = -0.008048 (0.031) x 0.3 = -0.008013 (0.031) (0.031) x (34) = 1.051206 (0.031) x (34) = 1.052567 (0.031) (0.219) x (1.23) = 0.269098 (0.219) x (1.27) = 0.278082 (0.219) (0.219) x (1.91) = 0.418109 (0.219) x (1.57) 0.342687 (0.219)

M14 = 1.7 M14 1.7

(32.8) = (32.8) (32.8) = (32.8) (32.8) (0.500) x 1.7 = -0.865182 (0.500) x 1.7 = -0.832661 (0.500)

M15 = (33.7) M15 = (33.6)

- = - - = - - (0.500) x (0.6) = 0.277581 (0.500) x (0.6) = 0.298116 (0.500)

M16 = 0.3 M16 = 0.3

- = - - = - - (0.027) x 0.1 = -0.001452 (0.027) x 0.1 = -0.001485 (0.027) (0.446) x 0.3 = -0.123861 (0.446) x 0.3 = -0.133024 (0.446) (0.446) x 1.1 = -0.47092 (0.446) x 1.0 = -0.441897 (0.446)

M17 = (0.6) M17 = (0.6)

- = - - = - - (0.027) x (0.6) = 0.016034 (0.027) x (0.6) = 0.015501 (0.027) (0.223) x (0.1) = 0.027948 (0.223) x (0.1) = 0.02796 (0.223) (0.027) x (0.42) = 0.011226 (0.027) x (0.42) = 0.011257 (0.027)

M18 0.1 M18 0.1

- = - - = - - (0.027) x 0.1 = -0.001485 (0.027) x 0.1 = -0.001472 (0.027) (0.027) x 5.0 = -0.134769 (0.027) x 5.0 = -0.134769 (0.027) (0.027) x (0.41) = 0.010931 (0.027) x (0.41) = 0.010926 (0.027)

M19 = (0.1) M19 = (0.1)

5.0 = 5.0 5.0 = 5.0 5.0 (0.027) x (0.1) = 0.00337 (0.027) x (0.1) = 0.00337 (0.027) (0.027) x 1.13 = -0.03051 (0.027) x 1.13 = -0.030508 (0.027)

M20 = 5.0 M20 = 5.0

-1.804688 = -1.80 -1.804688 = -1.80 -1.804688

(0.38) x 12.1 = -4.54 (0.38) x 12.1 = -4.54 (0.38)

(0.38) x 0.4 = -0.16 (0.38) x 0.4 = -0.16 (0.38)

(0.38) x 0.8 = -0.32 (0.38) x 0.8 = -0.32 (0.38)

(0.38) x 3.8 = -1.42 (0.38) x 3.7 = -1.38 (0.38)= -8.2 = -8.2

-1.40625 = -1.41 -1.40625 = -1.41 -1.40625

(0.38) x 1.5 = -0.56 (0.38) x 1.5 = -0.57 (0.38)

(0.38) x 0.8 = -0.31 (0.38) x 0.8 = -0.31 (0.38)

(0.38) x 1.0 = -0.36 (0.38) x 1.0 = -0.36 (0.38)

(0.38) x 1.8 = -0.66 (0.38) x 1.8 = -0.66 (0.38)= -3.3 = -3.3

-0.675 = -0.68 -0.675 = -0.68 -0.675

(0.38) x 1.1 = -0.41 (0.38) x 1.1 = -0.41 (0.38)

(0.38) x 0.3 = -0.12 (0.38) x 0.3 = -0.12 (0.38)

(0.38) x 0.1 = -0.05 (0.38) x 0.1 = -0.05 (0.38)

(0.38) x 6.8 = -2.56 (0.38) x 6.8 = -2.56 (0.38)= -3.8 = -3.8

Putaran 8Putaran 9

= 11.3 11.3 = 11.3 11.3 x (0.3) = 0.015938 (0.063) x (0.3) = 0.015912 (0.063) x x (1.8) = 0.806523 (0.438) x (1.8) = 0.806494 (0.438) x

MI = 12.2 MI 12.2

= - - = - - x 12.2 = -0.675243 (0.056) x 12.2 = -0.67524 (0.056) x x 0.3 = -0.015599 (0.056) x 0.3 = -0.015316 (0.056) xx (1.12) = 0.436254 (0.389) x (1.12) = 0.436312 (0.389) x

M2 = (0.3) M2 (0.3)

= - - = - - x (0.3) = 0.014144 (0.056) x (0.3) = 0.014125 (0.056) x x 3.9 = -0.219276 (0.056) x 3.8 = -0.212076 (0.056) xx (1.24) = 0.480819 (0.389) x (1.24) = 0.480639 (0.389) x

M3 = 0.3 M3 = 0.3

= - - = - - x 0.3 = -0.015316 (0.056) x 0.3 = -0.015705 (0.056) x x (55.2) = 3.068517 (0.056) x (55.2) = 3.064917 (0.056) x x (1.965) = 0.764169 (0.389) x (1.936) = 0.752869 (0.389) x

M4 = 3.8 M4 = 3.8

= (53.3) (53.3) = (53.3) (53.3) x 3.8 = -1.908685 (0.500) x 3.8 = -1.90104 (0.500) x

M5 (55.2) M5 (55.2)

= - - = - - x (0.2) = 0.00501 (0.031) x (0.1) = 0.004102 (0.031) x

M6 0.0 M6 0.0

= - - = - - x 0.0 = -0.000157 (0.031) x 0.0 = -0.000128 (0.031) x x 0.6 = -0.017759 (0.031) x 0.6 = -0.017774 (0.031) xx 0.26 = -0.056672 (0.219) x 0.25 = -0.054097 (0.219) xx 2.01 = -0.056672 (0.219) x 2.00 = -0.054097 (0.219) x

M7 = (0.1) M7 = (0.1)

= - - = - - x (0.1) = 0.004102 (0.031) x (0.1) = 0.00394 (0.031) x x (1.5) = 0.334469 (0.219) x (1.5) = 0.332937 (0.219) xx 0.68 = -0.02134 (0.031) x 0.68 = -0.021336 (0.031) xx (1.150) = 0.251527 (0.219) x (1.148) = 0.251082 (0.219) x

M8 = 0.6 M8 = 0.6

= - - = - - x (0.0) = 0.001212 (0.031) x (0.0) = 0.00121 (0.031) x x 0.6 = -0.017774 (0.031) x 0.6 = -0.017707 (0.031) xx (1.14) = 0.248836 (0.219) x (1.14) = 0.248822 (0.219) xx (2.06) = 0.450467 (0.219) x (2.06) = 0.450391 (0.219) x

M9 = 0.7 M9 = 0.7

= 2.5 2.5 = 2.5 2.5 x 0.7 = -0.022758 (0.033) x 0.7 = -0.022757 (0.033) x x 0.4 = -0.094075 (0.233) x 0.4 = -0.09407 (0.233) xx 10.35 = -2.414927 (0.233) x 10.35 = -2.414914 (0.233) x

M10 = (0.0) M10 = (0.0)

= 2.5 2.5 = 2.5 2.5 x 0.3 = -0.008957 (0.033) x 0.3 = -0.008959 (0.033) x x (1.4) = 0.337161 (0.233) x (1.4) = 0.337157 (0.233) xx 4.34 = -1.011829 (0.233) x 4.34 = -1.01183 (0.233) x

M11 = 1.8 M11 = 1.8

= - - = - - x 1.8 = -0.056544 (0.031) x 1.8 = -0.056544 (0.031) x x 0.3 = -0.008013 (0.031) x 0.3 = -0.008076 (0.031) x x (0.7) = 0.158267 (0.219) x (0.7) = 0.158273 (0.219) x x (0.8) = 0.175069 (0.219) x (0.8) = 0.175067 (0.219) x

M12 = 0.3 M12 = 0.3

= - - = - - x 1.7 = -0.052041 (0.031) x 1.7 = -0.051673 (0.031) x x 0.3 = -0.008399 (0.031) x 0.3 = -0.008398 (0.031) x x (0.6) = 0.135687 (0.219) x (0.6) = 0.135756 (0.219) x x (0.8) = 0.183201 (0.219) x (0.8) = 0.183668 (0.219) x

M13 0.3 M13 = 0.3

= - - = - - x 0.3 = -0.008076 (0.031) x 0.3 = -0.008105 (0.031) x x (34) = 1.05155 (0.031) x (34) = 1.051366 (0.031) xx (1.25) = 0.273745 (0.219) x (1.24) = 0.271625 (0.219) xx (1.54) 0.33633 (0.219) x (1.53) 0.335201 (0.219) x

M14 1.7 M14 1.7

= (32.8) (32.8) = (32.8) (32.8) x 1.7 = -0.826775 (0.500) x 1.7 = -0.825044 (0.500) x

M15 (33.6) M15 (33.6)

= - - = - - x (0.6) = 0.288203 (0.500) x (0.6) = 0.283358 (0.500) x

M16 0.3 M16 0.3

= - - = - - x 0.1 = -0.001472 (0.027) x 0.1 = -0.001463 (0.027) x x 0.3 = -0.1286 (0.446) x 0.3 = -0.126438 (0.446) xx 1.0 = -0.436643 (0.446) x 1.0 = -0.435099 (0.446) x

M17 = (0.6) M17 = (0.6)

= - - = - - x (0.6) = 0.01524 (0.027) x (0.6) = 0.01514 (0.027) x x (0.1) = 0.027959 (0.223) x (0.1) = 0.027957 (0.223) xx (0.42) = 0.011202 (0.027) x (0.42) = 0.011178 (0.027) x

M18 0.1 M18 = 0.1

= - - = - - x 0.1 = -0.001463 (0.027) x 0.1 = -0.00146 (0.027) x x 5.0 = -0.134769 (0.027) x 5.0 = -0.134769 (0.027) xx (0.41) = 0.010924 (0.027) x (0.41) = 0.010926 (0.027) x

M19 (0.1) M19 = (0.1)

= 5.0 5.0 = 5.0 5.0 x (0.1) = 0.00337 (0.027) x (0.1) = 0.00337 (0.027) x x 1.13 = -0.030507 (0.027) x 1.13 = -0.030507 (0.027) x

M20 5.0 M20 = 5.0

= -1.80 -1.804688 = -1.80 -1.804688

x 12.1 = -4.54 (0.38) x 12.1 = -4.54 (0.38)

x 0.4 = -0.16 (0.38) x 0.4 = -0.16 (0.38)

x 0.8 = -0.32 (0.38) x 0.9 = -0.32 (0.38)

x 3.7 = -1.38 (0.38) x 3.7 = -1.38 (0.38)= -8.2 = -8.2

= -1.41 -1.40625 = -1.41 -1.40625

x 1.5 = -0.57 (0.38) x 1.5 = -0.57 (0.38)

x 0.8 = -0.31 (0.38) x 0.8 = -0.31 (0.38)

x 1.0 = -0.36 (0.38) x 1.0 = -0.36 (0.38)

x 1.8 = -0.66 (0.38) x 1.8 = -0.66 (0.38)= -3.3 = -3.3

= -0.68 -0.675 = -0.68 -0.675

x 1.1 = -0.41 (0.38) x 1.1 = -0.41 (0.38)

x 0.3 = -0.12 (0.38) x 0.3 = -0.12 (0.38)

x 0.1 = -0.05 (0.38) x 0.1 = -0.05 (0.38)

x 6.8 = -2.56 (0.38) x 6.8 = -2.56 (0.38)= -3.8 = -3.8

= 11.3 11.3 = 11.3 11.3 (0.3) = 0.01589 (0.063) x (0.3) = 0.015914 (0.063) x (1.8) = 0.806486 (0.438) x (1.8) = 0.806484 (0.438) xMI 12.2 MI 12.2

= - - = - - 12.2 = -0.675238 (0.056) x 12.2 = -0.67524 (0.056) x 0.3 = -0.015705 (0.056) x 0.3 = -0.015799 (0.056) x (1.12) = 0.436322 (0.389) x (1.12) = 0.436278 (0.389) xM2 (0.3) M2 (0.3)

= - - = - - (0.3) = 0.014146 (0.056) x (0.3) = 0.014153 (0.056) x 3.8 = -0.211227 (0.056) x 3.8 = -0.211086 (0.056) x (1.24) = 0.481469 (0.389) x (1.24) = 0.48171 (0.389) xM3 0.3 M3 0.3

= - - = - - 0.3 = -0.015799 (0.056) x 0.3 = -0.015821 (0.056) x (55.2) = 3.064492 (0.056) x (55.2) = 3.064422 (0.056) x (1.931) = 0.75086 (0.389) x (1.929) = 0.750243 (0.389) x M4 = 3.8 M4 = 3.8

= (53.3) (53.3) = (53.3) (53.3) 3.8 = -1.899777 (0.500) x 3.8 = -1.899422 (0.500) x M5 (55.2) M5 = (55.2)

= - - = - - (0.1) = 0.00394 (0.031) x (0.1) = 0.003891 (0.031) x

M6 0.0 M6 = 0.0

= - - = - - 0.0 = -0.000123 (0.031) x 0.0 = -0.000122 (0.031) x 0.6 = -0.017707 (0.031) x 0.6 = -0.017688 (0.031) x 0.24 = -0.053339 (0.219) x 0.24 = -0.053072 (0.219) x 1.99 -0.053339 (0.219) x 1.99 -0.053072 (0.219) x

M7 (0.1) M7 (0.1)

= - - = - - (0.1) = 0.003891 (0.031) x (0.1) = 0.003874 (0.031) x (1.5) = 0.332566 (0.219) x (1.5) = 0.33248 (0.219) x 0.68 = -0.021335 (0.031) x 0.68 = -0.021338 (0.031) x (1.147) = 0.250884 (0.219) x (1.147) = 0.250824 (0.219) x

M8 = 0.6 M8 = 0.6

= - - = - - (0.0) = 0.00121 (0.031) x (0.0) = 0.00121 (0.031) x 0.6 = -0.017688 (0.031) x 0.6 = -0.017682 (0.031) x (1.14) = 0.248835 (0.219) x (1.14) = 0.248847 (0.219) x (2.06) = 0.450474 (0.219) x (2.06) = 0.450504 (0.219) x

M9 = 0.7 M9 = 0.7

= 2.5 2.5 = 2.5 2.5 0.7 = -0.022761 (0.033) x 0.7 = -0.022763 (0.033) x 0.4 = -0.094068 (0.233) x 0.4 = -0.094069 (0.233) x 10.35 = -2.414907 (0.233) x 10.35 = -2.414912 (0.233) x

M10 = (0.0) M10 = (0.0)

= 2.5 2.5 = 2.5 2.5 0.3 = -0.008957 (0.033) x 0.3 = -0.008956 (0.033) x (1.4) = 0.337156 (0.233) x (1.4) = 0.337158 (0.233) x 4.34 = -1.01183 (0.233) x 4.34 = -1.011829 (0.233) x

M11 = 1.8 M11 = 1.8

= - - = - - 1.8 = -0.056544 (0.031) x 1.8 = -0.056544 (0.031) x 0.3 = -0.008105 (0.031) x 0.3 = -0.008113 (0.031) x (0.7) = 0.158248 (0.219) x (0.7) = 0.158238 (0.219) x (0.8) = 0.175066 (0.219) x (0.8) = 0.175066 (0.219) x

M12 = 0.3 M12 = 0.3

= - - = - - 1.7 = -0.051565 (0.031) x 1.6 = -0.051527 (0.031) x 0.3 = -0.008396 (0.031) x 0.3 = -0.008395 (0.031) x (0.6) = 0.135784 (0.219) x (0.6) = 0.135793 (0.219) x (0.8) = 0.183804 (0.219) x (0.8) = 0.18384 (0.219) x

M13 = 0.3 M13 = 0.3

= - - = - - 0.3 = -0.008113 (0.031) x 0.3 = -0.008116 (0.031) x (34) = 1.051312 (0.031) x (34) = 1.051293 (0.031) x (1.24) = 0.270813 (0.219) x (1.24) = 0.270511 (0.219) x (1.53) = 0.334854 (0.219) x (1.53) 0.334732 (0.219) x

M14 = 1.6 M14 1.6

= (32.8) (32.8) = (32.8) (32.8) 1.6 = -0.824433 (0.500) x 1.6 = -0.82421 (0.500) x

M15 (33.6) M15 (33.6)

= - - = - - (0.6) = 0.2815 (0.500) x (0.6) = 0.280811 (0.500) x

M16 0.3 M16 0.3

= - - = - - 0.1 = -0.00146 (0.027) x 0.1 = -0.001458 (0.027) x 0.3 = -0.12561 (0.446) x 0.3 = -0.125302 (0.446) x 1.0 = -0.434553 (0.446) x 1.0 = -0.434355 (0.446) x

M17 = (0.6) M17 = (0.6)

= - - = - - (0.6) = 0.015103 (0.027) x (0.6) = 0.01509 (0.027) x (0.1) = 0.027956 (0.223) x (0.1) = 0.027955 (0.223) x (0.42) = 0.01117 (0.027) x (0.42) = 0.011168 (0.027) x

M18 0.1 M18 0.1

= - - = - - 0.1 = -0.001458 (0.027) x 0.1 = -0.001458 (0.027) x 5.0 = -0.134769 (0.027) x 5.0 = -0.134769 (0.027) x (0.41) = 0.010927 (0.027) x (0.41) = 0.010928 (0.027) x

M19 (0.1) M19 (0.1)

= 5.0 5.0 = 5.0 5.0 (0.1) = 0.00337 (0.027) x (0.1) = 0.00337 (0.027) x 1.13 = -0.030507 (0.027) x 1.13 = -0.030507 (0.027) x

M20 5.0 M20 5.0

= -1.80 -1.804688 = -1.80

x 12.1 = -4.54 (0.38) x 12.1 = -4.54

x 0.4 = -0.16 (0.38) x 0.4 = -0.16

x 0.9 = -0.32 (0.38) x 0.9 = -0.32

3.7 = -1.38 (0.38) x 3.7 = -1.38= -8.2 = -8.2

= -1.41 -1.40625 = -1.41

x 1.5 = -0.57 (0.38) x 1.5 = -0.57

x 0.8 = -0.31 (0.38) x 0.8 = -0.31

x 1.0 = -0.36 (0.38) x 1.0 = -0.36

1.8 = -0.66 (0.38) x 1.8 = -0.66= -3.3 = -3.3

= -0.68 -0.675 = -0.68

x 1.1 = -0.41 (0.38) x 1.1 = -0.41

x 0.3 = -0.12 (0.38) x 0.3 = -0.12

x 0.1 = -0.05 (0.38) x 0.1 = -0.05

x 6.8 = -2.56 (0.38) x 6.8 = -2.56= -3.8 = -3.8

= 11.3 11.3 = 11.3 11.3 (0.3) = 0.0159225673 (0.063) x (0.3) = 0.015925115 (0.063) (1.8) = 0.8064869417 (0.438) x (1.8) = 0.806488708 (0.438)MI 12.2 MI 12.2

= - - = - - 12.2 = -0.67524016 (0.056) x 12.2 = -0.6752404 (0.056) 0.3 = -0.015820939 (0.056) x 0.3 = -0.015826831 (0.056) (1.12) = 0.4362592614 (0.389) x (1.12) = 0.436253439 (0.389)M2 (0.3) M2 (0.3)

= - - = - - (0.3) = 0.0141556576 (0.056) x (0.3) = 0.014156322 (0.056) 3.8 = -0.21104691 (0.056) x 3.8 = -0.211033485 (0.056) (1.24) = 0.4817742111 (0.389) x (1.24) = 0.481793477 (0.389)M3 = 0.3 M3 0.3

= - - = - - 0.3 = -0.015826831 (0.056) x 0.3 = -0.015829 (0.056) (55.2) = 3.0644025524 (0.056) x (55.2) = 3.064396 (0.056) (1.929) = 0.7500270019 (0.389) x (1.928) = 0.749949 (0.389)M4 = 3.8 M4 3.8

= (53.3) (53.3) = (53.3) (53.3) 3.8 = -1.899301362 (0.500) x 3.8 = -1.899258139 (0.500)M5 (55.2) M5 (55.2)

= - - = - - (0.1) = 0.0038735426 (0.031) x (0.1) = 0.003867284 (0.031)

M6 0.0 M6 0.0

= - - = - - 0.0 = -0.000121 (0.031) x 0.0 = -0.000121 (0.031) 0.6 = -0.017682 (0.031) x 0.6 = -0.017681 (0.031) 0.24 = -0.052975 (0.219) x 0.24 = -0.052939 (0.219) 1.99 -0.052975 (0.219) x 1.99 -0.052939 (0.219)

M7 (0.1) M7 (0.1)

= - - = - - (0.1) = 0.003867 (0.031) x (0.1) = 0.003865 (0.031) (1.5) = 0.332457 (0.219) x (1.5) = 0.332450 (0.219) 0.68 = -0.021340 (0.031) x 0.68 = -0.021340 (0.031) (1.147) = 0.250805 (0.219) x (1.147) = 0.250799 (0.219)

M8 = 0.6 M8 = 0.6

= - - = - - (0.0) = 0.001210 (0.031) x (0.0) = 0.001210 (0.031) 0.6 = -0.017681 (0.031) x 0.6 = -0.017680 (0.031) (1.14) = 0.248851 (0.219) x (1.14) = 0.248851 (0.219) (2.06) = 0.450513 (0.219) x (2.06) = 0.450516 (0.219)

M9 = 0.7 M9 = 0.7

= 2.5 2.5 = 2.5 2.5 0.7 = -0.022763 (0.033) x 0.7 = -0.022763 (0.033) 0.4 = -0.094069 (0.233) x 0.4 = -0.094070 (0.233) 10.35 = -2.414915 (0.233) x 10.35 = -2.414916 (0.233)

M10 (0.0) M10 (0.0)

= 2.5 2.5 = 2.5 2.5 0.3 = -0.008955 (0.033) x 0.3 = -0.008955 (0.033) (1.4) = 0.337159 (0.233) x (1.4) = 0.337159 (0.233) 4.34 = -1.011829 (0.233) x 4.34 = -1.011829 (0.233)

M11 = 1.8 M11 1.8

= - - = - - 1.8 = -0.056544 (0.031) x 1.8 = -0.056544 (0.031) 0.3 = -0.008116 (0.031) x 0.3 = -0.008117 (0.031) (0.7) = 0.158238 (0.219) x (0.7) = 0.158234 (0.219) (0.8) = 0.175065 (0.219) x (0.8) = 0.175065 (0.219)

M12 = 0.3 M12 = 0.3

= - - = - - 1.6 = -0.051513 (0.031) x 1.6 = -0.051508 (0.031) 0.3 = -0.008395 (0.031) x 0.3 = -0.008395 (0.031) (0.6) = 0.135797 (0.219) x (0.6) = 0.135798 (0.219) (0.8) = 0.183851 (0.219) x (0.8) = 0.183854 (0.219)

M13 = 0.3 M13 = 0.3

= - - = - - 0.3 = -0.008117 (0.031) x 0.3 = -0.008117 (0.031) (34) = 1.051286 (0.031) x (34) = 1.051284 (0.031) (1.24) = 0.2704002772 (0.219) x (1.24) = 0.270375 (0.219) (1.53) 0.3346881782 (0.219) x (1.53) 0.334672 (0.219)

M14 1.6 M14 1.6

= (32.8) (32.8) = (32.8) (32.8) 1.6 = -0.824128943 (0.500) x 1.6 = -0.824107 (0.500)

M15 (33.6) M15 (33.6)

= - - = - - (0.6) = 0.2805577765 (0.500) x (0.6) = 0.280501 (0.500)

M16 0.3 M16 0.3

= - - = - - 0.1 = -0.001457927 (0.027) x 0.1 = -0.001458 (0.027) 0.3 = -0.125189127 (0.446) x 0.3 = -0.125164 (0.446) 1.0 = -0.434354937 (0.446) x 1.0 = -0.434263 (0.446)

M17 = (0.6) M17 = (0.6)

= - - = - - (0.6) = 0.0150867069 (0.027) x (0.6) = 0.015083549 (0.027) (0.1) = 0.0279551852 (0.223) x (0.1) = 0.027955143 (0.223) (0.42) = 0.0111673645 (0.027) x (0.42) = 0.0111671042 (0.027)

M18 0.1 M18 0.1

= - - = - - 0.1 = -0.001457819 (0.027) x 0.1 = -0.001457726 (0.027) 5.0 = -0.134769048 (0.027) x 5.0 = -0.134769047 (0.027) (0.41) = 0.0109279234 (0.027) x (0.41) = 0.01092806 (0.027)

M19 (0.1) M19 (0.1)

= 5.0 5.0 = 5.0 5.0 (0.1) = 0.0033695931 (0.027) x (0.1) = 0.003369587 (0.027) 1.13 = -0.030506946 (0.027) x 1.13 = -0.030506958 (0.027)

M20 5.0 M20 5.0

-1.804688 = -1.80 -1.804688 = -1.80

(0.38) x 12.1 = -4.54 (0.38) x 12.1 = -4.54

(0.38) x 0.4 = -0.16 (0.38) x 0.4 = -0.16

(0.38) x 0.9 = -0.32 (0.38) x 0.9 = -0.32

(0.38) x 3.7 = -1.38 (0.38) x 3.7 = -1.38= -8.2 = -8.2

-1.40625 = -1.41 -1.40625 = -1.41

(0.38) x 1.5 = -0.57 (0.38) x 1.5 = -0.57

(0.38) x 0.8 = -0.31 (0.38) x 0.8 = -0.31

(0.38) x 1.0 = -0.36 (0.38) x 1.0 = -0.36

(0.38) x 1.8 = -0.66 (0.38) x 1.8 = -0.66= -3.3 = -3.3

-0.675 = -0.68 -0.675 = -0.68

(0.38) x 1.1 = -0.41 (0.38) x 1.1 = -0.41

(0.38) x 0.3 = -0.12 (0.38) x 0.3 = -0.12

(0.38) x 0.1 = -0.05 (0.38) x 0.1 = -0.05

(0.38) x 6.8 = -2.56 (0.38) x 6.8 = -2.56= -3.8 = -3.8

Putaran 14

= 11.3 11.3 = 11.3 x (0.3) = 0.015925862 (0.063) x (0.3) = 0.0159260772x (1.8) = 0.806489371 (0.438) x (1.8) = 0.8064895924

MI 12.2 MI 12.2

= - - = - x 12.2 = -0.6752404781 (0.056) x 12.2 = -0.6752405023x 0.3 = -0.0158286841 (0.056) x 0.3 = -0.0158293129x (1.12) = 0.4362519273 (0.389) x (1.12) = 0.4362511198

M2 (0.3) M2 (0.3)

= - - = - x (0.3) = 0.0141565131 (0.056) x (0.3) = 0.0141565942x 3.8 = -0.2110286821 (0.056) x 3.8 = -0.2110269396x (1.24) = 0.4817998012 (0.389) x (1.24) = 0.4818018735

M3 0.3 M3 0.3

= - - = - x 0.3 = -0.0158293129 (0.056) x 0.3 = -0.0158295293 x (55.2) = 3.0643934383 (0.056) x (55.2) = 3.064392567 x (1.928) = 0.7499207877 (0.389) x (1.928) = 0.7499131406

M4 = 3.8 M4 = 3.8

= (53.3) (53.3) = (53.3) x 3.8 = -1.8992424565 (0.500) x 3.8 = -1.8992380891

M5 (55.2) M5 (55.2)

= - - = - x (0.1) = 0.0038650075 (0.031) x (0.1) = 0.003864393

M6 0.0 M6 0.0

= - - = - x 0.0 = -0.0001207815 (0.031) x 0.0 = -0.0001207623x 0.6 = -0.0176804289 (0.031) x 0.6 = -0.0176802624x 0.24 = -0.0529296827 (0.219) x 0.24 = -0.0529229501x 1.99 -0.0529296827 (0.219) x 1.99 -0.0529229501

M7 (0.1) M7 (0.1)

= - - = - x (0.1) = 0.0038644 (0.031) x (0.1) = 0.0038639664x (1.5) = 0.3324475 (0.219) x (1.5) = 0.3324466189x 0.68 = -0.0213405 (0.031) x 0.68 = -0.0213405908x (1.147) = 0.2507971 (0.219) x (1.146) = 0.2507963341

M8 0.6 M8 = 0.6

= - - = - x (0.0) = 0.001210 (0.031) x (0.0) = 0.0012099151x 0.6 = -0.017680 (0.031) x 0.6 = -0.0176801978x (1.14) = 0.248853 (0.219) x (1.14) = 0.2488527871x (2.06) = 0.450517 (0.219) x (2.06) = 0.4505169802

M9 = 0.7 M9 = 0.7

= 2.5 2.5 = 2.5 x 0.7 = -0.0227633 (0.033) x 0.7 = -0.0227633162x 0.4 = -0.0940699 (0.233) x 0.4 = -0.0940700112x 10.35 = -2.4149163 (0.233) x 10.35 = -2.4149163598

M10 (0.0) M10 (0.0)

= 2.5 2.5 = 2.5 x 0.3 = -0.0089546025 (0.033) x 0.3 = -0.0089545753x (1.4) = 0.3371590326 (0.233) x (1.4) = 0.3371590768x 4.34 = -1.0118294545 (0.233) x 4.34 = -1.0118294523

M11 1.8 M11 1.8

= - - = - x 1.8 = -0.0565439747 (0.031) x 1.8 = -0.056543977 x 0.3 = -0.0081171613 (0.031) x 0.3 = -0.0081172648 x (0.7) = 0.1582330518 (0.219) x (0.7) = 0.1582329252 x (0.8) = 0.1750653434 (0.219) x (0.8) = 0.1750653313

M12 = 0.3 M12 = 0.3

= - - = - x 1.6 = -0.0515066957 (0.031) x 1.6 = -0.0515057339 x 0.3 = -0.0083949143 (0.031) x 0.3 = -0.0083949067 x (0.6) = 0.1357987322 (0.219) x (0.6) = 0.1357989984 x (0.8) = 0.1838553507 (0.219) x (0.8) = 0.1838558031

M13 = 0.3 M13 = 0.3

= - - = - x 0.3 = -0.0081172648 (0.031) x 0.3 = -0.0081173175x (34) = 1.0512830679 (0.031) x (34) = 1.051282587x (1.24) = 0.2703497448 (0.219) x (1.24) = 0.2703409885x (1.53) 0.3346679384 (0.219) x (1.53) = 0.3346649523

M14 1.6 M14 1.6

= (32.8) (32.8) = (32.8) x 1.6 = -0.8240917432 (0.500) x 1.6 = -0.8240856052

M15 (33.6) M15 (33.6)

= - - = - x (0.6) = 0.2804422739 (0.500) x (0.6) = 0.2804222595

M16 0.3 M16 0.3

= - - = - x 0.1 = -0.0014577256 (0.027) x 0.1 = -0.0014576929x 0.3 = -0.1251375884 (0.446) x 0.3 = -0.1251286576x 1.0 = -0.4342492051 (0.446) x 1.0 = -0.4342437273

M17 = (0.6) M17 (0.6)

= - - = - x (0.6) = 0.0150824721 (0.027) x (0.6) = 0.0150820838x (0.1) = 0.0279550913 (0.223) x (0.1) = 0.027955079x (0.42) = 0.0111670152 (0.027) x (0.42) = 0.0111669698

M18 0.1 M18 0.1

= - - = - x 0.1 = -0.0014576929 (0.027) x 0.1 = -0.0014576809x 5.0 = -0.1347690464 (0.027) x 5.0 = -0.1347690462x (0.41) = 0.0109280817 (0.027) x (0.41) = 0.0109280882

M19 (0.1) M19 (0.1)

= 5.0 5.0 = 5.0 x (0.1) = 0.0033695854 (0.027) x (0.1) = 0.0033695849x 1.13 = -0.0305069663 (0.027) x 1.13 = -0.0305069683

M20 5.0 M20 5.0

-1.804688 = -1.80 -1.804688 = -1.80

(0.38) x 12.1 = -4.54 (0.38) x 12.1 = -4.54

(0.38) x 0.4 = -0.16 (0.38) x 0.4 = -0.16

(0.38) x 0.9 = -0.32 (0.38) x 0.9 = -0.32

(0.38) x 3.7 = -1.38 (0.38) x 3.7 = -1.38= -8.2 = -8.2

-1.40625 = -1.41 -1.40625 = -1.41

(0.38) x 1.5 = -0.57 (0.38) x 1.5 = -0.57

(0.38) x 0.8 = -0.31 (0.38) x 0.8 = -0.31

(0.38) x 1.0 = -0.36 (0.38) x 1.0 = -0.36

(0.38) x 1.8 = -0.66 (0.38) x 1.8 = -0.66= -3.3 = -3.3

-0.675 = -0.68 -0.675 = -0.68

(0.38) x 1.1 = -0.41 (0.38) x 1.1 = -0.41

(0.38) x 0.3 = -0.12 (0.38) x 0.3 = -0.12

(0.38) x 0.1 = -0.05 (0.38) x 0.1 = -0.05

(0.38) x 6.8 = -2.56 (0.38) x 6.8 = -2.56= -3.8 = -3.8

11.3 = 11.3 11.3 = 11.3 (0.063) x (0.3) = 0.0159261685 (0.063) x (0.3) = 0.015926197 (0.438) x (1.8) = 0.8064896752 (0.438) x (1.8) = 0.806489702

MI 12.2 MI 12.2

- = - - = - (0.056) x 12.2 = -0.675240512 (0.056) x 12.2 = -0.675240515 (0.056) x 0.3 = -0.0158295293 (0.056) x 0.3 = -0.015829602 (0.389) x (1.12) = 0.4362508949 (0.389) x (1.12) = 0.436250844

M2 (0.3) M2 (0.3)

- = - - = - (0.056) x (0.3) = 0.0141566192 (0.056) x (0.3) = 0.014156626 (0.056) x 3.8 = -0.2110264543 (0.056) x 3.8 = -0.211026142 (0.389) x (1.24) = 0.4818026778 (0.389) x (1.24) = 0.481803006

M3 0.3 M3 0.3

- = - - = - (0.056) x 0.3 = -0.0158296024 (0.056) x 0.3 = -0.015829638 (0.056) x (55.2) = 3.0643923244 (0.056) x (55.2) = 3.064392168 (0.389) x (1.928) = 0.7499078319 (0.389) x (1.928) = 0.749905713

M4 = 3.8 M4 = 3.8

(53.3) = (53.3) (53.3) = (53.3) (0.500) x 3.8 = -1.899235277 (0.500) x 3.8 = -1.899234121

M5 (55.2) M5 (55.2)

- = - - = - (0.031) x (0.1) = 0.0038639664 (0.031) x (0.1) = 0.003863796

M6 0.0 M6 0.0

- = - - = - (0.031) x 0.0 = -0.000120749 (0.031) x 0.0 = -0.000120744 (0.031) x 0.6 = -0.0176801978 (0.031) x 0.6 = -0.017680171 (0.219) x 0.24 = -0.0529202648 (0.219) x 0.24 = -0.052919266 (0.219) x 1.99 -0.0529202648 (0.219) x 1.99 -0.052919266

M7 (0.1) M7 (0.1)

- = - - = - (0.031) x (0.1) = 0.0038637961 (0.031) x (0.1) = 0.0038637 (0.219) x (1.5) = 0.3324463313 (0.219) x (1.5) = 0.3324462 (0.031) x 0.68 = -0.0213406089 (0.031) x 0.68 = -0.0213406 (0.219) (1.146) = 0.2507959648 (0.219) x (1.146) = 0.2507958

M8 = 0.6 M8 0.6

- = - - = - (0.031) x (0.0) = 0.001209921 (0.031) x (0.0) = 0.001209923 (0.031) x 0.6 = -0.0176801714 (0.031) x 0.6 = -0.01768016 (0.219) x (1.14) = 0.2488527871 (0.219) x (1.14) = 0.248852859 (0.219) x (2.06) = 0.4505170789 (0.219) x (2.06) = 0.450517107

M9 = 0.7 M9 = 0.7

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.7 = -0.0227633205 (0.033) x 0.7 = -0.022763324 (0.233) x 0.4 = -0.0940700284 (0.233) x 0.4 = -0.094070034 (0.233) x 10.35 = -2.4149164004 (0.233) x 10.35 = -2.414916413

M10 = (0.0) M10 = (0.0)

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.3 = -0.0089545672 (0.033) x 0.3 = -0.008954564 (0.233) x (1.4) = 0.3371590913 (0.233) x (1.4) = 0.337159096 (0.233) x 4.34 = -1.0118294517 (0.233) x 4.34 = -1.011829452

M11 = 1.8 M11 = 1.8

- = - - = - (0.031) x 1.8 = -0.0565439777 (0.031) x 1.8 = -0.056543978 (0.031) x 0.3 = -0.0081173175 (0.031) x 0.3 = -0.008117338 (0.219) x (0.7) = 0.1582328966 (0.219) x (0.7) = 0.158232872 (0.219) x (0.8) = 0.1750653272 (0.219) x (0.8) = 0.175065326

M12 = 0.3 M12 = 0.3

- = - - = - (0.031) x 1.6 = -0.0515053503 (0.031) x 1.6 = -0.051505208 (0.031) x 0.3 = -0.008394904 (0.031) x 0.3 = -0.008394903 (0.219) x (0.6) = 0.135799096 (0.219) x (0.6) = 0.135799132 (0.219) x (0.8) = 0.183855988 (0.219) x (0.8) = 0.183856066

M13 = 0.3 M13 = 0.3

- = - - = - (0.031) x 0.3 = -0.0081173384 (0.031) x 0.3 = -0.008117346 (0.031) x (34) = 1.0512823951 (0.031) x (34) = 1.051282324 (0.219) x (1.24) = 0.2703378295 (0.219) x (1.24) = 0.270336677 (0.219) x (1.53) 0.3346637604 (0.219) x (1.53) = 0.334663317

M14 1.6 M14 1.6

(32.8) = (32.8) (32.8) = (32.8) (0.500) x 1.6 = -0.8240833233 (0.500) x 1.6 = -0.824082485

M15 (33.6) M15 (33.6)

- = - - = - (0.500) x (0.6) = 0.2804150389 (0.500) x (0.6) = 0.280412404

M16 0.3 M16 0.3

- = - - = - (0.027) x 0.1 = -0.0014576809 (0.027) x 0.1 = -0.001457676 (0.446) x 0.3 = -0.1251254357 (0.446) x 0.3 = -0.12512426 (0.446) x 1.0 = -0.4342416909 (0.446) x 1.0 = -0.434240943

M17 (0.6) M17 (0.6)

- = - - = - (0.027) x (0.6) = 0.015081942 (0.027) x (0.6) = 0.01508189 (0.223) x (0.1) = 0.0279550748 (0.223) x (0.1) = 0.027955073 (0.027) x (0.42) = 0.0111669518 (0.027) x (0.42) = 0.0111669449

M18 0.1 M18 0.1

- = - - = - (0.027) x 0.1 = -0.0014576764 (0.027) x 0.1 = -0.001457675 (0.027) x 5.0 = -0.1347690461 (0.027) x 5.0 = -0.134769046 (0.027) x (0.41) = 0.0109280906 (0.027) x (0.41) = 0.010928092

M19 (0.1) M19 (0.1)

5.0 = 5.0 5.0 = 5.0 (0.027) x (0.1) = 0.0033695847 (0.027) x (0.1) = 0.003369585 (0.027) x 1.13 = -0.0305069689 (0.027) x 1.13 = -0.030506969

M20 5.0 M20 5.0

-1.804688 = -1.80 -1.8047 = -1.80

(0.38) x 12.1 = -4.54 (0.38) x 12.1 = -4.54

(0.38) x 0.4 = -0.16 (0.38) x 0.4 = -0.16

(0.38) x 0.9 = -0.32 (0.38) x 0.9 = -0.32

(0.38) x 3.7 = -1.38 (0.38) x 3.7 = -1.38= -8.2 = -8.2

-1.40625 = -1.41 -1.4063 = -1.41

(0.38) x 1.5 = -0.57 (0.38) x 1.5 = -0.57

(0.38) x 0.8 = -0.31 (0.38) x 0.8 = -0.31

(0.38) x 1.0 = -0.36 (0.38) x 1.0 = -0.36

(0.38) x 1.8 = -0.66 (0.38) x 1.8 = -0.66= -3.3 = -3.3

-0.675 = -0.68 -0.675 = -0.68

(0.38) x 1.1 = -0.41 (0.38) x 1.1 = -0.41

(0.38) x 0.3 = -0.12 (0.38) x 0.3 = -0.12

(0.38) x 0.1 = -0.05 (0.38) x 0.1 = -0.05

(0.38) x 6.8 = -2.56 (0.38) x 6.8 = -2.56= -3.8 = -3.8

11.3 = 11.3 11.3 = 11.3 (0.063) x (0.3) = 0.015926205 (0.063) x (0.3) = 0.0159262097 (0.438) x (1.8) = 0.806489712 (0.438) x (1.8) = 0.8064897152

MI 12.2 MI 12.2

- = - - = - (0.056) x 12.2 = -0.675240516 (0.056) x 12.2 = -0.675240517 (0.056) x 0.3 = -0.015829638 (0.056) x 0.3 = -0.015829653 (0.389) x (1.12) = 0.4362508 (0.389) x (1.12) = 0.436250787

M2 (0.3) M2 (0.3)

- = - - = - (0.056) x (0.3) = 0.014156631 (0.056) x (0.3) = 0.0141566324 (0.056) x 3.8 = -0.211026013 (0.056) x 3.8 = -0.211025965 (0.389) x (1.24) = 0.481803145 (0.389) x (1.24) = 0.4818032002

M3 0.3 M3 0.3

- = - - = - (0.056) x 0.3 = -0.015829653 (0.056) x 0.3 = -0.015829659 (0.056) x (55.2) = 3.064392104 (0.056) x (55.2) = 3.0643920799 (0.389) x (1.928) = 0.749904924 (0.389) x (1.928) = 0.7499046339

M4 = 3.8 M4 = 3.8

(53.3) = (53.3) (53.3) = (53.3) (0.500) x 3.8 = -1.899233687 (0.500) x 3.8 = -1.899233527

M5 (55.2) M5 (55.2)

- = - - = - (0.031) x (0.1) = 0.003863733 (0.031) x (0.1) = 0.0038637094

M6 0.0 M6 0.0

- = - - = - (0.031) x 0.0 = -0.000120742 (0.031) x 0.0 = -0.000120741 (0.031) x 0.6 = -0.01768016 (0.031) x 0.6 = -0.017680156 (0.219) x 0.24 = -0.0529189 (0.219) x 0.24 = -0.052918765 (0.219) x 1.99 -0.0529189 (0.219) x 1.99 = -0.052918765

M7 (0.1) - M7 = (0.1)

- = - - = - (0.031) x (0.1) = 0.003863709 (0.031) x (0.1) = 0.0038637009 (0.219) x (1.5) = 0.33244613 (0.219) x (1.5) = 0.3324461071 (0.031) x 0.68 = -0.021340617 (0.031) x 0.68 = -0.021340618 (0.219) x (1.146) = 0.250795762 (0.219) x (1.146) = 0.2507957409

M8 = 0.6 M8 = 0.6

- = - - = - (0.031) x (0.0) = 0.001209924 (0.031) x (0.0) = 0.0012099239 (0.031) x 0.6 = -0.017680156 (0.031) x 0.6 = -0.017680154 (0.219) x (1.14) = 0.24885287 (0.219) x (1.14) = 0.2488528733 (0.219) x (2.06) = 0.450517124 (0.219) x (2.06) = 0.4505171307

M9 = 0.7 M9 = 0.7

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.7 = -0.022763325 (0.033) x 0.7 = -0.022763326 (0.233) x 0.4 = -0.094070036 (0.233) x 0.4 = -0.094070036 (0.233) x 10.35 = -2.414916417 (0.233) x 10.35 = -2.414916419

M10 (0.0) M10 = (0.0)

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.3 = -0.008954563 (0.033) x 0.3 = -0.008954562 (0.233) x (1.4) = 0.337159098 (0.233) x (1.4) = 0.3371590988 (0.233) x 4.34 = -1.011829451 (0.233) x 4.34 = -1.011829451

M11 1.8 M11 = 1.8

- = - - = - (0.031) x 1.8 = -0.056543978 (0.031) x 1.8 = -0.056543978 (0.031) x 0.3 = -0.008117346 (0.031) x 0.3 = -0.00811735 (0.219) x (0.7) = 0.158232865 (0.219) x (0.7) = 0.158232862 (0.219) x (0.8) = 0.175065325 (0.219) x (0.8) = 0.1750653249

M12 = 0.3 M12 = 0.3

- = - - = - (0.031) x 1.6 = -0.051505155 (0.031) x 1.6 = -0.051505136 (0.031) x 0.3 = -0.008394902 (0.031) x 0.3 = -0.008394902 (0.219) x (0.6) = 0.135799145 (0.219) x (0.6) = 0.1357991499 (0.219) x (0.8) = 0.183856097 (0.219) x (0.8) = 0.1838561088

M13 = 0.3 M13 = 0.3

- = - - = - (0.031) x 0.3 = -0.00811735 (0.031) x 0.3 = -0.008117351 (0.031) x (34) = 1.051282298 (0.031) x (34) = 1.0512822881 (0.219) x (1.24) = 0.270336255 (0.219) x (1.24) = 0.2703361005 (0.219) x (1.53) = 0.334663153 (0.219) x (1.53) 0.3346630936

M14 1.6 M14 1.6

(32.8) = (32.8) (32.8) = (32.8) (0.500) x 1.6 = -0.824082178 (0.500) x 1.6 = -0.824082066

M15 (33.6) M15 (33.6)

- = - - = - (0.500) x (0.6) = 0.2804114397 (0.500) x (0.6) = 0.2804110868

M16 0.3 M16 0.3

- = - - = - (0.027) x 0.1 = -0.001457675 (0.027) x 0.1 = -0.001457674 (0.446) x 0.3 = -0.12512383 (0.446) x 0.3 = -0.125123672 (0.446) 1.0 -0.434240669 (0.446) x 1.0 = -0.434240569

M17 (0.6) M17 = (0.6)

- = - - = - (0.027) x (0.6) = 0.015081871 (0.027) x (0.6) = 0.0150818642 (0.223) x (0.1) = 0.027955073 (0.223) x (0.1) = 0.0279550724 (0.027) x (0.42) = 0.0111669422 (0.027) x (0.42) = 0.0111669413

M18 0.1 M18 0.1

- = - - = - (0.027) x 0.1 = -0.001457674 (0.027) x 0.1 = -0.001457674 (0.027) x 5.0 = -0.134769046 (0.027) x 5.0 = -0.134769046 (0.027) x (0.41) = 0.010928092 (0.027) x (0.41) = 0.0109280924

M19 (0.1) M19 (0.1)

5.0 = 5.0 5.0 = 5.0 (0.027) x (0.1) = 0.003369585 (0.027) x (0.1) = 0.0033695846 (0.027) x 1.13 = -0.030506969 (0.027) x 1.13 = -0.030506969

M20 5.0 M20 5.0

-1.8046875 = -1.80 -1.804688 =

(0.38) x 12.1 = -4.54 (0.38) x 12.1 =

(0.38) x 0.4 = -0.16 (0.38) x 0.4 =

(0.38) x 0.9 = -0.32 (0.38) x 0.9 =

(0.38) x 3.7 = -1.38 (0.38) x 3.7 == -8.2 =

-1.40625 = -1.41 -1.40625 =

(0.38) x 1.5 = -0.57 (0.38) x 1.5 =

(0.38) x 0.8 = -0.31 (0.38) x 0.8 =

(0.38) x 1.0 = -0.36 (0.38) x 1.0 =

(0.38) x 1.8 = -0.66 (0.38) x 1.8 == -3.3 =

-0.675 = -0.68 -0.675 =

(0.38) x 1.1 = -0.41 (0.38) x 1.1 =

(0.38) x 0.3 = -0.12 (0.38) x 0.3 =

(0.38) x 0.1 = -0.05 (0.38) x 0.1 =

(0.38) x 6.8 = -2.56 (0.38) x 6.8 == -3.8 =

11.3 = 11.3 11.3 = 11.3 (0.063) x (0.3) = 0.0159262114 (0.063) x (0.3) = 0.0159262121 (0.438) x (1.8) = 0.8064897165 (0.438) x (1.8) = 0.806489717

MI 12.2 MI 12.2

- = - - = - (0.056) x 12.2 = -0.6752405167 (0.056) x 12.2 = -0.6752405168 (0.056) x 0.3 = -0.0158296593 (0.056) x 0.3 = -0.0158296615 (0.389) x (1.12) = 0.4362507825 (0.389) x (1.1) = 0.4362507808

M2 (0.3) M2 (0.3)

- = - - = - (0.056) x (0.3) = 0.014156633 (0.056) x (0.3) = 0.0141566332 (0.056) x 3.8 = -0.2110259475 (0.056) x 3.8 = -0.2110259409 (0.389) x (1.24) = 0.4818032212 (0.389) x (1.24) = 0.4818032289

M3 0.3 M3 0.3

- = - - = - (0.056) x 0.3 = -0.0158296615 (0.056) x 0.3 = -0.0158296623 (0.056) x (55.2) = 3.064392071 (0.056) x (55.2) = 3.0643920677 (0.389) x (1.928) = 0.7499045274 (0.389) x (1.928) = 0.7499044884

M4 = 3.8 M4 = 3.8

(53.3) = (53.3) (53.3) = (53.3) (0.500) x 3.8 = -1.8992334685 (0.500) x 3.8 = -1.8992334469

M5 (55.2) M5 (55.2)

- = - - = - (0.031) x (0.1) = 0.0038637009 (0.031) x (0.1) = 0.0038636977

M6 0.0 M6 0.0

- = - - = - (0.031) x 0.0 = -0.0001207407 (0.031) x 0.0 = -0.0001207406 (0.031) x 0.6 = -0.0176801541 (0.031) x 0.6 = -0.0176801535 (0.219) x 0.24 = -0.0529187162 (0.219) x 0.24 = -0.0529186982 (0.219) x 1.99 = -0.0529187162 (0.219) x 1.99 = -0.0529186982 - M7 = (0.1) - M7 = (0.1)

- = - - = - (0.031) x (0.1) = 0.0038636977 (0.031) x (0.1) = 0.0038636966 (0.219) x (1.5) = 0.3324460985 (0.219) x (1.5) = 0.3324460985 (0.031) x 0.68 = -0.0213406179 (0.031) x 0.68 = -0.0213406181 (0.219) x (1.146) = 0.250795733 (0.219) x (1.146) = 0.2507957301

M8 = 0.6 M8 = 0.6

- = - - = - (0.031) x (0.0) = 0.0012099239 (0.031) x (0.0) = 0.001209924 (0.031) x 0.6 = -0.0176801535 (0.031) x 0.6 = -0.0176801533 (0.219) x (1.14) = 0.2488528745 (0.219) x (1.14) = 0.248852875 (0.219) x (2.06) = 0.450517133 (0.219) x (2.06) = 0.4505171338

M9 = 0.7 M9 = 0.7

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.7 = -0.0227633259 (0.033) x 0.7 = -0.022763326 (0.233) x 0.4 = -0.0940700368 (0.233) x 0.4 = -0.0940700369 (0.233) x 10.35 = -2.4149164201 (0.233) x 10.35 = -2.4149164204

M10 = (0.0) M10 (0.0)

2.5 = 2.5 2.5 = 2.5 (0.033) x 0.3 = -0.008954562 (0.033) x 0.3 = -0.0089545619 (0.233) x (1.4) = 0.3371590991 (0.233) x (1.4) = 0.3371590992 (0.233) x 4.34 = -1.0118294514 (0.233) x 4.34 = -1.0118294514

M11 = 1.8 M11 = 1.8

- = - - = - (0.031) x 1.8 = -0.0565439782 (0.031) x 1.8 = -0.0565439782 (0.031) x 0.3 = -0.0081173506 (0.031) x 0.3 = -0.0081173511 (0.219) x (0.7) = 0.1582328611 (0.219) x (0.7) = 0.1582328607 (0.219) x (0.8) = 0.1750653248 (0.219) x (0.8) = 0.1750653248

M12 0.3 M12 = 0.3

- = - - = - (0.031) x 1.6 = -0.0515051291 (0.031) x 1.6 = -0.0515051265 (0.031) x 0.3 = -0.0083949018 (0.031) x 0.3 = -0.0083949018 (0.219) x (0.6) = 0.1357991517 (0.219) x (0.6) = 0.1357991524 (0.219) x (0.8) = 0.1838561132 (0.219) x (0.8) = 0.1838561141

M13 = 0.3 M13 = 0.3

- = - - = - (0.031) x 0.3 = -0.0081173511 (0.031) x 0.3 = -0.0081173512 (0.031) x (34) = 1.0512822845 (0.031) x (34) = 1.0512822833 (0.219) x (1.24) = 0.2703360439 (0.219) x (1.24) = 0.2703360232 (0.219) x (1.53) 0.3346630716 (0.219) x (1.53) = 0.3346630635

M14 1.6 M14 = 1.6

(32.8) = (32.8) (32.8) = (32.8) (0.500) x 1.6 = -0.8240820245 (0.500) x 1.6 = -0.8240820094

M15 (33.6) M15 (33.6)

- = - - = - (0.500) x (0.6) = 0.2804109575 (0.500) x (0.6) = 0.2804109102

M16 0.3 M16 0.3

- = - - = - (0.027) x 0.1 = -0.001457674 (0.027) x 0.1 = -0.0014576739 (0.446) x 0.3 = -0.1251236145 (0.446) x 0.3 = -0.1251235934 (0.446) x 1.0 = -0.4342405318 (0.446) x 1.0 = -0.4342405183

M17 = (0.6) M17 = (0.6)

- = - - = - (0.027) x (0.6) = 0.0150818617 (0.027) x (0.6) = 0.0150818608 (0.223) x (0.1) = 0.0279550723 (0.223) x (0.1) = 0.0279550723 (0.027) x (0.42) = 0.0111669409 (0.027) x (0.42) = 0.0111669408

M18 0.1 M18 0.1

- = - - = - (0.027) x 0.1 = -0.0014576739 (0.027) x 0.1 = -0.0014576739 (0.027) x 5.0 = -0.1347690461 (0.027) x 5.0 = -0.1347690461 (0.027) x (0.41) = 0.0109280925 (0.027) x (0.41) = 0.0109280925

M19 (0.1) M19 (0.1)

5.0 = 5.0 5.0 = 5.0 (0.027) x (0.1) = 0.0033695846 (0.027) x (0.1) = 0.0033695846 (0.027) x 1.13 = -0.0305069692 (0.027) x 1.13 = -0.0305069693

M20 5.0 M20 5.0

Dari put 20 Ke Put 20

-1.80 -1.8046875 = -1.80 -1.8046875

-4.54 (0.38) x 12.1 = -4.54 (0.38) x

-0.16 (0.38) x 0.4 = -0.16 (0.38) x

-0.32 (0.38) x 0.9 = -0.32 (0.38) x

-1.38 (0.38) x 3.7 = -1.38-8.2 = -8.21

-1.41 -1.40625 = -1.41 -1.40625

-0.57 (0.38) x 1.5 = -0.57 (0.38) x

-0.31 (0.38) x 0.8 = -0.31 (0.38) x

-0.36 (0.38) x 1.0 = -0.36 (0.38) x

-0.66 (0.38) x 1.8 = -0.66-3.3 = -3.31

-0.68 -0.675 = -0.68 -0.675

-0.41 (0.38) x 1.1 = -0.41 (0.38) x

-0.12 (0.38) x 0.3 = -0.12 (0.38) x

-0.05 (0.38) x 0.1 = -0.05 (0.38) x

-2.56 (0.38) x 6.8 = -2.56-3.8 = -3.81

11.3 = 11.3 11.3 (0.063) x (0.3) = 0.0159262123 (0.063) x 2.4 (0.438) x (7.6) = 3.3424474664 (0.438) x 7.6

MI 14.7 MI

- = - - (0.056) x 14.7 = -0.8161270584 (0.056) x 7.9 (0.056) x 0.3 = -0.0158296623 (0.056) x 2.8 (0.389) x (8.33) = 3.2391656581 (0.389) x 9.58

M2 2.4 M2

- = - - (0.056) x 2.4 = -0.1337338299 (0.056) x (4.3) (0.056) x 3.8 = -0.2110259385 (0.056) x (0.2) (0.389) x (8.20) = 3.1895815515 (0.389) x 8.95

M3 2.8 M3

- = - - (0.056) x 2.8 = -0.1580456546 (0.056) x (3.2)

M4 (0.2) M4

(53.3) = (53.3) (53.3) (0.500) x (0.2) = 0.0790228273 (0.500) x 0.2

M5 (53.2) M5

- = - - (0.031) x (0.1) = 0.0038636966 (0.031) x 0.6

M6 0.0 M6

- = - - (0.031) x 0.0 = -0.0001207405 (0.031) x (0.0) (0.031) x 0.6 = -0.0176801533 (0.031) x (1.4) (0.219) x (1.50) = 0.3278941728 (0.219) x #REF! (0.219) x (5.80) 0.3278941728 (0.219) x 4.62 - M7 0.6 - M7

- = - - (0.031) x 0.6 = -0.0199371079 (0.031) x #REF! (0.219) x 6.5 = -1.4185154858 (0.219) x 16.8 (0.031) x (2.63) = 0.0820453847 (0.031) x #REF!

M8 (1.4) M8

- = - - 0.031 x (0.0) = -0.001209924 0.031 x 2.8 0.219 x (4.7) = -1.0204160969 0.219 x #REF! 0.219 x (3.53) = -0.7725454064 0.219 x #REF!

M9 (1.8) M9

2.5 = 2.5 2.5 (0.033) x (1.8) = 0.0598057142 (0.033) x #REF! (0.233) x 1.8 = -0.4221950369 (0.233) x #REF! (0.233) x (2.67) = 0.6230850825 (0.233) x #REF!

M10 2.8 M10

2.5 = 2.5 2.5 (0.033) x 2.8 = -0.0917909325 (0.033) x #REF! (0.233) x 3 = -0.6425365275 (0.233) x #REF!

#REF! x (2.16) = #REF! #REF! x #REF!M11 #REF! M11

- = - - (0.031) x #REF! = #REF! (0.031) x #REF!

0.3 #REF! 0.3

- = - - (0.031) x 1.6 = -0.0515051256 (0.031) x #REF!

M13 (0.1) M13

- = - - (0.031) x (0.1) = 0.0016095352 (0.031) x #REF! (0.031) x (34) = 1.0512822828 (0.031) x #REF! (0.219) x #REF! = #REF! (0.219) x #REF! (0.219) x #REF! #REF! (0.219) x #REF!

M14 #REF! M14

(32.8) = (32.8) (32.8) (0.500) x #REF! = #REF! (0.500) x #REF!

M15 #REF! M15

- = - - (0.500) x #REF! = #REF! (0.500) x #REF!

M16 #REF! M16

- = - - (0.027) x 0.1 = -0.0014576739 (0.027) x #REF! (0.446) x (4.4) = 1.9512402789 (0.446) x (0.6)

M17 1.9 M17

- = - - (0.027) x 1.9 = -0.0524343928 (0.027) x #REF! (0.223) x (0.1) = 0.0279550723 (0.223) x #REF! (0.027) x #REF! = #REF! (0.027) x #REF!

M18 #REF! M18

- = - - (0.027) x #REF! = #REF! (0.027) x #REF! (0.027) x 5.0 = -0.1347690461 (0.027) x #REF! (0.027) x #REF! = #REF! (0.027) x #REF!

M19 #REF! M19

M20 #REF! M20

= -1.80 -1.8046875 = -1.80

13.3 = 12.96 (0.38) x #REF! = #REF!

3.0 = -1.14 (0.38) x #REF! = #REF!

2.8 = -1.07 (0.38) x (3.3) = 1.22

8.94 #REF!

= -1.41 -1.40625 = -1.41

(3.2) = -3.53 (0.38) x #REF! = #REF!

(1.6) = 0.61 (0.38) x (3.7) = 1.38

#REF! = #REF! (0.38) x #REF! = #REF!

#REF! #REF!

= -0.68 -0.675 = -0.68

(1.8) = -2.17 (0.38) x #REF! = #REF!

(1.2) = 0.44 (0.38) x #REF! = #REF!

0.3 = -0.12 (0.38) x #REF! = #REF!

-2.52 #REF!

Putaran 22

= 11.3 11.3 = 11.3 = -0.1504505586 (0.063) x (4.3) = 0.2700713099= -3.3195660017 (0.438) x #REF! = #REF!

7.9 MI #REF!

= - - = - = -0.4367720451 (0.056) x #REF! = #REF!= -0.1580456546 (0.056) x (3.2) = 0.1794931042= -3.7263232584 (0.389) x #REF! = #REF!

(4.3) M2 #REF!

= - - = - = 0.2400633866 (0.056) x #REF! = #REF!= 0.0087803141 (0.056) x 0.2 = -0.0099718391= -3.4797195759 (0.389) x #REF! = #REF!

(3.2) M3 #REF!

= - - = - = 0.1794931042 (0.056) x #REF! = #REF!

0.2 M4 #REF!

= (53.3) (53.3) = (53.3)= -0.0897465521 (0.500) x #REF! = #REF!

(53.3) M5 #REF!

= - - = - = -0.0199371079 (0.031) x #REF! = #REF!

(0.0) M6 #REF!

= - - = - = 0.0006230346 (0.031) x #REF! = #REF!= 0.0423877253 (0.031) x #REF! = #REF!= #REF! (0.219) x #REF! = #REF!

#REF! (0.219) x #REF! #REF!#REF! - M7 #REF!

= - - = - = #REF! (0.031) x #REF! = #REF!= -3.6762870055 (0.219) x #REF! = #REF!= #REF! (0.031) x #REF! = #REF!

#REF! M8 #REF!

= - - = - = 0.0860539992 0.031 x #REF! = #REF!= #REF! 0.219 x #REF! = #REF!= #REF! 0.219 x #REF! = #REF!

#REF! M9 #REF!

= 2.5 2.5 = 2.5 = #REF! (0.033) x #REF! = #REF!= #REF! (0.233) x #REF! = #REF!= #REF! (0.233) x #REF! = #REF!

#REF! M10 #REF!

#REF! M11 #REF!

= - - = - = #REF! (0.031) x #REF! = #REF!

#REF! 0.3 #REF!

= - - = - = #REF! (0.031) x #REF! = #REF!

#REF! M13 #REF!

= (32.8) (32.8) = (32.8)= #REF! (0.500) x #REF! = #REF!

#REF! M15 #REF!

= - - = - = #REF! (0.500) x #REF! = #REF!

#REF! M16 #REF!

= - - = - = #REF! (0.027) x #REF! = #REF!= 0.2550397441 (0.446) x #REF! = #REF!

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

#REF! M20 #REF!

-1.8046875 = -1.80 -1.8046875

(0.38) x #REF! = #REF! (0.38) x #REF!

-1.40625 = -1.41 -1.40625

(0.38) x #REF! = #REF! (0.38) x #REF!

-0.675 = -0.68 -0.675

(0.38) x #REF! = #REF! (0.38) x #REF!

MI #REF! MI

M2 #REF! M2

M3 #REF! M3

- = - - = (0.056) x #REF! = #REF! (0.056) x #REF! =

M4 #REF! M4

(53.3) = (53.3) (53.3) = (0.500) x #REF! = #REF! (0.500) x #REF! =

M5 #REF! M5

- = - - = (0.031) x #REF! = #REF! (0.031) x #REF! =

M6 #REF! M6

- = - - = (0.031) x #REF! = #REF! (0.031) x #REF! = (0.031) x #REF! = #REF! (0.031) x #REF! = (0.219) x #REF! = #REF! (0.219) x #REF! = (0.219) x #REF! #REF! (0.219) x #REF! - M7 #REF! - M7

M8 #REF! M8

- = - - = 0.031 x #REF! = #REF! 0.031 x #REF! = 0.219 x #REF! = #REF! 0.219 x #REF! = 0.219 x #REF! = #REF! 0.219 x #REF! =

M9 #REF! M9

2.5 = 2.5 2.5 = (0.033) x #REF! = #REF! (0.033) x #REF! = (0.233) x #REF! = #REF! (0.233) x #REF! = (0.233) x #REF! = #REF! (0.233) x #REF! =

M10 #REF! M10

#REF! x #REF! = #REF! #REF! x #REF! =M11 #REF! M11

- = - - = (0.031) x #REF! = #REF! (0.031) x #REF! =

0.3 #REF! 0.3

- = - - = (0.031) x #REF! = #REF! (0.031) x #REF! =

M13 #REF! M13

M14 #REF! M14

(32.8) = (32.8) (32.8) = (0.500) x #REF! = #REF! (0.500) x #REF! =

M15 #REF! M15

- = - - = (0.500) x #REF! = #REF! (0.500) x #REF! =

M16 #REF! M16

- = - - = (0.027) x #REF! = #REF! (0.027) x #REF! = (0.446) x #REF! = #REF! (0.446) x #REF! =

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

M20 #REF! M20

= -1.80 -1.8046875 = -1.80

= #REF! (0.38) x #REF! = #REF!

#REF! #REF!

= -1.41 -1.40625 = -1.41

= #REF! (0.38) x #REF! = #REF!

#REF! #REF!

= -0.68 -0.675 = -0.68

= #REF! (0.38) x #REF! = #REF!

#REF! #REF!

11.3 11.3 = 11.3 11.3 #REF! (0.063) x #REF! = #REF! (0.063)#REF! (0.438) x #REF! = #REF! (0.438)#REF! MI #REF!

- - = - - #REF! (0.056) x #REF! = #REF! (0.056)

#REF! M4 #REF!

(53.3) (53.3) = (53.3) (53.3)#REF! (0.500) x #REF! = #REF! (0.500)#REF! M5 #REF!

- - = - - #REF! (0.031) x #REF! = #REF! (0.031)#REF! M6 #REF!

#REF! - M7 #REF! -

#REF! M8 #REF!

- - = - - #REF! 0.031 x #REF! = #REF! 0.031 #REF! 0.219 x #REF! = #REF! 0.219 #REF! 0.219 x #REF! = #REF! 0.219

#REF! M9 #REF!

2.5 2.5 = 2.5 2.5 #REF! (0.033) x #REF! = #REF! (0.033)#REF! (0.233) x #REF! = #REF! (0.233)#REF! (0.233) x #REF! = #REF! (0.233)

#REF! M10 #REF!

2.5 2.5 = 2.5 2.5 #REF! (0.033) x #REF! = #REF! (0.033)#REF! (0.233) x #REF! = #REF! (0.233)#REF! #REF! x #REF! = #REF! #REF!

#REF! M11 #REF!

- - = - - #REF! (0.031) x #REF! = #REF! (0.031)

#REF! 0.3 #REF!

- - = - - #REF! (0.031) x #REF! = #REF! (0.031)

#REF! M13 #REF!

#REF! M14 #REF!

(32.8) (32.8) = (32.8) (32.8)#REF! (0.500) x #REF! = #REF! (0.500)

#REF! M15 #REF!

- - = - - #REF! (0.500) x #REF! = #REF! (0.500)

#REF! M16 #REF!

- - = - - #REF! (0.027) x #REF! = #REF! (0.027)#REF! (0.446) x #REF! = #REF! (0.446)

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

5.0 5.0 = 5.0 5.0 #REF! (0.027) x #REF! = #REF! (0.027)#REF! (0.027) x #REF! = #REF! (0.027)

#REF! M20 #REF!

-1.8046875 = -1.80 -1.8046875

(0.38) x #REF! = #REF! (0.38) x #REF!

-1.40625 = -1.41 -1.40625

(0.38) x #REF! = #REF! (0.38) x #REF!

-0.675 = -0.68 -0.675

(0.38) x #REF! = #REF! (0.38) x #REF!

Putaran 27

MI #REF! MI

M2 #REF! M2

M3 #REF! M3

= - - = x #REF! = #REF! (0.056) x #REF! =

M4 #REF! M4

= (53.3) (53.3) = x #REF! = #REF! (0.500) x #REF! =

M5 #REF! M5

= - - = x #REF! = #REF! (0.031) x #REF! =

M6 #REF! M6

M7 #REF! - M7

M8 #REF! M8

= - - = x #REF! = #REF! 0.031 x #REF! =x #REF! = #REF! 0.219 x #REF! =x #REF! = #REF! 0.219 x #REF! =

M9 #REF! M9

= 2.5 2.5 = x #REF! = #REF! (0.033) x #REF! =x #REF! = #REF! (0.233) x #REF! =x #REF! = #REF! (0.233) x #REF! =

M10 #REF! M10

= 2.5 2.5 = x #REF! = #REF! (0.033) x #REF! =x #REF! = #REF! (0.233) x #REF! =x #REF! = #REF! #REF! x #REF! =

M11 #REF! M11

= - - = x #REF! = #REF! (0.031) x #REF! =

0.3 #REF! 0.3

= - - = x #REF! = #REF! (0.031) x #REF! =

M13 #REF! M13

M14 #REF! M14

= (32.8) (32.8) = x #REF! = #REF! (0.500) x #REF! =

M15 #REF! M15

= - - = x #REF! = #REF! (0.500) x #REF! =

M16 #REF! M16

= - - = x #REF! = #REF! (0.027) x #REF! =x #REF! = #REF! (0.446) x #REF! =

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

M20 #REF! M20

= -1.80 -1.8046875 = -1.80

= #REF! (0.38) x #REF! = #REF!

#REF! #REF!

= -1.41 -1.40625 = -1.41

= #REF! (0.38) x #REF! = #REF!

#REF! #REF!

= -0.68 -0.675 = -0.68

= #REF! (0.38) x #REF! = #REF!

#REF! #REF!

Putaran 28

- - = - #REF! (0.056) x #REF! = #REF!

#REF! M4 #REF!

#REF! - M7 #REF!

#REF! M8 #REF!

#REF! M9 #REF!

#REF! M10 #REF!

#REF! M11 #REF!

- - = - #REF! (0.031) x #REF! = #REF!

#REF! 0.3 #REF!

- - = - #REF! (0.031) x #REF! = #REF!

#REF! M13 #REF!

#REF! M14 #REF!

(32.8) (32.8) = (32.8)#REF! (0.500) x #REF! = #REF!

#REF! M15 #REF!

- - = - #REF! (0.500) x #REF! = #REF!

#REF! M16 #REF!

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

#REF! M20 #REF!

-1.8046875 = -1.80 -1.8046875

(0.38) x #REF! = #REF! (0.38)

-1.40625 = -1.41 -1.40625

(0.38) x #REF! = #REF! (0.38)

-0.675 = -0.68 -0.675

(0.38) x #REF! = #REF! (0.38)

MI #REF!

M2 #REF!

M3 #REF!

- = - - (0.056) x #REF! = #REF! (0.056) x

M4 #REF!

(53.3) = (53.3) (53.3) (0.500) x #REF! = #REF! (0.500) x

M5 #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x

M6 #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x (0.031) x #REF! = #REF! (0.031) x (0.219) x #REF! = #REF! (0.219) x (0.219) x #REF! #REF! (0.219) x - M7 #REF! -

M8 #REF!

- = - - 0.031 x #REF! = #REF! 0.031 x 0.219 x #REF! = #REF! 0.219 x 0.219 x #REF! = #REF! 0.219 x

M9 #REF!

2.5 = 2.5 2.5 (0.033) x #REF! = #REF! (0.033) x (0.233) x #REF! = #REF! (0.233) x (0.233) x #REF! = #REF! (0.233) x

M10 #REF!

#REF! x #REF! = #REF! #REF! xM11 #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x

0.3 #REF!

- = - - (0.031) x #REF! = #REF! (0.031) x

M13 #REF!

M14 #REF!

(32.8) = (32.8) (32.8) (0.500) x #REF! = #REF! (0.500) x

M15 #REF!

- = - - (0.500) x #REF! = #REF! (0.500) x

M16 #REF!

- = - - (0.027) x #REF! = #REF! (0.027) x (0.446) x #REF! = #REF! (0.446) x

M17 #REF!

M18 #REF!

M19 #REF!

M20 #REF!

= -1.80 -1.8046875

x #REF! = #REF! (0.38) x

= -1.41 -1.40625

x #REF! = #REF! (0.38) x

= -0.68 -0.675

x #REF! = #REF! (0.38) x

Putaran 31

MI #REF! MI

M2 #REF! M2

M3 #REF! M3

= - - #REF! = #REF! (0.056) x #REF!

M4 #REF! M4

= (53.3) (53.3)#REF! = #REF! (0.500) x #REF!

M5 #REF! M5

= - - #REF! = #REF! (0.031) x #REF!

M6 #REF! M6

M7 #REF! - M7

M8 #REF! M8

= - - #REF! = #REF! 0.031 x #REF!#REF! = #REF! 0.219 x #REF!#REF! = #REF! 0.219 x #REF!

M9 #REF! M9

= 2.5 2.5 #REF! = #REF! (0.033) x #REF!#REF! = #REF! (0.233) x #REF!#REF! = #REF! (0.233) x #REF!

M10 #REF! M10

= 2.5 2.5 #REF! = #REF! (0.033) x #REF!#REF! = #REF! (0.233) x #REF!#REF! = #REF! #REF! x #REF!

M11 #REF! M11

= - - #REF! = #REF! (0.031) x #REF!

0.3 #REF! 0.3

= - - #REF! = #REF! (0.031) x #REF!

M13 #REF! M13

M14 #REF! M14

= (32.8) (32.8)#REF! = #REF! (0.500) x #REF!

M15 #REF! M15

= - - #REF! = #REF! (0.500) x #REF!

M16 #REF! M16

= - - #REF! = #REF! (0.027) x #REF!#REF! = #REF! (0.446) x #REF!

M17 #REF! M17

M18 #REF! M18

M19 #REF! M19

M20 #REF! M20

= -1.80 -1.8046875

#REF! = #REF! (0.38) x #REF!

= -1.41 -1.40625

#REF! = #REF! (0.38) x #REF!

= -0.68 -0.675

#REF! = #REF! (0.38) x #REF!

Putaran 32

= 11.3 11.3 == #REF! (0.063) x #REF! == #REF! (0.438) x #REF! =

#REF! MI

#REF! M2

#REF! M3

= - - == #REF! (0.056) x #REF! =

#REF! M4

= (53.3) (53.3) == #REF! (0.500) x #REF! =

#REF! M5

= - - == #REF! (0.031) x #REF! =

#REF! M6

#REF! (0.219) x #REF!#REF! - M7

#REF! M8

#REF! M9

= 2.5 2.5 == #REF! (0.033) x #REF! == #REF! (0.233) x #REF! == #REF! (0.233) x #REF! =

#REF! M10

#REF! M11

= - - == #REF! (0.031) x #REF! =

#REF! 0.3

= - - == #REF! (0.031) x #REF! =

#REF! M13

#REF! (0.219) x #REF!#REF! M14

= (32.8) (32.8) == #REF! (0.500) x #REF! =

#REF! M15

= - - == #REF! (0.500) x #REF! =

#REF! M16

= - - == #REF! (0.027) x #REF! == #REF! (0.446) x #REF! =

#REF! M17

#REF! M18

#REF! M19

= 5.0 5.0 == #REF! (0.027) x #REF! == #REF! (0.027) x #REF! =

#REF! M20

= -1.80 -1.8046875 =

= #REF! (0.38) x #REF! =

= -1.41 -1.40625 =

= #REF! (0.38) x #REF! =

= -0.68 -0.675 =

= #REF! (0.38) x #REF! =

Putaran 33

- - = - #REF! (0.056) x #REF! = #REF!

#REF! M4 #REF!

#REF! - M7 #REF!

#REF! M8 #REF!

#REF! M9 #REF!

#REF! M10 #REF!

#REF! M11 #REF!

- - = - #REF! (0.031) x #REF! = #REF!

#REF! 0.3 #REF!

- - = - #REF! (0.031) x #REF! = #REF!

#REF! M13 #REF!

#REF! M14 #REF!

(32.8) (32.8) = (32.8)#REF! (0.500) x #REF! = #REF!

#REF! M15 #REF!

- - = - #REF! (0.500) x #REF! = #REF!

#REF! M16 #REF!

#REF! M17 #REF!

#REF! M18 #REF!

#REF! M19 #REF!

#REF! M20 #REF!

Tie Beam

Type TB 1 = 0.2 m x 0.4 m

Ring Balk

Type Balok 30/60 = 0.3 m x 0.6 m

Type Balok 30/40 = 0.3 m x 0.4 m

Type Balok 20/40 = 0.2 m x 0.4 m

Type Balok 20/30 = 0.2 m x 0.3 m

Gambar 4.1 Denah Portal Tinjauan Arah X

Inersia

a. Inersia Kolom

1 Type kolom K1 40.000 x 40 0.0833 213,333.333

b. Inersia Tie Beam

1 Type TB 1 20.000 x 40 0.0833 106,666.667

1 Dimensi RB1 30.000 x 40 0.0833 160,000.000

d. Inersia Balok

1 Type Balok 30/60 30.000 x 60 0.0833 540,000.000

2 Type Balok 30/40 30.000 x 40 0.0833 160,000.000

3 Type Balok 20/40 20.000 x 40 0.0833 106,666.667

4 Type Balok 20/30 20.000 x 30 0.0833 45,000.000

== -0.0833333333 x 8536.632512 x 64.000 = (45,528.7) - 7,998 = (53,526.8) kgm = (53.5) tm

Mf2-1 =

== -0.0833333333 x 8536.632512 x 6.250 = (4,446.2)= (4,446.2) kgm = (4.4) tm

== -0.0833333333 x 6,190.03 x 64.000 = (33,013.5) - 7459.064= (40,472.6) kgm = (40.5) tm

== -0.0833333333 x 6190.03 x 6.250 = (3,224.0)= (3,224.0) kgm = (3.2) tm

== -0.0833333333 x 6,190.03 x 64.000 = (33,013.5) - 7459.064= (40,472.6) kgm = (40.5) tm =

== -0.0833333333 x 6190.03 x 6.250 = (3,224.0)= (3,224.0) kgm = (3.2) tm =

Mf1-2 -1/12 x qL2 - (P1.a.b2/L2)

-Mf2-1

Mf2-2" -1/12 x qL2 - 1/8 PL

Mf2"-2

-Mf2-2"

Mf4-3 -1/12 x qL2 - 1/8 PL

-Mf4-3

Mf3-3" -1/12 x qL2

Mf3"-3

-Mf4-3

Mf5-6 -1/12 x qL2 - 1/8 PL

-Mf5-6

Mf6-6" -1/12 x qL2

Mf6"-6

-Mf6-6"

Mf7-8 -1/12 x qL2 - 1/8 PL

= -0.0833333333 x 6,190.03 x 64.000 = (33,013.5) - 7459.064= (40,472.6) kgm = (40.5) tm =

== -0.0833333333 x 6190.032512 x 6.250 = (3,224.0)= (3,224.0) kgm = (3.2) tm =

1 -53.527 53.53

2 -53.527 53.53

3 -4.446 4.45

4 40.473 (40.47)

5 -3.224 3.22

6 40.473 (40.47)

7 -3.224 3.22

8 -40.473 40.47

9 -3.224 3.22

10 40.473 (40.47)

T1 = +

T Nilai ρ Nilai

-53.527 1.219

4.446 1.371

-4.446 0.229

37.249 3.133

-3.224 0.771

-40.473 2.905

37.249 3.133

-3.224 0.771

-80.945 2.067

-3.224 0.771

Mf 8-7

-Mf7-8

Mf7-7" -1/12 x qL2

Mf 7"-7 -Mf7"-7

" M3"-3

M7-7''

M7''-7

T2" ρ

T3" ρ

T5 ρ5

T6" ρ

T7 ρ7

T7" ρ7'

-40.473 1.838

Joint 1

= = 0.076 = 0.063 ρ1 1.219

= = 0.533 = 0.438 ρ1 1.219

Joint 2

= = 0.076 = 0.056 ρ2 1.371

= = 0.5333 = 0.389 ρ2 1.371

Joint 3

= = 0.533 = 0.170 ρ3 3.133

= = 0.386 = 0.123 ρ3 3.133

= = 0.114 = 0.036 ρ3 3.133

= = 0.5333 = 0.170 ρ3 3.133

Joint 4

= = 0.386 = 0.133 ρ4 2.905

= = 0.533 = 0.184 ρ4 2.905

Joint 5

γ2-2"

γ2--1

K2-3γ

γ3-3"

K4-3γ

= = 0.386 = 0.133 ρ5 2.905

= = 0.533 = 0.184 ρ5 2.905

0.500 Joint 6

= = 0.386 = 0.123 ρ6 3.133

= = 0.114 = 0.036 ρ6 3.133

= = 0.533 = 0.170 ρ6 3.133

Joint 7

= = 0.114 = 0.055 ρ7 2.067

= = 0.386 = 0.187 ρ7 2.067

= = 0.533 = 0.258 ρ7 2.067

Joint 8

= = 0.386 = 0.210 ρ8 1.838

= = 0.533 = 0.290 ρ8 1.838

K5-6γ

K5-4γ5-4

K6-5γ

γ6-6"

γ7-7"

K8-7γ

M1 = -Mf / ρ1

= 53.5271.219

= 43.909 ton

No. Momen Nilai

1 M1 43.909

2 M2 -3.242

3 M2" 19.452

4 M3 -11.888

5 M3" 4.179

6 M4 13.933

7 M5 13.933

8 M6 -11.888

9 M6" 4.179

10 M7 39.167

11 M7" 4.179

12 M8 -22.019

= 2 x ( 0.5333 + 0.533

= 2.1333

T2 = 2 x ( 0.5333 + 0.53

= 2.1333

T3 = 2 x ( 0.53 + 0.53

= 2.1333

Perhitungan nilai t

2*(K1-2

2*(K4-5

+ K3-6

2*(K5-8

+ K6-7

= 0.750

No. t Nilai

1 0.750

2 0.750

3 0.750

4 0.750

5 0.750

6 0.750

7 0.750

Arah y

M1 = -h1(∑W)

= -3.500 x ( 2.20 )2.1333

= -3.609

M2 = -h2(∑W)

= -4.000 x ( 1.50 )2.1333

= -2.813

M3 = -h3(∑W)

= -3.600 x ( 0.80 )2.1333

= -1.350

Putaran 0

3.(K1-8

MI = MI(0) = 43.9 = γ 1 - 2 x M2(0) = (0.063)= γ 1 - 4 x MD 1+M4(0) = (0.438)

M2 = M2(0) = (3.2)= γ 2 - 1 x M1(1) = (0.056)= γ 2 - 2" x M2"(0) = (0.056)= γ 2 - 3 x MD 1+M3(0) = (0.389)

M3 = M3(0) = (11.9)= γ 3-4 x M4(0) = (0.123)= y 3-3" x M3"(0) = (0.036)= γ 3-2 x MD2+M6(0) = (0.170)= γ 3-6 x MD 1+M2(1) = (0.170)

M4 = M4(0) = 13.9 = γ 4-3 x M3(1) = (0.133)= γ 4-5 x MD(2)+M5(0) = (0.184)= γ 4-1 x MD(1)+M1(1) = (0.184)

M5 = M5(0) = 13.9 = γ 5-6 x M6(0) = (0.133)= γ 5-8 x MD3 + M8(0) = (0.184)= γ 5-4 x MD 2 + M4(1) = (0.184)

M6 = M6(0) = (11.9)= γ 6-5 x M5(1) = (0.123)= γ 6-6" x M6"(0) = (0.036)= γ 6-7 x MD 3+M7(0) = (0.170)= γ 6-3 x MD 2+M3(1) = (0.170)

M7 = M7(0) = 39.2 = γ 7-7" x M7"(0) = (0.055)= γ 7-8 x M8(0) = (0.187)= γ7-6 x MD 3+M6(1) = (0.258)

M8 = M8(0) = (22.0)= γ 8-7 x M7(1) = (0.210)= γ8-5 x MD 3+M5(1) = (0.290)

PERHITUNGAN MOMEN DESAIN BELUM

Joint 1

M1-2 = K 1-2 x + Mf1-2

M1-4 = K 1-4 x + Mf1-4

Joint 2

M2-1 = K 2-1 x + Mf2-1

M2-3 = K 2-3 x + Mf2-3

M2-2" = K 2-2" x + Mf2-2"

Joint 3

M3-2 = K 3-2 x + Mf3-2

M3-4 = K 3-4 x + Mf3-4

M3-6 = K 3-6 x + Mf3-6

M3-3" = K 3-2" x + Mf3-3"

Joint 4

M4-3 = K 4-3 x + Mf4-3

M4-1 = K 4-1 x + Mf4-1

M4-5 = K 4-5 x + Mf4-5

Joint 5

M5-6 = K 5-6 x + Mf5-6

M5-4 = K 5-4 x + Mf5-4

M5-8 = K 5-8 x + Mf5-8

Joint 6

M6-5 = K 6-5 x + Mf6-5

M6-7 = K 6-7 x + Mf6-7

M6-3 = K 6-3 x + Mf6-3

M6-6' = K 6-6'' x + Mf6-6''

Joint 7

M7-6 = K 7-6 x + Mf7-6

M7-8 = K 7-8 x + Mf7-8

M7-7" = K 7-7' x + Mf7-7'

Joint 8

M8-7 = K 8-7 x + Mf8-7

M8-5 = K 8-5 x + Mf8-5

{ 2M1(k) + M2(k) }

{2M1(k) + M4(k) }

{ 2M2(k) + M1(k) }

{2M2(k) + M3(k) }

{2M2(k) + M2"(k) }

{ 2M3(k) + M2(k) }

{2M3(k) + M4(k) }

{2M3(k) + M6(k) }

{2M3(k) + M3"(k) }

{ 2M4(k) + M3(k) }

{ 2M4(k) + M1(k) }

{ 2M4(k) + M3(k) }

{ 2M5(k) + M6(k) }

{ 2M5(k) + M4(k) }

{ 2M5(k) + M8(k) }

{ 2M6(k) + M5(k) }

{2M6(k) + M7(k) }

{2M6(k) + M3(k) }

{2M6(k) + M6"(k) }

{ 2M7(k) + M6(k) }

{2M7(k) + M8(k) }

{2M7(k) + M7'(k) }

{ 2M8(k) + M7(k) }

{2M8(k) + M5(k) }

1M1-2 -46.983

1.9250.08

0.6100.125 -0.241

M1-4 48.907 0.53 0.875 -1.684

M2-1 56.488

44.995

0.111 -4.999

M2-3 -6.550 0.53 0.778 -34.996

M2-2" -4.943 0.08 0.111 -4.999

M3-2 -8.752

-2.465

0.340 0.839

M3-4 36.384 0.39 0.246 0.607

M3-6 -25.291 0.53 0.340 0.839

M3-3" -4.806 0.11 0.073 0.180

M4-5 17.225

0.367 -1.258

M4-3 -40.728 0.39 0.266 -0.910

M4-1 26.927 0.53 0.367 -1.258

M5-4 29.503

0.367 -0.815

M5-6 -33.338 0.39 0.266 -0.590

M5-8 6.054 0.53 0.367 -0.815

M6-5 24.526

-32.368

0.246 7.969

M6-7 -6.315 0.53 0.340 11.019

M6-3 -39.628 0.53 0.340 11.019

M6-6' -10.951 0.11 0.073 2.361

M7-6 41.336

37.465

0.516 -19.337

M7-8 -13.334 0.39 0.373 -13.984

M7-7" 9.462 0.11 0.111 -4.144

8M8-7 30.393

0.7200.39

0.9190.420 -0.302

M8-5 -29.673 0.53 0.580 -0.418

Momen desain

K /∑K*∆M

∑`RA

No. JointM.Desain

1 M1-2 -47.223 8.537 7.459 - 8 37.876

2 M2-1 51.489 8.537 7.459 - 8 37.876

5 M3-4 36.991 6.190 7.459 - 8 28.490

6 M4-3 -41.637 6.190 7.459 - 8 28.490

7 M5-6 -33.927 6.190 7.459 - 8 28.490

8 M6-5 32.495 6.190 7.459 - 8 28.490

11 M7-8 -27.318 0.523 3.730 - 8 3.958

12 M8-7 30.091 0.523 3.730 - 8 3.958

RM x-y= Mx-y / L

RM y-x= Mx-y / L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RM y-x= Mx-y / L

RM x-y= Mx-y / L

1 M1-4 3.5 47.223 13.492

M4-1 3.5 25.670 7.334

2 M2-3 3.5 (41.547) (11.870)

M3-2 3.5 (7.913) (11.870)

3 M3-6 4.0 (24.452) (6.113)

M6-3 4.0 (28.609) (7.152)

4 M4-5 4.0 15.968 3.992

M5-4 4.0 28.688 7.172

5 M5-8 3.6 5.239 (11.870)

M8-5 3.6 (30.091) (2.261)

6 M6-7 3.6 4.704 1.307

M7-6 3.6 22.000 6.111

……………………………………………..FINISH……………………………………..

Kekakuan

0.5333

Kekakuan

0.0762

Kekakuan

0.1143

Kekakuan

0.3857

0.1143

0.0762

0.0321

- ( 7,998.081 )

- 0.125 x 7,459.064 x 8

Putaran 1

MI (1) MI (0)

(-t1-4

) x (M1( I ) + M4(I) )

(-t2-3

) x (M2( I ) + M3(I) )

MII(1) MII (0)

(-t4-5) x (M4( I ) + M5(I) )

(-t3-6) x (M3( I )+ M6(I))

MIII(1) MIII (0)

(-t5-8) x (M5 ( I ) + M8 (I) )

(-t6-7) x (M6 ( I )+ M7 (I))

= 43.91 43.9 x (3.242) = 0.20 (0.063)x 10.324 = (4.52) + (0.438)

MI 39.59

= (3.24) (3.2) x 39.595 = (2.20) (0.056)x 19.452 = (1.08) (0.056)x (15.497) = 6.03 + (0.389)

M2 (0.50)

= (11.89) (11.9) x 13.933 = (1.72) (0.123) x 4.179 = (0.15) (0.036)x (14.700) = 2.50 (0.123)x (4.105) = 0.70 + (0.170)

M3 (10.55)

= 13.93 13.9 x (10.555) = 1.40 + (0.133) x 11.121 = (2.04) (0.184) x 35.985 = (6.61) (0.184)

M4 6.69

= 13.93 13.9 x (11.888) = 1.58 (0.133) x (23.369) = 4.29 (0.184) x 3.873 = (0.71) + (0.184)

M5 19.09

= (11.89) (11.9) x 19.091 = (2.35) (0.123)x 4.179 = (0.15) (0.036)x 37.817 = (6.44) (0.170)x (13.367) = (6.44) + (0.170)

M6 = (27.26)

= 39.17 39.2 x 4.179 = (0.23) (0.055)x (22.019) = 4.11 (0.187)x (28.614) 7.38 + (0.258)

M7 50.43

= (22.02) (22.0) x 50.430 = (10.58) (0.210)x 17.741 = (5.15) + (0.290)

M8 (37.75)

= 0.076 x 85.891 + (53.5) =

= 0.533 x 91.701 + 0.0 =∑M =

= 0.076 x 38.869 + 53.5 =

= 0.533 x (12.282) + 0.0 =

= 0.076 x (6.516) + (4.4) =∑M =

= 0.533 x (16.410) + 0 =

= 0.386 x (10.599) + 40.5 =

= 0.533 x (47.420) + 0 =

= 0.114 x (13.844) + -3.2 =∑M =

= 0.386 x (0.661) + (40.5) =

= 0.533 x 50.489 + 0 =

= 0.533 x 32.298 + 0 =

∑M =

= 0.386 x 18.498 + (40.5) =

= 0.533 x 55.319 + 0 =

= 0.533 x 11.352 + 0 =∑M =

= 0.386 x (41.344) + 40.5 =

= 0.533 x (11.840) + 0.0 =

= 0.533 x (74.303) + 0 =

= 0.114 x (67.610) + -3.224 =∑M =

= 0.533 x 77.506 + 0 =

= 0.386 x 70.359 + -40.5 =

= 0.114 x 111.003 + -3.224 =∑M =

= 0.386 x (26.133) + 40.5 =

= 0.533 x (55.637) + 0.0 =∑M =

-47.2230.000

47.223

51.489

0.000-41.547

-9.942

-7.913

0.00036.991

-24.452

-4.626

15.968

0.000-41.637

25.670

28.688

0.000-33.927

32.495

0.0004.704

-28.609

-8.590

22.000

0.000-27.318

30.0910.000

-30.091

Koreksi Momen

∑`RA ∑`RB

RB RM x-y RM y-x ∑R'A ∑R'B R'A

37.876 (5.903) 6.436 50.215 25.537 50.215

28.490 4.624 (5.205) 18.661 38.318 18.661

28.490 (4.241) 4.062 36.792 20.187 36.792

3.958 (3.415) 3.761 11.134 (3.218) 11.134

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RM x-y = M x-y /L

RM y-x = M y-x /L

RA = 1/2P+ 1/2qL

RMy-x/L ∑RA ∑RB Da Kanan Da kanan

7.334 20.827 (20.827) 20.827 0.000

13.492 20.827 (20.827) 20.827 0.000

(2.261) (14.131) 14.131 (14.131) 0.000

(7.152) (13.265) 13.265 (13.265) 0.000

(7.152) (14.305) 14.305 (14.305) 0.000

7.172 11.164 (11.164) 11.164 0.000

3.992 11.164 (11.164) 11.164 0.000

(2.261) (14.131) 14.131 (14.131) 0.000

(11.870) (14.131) 14.131 (14.131) 0.000

6.111 7.418 (7.418) 7.418 0.000

1.307 7.418 (7.418) 7.418 0.000

……………………………………………..FINISH……………………………………..

-3.609 = -3.61

(0.75) x 46.3 = -34.71

(0.75) x (11.1) = 8.29-30.03

-2.813 = -2.81

(0.75) x 25.8 = -19.33

(0.75) x (37.8) = 28.36

-1.350 = -1.35

(0.75) x (18.7) = 13.99

(0.75) x 23.2 = -17.37

= 43.91 x (0.5) = 0.03 x 3.1 = (1.35)

MI 42.59

= (3.24) x 42.6 = (2.37)x 19.5 = (1.08)x (14.16) = 5.51

M2 (1.18)

= (11.89) x 6.7 = (0.82) x 4.2 = (0.15)x (30.1) = 3.70 x (4.79) = 0.82

M3 (8.35)

= 13.93 x (8.3) = 1.11 x 16.3 = (2.99) x 39.0 = (7.16)

M4 4.89

= 13.93 x (27.3) = 3.62 x (39.1) = 7.18 x 2.1 = (0.38)

M5 24.35

= (11.89) x 24.4 = (3.00)x 4.2 = (0.15)x 49.08 = (8.35)x (11.16) = (8.35)

M6 = (31.75)

= 39.17 x 4.2 = (0.23)x (37.7) = 7.05 x (33.10) = 8.54

M7 = 54.52

= (22.02) x 54.5 = (11.44)x 23.00 = (6.67)

M8 = (40.13)

(46.98)

48.91 + 1.9

(6.55)

(4.94) + 45.0

(8.75)

(25.29)

(4.81) + (2.5)

-40.727679

26.927439

17.225436 +

-33.337700

29.503322

6.054188 + 2.2

(6.31)

(39.63)

(10.95) + (32.4)

(13.33)

9.46 + 37.5

(29.67) + 0.7

Da kanan Db kiri Db kanan Dc kiri Dc kanan Dd kiri

50.215 (18.078) -18.078 (25.537) 0.000

18.661 (30.859) -30.859 (38.318) 0.000

36.792 (12.728) -12.728 (20.187) 0.000

11.134 6.948 6.948 3.218 0.000

-3.609 = -3.61 -3.609

(0.75) x 47.5 = -35.62 (0.75)

(0.75) x (9.5) = 7.14 (0.75)-32.08

-2.813 = -2.81 -2.813

(0.75) x 29.2 = -21.93 (0.75)

(0.75) x (40.1) = 30.07 (0.75)

-1.350 = -1.35 -1.350

(0.75) x (15.8) = 11.84 (0.75)

(0.75) x 22.8 = -17.08 (0.75)

Putaran 2 Putaran 3

43.9 = 43.91 43.9 (0.063) x (1.2) = 0.07 (0.063) x (0.438) x 1.3 = (0.56) (0.438) x

MI 43.42

(3.2) = (3.24) (3.2) (0.056) x 43.4 = (2.41) (0.056) x (0.056) x 19.5 = (1.08) (0.056) x (0.389) x (11.95) = 4.65 (0.389) x

M2 (2.09)

(11.9) = (11.89) (11.9) (0.123) x 4.9 = (0.60) (0.123) x (0.036) x 4.2 (0.15) (0.036) x (0.123) x (34.6) = 4.25 (0.123) x (0.170) x (5.70) = 0.97 (0.170) x

M3 (7.42)

13.9 = 13.93 13.9 (0.133) x (7.4) = 0.99 (0.133) x (0.184) x 21.5 = (3.95) (0.184) x (0.184) x 39.8 = (7.31) (0.184) x

M4 3.65

13.9 = 13.93 13.9 (0.133) x (31.7) = 4.22 (0.133) x (0.184) x (41.5) = 7.62 (0.184) x (0.184) x 0.8 = (0.15) (0.184) x

M5 25.61

(11.9) = (11.89) (11.9) (0.123) x 25.6 = (3.15) (0.123) x (0.036) x 4.2 = (0.15) (0.036) x (0.170) x 53.17 = (9.05) (0.170) x (0.170) x (10.23) (9.05) (0.170) x

M6 (33.29)

39.2 = 39.17 39.2 (0.055) x 4.2 = (0.23) (0.055) x (0.187) x (40.1) = 7.49 (0.187) x (0.258) x (34.64) 8.94 (0.258) x

M7 55.37

(22.0) = (22.02) (22.0) (0.210) x 55.4 = (11.62) (0.210) x (0.290) x 24.26 = (7.04) (0.290) x

M8 (40.68)

Dd kanan

= -3.61 -3.609

x 47.1 = -35.31 (0.75) x 47.3

x (9.5) = 7.13 (0.75) x (9.5)-31.79

= -2.81 -2.813

x 29.3 = -21.95 (0.75) x 29.2

x (40.7) = 30.54 (0.75) x (40.6)

= -1.35 -1.350

x (15.1) = 11.30 (0.75) x (14.8)

x 22.1 = -16.55 (0.75) x 21.9

Putaran 4

= 43.91 43.9 = (2.1) = 0.13 (0.063) x (2.5) = 0.0 = (0.02) (0.438) x (0.4) =MI 44.02 MI

= (3.24) (3.2) = 44.0 = (2.45) (0.056) x 44.2 = 19.5 = (1.08) (0.056) x 19.5 = (11.03) = 4.29 (0.389) x (10.62) =M2 (2.48) M2

= (11.89) (11.9) = 3.7 = (0.45) (0.123) x 3.3 = 4.2 = (0.15) (0.036) x 4.2 (36.1) = 4.44 (0.123) x (36.4) = (6.09) = 1.04 (0.170) x (6.26) =M3 (7.01) M3

= 13.93 13.9 = (7.0) = 0.93 (0.133) x (6.9) = 22.8 = (4.19) (0.184) x 23.2 = 40.4 = (7.42) (0.184) x 40.6 =M4 3.26 M4

= 13.93 13.9 = (33.3) = 4.42 (0.133) x (33.6) = (42.0) = 7.72 (0.184) x (42.2) = 0.4 = (0.08) (0.184) x 0.3 =M5 25.99 M5

= (11.89) (11.9) = 26.0 = (3.20) (0.123) x 26.1 = 4.2 = (0.15) (0.036) x 4.2 = 54.02 = (9.19) (0.170) x 54.20 = (9.82) (9.19) (0.170) x (9.70)

M6 (33.63) M6

= 39.17 39.2 = 4.2 = (0.23) (0.055) x 4.2 = (40.7) = 7.59 (0.187) x (40.8) = (34.98) 9.03 (0.258) x (35.05)

M7 55.55 M7

= (22.02) (22.0) = 55.6 = (11.66) (0.210) x 55.6 = 24.64 = (7.15) (0.290) x 24.73 =

M8 (40.83) M8

= -3.61 -3.609 = -3.61

= -35.46 (0.75) x 47.4 = -35.52

= 7.12 (0.75) x (9.5) = 7.15-31.95 -31.97

= -2.81 -2.813 = -2.81

= -21.94 (0.75) x 29.2 = -21.91

= 30.48 (0.75) x (40.6) = 30.45

5.73 5.72

= -1.35 -1.350 = -1.35

= 11.13 (0.75) x (14.8) = 11.09

= -16.44 (0.75) x 21.9 = -16.42

-6.67 -6.69

Putaran 5

43.91 43.9 = 43.91 0.15 (0.063) x (2.6) = 0.17 0.15 (0.438) x (0.5) = 0.21 44.22 MI 44.28

(3.24) (3.2) = (3.24) (2.46) (0.056) x 44.3 = (2.46) (1.08) (0.056) x 19.5 = (1.08) 4.13 (0.389) x (10.50) = 4.08 (2.65) M2 (2.70)

(11.89) (11.9) = (11.89) (0.40) (0.123) x 3.1 = (0.39) (0.15) (0.036) x 4.2 = (0.15) 4.49 (0.123) x (36.5) = 4.50 1.07 (0.170) x (6.31) = 1.07 (6.89) M3 (6.86)

13.93 13.9 = 13.93 0.91 (0.133) x (6.9) = 0.91 (4.26) (0.184) x 23.3 = (4.27) (7.46) (0.184) x 40.7 = (7.47) 3.14 M4 3.10

13.93 13.9 = 13.93 4.47 (0.133) x (33.7) = 4.48 7.74 (0.184) x (42.2) = 7.75 (0.06) (0.184) x 0.3 = (0.05) 26.08 M5 26.11

(11.89) (11.9) = (11.89) (3.21) (0.123) x 26.1 = (3.21) (0.15) (0.036) x 4.2 = (0.15) (9.23) (0.170) x 54.25 = (9.23) (9.23) (0.170) x (9.67) (9.23) (33.70) M6 (33.72)

39.17 39.2 = 39.17 (0.23) (0.055) x 4.2 = (0.23) 7.62 (0.187) x (40.9) = 7.63 9.05 (0.258) x (35.07) 9.05 55.60 M7 55.61

(22.02) (22.0) = (22.02) (11.67) (0.210) x 55.6 = (11.67) (7.18) (0.290) x 24.76 = (7.18) (40.86) M8 (40.87)

-3.609 = -3.61

(0.75) x 47.4 = -35.54

(0.75) x (9.6) = 7.17-31.98

-2.813 = -2.81

(0.75) x 29.2 = -21.91

(0.75) x (40.6) = 30.43

-1.350 = -1.35

(0.75) x (14.8) = 11.07

(0.75) x 21.9 = -16.42

Putaran 6

43.9 = 43.91 (0.063) x (2.7) = 0.17 (0.438) x (0.5) = 0.22

MI 44.3

(3.2) = (3.24) (0.056) x 44.3 = (2.46) (0.056) x 19.5 = (1.08) (0.389) x (10.47) = 4.07

M2 (2.71)

(11.9) = (11.9) (0.123) x 3.1 = (0.4) (0.036) x 4.2 (0.2) (0.123) x (36.5) = 4.5 (0.170) x (6.32) = 1.1

M3 (6.85)

13.9 = 13.93 (0.133) x (6.8) = 0.91 (0.184) x 23.3 = (4.28) (0.184) x 40.7 = (7.47)

M4 3.09

13.9 = 13.93 (0.133) x (33.7) = 4.48 (0.184) x (42.2) = 7.75 (0.184) x 0.3 = (0.05)

M5 26.11

(11.9) = (11.89) (0.123) x 26.1 = (3.21) (0.036) x 4.2 = (0.15) (0.170) x 54.26 = (9.24) (0.170) x (9.66) (9.24)

M6 (33.7)

39.2 = 39.17 (0.055) x 4.2 = (0.23) (0.187) x (40.9) = 7.63 (0.258) x (35.08) 9.05

M7 55.62

(22.0) = (22.02) (0.210) x 55.6 = (11.67) (0.290) x 24.76 = (7.18)

M8 (40.87)

-3.609 = -3.61

(0.75) x 47.4 = -35.55

(0.75) x (9.6) = 7.17-31.98

-2.813 = -2.81

(0.75) x 29.2 = -21.90

(0.75) x (40.6) = 30.43

-1.350 = -1.35

(0.75) x (14.8) = 11.07

(0.75) x 21.9 = -16.42

Putaran 7 Putaran 8

43.9 = 43.91 43.9 (0.063) x (2.7) = 0.17 (0.063) (0.438) x (0.5) = 0.23 (0.438)

MI 44.30

(3.2) = (3.24) (3.2) (0.056) x 44.3 = (2.46) (0.056) (0.056) x 19.5 = (1.08) (0.056) (0.389) x (10.46) = 4.07 (0.389)

M2 (2.72)

(11.9) = (11.89) (11.9) (0.123) x 3.1 = (0.38) (0.123) (0.036) x 4.2 (0.15) (0.036) (0.123) x (36.5) = 4.50 (0.123) (0.170) x (6.33) = 1.08 (0.170)

M3 (6.85)

13.9 = 13.93 13.9 (0.133) x (6.8) = 0.91 (0.133) (0.184) x 23.3 = (4.28) (0.184) (0.184) x 40.7 = (7.47) (0.184)

M4 3.1

13.9 = 13.93 13.9 (0.133) x (33.7) = 4.48 (0.133) (0.184) x (42.2) = 7.75 (0.184) (0.184) x 0.3 = (0.05) (0.184)

M5 26.11

(11.9) = (11.89) (11.9) (0.123) x 26.1 = (3.21) (0.123) (0.036) x 4.2 = (0.15) (0.036) (0.170) x 54.27 = (9.24) (0.170) (0.170) x (9.66) (9.24) (0.170)

M6 (33.7)

39.2 = 39.17 39.2 (0.055) x 4.2 = (0.23) (0.055) (0.187) x (40.9) = 7.63 (0.187) (0.258) x (35.08) 9.05 (0.258)

M7 55.62

(22.0) = (22.02) (22.0) (0.210) x 55.6 = (11.67) (0.210) (0.290) x 24.76 = (7.19) (0.290)

M8 (40.87)

-3.609 = -3.61 -3.609

(0.75) x 47.4 = -35.55 (0.75)

(0.75) x (9.6) = 7.17 (0.75)-31.98

-2.813 = -2.81 -2.813

(0.75) x 29.2 = -21.90 (0.75)

(0.75) x (40.6) = 30.43 (0.75)

-1.350 = -1.35 -1.350

(0.75) x (14.8) = 11.07 (0.75)

(0.75) x 21.9 = -16.42 (0.75)

Putaran 9

= 43.91 43.9 x (2.7) = 0.17 (0.063) x x (0.5) = 0.23 (0.438) x

MI 44.30

= (3.24) (3.2) x 44.3 = (2.46) (0.056) x x 19.5 = (1.08) (0.056) xx (10.46) = 4.07 (0.389) x

M2 (2.72)

= (11.89) (11.9) x 3.1 = (0.38) (0.123) x x 4.2 (0.15) (0.036) x x (36.5) = 4.50 (0.123) xx (6.33) = 1.08 (0.170) x

M3 (6.85)

= 13.93 13.9 x (6.8) = 0.91 (0.133) x x 23.3 = (4.28) (0.184) x x 40.7 = (7.47) (0.184) x

M4 3.09

= 13.93 13.9 x (33.7) = 4.48 (0.133) x x (42.2) = 7.75 (0.184) x x 0.3 = (0.05) (0.184) x

M5 26.11

= (11.89) (11.9) x 26.1 = (3.21) (0.123) x x 4.2 = (0.15) (0.036) xx 54.27 = (9.24) (0.170) xx (9.66) (9.24) (0.170) x

M6 (33.7)

= 39.17 39.2 x 4.2 = (0.23) (0.055) x x (40.9) = 7.63 (0.187) xx (35.08) 9.05 (0.258) x

M7 55.62

= (22.02) (22.0) x 55.6 = (11.67) (0.210) x x 24.76 = (7.19) (0.290) x

M8 (40.87)

= -3.61 -3.609

x 47.4 = -35.55 (0.75) x

x (9.6) = 7.17 (0.75) x-31.98

= -2.81 -2.813

x 29.2 = -21.90 (0.75) x

x (40.6) = 30.43 (0.75) x

= -1.35 -1.350

x (14.8) = 11.07 (0.75) x

x 21.9 = -16.42 (0.75) x

Putaran 10

= 43.909 43.9 (2.7) = 0.170 (0.063) x 7.6 (28.9) = 12.640 (0.438) x (48.9)MI 56.719 MI

= (3.242) (3.2) 56.7 = (3.151) (0.056) x 64.8 19.5 = (1.081) (0.056) x 19.5 (38.83) = 15.101 (0.389) x (54.94)M2 7.627 M2

= (11.888) (11.9) 3.1 = (0.381) (0.123) x 3.1 4.2 (0.152) (0.036) x 4.2 13.3 = (1.642) (0.123) x 12.3 (65.71) = 11.185 (0.170) x (87.03)M3 (2.878) M3

= 13.933 13.9 3.1 = (0.411) (0.133) x 3.1 31.8 = (5.844) (0.184) x 31.3 24.7 = (4.541) (0.184) x 12.8 M4 3.137 M4

= 13.933 13.9 (33.7) = 4.479 (0.133) x (35.0) (47.6) = 8.734 (0.184) x #REF! (28.8) = 5.296 (0.184) x (46.6)M5 32.443 M5

= (11.888) (11.9) 32.4 = (3.994) (0.123) x #REF! 4.2 = (0.152) (0.036) x 4.2 55.62 = (9.467) (0.170) x #REF! 2.84 (9.467) (0.170) x (0.24)

M6 (34.967) M6

= 39.167 39.2 4.2 = (0.231) (0.055) x 4.2 (40.9) = 7.629 (0.187) x #REF! (41.66) #REF! (0.258) x #REF!

M7 #REF! M7

= (22.019) (22.0)#REF! = #REF! (0.210) x #REF!

25.75 = (7.471) (0.290) x #REF!M8 #REF! M8

= -3.61 -3.609

59.9 = -44.89 (0.75) x 70.3

4.7 = -3.56 (0.75) x 14.3 -52.06

= -2.81 -2.813

35.6 = -26.68 (0.75) x #REF!

(37.8) = 28.38 (0.75) x #REF!

= -1.35 -1.350

#REF! = #REF! (0.75) x #REF!

= 43.909 43.9 == (0.477) (0.063) x 13.4 == 21.405 (0.438) x (61.6) =

64.837 MI

= (3.242) (3.2) == (3.602) (0.056) x 70.0 == (1.081) (0.056) x 19.5 == 21.366 (0.389) x (66.16) =

13.441 M2

= (11.888) (11.9) == (0.386) (0.123) x 5.4 =

(0.152) (0.036) x 4.2 = (1.518) (0.123) x #REF! == 14.814 (0.170) x #REF! =

0.870 M3

= 13.933 13.9 == (0.417) (0.133) x 5.4 == (5.752) (0.184) x #REF! == (2.345) (0.184) x 3.0 =

5.419 M4

= 13.933 13.9 == 4.643 (0.133) x #REF! == #REF! (0.184) x #REF! == 8.564 (0.184) x #REF! =

#REF! M5

#REF! (0.170) x #REF!#REF! M6

= 39.167 39.2 == (0.231) (0.055) x 4.2 == #REF! (0.187) x #REF! =

#REF! (0.258) x #REF!#REF! M7

= (22.019) (22.0) == #REF! (0.210) x #REF! == #REF! (0.290) x #REF! =

#REF! M8

= -3.61 -3.609

= -52.69 (0.75) x #REF!

= -10.73 (0.75) x #REF!-67.03

= -2.81 -2.813

= #REF! (0.75) x #REF!

= -1.35 -1.350

= #REF! (0.75) x #REF!

Putaran 12

43.909 43.9 = (0.840) (0.063) x 17.5 = 26.957 (0.438) x #REF! = 70.025 MI

(3.242) (3.2) = (3.890) (0.056) x #REF! = (1.081) (0.056) x 19.5 = 25.731 (0.389) x #REF! = 17.518 M2

(11.888) (11.9) = (0.667) (0.123) x #REF! = (0.152) (0.036) x 4.2

#REF! (0.123) x #REF! =#REF! (0.170) x #REF! =#REF! M3

13.933 13.9 = (0.720) (0.133) x #REF! =

#REF! (0.184) x #REF! = (0.549) (0.184) x #REF! =

#REF! M4

13.933 13.9 =#REF! (0.133) x #REF! =#REF! (0.184) x #REF! =#REF! (0.184) x #REF! =#REF! M5

(11.888) (11.9) =#REF! (0.123) x #REF! =

(0.152) (0.036) x 4.2 =#REF! (0.170) x #REF! =#REF! (0.170) x #REF!#REF! M6

39.167 39.2 = (0.231) (0.055) x 4.2 =

#REF! (0.187) x #REF! =#REF! (0.258) x #REF!#REF! M7

(22.019) (22.0) =#REF! (0.210) x #REF! =#REF! (0.290) x #REF! =#REF! M8

= -3.61 -3.609

= #REF! (0.75) x #REF!

= #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

= #REF! (0.75) x #REF!

= -1.35 -1.350

= #REF! (0.75) x #REF!

Putaran 13

43.909 43.9 = (1.095) (0.063) x #REF! =

#REF! (0.438) x #REF! =#REF! MI

(3.242) (3.2) =#REF! (0.056) x #REF! =

(1.081) (0.056) x 19.5 =#REF! (0.389) x #REF! =#REF! M2

(11.888) (11.9) =#REF! (0.123) x #REF! =

(0.152) (0.036) x 4.2 #REF! (0.123) x #REF! =#REF! (0.170) x #REF! =#REF! M3

(11.888) (11.9) =#REF! (0.123) x #REF! =

39.167 39.2 = (0.231) (0.055) x 4.2 =

= -3.61 -3.609

= #REF! (0.75) x #REF!

= #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

= #REF! (0.75) x #REF!

= -1.35 -1.350

= #REF! (0.75) x #REF!

Putaran 14

(3.242) (3.2) =#REF! (0.056) x #REF! =

(1.081) (0.056) x 19.5 =#REF! (0.389) x #REF! =#REF! M2

(11.888) (11.9) =#REF! (0.123) x #REF! =

39.167 39.2 = (0.231) (0.055) x 4.2 =

= -3.61 -3.609

= #REF! (0.75) x #REF!

= #REF! (0.75) x #REF!#REF!

= -2.81 -2.813

= #REF! (0.75) x #REF!

= -1.35 -1.350

= #REF! (0.75) x #REF!

(3.242) (3.2) =#REF! (0.056) x #REF! =

(1.081) (0.056) x 19.5 =#REF! (0.389) x #REF! =#REF! M2

(11.888) (11.9) =#REF! (0.123) x #REF! =

39.167 39.2 = (0.231) (0.055) x 4.2 =

= -3.61 -3.609 =

= #REF! (0.75) x #REF! =

= #REF! (0.75) x #REF! =#REF!

= -2.81 -2.813 =

= #REF! (0.75) x #REF! =

= -1.35 -1.350 =

= #REF! (0.75) x #REF! =

Putaran 16

(3.242) (3.2) = (3.242)#REF! (0.056) x #REF! = #REF!

(11.888) (11.9) = (11.888)#REF! (0.123) x #REF! = #REF!

(0.152) (0.036) x 4.2 (0.152)#REF! (0.123) x #REF! = #REF!#REF! (0.170) x #REF! = #REF!#REF! M3 #REF!

13.933 13.9 = 13.933 #REF! (0.133) x #REF! = #REF!#REF! (0.184) x #REF! = #REF!#REF! (0.184) x #REF! = #REF!#REF! M4 #REF!

13.933 13.9 = 13.933 #REF! (0.133) x #REF! = #REF!#REF! (0.184) x #REF! = #REF!#REF! (0.184) x #REF! = #REF!#REF! M5 #REF!

(11.888) (11.9) = (11.888)#REF! (0.123) x #REF! = #REF!

(0.152) (0.036) x 4.2 = (0.152)#REF! (0.170) x #REF! = #REF!#REF! (0.170) x #REF! #REF!#REF! M6 #REF!

39.167 39.2 = 39.167 (0.231) (0.055) x 4.2 = (0.231)

#REF! (0.187) x #REF! = #REF!#REF! (0.258) x #REF! #REF!#REF! M7 #REF!

(22.019) (22.0) = (22.019)#REF! (0.210) x #REF! = #REF!#REF! (0.290) x #REF! = #REF!#REF! M8 #REF!

-3.61 -3.609 = -3.61

#REF! (0.75) x #REF! = #REF!

-2.81 -2.813 = -2.81

#REF! (0.75) x #REF! = #REF!

#REF! #REF!

-1.35 -1.350 = -1.35

#REF! (0.75) x #REF! = #REF!

#REF! #REF!

Putaran 17

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

(11.9) = (11.888) (0.123) x #REF! = #REF! (0.036) x 4.2 (0.152) (0.123) x #REF! = #REF! (0.170) x #REF! = #REF!

M3 #REF!

13.9 = 13.933 (0.133) x #REF! = #REF! (0.184) x #REF! = #REF! (0.184) x #REF! = #REF!

M4 #REF!

M5 #REF!

(11.9) = (11.888) (0.123) x #REF! = #REF! (0.036) x 4.2 = (0.152) (0.170) x #REF! = #REF! (0.170) x #REF! #REF!

M6 #REF!

39.2 = 39.167 (0.055) x 4.2 = (0.231) (0.187) x #REF! = #REF! (0.258) x #REF! #REF!

M7 #REF!

(22.0) = (22.019) (0.210) x #REF! = #REF! (0.290) x #REF! = #REF!

M8 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

Putaran 17

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

M7 #REF!

(22.0) = (22.019) (0.210) x #REF! = #REF! (0.290) x #REF! = #REF!

M8 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

Putaran 18

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

M7 #REF!

(22.0) = (22.019) (0.210) x #REF! = #REF! (0.290) x #REF! = #REF!

M8 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

Putaran 19

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

M7 #REF!

(22.0) = (22.019) (0.210) x #REF! = #REF! (0.290) x #REF! = #REF!

M8 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

Putaran 20

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

M7 #REF!

(22.0) = (22.019) (0.210) x #REF! = #REF! (0.290) x #REF! = #REF!

M8 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

Putaran 21

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

M7 #REF!

(22.0) = (22.019) (0.210) x #REF! = #REF! (0.290) x #REF! = #REF!

M8 #REF!

-3.609 =

(0.75) x #REF! =

-2.813 =

(0.75) x #REF! =

-1.350 =

(0.75) x #REF! =

Putaran 22

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

M7 #REF!

(22.0) = (22.019) (0.210) x #REF! = #REF! (0.290) x #REF! = #REF!

M8 #REF!

-3.61 -3.609

#REF! (0.75) x #REF!

-2.81 -2.813

#REF! (0.75) x #REF!

-1.35 -1.350

#REF! (0.75) x #REF!

Putaran 23

43.9 = (0.063) x #REF! = (0.438) x #REF! =

(3.2) = (0.056) x #REF! = (0.056) x 19.5 = (0.389) x #REF! =

(11.9) = (0.123) x #REF! = (0.036) x 4.2 (0.123) x #REF! = (0.170) x #REF! =

13.9 = (0.133) x #REF! = (0.184) x #REF! = (0.184) x #REF! =

(11.9) = (0.123) x #REF! = (0.036) x 4.2 = (0.170) x #REF! = (0.170) x #REF!

39.2 = (0.055) x 4.2 = (0.187) x #REF! = (0.258) x #REF!

(22.0) = (0.210) x #REF! = (0.290) x #REF! =

= -3.61 -3.609

= #REF! (0.75) x

= #REF! (0.75) x#REF!

= -2.81 -2.813

= #REF! (0.75) x

= -1.35 -1.350

= #REF! (0.75) x

Putaran 24

(3.242) (3.2)#REF! (0.056) x #REF!

(1.081) (0.056) x 19.5 #REF! (0.389) x #REF!#REF! M2

(11.888) (11.9)#REF! (0.123) x #REF!

(0.152) (0.036) x 4.2 #REF! (0.123) x #REF!#REF! (0.170) x #REF!#REF! M3

13.933 13.9 #REF! (0.133) x #REF!#REF! (0.184) x #REF!#REF! (0.184) x #REF!#REF! M4

13.933 13.9 #REF! (0.133) x #REF!#REF! (0.184) x #REF!#REF! (0.184) x #REF!#REF! M5

(11.888) (11.9)#REF! (0.123) x #REF!

(0.152) (0.036) x 4.2 #REF! (0.170) x #REF!#REF! (0.170) x #REF!#REF! M6

39.167 39.2 (0.231) (0.055) x 4.2

#REF! (0.187) x #REF!#REF! (0.258) x #REF!#REF! M7

(22.019) (22.0)#REF! (0.210) x #REF!#REF! (0.290) x #REF!#REF! M8

= -3.61 -3.609

#REF! = #REF! (0.75)

#REF! = #REF! (0.75)#REF!

= -2.81 -2.813

#REF! = #REF! (0.75)

= -1.35 -1.350

#REF! = #REF! (0.75)

Putaran 25

= 43.909 43.9 = #REF! (0.063) x = #REF! (0.438) x

= (3.242) (3.2)= #REF! (0.056) x = (1.081) (0.056) x= #REF! (0.389) x

= (11.888) (11.9)= #REF! (0.123) x

(0.152) (0.036) x = #REF! (0.123) x= #REF! (0.170) x

= 13.933 13.9 = #REF! (0.133) x = #REF! (0.184) x = #REF! (0.184) x

= (11.888) (11.9)= #REF! (0.123) x = (0.152) (0.036) x= #REF! (0.170) x

#REF! (0.170) x#REF!

= 39.167 39.2 = (0.231) (0.055) x = #REF! (0.187) x

#REF! (0.258) x#REF!

= (22.019) (22.0)= #REF! (0.210) x = #REF! (0.290) x

= -3.61

x #REF! = #REF!

= -2.81

x #REF! = #REF!

= -1.35

x #REF! = #REF!

Putaran 26

= 43.909 43.9 #REF! = #REF! (0.063)#REF! = #REF! (0.438)

MI #REF!

= (3.242) (3.2)#REF! = #REF! (0.056)

19.5 = (1.081) (0.056)#REF! = #REF! (0.389)

M2 #REF!

= (11.888) (11.9)#REF! = #REF! (0.123)

4.2 (0.152) (0.036)#REF! = #REF! (0.123)#REF! = #REF! (0.170)

M3 #REF!

= 13.933 13.9 #REF! = #REF! (0.133)#REF! = #REF! (0.184)#REF! = #REF! (0.184)

M4 #REF!

M5 #REF!

= (11.888) (11.9)#REF! = #REF! (0.123)

4.2 = (0.152) (0.036)#REF! = #REF! (0.170)#REF! #REF! (0.170)

M6 #REF!

= 39.167 39.2 4.2 = (0.231) (0.055)

#REF! = #REF! (0.187)#REF! #REF! (0.258)

M7 #REF!

= (22.019) (22.0)#REF! = #REF! (0.210)#REF! = #REF! (0.290)

M8 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

= 43.909 x #REF! = #REF!x #REF! = #REF!

MI #REF!

M2 #REF!

= (11.888) x #REF! = #REF! x 4.2 (0.152)x #REF! = #REF!x #REF! = #REF!

M3 #REF!

M4 #REF!

M5 #REF!

= (11.888) x #REF! = #REF!x 4.2 = (0.152)x #REF! = #REF!x #REF! #REF!

M6 #REF!

= 39.167 x 4.2 = (0.231)x #REF! = #REF!x #REF! #REF!

M7 #REF!

= (22.019) x #REF! = #REF!x #REF! = #REF!

M8 #REF!

-3.609 =

(0.75) x #REF! =

-2.813 =

(0.75) x #REF! =

-1.350 =

(0.75) x #REF! =

Putaran 27

43.9 = 43.909 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

M2 #REF!

M3 #REF!

M4 #REF!

M5 #REF!

M6 #REF!

M7 #REF!

(22.0) = (22.019) (0.210) x #REF! = #REF! (0.290) x #REF! = #REF!

M8 #REF!

-3.61 -3.609

#REF! (0.75) x #REF!

-2.81 -2.813

#REF! (0.75) x #REF!

-1.35 -1.350

#REF! (0.75) x #REF!

Putaran 28

43.9 = (0.063) x #REF! = (0.438) x #REF! =

(3.2) = (0.056) x #REF! = (0.056) x 19.5 = (0.389) x #REF! =

(11.9) = (0.123) x #REF! = (0.036) x 4.2 (0.123) x #REF! = (0.170) x #REF! =

13.9 = (0.133) x #REF! = (0.184) x #REF! = (0.184) x #REF! =

(11.9) = (0.123) x #REF! = (0.036) x 4.2 = (0.170) x #REF! = (0.170) x #REF!

39.2 = (0.055) x 4.2 = (0.187) x #REF! = (0.258) x #REF!

(22.0) = (0.210) x #REF! = (0.290) x #REF! =

= -3.61 -3.609

= #REF! (0.75)

= #REF! (0.75)#REF!

= -2.81 -2.813

= #REF! (0.75)

= -1.35 -1.350

= #REF! (0.75)

Putaran 29

43.909 43.9 #REF! (0.063) x #REF! (0.438) x#REF!

(3.242) (3.2)#REF! (0.056) x

(1.081) (0.056) x#REF! (0.389) x#REF!

(11.888) (11.9)#REF! (0.123) x

(0.152) (0.036) x #REF! (0.123) x#REF! (0.170) x#REF!

13.933 13.9 #REF! (0.133) x #REF! (0.184) x #REF! (0.184) x #REF!

(11.888) (11.9)#REF! (0.123) x

(0.152) (0.036) x#REF! (0.170) x#REF! (0.170) x#REF!

39.167 39.2 (0.231) (0.055) x

#REF! (0.187) x#REF! (0.258) x#REF!

(22.019) (22.0)#REF! (0.210) x #REF! (0.290) x#REF!

= -3.61

x #REF! = #REF!

= -2.81

x #REF! = #REF!

= -1.35

x #REF! = #REF!

Putaran 30

= 43.909 43.9 #REF! = #REF! (0.063)#REF! = #REF! (0.438)

MI #REF!

= (3.242) (3.2)#REF! = #REF! (0.056)

19.5 = (1.081) (0.056)#REF! = #REF! (0.389)

M2 #REF!

= (11.888) (11.9)#REF! = #REF! (0.123)

4.2 (0.152) (0.036)#REF! = #REF! (0.123)#REF! = #REF! (0.170)

M3 #REF!

M4 #REF!

M5 #REF!

= (11.888) (11.9)#REF! = #REF! (0.123)

4.2 = (0.152) (0.036)#REF! = #REF! (0.170)#REF! #REF! (0.170)

M6 #REF!

= 39.167 39.2 4.2 = (0.231) (0.055)

#REF! = #REF! (0.187)#REF! #REF! (0.258)

M7 #REF!

= (22.019) (22.0)#REF! = #REF! (0.210)#REF! = #REF! (0.290)

M8 #REF!

-3.609 = -3.61

(0.75) x #REF! = #REF!

(0.75) x #REF! = #REF!#REF!

-2.813 = -2.81

(0.75) x #REF! = #REF!

-1.350 = -1.35

(0.75) x #REF! = #REF!

= 43.909 x #REF! = #REF!x #REF! = #REF!

MI #REF!

M2 #REF!

= (11.888) x #REF! = #REF! x 4.2 (0.152)x #REF! = #REF!x #REF! = #REF!

M3 #REF!

M4 #REF!

M5 #REF!

= (11.888) x #REF! = #REF!x 4.2 = (0.152)x #REF! = #REF!x #REF! #REF!

M6 #REF!

= 39.167 x 4.2 = (0.231)x #REF! = #REF!x #REF! #REF!

M7 #REF!

= (22.019) x #REF! = #REF!x #REF! = #REF!

M8 #REF!

-3.609

(0.75) x #REF!

-2.813

(0.75) x #REF!

-1.350

(0.75) x #REF!

Putaran 31

43.9 = (0.063) x #REF! = (0.438) x #REF! =

(3.2) = (0.056) x #REF! = (0.056) x 19.5 = (0.389) x #REF! =

(11.9) = (0.123) x #REF! = (0.036) x 4.2 (0.123) x #REF! = (0.170) x #REF! =

13.9 = (0.133) x #REF! = (0.184) x #REF! = (0.184) x #REF! =

(11.9) = (0.123) x #REF! = (0.036) x 4.2 = (0.170) x #REF! = (0.170) x #REF!

39.2 = (0.055) x 4.2 = (0.187) x #REF! = (0.258) x #REF!

(22.0) = (0.210) x #REF! = (0.290) x #REF! =

= -3.61 -3.609

= #REF! (0.75)

= #REF! (0.75)#REF!

= -2.81 -2.813

= #REF! (0.75)

= -1.35 -1.350

= #REF! (0.75)

Putaran 32

43.909 43.9 #REF! (0.063) x #REF! (0.438) x#REF!

(3.242) (3.2)#REF! (0.056) x

(1.081) (0.056) x#REF! (0.389) x#REF!

(11.888) (11.9)#REF! (0.123) x

(0.152) (0.036) x #REF! (0.123) x#REF! (0.170) x#REF!

13.933 13.9 #REF! (0.133) x #REF! (0.184) x #REF! (0.184) x #REF!

(11.888) (11.9)#REF! (0.123) x

(0.152) (0.036) x#REF! (0.170) x#REF! (0.170) x#REF!

39.167 39.2 (0.231) (0.055) x

#REF! (0.187) x#REF! (0.258) x#REF!

(22.019) (22.0)#REF! (0.210) x #REF! (0.290) x#REF!

= -3.61

x #REF! = #REF!

= -2.81

x #REF! = #REF!

= -1.35

x #REF! = #REF!

= 43.909 #REF! = #REF!#REF! = #REF!

MI #REF!

= (3.242)#REF! = #REF!

19.5 = (1.081)#REF! = #REF!

M2 #REF!

= (11.888)#REF! = #REF!

4.2 (0.152)#REF! = #REF!#REF! = #REF!

M3 #REF!

M4 #REF!

M5 #REF!

= (11.888)#REF! = #REF!

4.2 = (0.152)#REF! = #REF!#REF! #REF!

M6 #REF!

= 39.167 4.2 = (0.231)

#REF! = #REF!#REF! #REF!

M7 #REF!

= (22.019)#REF! = #REF!#REF! = #REF!

M8 #REF!

-3.609375 =

(0.75) x #REF! =

-2.8125 =

(0.75) x #REF! =

(0.75) x #REF! = (0.75) x #REF! =

-1.35 =

(0.75) x #REF! =

(0.75) x #REF! = (0.75) x #REF! =

Putaran 33

43.9 = 43.9 (0.063) x #REF! = #REF! (0.438) x #REF! = #REF!

MI #REF!

(3.2) = (3.2) (0.056) x #REF! = #REF! (0.056) x #REF! = #REF! (0.389) x #REF! = #REF!

M2 #REF!

(11.9) = (11.9) (0.123) x #REF! = #REF!

(0.123) x #REF! = #REF! (0.170) x #REF! = #REF!

M3 #REF!

13.9 = 13.9 (0.133) x #REF! = #REF!

M4 #REF!

13.9 = 13.9 (0.133) x #REF! = #REF!

M5 #REF!

(11.9) = (11.9) (0.123) x #REF! = #REF! (0.036) x #REF! = #REF! (0.170) x #REF! = #REF! (0.170) x #REF! #REF!

M6 #REF!

39.2 = 39.2 (0.055) x #REF! = #REF! (0.187) x #REF! = #REF! (0.258) x #REF! #REF!

M7 #REF!

(22.0) = (22.0) (0.210) x #REF! = #REF! (0.290) x #REF! = #REF!

M8 #REF!

#REF!#REF!

#REF!#REF!#REF!

ANALISA BEBEAN GEMPA METODE STATIKA EKIVALEN

Pehitungan Berat Lantai Dan Berat Gedung

DATA KONSTRUKSI Jarak antar kolom arah x 4.00 Jarak antar kolom arah y 4.00 Spasi Kolom Arah x 3.00 Spasi Kolom Arah y 5.00 Tinggi antar Lantai 1-3 4.00 Tebal Plat Atap 0.10 Tebal Plat Lantai 0.12 Dimensi Kolom Lantai 1, 2, 3 0.40 0.40 Dimensi Kolom Lantai 2, 3 0.10 0.40 Dimensi Kolom KP 0.10 ###Dimensi TB1 0.20 0.40 Dimensi RB1 0.20 0.30 Dimensi RB2 0.15 0.20 Dimensi Balok 30/40 0.30 0.40 Dimensi Balok 20/30 0.20 0.30 Dimensi Balok 20/40 0.20 0.40 Dimensi Balok 30/60 0.30 0.60 Dimensi Balok 30/50 0.30 0.50

Jumlah Balok Arah x Rangka Atap(RB1)TYPE RB1 10.5 m 1.00 Jumlah Balok Arah x lantai dakTYPE BL4 3.5 m 28.00 TYPE BL4 2 m 6.00 TYPE BL4 3 m 6.00 TYPE BL4 1 m 2.00 TYPE BL5 3.5 m 28.00 Jumlah Balok Arah x lantai 3 - TYPE BL4 10 m 20.00 TYPE BL5 3 m 6.00 TYPE Bl1 3.5 m 70.00 Jumlah Balok Arah x lantai 2 - TYPE Bl1 3.5 m 44.00 TYPE Bl1 4 m 2.00 TYPE BL4 3.5 m 8.00 TYPE BL4 4 m 2.00 TYPE BL4 3 m 8.00 TYPE BL5 3.5 m 2.00 TYPE BL5 1.75 m 2.00 Jumlah Balok Arah x lantai dasarTYPE TB2 7 m 24.00 TYPE TB2 6 m 14.00 TYPE TB3 3.5 m 10.00 TYPE TB3 3 m 6.00 TYPE TB3 4 m 6.00 TYPE TB3 5 m 2.00 TYPE TB4 3.5 m 2.00 TYPE TB4 3 m 4.00 TYPE TB4 2.5 m 8.00 TYPE TB4 4 m 4.00

TYPE TB4 1.75 m 2.00 TYPE TB4 1 m 2.00 Jumlah Balok Arah y Rangka atapTYPE RB1 4 m 8.00 TYPE RB1 6 m 4.00 TYPE RB1 4 m 4.00 Jumlah Balok Arah y Lantai dakTYPE BL6 8 m 4.00 TYPE BL6 2 m 2.00 TYPE BL5 2 m 14.00 TYPE BL4 4 m 74.00 Jumlah Balok arah y Lantai 3TYPE BL4 4 m 72.00 TYPE BL4 2 m 10.00 TYPE BL5 2 m 14.00 TYPE BL2 4 m 26.00 Jumlah Balok arah y Lantai 2 - TYPE BL4 4 m 52.00 TYPE BL4 1 m 16.00 TYPE BL4 2 m 10.00 TYPE BL4 2 m 12.00 TYPE BL5 2 m 14.00 TYPE BL2 4 m 12.00 Jumlah Balok arah y Lantai 1TYPE TB2 4 m 28.00 TYPE TB4 4 m 44.00 TYPE TB4 2 m 12.00 TYPE TB1 4 m 4.00 TYPE TB3 2 m 18.00 Beban Air Hujan 100.00 Beban Hidup Ruang kantor 250.00 Berat Spesi 21.00 Berat Tegel 24.00 Berat Plafond + Rangka 50.00 Berat Dinding 250.00 Berat Jenis Beton 2,400.00 Lokasi Gedung Wilayah Gempa 2Kondisi Tanah KerasJumlah Kolom lantai dak 12.00 Type K1 29.00 Type Kp 34.00 Jumlah Kolom lantai 3Type K1 36.00

4.00 6.00 4.00

Type Kp 80.00 Jumlah Kolom lantai 2 - Type K1 54.00

12.00 Type Kp 112.00

8.00 8.00

Jumlah Kolom lantai 1 -

Type K1 54.00 4.00 4.00 4.00 62.00

Type Kp 8.00 Luas Lantai 49,5 m x 21,5 m 1,064.25 Luas Plat Atap 501.00

PERHITUNGAN BERAT RANGKA ATAPBeban Mati Rangka AtapBeban Sendiri Rangka Atap 39.13 Beban Balok Arah x 1,512.00 Beban Balok Arah y 10,368.00 Beban Balok anak arah x #VALUE!Beban Balok anak arah y #VALUE!Berat Plafon 53,212.50 Berat Kolom - Berat DindingJumlah Beban Mati Rangka Atap #VALUE!

Beban Hidup Lantai Atap (Watap)

Beban Hidup Atap 161,156.00

#VALUE! Jumlah beban mati + beban hidup pada Atap

Perhitungan Berat Lantai dak AtapBeban Mati dak atapBeban Sendiri Pelat atap 120,240.00 Berat Balok Arah x #VALUE!Berat Balok Arah y #VALUE!Berat Plafon 53,212.50 Berat Spesi 22,349.25 Berat Tegel 25,542.00 Berat Kolom #VALUE!Berat Dinding 21,312.50 Jumlah Beban Mati Lantai dak #VALUE!

Beban Hidup Lantai dakBeban Hidup 53,212.50

Berat Lantai dak atap #VALUE!

Perhitungan Berat Lantai 3Beban Mati Lantai 3Beban Sendiri Pelat lantai 306,504.00 Berat Balok Arah x #VALUE!Berat Balok Arah y #VALUE!Berat Plafon 53,212.50 Berat Spesi 22,349.25 Beban Tangga 4,418.15 Berat Tegel 25,542.00 Berat Kolom #VALUE!Berat Dinding 208,968.00 Jumlah Beban Mati Lantai dak #VALUE!

Berat Atap ( Watap )

Beban Hidup Lantai 3Beban Hidup 133,031.25

Berat Lantai ( W Lt3) #VALUE!

karena jaraknya yang simetris sehingga beban yang akan diterima oleh tiap -tiap lantai adalah Lantai dak = #VALUE! kg

Lt.3 = #VALUE! kg Lt. 2 = #VALUE! kg Lt. 1 = #VALUE!

#VALUE!Berat Gedung ( W t ) #VALUE!Jumlah Lantai ( n ) 5Tinggi Gedung ( H ) 18.14 mLebar Arah x ( Bx ) 20Lebar Arah y ( By ) 48Waktu Getar Alami ( Tx ) = 0.09*H*( Bx ^ 0,5 ) = 7.30 Waktu Getar Alami ( Ty ) = 0,09*H*( By ^ 0,5 ) = 11.31 Koefesien Respon Gempa

Respon Struktur Terhadap Gempa Rencana Arah x ( Cx ) 0.02 Respon Struktur Terhadap Gempa Rencana Arah y ( Cy ) 0.01 Faktor Keutamaan Gedung ( I ) 1.00 Faktor Daktatitas Struktur ( R ) 6.40 Beban Geser Dasar Statik Ekivalen Arah x (Vx ) #VALUE!Beban Geser Dasar Statik Ekivalen Arah y (Vy ) #VALUE!

Tabel Disribusi Gaya GeserTingkat Tinggi Wi Zi Wi*Zi Fix

4 5.14 #VALUE! 18.14 #VALUE! #VALUE!3 4 #VALUE! 14.14 #VALUE! #VALUE!2 4 #VALUE! 10.14 #VALUE! #VALUE!1 5 #VALUE! 5.14 #VALUE! #VALUE!

Jumlah 18.14 #VALUE! 104.1 #VALUE! #VALUE!

jumlah Wi * Zi

Percepatan Garvitasi (g) 9.80 Simpangan pada struktur pada arah x (Sx) 0.03 Simpangan pada struktur arah y (Sy) 0.02

Tingkat Zi Wi Rotasi Mi 4 18.140 #VALUE! 1.0000 #VALUE! #VALUE!3 14.140 #VALUE! 0.7795 #VALUE! #VALUE!2 10.140 #VALUE! 0.7171 #VALUE! #VALUE!1 5.140 #VALUE! 0.5069 #VALUE! #VALUE!0 0.000 #VALUE! 0.0000 #VALUE! #VALUE!

Jumlah #VALUE! #VALUE!

g = 9,8100Mi = Wi / g R=1,6 Mi * = Mi . Rotasi ^2 I= 1 L* = Mi* . Rotasi

1ωi²

simpangan pada struktur arah X (Sax) Sax = Cx . I . G / RSax = 0,049 . 1 . 9,8100/ 1,6

0.30043125

0.36174375

Tingkat Zi Wi WiZi Fix Fiy

Fi = Wi . Zi x V

Frekwensi Alami gedung (ώx)

Frekwensi Alami gedung (ώy)

Ui = Ʃ Li* . x SaiƩ Mi*

4 18.14 #VALUE! #VALUE! #VALUE! #VALUE!3 14.14 #VALUE! #VALUE! #VALUE! #VALUE!2 10.14 #VALUE! #VALUE! #VALUE! #VALUE!1 5.14 #VALUE! #VALUE! #VALUE! #VALUE!

Jumlah #VALUE! #VALUE! #VALUE! #VALUE!

- Waktu getar alami berdasarkan persamaan Rayleigh (Tx) #VALUE!- Waktu getar alami berdasarkan persamaan Rayleigh (Ty) #VALUE!- Jumlah lantai (n) 4.00 - Faktor waktu getar alami 0.19 - Pembatasan waktu getar alami fundamental 1.52 - nilai respon struktur terhadap gempa dengan nilai T baru (Cx) #VALUE!- nilai respon struktur terhadap gempa dengan nilai T baru (Cy) #VALUE!

- Gaya geser dasar nominal statik ekivalen baru arah x #VALUE!

- Gaya geser dasar nominal statik ekivalen baru arah y #VALUE!

oke! Tabel Distribusi Beban Gempa pada tiap lantai

Tingkat Zi Wi WiZi Vx Vy 4 18.14 #VALUE! #VALUE! #VALUE! 16,176.53 3 14.14 #VALUE! #VALUE! #VALUE! 16,176.53 2 10.14 #VALUE! #VALUE! #VALUE! 16,176.53 1 5.14 #VALUE! #VALUE! #VALUE! 16,176.53

47.56 #VALUE! #VALUE!

ANALISA BEBEAN GEMPA METODE STATIKA EKIVALEN

Pehitungan Berat Lantai Dan Berat Gedung

DATA KONSTRUKSI mmbhbhmmmmmmm 0.28 m 0.18 m 0.08 m 0.30 m 0.20 mm 0.50

berat sendiri Balokbh 10.50 bh 10.50 bh 98.00 #VALUE! 14bh 12.00 #VALUE! 3bh 18.00 #VALUE! 3bh 2.00 #VALUE! 1bh 98.00 #VALUE! 14bh 228.00 #VALUE!bh 200.00 #VALUE! 10bh 18.00 #VALUE! 3bh 245.00 52,920.00 35bh 463.00 #VALUE!bh 154.00 33,264.00 22bh 8.00 1,728.00 1bh 28.00 #VALUE! 4bh 8.00 #VALUE! 1bh 24.00 #VALUE! 4bh 7.00 #VALUE! 1bh 3.50 #VALUE! 1bh 232.50 #VALUE!bh 168.00 #VALUE! 12bh 84.00 #VALUE! 7bh 35.00 #VALUE! 5bh 18.00 #VALUE! 3bh 24.00 #VALUE! 3bh 10.00 #VALUE! 1bh 7.00 #VALUE! 1bh 12.00 #VALUE! 2bh 20.00 #VALUE! 4bh 16.00 #VALUE! 2

bh 3.50 #VALUE! 1bh 2.00 #VALUE! 1bh 399.50 #VALUE!bh 32.00 2,764.80 4bh 24.00 2,073.60 2bh 16.00 1,382.40 2bh 72.00 6,220.80 bh 32.00 #VALUE! 2bh 4.00 #VALUE! 1bh 28.00 #VALUE! 7bh 296.00 #VALUE! 37bh 360.00 #VALUE!bh 288.00 #VALUE! 36bh 20.00 #VALUE! 5bh 28.00 #VALUE! 7bh 104.00 9,984.00 13bh 440.00 #VALUE!bh 208.00 #VALUE! 26bh 16.00 #VALUE! 8bh 20.00 #VALUE! 5bh 24.00 #VALUE! 6bh 28.00 #VALUE! 7bh 48.00 4,608.00 6bh 344.00 #VALUE!bh 112.00 #VALUE! 14bh 176.00 #VALUE! 22bh 24.00 #VALUE! 6bh 16.00 2,150.40 2bh 36.00 #VALUE! 9kg/m 364.00 #VALUE!kg/mkg/mkg/mkg/mkg/mkg/m

Wilayah Gempa 2 TC = 0,15 / TKeras Tx = 0,09 . 28 ( 11,6^0,5)

bh 0bh #VALUE!bh 8,388.48

#VALUE!bh #VALUE!bh #VALUE! 28bh #VALUE! 2bh 768.00 3bh 15,360.00 2

#VALUE! 40bh #VALUE!bh 18,432.00 24bh #VALUE! 6bh #VALUE! 56bh #VALUE! 4

#VALUE! 4

bhbh 7,680.00 18bh 11,520.00 2bh 5,760.00 2bh #VALUE! 2bh 1,920.00 31m^2 #VALUE! 4 Ty = 0,09 . 28 ( 7,8 ^0,5 )

PERHITUNGAN BERAT RANGKA ATAPBeban Mati Rangka Atap

kg 36 x 0.12 x 2400kg 0.40 x ( 0.60 - 0.12 ) x 2400 x 6 x 4kg 0.40 x ( 0.60 - 0.12 ) x 2400 x 6 x 3kgkgkg 36 x 50kg 0.60 x 0.60 x 1.5 x 2400 x 12kg 6 x 1.5 x 250 x 4kg

kg 36 x 100 x 0.5

kg Wl8 = Wdl8 + Wll8Wl8 = 58098.6 + 1800

Perhitungan Berat Lantai dak Atap

kg 36 x 0.12 x 2400kg 0.40 x ( 0.60 - 0.12 ) x 2400 x 6 x 4kg 0.40 x ( 0.60 - 0.12 ) x 2400 x 6 x 3kg 36 x 50kg 36 x 24kg 36 x 21kg 0.60 x 0.60 x 3 x 2400 x 12kg 6 x 3 x 250 x 4kg

kg 36 x 250 x 0.5

kg Wl7 = Wdl7 + Wll7

Perhitungan Berat Lantai 3

kgkgkgkgkg Luasan dindingkgkg LT.1 185.94kg 40.234kg 226.174kg

LT.2 77192

kg 17.516

kg 4.3

Perhitungan Berat Lantai 2 2.5309.3

kg 618.6kgkg LT.3kg 48kg 2Kgkg 28kg 24kg 10.5kg 16

6.23426

kg 8208.968

Perhitungan Berat Lantai 1

kgkgkgkgkgkgkgkgkgkg

Fiy Cx = Tc / Tx Vx#VALUE! 0.15 #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE!

Vx = Cx . R . WtR

Vx = 0,048 . 1 . 10558851.6

#VALUE! kg / KN#VALUE! KN

Vy = 0,059 .1 . 1055885

38935.76 kg / KN389.3576 KN

L * Uix Uiy Fix Fiy 0.860132#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0.860132#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0.860132#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0.860132#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0.860132#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0.860132

#VALUE! #VALUE! #VALUE!

dix diy Widix^2 Widiy^2 Fix*di Fiy*di

0.0425 0.0659 #VALUE! #VALUE! #VALUE! #VALUE!0.0331 0.0513 #VALUE! #VALUE! #VALUE! #VALUE!0.0305 0.0472 #VALUE! #VALUE! #VALUE! #VALUE!0.0216 0.0334 #VALUE! #VALUE! #VALUE! #VALUE!

0 #VALUE! #VALUE! #VALUE! #VALUE!

#VALUE!

> #VALUE!

Fix Fiy #VALUE! #VALUE! jumlah Wi * Zi#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!

#VALUE! #VALUE!

Fi = Wi . Zi x V

luasan plat atap315

160179

0.40 x ( 0.60 - 0.12 ) x 2400 x 6 x 4 5010.40 x ( 0.60 - 0.12 ) x 2400 x 6 x 3

0.40 x ( 0.60 - 0.12 ) x 2400 x 6 x 40.40 x ( 0.60 - 0.12 ) x 2400 x 6 x 3

Vy#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!#VALUE! #VALUE!

g0.555212 9.8 0.03 0.02 0.555212 9.8 0.03 0.02 0.555212 9.8 0.03 0.02 0.555212 9.8 0.03 0.02 0.555212 9.8 0.03 0.02 0.555212 9.8

BEBAN TANGGA

Tangga Tipe 1

No. Uraian Dimensi

L Volume Berat

n p l t m^3 kg/m^3

1 Plat Tangga 1.92 3.50 0.19 6.72 1.292256 2400 2

2 Anak Tangga 0.45 0.30 0.19 0.07 0.14 2400 25

3 Spesi 0.30 1.92 0.01 0.58 0.00576 2100 25

4 Pasir 0.30 1.92 0.01 0.58 0.00576 1600 25

5 Penutup Lantai 0.30 1.92 0.01 0.58 0.00576 2400 25

Tangga Tipe 2

No. Uraian Dimensi

L Volume Berat

n p l t m^3 kg/m^3

1 Plat Tangga 0.80 0.80 0.19 0.64 0.123072 2400 2

2 Anak Tangga 0.45 0.30 0.19 0.07 0.06 2400 25

3 Spesi 0.30 0.80 0.01 0.24 0.0024 2100 25

4 Pasir 0.30 0.80 0.01 0.24 0.0024 1600 25

5 Penutup Lantai 0.30 0.80 0.01 0.24 0.0024 2400 25

Total Berat

6202.8288

8307.36

15388.5888

61554.3552

Total Berat

590.7456

3461.4

4418.1456

No. Judul Gambar Kode 1 Denah Tinjauan Gambar 4.12 Portal Arah Y Gambar 4.2

Peritungan SAP 200 Versi 9

Tabel data-data konstruksi

DATA KONSTRUKSI Jarak antar kolom arah x 4.00 mJarak antar kolom arah y 4.00 mSpasi Kolom Arah x 3.00 bhSpasi Kolom Arah y 5.00 bhTinggi antar Lantai 1-3 4.00 mTebal Plat Atap 0.10 mTebal Plat Lantai 0.12 m

Dimensi P(m) L(m)

Dimensi Kolom K1 0.60 ### mDimensi Kolom K2 0.50 ### mDimensi Kolom K3 0.30 ### mDimensi Kolom K4 0.40 ### mDimensi Kolom K5 0.40 0.60 mDimensi Kolom K6 0.20 0.30 mDimensi Kolom K7 0.30 0.50 mDimensi Kolom KP 0.10 ### mDimensi TB1 0.40 0.70 mDimensi TB2 0.30 0.70 mDimensi TB3 0.30 0.50 mDimensi TB4 0.30 0.40 mDimensi TB5 0.15 0.20 mDimensi RB1 0.20 0.30 mDimensi RB2 0.15 0.20 mDimensi Balok B1 0.40 0.60 mDimensi Balok B2 0.40 0.70 mDimensi Balok B3 0.30 ### mDimensi Balok B4 0.30 0.40 m

Dimensi Balok B5 0.20 0.30 mDimensi Balok B6 0.10 0.60 mDimensi Balok BLA 0.60 1.00 mDimensi Balok BLB 0.30 1.00 mDimensi Balok BLC 0.30 0.50

Mutu beton yang digunakan adalah F'c = 25 Mpa

= 250 = 2,500 t/m

Mutu baja tulangan Fy = 400 Mpa

= 4000= 40,000 t/m

Modulus Elastisitas

E == 4700 15.8114

= 74313.5

= 7.43E+05

Loads Combination 1 1,2 LD + 1,6 LL2 1,2LD + 1,6 LL + QL

Kg/cm2

4700*(F'c)^0,5

Kg/cm2

Recoverd Xls File(515)

Documents

Transcript of Recoverd Xls File(515)

€¦ · XLS file · Web viewETHYL CHLORIDE/VARTER RITTER VL.S.TA 100% W/W FLx100 ML N01BX01 ETHYL CHLORIDE ΒΕΡΟΙΟΠΟΥΛΟΣ Α.Δ. & ΣΙΑ Ο.Ε. 2801927301014 1927301

gmg2/4000/excel/EO… · XLS file · Web view · 2005-01-18EPQ EOQ EOQ Calculator with backorders K c h b

€¦ · XLS file · Web view · 2007-06-281013 hypothetical protein - slr1450 1014 unknown protein - slr1451 3025 hypothetical protein - slr1452 3027 ... ssyA probable inositol

€¦ · XLS file · Web view · 2016-11-06giannoulis 00:41:29 sarantopoulou sesilia 00:41:37 aliferi viky 00:42:14 anavaloglou 00:42:15 koronaiou aliki 00:42:19 kanellias makis

€¦ · XLS file · Web view · 2017-09-19... from the rat embryonic hippocampus [1]. Aucubin significantly reversed the elevated gene and protein expression of MMP-3, MMP-9, MMP-13,

Omar Abdulrahman Srour Presented BY: 6 σ Myths Demystified Course: CEM 515, Project Quality Management Dr. Abdulaziz A. Bubshait.

ΤΟΜΗ Τ.515 26 Απριλίου 2012

pefni.files.wordpress.com€¦ · XLS file · Web viewPRICELIST Κωδικός BARCODE Ονομασία Μορφή Περιεκτικότητα ATC Αρν. λίστα ΜΗ. ΣΥ.

Additional file 1:

mistakidis file

olmesch.files.wordpress.com€¦ · XLS file · Web viewΠΟΥΛΙΟΥ ΜΑΡΙΑ Nikihasapi ... ΚΛΑΙΡΗ clairekyriakou@yahoo.gr

· XLS file · Web view2016-11-16 · Γνωστικό Αντικείμενο: Ευφυών Συστημάτων και Διαδικτυακών Εφαρμογών Εσωτερικά

Lecture 16 Regression with Time-to-event outcomescourses.washington.edu/b515/l16.pdf · Lecture 16 Regression with Time-to-event outcomes BIOST 515 March 2, 2004 BIOST 515, Lecture

THE XLS XLS 1000 - Future Projections · THE XLS Series of power amplifiers from Crown define the standard for live sound systems with unmatched performance, technology, and affordability.

Lecture 10 Polynomial regression - University of Washingtoncourses.washington.edu/b515/l10.pdf · Lecture 10 Polynomial regression BIOST 515 February 5, 2004 BIOST 515, Lecture 10.

CHEM 515 Spectroscopy Vibrational Spectroscopy I.

EE415/515 Fundamentals of Semiconductor Devices Fall 2012 ...

UNIFAC - DDBST GmbH · “A Modified UNIFAC Model. 1. Prediction of VLE, hE, and γ∞” ... The table can be saved as Microsoft Excel (“xls”) file or copied to the Windows clipboard.

3 MSE 515 copy(1).docx · Web viewLecture 3 MSE 515 Solutions of Schrodinger equation for special cases Last time:-ħ 2 2m ∇ 2 ψ+Vψ=Eψ=iℏ ∂ Ψ ∂t Ψ is called a wavefunction

Lecture 5 Hypothesis Testing in Multiple Linear Regression · Lecture 5 Hypothesis Testing in Multiple Linear Regression BIOST 515 January 20, 2004