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DATA PERENCANAAN KUDA - KUDA Dimensi - Bentang kuda-kuda (L) = 15 m - Jarak antar kuda-kuda (s) = 3m - Jarak antar skur kuda-kuda (x) = 2.5 m - Jarak overlap = 30 cm - Jarak efektif gording (Lk) = 1.5 m - Kemiringan atap = 22 o Beban Perencanaan - Berat penutup atap seng BJLS = 10 kg - Beban pekerja + alat = 100 kg - Beban air hujan = 10 kg - Beban angin = 25 kg Kayu kelas I - Elastisitas = 125000 - Berat Jenis (BJ) = 810 kg/m3 - Tegangan Ijin σ lt = 150 kg/cm 2 σ tk // = σ tr // = 130 kg/cm 2 σ tk = 40 kg/cm 2 τ // = 20 kg/cm 2 Ukuran L 1 = 2.425 m L 2 = 2.425 m L 3 = 2.650 m L 4 = 2.650 m L 5 = 2.420 m L 6 = 2.420 m H 1 = 1.080 m H 2 = 1.080 m H 3 = 1.390 m H 4 = 0.520 m H 5 = 0.560 m H 6 = 0.520 m H 7 = 1.950 m
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Hitung Kuda Kuda

Jul 19, 2016

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Page 1: Hitung Kuda Kuda

DATA PERENCANAAN KUDA - KUDA

Dimensi

- Bentang kuda-kuda (L) = 15 m

- Jarak antar kuda-kuda (s) = 3 m

- Jarak antar skur kuda-kuda (x) = 2.5 m

- Jarak overlap = 30 cm

- Jarak efektif gording (Lk) = 1.5 m

- Kemiringan atap = 22 o

Beban Perencanaan

- Berat penutup atap seng BJLS = 10 kg

- Beban pekerja + alat = 100 kg

- Beban air hujan = 10 kg

- Beban angin = 25 kg

Kayu kelas I

- Elastisitas = 125000

- Berat Jenis (BJ) = 810 kg/m3

- Tegangan Ijin σlt = 150 kg/cm2

σtk // = σtr // = 130 kg/cm2

σtk ┴ = 40 kg/cm2

τ// = 20 kg/cm2

Ukuran

L1 = 2.425 m

L2 = 2.425 m

L3 = 2.650 m

L4 = 2.650 m

L5 = 2.420 m

L6 = 2.420 m

H1 = 1.080 m

H2 = 1.080 m

H3 = 1.390 m

H4 = 0.520 m

H5 = 0.560 m

H6 = 0.520 m

H7 = 1.950 m

Page 2: Hitung Kuda Kuda
Page 3: Hitung Kuda Kuda

Sudut-sudut

αo = 22 o γo = o

tan αo = 0.404 tan γo = s13 - 2 tan 12 0.037019098

sin αo = 0.375 sin γo =

cos αo = 0.927 cos γo =

βo = 11 o δo = o

tan βo = 0.194 tan δo = s15 - 2 tan 12 #############

sin βo = 0.191 sin δo =

cos βo = 0.982 cos δo =

Panjang Batang

L1 L1

cos αo cos βo

L2 S13 = L1 tan αo - L1 tan βo

cos αo = 0.508 m

L3 L2

cos αo cos γo

L4 S15 = (L1 + L2) x tan αo - (L1 + L2) x tan βo

cos αo = 1.017 m

L5 L3

cos αo cos δo

L6 S17 = (L1 + L2 + L3 ) x tan αo - (L1 + L2 + L3) x tan βo

cos αo = 1.570 m

L6 L4

cos βo cos δo

L5 S19 = (L5 + L6) x tan αo - (L5 + L6) x tan βo

cos βo = 1.015 m

L4 L5

cos βo cos γo

L3 S21 = L6 tan αo - L6 tan βo

cos βo = 0.507 m

L2

cos βo

m

S16 = = 2.716 m

S12 = = 2.470 m

m

S14 = = 2.425 m

S18 = = 2.716

S11 = = 2.470 m

S20 = = 2.420

S10 = = 2.70 m

S9 = = 2.70 m

S8 = = 2.4653 m

S7 = = 2.4653 m

S6 = = 2.610 m

S5 = = 2.610 m

S4 = = 2.858 m

S3 = = 2.610 m

S2 = = 2.858 m

=S1 = 2.615 m

0.875

0.015

0.015

1.000

12.676

0.225

0.219

0.976

Page 4: Hitung Kuda Kuda

Tabel Panjang Batang

(3)

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

meter

(1) (2)

S1

S2

S3

S4

2.615

2.858

2.610

2.858

S14

S15

S16

S17

S18

S19

S20

S21

S5

S6

S7

S8

S9

S10

S11

S12

S13

2.425

1.017

2.716

1.570

2.716

1.015

2.420

0.507

2.610

2.610

2.465

2.465

2.700

2.700

2.470

2.470

0.508

Btg. Rangkap

Btg. Tunggal

Btg. Tunggal

Btg. Tunggal

Btg. Rangkap

Btg. Tunggal

Btg. Rangkap

Btg. Tunggal

Btg. Tunggal

Btg. Tunggal

Btg. Tunggal

Btg. Tunggal

Btg. Rangkap

46.328Total Panjang meter

Kode Batang Panjang Batang Satuan Keterangan

(4)

Btg. Tunggal

Btg. Tunggal

Btg. Tunggal

Btg. Tunggal

Btg. Tunggal

Btg. Tunggal

Btg. Tunggal

Btg. Tunggal

Page 5: Hitung Kuda Kuda

PERENCANAAN GORDING

PERHITUNGAN PEMBEBANAN PADA GORDING

Beban Mati (DL)

Berat penutub atap seng BJLS = berat BJLS x jarak efektif gording = 15 kg/m

Berat gording kayu 8/15 = luas penampang balok x BJ kayu = 5.832 kg/m

Jumlah berat = 20.832 kg/m

Berat alat penyambung 10% = Jumlah berat x 10% = 2.0832 kg/m

Total berat = 22.915 kg/m

Beban Mati Total (q) = 22.915 ≈ 23 kg/m

qy = q beban mati x cos α = 21.325 kg/m

qx = q beban mati x sin α = 8.616 kg/m

M.qy = 1/8 x qx x 2.52 = 16.660 kg.m

M.qx = 1/8 x qy x (2.5/2)2 = 4.165 kg.m

Beban Hidup (LL)

Beban Hidup Total (P) = 100 kg/m

Py = P beban hidup x cos α = 92.718 kg/m

Px = P beban hidup x sin α = 37.461 kg/m

M.Py = 1/4 X Px X L = 23.413 kg.m

M.Px = 1/4 X Py X (L/2) = 28.974 kg.m

Beban Air Hujan (GL)

Beban Air Hujan Total (G) = 10 kg/m

Gy = G beban hidup x cos α = 9.272 kg/m

Gx = G beban hidup x sin α = 3.746 kg/m

M.Gy = 1/4 X Gx X L = 2.341 kg.m

M.Gx = 1/4 X Gy X (L/2) = 2.897 kg.m

qy

qx

x y

q

α°

py

px

x

y

p

α°

Gy

Gx

x

y

G

α°

Page 6: Hitung Kuda Kuda
Page 7: Hitung Kuda Kuda

Beban Angin (WL)

Beban Angin Total (WL) = 25 kg/m

1. Angin tekan

WL tekan = (0.02 x α - 0.4) x WL x jrk. gording = 1.5 kg/m

M.WL tekan = 1/8 x WL x L2 = 1.172 kg.m

2. Angin hisap

WL hisap = – 0.4 x WL x jarak gording = -15 kg/m

M.WL hisap = 1/8 x WL x L2 = -11.719 kg.m

Tabel Pembebanan Momen

Beban

Mati A. Tekan A. Hisap

1 4 5 7

36.037

42.415

6

33.140

40.073

Pembebanan

Tetap Sementara

kg.m

Beban AnginMomen

Mx

My

4.165

16.660

28.974

23.413

2.897

2.341

-

1.172

-

-11.719

Beban

Air Hujan

3

Beban

Hidup

2

W tekan

y α°

Whisap

y

α°

Page 8: Hitung Kuda Kuda
Page 9: Hitung Kuda Kuda

Kontrol tegangan lentur

Karena konstruksi terlindung dan tegangan akibat beban tetap dan sementara

maka tegangan lentur dinaikkan 25%

τlt = 150 x 1.25

= 187.5 kg/cm2

Coba-coba pakai balok dimensi 6/12

Dik:

b = 6 cm

h = 12 cm

Momen sementara

Mx = 3603.703 kg.cm

My = 4241.454 kg.cm

Ix = 1/12 x b x h3 Iy = 1/12 x b3 x h

= 864 cm4 = 216 cm4

Wx = Ix Wy = Iy

0.5h 0.5h

= 144 cm3 = 36 cm3

τmax = ( Mx / Wx ) + ( My / Wy )

= 142.844 kg/cm2 < kg/cm2 OK…!

Kontrol lendutan

ḟ =

= 1 cm

fx =

= +

= 0.852 cm

fy =

= +

= 0.213 cm

f = {( fx 2 ) + ( fy

2 )}0,5

= 0.879 cm < cm OK…!

Kesimpulan : Balok dengan dimensi tersebut bisa digunakan.

0.208 0.005

+

187.50

jarak antar kuda-kuda

300

+1 x P cos α x s3

48 x E x Iy

0.019

1 x P cos α x s3

48 x E x Iy384 x E x Iy

5 x q cos α x s4

384 x E x Iy

5 x q cos α x s4

0.833

1

Page 10: Hitung Kuda Kuda
Page 11: Hitung Kuda Kuda

PERENCANAAN KUDA -KUDA

Perencanaan Pembebanan pada kuda - kuda

Beban Mati Akibat Beban Atap

Beban Mati Atap = Beban q x Jarak Kuda-kuda = 69 kg

Berat Gording = Berat Gording x Jarak Kuda-kuda = 17.496 kg

Berat Sendiri Kuda-kuda = L. Penmpng x P. Total kayu x BJ kayu = 270.1838 kg

Berat Alat Penyambung 10% = Berat Sendiri Kuda-kuda x 10% = 27.01838 kg

Total berat = 383.698 kg

Beban hidup akibat Beban pekerja

P = 100 kg

Beban angin

1. Angin tekan = WL tekan x Jarak kuda-kuda = 4.5 kg

2. Angin hisap = WL hisap x Jarak kuda-kuda = -45 kg

Beban air hujan = GL x jarak gording x jarak kuda-kuda = 45 kg

Tabel Perencanaan Pembebanan

Kode Beban Beban

Beban Mati Hidup

Beban Sin α

1 2 3 5 6

P1 31.975 50 -22.5 -8.429

P2 63.950 100 -45 -16.857

P3 63.950 100 -45 -16.857

P4 63.950 100 -22.5 -8.429

P5 63.950 100 - -

P6 63.950 100 - -

P7 31.975 50 - -

Beban Angin

Angin Tekan

-

kg383.698

6

Angin Hisap

-

Sin α

9

0.843

1.686

1.686

0.843

Jadi Beban Untuk Satu Titik Buhul = = 63.950

Beban

Air Hujan

4

22.5

-

-

-

45

2.25

Cos α

7

-20.862

-41.723

-41.723

-20.862

-

45

Cos α

10

2.086

4.172

4.172

2.086

-

-

-

-

-

-

45

45

45

22.5

Beban

8

2.25

4.5

4.5

Page 12: Hitung Kuda Kuda

• Panjang Jarak dan Beban

L1 = 2.425 m H1 = 0.980 m P1 = kg

L2 = 2.425 m H2 = 0.980 m P2 = kg

L3 = 2.650 m H3 = 1.071 m P3 = kg

L4 = 2.650 m H4 = 0.470 m P4 = kg

L5 = 2.420 m H5 = 0.509 m P5 = kg

L6 = 2.420 m H6 = 0.039 m P6 = kg

H7 = 1.570 m P7 = kg

L7 = L1 + L2 + L3 + L4 + L5 + L6 = m

L8 = L2 + L3 + L4 + L5 + L6 = m

L9 = L3 + L4 + L5 + L6 = m

L10 = L4 + L5 + L6 = m

L11 = L5 + L6 = m

L12 = L1 + L2 = m

L13 = L1 + L2 + L3 = m

L14 = L1 + L2 + L3 + L4 = m

L15 = L1 + L2 + L3 + L4 + L5 = m

• Sudut - sudut :

*) αo = 22.0 o *) γo = 0.875 o

tan αo = 0.40 tan γo = 0.015

sin αo = 0.37 sin γo = 0.015

cos αo = 0.93 cos γo = 0.9999

*) βo = 11.0 o *) δo = 12.676 o

tan βo = 0.19 tan δo = 0.225

sin βo = 0.19 sin δo = 0.219

cos βo = 0.98 cos δo = 0.976

31.975

63.950

63.950

63.950

63.950

63.950

31.975

12.570

PERHITUNGAN GAYA-GAYA BATANG AKIBAT BEBAN MATI

14.990

12.565

10.140

7.490

4.840

4.850

7.500

10.150

A

B

C D

E

F

G

H

I

J

K

L

δo

γo

αo βo

P7

P6

P5

P4

P3

P2

P1 S1

S2

S3 S4

S5

S6

S7

S8

S9 S10

S11

S12

S13

S14

S15

S16

S17

S18 S19

S20

S21

L1 L2 L3 L4 L5 L6

H3

H2

H1

H7

H6

H4

H5

RAV RLV

Page 13: Hitung Kuda Kuda

• Reaksi Perletakan

Σ ML = 0

Σ MA = 0

Kontrol Σ V = 0

= 0

= 0 ............ Ok

• Gaya - Gaya Batang

◊ Joint A

Σ V = 0

RAV - P1 + S1 sin α + S12 sin β = 0

0, 41 S1 + 0,21 S12 = ..Pers. 1

Σ H = 0

S1 cos α + S12 cos β = 0

0, 91 S1 + 0,98 S12 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.19 S12 =

S12 = kg

Subtitusi ke Pers. 1

=

= kg

0, 41 S1 + 0,21 S12

S1

0.93

0.37

-148.154

776.450

-159.79

0, 41 S1 + 0,21 S12

0, 91 S1 + 0,98 S12

0,37 S1 + 0,19 S12

0,37 S1 + 0,40 S12

-159.789

0.000

-148.154

0.000

-822.043

RLV =P7 ( L7 ) + P6 ( L15 ) + P5 ( L14 ) + P4 ( L13 ) + P3 ( L12 ) + P2 (L1)

=L7

RAV =L7

P1 ( L7 ) + P2 ( L8 ) + P3 ( L9 ) + P4 ( L10 ) + P5 ( L11 ) + P6 ( L6 )

0.000

-159.789

RAV + RLV - P1 - P2 - P3 - P4 - P5 - P6 - P7

0

kg

191.93 kg

191.76=

A

αo βo

P1

S1

S12

RAV

Page 14: Hitung Kuda Kuda

◊ Joint B

Σ H = 0

- S12 cos β + S11 cos β = 0

S11 = kg

Σ V = 0

- S12 sin β + S13 + S11 sin β = 0

S13 = S12 sin β - S11 sin β

S13 = kg

◊ Joint C

Σ V = 0

- S1 sin α - S13 - P2 + S2 sin α - S14 sin γ = 0

0,41 S2 - 0,02 S14 = ..Pers. 1

Σ H = 0

- S1 cos α + S2 cos α + S14 cos γ = 0

0,91 S2 + 0,9998 S14 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.39 S14 =

S14 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint D

Σ H = 0

- S11 cos β - S14 cos γ + S10 cos β = 0

S10 = kg

-243.993

-762.185

0, 41 S2 - 0,02 S14 -243.993 0.93

776.450

=S11 cos β

S12 cos β

0.000

0,37 S1 + 0,41 S14 -285.519

59.293

-152.535

0, 41 S2 - 0,02 S14 -243.99

0, 91 S2 + 0,9998 S14 -762.185 0.37

0,37 S1 - 0,02 S14 -226.226

621.078

S2

cos β

S11 cos β + S14 cos γ=S10

-657.547

B

βo

S11

S12

S13

C γo

αo

P2

S1

S2

S14

S13

D

S10

S11

S14

S15

βo γo

Page 15: Hitung Kuda Kuda

Σ V = 0

- S11 sin β + S14 sin γ + S10 sin β + S15 = 0

S15 = S11 sin β - S14 sin γ - S10 sin β

S15 = kg

◊ Joint E

Σ V = 0

- S2 sin α - S15 - P3 + S3 sin α - S16 sin δ = 0

0,41 S3 - 0,25 S16 = ..Pers. 1

Σ H = 0

- S2 cos α + S3 cos α + S16 cos δ = 0

0,91 S3 + 0,97 S16 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.57 S16 =

S16 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint F

Σ H = 0

- S3 cos α + S4 cos α = 0

S4 = kg

Σ V = 0

- S3 sin α - P4 - S17 - S4 sin α = 0

S17 = kg

31.975

-150.40

-609.67

0,37 S3 - 0,22 S16 -139.45

0,37 S3 + 0,39 S16 -228.39

88.94

0, 41 S3 - 0,25 S16 -150.40 0.93

0, 91 S3 + 0,97 S16 -609.67 0.37

S3 cos α=S4

-156.329

0, 41 S3 - 0,22 S16 -150.40

S3 -493.051

-493.051

cos α

305.450

E

δo

αo

P3

S2

S3

S15

S16

F

P4

S3 S4

S17

αo αo

Page 16: Hitung Kuda Kuda

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

S1

S2

S3

-822.043

-657.547

-493.051

-493.051

-657.547

-822.043

2.615

2.858

2.610

2.858

2.610

2.610

S9

S10

Kode Batang Panjang Batang

S4

S5

S6

S7

S8

Gaya Batang

1 2 3

2.465

2.465

2.700

-156.329

31.975

-152.535

0.000

31.975

-156.329

305.450

2.700

2.470

2.470

0.508

2.425

1.017

2.716

1.570

2.716

776.450

776.450

S21

1.015

2.420

0.507

621.078

621.078

776.450

776.450

Tarik

Tarik

-

Tekan

0.000

-152.535

S20

S11

S12

S13

S14

S15

S16

S17

S18

S19

Tabel Rekapitulasi Gaya - Gaya Batang Akibat Beban Mati

Tarik

Tekan

Tarik

Tekan

Tarik

Tekan

-

Keterangan

4

Tekan

Tekan

Tekan

Tekan

Tekan

Tekan

Tarik

Tarik

Tarik

Tarik

Page 17: Hitung Kuda Kuda

• Panjang Jarak dan Beban

L1 = 2.425 m H1 = 0.980 m P1 = kg

L2 = 2.425 m H2 = 0.980 m P2 = kg

L3 = 2.650 m H3 = 1.071 m P3 = kg

L4 = 2.650 m H4 = 0.470 m P4 = kg

L5 = 2.420 m H5 = 0.509 m P5 = kg

L6 = 2.420 m H6 = 0.039 m P6 = kg

H7 = 1.570 m P7 = kg

L7 = L1 + L2 + L3 + L4 + L5 + L6 = m

L8 = L2 + L3 + L4 + L5 + L6 = m

L9 = L3 + L4 + L5 + L6 = m

L10 = L4 + L5 + L6 = m

L11 = L5 + L6 = m

L12 = L1 + L2 = m

L13 = L1 + L2 + L3 = m

L14 = L1 + L2 + L3 + L4 = m

L15 = L1 + L2 + L3 + L4 + L5 = m

• Sudut - sudut :

*) αo = 22.0 o *) γo = 0.875 o

tan αo = 0.40 tan γo = 0.015

sin αo = 0.37 sin γo = 0.015

cos αo = 0.93 cos γo = 0.9999

*) βo = 11.0 o *) δo = 12.676 o

tan βo = 0.19 tan δo = 0.225

sin βo = 0.19 sin δo = 0.219

cos βo = 0.98 cos δo = 0.976

100.000

50.000

14.990

12.565

10.140

7.490

PERHITUNGAN GAYA-GAYA BATANG AKIBAT BEBAN HIDUP

50.000

100.000

100.000

100.000

100.000

4.840

4.850

7.500

10.150

12.570

A

B

C D

E

F

G

H

I

J

K

L

δo

γo

αo βo

P7

P6

P5

P4

P3

P2

P1 S1

S2

S3 S4

S5

S6

S7

S8

S9 S10

S11

S12

S13

S14

S15

S16

S17

S18 S19

S20

S21

L1 L2 L3 L4 L5 L6

H3

H2

H1

H7

H6

H4

H5

RAV RLV

Page 18: Hitung Kuda Kuda

• Reaksi Perletakan

Σ ML = 0

Σ MA = 0

Kontrol Σ V = 0

= 0

= 0 ............ Ok

• Gaya - Gaya Batang

◊ Joint A

Σ V = 0

RAV - P1 + S1 sin α + S12 sin β = 0

0, 41 S1 + 0,21 S12 = ..Pers. 1

Σ H = 0

S1 cos α + S12 cos β = 0

0, 91 S1 + 0,98 S12 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.19 S12 =

S12 = kg

Subtitusi ke Pers. 1

=

= kg

kgL7

RLV =P7 ( L7 ) + P6 ( L15 ) + P5 ( L14 ) + P4 ( L13 ) + P3 ( L12 ) + P2 (L1)

= 300.13 kg

RAV =P1 ( L7 ) + P2 ( L8 ) + P3 ( L9 ) + P4 ( L10 ) + P5 ( L11 ) + P6 ( L6 )

L7

RAV + RLV - P1 - P2 - P3 - P4 - P5 - P6 - P7

0

-249.867

0.000

0, 41 S1 + 0,21 S12 -249.867 0.93

= 299.87

-231.672

1214.158

0, 41 S1 + 0,21 S12 -249.87

S1 -1285.452

0, 91 S1 + 0,98 S12 0.000 0.37

0,37 S1 + 0,19 S12 -231.672

0,37 S1 + 0,40 S12 0.000

A

αo βo

P1

S1

S12

RAV

Page 19: Hitung Kuda Kuda

◊ Joint B

Σ H = 0

- S12 cos β + S11 cos β = 0

S11 = kg

Σ V = 0

- S12 sin β + S13 + S11 sin β = 0

S13 = S12 sin β - S11 sin β

S13 = kg

◊ Joint C

Σ V = 0

- S1 sin α - S13 - P2 + S2 sin α - S14 sin γ = 0

0,41 S2 - 0,02 S14 = ..Pers. 1

Σ H = 0

- S1 cos α + S2 cos α + S14 cos γ = 0

0,91 S2 + 0,9998 S14 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.39 S14 =

S14 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint D

Σ H = 0

- S11 cos β - S14 cos γ + S10 cos β = 0

S10 = kg

-381.539

-1191.850

0, 41 S2 - 0,02 S14 -381.539 0.93

0, 91 S2 + 0,9998 S14 -1191.85 0.37

S11 =S12 cos β

cos β

1214.158

0.000

0, 41 S2 - 0,02 S14 -381.54

S2 -1028.226

S10 =S11 cos β + S14 cos γ

cos β

0,37 S1 - 0,02 S14 -353.757

0,37 S1 + 0,41 S14 -446.475

92.718

-238.524

971.198

B

βo

S11

S12

S13

C γo

αo

P2

S1

S2

S14

S13

D

S10

S11

S14

S15

βo γo

Page 20: Hitung Kuda Kuda

Σ V = 0

- S11 sin β + S14 sin γ + S10 sin β + S15 = 0

S15 = S11 sin β - S14 sin γ - S10 sin β

S15 = kg

◊ Joint E

Σ V = 0

- S2 sin α - S15 - P3 + S3 sin α - S16 sin δ = 0

0,41 S3 - 0,25 S16 = ..Pers. 1

Σ H = 0

- S2 cos α + S3 cos α + S16 cos δ = 0

0,91 S3 + 0,97 S16 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.57 S16 =

S16 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint F

Σ H = 0

- S3 cos α + S4 cos α = 0

S4 = kg

Σ V = 0

- S3 sin α - P4 - S17 - S4 sin α = 0

S17 = kg

0, 91 S3 + 0,97 S16 -953.35 0.37

0,37 S3 - 0,22 S16 -218.06

0,37 S3 + 0,39 S16 -357.13

50.000

-235.18

-953.35

0, 41 S3 - 0,25 S16 -235.18 0.93

S4 =S3 cos α

cos α

-770.998

477.642

139.08

-244.456

0, 41 S3 - 0,22 S16 -235.18

S3 -770.998

E

δo

αo

P3

S2

S3

S15

S16

F

P4

S3 S4

S17

αo αo

Page 21: Hitung Kuda Kuda

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

Tabel Rekapitulasi Gaya - Gaya Batang Akibat Beban Hidup

S1 2.615 -1285.452 Tekan

S2 2.858 -1028.226 Tekan

Kode Batang Panjang Batang Gaya Batang Keterangan

1 2 3 4

S5 2.610 -1028.226 Tekan

S6 2.610 -1285.452 Tekan

S3 2.610 -770.998 Tekan

S4 2.858 -770.998 Tekan

S9 2.700 971.198 Tarik

S10 2.700 971.198 Tarik

S7 2.465 1214.158 Tarik

S8 2.465 1214.158 Tarik

S13 0.508 0.000 -

S14 2.425 -238.524 Tekan

S11 2.470 1214.158 Tarik

S12 2.470 1214.158 Tarik

S17 1.570 477.642 Tarik

S18 2.716 -244.456 Tekan

S15 1.017 50.000 Tarik

S16 2.716 -244.456 Tekan

S21 0.507 0.000 -

S19 1.015 50.000 Tarik

S20 2.420 -238.524 Tekan

Page 22: Hitung Kuda Kuda

• Panjang Jarak dan Beban

L1 = 2.425 m H1 = 0.980 m P1 = kg

L2 = 2.425 m H2 = 0.980 m P2 = kg

L3 = 2.650 m H3 = 1.071 m P3 = kg

L4 = 2.650 m H4 = 0.470 m P4 = kg

L5 = 2.420 m H5 = 0.509 m P5 = kg

L6 = 2.420 m H6 = 0.039 m P6 = kg

H7 = 1.570 m P7 = kg

L7 = L1 + L2 + L3 + L4 + L5 + L6 = m

L8 = L2 + L3 + L4 + L5 + L6 = m

L9 = L3 + L4 + L5 + L6 = m

L10 = L4 + L5 + L6 = m

L11 = L5 + L6 = m

L12 = L1 + L2 = m

L13 = L1 + L2 + L3 = m

L14 = L1 + L2 + L3 + L4 = m

L15 = L1 + L2 + L3 + L4 + L5 = m

• Sudut - sudut :

*) αo = 22.0 o *) γo = 0.875 o

tan αo = 0.40 tan γo = 0.015

sin αo = 0.37 sin γo = 0.015

cos αo = 0.93 cos γo = 0.9999

*) βo = 11.0 o *) δo = 12.676 o

tan βo = 0.19 tan δo = 0.225

sin βo = 0.19 sin δo = 0.219

cos βo = 0.98 cos δo = 0.976

45.000

22.500

14.990

12.565

10.140

7.490

PERHITUNGAN GAYA-GAYA BATANG AKIBAT BEBAN AIR HUJAN

22.500

45.000

45.000

45.000

45.000

4.840

4.850

7.500

10.150

12.570

A

B

C D

E

F

G

H

I

J

K

L

δo

γo

αo βo

P7

P6

P5

P4

P3

P2

P1 S1

S2

S3 S4

S5

S6

S7

S8

S9 S10

S11

S12

S13

S14

S15

S16

S17

S18 S19

S20

S21

L1 L2 L3 L4 L5 L6

H3

H2

H1

H7

H6

H4

H5

RAV RLV

Page 23: Hitung Kuda Kuda

• Reaksi Perletakan

Σ ML = 0

Σ MA = 0

Kontrol Σ V = 0

= 0

= 0 ............ Ok

• Gaya - Gaya Batang

◊ Joint A

Σ V = 0

RAV - P1 + S1 sin α + S12 sin β = 0

0, 41 S1 + 0,21 S12 = ..Pers. 1

Σ H = 0

S1 cos α + S12 cos β = 0

0, 91 S1 + 0,98 S12 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.19 S12 =

S12 = kg

Subtitusi ke Pers. 1

=

= kg

kgL7

RLV =P7 ( L7 ) + P6 ( L15 ) + P5 ( L14 ) + P4 ( L13 ) + P3 ( L12 ) + P2 (L1)

= 135.06 kg

RAV =P1 ( L7 ) + P2 ( L8 ) + P3 ( L9 ) + P4 ( L10 ) + P5 ( L11 ) + P6 ( L6 )

L7

RAV + RLV - P1 - P2 - P3 - P4 - P5 - P6 - P7

0

-112.440

0.000

0, 41 S1 + 0,21 S12 -112.440 0.93

= 134.94

-104.253

546.371

0, 41 S1 + 0,21 S12 -112.44

S1 -578.453

0, 91 S1 + 0,98 S12 0.000 0.37

0,37 S1 + 0,19 S12 -104.253

0,37 S1 + 0,40 S12 0.000

A

αo βo

P1

S1

S12

RAV

Page 24: Hitung Kuda Kuda

◊ Joint B

Σ H = 0

- S12 cos β + S11 cos β = 0

S11 = kg

Σ V = 0

- S12 sin β + S13 + S11 sin β = 0

S13 = S12 sin β - S11 sin β

S13 = kg

◊ Joint C

Σ V = 0

- S1 sin α - S13 - P2 + S2 sin α - S14 sin γ = 0

0,41 S2 - 0,02 S14 = ..Pers. 1

Σ H = 0

- S1 cos α + S2 cos α + S14 cos γ = 0

0,91 S2 + 0,9998 S14 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.39 S14 =

S14 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint D

Σ H = 0

- S11 cos β - S14 cos γ + S10 cos β = 0

S10 = kg

-171.692

-536.333

0, 41 S2 - 0,02 S14 -171.692 0.93

0, 91 S2 + 0,9998 S14 -536.33 0.37

S11 =S12 cos β

cos β

546.371

0.000

0, 41 S2 - 0,02 S14 -171.69

S2 -462.702

S10 =S11 cos β + S14 cos γ

cos β

0,37 S1 - 0,02 S14 -159.190

0,37 S1 + 0,41 S14 -200.914

41.723

-107.336

437.039

B

βo

S11

S12

S13

C γo

αo

P2

S1

S2

S14

S13

D

S10

S11

S14

S15

βo γo

Page 25: Hitung Kuda Kuda

Σ V = 0

- S11 sin β + S14 sin γ + S10 sin β + S15 = 0

S15 = S11 sin β - S14 sin γ - S10 sin β

S15 = kg

◊ Joint E

Σ V = 0

- S2 sin α - S15 - P3 + S3 sin α - S16 sin δ = 0

0,41 S3 - 0,25 S16 = ..Pers. 1

Σ H = 0

- S2 cos α + S3 cos α + S16 cos δ = 0

0,91 S3 + 0,97 S16 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.57 S16 =

S16 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint F

Σ H = 0

- S3 cos α + S4 cos α = 0

S4 = kg

Σ V = 0

- S3 sin α - P4 - S17 - S4 sin α = 0

S17 = kg

0, 91 S3 + 0,97 S16 -429.01 0.37

0,37 S3 - 0,22 S16 -98.12

0,37 S3 + 0,39 S16 -160.71

22.500

-105.83

-429.01

0, 41 S3 - 0,25 S16 -105.83 0.93

S4 =S3 cos α

cos α

-346.949

214.939

62.59

-110.005

0, 41 S3 - 0,22 S16 -105.83

S3 -346.949

E

δo

αo

P3

S2

S3

S15

S16

F

P4

S3 S4

S17

αo αo

Page 26: Hitung Kuda Kuda

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

Tabel Rekapitulasi Gaya - Gaya Batang Akibat Beban Air Hujan

S1 2.615 -578.453 Tekan

S2 2.858 -462.702 Tekan

Kode Batang Panjang Batang Gaya Batang Keterangan

1 2 3 4

S5 2.610 -462.702 Tekan

S6 2.610 -578.453 Tekan

S3 2.610 -346.949 Tekan

S4 2.858 -346.949 Tekan

S9 2.700 437.039 Tarik

S10 2.700 437.039 Tarik

S7 2.465 546.371 Tarik

S8 2.465 546.371 Tarik

S13 0.508 0.000 -

S14 2.425 -107.336 Tekan

S11 2.470 546.371 Tarik

S12 2.470 546.371 Tarik

S17 1.570 214.939 Tarik

S18 2.716 -110.005 Tekan

S15 1.017 22.500 Tarik

S16 2.716 -110.005 Tekan

S21 0.507 0.000 -

S19 1.015 22.500 Tarik

S20 2.420 -107.336 Tekan

Page 27: Hitung Kuda Kuda

PERHITUNGAN GAYA-GAYA BATANG AKIBAT BEBAN ANGIN TEKAN

• Panjang Jarak dan Beban

L1 = 2.425 m H1 = 0.980 m P1 = 2.250 kg

L2 = 2.425 m H2 = 0.980 m P2 = 4.500 kg

L3 = 2.650 m H3 = 1.071 m P3 = 4.500 kg

L4 = 2.650 m H4 = 0.470 m P4 = 2.250 kg

L5 = 2.420 m H5 = 0.470 m

L6 = 2.420 m H6 = 0.515 m

H7 = 1.570 m

L7 = L1 + L2 + L3 + L4 + L5 + L6 = m

L8 = L2 + L3 + L4 + L5 + L6 = m

L9 = L3 + L4 + L5 + L6 = m

L10 = L4 + L5 + L6 = m

L11 = L5 + L6 = m

L12 = L1 + L2 = m

L13 = L1 + L2 + L3 = m

L14 = L1 + L2 + L3 + L4 = m

L15 = L1 + L2 + L3 + L4 + L5 = m

• Sudut - sudut :

*) αo = 22.00 o *) γo = 0.875 o

tan αo = 0.404 tan γo = 0.015

sin αo = 0.375 sin γo = 0.015

cos αo = 0.927 cos γo = 0.9999

*) βo = 11.00 o *) δo = 12.676 o

tan βo = 0.194 tan δo = 0.225

sin βo = 0.191 sin δo = 0.219

cos βo = 0.982 cos δo = 0.976

12.570

14.990

12.565

10.140

7.490

4.840

4.850

7.500

10.150

A

B

C D

E

F

G

H

I

J

K

L

δo

γo

αo βo

P4

P3

P2

P1 S1

S2

S3 S4

S5

S6

S7

S8

S9 S10

S11

S12

S13

S14

S15

S16

S17

S18 S19

S20 S21

L1 L2 L3 L4 L5 L6

H3

H2

H1

H7

H6

H4

H5

RAV RLV

RAH

Page 28: Hitung Kuda Kuda

• Reaksi Perletakan

Σ H = 0

= cos αo ( P1 + P2 + P3 + P4 )

= kg

Σ ML = 0

Σ MA = 0

Kontrol Σ V = 0

= 0.000

= 0.000 ............ Ok !

• Gaya - Gaya Batang

◊ Joint A

Σ V = 0

RAV - P1 sin α + S1 sin α + S12 sin β = 0

0, 41 S1 + 0,21 S12 =

Σ H = 0

P1 cos α + S1 cos α + S12 cos β - RAH = 0

0, 91 S1 + 0,98 S12 =

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.191 S12 =

S12 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint B

Σ H = 0

RAH

RAH

RAV =

0, 91 S1 + 0,98 S12 10.431 0.375

0,37 S1 + 0,19 S12 -1.608

RAV + RLV - sin αo (P1 + P2 + P3 + P4)

0.000

0, 41 S1 + 0,21 S12 -1.735

-1.735

10.431

kg

= 2.48

3.907

0.927

kg

..Pers. 1

..Pers. 2

L7

P2 sin αo (L1) + P3 sin αo (L12) + P4 sin αo (L13) + P2 cos αo (H1)

+ P3 cos αo (H1 + H2) + P4 cos αo (H1 + H2 + H3)

- P2 cos αo (H1) - P3 cos αo (H1 + H2) - P4 cos αo (H1 + H2 + H3)

P1 sin αo (L7) + P2 sin αo (L8) + P3 sin αo (L9) + P4 sin αo (L10)

= 2.578

12.517

-5.516

28.907

0,37 S1 + 0,40 S12

0, 41 S1 + 0,21 S12 -1.735

S1 -19.35481

L7

RLV =

A

αo βo

P1

S1

S12

RAV

RAH

Page 29: Hitung Kuda Kuda

- S12 cos β + S11 cos β = 0

S11 = kg

Σ V = 0

- S12 sin β + S13 + S11 sin β = 0

S13 = S12 sin β - S11 sin β

S13 = kg

◊ Joint C

Σ V = 0

- S1 sin α - S13 - P2 sin α + S2 sin α - S14 sin γ = 0

0,41 S2 - 0,02 S14 = ..Pers. 1

Σ H = 0

- S1 cos α + S2 cos α + S14 cos γ + P2 cos α = 0

0,91 S2 + 0,9998 S14 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.389 S14 =

S14 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint D

Σ H = 0

- S11 cos β - S14 cos γ + S10 cos β = 0

S10 = kg

S11 =S12 cos β

cos β

28.907

-5.565

0.000

0,37 S1 - 0,02 S14 -5.160

0,37 S1 + 0,41 S14 -8.285

3.126

-8.042

-22.118

0, 41 S2 - 0,02 S14 -5.565 0.93

0, 91 S2 + 0,9998 S14 -22.118 0.37

0, 41 S2 - 0,02 S14 -5.565

S2 -15.18253

S10 =S11 cos β + S14 cos γ

cos β

20.716

B

βo

S11

S12

S13

D

S10

S11

S14

S15

βo γo

C

γo

αo

P2

S1

S2

S14

S13

Page 30: Hitung Kuda Kuda

Σ V = 0

- S11 sin β + S14 sin γ + S10 sin β + S15 = 0

S15 = S11 sin β - S14 sin γ - S10 sin β

S15 = kg

◊ Joint E

Σ V = 0

- S2 sin α - S15 - P3 sin α + S3 sin α - S16 sin δ = 0

0,41 S3 - 0,25 S16 = ..Pers. 1

Σ H = 0

- S2 cos α + S3 cos α + S16 cos δ + P2 cos α = 0

0,91 S3 + 0,97 S16 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.57 S16 =

S16 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint F

Σ H = 0

- S3 cos α + S4 cos α + P4 cos α = 0

S4 = kg

Σ V = 0

- S3 sin α - P4 sin α- S17 - S4 sin α = 0

S17 = kg

1.686

-2.316

-18.249

0, 41 S3 - 0,25 S16 -2.316 0.93

0,37 S3 - 0,23 S16 -2.147

0,37 S3 + 0,39 S16 -6.836

S4 =

-13.260

8.249

cos α (S3 - P4)

cos α

0, 91 S3 + 0,97 S16 -18.249 0.37

4.689

-8.242

0, 41 S3 - 0,25 S16 -2.316

S3 -11.01019

E

δo

αo

P3

S2

S3

S15

S16

F

P4

S3 S4

S17

αo αo

Page 31: Hitung Kuda Kuda

◊ Joint G

Σ V = 0

S16 sin δ + S17 + S18 sin δ - S10 sin β - S9 sin β = 0

- 0,21 S9 + 0,25 S18 = ..Pers. 1

Σ H = 0

- S16 cos δ + S18 cos δ - S10 cos β + S9 cos β = 0

0,98 S9 + 0,97 S18 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

0.40 S18 =

S18 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint H

Σ H = 0

- S4 cos α + S5 cos α - S18 cos δ = 0

Σ V = 0

S4 sin α - S5 sin α - S18 sin δ - S19 = 0

S19 = S4 sin α - S5 sin α - S18 sin δ

S19 = kg

◊ Joint I

Σ V = 0

S20 sin γ + S19 + S9 sin β - S8 sin β = 0

- 0,21 S8 + 0,02 S20 = ..Pers. 1

Σ H = 0

S20 cos γ - S9 cos β + S8 cos β = 0

0,98 S8 + 0,998 S20 = ..Pers. 2

-2.582

12.528

-13.512 kg

0.147

S4 cos α + S18 cos δ

cos α= =

-0.19

S9 12.762

0, 98 S9 + 0,97 S18 12.295

- 0,20 S9 + 0,24 S18 -2.442

- 0,20 S9 - 0,20 S18

- 0, 21 S9 + 0,25 S18 -2.488

-2.346

-2.488

12.295

0.982

S5

-0.096

-0.239

- 0, 21 S9 + 0,25 S18 -2.488

G S10 S9

S17

βo βo

δo δo

S16 S18

H

δo

αo

S5

S4

S19

S18

I

S9

S8

S20

S19

βo γo

Page 32: Hitung Kuda Kuda

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

0.21 S20 =

S20 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint J

Σ H = 0

- S5 cos α + S6 cos α - S20 cos γ = 0

Σ V = 0

S5 sin α - S6 sin α - S20 sin γ - S21 = 0

S21 = S5 sin α - S6 sin α - S20 sin γ

S21 = kg

◊ Joint K

Σ H = 0

- S8 cos β + S7 cos β = 0

Kontrol Σ V

Σ V = 0

S8 sin β - S7 sin β + S21 = 0

S7 =sin β

S8 sin β + S21= 15.014 kg

= -14.267 kgcos α

0.294

S6 =S5 cos α + S20 cos γ

S7 =S8 cos β

= 13.476 kgcos β

- 0,20 S8 - 0,21 S20 -2.390

-0.144

-0.700

- 0, 21 S8 + 0,02 S20 -2.582

S8 13.476

12.528

- 0, 21 S8 + 0,02 S20 -2.582 0.98

0, 98 S8 + 0,998 S20 -0.19

- 0,20 S8 + 0,02 S20 -2.535

.....OK

J γo

αo S6

S5

S20

S21

K

βo S8

S7

S21

Page 33: Hitung Kuda Kuda

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

S11

S12

S13

S6

S7

S8

S9

S4

S5

1

S1

S2

S3

Kode Batang

2.615

2.858

2.610

2.858

2.610

2.610

2.465

2.465

2.700

2.700

2.470

2.470

0.508

2.425

1.017

2.716

1.570

2.716

S14

S15

S16

S17

S10

1.686

-8.242

8.249

-0.239

0.147

-0.700

0.294

S18

S19

S20

S21

Tarik

2 3

Panjang Batang Gaya Batang

Tekan

Tarik

1.015

2.420

0.507

-19.355

-15.183

-11.010

-13.260

-13.512

-14.267

13.476

13.476

0.147

20.716

28.907

28.907

0.000

-8.042

Tabel Rekapitulasi Gaya - Gaya Batang Akibat Beban Angin Tekan

Keterangan

4

Tekan

Tekan

Tekan

Tekan

Tekan

Tekan

Tarik

Tarik

Tarik

Tarik

Tarik

Tarik

-

Tekan

Tarik

Tekan

Tarik

Tekan

Page 34: Hitung Kuda Kuda

• Panjang Jarak dan Beban

L1 = 2.425 m H1 = 0.980 m P1 = kg

L2 = 2.425 m H2 = 0.980 m P2 = kg

L3 = 2.650 m H3 = 1.071 m P3 = kg

L4 = 2.650 m H4 = 0.470 m P4 = kg

L5 = 2.420 m H5 = 0.470 m

L6 = 2.420 m H6 = 0.515 m

H7 = 1.570 m

L7 = L1 + L2 + L3 + L4 + L5 + L6 = m

L8 = L2 + L3 + L4 + L5 + L6 = m

L9 = L3 + L4 + L5 + L6 = m

L10 = L4 + L5 + L6 = m

L11 = L5 + L6 = m

L12 = L1 + L2 = m

L13 = L1 + L2 + L3 = m

L14 = L1 + L2 + L3 + L4 = m

L15 = L1 + L2 + L3 + L4 + L5 = m

• Sudut - sudut :

*) αo = 22.0 o *) γo = 0.875 o

tan αo = 0.40 tan γo = 0.015

sin αo = 0.37 sin γo = 0.015

cos αo = 0.93 cos γo = 0.9999

*) βo = 11.0 o *) δo = 12.676 o

tan βo = 0.19 tan δo = 0.225

sin βo = 0.19 sin δo = 0.219

cos βo = 0.98 cos δo = 0.976

22.500

45.000

45.000

22.500

12.570

PERHITUNGAN GAYA-GAYA BATANG AKIBAT BEBAN ANGIN HISAP

14.990

12.565

10.140

7.490

4.840

4.850

7.500

10.150

RAH A

B

C D

E

F

G

H

I

J

K

L

δo

γo

αo βo

P4

P3

P

P1

S1

S2

S3 S4

S5

S6

S7

S8

S9 S10

S11

S12

S1

S14

S15

S16

S17

S18 S19

S20

S21

L1 L2 L3 L4 L5 L6

H3

H2

H1

H7

H6

H4

H5

RA RL

Page 35: Hitung Kuda Kuda

• Reaksi Perletakan

Σ H = 0

= cos αo ( P1 + P2 + P3 + P4 )

= kg

Σ ML = 0

Σ MA = 0

Kontrol Σ V = 0

= 0.000

= 0.000 ............ Ok !

• Gaya - Gaya Batang

◊ Joint L

Σ V = 0

- RLV + P4 sin α + S6 sin α + S7 sin β = 0

0, 41 S6 + 0,21 S7 = ..Pers. 1

Σ H = 0

P4 cos α - S6 cos α - S7 cos β = 0

0, 91 S6 + 0,98 S7 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.19 S7 =

S7 = kg

Subtitusi ke Pers. 1

=

= kg

kg

RLV =- P3 cos αo (H1) - P2 cos αo (H1 + H2) - P1 cos αo (H1 + H2 + H3)

L7

RAH

RAH

P1 sin αo (L10) + P2 sin αo (L11) + P3 sin αo (L6)= 24.774 kg

RAV =+ P3 cos αo (H1) + P2 cos αo (H1 + H2) + P1 cos αo (H1 + H2 + H3)

125.170

- RAV - RLV + sin αo (P1 + P2 + P3 + P4)

0.000

17.369

20.862

0, 41 S6 + 0,21 S7 17.369 0.93

L7

P4 sin αo (L7) + P3 sin αo (L15) + P2 sin αo (L14) + P1 sin αo (L13)= 25.798

8.289

-43.443

0, 41 S6 + 0,21 S7 17.369

S6 68.494

0, 91 S6 + 0,98 S7 20.862 0.37

0,37 S6 + 0,19 S7 16.104

0,37 S6 + 0,40 S7 7.815

L

αo βo

P4

S6

S7

RLV

Page 36: Hitung Kuda Kuda

◊ Joint K

Σ H = 0

S7 cos β - S8 cos β = 0

S8 = kg

Σ V = 0

- S7 sin β + S21 + S8 sin β = 0

S21 = S7 sin β - S8 sin β

S21 = 0.000 kg

◊ Joint J

Σ V = 0

- S6 sin α - S21 + P3 sin α + S5 sin α - S20 sin γ = 0

0,41 S5 - 0,02 S20 = ..Pers. 1

Σ H = 0

S6 cos α - S5 cos α - S20 cos γ + P3 cos α = 0

0,91 S5 + 0,9998 S20 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.39 S20 =

S20 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint I

Σ H = 0

S8 cos β + S20 cos γ - S9 cos β = 0

S9 = kg

105.230

0, 41 S5 - 0,02 S20 8.801 0.93

0, 91 S5 + 0,9998 S20 105.230 0.37

S8 =S7 cos β

cos β

-43.443

8.801

0, 41 S5 - 0,02 S20 8.801

S5 26.771

S9 =S8 cos β + S20 cos γ

cos β

0,37 S5 - 0,02 S20 8.160

0,37 S5 + 0,41 S20 39.420

-31.260

80.417

38.470

K

βo

S8

S7

S21

I

S9

S8

S20

S19

βo γo

J γo

αo

P3

S6

S5

S20

S21

Page 37: Hitung Kuda Kuda

Σ V = 0

- S8 sin β + S20 sin γ + S9 sin β + S19 = 0

S19 = S8 sin β - S20 sin γ - S9 sin β

S19 = kg

◊ Joint H

Σ V = 0

- S5 sin α - S19 + P2 sin α + S4 sin α - S18 sin δ = 0

0,41 S4 - 0,25 S18 = ..Pers. 1

Σ H = 0

S5 cos α - S4 cos α - S18 cos δ + P2 cos α = 0

0,91 S4 + 0,97 S18 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

-0.57 S18 =

S18 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint F

Σ H = 0

- S3 cos α + S4 cos α + P1 cos α = 0

S3 = kg

Σ V = 0

- S3 sin α + P1 sin α- S17 - S4 sin α = 0

S17 = kg

0, 91 S4 + 0,97 S18 66.545 0.37

0,37 S4 - 0,22 S18 -21.961

0,37 S4 + 0,39 S18 24.928

-16.857

-23.686

66.545

0, 41 S4 - 0,25 S18 -23.686 0.93

S3 =cos α (S4 + P1)

cos α

7.548

11.202

-46.890

82.417

0, 41 S4 - 0,25 S18 -23.686

S4 -14.9522

H

δo

αo

P2

S5

S4

S19

S18

F

P1

S3 S4

S17

αo αo

Page 38: Hitung Kuda Kuda

◊ Joint G

Σ V = 0

S16 sin δ + S17 + S18 sin δ - S10 sin β - S9 sin β = 0

- 0,21 S10 + 0,25 S16 = ..Pers. 1

Σ H = 0

- S16 cos δ + S18 cos δ - S10 cos β + S9 cos β = 0

0,98 S10 + 0,97 S16 = ..Pers. 2

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

0.40 S16 =

S16 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint E

Σ H = 0

+ S3 cos α - S2 cos α + S16 cos δ = 0

Σ V = 0

S3 sin α - S2 sin α - S16 sin δ - S15 = 0

S15 = S3 sin α - S2 sin α - S16 sin δ

S15 = kg

◊ Joint D

Σ V = 0

S14 sin γ + S15 + S10 sin β - S11 sin β = 0

- 0,21 S11 + 0,02 S14 = ..Pers. 1

Σ H = 0

- S14 cos γ + S10 cos β - S11 cos β = 0

0,98 S11 + 0,998 S14 = ..Pers. 2

- 0,20 S10 + 0,24 S16 -21.544

- 0,20 S10 - 0,20 S16 -22.548

1.005

2.502

-21.947

118.172

- 0, 21 S10 + 0,25 S16 -21.947 0.98

0, 98 S10 + 0,97 S16 118.172 -0.19

kgcos α

-1.535

-20.961

- 0, 21 S10 + 0,25 S16 -21.947

S10 117.897

S2 =S3 cos α + S16 cos δ

115.731

= 10.180

G S10 S9

S17

βo βo

δo δo

S16 S18

E

δo

αo

S2

S3

S15

S16

D

S10

S11

S14

S15

βo γo

Page 39: Hitung Kuda Kuda

Eliminasi Pers. 1 dan Pers. 2

= x

= x

=

= -

0.21 S14 =

S14 = kg

Subtitusi ke Pers. 1

=

= kg

◊ Joint C

Σ H = 0

- S1 cos α + S2 cos α + S14 cos γ = 0

Σ V = 0

S2 sin α - S1 sin α - S14 sin γ - S13 = 0

S13 = S2 sin α - S1 sin α - S14 sin γ

S13 = kg

◊ Joint B

Σ H = 0

- S12 cos β + S11 cos β = 0

Kontrol Σ V

Σ V = 0

S8 sin β - S7 sin β + S13 = 0

- 0, 21 S11 + 0,02 S14 -20.961 0.98

0, 98 S11 + 0,998 S14 115.731 -0.19

- 0, 21 S11 + 0,02 S14 -20.961

S11 109.852

S1 =S2 cos α + S14 cos γ

- 0,20 S11 + 0,02 S14 -20.576

- 0,20 S11 - 0,21 S14 -22.082

1.507

0.000

= 10.180 kgcos α

0.000

S12 =S11 cos β

= 109.852 kgcos β

S12 =S11 sin β + S13

= 109.85 kg .....OKsin β

C

γo

αo

S1

S2

S14

S13

B

βo

S11

S12

S13

Page 40: Hitung Kuda Kuda

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

m kg

Panjang BatangKode Batang Gaya Batang Keterangan

2 3

Tabel Rekapitulasi Gaya - Gaya Batang Akibat Beban Angin Hisap

1

S5

S6

S7

S8

S1

S2

S3

S4

S20 2.420

S13

S14

S15

S16

S9

S10

S11

S12

2.716

1.015

S17

S18

S21

2.615

2.858

2.610

2.858

2.610

2.610

2.465

2.465

2.700

2.700

2.470

2.470

0.508

2.425

1.017

2.716

1.570

S19

0.507

10.180

10.180

7.548

-14.952

26.771

68.494

-43.443

-43.443

38.470

117.897

109.852

109.852

0.000

0.000

-1.535

2.502

0.000

11.202

82.417

-16.857

80.417

4

Tarik

Tarik

Tarik

Tekan

Tarik

Tarik

Tekan

Tekan

Tarik

Tarik

Tarik

Tarik

Tarik

Tarik

Tekan

-

Tarik

-

-

Tekan

Tarik

Page 41: Hitung Kuda Kuda

Kode Beban Beban Beban B. Angin B. Angin Kombinasi I Kombinasi II Kombinasi III Kombinasi IV Kombinasi V Beban

Batang Mati Hidup Air hujan tekan hisap 1,4 D 1,2 D + 1,6 L 1,2 D + 1,6 H 1,2 D + 1,3 W1 1,2 D - 1,3 W2 Maksimum

(D) (L) (H) (W1) (W2) + 0,5 H + 0,5 L + 0,5 L + 0,5 H + 0,5 L + 0,5 H

1 2 3 4 5 6 7 8 9 10 11 14

S1 -822.04 -1285.45 -578.45 -19.35 10.18 -1150.86 -3332.40 -2554.70 -1943.57 -1893.24 -3332.40

S2 -657.55 -1028.23 -462.70 -15.18 10.18 -920.57 -2665.57 -2043.49 -1554.26 -1514.78 -2665.57

S3 -493.05 -771.00 -346.95 -11.01 7.55 -690.27 -1998.73 -1532.28 -1164.95 -1136.32 -1998.73

S4 -493.05 -771.00 -346.95 -13.26 -14.95 -690.27 -1998.73 -1532.28 -1167.87 -1133.40 -1998.73

S5 -657.55 -1028.23 -462.70 -13.51 26.77 -920.57 -2665.57 -2043.49 -1552.09 -1516.96 -2665.57

S6 -822.04 -1285.45 -578.45 -14.27 68.49 -1150.86 -3332.40 -2554.70 -1936.95 -1899.86 -3332.40

S7 776.45 1214.16 546.37 13.48 -43.44 1087.03 3147.58 2413.01 1829.52 1794.49 3147.58

S8 776.45 1214.16 546.37 13.48 -43.44 1087.03 3147.58 2413.01 1829.52 1794.49 3147.58

S9 621.08 971.20 437.04 0.15 38.47 869.51 2517.73 1930.16 1449.60 1449.22 2517.73

S10 621.08 971.20 437.04 20.72 117.90 869.51 2517.73 1930.16 1476.34 1422.48 2517.73

S11 776.45 1214.16 546.37 28.91 109.85 1087.03 3147.58 2413.01 1849.58 1774.43 3147.58

S12 776.45 1214.16 546.37 28.91 109.85 1087.03 3147.58 2413.01 1849.58 1774.43 3147.58

S13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

S14 -152.54 -238.52 -107.34 -8.04 0.00 -213.55 -618.35 -474.04 -366.43 -345.52 -618.35

S15 31.98 50.00 22.50 1.69 -1.54 44.77 129.62 99.37 76.81 72.43 129.62

S16 -156.33 -244.46 -110.01 -8.24 2.50 -218.86 -633.73 -485.83 -375.54 -354.11 -633.73

S17 305.45 477.64 214.94 8.25 11.20 427.63 1238.24 949.26 723.55 702.11 1238.24

S18 -156.33 -244.46 -110.01 -0.24 82.42 -218.86 -633.73 -485.83 -365.14 -364.51 -633.73

S19 31.98 50.00 22.50 0.15 -16.86 44.77 129.62 99.37 74.81 74.43 129.62

S20 -152.54 -238.52 -107.34 -0.70 80.42 -213.55 -618.35 -474.04 -356.88 -355.06 -618.35

S21 0.00 0.00 0.00 0.29 0.00 0.00 0.00 0.00 0.38 -0.38 -0.38

Kesimpulan:

- Batang tunggal yang menerima gaya batang tekan terbesar

S1 = -3332.40

- Batang tunggal yang menerima gaya batang tarik terbesar

S7 = 3147.58 kg

- Batang rangkap yang menerima gaya batang tarik terbesar

S15 = 129.62 kg

TABEL GAYA - GAYA BATANG AKIBAT BEBAN YANG BEKERJA

Beban tetap Beban Angin

Page 42: Hitung Kuda Kuda

KONTROL KEKUATAN BATANG

- Batang tunggal yang menerima gaya batang tekan terbesar

b = 6 cm

h = 12 cm

S1 = -3332.40 kg

Lk = 261.545 cm

ix = 0.289 x h

= 3.468 cm

iy = 0.289 x b

= 1.734 cm

Lk

imin

Maka :

ω = 2.73 ( Lihat tabel faktor tekuk kayu )

Ʈtk = 130 kg/cm2 ( Lihat tabel tegangan ijin kayu )

Kontrol Tegangan :

ω . S

b . h

= 126.354 kg/cm2 < 130 kg/cm2 .....OK

151=λ = 150.833 ≈

=Ʈtk

h

b

Page 43: Hitung Kuda Kuda

- Batang tunggal yang menerima gaya Batang tarik terbesar

b = 6 cm

h = 12 cm

S7 = 3147.58 kg

Fnetto = h . b - ( 20% . h . b )

= 57.6

S

Fnetto

= 54.6455 kg/cm2 < 130 kg/cm2 .....OK

- Batang rangkap yang menerima gaya Batang tarik terbesar

b = 3 cm

h = 12 cm

S15 = 129.62 kg

Fnetto = h . b - ( 20% . h . b )

= 28.8

S

Fnetto

= 2.25036 kg/cm2 < 130 kg/cm2 .....OK

Ʈtr =

=Ʈtr

h

b

h

b

h

b

Page 44: Hitung Kuda Kuda

PERENCANAAN SAMBUNGAN

□ JOINT A

Digunakan sambungan gigi rangkap.

- Batang S1 = kg

- Sudut θ = 11.00 o

- Mencari tegangan ijin

Gigi belakang σds = σds a = σds // - ( σds // - σds ┴ ) sin θo

=

Gigi muka σds = σds ½ a = σds // - ( σds // - σds ┴ ) sin ½ θo

=

- Mencari ukuran gigi belakang (tv2 dan tm2)

Besarnya S2 diambil = = 1666.2 kg

dipakai tinggi gigi belakang = 3.00 cm

Dengan demikian gigi kedua dapat mendukung gaya S2 = kg

- Mencari ukuran gigi muka (tv1 dan tm1)

Besarnya S1 = = 1284.47 kg

dipakai tinggi gigi muka = 2.00 cm, sehingga tv2 - tv1 = 1 cm

- Mencari panjang muka gigi (panjang penyaluran = l m )

Maka pakai : l m1 = 15.00 cm

Maka pakai : l m2 = 15.00 cm

½ x S

Tinggi gigi muka tv1 =S1 x cos2 ½ θ

=

111.29

120.59

2047.9

3332.40

cm

=tv2

cos θ

= = 2.39S2 x cos2 θ

=

Tinggi gigi belakang tv2

Kemiringan gigi belakang tm2

b x σds a

1.76

l m1 = 10.47 cmPanjang kayu muka, =

cmcos θ

= 3 cm

S1 x cos θ

τ// x b< 15.0 cm

b x σds ½ a

S - S2

cm

3.07 cm

Kemiringan gigi muka tm1 =

cm < 15.0 cmτ// x b

13.58Panjang kayu belakang, l m2 =S2 x cos θ

=

tv2= 2.04

58,3915

2,04

3

3,1

84°

84°

24°

12°

12°

2

S

S1

S2

h

Page 45: Hitung Kuda Kuda

□ JOINT B

Digunakan sambungan bertampang dua

- Batang S11 = kg

- Direncanakan dengan baut berdiameter Ø = 3/8 " = cm

- Gol. Kelas Kuat I dgn sambungan tampang dua, didapat kekuatan perbaut

S = 125 x d x b3 x (1 - 0.6 sin θ) = kg

S = 250 x d x b1 x (1 - 0.6 sin θ) = kg

S = 480 x d2 x (1 - 0.35 sin θ) = kg

diambil S yang terkecil = kg

- Baut yang dibutuhkan = 0 / 299.64 = 0 ≈ 1 buah

- Jarak minimum antar sumbu baut dan ujung kayu = 7 d = 6.9 cm ≈ 7 cm

- Jarak minimum antara sumbu baut dalam arah gaya = 5 d = 4.9 cm ≈ 5 cm

- Jarak minimum antara baut tegak lurus arah gaya = 3 d = 3 x 0.98 = 2.94 cm

- Jarak minimum antara sumbu baut dgn tepi kayu = 2 d = 2 x 0.98 = 1.96 cm

□ JOINT C

Digunakan sambungan gigi tunggal.

- Batang S14 = kg

- Sudut θ = 22.87 o

- Mencari tegangan ijin

σds = σds ½ a = σds // - ( σds // - σds ┴ ) sin ½ θo

=

Mencari ukuran gigi belakang (tv dan tm)

Syarat untuk θ ≤ 50o tm harus ≤ ¼ h = 3.0 cm

Mencari panjang muka gigi (panjang penyaluran = l m )

Maka pakai : l m = 15.00 cm

< ¼ x h

= 0.88 cm

0.00

299.64

b x σds ½ a

Tinggi gigi tv =

0.98

147.00

294.00

299.64

618.35

112.15

S x cos θPanjang kayu muka,

tvKemiringan gigi tm = = 0.96 cm

cos θ

l m

S x cos2 ½ θ-

-

15.0 cmτ// x b

= = 4.75 cm <

58,3915

2,04

3

3,1

84°

84°

24°

12°

12°

2

S

S1

S2

h

12°

S

12

90°

12

Page 46: Hitung Kuda Kuda

Digunakan sambungan bertampang dua.

Batang S11 = kg

Direncanakan dengan baut berdiameter Ø = 3/8 " = cm

Gol. Kelas Kuat I dgn sambungan tampang dua, didapat kekuatan perbaut

- S = 125 x d x b3 x (1 - 0.6 sin 90) = kg

S = 250 x d x b1 x (1 - 0.6 sin 90) = kg

S = 480 x d2 x (1 - 0.35 sin 90) = kg

diambil S yang terkecil = kg

Baut yang dibutuhkan = 0 / 294 = 0 ≈ 1 buah

- Jarak minimum antar sumbu baut dan ujung kayu = 7 d = 6.9 cm ≈ 7 cm

- Jarak minimum antara sumbu baut dalam arah gaya = 5 d = 4.9 cm ≈ 5 cm

- Jarak minimum antara baut tegak lurus arah gaya = 3 d = 3 x 0.98 = 2.94 cm

- Jarak minimum antara sumbu baut dgn tepi kayu = 2 d = 2 x 0.98 = 1.96 cm

□ JOINT D

Digunakan sambungan gigi tunggal.

- Batang S14 = kg

- Sudut θ = 11.87 o

- Mencari tegangan ijin

σds = σds ½ a = σds // - ( σds // - σds ┴ ) sin ½ θo

=

Mencari ukuran gigi belakang (tv dan tm)

Syarat untuk θ ≤ 50o tm harus ≤ ¼ h = 3.0 cm

Mencari panjang muka gigi (panjang penyaluran = l m )

Maka pakai : l m = 15.00 cm

0.00

0.98

294.00

618.35

120.69

- Tinggi gigi tv =S x cos2 ½ θ

294.00

299.64

294.00

b x σds ½ a

- Kemiringan gigi tm =tv

= 0.86 cm

= 0.84 cm

< ¼ x hcos θ

Panjang kayu muka, l m =S x cos θ

= 5.04 cm < 15.0 cmτ// x b

12

12

12

25°

S

77°

0,810,73

24°

Page 47: Hitung Kuda Kuda

Digunakan sambungan bertampang dua.

Batang S15 = kg

Direncanakan dengan baut berdiameter Ø = 3/8 " = cm

Gol. Kelas Kuat I dgn sambungan tampang dua, didapat kekuatan perbaut

- S = 125 x d x b3 x (1 - 0.6 sin 90) = kg

S = 250 x d x b1 x (1 - 0.6 sin 90) = kg

S = 480 x d2 x (1 - 0.35 sin 90) = kg

diambil S yang terkecil = kg

Baut yang dibutuhkan = 129.62 / 294 = 0.4 ≈ 1 buah

- Jarak minimum antar sumbu baut dan ujung kayu = 7 d = 6.9 cm ≈ 7 cm

- Jarak minimum antara sumbu baut dalam arah gaya = 5 d = 4.9 cm ≈ 5 cm

- Jarak minimum antara baut tegak lurus arah gaya = 3 d = 3 x 0.98 = 2.94 cm

- Jarak minimum antara sumbu baut dgn tepi kayu = 2 d = 2 x 0.98 = 1.96 cm

□ JOINT E

Digunakan sambungan gigi tunggal.

- Batang S16 = kg

- Sudut θ = 34.68 o

- Mencari tegangan ijin

σds = σds ½ a = σds // - ( σds // - σds ┴ ) sin ½ θo

=

Mencari ukuran gigi belakang (tv dan tm)

Syarat untuk θ ≤ 50o tm harus ≤ ¼ h = 3.0 cm

Mencari panjang muka gigi (panjang penyaluran = l m )

Maka pakai : l m = 15.00 cm

294.00

299.64

294.00

633.73

103.18

129.62

0.98

294.00

0.93 cm- Tinggi gigi tv =S x cos2 ½ θ

=b x σds ½ a

1.13 cmcos θ

- Kemiringan gigi tm =tv

= < ¼ x h

4.34 cm < 15.0 cmPanjang kayu muka, l m =S x cos θ

=τ// x b

12

12

13° 0,7

0,72

83°

S

12

S

12

Page 48: Hitung Kuda Kuda

Digunakan sambungan bertampang dua.

Batang S15 = kg

Direncanakan dengan baut berdiameter Ø = 3/8 " = cm

Gol. Kelas Kuat I dgn sambungan tampang dua, didapat kekuatan perbaut

- S = 125 x d x b3 x (1 - 0.6 sin 90) = kg

S = 250 x d x b1 x (1 - 0.6 sin 90) = kg

S = 480 x d2 x (1 - 0.35 sin 90) = kg

diambil S yang terkecil = kg

Baut yang dibutuhkan = 129.62 / 294 = 0.4 ≈ 1 buah

- Jarak minimum antar sumbu baut dan ujung kayu = 7 d = 6.9 cm ≈ 7 cm

- Jarak minimum antara sumbu baut dalam arah gaya = 5 d = 4.9 cm ≈ 5 cm

- Jarak minimum antara baut tegak lurus arah gaya = 3 d = 3 x 0.98 = 2.94 cm

- Jarak minimum antara sumbu baut dgn tepi kayu = 2 d = 2 x 0.98 = 1.96 cm

□ JOINT F

Digunakan sambungan gigi rangkap.

- Batang S3 = kg

- Sudut θ = 68.00 o

- Mencari tegangan ijin

Gigi belakang σds = σds a = σds // - ( σds // - σds ┴ ) sin θo

=

Gigi muka σds = σds ½ a = σds // - ( σds // - σds ┴ ) cos ½ θo

=

- Mencari ukuran gigi belakang (tv2 dan tm2)

Besarnya S2 diambil = = 999.366 kg

dipakai tinggi gigi belakang = 2.00 cm

Dengan demikian gigi kedua dapat mendukung gaya S2 = kg

294.00

½ x S

294.00

299.64

294.00

1998.73

129.62

0.98

46.55

50.91

Tinggi gigi belakang tv2 = =b x σds a

S2 x cos2 θ0.50 cm < 1/6 x h = 2 cm

5.34 cmtv2

Kemiringan gigi belakang tm2 = =cos θ

1491.3

0,990,77

71°

12

12

38°

12

12

S

S

Page 49: Hitung Kuda Kuda

- Mencari ukuran gigi muka (tv2 dan tm2)

Besarnya S1 = = 507.46 kg

dipakai tinggi gigi muka = 1.00 cm, sehingga tv2 - tv1 = 1 cm

- Mencari panjang muka gigi (panjang penyaluran = l m )

Maka pakai : l m1 = 15.00 cm

Maka pakai : l m2 = 15.00 cm

□ JOINT G

Digunakan sambungan gigi rangkap.

- Batang S10 = kg

- Sudut θ = 51.00 o

- Mencari tegangan ijin

Gigi belakang σds = σds a = σds // - ( σds // - σds ┴ ) cos θo

=

Gigi muka σds = σds ½ a = σds // - ( σds // - σds ┴ ) cos ½ θo

=

- Mencari ukuran gigi belakang (tv2 dan tm2)

Besarnya S2 diambil = = 1258.87 kg

dipakai tinggi gigi belakang = 2.00 cm

Dengan demikian gigi kedua dapat mendukung gaya S2 = kg1132.8

= 1.73 cm < 1/6 x h = 2 cmb x σds a

Kemiringan gigi belakang tm2 =tv2

= 2.57 cmsin θ

S - S2

Tinggi gigi muka tv1 =S1 x sin2 ½ θ

= 0.38 cmb x σds ½ a

cmsin θ

Panjang kayu muka, l m1 =S1 x sin θ

= 3.92 cm

Kemiringan gigi muka tm1 =tv2

= 1.19

< 15.0 cmτ// x b

Panjang kayu belakang, l m2 =S2 x cos θ

= 3.12 cm < 15.0 cmτ// x b

2517.73

73.36

48.77

½ x S

Tinggi gigi belakang tv2 =S2 x sin2 θ

57°

57°

4,92

2

1

15

21,4

1

12 12

12

SS66°

1,19

Page 50: Hitung Kuda Kuda

- Mencari ukuran gigi muka (tv2 dan tm2)

Besarnya S1 = = 1384.95 kg

dipakai tinggi gigi muka = 1.00 cm, sehingga tv2 - tv1 = 1 cm

- Mencari panjang muka gigi (panjang penyaluran = l m )

Maka pakai : l m1 = 15.00 cm

Maka pakai : l m2 = 15.00 cm

Digunakan sambungan gigi tunggal.

- Batang S16 = kg

- Sudut θ = 23.68 o

- Mencari tegangan ijin

σds = σds ½ a = σds // - ( σds // - σds ┴ ) sin ½ θo

=

Mencari ukuran gigi belakang (tv dan tm)

Syarat untuk θ ≤ 50o tm harus ≤ ¼ h = 3.0 cm

Mencari panjang muka gigi (panjang penyaluran = l m )

Maka pakai : l m = 15.00 cm

cmτ// x b

Panjang kayu belakang, l m2 =S2 x sin θ

= 8.15 cm < 15.0 cmτ// x b

Panjang kayu muka, l m1 =S1 x sin θ

= 8.97 cm < 15.0

b x σds ½ a

Kemiringan gigi muka tm1 =tv2

= 1.29 cmsin θ

S - S2

Tinggi gigi muka tv1 =S1 x sin2 ½ θ

= 0.88 cm

633.73

111.54

0.99 cm < ¼ x h

0.91 cm

= 4.84 cm < 15.0 cmPanjang kayu muka, l m

S x cos θ=

τ// x b

- Tinggi gigi tv =S x cos2 ½ θ

=b x σds ½ a

- Kemiringan gigi tm =tv

=cos θ

1,29

2,57

1

2

0,84

0,75

26°

102°

51°

51°

12

12

SS

S S

12

Page 51: Hitung Kuda Kuda

PERENCANAAN KANTILEVER

Sudut :

αo = 24 o

tan α= 0.44523

sin α= 0.40674

cos α= 0.91355

Ukuran

L1 = 0.75 m

L2 = 0.75 m

H1 = 0.33392 m

H2 = 0.33392 m

Dimensi Kayu

b = 6 cm

h = 12 cm

Panjang Total Batang = 3.32 m

Pembebanan

Beban Sendiri = b x h x P.total Batang x BJ Kayu = 19.3782 kg

Beban Hidup = 100 kg

Beban Atap = Jarak efektif gording x Berat BJLS = 15 kg

= 134.378 kg

Σ MD = 0

Σ H = 0

301.82 kg

Σ V = 0

RDV = P1 + P2

RDV = 268.756 kg

Cek dimensi

S = 268.756 kg

Lk = 66.7843 cm

ix = 0.289 x b = 1.734 cm

iy = 0.289 x h = 3.468 cm

REH = RDH =

P1 = P2

REH =P1 x ( L1 + L2 )

H1 + H2

= 301.82 kg

RDH

RDV

A B

C

D

E

αo

P1

L1 L2

H2

H1

REH

P2

Page 52: Hitung Kuda Kuda

Lk

imin

Maka :

ω = 1.35 ( Lihat tabel faktor tekuk kayu )

Ʈtk = 96 kg/cm2 ( Lihat tabel faktor tekuk kayu )

Kontrol Tegangan :

ω . S

b . h

= 5.03918 kg/cm2 < 96 kg/cm2 .....OK

≈ 39

Ʈtk =

λ = = 38.51459215

Page 53: Hitung Kuda Kuda

PERENCANAAN KOLOM

Direncanakan :

- Dimensi Kolom = b = 20 cm

h = 20 cm

L = 700 cm

b x h2

6

- i x = 0.289 x h = 5.78 cm

- i y = 0.289 x b = 5.78 cm

- Luas Penampang Bruto (Fbr) = b x h = 400 cm2

- Luas Penampang Bersih (Fnt) = Fbr / 1.25 = 320 cm2

- Tegangan Ijin Kayu Kelas Kuat I

• σlt = 150 kg/cm2

• σtk // = σtr // = 130 kg/cm2

• σtk ┴ = 40 kg/cm2

• τ// = 20 kg/cm2

• α = σtk // / σlt = 0.86667

- Pembebanan yang terjadi arah vertikal (RV) :

Beban Atap = 777.37305 kg

Beban Sendiri = 672 kg

Total = 1449.3731 kg

- Pembebanan yang terjadi arah horizontal (RH) :

Beban Atap = -16.27208 kg

- Momen Yang Terjadi Pada kolom :

Mu = RH x L = 11390.454 kg.cm

- Mencari Faktor Tekuk (ω)

= 700 cm

l k =

i min

Maka diperoleh ω = 4.73 (lihat tabel faktor tekuk)

- Kontrol Tegangan

α x M ω x P

W Fnt

σ = 28.827 kg/cm2 < 130 kg/cm2 .....OK !

Maka kolom dengan dimensi 20/20 cm dapat digunakan.

cm3

Panjang Tekuk (l k ) = L

Momen Tahanan Batang (W)- = = 1333.33

122

σ = +

Angka Kelangsingan, λ = 121.107

30 cm

700 cm

30

Page 54: Hitung Kuda Kuda

PERENCANAAN SLOOF

→ Pembebanan yang terjadi :

- Berat sendiri Sloof : 0,20 m x 0,40 m x 2400 kg = Kg

- Berat sendiri Dinding : 4,00 m x 250 kg x 1,00 = Kg

= Kg/m'

→ = q x 1,2

= 1192 kg/m' x 1,2

= Kg/m' -------> Knm

→ Momen Maksimal

- Mlap = 1/11 Wu L²

= 1/11 x 14,304 Kn/m' x 4²

= 20.81 Knm

- Mtump = 1/10 Wu L²

= 1/10 x 14,304 Kn/m' x 4²

= 22.89 Knm

→ Perhitungan Sloof

- F'c = 25 Mpa

Fy = 240 Mpa

d = h - Sb - Ø senkong - ½Ø Tulangan utama

= 400 - 70 - 10 - ½ 16

= 312 mm

192.00

1000.00

1000.00q

1430.4

- =0,2 (0,312)²

20.81= 10.689 Kn/m² ----->ρ = 0,0053

14.304

Mu Lap

b.d²

1/2 P P P P P P P

1/10 1/24

1/11 1/16

4,00 4,00 4,00 4,00 4,00 4,00 20 cm

40 cm

Page 55: Hitung Kuda Kuda

= p x b x d

= 0,0053 x 200 x 312

= mm² ---------------> 2 Ø 16 = 405 mm²

= p x b x d

= 0,0061 x 200 x 312

= mm² ---------------> 2 Ø 16 = 402 mm²

→ Check Tulangan Geser

- Vu = ½ . Wu . L

= ½ x 14,304 x 4

= Kg -------> Kn

Fc'

6

25

6

Vu

Ø

Vu

Ø

Vu

Ø

Tidak memerlukan tulangan geser, maka digunakan tulangan geser praktis

dengan dmax = 312

2

(dipakai Ø 10 - 150 mm)

b.d² 0,2 (0,312)²

As Lap

330.72

-Mu tump

=22.9

28.608

= 11.762 Kn/m² ----->ρ = 0,0061

Vc-

As tump

380.64

28608

= x

b.d

1000x=

47,7 Kn

200 x 312

1000= 52 Kn

- =28.608

0.6=

- ≤ Vc + 2/3 Fc'b.d

1000

≤ 52 + 2/3 25200 x 12

100047.7

= 156 mm

Ukuran penampang memenuhi (ok)

- ≤ Vc ---> 47,7 Kn ≤ 52 Kn

47.7 ≤ 2008 Kn ------->

Page 56: Hitung Kuda Kuda

PERENCANAAN PONDASI TELAPAK

→ Pembebanan :

- Beban konstruksi atas (kuda-kuda) = Kg

- Beban Kolom (0,20 x 0,20 x 2400 x 7,00) = Kg

- Beban Sloof (0,20 x 0,40 x 2400 x 1,00) = Kg

- Beban Lantai Kerja (0,05 x 1,20 x 2400 x 1,20) = Kg

- Beban Pondasi (0,25 x 1,20 x 2400 x 1,20) = Kg

- Beban Tanah Urug (1,20 x 1,20 x 1,00) x (0,20 x 0,40 x 0,8) x = Kg

(1,20 x 1,20 x 0,25) x 1100

∑G = Kg

→ Momen yang terjadi :

M = (5550,4 - 352,94) x 7,00 = 36642,093 Kgm

2588

676.8

192

172.8

864

1152.8

5550.4

Page 57: Hitung Kuda Kuda

→ Tegangan :

∑G M

A W

= ±

σ1 = 0,398 Kg/cm²

σ2 = 0,372 Kg/cm² ≤ σtanah = 0,52 Kg/cm²

→ Perhitungan Plat Pondasi

Beban yang diterima plat pondasi :

- Beban kuda-kuda = Kg

- Beban kolom = Kg

- Beban sloof = Kg

ℓ = Kg

→ Beban terfaktor :

= Kg

→ Momen max

- Mu = ½ . q . L²

= ½ x 3734,2 x 0,6²

= Kg -------> Kn m

- d = 250 - 70 - ½ 16

=

- b = 1.00 mm

± = ±5550.4

120 x 120

36642.093

1,6 x 120³

0.385 0.0132

σ =

L

2588

676.8

192

3460.8

b.L1.6=q

3734.2

672.2 6.58

172 mm

= 1.6 1.001,20 x 1,20

3460.8

Page 58: Hitung Kuda Kuda

1.4

fy

- As = ℓ min x b x d

= 0,0058 x 1000 x 172

= =====> 998 mm² (Ø 16 - 200 = 1005 mm²)

-Mu

=6.58

= Kg/m²b . d² 1,00 (0,172)²

=1.4

240=

222.400

0.0058- didapat ℓ = 0,0024 < ℓ = ………….. Ok

997.6

Page 59: Hitung Kuda Kuda

PERENCANAAN PONDASI BATU KALI

→ Pembebanan :

- Gaya normal akibat berat sendiri kolom praktis

(0,15 x 0,15) x 2400 x 4,00 = Kg

- B.S dinding ½ bata (0,15 x 250 x 7,00) = Kg

- B.S Sloof (0,20 x 0,40 x 2400 x 1,00) = Kg

- B.S Pondasi ½ (0,3 x 0,6) x 2200 x 1,00 = Kg

- B.S Tanah Urug (0,6 x 1,3 x 1,00) - (0,20 x 0,40 x 1,00) - = Kg

(½ x 0,3 x 0,6) 1,00 x 1100

∑G = Kg

→ Momen yang terjadi :

M = (5550,4 - 352,94) x 7,00 = 36642,093 Kgm

→ Tegangan :

∑G

A

= 0,485 Kg/cm² ≤ σtanah = 0,52 Kg/cm² …….. Ok

2331.5

σ =

216

262.5

192

990

671

=2331.5

60 x 80

Page 60: Hitung Kuda Kuda

DAFTAR ISI

1. PERHITUNGAN PEMBEBANAN PADA GORDING

2. DATA PERENCANAAN KUDA - KUDA

3. PERHITUNGAN GAYA-GAYA BATANG AKIBAT BEBAN MATI

4. PERHITUNGAN GAYA-GAYA BATANG AKIBAT BEBAN HIDUP

5. PERHITUNGAN GAYA-GAYA BATANG AKIBAT BEBAN AIR HUJAN

6. PERHITUNGAN GAYA-GAYA BATANG AKIBAT BEBAN ANGIN TEKAN

7. PERHITUNGAN GAYA-GAYA BATANG AKIBAT BEBAN ANGIN HISAP

8. KONTROL KEKUATAN BATANG

9. PERENCANAAN SAMBUNGAN

10. PERENCANAAN KANTILEVER

11. PERENCANAAN KOLOM DAN SLOOF

12. PERENCANAAN PONDASI TELAPAK

Page 61: Hitung Kuda Kuda
Page 62: Hitung Kuda Kuda

1,50

Tanah Urug

Tanah Asli

1,20

0,30

1/2 P P P P P P P

1/10 1/24

1/11 1/16

4,00 4,00 4,00 4,00 4,00 4,00

20 cm

40 cm

Page 63: Hitung Kuda Kuda

Kolom 30/30

- 0,05 Lantai - 0,15 Pasir

- 0,55 Sloof 20/40

- 1,40

- 1,70 Lantai Kerja - 1,65

- 0,85 Pasir Urug

P

Page 64: Hitung Kuda Kuda