Tugas Struktur Baja I - Rangka Batang (Alfian)

TUGAS FINAL STRUKTUR BAJA I Nama : M. ALFIANSYAH SYUKUR NIM : D111 10 902 JURUSAN SIPIL FAKULTAS TEKNIK UNIVERSITAS HASANUDDIN

Diketa Diketahui hui suatu suatu rangka rangka kap kap dengan dengan data data sebaga sebagaii beriku berikut! t!

Keterangan:

(P dalam dalam ton) ton) (L dalam meter) P3 =

12.5

Beban (P) Panjang per segmen Profil yang digunakan Mutu baja yg tersedia

ton

D S3

S2

P2 =

12.5

: : : : :

ton

P4 =

12.5

ton

Mohon diisi  maks. 58 ton maks. 14.5 meter  Profil L sama kaki  BJ 33 BJ 37  BJ 44 BJ 52

S11 E

C S10

S1

P1 =

12.5 A

t on

KONTROL ∑V

=

P5 =

30 S5

Menghitung Reaksi Perletakan ∑MA = 0 -RBV 10 + -RBV 10 + -RBV 10 + -RBV 10 = RBV =

= 10 10 10 10

S4 S13

F

S6

L1 2.5 m

∑MB RAV RAV RAV RAV RAV

S12

S9

0 = =

0

G

L2 2.5 m

P5 12.5 125 31.25

P1 12.5 125 312.5 31.25

10 10

S7

H

ton

B

S8

L3 2.5 m

12.5

L4 2.5 m

+ + +

P4 12.5 93.75

7.5 7.5

+ + +

P3 12.5 62.5

5 5

+ + +

P2 12.5 31.25

2.5 2.5

= = =

0 0 0

-

P2 12.5 93.75

7.5 7.5

-

P3 12.5 62.5

5 5

-

P4 12.5 31.25

2.5 2.5

= = =

0 0 0

312.5 ton

10 10

ton

RAV 31.25

+ +

RBV 31.25

-

P1 12.5

-

P2 12.5

-

P3 12.5

-

P4 12.5

-

P5 12.5 0

= = =

0 0 0

30

= = = =

0 0 -18.75 -37.5

OK

Menghitung Gaya-Gaya Batang

TITIK BUHUL A ∑V RAV 31.25

S1

P1 =

12.5

ton

31.25

0 P1 12.5

+ +

30

A

RAV =

= -

S1 S1 S1 S1

sin 0.5 0.5

S5 S5 S5 S5

= = = =

0 0 0 32.476

S2 S2 S2 S2

ton

S5 ∑H S1 -37.5 -32.476

ton

= cos 0.866

0 30

+ + +

ton

TITIK BUHUL F ∑V S9

= =

0 0

= + +

0 S6 S6 S6

S9

S5 =

3 2.4 76

to n

F

S6

∑H -S5 -32.476

= = =

0 0 32.476

-

P2 12.5 12.5

+ + +

+ + +

S2 S2 S2 S2

cos 0.866 0.866 0.866

ton

TITIK BUHUL C

S2

P2 =

12.5

ton

∑V S1 37.5 18.75

= sin 0.5

30

0

∑H S1 37.5 32.476

= cos 0.866

30

C S1 =

37.5

30

S10

ton S9

sin 0.5 0.5 0.5

30

-

S10 S10 S10 S10

sin 0.5 0.5 0.5

30

0 30

+ + + +

S10 S10 S10 S10

cos 0.866 0.866 0.866

30

= = = =

0 0 0 -32.476

= = = =

0 0 0 -6.25

METODE ELEMINASI S2 0.866 S2 0.5

S2 S2 S2 S2 S2

0.5 0.5 0.5 0.5

+ -

S10 S10

0.866 0.5

= =

-32.476 -6.25

x x

+

S10 -12.5 6.25

0.5 0.5

= = = = =

-6.25 -6.25 -6.25 -12.5 -25

∑V S2 25 12.5

= sin 0.5

30

∑H S2 25 21.651

= cos 0.866

30

-

S11 S11 S11 S11 S11

1 1.732

S2 S2

0.866 0.866

+ -

S10 S10 S10 S10

0.866 0.866 1.732

= = = =

-

P3 12.5 12.5

-

S11 S11 S11 S11

-

S3 S3 S3 S3

sin 0.5 0.5 0.5

+ + +

S3 S3 S3 S3 S3

cos 0.866 0.866 0.866

S3 -25 12.5

0.5 0.5

= = = = =

-32.476 -10.825 -21.651 -12.5 ton

ton

TITIK BUHUL D P3 =

12.5

ton

D S2 =

25

30

0

S3

ton

S11

0

+

30

= = = = = 0 0 0 -12.5 12.5

ton

0 0 0 -21.651 -25 ton

30

= = = =

0 0 0 0

TITIK BUHUL G S11 =

S10 =

12.5

12.5

ton

ton

∑V -S10 -12.5 -6.25

32.476

ton

∑H -S6 -32.476 -32.476 S7

REKAPITULASI GAYA-GAYA BATANG

Nama Batang

Tekan (ton)

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13

37.5 25 25 37.5

0 12.5

Tarik (ton)

Panjang (meter)

32.476 32.476 32.476 32.476 0

2.887 2.887 2.887 2.887 2.500 2.500 2.500 2.500 1.443 2.887 2.887 2.887 1.443

12.5 12.5 0

0 30

+ + +

S11 12.5 12.5

+ + +

S12

30 S6 =

= sin 0.5

0

= + + +

0 S10 12.5 10.825

cos 0.866

30

+ + +

S12 S12 S12 S12 S12

sin 0.5 0.5 0.5

S12 -12.5 -10.825

cos 0.866

30

30

= = = = =

0 0 0 -6.25 -12.5

+ + +

S7 S7 S7 S7

ton

= = = =

0 0 0 32.476

ton

PERHITUNGAN BATANG TARIK BATANG BAWAH (S5, S6, S7, S8) Direncanakan menggunakan baja BJ 33 33 fy = 200 MPa = P max = 32.48 ton = Lk = 2.50 meter =

A

P max fy

=

= =

Digunakan profil L sama kaki Luas penampang profil (Ag)

Jari-jari inersia (i x)

75.75.12 16.7 cm²

2.22

Kontrol Kelangsingan Batang λ 240 <

cm

Silakan pilih

2000 32476 250.00 32476 2000 16.24

kg/cm² kg cm

BATANG TEGAK (S9, S11, S13) Direncanakan menggunakan baja BJ 33 33 fy = 200 MPa = P max = 12.50 ton = Lk = 2.89 meter =

A

P max fy

=

=

cm²

lihat Buku Teknik Sipil, Hal 255-258

= Digunakan profil L sama kaki Luas penampang profil (Ag)

Jari-jari inersia (ix)

55.55.6 6.31

cm²

1.66

cm

Kontrol Kelangsingan Batang λ 240 <

Lk ix

<

240

Lk ix

<

240

250 2.22

<

240

288.675 1.66

<

240

112.6126

<

240

173.9007

<

240

OK

OK

Silakan pilih

2000 12500 288.68

kg/cm² kg cm

12500 2000 6.25

cm²

lihat Buku Teknik Sipil, Hal 255-258

PERHITUNGAN BATANG TEKAN BATANG ATAS (S1, S2, S3, S4) Direncanakan menggunakan baja BJ 33 33 fy = 200 MPa = P max = 37.50 ton = Lk = 2.89 meter = Imin

2000 37500 288.68

kg/cm² kg cm

=

1.69

x

P max

x

Lk²

= =

1.69 528.13

x

37.50

x

2.89

Digunakan profil L sama kaki Momen Inersia (IX)

130.130.14 540

cm⁴

34.7

cm²

3.94

cm

lihat Buku Teknik Sipil, Hal 255-258

288.68 3.94 73.27

1.69

x

P max

x

Lk²

1.69 176.04

x

12.50

x

2.89

Digunakan profil L sama kaki Momen Inersia (IX)

= ≈

=

74 =

1.432

100.100.10

288.68 3.04 94.96

Kontrol

1.432

37500 34.7

1547.55

177

cm⁴

19.2

cm²

3.04

cm

lihat Buku Teknik Sipil, Hal 255-258

fy

≤

2000

≤

2000

ω

P max Ag

1.736

12500 19.2

OK

≈

95

Berdasarkan nilai λ di atas, diperoleh faktor tekuk (ω)

Kontrol ≤

1130.21

²

cm⁴

(lihat Buku Teknik Sipil, Hal 321-325)

P max

kg/cm² kg cm

= =

(lihat Buku Teknik Sipil, Hal 321-325)

Ag

2000 12500 288.68

Menentukan faktor tekuk ( ω) Lk λ = ix

Berdasarkan nilai λ di atas, diperoleh faktor tekuk (ω)

ω

Silakan pilih

=

Luas Penampang Profil (Ag) Jari-Jari Inersia (i x)

Menentukan faktor tekuk ( ω) Lk λ = ix

=

Imin ²

cm⁴

Luas Penampang Profil (Ag) Jari-Jari Inersia (ix)

=

BATANG DIAGONAL TENGAH (S10, S12) Direncanakan menggunakan baja BJ 33 33 fy = 200 MPa = P max = 12.50 ton = Lk = 2.89 meter =

Silakan pilih

≤

fy

≤

2000

≤

2000

OK

=

1.736

PERHITUNGAN JUMLAH BAUT PROFIL BAJA L

75.75.12

Luas penampang Profil (Ag) Tebal plat (t) Lebar penampang Kuat Leleh (fy) Kuat Putus (fu)

16.7 12 75 200 330

Tipe Baut Diameter Baut (d)

A325

cm² mm mm Mpa MPa

=

Ø1/2" b

Kuat tarik baut (fu ) Diameter Lubang Baut (D)

825 13.7

Luas Penampang Baut (Ab)

= = =

Asumsi

2

1670

mm²

(lihat nama profil,  XX.XX.(tebal plat) ) (lihat nama profil, (lebar penampang).XX.XX  )

=

MPa mm π . d² 4 3.14

12.7 4 126.61 mm²

12.7

mm

²

baris

Kapasitas Batang (diambil ΦTn minimum)

Luas Netto Profil (Ae)

ΦTn

= = =

Diambil ΦTn

=

Ag

= =

1670 1341.2

0.9 Ag 0.9 1670 300600.00 N

-

n

D

t

-

2

13.7

12

ΦTn

= = =

mm² fy 200

0.75 Ae 0.75 1341.2 331947.00 N

fu 330

300600.00 N

Kapasitas Sambungan Baut (diambil ΦRn maksimum) Diambil ΦRn

Terhadap ulir dalam bidang geser ΦRn

= = =

b

Φ 0.40 0.75 0.40 62673.26 N

fu 825

Φ 0.75 0.75 0.75 58756.18 N

fu 825

Ab 126.61

Φ 0.75 90525.6

d 12.7

t 12

n 2

Ab 126.61

Terhadap gaya tarik ΦRn

= = =

Terhadap tumpu ΦRn = = =

2.4 2.4 N

b

JUMLAH BAUT ΦTn = ΦRn = ≈

fu 330

90525.60 N

300600.00 90525.60 3.32 4

baut

PERHITUNGAN JUMLAH BAUT PROFIL BAJA L

55.55.6

Luas penampang Profil (Ag) Tebal plat (t) Lebar penampang Kuat Leleh (fy) Kuat Putus (fu)

6.31 6 55 200 330

Tipe Baut Diameter Baut (d)

A325

cm² mm mm Mpa MPa

=

Ø1/2" b

Kuat tarik baut (fu ) Diameter Lubang Baut (D)

825 13.7

Luas Penampang Baut (Ab)

= = =

Asumsi

2

631

mm²

(lihat nama profil,  XX.XX.(tebal plat) ) (lihat nama profil, (lebar penampang).XX.XX  )

=

MPa mm π . d² 4 3.14

12.7 4 126.61 mm²

12.7

mm

²

baris

Kapasitas Batang (diambil ΦTn minimum)

Luas Netto Profil (Ae)

ΦTn

= = =

Diambil ΦTn

=

Ag

= =

631 466.6

0.9 Ag 0.9 631 113580.00 N

-

n

D

t

-

2

13.7

6

ΦTn

= = =

mm² fy 200

0.75 Ae 0.75 466.6 115483.50 N

fu 330

113580.00 N

Kapasitas Sambungan Baut (diambil ΦRn maksimum) Diambil ΦRn

Terhadap ulir dalam bidang geser ΦRn

= = =

b

Φ 0.40 0.75 0.40 62673.26 N

fu 825

Φ 0.75 0.75 0.75 58756.18 N

fu 825

Ab 126.61

Φ 0.75 45262.8

d 12.7

t 6

n 2

Ab 126.61

Terhadap gaya tarik ΦRn

= = =

Terhadap tumpu ΦRn = = =

2.4 2.4 N

b

JUMLAH BAUT ΦTn = ΦRn = ≈

fu 330

62673.26 N

113580.00 62673.26 1.81 2

baut

PERHITUNGAN JUMLAH BAUT PROFIL BAJA L

130.130.14

Luas penampang Profil (Ag) Tebal plat (t) Lebar penampang Kuat Leleh (fy) Kuat Putus (fu)

34.7 14 130 200 330

Tipe Baut Diameter Baut (d)

A325

cm² mm mm Mpa MPa

=

825 13.7

Luas Penampang Baut (Ab)

= = =

Asumsi

2

mm²

(lihat nama profil, (lebar penampang).XX.XX  )

Ø1/2" b

Kuat tarik baut (fu ) Diameter Lubang Baut (D)

3470

(lihat nama profil,  XX.XX.(tebal plat) )

=

MPa mm π . d² 4 3.14

12.7 4 126.61 mm²

12.7

mm

²

baris

Kapasitas Batang (diambil ΦTn minimum)

Luas Netto Profil (Ae)

ΦTn

= = =

Diambil ΦTn

=

Ag

= =

3470 3086.4

0.9 Ag 0.9 3470 624600.00 N

-

n

D

t

-

2

13.7

14

ΦTn

= = =

mm² fy 200

0.75 Ae 0.75 3086.4 763884.00 N

fu 330

624600.00 N

Kapasitas Sambungan Baut (diambil ΦRn maksimum) Diambil ΦRn

Terhadap ulir dalam bidang geser b

Φ 0.40 0.75 0.40 62673.26 N

fu 825

= = =

Φ 0.75 0.75 0.75 58756.18 N

fu 825

Ab 126.61

Terhadap tumpu ΦRn = = =

Φ 2.4 0.75 2.4 105613.2 N

d 12.7

t 14

ΦRn

= = =

n 2

Ab 126.61

Terhadap gaya tarik ΦRn

b

JUMLAH BAUT ΦTn = ΦRn = ≈

fu 330

105613.20 N

624600.00 105613.20 5.91 6

baut

PERHITUNGAN JUMLAH BAUT PROFIL BAJA L

100.100.10

Luas penampang Profil (Ag) Tebal plat (t) Lebar penampang Kuat Leleh (fy) Kuat Putus (fu)

19.2 10 100 200 330

Tipe Baut Diameter Baut (d)

A325

cm² mm mm Mpa MPa

=

825 13.7

Luas Penampang Baut (Ab)

= = =

Asumsi

2

mm²

(lihat nama profil, (lebar penampang).XX.XX  )

Ø1/2" b

Kuat tarik baut (fu ) Diameter Lubang Baut (D)

1920

(lihat nama profil,  XX.XX.(tebal plat) )

=

MPa mm π . d² 4 3.14

12.7 4 126.61 mm²

12.7

mm

²

baris

Kapasitas Batang (diambil ΦTn minimum)

Luas Netto Profil (Ae)

ΦTn

= = =

Diambil ΦTn

=

Ag

= =

1920 1646

0.9 Ag 0.9 1920 345600.00 N

-

n

D

t

-

2

13.7

10

ΦTn

= = =

mm² fy 200

0.75 Ae 0.75 1646 407385.00 N

fu 330

345600.00 N

Kapasitas Sambungan Baut (diambil ΦRn maksimum) Diambil ΦRn

Terhadap ulir dalam bidang geser ΦRn

= = =

b

Φ 0.40 0.75 0.40 62673.26 N

fu 825

n 2

Φ 0.75 0.75 0.75 58756.18 N

fu 825

Ab 126.61

d 12.7

t 10

Ab 126.61

Terhadap gaya tarik ΦRn

= = =

Terhadap tumpu ΦRn = = =

Φ 0.75 75438

2.4 2.4 N

b

JUMLAH BAUT ΦTn = ΦRn = ≈

fu 330

75438.00 N

345600.00 75438.00 4.58 6

baut

MUTU BAJA

Mutu 33 37 44 52

Tegangan Leleh (Mpa) 200 240 280 360

PROFIL BAJA L TABEL PROFIL UNTUK PEMILIHAN PROFIL BATANG TARIK Luas Penampang (A) cm² 0.82 1.05 1.12 1.42 1.45 1.74 1.85 2.26 2.27 2.67 2.78 3.08 3.79 3.87 4.3 4.48 4.8 5.69 5.86 6.31 6.56 6.91 8.23 8.24 8.7 9.03 9.4 10.1 10.1

Profil

15.15.3 15.15.4 20.20.3 25.25.3 20.20.4 30.30.3 25.25.4 25.25.5 30.30.4 35.35.4 30.30.5 40.40.4 40.40.5 35.35.6 45.45.5 40.40.6 50.50.5 50.50.6 45.45.7 55.55.6 50.50.7 60.60.6 55.55.8 50.50.9 65.65.7 60.60.8 70.70.7 55.55.10 75.75.7

Momen Inersia (Ix)

Jari-Jari Inersia (ix)

cm⁴

cm

0.15 0.19 0.39 0.79 0.48 1.41 1.01 1.18 1.81 2.96 2.16 4.48 5.43 4.14 7.83 6.33 11 12.8 10.4 17.3 14.6 22.8 22.1 17.9 33.4 29.1 42.4 26.3 52.4

0.43 0.42 0.59 0.75 0.58 0.9 0.74 0.72 0.89 1.05 0.88 1.21 1.2 1.04 1.35 1.19 1.51 1.5 1.33 1.66 1.49 1.82 1.64 1.47 1.96 1.8 2.12 1.62 2.28

11 11.1 11.5 11.9 12.3 13.2 14.1 14.3 15.1 15.5 16.7 17.9 18.7 19.2 20.6 21.2 21.8 22.7 25.1 25.4 26.2 29 29.7 30 33.9 34.7 35 39.3 40 40.3 45 45.7 46.1 51 51.8 55.4 57.5 61.8 61.9 68.4 69.1 76.4

65.65.9 60.60.10 75.75.8 70.70.9 80.80.8 65.65.11 75.75.10 70.70.11 80.80.10 90.90.9 75.75.12 80.80.12 90.90.11 100.100.10 80.80.14 110.110.10 90.90.13 100.100.12 110.110.12 120.120.11 100.100.14 110.110.14 120.120.13 130.130.12 120.120.15 130.130.14 140.140.13 130.130.16 140.140.15 150.150.14 140.140.17 150.150.16 160.160.15 150.150.18 160.160.17 180.180.16 160.160.19 200.200.16 180.180.18 180.180.20 200.200.18 200.200.20

41.3 34.9 58.9 52.6 72.3 48.8 71.4 61.8 87.5 116 82.4 102 138 177 115 239 158 207 280 341 235 319 394 472 446 540 638 605 723 845 805 949 1100 1050 1230 1680 1350 2340 1870 2040 2600 2850

1.94 1.78 2.26 2.1 2.42 1.91 2.25 2.08 2.41 2.74 2.22 2.39 2.72 3.04 2.36 3.36 2.69 3.02 3.34 3.66 3 3.32 3.64 3.97 3.63 3.94 4.27 3.92 4.25 4.58 4.23 4.56 4.88 4.54 4.86 5.51 4.84 6.15 5.49 5.47 6.13 6.11

TABEL PROFIL UNTUK PEMILIHAN PROFIL BATANG TEKAN Momen Inersia (Ix) cm⁴ 0.15 0.19 0.39 0.48 0.79 1.01 1.18 1.41 1.81 2.16 2.96 4.14 4.48 5.43 6.33 7.83 10.4 11 12.8 14.6 17.3 17.9 22.1 22.8 26.3 29.1 33.4 34.9 41.3

Profil

15.15.3 15.15.4 20.20.3 20.20.4 25.25.3 25.25.4 25.25.5 30.30.3 30.30.4 30.30.5 35.35.4 35.35.6 40.40.4 40.40.5 40.40.6 45.45.5 45.45.7 50.50.5 50.50.6 50.50.7 55.55.6 50.50.9 55.55.8 60.60.6 55.55.10 60.60.8 65.65.7 60.60.10 65.65.9

Luas Penampang (A)

Jari-Jari Inersia (ix)

cm²

cm

0.82 1.05 1.12 1.45 1.42 1.85 2.26 1.74 2.27 2.78 2.67 3.87 3.08 3.79 4.48 4.3 5.86 4.8 5.69 6.56 6.31 8.24 8.23 6.91 10.1 9.03 8.7 11.1 11

0.43 0.42 0.59 0.58 0.75 0.74 0.72 0.9 0.89 0.88 1.05 1.04 1.21 1.2 1.19 1.35 1.33 1.51 1.5 1.49 1.66 1.47 1.64 1.82 1.62 1.8 1.96 1.78 1.94

42.4 48.8 52.4 52.6 58.9 61.8 71.4 72.3 82.4 87.5 102 115 116 138 158 177 207 235 239 280 319 341 394 446 472 540 605 638 723 805 845 949 1050 1100 1230 1350 1680 1870 2040 2340 2600 2850

70.70.7 65.65.11 75.75.7 70.70.9 75.75.8 70.70.11 75.75.10 80.80.8 75.75.12 80.80.10 80.80.12 80.80.14 90.90.9 90.90.11 90.90.13 100.100.10 100.100.12 100.100.14 110.110.10 110.110.12 110.110.14 120.120.11 120.120.13 120.120.15 130.130.12 130.130.14 130.130.16 140.140.13 140.140.15 140.140.17 150.150.14 150.150.16 150.150.18 160.160.15 160.160.17 160.160.19 180.180.16 180.180.18 180.180.20 200.200.16 200.200.18 200.200.20

9.4 13.2 10.1 11.9 11.5 14.3 14.1 12.3 16.7 15.1 17.9 20.6 15.5 18.7 21.8 19.2 22.7 26.2 21.2 25.1 29 25.4 29.7 33.9 30 34.7 39.3 35 40 45 40.3 45.7 51 46.1 51.8 57.5 55.4 61.9 68.4 61.8 69.1 76.4

2.12 1.91 2.28 2.1 2.26 2.08 2.25 2.42 2.22 2.41 2.39 2.36 2.74 2.72 2.69 3.04 3.02 3 3.36 3.34 3.32 3.66 3.64 3.63 3.97 3.94 3.92 4.27 4.25 4.23 4.58 4.56 4.54 4.88 4.86 4.84 5.51 5.49 5.47 6.15 6.13 6.11