Tugas Struktur Baja I - Rangka Batang (Alfian)

TUGAS FINAL STRUKTUR BAJA I

Nama : M. ALFIANSYAH SYUKURNIM : D111 10 902JURUSAN SIPIL FAKULTAS TEKNIK UNIVERSITAS HASANUDDIN

Diketahui suatu rangka kap dengan data sebagai berikut! (P dalam ton) Keterangan:(L dalam meter) : Mohon diisi

Beban (P) : maks. 58 tonP3 = 12.5 ton Panjang per segmen : maks. 14.5 meter

Profil yang digunakan : Profil L sama kakiMutu baja yg tersedia : BJ 33

BJ 37BJ 44

P2 = 12.5 ton P4 = 12.5 ton BJ 52

P1 = 12.5 ton P5 = 12.5 ton

30

L1 L2 L3 L42.5 m 2.5 m 2.5 m 2.5 m

Menghitung Reaksi Perletakan ∑MA = 0-RBV 10 + P5 10 + P4 7.5 + P3 5 + P2 2.5 = 0-RBV 10 + 12.5 10 + 12.5 7.5 + 12.5 5 + 12.5 2.5 = 0-RBV 10 + 125 + 93.75 + 62.5 + 31.25 = 0-RBV 10 = - 312.5RBV = 31.25 ton

∑MB = 0RAV 10 - P1 10 - P2 7.5 - P3 5 - P4 2.5 = 0RAV 10 - 12.5 10 - 12.5 7.5 - 12.5 5 - 12.5 2.5 = 0RAV 10 - 125 - 93.75 - 62.5 - 31.25 = 0RAV 10 = 312.5RAV = 31.25 ton

A B

C

D

E

F G H

S1

S2 S3

S4

S5 S6 S7 S8

S9

S10 S12

S11

S13

KONTROL∑V = 0

RAV + RBV - P1 - P2 - P3 - P4 - P5 = 031.25 + 31.25 - 12.5 - 12.5 - 12.5 - 12.5 - 12.5 = 0

0 = 0 OK

Menghitung Gaya-Gaya Batang

TITIK BUHUL A

∑V = 0RAV - P1 + S1 sin 30 = 0

P1 = 12.5 ton 31.25 - 12.5 + S1 0.5 = 0S1 0.5 = -18.75

30 S1 = -37.5 ton

∑H = 0RAV = 31.25 ton S1 cos 30 + S5 = 0

-37.5 0.866 + S5 = 0-32.476 + S5 = 0

S5 = 32.476 ton

TITIK BUHUL F

∑V = 0S9 = 0

∑H = 0-S5 + S6 = 0

S5 = 32.476 ton -32.476 + S6 = 0S6 = 32.476 ton

TITIK BUHUL C

∑V = 0S1 sin 30 - P2 + S2 sin 30 - S10 sin 30 = 0

P2 = 12.5 ton 37.5 0.5 - 12.5 + S2 0.5 - S10 0.5 = 018.75 - 12.5 + S2 0.5 - S10 0.5 = 0

S2 0.5 - S10 0.5 = -6.25

S1 = 37.5 ton ∑H = 0S1 cos 30 + S2 cos 30 + S10 cos 30 = 0

S1

S5

F S6

S9

C

S2

S10

A

37.5 0.866 + S2 0.866 + S10 0.866 = 030 32.476 + S2 0.866 + S10 0.866 = 0

S2 0.866 + S10 0.866 = -32.476

METODE ELEMINASIS2 0.866 + S10 0.866 = -32.476 x 1 S2 0.866 + S10 0.866 = -32.476S2 0.5 - S10 0.5 = -6.25 x 1.732 S2 0.866 - S10 0.866 = -10.825 -

S10 1.732 = -21.651S10 = -12.5 ton

S2 0.5 - S10 0.5 = -6.25S2 0.5 - -12.5 0.5 = -6.25S2 0.5 + 6.25 = -6.25S2 0.5 = -12.5S2 = -25 ton

TITIK BUHUL D

P3 = 12.5 ton ∑V = 0S2 sin 30 - P3 - S11 - S3 sin 30 = 025 0.5 - 12.5 - S11 - S3 0.5 = 0

12.5 - 12.5 - S11 - S3 0.5 = 0S2 = 25 ton - S11 - S3 0.5 = 0

∑H = 030 S2 cos 30 + S3 cos 30 = 0

25 0.866 + S3 0.866 = 021.651 + S3 0.866 = 0

S3 0.866 = -21.651S3 = -25 ton

- S11 - S3 0.5 = 0- S11 - -25 0.5 = 0- S11 + 12.5 = 0- S11 = -12.5

S11 = 12.5 ton

S9

D

S3

S11

TITIK BUHUL G

S11 = 12.5 ton ∑V = 0-S10 sin 30 + S11 + S12 sin 30 = 0-12.5 0.5 + 12.5 + S12 0.5 = 0-6.25 + 12.5 + S12 0.5 = 0

S12 0.5 = -6.25S10 = 12.5 ton S12 = -12.5 ton

∑H = 0-S6 + S10 cos 30 + S12 cos 30 + S7 = 0

-32.476 + 12.5 0.866 + -12.5 0.866 + S7 = 030 -32.476 + 10.825 + -10.825 + S7 = 0

S6 = 32.476 ton S7 = 32.476 ton

REKAPITULASI GAYA-GAYA BATANG

Nama Tekan Tarik PanjangBatang (ton) (ton) (meter)

S1 37.5 2.887S2 25 2.887S3 25 2.887S4 37.5 2.887S5 32.476 2.500S6 32.476 2.500S7 32.476 2.500S8 32.476 2.500S9 0 0 1.443

S10 12.5 2.887S11 12.5 2.887S12 12.5 2.887S13 0 0 1.443

S7

S12

PERHITUNGAN BATANG TARIK

BATANG BAWAH (S5, S6, S7, S8) BATANG TEGAK (S9, S11, S13)Direncanakan menggunakan baja BJ 33 Silakan pilih Direncanakan menggunakan baja BJ 33 Silakan pilih

fy = 200 MPa = 2000 fy = 200 MPa = 2000P max = 32.48 ton = 32476 kg P max = 12.50 ton = 12500 kg

Lk = 2.50 meter = 250.00 cm Lk = 2.89 meter = 288.68 cm

A =P max

=32476

A =P max

=12500

fy 2000 fy 2000= 16.24 = 6.25

Digunakan profil L sama kaki 75.75.12 Digunakan profil L sama kaki 55.55.6Luas penampang profil (Ag) 16.7 lihat Buku Teknik Sipil, Hal 255-258 Luas penampang profil (Ag) 6.31 lihat Buku Teknik Sipil, Hal 255-258

2.22 cm Jari-jari inersia (ix) 1.66 cm

Kontrol Kelangsingan Batang Kontrol Kelangsingan Batangλ < 240 λ < 240

Lk< 240

Lk< 240

250< 240

288.675< 240

2.22 1.66

112.6126 < 240 OK 173.9007 < 240 OK

kg/cm² kg/cm²

cm² cm²

cm² cm²

Jari-jari inersia (ix)

ix ix

PERHITUNGAN BATANG TEKAN

BATANG ATAS (S1, S2, S3, S4) BATANG DIAGONAL TENGAH (S10, S12)Direncanakan menggunakan baja BJ 33 Silakan pilih Direncanakan menggunakan baja BJ 33 Silakan pilih

fy = 200 MPa = 2000 fy = 200 MPa = 2000P max = 37.50 ton = 37500 kg P max = 12.50 ton = 12500 kg

Lk = 2.89 meter = 288.68 cm Lk = 2.89 meter = 288.68 cm

= 1.69 x P max x Lk² = 1.69 x P max x Lk²= 1.69 x 37.50 x 2.89 ² = 1.69 x 12.50 x 2.89 ²= 528.13 cm⁴ = 176.04 cm⁴

Digunakan profil L sama kaki 130.130.14 Digunakan profil L sama kaki 100.100.10

540 cm⁴ lihat Buku Teknik Sipil, Hal 255-258 177 cm⁴ lihat Buku Teknik Sipil, Hal 255-258Luas Penampang Profil (Ag) 34.7 cm² Luas Penampang Profil (Ag) 19.2 cm²

3.94 cm 3.04 cm

λ =Lk

λ =Lk

=288.68

=288.68

3.94 3.04= 73.27 ≈ 74 = 94.96 ≈ 95

= 1.432 = 1.736(lihat Buku Teknik Sipil, Hal 321-325) (lihat Buku Teknik Sipil, Hal 321-325)

Kontrol Kontrol

ω P max≤ fy

ω P max≤ fy

Ag Ag

1.432 37500≤ 2000

1.736 12500≤ 2000

34.7 19.2

1547.55 ≤ 2000 OK 1130.21 ≤ 2000 OK

kg/cm² kg/cm²

Imin Imin

Momen Inersia (IX) Momen Inersia (IX)

Jari-Jari Inersia (ix) Jari-Jari Inersia (ix)

Menentukan faktor tekuk (ω) Menentukan faktor tekuk (ω)

ix ix

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

PERHITUNGAN JUMLAH BAUT

PROFIL BAJA L 75.75.12

Luas penampang Profil (Ag) 16.7 = 1670Tebal plat (t) 12 mmLebar penampang 75 mmKuat Leleh (fy) 200 MpaKuat Putus (fu) 330 MPa

Tipe Baut A325Diameter Baut (d) Ø1/2" = 12.7 mm

825 MPaDiameter Lubang Baut (D) 13.7 mm

Luas Penampang Baut (Ab) =π . d²

4

=3.14 12.7 ²

4= 126.61

Asumsi 2 baris

Luas Netto Profil (Ae) = Ag - n D t

= 1670 - 2 13.7 12= 1341.2

ΦTn = 0.9 Ag fy ΦTn = 0.75 Ae fu= 0.9 1670 200 = 0.75 1341.2 330= 300600.00 N = 331947.00 N

Diambil ΦTn 300600.00 N

Kapasitas Sambungan Baut (diambil ΦRn maksimum)

Terhadap ulir dalam bidang geser Diambil ΦRn 90525.60 N

ΦRn = Φ 0.40 n Ab= 0.75 0.40 825 2 126.61 JUMLAH BAUT= 62673.26 N ΦTn

=300600.00

ΦRn 90525.60Terhadap gaya tarik = 3.32

ΦRn = Φ 0.75 Ab ≈ 4 baut= 0.75 0.75 825 126.61= 58756.18 N

Terhadap tumpuΦRn = Φ 2.4 d t fu

= 0.75 2.4 12.7 12 330= 90525.6 N

cm² mm²(lihat nama profil, XX.XX.(tebal plat))(lihat nama profil, (lebar penampang).XX.XX)

Kuat tarik baut (fub)

mm²

Kapasitas Batang (diambil ΦTn minimum)

mm²

fub

fub

PERHITUNGAN JUMLAH BAUT

PROFIL BAJA L 55.55.6

Luas penampang Profil (Ag) 6.31 = 631Tebal plat (t) 6 mmLebar penampang 55 mmKuat Leleh (fy) 200 MpaKuat Putus (fu) 330 MPa

Tipe Baut A325Diameter Baut (d) Ø1/2" = 12.7 mm

825 MPaDiameter Lubang Baut (D) 13.7 mm

Luas Penampang Baut (Ab) =π . d²

4

=3.14 12.7 ²

4= 126.61

Asumsi 2 baris

Luas Netto Profil (Ae) = Ag - n D t

= 631 - 2 13.7 6= 466.6

ΦTn = 0.9 Ag fy ΦTn = 0.75 Ae fu= 0.9 631 200 = 0.75 466.6 330= 113580.00 N = 115483.50 N

Diambil ΦTn 113580.00 N

Kapasitas Sambungan Baut (diambil ΦRn maksimum)

Terhadap ulir dalam bidang geser Diambil ΦRn 62673.26 N

ΦRn = Φ 0.40 n Ab= 0.75 0.40 825 2 126.61 JUMLAH BAUT= 62673.26 N ΦTn

=113580.00

ΦRn 62673.26Terhadap gaya tarik = 1.81

ΦRn = Φ 0.75 Ab ≈ 2 baut= 0.75 0.75 825 126.61= 58756.18 N

Terhadap tumpuΦRn = Φ 2.4 d t fu

cm² mm²(lihat nama profil, XX.XX.(tebal plat))(lihat nama profil, (lebar penampang).XX.XX)

Kuat tarik baut (fub)

mm²

Kapasitas Batang (diambil ΦTn minimum)

mm²

fub

fub

PERHITUNGAN JUMLAH BAUT

= 0.75 2.4 12.7 6 330= 45262.8 N

PROFIL BAJA L 130.130.14

Luas penampang Profil (Ag) 34.7 = 3470Tebal plat (t) 14 mmLebar penampang 130 mmKuat Leleh (fy) 200 MpaKuat Putus (fu) 330 MPa

Tipe Baut A325Diameter Baut (d) Ø1/2" = 12.7 mm

825 MPaDiameter Lubang Baut (D) 13.7 mm

Luas Penampang Baut (Ab) =π . d²

4

=3.14 12.7 ²

4= 126.61

Asumsi 2 baris

Luas Netto Profil (Ae) = Ag - n D t

= 3470 - 2 13.7 14= 3086.4

ΦTn = 0.9 Ag fy ΦTn = 0.75 Ae fu= 0.9 3470 200 = 0.75 3086.4 330= 624600.00 N = 763884.00 N

Diambil ΦTn 624600.00 N

Kapasitas Sambungan Baut (diambil ΦRn maksimum)

Terhadap ulir dalam bidang geser Diambil ΦRn 105613.20 N

ΦRn = Φ 0.40 n Ab= 0.75 0.40 825 2 126.61 JUMLAH BAUT= 62673.26 N ΦTn

=624600.00

ΦRn 105613.20Terhadap gaya tarik = 5.91

ΦRn = Φ 0.75 Ab ≈ 6 baut= 0.75 0.75 825 126.61= 58756.18 N

cm² mm²(lihat nama profil, XX.XX.(tebal plat))(lihat nama profil, (lebar penampang).XX.XX)

Kuat tarik baut (fub)

mm²

Kapasitas Batang (diambil ΦTn minimum)

mm²

fub

fub

PERHITUNGAN JUMLAH BAUT

Terhadap tumpuΦRn = Φ 2.4 d t fu

= 0.75 2.4 12.7 14 330= 105613.2 N

PROFIL BAJA L 100.100.10

Luas penampang Profil (Ag) 19.2 = 1920Tebal plat (t) 10 mmLebar penampang 100 mmKuat Leleh (fy) 200 MpaKuat Putus (fu) 330 MPa

Tipe Baut A325Diameter Baut (d) Ø1/2" = 12.7 mm

825 MPaDiameter Lubang Baut (D) 13.7 mm

Luas Penampang Baut (Ab) =π . d²

4

=3.14 12.7 ²

4= 126.61

Asumsi 2 baris

Luas Netto Profil (Ae) = Ag - n D t

= 1920 - 2 13.7 10= 1646

ΦTn = 0.9 Ag fy ΦTn = 0.75 Ae fu= 0.9 1920 200 = 0.75 1646 330= 345600.00 N = 407385.00 N

Diambil ΦTn 345600.00 N

Kapasitas Sambungan Baut (diambil ΦRn maksimum)

Terhadap ulir dalam bidang geser Diambil ΦRn 75438.00 N

ΦRn = Φ 0.40 n Ab= 0.75 0.40 825 2 126.61 JUMLAH BAUT= 62673.26 N ΦTn

=345600.00

ΦRn 75438.00Terhadap gaya tarik = 4.58

ΦRn = Φ 0.75 Ab ≈ 6 baut= 0.75 0.75 825 126.61

cm² mm²(lihat nama profil, XX.XX.(tebal plat))(lihat nama profil, (lebar penampang).XX.XX)

Kuat tarik baut (fub)

mm²

Kapasitas Batang (diambil ΦTn minimum)

mm²

fub

fub

PERHITUNGAN JUMLAH BAUT

= 58756.18 N

Terhadap tumpuΦRn = Φ 2.4 d t fu

= 0.75 2.4 12.7 10 330= 75438 N

MUTU BAJA

MutuTegangan Leleh

(Mpa)33 20037 24044 28052 360

PROFIL BAJA L

TABEL PROFIL UNTUK PEMILIHAN PROFIL BATANG TARIK

Luas Penampang (A)Profil

cm² cm

0.82 15.15.3 0.15 0.431.05 15.15.4 0.19 0.421.12 20.20.3 0.39 0.591.42 25.25.3 0.79 0.751.45 20.20.4 0.48 0.581.74 30.30.3 1.41 0.91.85 25.25.4 1.01 0.742.26 25.25.5 1.18 0.722.27 30.30.4 1.81 0.892.67 35.35.4 2.96 1.052.78 30.30.5 2.16 0.883.08 40.40.4 4.48 1.213.79 40.40.5 5.43 1.23.87 35.35.6 4.14 1.044.3 45.45.5 7.83 1.35

4.48 40.40.6 6.33 1.194.8 50.50.5 11 1.51

5.69 50.50.6 12.8 1.55.86 45.45.7 10.4 1.336.31 55.55.6 17.3 1.666.56 50.50.7 14.6 1.496.91 60.60.6 22.8 1.828.23 55.55.8 22.1 1.648.24 50.50.9 17.9 1.478.7 65.65.7 33.4 1.96

9.03 60.60.8 29.1 1.89.4 70.70.7 42.4 2.12

10.1 55.55.10 26.3 1.62

Momen Inersia (Ix) Jari-Jari Inersia (ix)cm⁴

10.1 75.75.7 52.4 2.2811 65.65.9 41.3 1.94

11.1 60.60.10 34.9 1.7811.5 75.75.8 58.9 2.2611.9 70.70.9 52.6 2.112.3 80.80.8 72.3 2.4213.2 65.65.11 48.8 1.9114.1 75.75.10 71.4 2.2514.3 70.70.11 61.8 2.0815.1 80.80.10 87.5 2.4115.5 90.90.9 116 2.7416.7 75.75.12 82.4 2.2217.9 80.80.12 102 2.3918.7 90.90.11 138 2.7219.2 100.100.10 177 3.0420.6 80.80.14 115 2.3621.2 110.110.10 239 3.3621.8 90.90.13 158 2.6922.7 100.100.12 207 3.0225.1 110.110.12 280 3.3425.4 120.120.11 341 3.6626.2 100.100.14 235 329 110.110.14 319 3.32

29.7 120.120.13 394 3.6430 130.130.12 472 3.97

33.9 120.120.15 446 3.6334.7 130.130.14 540 3.9435 140.140.13 638 4.27

39.3 130.130.16 605 3.9240 140.140.15 723 4.25

40.3 150.150.14 845 4.5845 140.140.17 805 4.23

45.7 150.150.16 949 4.5646.1 160.160.15 1100 4.8851 150.150.18 1050 4.54

51.8 160.160.17 1230 4.8655.4 180.180.16 1680 5.5157.5 160.160.19 1350 4.8461.8 200.200.16 2340 6.1561.9 180.180.18 1870 5.4968.4 180.180.20 2040 5.4769.1 200.200.18 2600 6.1376.4 200.200.20 2850 6.11

TABEL PROFIL UNTUK PEMILIHAN PROFIL BATANG TEKAN

ProfilLuas Penampang (A)

cm² cm

0.15 15.15.3 0.82 0.430.19 15.15.4 1.05 0.420.39 20.20.3 1.12 0.590.48 20.20.4 1.45 0.580.79 25.25.3 1.42 0.751.01 25.25.4 1.85 0.741.18 25.25.5 2.26 0.721.41 30.30.3 1.74 0.91.81 30.30.4 2.27 0.892.16 30.30.5 2.78 0.882.96 35.35.4 2.67 1.054.14 35.35.6 3.87 1.044.48 40.40.4 3.08 1.215.43 40.40.5 3.79 1.26.33 40.40.6 4.48 1.197.83 45.45.5 4.3 1.3510.4 45.45.7 5.86 1.3311 50.50.5 4.8 1.51

12.8 50.50.6 5.69 1.514.6 50.50.7 6.56 1.4917.3 55.55.6 6.31 1.6617.9 50.50.9 8.24 1.4722.1 55.55.8 8.23 1.6422.8 60.60.6 6.91 1.8226.3 55.55.10 10.1 1.6229.1 60.60.8 9.03 1.833.4 65.65.7 8.7 1.9634.9 60.60.10 11.1 1.78

Momen Inersia (Ix) Jari-Jari Inersia (ix)cm⁴

41.3 65.65.9 11 1.9442.4 70.70.7 9.4 2.1248.8 65.65.11 13.2 1.9152.4 75.75.7 10.1 2.2852.6 70.70.9 11.9 2.158.9 75.75.8 11.5 2.2661.8 70.70.11 14.3 2.0871.4 75.75.10 14.1 2.2572.3 80.80.8 12.3 2.4282.4 75.75.12 16.7 2.2287.5 80.80.10 15.1 2.41102 80.80.12 17.9 2.39115 80.80.14 20.6 2.36116 90.90.9 15.5 2.74138 90.90.11 18.7 2.72158 90.90.13 21.8 2.69177 100.100.10 19.2 3.04207 100.100.12 22.7 3.02235 100.100.14 26.2 3239 110.110.10 21.2 3.36280 110.110.12 25.1 3.34319 110.110.14 29 3.32341 120.120.11 25.4 3.66394 120.120.13 29.7 3.64446 120.120.15 33.9 3.63472 130.130.12 30 3.97540 130.130.14 34.7 3.94605 130.130.16 39.3 3.92638 140.140.13 35 4.27723 140.140.15 40 4.25805 140.140.17 45 4.23845 150.150.14 40.3 4.58949 150.150.16 45.7 4.56

1050 150.150.18 51 4.541100 160.160.15 46.1 4.881230 160.160.17 51.8 4.861350 160.160.19 57.5 4.841680 180.180.16 55.4 5.511870 180.180.18 61.9 5.492040 180.180.20 68.4 5.472340 200.200.16 61.8 6.152600 200.200.18 69.1 6.132850 200.200.20 76.4 6.11