Abutment Jembatan

(1)

BAB IV

PERENCANAAN ABUTMENT (PANGKAL JEMBATAN)

4.1 Data Beban (dari hitungan terdahulu) Beban Mati

QD = 5,6273 + 13,8590 = 19,4863 ton Beban Hidup

QH = 12.9500 + 11.0989 = 24,0489 ton 4.2 Data Lokasi dan Rencana Abutment

Data lokasi dapat dilihat pada gambar 4.1. Ketentuan abutment sebagai berikut : a. Tipe Abutmen = Cantilever Retaining Wall (CRW) tanpa angkur dan counterfort. b. Tinggi Abutment = 7 m

c. Pondasi = sumuran d. f’c = 25 MPa e. fy = 390 MPa f. γ beton = 2,4 t/m3

g. kedalaman muka air tanah = -3,0 m

(2)

4.3 Analisi Data Tanah

Koefisien tanah aktif (tekanan tanah pasif diabaikan) Ka = tan2 (45o – ϕ/2)

= tan2 (45o – 30o/2) = 1/3 Data karakteristik tanah

a. γ tanah = 1,90 ton/m3 b. Sudut gesek tanah = 30o

c. Kadar air ( w ) = 0,25 d. Angka pori ( n ) = 0,43 Berat Jenis tanah adalah sbb :

γk = γs (1 - n) = 1,90 (1 - 0,43) = 1,0830 t/m3 γb = γk (1 + w) = 1,0830 (1 + 0,25) = 1,3538 t/m3 γsat = γk + n = 1,0830 + 0,43 = 1,5130 t/m3 γ’ = γsat - 1 = 1,5130 - 1 = 0,5130 t/m3 4.4 Analisa Mekanika

(3)

h = 7 m P = 4,36364 t γk = 1,0830 t/m3 h1 = 3 m Q = 0,8000 t/m2 γb = 1,3538 t/m3 h2 = 4 m γsat = 1,5130 t/m3 γ’ = 0,5130 t/m3 h’ = l tan (45o +ϕ/2) – l tan ϕ = 2,5 tan (45 o +30 o/2) – 2,5 tan 30 o = 4,33 – 1,44 = 2,89

Tekanan tanah aktif

Ea1 = h q Ka Ea4 = ½ h22γw

Ea2 = ½ h12γb Ka Ea5 = ½ h22γ’ Ka

Ea3 = h1 h2γb Ka Ea₆ = ½ P K h’_a

Tabel 4.1 Perhitungan Gaya Horisontal (Ea) dan Momen (t-m), ditinjau untuk tiap 1 m

h b Ka H (ton) ke A (m) Momen (t-m)

Akibat beban merata

1 7 0,8000 1/3 b h Ka 1,8667 3,5000 6,5334

2 3 4,0614 1/3 ½ b h Ka 2,0307 5,0000 10,1535

3 4 4,0614 1/3 b h Ka 5,4152 2,0000 10,8304

4 4 4,0000 - ½ b h 8,0000 1,3333 10,6664

5 4 2,0520 1/3 ½ b h Ka 1,3680 1,3333 1,8240

Akibat baban titik

6 2,89 2,5193 ½ b h 3,6404 4,5967 16,7338

22,3210 56,7415

Tabel 4.2 Perhitungan Gaya vertikal dan Momen (t-m) Abutment

h b A (m2) 1 0,3 0,5 0,15 2 1,1 0,8 0,88 3 1,6 0,8 0,64 4 4,8 0,8 3,84 5 0,8 6,0 4,80 Σ A = 10,31 Titik berat abutment, x = 2,881 m

y = 2,317 m

Berat abutment = 10,31 × 1,0 × 2,4 = 24,7440 ton

(4)

Tanah pengisi

Berat (ton) Lengan (m) Momen (t-m)

a 1,8 × 0,3 × 1,0 × 1,90 = 1,0260 2,10 2,1546 b 0,3 × 0,3 × 1,0 × 1,90 = 0,1710 1,05 0,1796 c 1,8 × 1,1 × 1,0 × 1,90 = 3,7620 2,10 7,9002 d 1,8 × 1,6 × 1,0 × 1,90 = 5,7420 2,10 11,4912 e ½ 0,8 × 1,6 × 1,0 × 1,90 = 1,2160 0,93 1,1309 f 2,6 × 3,2 × 1,0 × 0,5130 = 4,2682 1,70 7,2559 = 16,1852 30,1121

A. Kontrol Tegangan tanah

Kontrol tegangan tanah di dasar abutment sebelum jembatan dipasang V = 24,7440 + 16,1852 = 40,9292 ton M = - 2,9445 - 30,1121 + 56,7415 = 23,6849 t-m A = 6 × 1 = 6 m2 W = 1/6 × 1,0 × 62 = 6 m3 W M A V ± = σ 7690 , 10 6 23,6849 6 40,9292₊ ₌ = maks σ t/m2 8741 , 2 6 23,6849 6 40,9292 min = − = σ t/m2

Kontrol tegangan-tegangan tanah di dasar abutment setelah jembatan dipasang Kombinasi 1 (100% qa)

Jarak titik berat beban mati dan beban hidup terhadap titik berat tumpuan = 3,0-2,881

= 0,119 m Beban V (ton) M (t-m) Mati 19,4863 2,3187 Hidup 24,0489 2,8618 Abutment 24,7440 - 2,9445 Tanah pengisi 16,1852 - 30,1121 Tekanan tanah aktif 56,7415

84,4644 28,1909 7759 , 18 6 1909 , 28 6 4644 , 84 ₊ ₌ = maks σ t/m2

(5)

3789 , 9 6 1909 , 28 6 4644 , 84 min = − = σ t/m2

di dasar sumuran, Berat jenis beton siklop = 2,2 t/m3

(

) (

)

(

)

6 2 , 2 6 6 , 0 6 , 5 1 6 6 5130 , 0 6 6 , 0 6 , 5 6 4644 , 84 ₊ × × × ₊ × − × × × = maks σ 6091 , 21 8080 , 5 7237 , 1 0774 , 14 + + = = maks σ t/m2 < qa = 2,25 kg/cm2 (22,5 t/m2) Kombinasi 2 (125% qa)

Jarak titik berat beban mati dan beban hidup terhadap titik berat tumpuan = 3,0-2,881

= 0,119 m

gaya memanjang karena gesekan tumpuan = 0,25 × M = 0,25 × 19,4863 = 4,8716 ton Momen = 4,8716 × 0,119 = 0,5797 tm

Beban V (ton) M (t-m)

Mati 19,4863 2,3187

Abutment 24,7440 - 2,9445 Tanah pengisi 16,1852 - 30,1121 Tekanan tanah aktif 56,7415 F 0,5797 60,4155 26,5833 4998 , 14 6 5833 , 26 6 4155 , 60 ₊ ₌ = maks σ t/m2 6387 , 5 6 5833 , 26 6 4155 , 60 min = − = σ t/m2

didasar sumuran, Berat jenis siklop = 2,2 t/m3

(

) (

)

(

)

6 2 , 2 6 6 , 0 6 , 5 1 6 6 5130 , 0 6 6 , 0 6 , 5 6 4155 , 60 ₊ × × × ₊ × − × × × = maks σ 6010 , 17 8080 , 5 7237 , 1 0693 , 10 + + = = maks σ t/m2 < 1,25 qa = 2,8125 kg/cm2 (28,125 t/m2)

B. Kontrol Stabilitas terhadap Penggulingan

Momen yang menggulingkan = 56,7415 + 0,5797 = 57,3212 tm Momen yang menahan guling (titik penggulingan pada tepi luar)

a. Abutment = 24,7440 × (6 – 2,881) = 77,1765 tm

b. Tanah pengisi = 30,1121 tm

c. Mati = 19,4863 × 3 = 58,4589 tm

d. Hidup = 24,0489 × 3 = 72,1467 tm

(6)

Angka keamanan terhadap penggulingan, n = 4,15 3212 , 57 8942 , 237 ₌ _{> 1,5 O K}

C. Kontrol Stabilitas terhadap Penggeseran Gaya geser = 22,3210 ton

Gaya geser penahan = Σ V tan ϕ (diasumsikan ϕ = 30o) = (24,7440 + 16,1852 ) tan 30o

= 23,6305 ton

Angka keamanan terhadap penggeseran, n = 1,06 3210 , 22 6305 , 23 ₌ 4.5 Penulangan Abutment A. Penulangan Titik I

Tabel 4.3 Perhitungan Gaya Horisontal (Ea) dan Momen (t-m), ditinjau untuk tiap 1 m thd ttk I

h b Ka H (ton) ke I (m) Momen (t-m)

Akibat beban merata

1 6,2 0,8000 1/3 b h Ka 1,6533 3,1000 5,1252

2 3 4,0614 1/3 ½ b h Ka 2,0307 4,2000 8,5289

3 3,2 4,0614 1/3 b h Ka 4,3322 1,6000 6,9315

4 3,2 4,0000 - ½ b h 6,4000 1,0667 6,8269

5 3,2 2,0520 1/3 ½ b h Ka 1,0944 1,0667 1,1674

Akibat baban titik

6 2,89 2,5193 ½ b h 3,6404 3,7967 13,8215

42,4014

Perhitungan baja tulangan

M = 424,0140 KNm

h = 800 mm ρperlu = 2,5410 × 10-3

d = 740 mm Asperlu = 2656,3780 mm2

k = 0,9679 MPa Tulangan pokok = ∅16-75

ρb = 0,028069 Asterpakai = 2800,8253

ρmaks = 0,02105175 Tulangan bagi = ∅16-250

(7)

B. Penulangan Titik J

Tabel 4.4 Perhitungan Gaya Horisontal (Ea) dan Momen (t-m), ditinjau untuk tiap 1 m thd ttk J

h b Ka H ke J (m) Momen (tm)

Akibat beban merata

1 3,0 0,8000 1/3 b h Ka 0,8 1,5000 1,2000

2 3,0 4,0614 1/3 ½ b h Ka 2,0307 1,0000 2,0307

Akibat baban titik

6a 1,56 1,3599 ½ b h 1,0607 1,04 1,1031

6b 1,56 1,1594 b h 1,8087 0,78 1,4108

5,7446

M = 57,4460 KNm

h = 800 mm ρperlu = 3,3720 × 10-3

d = 740 mm Asperlu = 2656,3780 mm2

ρb = 0,028069 Asterpakai = 2800,8253

ρmin = 3,5897 × 10-3

C. Penulangan Titik K

Tabel 4.5 Perhitungan Gaya Horisontal (Ea) dan Momen (t-m), ditinjau untuk tiap 1 m thd ttk K

h b Ka H ke J (m) Momen (tm)

Akibat beban merata

1 1,4 0,8000 1/3 b h Ka 0,3733 0,7000 0,2613

2 1,4 4,0614 1/3 ½ b h Ka 0,9477 0,4667 0,4423

0,7036

M = 7,0360 KNm

h = 500 mm ρperlu = 1,1653 × 10-4

d = 440 mm Asperlu = 1579,4680 mm2

ρb = 0,028069 Asterpakai = 1680,4952

(8)

D. Penulangan Dasar Abutment 7039 , 14 3970 , 9 6 4 , 3 3789 , 9 1 = + = y t/m2 4509 , 13 3970 , 9 6 6 , 2 3789 , 9 2 = + = y t/m2

bagian depan dinding

(

)

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ _× ₋ _× _× _× × + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ _× _× _× = 3 6 , 2 2 6 , 2 0 , 1 7039 , 14 7759 , 18 2 1 2 6 , 2 6 , 2 0 , 1 7039 , 14 maks M = 49,6992 + 9,1756 = 58,8748 tm Perhitungan baja tulangan

M = 588,7480 KNm

h = 800 mm ρperlu = 3,5623 × 10-3

d = 740 mm Asperlu = 2656,3780 mm2

ρb = 0,028069 Asterpakai = 2800,8253

ρmin = 3,5897 × 10-3

bagian belakang dinding 1.momen akibat tanah pengisi

Berat (ton) Lengan (m) Momen (t-m)

a 1,8 × 0,3 × 1,0 × 1,90 = 1,0260 1,70 1,7442 b 0,3 × 0,3 × 1,0 × 1,90 = 0,1710 0,65 0,1112 c 1,8 × 1,1 × 1,0 × 1,90 = 3,7620 1,70 6,3954 d 1,8 × 1,6 × 1,0 × 1,90 = 5,7420 1,70 9,7614 e ½ 0,8 × 1,6 × 1,0 × 1,90 = 1,2160 0,5333 0,6485 f 2,6 × 3,2 × 1,0 × 0,5130 = 4,2682 1,30 5,5487 = 16,1852 24,2094

2. momen akibat berat abutment

= 24,7440 × ( 2,881 – 2,6 ) = 6,9531 t-m 18,7759 9,3789 y2 y1 0,8 m 2,6 m 2,6 m

(9)

3. momen akibat tekanan tanah

Akibat beban merata

1 6,2 0,8000 1/3 b h Ka 1,6533 3,1000 5,1252

2 3 4,0614 1/3 ½ b h Ka 2,0307 4,2000 8,5289

3 3,2 4,0614 1/3 b h Ka 4,3322 1,6000 6,9315

4 3,2 4,0000 - ½ b h 6,4000 1,0667 6,8269

5 3,2 2,0520 1/3 ½ b h Ka 1,0944 1,0667 1,1674

Akibat baban titik

6 2,89 2,5193 ½ b h 3,6404 3,7967 13,8215

42,4014

Momen total = 42,4014 – (24,2094 + 6,9531) = 11,2389 tm Perhitungan baja tulangan

M = 112,3890 KNm

h = 800 mm ρperlu = 6,6171 × 10-4

d = 740 mm Asperlu = 2656,3780 mm2

ρb = 0,028069 Asterpakai = 2800,8253

ρmin = 3,5897 × 10-3

E. Penulangan Sayap

Bentuk garis leleh disederhanakan sebagai berikut :

2,6 m 6,2 m b im im m A B C D E

(10)

Perhitungan Gaya Horisontal (Ea) dan Momen (t-m), ditinjau untuk tiap 1 m

Akibat beban merata

1 6,2 0,8000 1/3 b h Ka 1,6533 3,1000 5,1252

2 3 4,0614 1/3 ½ b h Ka 2,0307 4,2000 8,5289

3 3,2 4,0614 1/3 b h Ka 4,3322 1,6000 6,9315

4 3,2 4,0000 - ½ b h 6,4000 1,0667 6,8269

5 3,2 2,0520 1/3 ½ b h Ka 1,0944 1,0667 1,1674

Akibat baban titik

6 2,89 2,5193 ½ b h 3,6404 3,7967 13,8215 42,4014 im = m 3 min 3,5897 10 390 4 , 1 4 , 1 ₌ ₌ _× − = y f ρ As = ρ x b x d = 3,5897 x10-3 x 1000 x 140 = 502,558 mm2 2 , 9 1000 25 85 , 0 390 502,558 85 , 0 ' × × = × = × × × = b f f A a c y s mm

(

2

)

a y s u A f d m =φ× × −

(

140

)

10 21,2305 390 558 , 502 8 , 0 × × × −9₂,2 × 6 = = − KNm Bagian CDE

(

)

(

2

)

3 1 ₂_,₆ 6 , 2 b u b q m im+ × = × × × 2 766 , 254 b q_u = 1) Bagian ABCE

(

)

(

)

(

)

2₂,6 3 6 , 2 2 1 ₂_,₆ ₆_,₂ ₂_,₆ 2 , 6 = × × × + − × × × +m q b q b im _u _u b q_u 52 , 13 736 , 125 5492 , 1579 − = 2) 1) = 2) b b 125,736 13,52 5492 , 1579 766 , 254 2 = − 0 2578 , 32033 4363 , 3444 5492 , 1579 b2+ b− = b = 3,5431 m

(11)

2943 , 20 5431 , 3 766 , 254 2 = = u q KN/m Arah CD

(

2,6 3,5431

)

110,3985 2943 , 20 3,5431₃ 2 1× × × = × =

m KNm (untuk lebar plat 2,6 m)

M = 110,3985 KNm h = 200 mm d = 200 - 60 = 140 mm 7080 , 2 140 2600 8 , 0 10 110,3985 2 6 2 × × = × = × × = d b M k φ MPa 028069 , 0 200000 390 003 , 0 003 , 0 390 85 , 0 25 85 , 0 003 , 0 003 , 0 85 , 0 1 ' = + × × = + × × = s y y c b E f f f β ρ ρmaks = 0,75ρb = 0,75 x 0,028069 = 0,02105175 3 ' ' 10 4534 , 7 25 85 , 0 7080 , 2 2 1 1 390 25 85 , 0 85 , 0 2 1 1 85 , 0 _⎟⎟= × − ⎠ ⎞ ⎜⎜ ⎝ ⎛ × × − − = ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − − = c y c perlu f k f f ρ 3 min 3,5897 10 390 4 , 1 4 , 1 ₌ ₌ _× − = y f ρ As = ρ x b x d = 7,4534 x10-3 x 2600 x 140 = 2713,0376 mm2 Dipakai tulangan ∅16 (As = 210,0619 mm2

), dengan jarak antar tulangan 3098 , 201 2713,0376 2600 210,0619× ₌ = perlu s mm dipakai tulangan ∅16-200 mm 8047 , 2730 200 2600 210,0619× ₌ = s A mm2 tulangan bagi = 20 % × 2730,8407 = 546,1609 mm2 dipakai tulangan ∅16-250 mm Arah AC

(

₂1×2,6×

)

×2₃,6+

(

6,2−

)

×2,6

)

×2₂,6=263,2617 =q b q b

m _u _u KNm (untuk lebar plat 6,2 m)

M = 263,2617 KNm h = 200 mm d = 200 - 60 = 140 mm 7080 , 2 140 6200 8 , 0 10 263,2617 2 6 2 × × = × = × × = d b M k φ MPa

(12)

028069 , 0 200000 390 003 , 0 003 , 0 390 85 , 0 25 85 , 0 003 , 0 003 , 0 85 , 0 1 ' = + × × = + × × = s y y c b E f f f β ρ ρmaks = 0,75ρb = 0,75 x 0,028069 = 0,02105175 3 ' ' 10 4534 , 7 25 85 , 0 7080 , 2 2 1 1 390 25 85 , 0 85 , 0 2 1 1 85 , 0 _⎟⎟= × − ⎠ ⎞ ⎜⎜ ⎝ ⎛ × × − − = ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − − = c y c perlu f k f f ρ 3 min 3,5897 10 390 4 , 1 4 , 1 ₌ ₌ _× − = y f ρ As = ρ x b x d = 7,4534 x10-3 x 6200 x 140 = 6469,5512 mm2 Dipakai tulangan ∅16 (As = 210,0619 mm2

), dengan jarak antar tulangan 3098 , 201 6469,5512 6200 210,0619× ₌ = perlu s mm dipakai tulangan ∅16-200 mm 9189 , 6511 200 6200 210,0619× ₌ = s A mm2 tulangan bagi = 20 % × 6511,9189 = 1302,3838 mm2 dipakai tulangan ∅16-250 mm

Tabel 4.6. Penulangan Abutment

Tulangan No. Elemen struktur

pokok bagi

1 Dinding (titik I) ∅16-75 ∅16-250

2 (titik J) ∅16-75 ∅16-250

3 Parapet (titik K) ∅16-125 ∅16-250

4 Dasar abutment

Bagian depan dinding ∅16-75 ∅16-250

Bagian belakang dinding ∅16-75 ∅16-250