abutment jembatan

ANALISIS STRUKTUR JEMBATAN

PERENCANAAN ABUTMENT

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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

Gambar 4.1 Topografi dan Rencana Abutment



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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

Gambar 4.2 Diagram tekanan tanah aktif dan pembebanan abutment



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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 h22 γw

Ea2 = ½ h12 γb Ka Ea5 = ½ h2

2 γ’ Ka

Ea3 = h1 h2 γb Ka Ea6 = ½ P aK h’

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

Momen terhadap pusat dasar abutment = 24,7440 × ( 3,0 – 2,881 ) = 2,9445 t-m



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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

WM

AV±=σ

7690,106

23,68496

40,9292=+=maksσ t/m2

8741,26

23,68496

40,9292min =−=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 2,3187Hidup 24,0489 2,8618 Abutment 24,7440 - 2,9445Tanah pengisi 16,1852 - 30,1121Tekanan tanah aktif 56,7415 84,4644 28,1909

7759,1861909,28

64644,84

=+=maksσ t/m2



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3789,961909,28

64644,84

min =−=σ t/m2

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

( ) ( )( )6

2,266,06,5166

5130,066,06,564644,84 ×××−×

+×××

+=maksσ

6091,218080,57237,10774,14 =++=maksσ 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 - 2,9445Tanah pengisi 16,1852 - 30,1121Tekanan tanah aktif 56,7415F 0,5797 60,4155 26,5833

4998,1465833,26

64155,60

=+=maksσ t/m2

6387,565833,26

64155,60

min =−=σ t/m2

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

( ) ( )( )6

2,266,06,5166

5130,066,06,564155,60 ×××−×

+×××

+=maksσ

6010,178080,57237,10693,10 =++=maksσ 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 = 237,8942 tm



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Angka keamanan terhadap penggulingan, n = 15,43212,578942,237

= > 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 = 06,13210,226305,23

=

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


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 ρmin = 3,5897 × 10-3



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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



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





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D. Penulangan Dasar Abutment

7039,143970,964,33789,91 =+=y t/m2

4509,133970,966,23789,92 =+=y t/m2

bagian depan dinding

( ) ⎟⎠⎞

⎜⎝⎛ ×

×××−×+⎟⎠⎞

⎜⎝⎛ ×××=

36,226,20,17039,147759,18

21

26,26,20,17039,14maksM

= 49,6992 + 9,1756 = 58,8748 tm



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



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3. momen akibat tekanan tanah




42,4014

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



E. Penulangan Sayap

Bentuk garis leleh disederhanakan sebagai berikut :

2,6 m

6,2 m

b

im

im

m

A B

C D

E



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




42,4014

im = m

3min 105897,3

3904,14,1 −×===

yfρ

As = ρ x b x d = 3,5897 x10-3 x 1000 x 140 = 502,558 mm2

2,910002585,0390502,558

85,0 ' =×××

=××

×=

bffA

ac

ys mm

( )2a

ysu dfAm −××=φ

( ) 2305,2110140390558,5028,0 622,9 =×−×××= − KNm

Bagian CDE

( ) ( ) 321 6,26,2 b

u bqmim ×××=×+

2766,254

bqu = 1)

Bagian ABCE

( ) ( ) ( )( ) 26,2

36,2

21 6,22,66,22,6 ××−+×××=×+ bqbqmim uu

bqu 52,13736,125

5492,1579−

= 2)

1) = 2)

bb 52,13736,1255492,1579766,254

2 −=

02578,320334363,34445492,1579 2 =−+ bb

b = 3,5431 m



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2943,205431,3

766,2542 ==uq KN/m

Arah CD

( ) 3985,1105431,36,22943,20 35431,3

21 =××××=m KNm (untuk lebar plat 2,6 m)

M = 110,3985 KNm

h = 200 mm d = 200 - 60 = 140 mm

7080,214026008,010 110,3985

2

6

2 =×××

=××

=db

Mkφ

MPa

028069,0

200000390003,0

003,0390

85,02585,0003,0

003,085,0 1'

=+

××

=+

××

=

s

yy

cb

Eff

f βρ

ρmaks = 0,75 ρb = 0,75 x 0,028069 = 0,02105175

3'

'

104534,72585,0

7080,22113902585,0

85,021185,0 −×=⎟⎟

⎠

⎞⎜⎜⎝

⎛×

×−−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−−=

cy

cperlu f

kff

ρ

3min 105897,3

3904,14,1 −×===

yfρ

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

3098,2012713,0376

2600210,0619=

×=perlus mm

dipakai tulangan ∅16-200 mm

8047,2730200

2600210,0619=

×=sA mm2

tulangan bagi = 20 % × 2730,8407 = 546,1609 mm2


Arah AC

( ) ( )( ) 2617,2636,22,66,2 26,2

36,2

21 =××−+×××= bqbqm uu KNm (untuk lebar plat 6,2 m)

M = 263,2617 KNm

h = 200 mm d = 200 - 60 = 140 mm

7080,214062008,010 263,2617

2

6

2 =×××

=××

=db

Mkφ

MPa



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028069,0

200000390003,0

003,0390

85,02585,0003,0

003,085,0 1'

=+

××

=+

××

=

s

yy

cb

Eff

f βρ

ρmaks = 0,75 ρb = 0,75 x 0,028069 = 0,02105175

3'

'

104534,72585,0

7080,22113902585,0

85,021185,0 −×=⎟⎟

⎠

⎞⎜⎜⎝

⎛×

×−−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−−=

cy

cperlu f

kff

ρ

3min 105897,3

3904,14,1 −×===

yfρ

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

3098,2016469,5512

6200210,0619=

×=perlus mm


9189,6511200

6200210,0619=

×=sA mm2

tulangan bagi = 20 % × 6511,9189 = 1302,3838 mm2


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 5 Sayap ∅16-200 ∅16-250

abutment jembatan

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