contoh perhitungan breakwater
TRANSCRIPT
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TUGAS BESAR
KL-4111 PERENCANAAN PRASARANA PELABUHAN
Dosen:
Prof. Hang Tuah
Asisten:
Muhammad Ali Rini, S.T.
Firmansyah Pedana
15506005
Program Studi Teknik Kelautan
Fakultas Teknik Sipil dan Lingkungan
Institut Teknologi Bandung
2010
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Diketahui:
Hs 5 Storm Surge 0.5 Armor Posisi Kd KΔLWS 0 Seasonal Variation 0.3 Rock (Acak) Head 2.8 1.15HWS 2.71 Sea Level Rise 0.5 Trunk 4T 11 Tetrapod(acak) Head 5.5 1.04h 6 Trunk 8
A-Jack(acak) Head 15 1ɣ Air 1024 Kg/m3 Trunk 15ɣ beton 2400 Kg/m3 Cube(acak) Head 5 1.1ɣ Batu 2650 Kg/m3 Trunk 7.5g 9.81 Kg/m2
Perhitungan Rubble Mound Breakwater
Armor: RockA. Head
Kd=2.8 , slope = 1:3
1. Elevasi Puncak
Mencari nilai L0 dengan menggunakan persamaan disperse:
ω2=gk tanh kh (ω=2πT
, k=2πL
)
Maka akan didapat:
L0=gT2/2π=9,81x 112/2(3,14)=188,92m .
ζ= tan θ
(H /Lo)0,5= 0,33
( 5188,92
)0,5
=3,07.
Dari grafik: Ru
H=0,8 Ru = 0,8 x 5 = 4 m.
Elevasi=HWS+Storm Surge+SeasonalVariation+Sea Level Rise+ freeboard+Ru
= 2,71 + 0,5 + 0,3 + 0,5+0.5 + 4= 8.51 m (dari LWS).
2. Berat Armor
Mencari berat armor dengan menggunakan rumus Hudson:
W=γrH
3
K D( γbatuγa −1)3
cotθ
Maka didapat:
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W= 2,6 x53
2,8 ( 2,61,025
−1)3
x3=10,61 ton.
3. Lebar puncak
Mencari berat armor dengan menggunakan:
B=n k∆[Wγr ]13 ¿)
Maka didapat:
B=3 x1,15 [ 10,612,55
]13=5,51m .
4. Tebal Layer
a. Armor Layer
r=nk∆(Wγ r )13
r=2x 1,15( 10,612,55
)13=3,67m .
b. Underlayer
ru=nk ∆(W /10γ r )
13
ru=nk ∆(W /10γ r
)13=2 x1,15 (1,06
2,55)13=1,7m .
5. Lebar Kaki
B=3 xru=3 x1,7=4,2m .
6. Tebal Kaki
t=2 xru=2x 1,7=3,4m .
B. Trunk
Kd=4,0 ; Slope = 1 : 3
Cat: rumus yang digunakan sama dengan mencari armor rock.
1. Elevasi Puncak
L0=gT2/2π=9,81x 112/2(3,14)=188,92m .
ζ= tan θ
(H /Lo)0,5= 0,33
( 5188,92
)0,5
=3,07 .
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Dari grafik: Ru
H=¿ 0,8 Ru = 0,8 x 5 = 4 m.
Elevasi=HWS+Storm Surge+SeasonalVariation+Sea Level Rise+ freeboard+Ru
= 2,71 + 0,5 + 0,3 + 0,5 +0,5+ 4 = 8,51 m (dari LWS).
2. Berat Armor
W=
γ rH3
K D(γrγa
−1)3
cot θ
= 2,6 x53
4,0 ( 2,61,024
−1)3
x3=7,42ton .
3. Lebar Puncak
B=n k∆[Wγ r
]13=3 x1,15[ 7,42
2,55]13=4,89m
4. Tebal Layer
a. Armor
r=nk∆(Wγ r )13=2 x1,15( 7,422,55 )
13=3,26m
b. Underlayer
ru=nk ∆(W /10γ r
)13=1,51m
5. Lebar Kaki
B=3 xru=3 x1,51=4,53m
6. Tebal Kaki
t=2 xru=2x 1,51=3,02m
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Perhitungan Rubble Mound Breakwater
Armor: Tetrapod A. Head
Kd=5,5 ; Slope = 1 : 3
1. Elevasi Puncak
L0=gT2/2π=9,81x 112/2(3,14)=188,92meter .
ζ= tan θ
(H /Lo)0,5= 0,33
( 5188,92
)0,5
=3,07
Dari grafik: Ru
H=0,65 Ru = 0,65 x 5 = 3,25 m.
Elevasi=HWS+Storm Surge+SeasonalVariation+Sea Level Rise+ freeboard+Ru
= 2,71 + 0,5 + 0,3 + 0,5 +0,5+ 3,25 = 7,76 m.
2. Berat Armor
W=
γ rH3
K D(γrγa
−1)3
cot θ
= 2,4 x53
5,5( 2,41,025
−1)3
x 3=7,49 ton.
3. Lebar Puncak
B=n k∆[Wγ r
]13=3 x1,04 [ 7,49
2,4]13=4,5m
4. Tebal Layer
a. Armor
r=nk∆(Wγ r
)13=2x 1,04 ( 7,49
2,4)13=3,04m
b. Underlayer
ru=nk ∆(W /5γ r
)13=2 x1,0 4( 1,49
2,4)13=1,41m
5. Lebar Kaki
B=3 xru=3 x1,41=4,22m
6. Tebal Kaki
t=2 xru=2x 1,41=2,82m
B. Trunk
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Kd=8 ; Slope = 1:3
1. Elevasi Puncak
L0=gT2/2π=9,81x 112/2(3,14)=188,92meter .
ζ= tan θ
(H /Lo)0,5= 0,33
( 5188,92
)0,5
=3,07
Dari grafik: Ru
H=¿ 0,65 Ru = 0,65 x 5 = 3,25 m.
Elevasi=HWS+Storm Surge+SeasonalVariation+Sea Level Rise+Freeboard+Ru
= 2,71 + 0,5 + 0,3 + 0,5 +0,5+ 3,25= 7,76 m
2. Berat Armor
W=
γ rH3
K D(γrγa
−1)3
cot θ
= 2,4 x53
8( 2,41,025
−1)3
x 3=5,15 ton.
3. Lebar Puncak
B=n k∆[Wγ r
]13=3 x1,04 [ 5,15
2,4]13=4,02m
4. Tebal Layer
a. Armor
r=nk∆(Wγ r
)13=2x 1,04 ( 5,15
2,4)13=2,68m
b. Underlayer
rfilter=nk∆ (W /5γr
)13=2 x1,04 ( 2,57
2,4)13=1,24m
5. Lebar Kaki
B=3 xru=3 x1,24=3,72m
6. Tebal Kaki
t=2 xru=2x 1,24=2,48m
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Perhitungan Rubble Mound Breakwater
Armor: Cube A. Head
Kd=5 ; Slope = 1 : 3
1. Elevasi Puncak
L0=gT2/2π=9,81x 112/2(3,14)=188,92meter .
ζ= tan θ
(H /Lo)0,5= 0,33
( 5188,92
)0,5
=3,07
Dari grafik
Ru
H=¿ 08 Ru = 0,8 x 5 =4 m
Elevasi=HWS+Storm Surge+SeasonalVariation+Sea Level Rise+Freeboard+Ru
= 2,71 + 0,5 + 0,3 + 0,5 +0,5+ 4 = 8,51 m
2. Berat Armor
W=
γ rH3
K D(γrγa
−1)3
cot θ
= 2,4 x53
5( 2,41,025
−1)3
x 3=8,24 ton.
3. Lebar Puncak
B=n k∆[Wγ r
]13=3 x1,1[ 8,24
2,4]13=4,97m
4. Tebal Layer
a. Armor
r=nk∆(Wγ r
)13=2x 1,1( 8,24
2,4)13=3,31m
b. Underlayer
ru=nk ∆(W /5γ r
)13=2 x1,1( 1.64
2,4)13=1,54m
5. Lebar Kaki
B=3 xru=3 x1.54=4,62m
6. Tebal Kaki
t=2 xru=2x 1.54=3,08m
Gambar 5
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B. Trunk
Kd=7,5 ; Slope = 1 : 3
1. Elevasi Puncak
L0=gT2/2π=9,81x 112/2(3,14)=188,92meter .
ζ= tan θ
(H /Lo)0,5= 0,5
( 5188,92
)0,5
=3,07
Dari grafik: Ru
H=¿ 0,8 Ru = 0,8 x 5 = 4 m.
Elevasi=HWS+Storm Surge+SeasonalVariation+Sea Level Rise+ freeboard+Ru
= 2,71 + 0,5 + 0,3 + 0,5 +0,5+ 4 = 8,51 m
2. Berat Armor
W=
γ rH3
K D(γrγa
−1)3
cot θ
= 2,4 x53
7,5( 2,41,025
−1)3
x 3=5,5 ton.
3. Lebar Puncak
B=n k∆[Wγ r
]13=3 x1,1[ 5,5
2,4]13=4,34m
4. Tebal Layer
a. Armor
r=nk∆(Wγ r
)13=2x 1,1( 5,5
2,4)13=2,89m
b. Underlayer
ru=nk ∆(W /5γ r
)13=2 x1,1( 1,1
2,4)13=1,34m
5. Lebar Kaki
B=3 xru=3 x1,34=5,02m
6. Tebal Kaki
t=2 xru=2x 1,34=2,68m
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Perhitungan Rubble Mound Breakwater
Armor: A-Jack A. Head
Kd=15 ; Slope = 1 : 3
1. Elevasi Puncak
L0=gT2/2π=9,81x 112/2(3,14)=188,92meter .
ζ= tan θ
(H /Lo)0,5= 0,33
( 5188,92
)0,5
=3,07
Dari grafik: Ru
H=¿ 0,65 Ru = 0,65 x 5 = 3,25 m.
Elevasi=HWS+Storm Surge+SeasonalVariation+Sea Level Rise++ freeboard+Ru
= 2,71 + 0,5 + 0,3 + 0,5 + 0,5 + 3,25 = 7,76 m
2. Berat Armor
W=
γ rH3
K D(γrγa
−1)3
cot θ
= 2,4 x53
15( 2,41,025
−1)3
x 3=2,74 ton.
3. Lebar Puncak
B=n k∆[Wγ r
]13=3 x0,94 [ 2,74
2,4]13=3,13m
4. Tebal Layer
a. Armor
r=nk∆(Wγ r
)13=1x 1( 2,74
2,4)13=2,09m
b. Underlayer
ru=nk ∆(W /5γ r
)13=2 x1( 0,54
2,4)13=0,97m
5. Lebar Kaki
B=3 xru=3 x0,97=1,91m
6. Tebal Kaki
t=2 xru=2x 0,97=1,94m
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B. Trunk
Kd=15 ; Slope = 1 : 3
1. Elevasi Puncak
L0=gT2/2π=9,81x 112/2(3,14)=188,92meter .
ζ= tan θ
(H /Lo)0,5= 0,33
( 5188,92
)0,5
=3,07
Dari grafik: Ru
H=¿ 0,65 Ru = 0,65 x 5 = 3,25 m.
Elevasi=HWS+Storm Surge+SeasonalVariation+Sea Level Rise+ fr eeboard+Ru
= 2,71 + 0,5 + 0,3 + 0,5 +0,5+ 3,25 = 7,76 m
2. Berat Armor
W=
γ rH3
K D(γrγa
−1)3
cot θ
= 2,4 x53
15( 2,41,024
−1)3
x3=2,74 ton .
3. Lebar Puncak
B=n k∆[Wγ r
]13=3 x0,94 [ 2,74
2,4]13=3,13m
4. Tebal Layer
a. Armor
r=nk∆(Wγ r
)13=1x 0,94 (2,74
2,4)13=2,09m
b. Underlayer
ru=nk ∆(W /5γ r
)13=2 x 0,94( 0,54
2,4)13=0,97m
5. Lebar Kaki
B=3 xru=3 x0,97=2,91m
6. Tebal Kaki
t=2 xru=2 x0,97=1,94m
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Perhitungan Breakwater Vertikal (Caisson)
1. Tinggi total caisson (dari dasar laut)
Tinggi caisson diatas HWS = 43−32Hs (diambil
2,742
Hs = 1,37x5) =6,85
Tinggi total(T)= Hws + h + tinggi diatas HWS = 2,71+6+6,85=15,56 m
2. Panjang caisson
P= 14Lo=1
4xgT 2
2π=14x9,81x 112
2π=14x188,92m=47,23m
3. Lebar caisson
L=34Tc=3
4x 15,56=11,67m
4. Gaya pada caisson
∂o=π Hs2
Lox cot(¿ 2πh
Lo)= π 52
188,92xcot (¿ 2 π 6
188,92)=2,055607¿¿
p3=ρw x g x (Hs−∂o )=1024 x 9,81x (5−2,055607 )=29577,73N /m
p2= ρw x g x Hs
cosh (¿2πdLo
)=1024 x 9,81x 5
cosh (¿2π 6188,92
)=49243,49N /m¿¿
p1=( p2+( ρw x g x d ) )x (Hs+∂o )d+Hs+∂o
=(49243,49+(1024 x 9,81x 6 ) ) x (5+2,055607 )6+5+2,055607
=59185,51N /m
Gaya pada crest :
Fc=¿534.081,8 𝑁Gaya pada trough :
Ft=¿
Gaya hidrostatis :
FH=0,5 x ρw x gx d2=180.871,9N
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Perhitungan Komposit Vertikal1. Tinggi total (dari dasar laut)
Tinggi caisson di atas HWS = 43−32Hs (diambil
2,742
Hs = 1,37x5) =6,85
Tinggi total(T)= Hws+h+tinggi diatas permukaan air=2,71+6+6,85=15,56 m
2. Panjang
P= 14Lo=1
4xgT 2
2π=14x9,81x 112
2π=14x188,92m=47,23m
3. Lebar caisson
L=34Tc=3
4x 15,56=11,67m
4. Desain kaki
tinggi kaki: r=4 m; slope 1:2
hs=kedalaman; h=kedalaman-tinggi kaki
h/hs=2/6=0,3333 – Dengan grafik: diperoleh Ns3=14
Lebar kaki : B=0,4hs=2,4m ; b=r/slope=4x2=8m
Δ=( γ rγ a−1)=( 26001024−1)=1,54
Dn50= HsΔNs
=1,347m
W 50= ρbatu x Dn503=2600 x1,3473=6367,758kg
Tebal layer kaki:
r=nk∆(Wγ r
)13=2x 1,0( 6367,758
2600)13=2,695m
Panjang total breakwater:
Lp= lebar caisson+ 2xb + 2xB = 32,47 m
5. Gaya
Hmax=1,8 x Hs=9m dc=HWS+tinggicaissondi atas HWS=9,56m d ’=h+r=4,695m dbw=(kemiringandasar laut x5 xHs )+d=6,8333m
α 1=0,6+ 12(( 4 πdLo
)/ (sinh( 4 πdLo
)))2
=1,047
α 2=min( dbw−h3dbw (Hmaxh )
2
;2dHmax )=min (2,21 ;1,333 )−ambil yang lebih kecil
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α 3=1−
d '
d (1− 1
cosh ( 2πdLo ))=0,008811 p1=1
2(1+cos β ) (α 1+α 2cos2 β ) γ oHmax=208,8156 t /m2
p2= p1
cosh ( 2πdLo )=200,35 t /m2
p3=α 3x p1=1,84 t /m2
pu=12
(1+cos β )α 1α 3 γ oHmax=0,84 t /m2
η∗¿0,75 (1+cos β )Hmax=13,27 dc∗¿min (η∗;dc )=min (13,27 ;9,56)
Karena ¿>dc , maka p4=p1¿
P=0,5 (p1+ p3 )d '+0,5 (p1+ p4 )dc∗¿631.709,8N
Mp=16
(2 p1+ p3 )d '2+0,5 ( p1+p 4 )d ' dc∗+16
( p1+2 p4 )dc∗¿2=12.498,47Nm¿
U=0,5 puB=4,9079N
MU=23UB=38,18Nm
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Perhitungan Komposit Horizontal
1. Tinggi total (dari dasar laut)
Tinggi caisson di atas HWS = 43−32Hs (diambil
2,742
Hs = 1,37x5) =6,85
Tinggi total(T)= Hws+h+tinggi diatas permukaan air=2,71+6+6,85=15,56 m
2. Panjang
P= 14Lo=1
4xgT 2
2π=14x9,81x 112
2π=14x188,92m=47,23m
3. Lebar caisson
L=34Tc=3
4x 15,56=11,67m
4. Desain rubble mound
kaki:
tinggi kaki r = 2 m; slope 1:2
hs=kedalaman;h=kedalaman-tinggi kaki
h/hs=4/6=0,66667 – Dengan grafik: diperoleh Ns3=230
Lebar kaki : B=0,4hs=2,4m ; b=r/slope= 4 m
Δ=( γ rγ a−1)=( 26001024−1)=1,54
Dn50= HsΔNs
=0,53m
W 50= ρbatu x Dn503=2600 x0,533=387,6kg
Tebal layer kaki:
r=nk∆(Wγ r
)13=2x 1,0( 387,6
2600)13=1,06m
Armor:
slope=1:1,5
Hw=Tc−r=15,56−2=13,56m
Lebar dasar ¿Hwslope
=20,34m
Lebar atas ¿0,5Hw=6,78m
Panjang total:
Lp=Lebar dasar + lebar atas + lebar caisson + 2xb + 2xB = 51,59 m
24 Firmansyah Perdana (15506005)Perencanaan Prasaran Pelabuhan
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25 Firmansyah Perdana (15506005)Perencanaan Prasaran Pelabuhan