TUGAS
ANALISA PERENCANAAN JEMBATAN KOMPOSIT DENGAN ANALISA PLASTIS
2
P ro fil B a ja P ip a G a lv a n is 2 Ø 2 ,5 " 0 .5 0 Ø 1 4 - 15 0 m m
A s p a l t = 5 cm 1 .0 0
Ø 1 4 - 20 0 m m
C e n te r L in e 1 ,5 %
0 .6 0
1 .2 5
D E T A IL A
0 .9 0 0 .9 5
1 ,5 %
1 .2 5
1 .2 5
1 .2 5
1 .2 5
1 .2 5
0 .6 0
3 .7 5 7 .5 0
P O T O N G A N M E L IN T A N G
P E R E N C A N A A N J E M B A T A N K O M P O S IT S ka la 1 : 1 5 0
Data Perencanaan : Jembatan Kelas I Bentangan Jembatan Lebar Jembatan Lebar Trotoar Jarak Gelegar (S) Tebal Aspal Tebal Lantai Pipa Reling/Sandaran Pipa Saluran Baja yang digunakan Fe. 360 (Tegangan Ultimed) Beton yang digunakan K.225 Berat Jenis Beton Bertulang Berat Jenis Beton Berat Jenis Air Hujan Berat Jenis Aspal Rencana Gelegar Memanjang
= H B t1 t2 Fs G
H
t2 t1
B
a
= = = = = = = = σy = fc' = = = = =
25.00 7.50 1.00 1.25 0.05 0.20 2.50 4.00 240 25 2,400 2,000 1,000 2,200
m m m m m m Inchi Inchi MPa MPa Kg/m3 Kg/m3 Kg/m3 Kg/m3
Profile Flens Lebar Din 85 = = = = = =
850 300 19 36 372 292
mm mm mm mm cm2 Kg/m'
Ix Iy ix iy Wx Wy
= = = = = =
443890 16270 34.6 6.61 10440 1080
be
Cm4 Cm4 cm cm Cm3 Cm3
0 .0 5 0 .2 0
0 .0 5
a
be
0 .0 5 0 .2 0
.λ
e
0 .0 5
λ .
S Menentukan Lebar Efektif Balok Komposit e
= = =
30 + 30 + 40 cm
5 10
S 125 2a 2a a
= = = = =
2a + 2a + 125 85 42.5
e 40 40 cm cm
e
a/L =
42.5 cm = 42.5 cm = 25 m 2500 cm Harga λ, ditentukan dari tabel berikut ini :
+
5
0.017
~
a/L
0.05
0.1
0.15
0.2
0.25
0.3
λ/a
1
0.89
0.78
0.68
0.58
0.5
0.05
berdasarkan tabel harga λ diatas didapat sebagai berikut : Untuk harga a/L = 0.05 ; Lihat tabel harga λ λ/a λ λ
= = =
1 a 42.50 cm
be 0 .0 5 0 .2 0 0 .0 5
e
λ . S
Jadi Lebar Efektif Balok Komposit Sebagai berikut : be = 2λ + e = 2 x 42.5 + 42.5 = 85 + 42.5 = 127.50 cm
◘ PEMBEBANAN Beban Mati (Dead Load)/(DL)
Gelegar Memanjang Tengah Lantai Voute
= =
0.20 0.05
x x
1.275 0.4 + 2
x 0.3
2,400 x 2,400
= =
612.00 Kg/m' 42.00 Kg/m'
= = =
292.00 Kg/m' 87.60 Kg/m' 1033.6 Kg/m'
= =
51.68 Kg/m' 1085.3 Kg/m'
= =
588.00 Kg/m' 42.00 Kg/m'
= = =
292.00 Kg/m' 87.60 Kg/m' 1009.6 Kg/m'
qDL
= =
50.48 Kg/m' 1060.1 Kg/m'
qSDL
= = =
140.25 Kg/m' 25.50 Kg/m' 165.75 Kg/m'
Gelegar Memanjang (Profile Din 85) Diafragmanya 30%
Berat Baut
=
5%
x
1,034 qDL
Momen DL
= 1/8 = =
Gaya Lintang DL
qDL
x
0.125 x 1085.3 84,787.50 Kg m
= 1/2 = =
x
x
qDL
x
0.5 x 1085.3 13,566.00 Kg
L2 x
25.00
2
L x
25.00
Gelegar Memanjang Tepi Lantai Voute
= =
0.20 0.05
x x
1.225 0.4 + 2
x 0.3
2,400 x 2,400
Gelegar Memanjang (Profile Din 85) Diafragmanya 30%
Berat Baut
Momen DL
=
= 1/8 = =
Gaya Lintang DL
5%
x
1009.6
qDL
x
0.125 x 1060.1 82,818.75 Kg m
= 1/2 = =
x
x
qDL
L2 x
25.00
x
L
0.5 x 1060.1 13,251.00 Kg
x
25.00
x x
2,200 1,000
2
Superimposed Dead Load/(SDL) Gelegar Memanjang Tengah Aspal Air Hujan
Momen SDL
= =
0.05 0.02
= 1/8 = =
x
x x
1.275 1.275
qSDL
x
0.125 x 165.75 12,949.22 Kg m
L2 x
25.00
2
Gaya Lintang SDL
= 1/2 = =
x
qSDL
x
L
0.5 x 165.75 2,071.88 Kg
x
25.00
x x
2,400 2,400
Gelegar Memanjang Tepi Trotoar Dinding Tepi Tiang dan Relling
= =
0.20 0.20
x x
1.00 0.55
qSDL Momen SDL
= 1/8 = =
Gaya Lintang SDL
x
qSDL
= =
x
qDL
480.00 264.00 50.00 794.00
Kg/m' Kg/m' Kg/m' Kg/m'
L2
x
0.125 x 794.00 62,031.25 Kg m
= 1/2
= = = =
x
x
L
0.5 x 794.0 9,925.00 Kg
x
25.00
2
25.00
beban Hidup (Live Load)/(LL) Gelegar Memanjang Tengah Beban Merata Bentangan L = 25 m (Standar Pembebanan Jembatan) q' = q x α x 2.75 = 2.2 x 1 x 2.75 = 1.00 t/m' =
Dimana; S
1
+ 50
Momen LL
= 1/8 = =
x q'
0.125
x
L2
+
25 x 1.267 121306.818 Kg m
=
1
=
1
1,000.00 Kg/m'
=
1,000
2.2 t/m'
1.25
20 + 25 x
=
Dimana ; α
Beban Terpusat Beban garis / terpusat Dimana; P (Standar Pembebanan Jembatan) P' = P x α x S 2.75 = 12 x 1 x 1.25 2.75 = 5.45 t = 5,454.545 Kg Faktor Kejut k = 1 + 20 50 + L =
q
x
=
12 t Dimana ; α
Dimana ; L
=
25 m
1.267
1/4 25
x 2
P' +
x
L
0.25
x
k
x
5454.545
x
Gaya Lintang LL
= 1/2 = = =
x
L
+ 1/2
x
0.5 x 1000.0 1.267 12,500.00 Kg + 15,954.55 Kg
x
qLL
x
25.00
+
3454.55
PLL
x
0.5
k x
5,454.545
x
Kg
Gelegar Memanjang Tepi Beban Merata Bentangan L = 25 m (Standar Pembebanan Jembatan) q' = q x 1 m = 500 x 1 m = 350 Kg/m'
Dimana;
q
=
500
Kg/m2
Beban Terpusat Beban garis / terpusat Dimana; P = 12 t (Standar Pembebanan Jembatan) P' = P x α x 1/2 S Dimana ; α 2.75 = 12 x 1 x 0.63 2.75 = 2.727 t = 2,727.273 Kg Faktor Kejut k
=
=
Momen LL
1
1
= 1/8
+
+
20 50 +
x
=
0.125
=
25 x 1.267 48934.659 Kg m
Gaya Lintang LL
x
= 1/2 = = =
Dimana ; L
=
L2
350
x
=
1
25 m
L
20 50 + 25
x q'
=
1.267
+
1/4
x
25
qLL
x 2
P'
x
+
L
0.25
x
L
+ 1/2
x
0.5 x 350.0 1.267 4,375.00 Kg + 6,102.27 Kg
x
25.00
+
1727.27
x
k
x
2727.273
PLL 0.5
x
x
k x
2,727.273
Kg
KETERANGAN ; ◘
Momen Gelegar Memanjang Tengah
MDL
=
MSDL
=
12,949.219 Kg m
MLL
=
121,306.818 Kg m
84,787.500 Kg m
219,043.537 Kg m
+
x
Gelegar Memanjang Tepi
MDL
=
82,818.750 Kg m
MSDL
=
62,031.250 Kg m
MLL
=
48,934.659 Kg m
+
193,784.659 Kg m
Lintang
◘
Gelegar Memanjang Tengah
DDL
=
DSDL
=
2,071.875 Kg
DLL
=
15,954.545 Kg
13,566.000 Kg +
31,592.420 Kg Gelegar Memanjang Tepi
DDL
=
13,251.000 Kg
DSDL
=
9,925.000 Kg
DLL
=
6,102.273 Kg
+
29,278.273 Kg
Dari hasil momen dan Lintang yang didapat maka untuk mendeasain jembatan kumposit diambil momen dan lintang yang terbesar yaitu Gelegar memanjang tengah dengan momen dan nilai lintang =
219,043.537 Kg m;
dan
31,592.420 Kg
◘ MENENTUKAN GARIS NETRAL DAN INERSIA KOMPOSIT σc 0 .2 0 0 .0 5
t2
dc a
yc dt
GA RIS N ETRA L
H t1
ys
0 .2 0 0 .0 5
yc
dc
t2
dt
a
GA RIS N ETRA L
H ys
t1
σs B
dimana diketahui ; H B t1 t2 Fs G Fs Fb
= = = = = =
850 300 19 36 372 292
= 372 cm2 = b/n x 20 cm = 128 / 20 x = 6 x 20 = 128 cm2
mm mm mm mm cm2 Kg/m'
Ix Iy ix iy Wx Wy
443890 16270 34.6 6.61 10440 1080
Cm4 Cm4 cm cm Cm3 Cm3
Dimana;
n
dt
= = = =
1/2 x H + 1/2 1 x 85 + 42.5 + 10 57.5 cm
Statis Momen terhadap titik berat beton Fb x 0 + Fs x dt = Ft 0 + 372 x 57.5 dc
x = =
dc
=
dc 499.5 x 21390 499.5 42.823 cm
Ft
= = =
a
= dc 5 + 1/2 x 20 = 42.823 5 + 10 = 42.823 - 15 = 27.823 cm
yc
= = =
It
= 1/12 x b/n =
0.083
x
=
57.177 4250
+
=
+ 20 25 x
20
6
ys
3
x
42.50 233809
762084.82 cm
20
20
Fs + Fb 372 + 127.5 499.5 cm2
a + 5 27.823 + 52.823 cm
=
= = = = = =
4
+ Fb 8000
x +
dc 128
= = = 2
x
42.823
2
+
443890
+
+
80136
20 + x 20 5
5 +
5
dc
85 85 57.177 cm
+ Ixs
x 1 +
Fs 2
a 27.823 x
ys
-
+
443890
42.50 +
2
372
x
AKIBAT CREEP n'
Fb'
= = = =
n 20 20 60
x x x
1 1 3
+ +
ψ 2
= b/n' x 20 cm = 128 / 60 x = 2 x 20 = 43 cm2
Dimana, Komposit ψ
Ft 20
Statis Momen terhadap titik berat beton Fb x 0 + Fs x dt = Ft dc'
x =
dc'
=
a
= = =
dc' Fs
x Ft 372
=
2
Fs + Fb' 372 + 414.5 cm2
42.5
dt x 57.5 414.5
=
51.604 cm
= dc' 5 + 1/2 x 20 = 51.604 5 + 10 = 51.604 - 15 = 36.604 cm
yc'
= = =
It'
= 1/12 x b/n' x = = =
a + 5 36.604 + 61.604 cm
0.083 48.396 1416.7
x +
+ 20 25
20
2
3
x
42.50 159780
618017.42 cm
ys'
+ Fb 8000
= = = 2
85 85 48.396 cm
x
dc'
+ Ixs
+
60
x
+
12930
+
51.604
Fs
a 36.604
x
ys'
+
443890
+
102
x
2
-
42.50
2
372
2
+
443890
4
Tegangan Baja Maksimum yang terjadi σs
= = = = =
MDL
x
102
+
MSDL
x
102
x
ys'
+
MLL
x
Wxs It' It 8,478,750.00 1294921.88 x 48.396 12,130,681.818 x + + 10440 618017.42 762084.82 812.14 + 101.4 + 910.1 1,823.676 Kg/cm2 σy = 182.368 MPa ≤ 240 MPa …………….Ok !
ys 57.177
x
SF
=
240
MPa =
1.316
182.37 MPa Tegangan Beton Maksimum yang terjadi σc
= = = =
SF
MSDL
x
102
x
yc'
It' x n' 1294921.88 x 61.604 618017.42 x 60 2.151 + 42.041 44.192 Kg/cm2
=
4.419
MPa ≤
=
25
MPa =
4.419
fc'
MLL
+
It x 12,130,681.818 762084.82 x
+
=
102
x
x
yc
n' x 52.823 20
MPa …………….Ok !
25
5.66
MPa
Cek Lendutan Yang kita gunakan hanya beban hidup pada gelegar tengah untuk menentukan besar lendutan P' = 5454.55 Kg L = 2,500.00 cm q'
=
10.0
Kg/cm'
Es
=
2.1
x
1
5454.545
106 Kg/cm2
Lendutan yang terjadi
δ
=
δ
=
5 384
. q' . L4 Es . It
5
10.0
384
2.1 10
Lendutan Izin L = 500 Kontrol :
=
6
+
1 . P' . L3 48 Es. It
2.5004
762084.82
2500 500
δ
≤
4.288
≤
=
+
48 2.1
10
6
2.5003 762084.82
5 cm
5 …………….Ok !
Jadi Gelegar Memanjang Profile Lebar Din 85 aman untuk digunakan
◘ PERENCANAAN SHEAR CONNECTOR (Penghubung Geser) Perencanaan Cannal Connector : L t d
=
4.288 cm
Profil Cannal Connector yang digunakan adalah Baja Profil Cannal C 14,
t
dimana :
d ht b
b
=
6
;
Lebar Flens (cm)
ht
=
14
;
Tinggi Flens (cm)
t
=
1
;
Tebal Flens (cm)
d
=
7
;
Tebal Badan (cm)
L
=
15
;
Lebar Flens (cm)
σc
= Tegangan beton K.225
σc
=
Q
= Kekuatan Cannal Connector (Kg)
25 MPa =
250
Q 20 t 5 2 . L .
Kekuatan Untuk 1 bh Cannal Connector adalah ; Q = 20 x t + 5/2 x L x = 20 x 1 + 2.5 x 15 x = 16602.0 Kg
σc 250
Digunakan 1Bh Cannal Shear Connector =
x
1
Kg/cm2
c
16601.958 =
16601.958 Kg
be
d dc
Statis Momen komposit (S) S
= = =
b
x n 127.5
d
x
dc
x 20 x 20 5459.91 cm3
S' 42.823
= =
GAYA GESER (Longitudinal Shear) Besarnya gaya geser persatuan panjang bentangan jembatan q
=
0.5
x
DDL + DSDL x It'
=
S'
+
DLL x It
S
b
x n' 127.5
d
x
dc'
x 20 x 60 6579.55 cm3
51.604
= =
0.5
x
13566
206.822
+ 2,071.875 618017.42
x
5459.9
+
15954.545 x 6579.6 762084.82
Kg/cm
Jarak Stud Connector X
=
Q Total q
=
16601.958 = 206.822
80.27
~
80.00 cm
Cek Jarak Shear Connector q
x
X
206.822
≤
Q
x
80
16545.791 Kg
≤
16601.958 Kg
≤
16601.958 Kg …………….Ok !
0 .8 0
0 .8 0 0 .1 4
0 .8 5
Jumlah Cannal Connector n =
L X
=
2,500.00 80
=
31.25
~
31.00
Buah
Jumlah Cannal Connector untuk 1 gelegar memanjang adalah
31.00 buah
◘ PERENCANAAN DIAFRAGMA (PENGAKU)
4 .0 0
4 .0 0 2 5 .0 0
beban yang digunakan untuk menentukan dimensi diafragma : P = P1 + L1 4 x P2 x k 4 diaman : P = beban fiktif P1 = tekanan roda tengah / belakang (10 Ton) ---> Untuk Jembatan Kelas I
P2 L1 k
= tekanan roda depan (2,5 Ton) ---> Untuk Jembatan Kelas I = jarak diafragma (Mak. 6 m) = koefisen kejut
P
=
10
+
4.00
-
4
x
2.5
x
1.267
4 = = = =
10 + 0.000 x 2.5 10.000 x 1.267 12.667 Ton 12666.667 Kg
x
1.267
P =
S=
Mmax
= 1/4 = =
σ
P
x
1.25 m
S
0.25 x 12666.667 x 1.25 3958.3 Kg m = 395833.33 Kg cm
Mmax
=
x
12666.667 Kg
σl
≤
W
=
Mmax
W
Wx
=
Wx
=
σl
395833.33 Kg cm 240 MPA 164.93 cm3
=
39583.333 MPA 240 MPA
berdasarkan tabel didapatkan profile yang akan digunakan sebagai berikut : direncanakan menggunakan Profile H 250/125 mm H B t1 t2 Fs G
t2 H t1
= = = = = =
250.00 125.00 6.00 9.00 37.66 36.70
mm mm mm mm cm2 Kg/m'
Ix Iy ix iy Wx Wy
= = = = = =
4050.0 294.00 10.40 2.79 324.00 47.00
B
Cek berat yang direncanakan = 0.3 x berat gelegar memanjang ≥ = 0.3 x 292.0 kg/m' ≥ 1.25 =
87.60 Kg/m'
Cek Tegangan Ultimed
≥
45.88 Kg/m'
S x
x 36.70 Kg/m' 36.70 Kg/m'
…………….Ok !
Cm4 Cm4 cm cm Cm3 Cm3
σ
=
Mmax
≤
σy
Wx σ
=
395833.3333
≤
σy
=
240 Mpa
324 = SF
=
122.171 240 MPa =
MPa
≤
240 MPa
…………….Ok !
1.96
122.17 MPa
Jadi Gelegar Memanjang Profile H 250 x 125 aman untuk digunakan
