![Perhitungan Struktur Jembatan Beton [PDF]](https://pdfs.asia/img/200x200/perhitungan-struktur-jembatan-beton.jpg)
12 0 2 MB
TUGAS JEMBATAN BETON BERTULANG Nama Mahasiswa : Farah Savira NRP : 3114041071 Nama Asisten : Ir. Agung Budipriyanto, M Eng, PhD Tanda Tanga Asisten :
: entry data : data otomatis
DATA JEMBATAN Jembatan gelagar beton bertulang 1 bentang dengan abutment berpondasi tiang pancang Mutu Beton fc' : Mutu Baja Tulangan D>12 mm fy : Mutu Baja Tulangan D≤12 mm, fy : Syarat terkait beton bertulang jembatan mengaccu pada RSNI T 12-02-2004 BANGUNAN ATAS Bentang jembatan, L : Spasi girder, s : Lebar Lantai Kendaraan, B : Lebar Lantai Trotoir : Tebal Lantai Jembatan, ts : Dimensi Girder :
Dimensi Diafragma :
Dimensi Tiang Sandaran :
Dimesi Kerb :
L: S: B:
Tinggi Girder Lebar Girder Jumlah Girder Tinggi Diafragma Lebar Diafragma Jumlah Diafragma Tinggi Tiang Lebar Tiang Tebal Tiang Jumlah Tiang d kerb :
ts : h: Bw : n: hd : bd : n: hd : bd : td : n: h:
25 Mpa 320 Mpa 240 Mpa
16 m 1.75 m 7m 1.2 m 250 mm 1.4 m 0.8 m 5 buah 0.5 m 0.3 m 4 buah 1.5 m 0.2 m 0.2 m 9 buah 0.25 m
ts OK
(BMS BDM1992 hal 3-24) 4 0.45 0.15 4
b kerb : Bahan untuk penutup lantai trotoir tebal aspal, Beban Hidup Jembatan =>
BANGUNAN BAWAH Tinggi ruang bebas terhadap MAB, Tinggi MAB tehadap MAN : Posisi dasar pile cap Tebal pile cap Macam pile, dimensi pile, jumlah dan konfigurasi Tebal dinding abument Tebal dinding longitudinal stopper Dimensi dan tebal wingwall Dimensi dan tebal plat injak Data tanah Beban gempa Peta gempa Lokasi jembatan
b: 0.15 m : paving ta : 7 cm T: 11.25 t BTR : 0.9 t/m2 BGT : 4.9 Mtu W:
2m 2m
paving
Sesuai dengan RSNI T-02-2005
170 1/12 L ≥h≥ 1/15 L 2/3 h ≤b≤ 1/3 h
7
1.2
kontrol nominal gelagar
9.4
1.125
PRELIMINARY DESIGN Menentukan tebal plat lantai kendaraan ts ≥ 200 mm ts ≥ 100 + 0.04 L mm ≥ 100 + 0.04 1750 mm ≥ 170 mm
(RSNI T-12-2004 Pasal 5.5.2) (RSNI T-12-2004 Pasal 5.5.2)
Jadi dipakai ts = 250 mm = 0.25 m Menetukan dimensi girder Tinggi girder 1/12 L 0.0833 L
(1/12 L ≥ =
≥
h
1333.3 mm
Jadi tinggi girder (h) yang digunakan Kontrol tinggi nominal girder h ≥ 165 + 1400 ≥ 165 + 1400 ≥ 1125 OK Lebar girder (2/3 h) 2/3 h 0.6667 h =
1/15 L)
=
Jadi lebar girder (bw) yang digunakan
1400 mm
≥ ≥ ≥
(1/3h) 1400 (1/3h) 1400 0.3333 h =
=
16000
Diambil yang terkecil, sehingga b eff balok =
0.06 S mm 0.06 1750 mm
(pendekatan) 466.67 mm
800 mm
3) b eff = 12 x ts = 12 x = 3000 mm
2) b eff = Jarak ke pusat antar badan balok = 1750 mm
Menetukan dimensi diafragma Tinggi diafragma h ≥ 165 + h ≥ 165 + h ≥ 270 mm
1066.7 mm
0.06 L mm 0.06 16000 mm
≥ bw ≥ bw 933.33 mm
Lebar efektif balok 1) b eff = 1/5 L = 0.2 x = 3200 mm
(pendekatan) 1/15 L 0.0667 L =
1750 mm
250
Jadi tinggi difragma yang digunakan
=
500 mm
=
300 mm
Lebar diafragma b = h/3 = 166.67 Jadi lebar diafragma yang digunakan
PERENCANAAN PIPA SANDARAN Data -data perencanaan pipa sandaran Panjang bentang jembatan L: Jarak tiang sandaran d: Bahan yang digunakan : 1. Tiang Sandaran Mutu beton Mutu baja 2. Pipa Sandaran Diameter luar Tebal pipa Berat pipa Section of Modulus Mutu baja
BJ- 37
16 m 2m
fc' : fy :
25 MPa 240 MPa
do : t: q: w: fu : fy :
76.3 mm 2.8 mm 5.08 kg/m 11.5 cm³ 370 MPa 240 MPa
Pembebanan dan Perhitungan Momen pada Tiang Sandaran Beban pipa sandaran yang bekerja arah vertikal q vertikal = W sandaran + Berat Pipa = 0.75 kN/m + 5.08 x = 0.75 kN/m + 0.0508 kN/m = 0.8008 kN/m
0.01 kN/m
Beban pipa sandaran yang bekerja arah horizontal q horizontal = W sandaran = 0.75 kN/m M vertikal
M horizontal
MR resultan
= = = =
( 1/12 x 0.083333 x 0.083333 x 0.266933 kN.m'
q vertikal 0.8008 0.8008
x x x
L² )
= = = =
( 1/12 x 0.083333 x 0.083333 x 0.25 kN.m'
q vertikal 0.75 0.75
x x x
L² )
= = = =
Mv ² + 0.071253 + 0.133753 0.365723 kN.m'
Mh² 0.0625
Cek kekuatan profil pipa sandaran Batas kelangsingan profil
2² 4
2² 4
λ=
do t λp = 14800 fy Syarat
= =
λ 27.25
76.3 2.8 14800 240
=
27.25
=
61.66667
< < OK
λp 61.66667
Kuat Lentur Nominal w = 11500 mm³ Mn = w x = 11500 x = 3E+06 N.mm = 2.76 kN.m ϕ.Mn = =
0.9 x 2.484 kN.m Syarat,
ϕ.Mn 2.484
fy 240
2.76
> > OK
MR 0.365723
PERENCANAAN TIANG SANDARAN Data -data perencanaan tiang sandaran b= 20 cm d= 20 cm
h= γ beton bertulang =
Pembebanan pada tiang sandaran 1. Beban Mati a. Beban Sendiri Tiang K= 1.3 P1= b x d x = 0.2 x 0.2 x = 1.872 kN b. Berat Pipa Sandaran 1 P2= w x = 0.0508 x = 0.11176 kN b. Berat Pipa Sandaran 2 P2= w x = 0.0508 x = 0.11176 kN P total = =
1.872 + 2.09552 kN
h 1.5
150 cm 24 kN/m³
x x
γ 24
x x
K= 1.1 dt 2
x x
1.1 1.1
x x
1.1 1.1
+
0.11176
K= 1.1 dt 2
0.11176
2. Beban Hidup Vh = 0.75 kN/m Momen pada Tiang Sandaran s= 0.75 m (jarak as pipa sandaran atas ke dasar tiang sandaran) Mh = Vh x = 0.75 x = 1.125 kN.m = 1.13E+06 N.mm
s 0.75
Penulangan tiang sandaran 1.Penulangan Lentur Tiang Sandaran Dimensi tiang sandaran Selimut beton (decking) Diameter tulangan utama Diameter tulangan sengkang d=
h
-
x x
2 2
= 20 x 20 cm = 30 mm = 12 mm = 10 mm
h selimut
-
φ sengkang
-
1/2 φ tul utama
1.3 1.3
= =
200 154
mm
30
-
10
-
x
1.13E+06 200 x
6
Mu = 1.13E+06 N.mm
Rn =
Mu ϕ b d²
= 0.8
0.2964771 N/mm²
= m=
fy 0.85
= x
fc'
0.85
240 x
ρ min =
1.4 fy
=
1.4 240
=
0.00583333
ρb=
0.85
x
fc' fy
x
β1
25 240
x
ρb
=
=
0.85
154 ²
x
0.85
=
11.2941
600
600 +
fy
600
600 +
240
25
x
x
= 0.0537574 ρ maks =
0.75
ρ perlu =
1 m
=
x x
1 -
1 -
1 x 11.294118
1 -
1 -
0.75
x
0.05376
=
0.040318
2
x
m fy
x
Rn
2
x
11.2941 240
x
0.296477
<
ρ perlu 0.00124
ρ min
0.00583
b 200
φ
x x
12
d 154
As =
226.195 mm²
Jumlah Tulangan
n
As =
2
226.195 mm² OK
2.Penulangan Geser Tiang Sandaran Gaya geser pada Tiang Sandaran Vu=Vh = 0.75 x
K
K =2 = = =
0.75 x 1.5 kN 1500 N
2
Penulangan Geser Tiang Sandaran Vc =
fc' 6
x
x 25 6 = 25666.667 N =
φ Vc = 0.5 φ Vc =
0.75 0.5 Syarat,
x x
b
x
d
200
x
154
25666.667 19250
= =
19250 9625
0.5 φ Vc Vu > 1500 < 9625 Tidak Perlu Tulangan Geser Dipasang Sengkang Praktis φ - 10 jarak 200
3.Kontrol Penampang Tiang Sandaran Kontrol Jarak Tulangan s= b 2h selimut n = 200 60 2 = 96 mm Syarat,
-
2φ sengkang
1 20 1
-
n
φ tul utama
-
2
12
> 40 > 40 OK Jarak antar Tulangan Memenuhi
Kontrol Kemampuan Penampang a= As x 0.85 x fc' = 226.195 x 0.85 x 25 = 12.773346 mm Mn aktual =
As
x
fy
s 96
fy x 240 x
200
d
-
b
a
= 226.19467 = Mn =
x
240
d
-
154
-
2 12.7733 2
8013444 N.mm Mu ϕ Srayat,
=
1.13E+06 0.8
=
1.41E+06 N.mm
Mn aktual 8013443.50316814
> >
Mn 1406250
Penampang Kuat
PERENCANAAN KERB Data -data perencanaan kerb h= 0.25 m b1 = 0.15 m
b2 = L=
Pembebanan pada Kerb 1. Beban Mati K= 1.3 Berat Sendiri = b1 + 2 = 0.15 + 2 = 1.05 kN/m = 1.05 kN/m = 1.365 kN Berat Hidup = = =
w 15
x x
γ beton = w=
0.2 m 1m
b2
x
h
x
γ
0.2
x
0.25
x
24
x x
K 1.3
x x
L 1
L 1
24 kN/m³ 15 kN/m
(BMS,BDM hal 2.67)
15 kN
2. Analisa Gaya Dalam Mu = P hidup x = 15 x = 7.5 kN.m = 8E+06 N.mm
K= 2 L 1
x x
h 0.25
x x
K 2
3. Penulangan Kerb fc' = fy = tebal selimut = d= = =
h 250 202 mm
h selimut 30
Mu
=
Rn =
d²
b m=
ρ min =
φ sengkang = φ tul pokok =
25 MPa 240 MPa 30 mm
fy
φ sengkang 12
-
7500000
fc'
1.4 fy
=
1.4 240
0.5 φ tul pokok 6
= 202 ²
250 x =
0.85
-
12 mm 12 mm
0.85
240 x
=
0.00583
= 25
11.2941
0.73522 N/mm²
ρ b = 0.85
x
= 0.85
x
fc' fy
x
25 240
x
ρb
=
β1
x
0.85
x
600
600 +
fy
600
600 +
240
= 0.05376 ρ maks = 0.75 ρ perlu =
=
x
1 m
x
1 -
1 -
1 11.29
x
1 -
1 -
0.75
x
0.05376
=
0.04032
2
x
m fy
x
Rn
2
x
11.2941 240
x
0.73522
ρ perlu 0.00312
<
Sehingga dipakai ρ min As perlu = ρ x = 0.00583 x = 294.583 mm²
b 250
x x
π x 4 π = x 4 = 376.991 mm² Syarat,
d² 144
d 202
φ 12
Kerb direncanakan menggunakan As pasang =
0.00583
L s 1000 300
As terpasang
376.991
≥
As Perlu
≥ OK
294.583
Penulangan Pembagi Tulangan bagi direncanakan menggunakan Jumlah tulangan n= 4 As' = 50%
As pakai =
π
x
As pakai
x
d²
As = 113.097 mm²
φ 12
= = x
n
50% x 188.496 mm²
376.991
4 π 4 452.389
=
144
x
4
Jarak Tulangan yang diperlukan s= 0.25 π x
x
b
= 0.25 π
d² As' 144 188.4956
x
1000
=
=
x
x
600 mm
Agar memudahkan pemasangan di lapangan dipasang Kait dipasang sepanjang 12d dengan bengkokan 90° = 12 x d = 12 x 12 = 144 mm
φ 12
jarak
300
PERHITUNGAN LANTAI JEMBATAN BETON
A. DATA - DATA JEMBATAN Tebal Slab Jembatan Tebal Lapisan Aspal + overlay Tebal genangan air hujan Jarak antar girder Lebar jalur lalu lintas Lebar trotoar Lebar total jembatan Panjang bentang jembatan
ts ta th S B b trotoar b total L
= = = = = = = =
fc' = 0.83 K/10 Ec = 4700 √fc' μ G = Ec/[2*(1+μ)] α
= = = = =
25 MPa 23500 MPa 0.2 9791.6667 MPa 1.00E-05 /°C
U fy = U*10 U fy = U*10
= = = =
40 400 MPa 24 240 MPa
Wc W'c Wa Ww Ws
= = = = =
24 kN/m³ 22 kN/m³ 22 kN/m³ 9.8 kN/m³ 77 kN/m³
25 cm 7 cm 5 cm 175 cm 700 cm 120 cm 940 cm 1600 cm
B. DATA MATERIAL Mutu Beton Kuat tekan beton Modulus elastisitas Angka poison Modulus geser Koefisien muai panjang untuk beton Mutu Baja Mutu Baja Tulangan D>12 mm Tegangan leleh baja Mutu Baja Tulangan D≤12 mm Tegangan leleh baja Berat Jenis Berat beton bertulang Berat beton tidak bertulang Berat aspal Berat air Berat baja
B. ANALISIS BEBAN 1. BERAT SENDIRI (MS) Faktor beban layan Faktor beban ultimit No.
= =
Ksms Kums
Tebal m 0.25
Jenis Beban 1 Lantai jembatan
2. BEBAN MATI TAMBAHAN (MA) Faktor beban layan Faktor beban ultimit No.
Tebal m 0.07 0.05
Jenis Beban 1 Lantai jembatan 2 Air hujan
Kstt Kutt T FBD
Beban Trruk "T" menjadi Ptt = (1 + = 1 + = 157.5 kN 4. BEBAN ANGIN (EW) Faktor beban layan Faktor beban ultimit Koefisien Seret Kecepatan angin rencana Tew
= = =
Pew
=
0.0012 x 0.0012 x 1.296 kN/m
x x
1 2 Berat kN/m³ 22 9.8 Qma
= = Tew b
RSNI T-02-2005
Beban kN/m' 6 6
RSNI T-02-2005
Beban kN/m' 1.54 0.49 2.03
1 RSNI T-02-2005 1.8 112.5 kN 0.4
x x
= = = = Cw 1.2
h b h 2
= = = =
FBD) 0.4
Ksew Kuew Cw Vw
Tinggi rata-rata kendaraan Jarak antar roda kendaraan
Berat kN/m³ 24 Qms
= =
Ksma Kuma
3. BEBAN TRUK "T" (TT) Faktor beban layan Faktor beban ultimit Beban truk pada lantai jembatan Faktor Beban dinamis
1 1.3
T 112.5
1 RSNI T-02-2005 1.2 1.2 30 m/s x x
Vw ² 30 ²
2m 1.75 m
= =
2 x 2 0.74057143 kN/m
5. PENGARUH TEMPERATUR (ET) Faktor beban layan Faktor beban ultimit Temperatur rata-rata maksimum Temperatur rata-rata minimum ΔT
= = =
T max 40 25
Kstt Kutt T max T min -
1.296 1.75
= = = =
1 RSNI T-02-2005 1.2 40 °C 15 °C
T min 15
°C
6. MOMEN PADA LANTAI JEMBATAN a) akibat beban sendiri
Berat sendiri Jarak girder
Q ms S
= =
6 kN/m' 1.75 m
Momen tumpuan maks, M mst = 0.08333333 x = 0.08333333 x = 1.53125 kN.m'
Qms 6
x x
S² 1.75 ²
Momen lapangan maks, M msl = 0.04166667 = 0.04166667 = 0.765625
Qms 6
x x
S² 1.75 ²
x x
b) akibat beban mati tambahan
Berat sendiri
Q ms
=
2.03 kN/m'
Jarak girder
S
=
1.75 m
Momen tumpuan maks, M mat = 0.10416667 x = 0.10416667 x = 0.64759115 kN.m'
Qms 2.03
x x
S² 1.75 ²
Momen lapangan maks, M mal = 0.05208333 x = 0.05208333 x = 0.32379557 kN.m'
Qms 2.03
x x
S² 1.75 ²
c) akibat beban truk T (Ptt)
Beban truk "T" Jarak girder
Ptt S
Momen tumpuan maks, M mttt = 0.15625 x = 0.15625 x = 43.0664063 kN.m' Momen lapangan maks, M ttl = 0.140625 x = 0.140625 x = 38.7597656 kN.m' d) akibat beban angin (Pew) Beban kondisi ultimit Jarak girder
Pewu S
Kondisi ultimit Momen tumpuan maks Mew TU = 0.15625 x = 0.15625 x = 0.2025 kN.m' Momen lapangan maks Mew LU = 0.140625
x
= =
Ptt 157.5
Ptt 157.5
= =
157.5 kN/m' 1.75 m
x x
S 1.75
x x
S 1.75
0.7405714 kN/m' 1.75 m
Pew U 0.7405714
x x
S 1.75
Pew U
x
S
= =
0.140625 x 0.18225 kN.m'
e) akibat pengaruh temperatur (T) Momen inersia lantai = 0.08333333 x I = 0.08333333 x = 1302083333 mm⁴ Modulus elastisitas Ec α Koefisien muai Tebal lantai h
0.7405714
x
b 1000
x x
= = =
1.75
h³ 250 ³
23500 MPa 1.00E-05 /°C 250 mm
Momen tumpuan maks Met T = 0.25 x = 0.25 x = 5.88E-08 kN.m'
ΔT 25
x x
α 1.00E-05
x x
EI/h 94
Momen lapangan maks Met L = 0.875 x = 0.875 x = 2.06E-07 kN.m'
ΔT 25
x x
α 1.00E-05
x x
EI/h 94
Daya Layan
Keadaan Ulimit
M Lapangan (kN.m')
M Tumpuan (kN.m')
f) Kombinasi momen No
Jenis Beban 1 Berat Sendiri 2 Beban mati tambahan 3 Beban truk 4 Beban angin 5 Pengaruh temperatur
Faktor Beban Kms Kma Ktt Kew Ket
1 1 1 1 1
1.3 2 2 1.2 1.2
0.765625 1.53125 0.3237956 0.6475911 38.759766 43.066406 0.18225 0.2025 2.06E-07 5.88E-08
KOMBINASI 1 No.
Jenis Beban 1 Berat Sendiri 2 Beban mati tambahan 3 Beban truk 4 Beban angin 5 Pengaruh temperatur
Faktor Beban 1.3 2 2 1 1
M Lapangan (kN.m')
M Tumpuan (kN.m')
Mu Lapangan Mu Tumpuan (kN.m') (kN.m')
0.765625 1.53125 0.9953125 1.990625 0.3237956 0.6475911 0.6475911 1.2951823 38.759766 43.066406 77.519531 86.132813 0.18225 0.2025 0.18225 0.2025 2.056E-07 5.875E-08 2.056E-07 5.875E-08 Total Mu = 79.344685 89.62112
KOMBINASI 2 No.
Jenis Beban 1 Berat Sendiri 2 Beban mati tambahan 3 Beban truk 4 Beban angin
Faktor Beban
M Lapangan (kN.m')
M Tumpuan (kN.m')
Mu Lapangan Mu Tumpuan (kN.m') (kN.m')
1.3 0.765625 1.53125 0.9953125 1.990625 2 0.3237956 0.6475911 0.6475911 1.2951823 1 38.759766 43.066406 38.759766 43.066406 1.2 0.18225 0.2025 0.2187 0.243
5 Pengaruh temperatur
1.2 2.056E-07 5.875E-08 2.468E-07 7.05E-08 Total Mu = 40.62137 46.595214
C. RENCANA TULANGAN PLAT LANTAI TULANGAN LAPANGAN (Tulangan lentur positip) Mu = 79.344685 kN.m' d=(h-d') fc' = 25 MPa b fy = 400 MPa Φ Mn=Mu/Φ h = 250 mm d' = 40 mm Ρb=
0.85
β1
x
=
0.85
0.85
x
= = = =
fc' fy 25 400
x
210 mm 1000 mm 0.8 99.180856 kN.m'
600 x 600
600 + 600 +
400
x x x x
fy fc' 400 25
fy
= 0.0270938 Ρ maks = 0.75 = 0.75 = 0.0203203
x x
Ρb 0.02709375
R maks = Ρ maks
x
fy
x
1-
1/2 Ρ maks 0.85
x
400
x
1-
1/2 0.024384
= 0.0203203
0.85 = 6.5736211 Mn =
Mu Φ
=
79.3446851 0.8
=
99.180856 kN.m
Rn =
Mn b
x x
1.00E+06 d²
= =
99.180856 1000 2.248999
Rn 2.24899901
<
>
0.75
x
540 mm 840 mm 840
579600 mm²
25 MPa 157.5 kN 0.7
Kekuatan nominal lantai terhadap geser tanpa tulangan geser Vc = 1 fc' x b' x 6 = 1 25 x 2760 x 6 = 483000 N = 483 kN Kekuatan geser terfaktor, Vu = ϕ Vc =
= = x
483
d 210
=
Ptt 157.5
Pelat lantai tanpa tulangan geser aman terhadap geser pons
362.25 kN
PERENCANAAN PELAT KANTILEVER A. Pembebanan pelat kantilever 1. Beban Mati (q DL) Beban Merata Berat pelat = ts x = 0.25 x = 6 kN/m'
b 1
x x
γ beton 24
Beton rabat = = =
tebal 0.25 5.5
x x kN/m'
b 1
x x
γ beton 22
Kerb = = =
tebal 0.25
x x 6 kN/m'
b 1
x x
γ beton 24
q DL =
17.5 kN/m'
Beban mati terpusat akibat tiang sandaran P1 (Beban pipa 1) = 0.11176 kN P2 (Beban pipa 2) = 0.11176 kN P2 (Beban tiang) = 1.872 kN p DL = 2.09552 kN 2. Beban Hidup Merata (q LL) Pejala Kaki = 5 kN/m² Air Hujan = 0.49 kN/m² q LL = 5.49 kN/m²
B. Perhitungan momen pelat kantilever 1. Akibat Beban Mati Terpusat MD1 = P1 x L = 0.11176 x (b/2 + jarak tiang terhadap garis jepit) = 0.11176 0.2 0.95 x + 2 = 0.11176 x 1.05 = 0.117348 kN.m MD1 = = =
P2 P2 0.11176
x x x
= 0.11176 x = 0.117348 kN.m MD2 = = = = =
P3 P3 1.872
x x x
1.872 x 1.9656 kN.m
L (b/2 + jarak tiang terhadap garis jepit) 0.2 0.95 + 2 1.05
L (b/2 + jarak tiang terhadap garis jepit) 0.2 0.95 + 2 1.05
Mp DL = 2.200296 kN.m 2. Akibat Beban Mati Merata M q DL tumpuan = -q DL x
1/2 L²
= -q DL x = -17.5 x =
-9.647 kN.m
M q DL lapangan = q DL = q DL = 17.5 =
x x x
1/2 L² 1/2 (b/2 x jarak tiang terhadap garis jepit)² 1 0.2 0.95 ² x + 2 2
9.647 kN.m
3. Akibat Beban Hidup Merata M q LL tumpuan = -q LL x = -q LL x = -5.49 x =
1/2 (b/2 x jarak tiang terhadap garis jepit)² 1 0.2 0.95 ² x + 2 2
-3.026 kN.m
1/2 L² 1/2 (b/2 x jarak tiang terhadap garis jepit)² 1 0.2 0.95 ² x + 2 2
M q LL lapangan = q LL = q LL = 5.49 =
x x x
1/2 L² 1/2 (b/2 x jarak tiang terhadap garis jepit)² 1 0.2 0.95 ² x + 2 2
3.026 kN.m
Kombinasi Penulangan = 1.3 Mu tumpuan = 1.3 x = 1.3 x = -18.59366 kN.m Mu lapangan = 1.3 x = 1.3 x = 18.594 kN.m
M DL M DL -9.647
+ + +
2 2 2
M DL 9.647
+ +
2 2
M LL x M LL x -3.026 x x
M LL 3.026
C. Penulangan Pelat kantilever 1. Dimensi Pelat Lebar (b) = 1000 mm ts (tebal slab) = 250 mm ta (aspal + overlay) =
70 mm
2. Data Bahan fc' = 25 MPa φ Tul. Lentur = D 16 fy = 320 MPa φ Tul. Geser = D 13 fy = 240 MPa Luas Tul. Geser = 132.732 mm² Decking = 30 mm d= ts = 250 = 199 mm Kcr = 0.75
decking 30
φ tul.geser 13
-
-
1/2 φ tul lentur 8
Penulangan Lentur Mu akibat tumpuan = M* = Mu/Kcr =
-18.594 kN.m -24.79155 kN.m D 16
Direncanakan menggunakan tulangan π D tul lentur² Ast = x 4 π = 256 x 4 = 1608.4954 mm²/m' T= Ast x = 1608.4954 x = 386038.91 N
x x
jarak lebar pelat jarak tulangan 1000 125
fy 240
a=
T 0.85 x fc x = 386038.905273114 0.85 x 25 x = 18.166537 mm
Mn =
T = 386038.91
x
d
-
x
199
-
= 73315247 N.mm
b 1000
1 2 1 2
a 18.166537
125
= 73.315247 kN.m Syarat, Mu akibat lapangan = M* = Mu/Kcr =
Mn > 73.315247 >
18.594 kN.m 24.79155 kN.m D 16
Direncanakan menggunakan tulangan π D tul lentur² Ast = x 4 π = 256 x 4 = 1608.4954 mm²/m' T= Ast x = 1608.4954 x = 386038.91 N
Mu/Kcr 24.7916 OK
x x
jarak lebar pelat jarak tulangan 1000 125
125
fy 240
a=
T 0.85 x fc x = 386038.905273114 0.85 x 25 x = 18.166537 mm
Mn =
T = 386038.91
x
d
-
x
199
-
b 1000
1 2 1 2
a 18.166537
= 73315247 N.mm = 73.315247 kN.m Syarat, Maka dipasang tulangan lentur Penulangan Pembagi Direncanakan tulangan pembagi 20%
x
π x 4 π = x 4 = 884.88193 mm²
As pakai =
D
D 13
As pasang
Mn > Mu/Kcr 73.315247 > 24.7916 OK 16 jarak 125
jarak = =
150
20% x mm² 322
D tul bagi²
x
169
x
1608.4954
lebar pelat jarak tulangan 1000 150
PERENCANAAN GIRDER A. Pembebaban Girder 1) Balok Tepi a. Beban Mati Beban Mati Merata Berat trotoar paving ts x b x 0.25 x 1 x Berat sendiri balok h x bw 1.5 x 0.6
x x
BJ beton 2.2
=
BJ beton 2.4
=
0.55 T/m'
B. Pembebaban G 2) Balok Tengah a. Beban Mati Beban Mati Mera Berat sendiri balok h 1.5
2.16 T/m'
Berat sendiri plat ts 0.25 Berat aspal ts 0.1
Berat sendiri plat ts x (s-bw) 0.25 x 0.95
x x
BJ beton 2.4
=
0.57 T/m'
Berat plat katilever ts x b 0.25 x 1
x x
BJ beton 2.4
=
0.6 T/m'
Berat kerb ts x 0.25 x
b 0.15
x x
BJ beton 2.4
=
0.09 T/m'
Berat aspal ts x 0.1 x
s 1.75
x x
BJ aspal 2.2 q DL
Beban Mati Terpusat Berat diaframa b x h x 0.3 x 0.5 x
(s-bw) 0.95
Berat tiang sandaran dan pipa P1 + P2 + P3 0.187 + 0.011 + 0.011 p DL b. Beban Hidup Beban Hidup Merata Beban Lajur "D" (BTR) L ≤ 30m, q = 0.9 t/m² L < 50m, DLA = 0.4
x x
BJ Beton 2.4
=
0.385 T/m'
=
4.355 T/m'
=
0.342 T
=
0.21 T
=
0.552 T
Beban Mati Terpu Berat diaframa b 0.3
b. Beban Hidup Beban Hidup Mer Beban Lajur "D" L ≤ 30m, q = L < 50m, DLA =
Beban UDL (beban UDL 0.9 Beban air hujan ts 0.05
Beban Hidup Terp Beban KEL BGT Sesuai dengan RSNI T-02-2005 Sesuai dengan RSNI T-02-2005
Beban KEL (beban p KEL
4.9 50 % beban UDL (beban lajur "D") q x s x 50% 0.9 x 1.75 x 50% Beban air hujan ts x s 0.05 x 1.75
x x
BJ air 1 q LL
Beban Hidup Terpusat Beban KEL (BGT) BGT = 4.9 t/m' 50 % beban KEL (beban BGT) BGT x 1 + DLA 4.9 x 1 + 0.4
=
0.788 T/m'
= =
0.088 T/m' 0.875 T/m'
Sesuai dengan RSNI T-02-2005
x x
s 1.75
x x
50% 50% p LL
= =
6.003 T/m' 6.003 T/m'
B. Pembebaban Girder 2) Balok Tengah a. Beban Mati Beban Mati Merata Berat sendiri balok x bw x x 0.6 x
BJ beton 2.4
=
2.16 T/m'
Berat sendiri plat x (s-bw) x 0.95
x x
BJ beton 2.4
=
0.57 T/m'
Berat aspal x x
x x
BJ aspal 2.2
=
0.209 T/m'
q DL
=
2.939 T/m'
BJ Beton 2.4
=
0.342 T
p DL
=
0.342 T
(s-bw) 0.95
Beban Mati Terpusat Berat diaframa x h x x 0.5 x
(s-bw) 0.95
b. Beban Hidup Beban Hidup Merata Beban Lajur "D" (BTR) L ≤ 30m, q = 0.9 t/m² L < 50m, DLA = 0.4
Sesuai dengan RSNI T-02-2005 Sesuai dengan RSNI T-02-2005
Beban UDL (beban lajur "D") x b eff x 1.75 Beban air hujan x s x 1.75
x x
BJ air 1 q LL
Beban Hidup Terpusat Beban KEL (BGT) = 4.9 t/m' Beban KEL (beban BGT) x b eff x
x x
=
1.575 T/m'
= =
0.088 T/m' 1.663 T/m'
Sesuai dengan RSNI T-02-2005
1
+
DLA
x
1.75
x
1
+
0.4 p LL
= =
12.01 T 12.01 T
Analisis pembebanan pada girder
PERENCANAAN GIRDER A. Pembebaban Gelagar Bentang jembatan Tinggi girder Lebar girder
L= h= bw =
Mutu Beton Tulangan utama Tulangan sengkang
fc' = fy = fy =
1. Beban Mati Berat Plat
16000 mm 1400 mm 800 mm
d' d
= =
25 320 240
= = =
ts x 0.25 x 0.57 T/m'
(s-bw) 0.95
x x
BJ Beton 2.4
Berat Aspal
= = =
ta x 0.07 x 0.2695 T/m'
s 1.75
x x
BJ Aspal 2.2
Berat Girder
= = =
h girder x 1.4 x 2.688 T/m'
bw 0.8
x x
BJ Beton 2.4
= =
4.4811 T/m' 4.4811 x
q DL qu DL
P diafragma
= h diafragma = 0.5 = 2.15237 T
110 mm 1290 mm
x x
1.3
=
5.82543 T/m'
b diafragma 0.3
x x
(s-bw) 0.95
x x
BJ Beton 2.4
Pu diafragma
x x
Ku 1.3
= = =
BTR x 0.9 x 1.575 T/m'
s 1.75
Beban air hujan
= = =
ts x 0.05 x 0.08575 T/m'
s 1.75
x x
q LL qu LL
= =
0.198 T/m' 0.198 x
1.8
=
0.3564 T/m'
P BGT
= = =
BGT 4.9 1.078 T
x x
s 1.75
x x
KD 1.4
Pu BGT
= = =
P BGT 1.078 1.9404 T
x x
Ku 1.8
2. Beban Hidup Beban merata BTR
= P diafragma = 2.15237 = 2.798081 T
BJ air 0.98
BEBAN MATI (DL) Menghitung Rva dan Rvb akibat beban merata q DL
=
4.355 T/m'
A
B
L= Rva =
q DL = 4.355 =
x 2 x 2
L
Rvb =
16
q DL = 4.355
34.84 T
=
16 m x 2 x 2
L
Segmen Jarak Menghitung Ra dan Ra =
16
34.84 T =
Menghitung Rva dan Rvb akibat beban terpusat Pdia = A
Rva =
P dia = 0.342 =
Rva =
x 2 x 2
n dia
B
Rvb =
5
= 0.342
0.855 T 34.84 T 0.855 T 35.695 T
P dia
= Rvb =
0.855 T 34.84 T 0.855 T 35.695 T
x 2 x 2
0.342 T
=
Menghitung Ra u da Ra u=
n dia
=
5
= Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL =
Menghitung Ruva dan Ruvb akibat beban merata qu DL =
5.6615 T/m'
A
B
L= Ruva = qu DL = 5.6615
x 2 x 2
L
Ruvb = qu DL
16
= 5.6615
= 45.292 T
Menghitung Vu total Vu total =
16 m x 2 x 2
L 16
= 45.292 T φ*Vs perlu =
Menghitung Ruva dan Ruvb akibat beban terpusat Pu dia = 0.4446 T A
B
Dipasang sengk φ*Vs pasang =
Rva =
Pu dia = 0.4446 = 1.1115 T
x 2 x 2
n dia 5
Rvb =
Pu dia = 0.4446
x 2 x 2
n dia 5
= 1.1115 T Kontrol
Ruva = 45.292 T 1.1115 T 46.404 T
Ruvb = 45.292 T 1.1115 T 46.404 T
Mu q DL =
Mu pDL =
Mu qLL =
Mu LL =
Mu total =
Dipasang tulangan m As terpasang
Mu terpasang
Kontrol
kontrol tulangan ran Mn perlu =
x max = a max = C max =
Mu max =
P dia
P BGT q DL
Rva
q LL
Ra
Segmen
0m x= 0m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 0 2 L + 0.875 x 16 6.0025 x 16 0 2 16 13.003 T Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 0 2 L + 1.575 x 16 10.805 x 16 0 2 16 23.405 T Menghitung Vu DL Vu DL = Ruva = = 46.404 T
Ruvb
Rb =
q LL = 0.875 =
Rb u=
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
0
x L x 16
0
0
7T
qu LL = 1.575 =
x 2 x 2
12.6 T
x 2 x 2
0
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 23.405 T Menghitung Vu total Vu total = Vu DL + = 69.808 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
51.6 T
φ*Vs perlu = Vu total = 69.808 = 18.208 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
φ*Vc 51.6
-
12 * s * 300
jarak fy * 240 *
* 10000 * 10000
300 d 1290
= 23.343 T Vs terpasang 23.3432900532
> > OK
Vs perlu 18.208
d 10000 1290 10000
qu DL
*
L 2 16 2
*
x
-
qu DL
= 5.8254
*
*
0
-
5.8254
-
1
*
-
1
L 2 16 2
Pu BGT =
1.9404
=
0 T.m
= =
Mu q DL 0 0
Mu q DL =
= Mu pDL = = =
n diafragma 2 4 2 0 T.m *
= 0.3564
*
= Mu LL =
Mu total =
x²
Pu diafragma
*
x
*
2.798081
*
0
*
x
-
qu LL
x²
*
0
-
0.3564
* 2 * 2
*
L
x
*
x
*
16
L 16
0
*
0
+ +
Mu qLL 0
0
0 T.m
qu LL
Mu qLL =
* 2 * 2
0
0 T.m
+ + T.m
Mu pDL 0
+ +
Mu LL 0
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 2642.1 mm²
29 sejumlah π * 3.1416
*
T
= = =
As * fy 2642.1 * 320 845465.414934 N
a
=
T 0.85 * fc' * 845465.414934085 0.85 * 25 * 49.733 mm
= = Mu terpasang
4 d²
*
n
841
*
4
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
845465.414934
*
1290
-
= =
855701207.792 N. Mm 85.5701207792 T.m
Mu terpasang 85.5701207792
> >
Mu perlu (Mu total) 0
DESAIN OK
a 2 49.733 2
kontrol tulangan rangkap Mu = 0.000 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
=
0
ξ cu ξ cu + 0.003 0.003 + 0.0016 841.3 mm
T.m
ξy
=
ξ cu
= =
x max = 75% a max = β1 C max = 0.85
xb x max fc'
As tulangan tunggal As = Cmax = fy Mu max = Cmax
kontrol
0.000 0.8
d
= = b
75% 0.85 a max
9E+06 320
=
-
a max 2
x x =
841.3043478 630.9782609 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
9117635.87
> >
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
1400
-
Mn perlu 0
536.33 2
=
0
fy E
=
320 200000
=
0.0016
800
x
536.33
=
9117635.86957 N
=
10319652457 N.mm
tidak diperlukan tulangan rangkap
Rekapitulasi Penulangan Girder Tepi per segmen
2m
2m P BGT
P dia q DL
q LL
Rva
Ra
Segmen ( 0 - 2) m Jarak x= 2m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra = q LL x L P BGT x L 2 2 L + = 0.875 x 16 6.0025 x 16 2 2 16 = 12.252 T
Rb =
= 0.875
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
2
x L x 16
2
2
= 7.7503 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x Ra u= qu LL x L 16 2 2 L + = 1.575 x 16 10.805 x 16 2 2 16 = 22.054 T Menghitung Vu DL Vu DL = Ruva = 34.636 T
q LL
Pu dia
Rb u=
qu LL = 1.575 = 13.951 T
x 2 x 2
2
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 22.054 T Menghitung Vu total Vu total = Vu DL + = 56.69 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
51.6 T
φ*Vs perlu = Vu total = 56.6898375 = 5.0898 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 300
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
300 d 1290
= 23.343 T Kontrol
Vs terpasang 23.3432900532
> > OK
Vs perlu 5.0898375
d 10000 1290 10000
qu DL
*
= 5.8254
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
2
-
5.8254
-
1
*
-
1
L 2 16 2
Pu BGT 1.9404
* 2 * 2
x²
Pu diafragma
*
x
*
2.798081
*
2
*
x
-
qu LL
x²
*
2
-
0.3564
* 2 * 2
*
L
x
*
x
*
16
L 16
2
*
2
Mu pDL 5.596162
+ +
Mu qLL 4.9896
4
= 81.556 T.m Mu pDL =
n diafragma 2 = 4 2 = 5.5962 T.m qu LL
*
= 0.3564
*
Mu qLL =
4
= 4.9896 T.m Mu LL = =
= 3.3957 T.m Mu total = = =
Mu q DL 81.55602 95.537482
+ + T.m
+ +
Mu LL 3.3957
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 3963.1 mm² T
= = =
a
=
*
841
*
n
*
6
As * fy 3963.1 * 320 1268198.1224 N
= =
0.8
*
T
*
d
-
=
0.8
*
1268198.1224
*
1290
-
= =
Kontrol
3.1416
6
T 0.85 * fc' * 1268198.12240113 0.85 * 25 * 74.6 mm
=
Mu terpasang
29 sejumlah π d² *
bw 800
1270937486.37 N. Mm 127.093748637 T.m
Mu terpasang 127.093748637
> >
Mu perlu (Mu total) 95.537482
DESAIN OK
a 2 74.6 2
kontrol tulangan rangkap Mu = 95.537 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
95.537 0.8
119.4218525 T.m
ξ cu ξ cu + 0.003 0.003 + 0.0016 841.3 mm
ξy
=
ξ cu
= =
x max = 75% a max = β1 C max = 0.85
xb x max fc'
= = b
75% 0.85 a max
As tul tunggal As = Cmax fy
=
9E+06 320
=
Mu max = Cmax
d
-
a max 2
kontrol
=
x x =
841.3 630.98 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
9E+06
> >
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
1400
-
Mn perlu 1194218525
536.33 2
=
1194218525
fy E
=
320 200000
=
0.0016
800
x
536.33
=
9117635.86957 N
=
10319652457 N.mm
tidak diperlukan tulangan rangkap
4m
4m P BGT
P dia q DL
q LL
Rva
Ra
Segmen (2 - 4) m Jarak x= 4m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra = q LL x L P BGT x L 4 2 L + = 0.875 x 16 6.0025 x 16 4 2 16 = 11.502 T
Rb =
= 0.875
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
4
x L x 16
4
4
= 8.5006 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x Ra u= qu LL x L L 4 2 L + = 1.575 x 16 10.805 x 16 4 2 16 = 20.703 T Menghitung Vu DL Vu DL = Ruva = 23.313 T
q LL
Pu dia
Rb u=
qu LL = 1.575 = 15.301 T
x 2 x 2
4
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 20.703 T Menghitung Vu total Vu total = Vu DL + = 44.016 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
51.6 T
φ*Vs perlu = Vu total = 44.016275 = -7.5837 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
φ*Vc 51.6
-
12 * s * -900
jarak fy * 240 *
* 10000 * 10000
-900 d 1290
= -7.7811 T Kontrol
Vs terpasang -7.7810966844
> > OK
Vs perlu -7.583725
d 10000 1290 10000
qu DL
*
= 5.8254
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
4
-
5.8254
-
1
*
Pu diafragma
*
x
-
1
*
2.798081
*
4
L 2 16 2
*
x
-
qu LL
x²
*
4
-
0.3564
* 2 * 2
Pu BGT
*
L
x
*
x
1.9404
*
16
L 16
4
*
4
Mu pDL 11.192324
+ +
Mu qLL 8.5536
* 2 * 2
x² 16
= 139.81 T.m Mu pDL =
n diafragma 2 = 4 2 = 11.192 T.m qu LL
*
= 0.3564
*
Mu qLL =
16
= 8.5536 T.m Mu LL = =
= 5.8212 T.m Mu total = = =
Mu q DL 139.81032 165.377444
+ + T.m
+ +
Mu LL 5.8212
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 6605.2 mm²
3.1416
*
T
= = =
As * fy 6605.2 * 320 2113663.53734 N
a
=
T 0.85 * fc' * 2113663.53733521 0.85 * 25 * 124.33 mm
= = Mu terpasang
841
10 *
n
*
10
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
2113663.53734
*
1290
-
= =
Kontrol
29 sejumlah π d² *
2076181392.9 N. Mm 207.61813929 T.m
Mu terpasang 207.61813929
> >
Mu perlu (Mu total) 165.377444
DESAIN OK
a 2 124.33 2
kontrol tulangan rangkap Mu = 165.377 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
165.377 0.8
206.721805
T.m
ξy
=
ξ cu ξ cu + 0.003 0.003 + 0.0016 841.3 mm ξ cu
= =
x max = 75% a max = β1 C max = 0.85
xb x max fc'
= = b
75% 0.85 a max
As tul tunggal As = Cmax fy
=
9E+06 320
=
Mu max = Cmax
d
-
a max 2
kontrol
=
x x =
841.3 630.98 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
9E+06
> >
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
1400
-
Mn perlu 2067218050
536.33 2
=
2067218050
fy E
=
320 200000
=
0.0016
800
x
536.33
=
9117635.86957 N
=
10319652457 N.mm
tidak diperlukan tulangan rangkap
6m
6m
P dia
P BGT q DL
Rva
Ra
Segmen (4 - 6) m Jarak x= 6m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra = q LL x L P BGT x L 6 2 L + = 0.875 x 16 6.0025 x 16 6 2 16 = 10.752 T
q LL Rb =
= 0.875
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
6
x L x 16
6
6
= 9.2509 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x Ra u= qu LL x L L 6 2 L + = 1.575 x 16 10.805 x 16 6 2 16 = 19.353 T Menghitung Vu DL Vu DL = Ruva = 11.545 T
q LL
Pu dia
Rb u=
qu LL = 1.575 = 16.652 T
x 2 x 2
6
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 19.353 T Menghitung Vu total Vu total = Vu DL + = 30.898 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
51.6 T
φ*Vs perlu = Vu total = 30.8981125 = 20.702 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 300
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
300 d 1290
= 23.343 T Kontrol
Vs terpasang 23.3432900532
> > OK
Vs perlu 20.7018875
d 10000 1290 10000
qu DL
*
= 5.8254
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
6
-
5.8254
-
1
*
Pu diafragma
*
x
-
1
*
2.798081
*
6
L 2 16 2
*
x
-
qu LL
x²
*
6
-
0.3564
* 2 * 2
Pu BGT
*
L
x
*
x
1.9404
*
16
L 16
6
*
6
Mu pDL 16.788486
+ +
Mu qLL 10.692
* 2 * 2
x² 36
= 174.76 T.m Mu pDL =
n diafragma 2 = 4 2 = 16.788 T.m qu LL
*
= 0.3564
*
Mu qLL =
36
= 10.692 T.m Mu LL = =
= 7.2765 T.m Mu total = = =
Mu q DL 174.7629 209.519886
+ + T.m
+ +
Mu LL 7.2765
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 9247.3 mm²
3.1416
*
T
= = =
As * fy 9247.3 * 320 2959128.95227 N
a
=
T 0.85 * fc' * 2959128.9522693 0.85 * 25 * 174.07 mm
= = Mu terpasang
841
14 *
n
*
14
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
2959128.95227
*
1290
-
= =
Kontrol
29 sejumlah π d² *
2847787098.6 N. Mm 284.77870986 T.m
Mu terpasang 284.77870986
> >
Mu perlu (Mu total) 209.519886
DESAIN OK
a 2 174.07 2
kontrol tulangan rangkap Mu = 209.520 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
209.520 0.8
261.8998575 T.m
ξ cu ξ cu + 0.003 0.003 + 0.0016 841.3 mm
ξy
=
ξ cu
= =
x max = 75% a max = β1 C max = 0.85
xb x max fc'
= = b
75% 0.85 a max
As tul tunggal As = Cmax fy
=
9E+06 320
=
Mu max = Cmax
d
-
a max 2
kontrol
=
x x =
841.3 630.98 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
9E+06
> >
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
1400
-
Mn perlu 2618998575
536.33 2
=
2618998575
fy E
=
320 200000
=
0.0016
800
x
536.33
=
9117635.86957 N
=
10319652457 N.mm
tidak diperlukan tulangan rangkap
8m
8m
P dia
P BGT q DL
q LL
Rva
Ra
Segmen (6 - 8) m Jarak x= 8m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra = q LL x L P BGT x L 8 2 L + = 0.875 x 16 6.0025 x 16 8 2 16 = 10.001 T
Rb =
= 0.875
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
8
x L x 16
8
8
= 10.001 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x Ra u= qu LL x L L 8 2 L + = 1.575 x 16 10.805 x 16 8 2 16 = 18.002 T Menghitung Vu DL Vu DL = Ruva = 0.2223 T
q LL
Pu dia
Rb u=
qu LL = 1.575 = 18.002 T
x 2 x 2
8
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 18.002 T Menghitung Vu total Vu total = Vu DL + = 18.225 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
Dipasang sengkang As
= 226.19
φ*Vc 51.6
-
12 * s * 200
jarak fy * 240 *
* 10000 * 10000
200 d 1290
= 35.015 T Kontrol
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 18.22455 = 33.375 T
φ*Vs pasang =
fc'
Vs terpasang 35.0149350799
> > OK
Vs perlu 33.37545
Dipasang sengka
qu DL
*
= 5.8254
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
8
-
5.8254
-
1
*
Pu diafragma
*
x
-
1
*
2.798081
*
8
L 2 16 2
*
x
-
qu LL
x²
*
8
-
0.3564
* 2 * 2
Pu BGT
*
L
x
*
x
1.9404
*
16
L 16
8
*
8
Mu pDL 22.384648
+ +
Mu qLL 11.4048
* 2 * 2
x² 64
= 186.41 T.m Mu pDL =
n diafragma 2 = 4 2 = 22.385 T.m qu LL
*
= 0.3564
*
Mu qLL =
64
= 11.405 T.m Mu LL = =
= 7.7616 T.m Mu total = = =
Mu q DL 186.41376 227.964808
+ + T.m
+ +
Mu LL 7.7616
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 10568 mm²
3.1416
*
T
= = =
As * fy 10568 * 320 3381861.65974 N
a
=
T 0.85 * fc' * 3381861.65973634 0.85 * 25 * 198.93 mm
= = Mu terpasang
841
16 *
n
*
16
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
3381861.65974
*
1290
-
= =
Kontrol
29 sejumlah π d² *
3220975626.13 N. Mm 322.097562613 T.m
Mu terpasang 322.097562613
> >
Mu perlu (Mu total) 227.964808
DESAIN OK
a 2 198.93 2
kontrol tulangan rangkap Mu = 227.965 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
227.965 0.8
284.95601
T.m
ξy
=
ξ cu ξ cu + 0.003 0.003 + 0.0016 841.3 mm ξ cu
= =
x max = 75% a max = β1 C max = 0.85
xb x max fc'
= = b
75% 0.85 a max
As tul tunggal As = Cmax fy
=
9E+06 320
=
Mu max = Cmax
d
-
a max 2
kontrol
=
x x =
841.3 630.98 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
9E+06
> >
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
1400
-
Mn perlu 2849560100
536.33 2
=
2849560100
fy E
=
320 200000
=
0.0016
800
x
536.33
=
9117635.86957 N
=
10319652457 N.mm
tidak diperlukan tulangan rangkap
8m
8m P dia
P BGT q DL
q LL
Rva
Ra
Segmen (8 - 10) m Jarak x= 8 m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra = q LL x L P BGT x L 8 2 L + = 0.875 x 16 6.0025 x 16 8 2 16 = 10.001 T
Rb =
= 0.875
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
8
x L x 16
8
8
= 10.001 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x Ra u= qu LL x L L 8 2 L + = 1.575 x 16 10.805 x 16 8 2 16 = 18.002 T Menghitung Vu DL Vu DL = - Ruva = -0.2223 T
q LL
Pu dia
Rb u=
qu LL = 1.575 = 18.002 T
x 2 x 2
8
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = -18 T Menghitung Vu total Vu total = Vu DL + = 18.225 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
51.6 T
φ*Vs perlu = Vu total = 18.22455 = 33.375 T Dipasang sengkang φ*Vs pasang =
fc'
12 As
= 226.19
φ*Vc 51.6
-
* s * 200
jarak fy * 240 *
* 10000 * 10000
200 d 1290
= 35.015 T Kontrol
Vs terpasang 35.0149350799
> > OK
Vs perlu 33.37545
d 10000 1290 10000
qu DL
*
= 5.8254
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
8
-
5.8254
-
1
*
Pu diafragma
*
x
-
1
*
2.798081
*
8
L 2 16 2
*
x
-
qu LL
x²
*
8
-
0.3564
* 2 * 2
Pu BGT
*
L
x
*
x
1.9404
*
16
L 16
8
*
8
Mu pDL 22.384648
+ +
Mu qLL 11.4048
* 2 * 2
x² 64
= 186.41 T.m Mu pDL =
n diafragma 2 = 4 2 = 22.385 T.m qu LL
*
= 0.3564
*
Mu qLL =
64
= 11.4048 T.m Mu LL = =
= 7.7616 T.m Mu total = = =
Mu q DL 186.41376 227.964808
+ + T.m
+ +
Mu LL 7.7616
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 10568 mm²
3.1416
*
T
= = =
As * fy 10568 * 320 3381861.65974 N
a
=
T 0.85 * fc' * 3381861.65973634 0.85 * 25 * 198.93 mm
= = Mu terpasang
841
16 *
n
*
16
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
3381861.65974
*
1290
-
= =
Kontrol
29 sejumlah π d² *
3220975626.13 N. Mm 322.097562613 T.m
Mu terpasang 322.097562613
> >
Mu perlu (Mu total) 227.964808
DESAIN OK
a 2 198.93 2
kontrol tulangan rangkap Mu = 227.965 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
227.965 0.8
284.95601
ξ cu ξ cu + 0.003 0.003 + 0.0016 841.3 mm
ξy
T.m
=
ξ cu
= =
x max = 75% a max = β1 C max = 0.85
xb x max fc'
= = b
75% 0.85 a max
As tul tunggal As = Cmax fy
=
9E+06 320
=
Mu max = Cmax
d
-
a max 2
kontrol
=
x x =
841.3 630.98 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
9E+06
> >
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
1400
-
Mn perlu 2849560100
536.33 2
=
2849560100
fy E
=
320 200000
=
0.0016
800
x
536.33
=
9117635.86957 N
=
10319652457 N.mm
tidak diperlukan tulangan rangkap
6m
6m P dia
P BGT q DL
q LL
Rva
Ra
Segmen (10 - 12) m Jarak x= 6 m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra = q LL x L P BGT x L 6 2 L + = 0.875 x 16 6.0025 x 16 6 2 16 = 10.752 T
Rb =
= 0.875
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
6
x L x 16
6
6
= 9.2509 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x Ra u= qu LL x L L 6 2 L + = 1.575 x 16 10.805 x 16 6 2 16 = 19.353 T Menghitung Vu DL Vu DL = - Ruva = -11.545 T
q LL
Pu dia
Rb u=
qu LL = 1.575 = 16.652 T
x 2 x 2
6
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = -19.353 T Menghitung Vu total Vu total = Vu DL + = 30.898 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
51.6 T
φ*Vs perlu = Vu total = 30.8981125 = 20.702 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 300
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
300 d 1290
= 23.343 T Kontrol
Vs terpasang 23.3432900532
> > OK
Vs perlu 20.7018875
d 10000 1290 10000
qu DL
*
= 5.8254
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
6
-
5.8254
-
1
*
Pu diafragma
*
x
-
1
*
2.798081
*
6
L 2 16 2
*
x
-
qu LL
x²
*
6
-
0.3564
* 2 * 2
Pu BGT
*
L
x
*
x
1.9404
*
16
L 16
6
*
6
Mu pDL 16.788486
+ +
Mu qLL 10.692
* 2 * 2
x² 36
= 174.76 T.m Mu pDL =
n diafragma 2 = 4 2 = 16.788 T.m qu LL
*
= 0.3564
*
Mu qLL =
36
= 10.692 T.m Mu LL = =
= 7.2765 T.m Mu total = = =
Mu q DL 174.7629 209.519886
+ + T.m
+ +
Mu LL 7.2765
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 9247.3 mm²
3.1416
*
T
= = =
As * fy 9247.3 * 320 2959128.95227 N
a
=
T 0.85 * fc' * 2959128.9522693 0.85 * 25 * 174.07 mm
= = Mu terpasang
841
14 *
n
*
14
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
2959128.95227
*
1290
-
= =
Kontrol
29 sejumlah π d² *
2847787098.6 N. Mm 284.77870986 T.m
Mu terpasang 284.77870986
> >
Mu perlu (Mu total) 209.519886
DESAIN OK
a 2 174.07 2
kontrol tulangan rangkap Mu = 209.520 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
209.520 0.8
261.8998575 T.m
ξ cu ξ cu + 0.003 0.003 + 0.0016 841.3 mm
ξy
=
ξ cu
= =
x max = 75% a max = β1 C max = 0.85
xb x max fc'
= = b
75% 0.85 a max
As tul tunggal As = Cmax fy
=
9E+06 320
=
Mu max = Cmax
d
-
a max 2
kontrol
=
x x =
841.3 630.98 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
9E+06
> >
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
1400
-
Mn perlu 2618998575
536.33 2
=
2618998575
fy E
=
320 200000
=
0.0016
800
x
536.33
=
9117635.86957 N
=
10319652457 N.mm
tidak diperlukan tulangan rangkap
4m
4m P BGT
P dia q DL
q LL
Rva
Ra
Segmen (12 - 14) m Jarak x= 4 m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra = q LL x L P BGT x L 4 2 L + = 0.875 x 16 6.0025 x 16 4 2 16 = 11.502 T
Rb =
= 0.875
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
4
x L x 16
4
4
= 8.5006 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x Ra u= qu LL x L L 4 2 L + = 1.575 x 16 10.805 x 16 4 2 16 = 20.703 T Menghitung Vu DL Vu DL = - Ruva = -23.313 T
q LL
Pu dia
Rb u=
qu LL = 1.575 = 15.301 T
x 2 x 2
4
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = -20.703 T Menghitung Vu total Vu total = Vu DL + = 44.016 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
51.6 T
φ*Vs perlu = Vu total = 44.016275 = 7.5837 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
φ*Vc 51.6
-
12 * s * 300
jarak fy * 240 *
* 10000 * 10000
300 d 1290
= 23.343 T Kontrol
Vs terpasang 23.3432900532
> > OK
Vs perlu 7.583725
d 10000 1290 10000
qu DL
*
= 5.8254
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
4
-
5.8254
-
1
*
Pu diafragma
*
x
-
1
*
2.798081
*
4
L 2 16 2
*
x
-
qu LL
x²
*
4
-
0.3564
* 2 * 2
Pu BGT
*
L
x
*
x
1.9404
*
16
L 16
4
*
4
Mu pDL 11.192324
+ +
Mu qLL 8.5536
* 2 * 2
x² 16
= 139.81 T.m Mu pDL =
n diafragma 2 = 4 2 = 11.192 T.m qu LL
*
= 0.3564
*
Mu qLL =
16
= 8.5536 T.m Mu LL = =
= 5.8212 T.m Mu total = = =
Mu q DL 139.81032 165.377444
+ + T.m
+ +
Mu LL 5.8212
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 6605.2 mm²
3.1416
*
T
= = =
As * fy 6605.2 * 320 2113663.53734 N
a
=
T 0.85 * fc' * 2113663.53733521 0.85 * 25 * 124.33 mm
= = Mu terpasang
841
10 *
n
*
10
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
2113663.53734
*
1290
-
= =
Kontrol
29 sejumlah π d² *
2076181392.9 N. Mm 207.61813929 T.m
Mu terpasang 207.61813929
> >
Mu perlu (Mu total) 165.377444
DESAIN OK
a 2 124.33 2
kontrol tulangan rangkap Mu = 165.377 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
165.377 0.8
206.721805
T.m
ξy
=
ξ cu ξ cu + 0.003 0.003 + 0.0016 841.3 mm ξ cu
= =
x max = 75% a max = β1 C max = 0.85
xb x max fc'
= = b
75% 0.85 a max
As tul tunggal As = Cmax fy
=
9E+06 320
=
Mu max = Cmax
d
-
a max 2
kontrol
=
x x =
841.3 630.98 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
9E+06
> >
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
1400
-
Mn perlu 2067218050
536.33 2
=
2067218050
fy E
=
320 200000
=
0.0016
800
x
536.33
=
9117635.86957 N
=
10319652457 N.mm
tidak diperlukan tulangan rangkap
2m
2m P BGT
P dia q DL
q LL
Rva
Ra
Segmen (14 - 16) m Jarak x= 2 m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra = q LL x L P BGT x L 2 2 L + = 0.875 x 16 6.0025 x 16 2 2 16 = 12.252 T
Rb =
= 0.875
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
2
x L x 16
2
2
= 7.7503 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x Ra u= qu LL x L L 2 2 L + = 1.575 x 16 10.805 x 16 2 2 16 = 22.054 T Menghitung Vu DL Vu DL = - Ruva = -34.636 T
q LL
Pu dia
Rb u=
qu LL = 1.575 = 13.951 T
x 2 x 2
2
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = -22.054 T Menghitung Vu total Vu total = Vu DL + = 56.69 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
51.6 T
φ*Vs perlu = Vu total = 56.6898375 = 5.0898 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 300
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
300 d 1290
= 23.343 T Kontrol
Vs terpasang 23.3432900532
> > OK
Vs perlu 5.0898375
d 10000 1290 10000
qu DL
*
= 5.8254
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
2
-
5.8254
-
1
*
-
1
L 2 16 2
Pu BGT 1.9404
* 2 * 2
x²
Pu diafragma
*
x
*
2.798081
*
2
*
x
-
qu LL
x²
*
2
-
0.3564
* 2 * 2
*
L
x
*
x
*
16
L 16
2
*
2
Mu pDL 5.596162
+ +
Mu qLL 4.9896
4
= 81.556 T.m Mu pDL =
n diafragma 2 = 4 2 = 5.5962 T.m qu LL
*
= 0.3564
*
Mu qLL =
4
= 4.9896 T.m Mu LL = =
= 3.3957 T.m Mu total = = =
Mu q DL 81.55602 95.537482
+ + T.m
+ +
Mu LL 3.3957
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 3963.1 mm² T
= = =
a
=
*
841
*
n
*
6
As * fy 3963.1 * 320 1268198.1224 N
= =
0.8
*
T
*
d
-
=
0.8
*
1268198.1224
*
1290
-
= =
Kontrol
3.1416
6
T 0.85 * fc' * 1268198.12240113 0.85 * 25 * 74.6 mm
=
Mu terpasang
29 sejumlah π d² *
bw 800
1270937486.37 N. Mm 127.093748637 T.m
Mu terpasang 127.093748637
> >
Mu perlu (Mu total) 95.537482
DESAIN OK
a 2 74.6 2
kontrol tulangan rangkap Mu = 95.537 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
95.537 0.8
119.4218525 T.m
ξ cu ξ cu + 0.003 0.003 + 0.0016 841.3 mm
ξy
=
ξ cu
= =
x max = 75% a max = β1 C max = 0.85
xb x max fc'
= = b
75% 0.85 a max
As tul tunggal As = Cmax fy
=
9E+06 320
=
Mu max = Cmax
d
-
a max 2
kontrol
=
x x =
841.3 630.98 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
9E+06
> >
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
1400
-
Mn perlu 1194218525
536.33 2
=
1194218525
fy E
=
320 200000
=
0.0016
800
x
536.33
=
9117635.86957 N
=
10319652457 N.mm
tidak diperlukan tulangan rangkap
P dia
P BGT q DL
q LL
Rva Segmen (16 -18) m Jarak x= 0 m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra = q LL x L P BGT x L 0 2 L + = 0.875 x 16 6.0025 x 16 0 2 16 = 13.003 T Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x Ra u= qu LL x L L 0 2 L + = 1.575 x 16 10.805 x 16 0 2 16 = 23.405 T Menghitung Vu DL Vu DL = - Ruvb = -43.605 T
Ra
Rb =
q LL = 0.875 =
Rb u=
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
0
x L x 16
0
0
7T
qu LL = 1.575 =
x 2 x 2
12.6 T
x 2 x 2
0
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = -23.405 T Menghitung Vu total Vu total = Vu DL + = 67.01 T φ *Vc=
0.6
*
=
0.6
*
= φ*Vs perlu = = =
1 6 1 6
fc'
*
bw
*
25
*
800
*
51.6 T Vu total 67.009919 15.41 T
Dipasang sengkang φ*Vs pasang =
Vu LL
As
= 226.19
φ*Vc 51.6
-
12 * s * 300
jarak fy * 240 *
* 10000 * 10000
300 d 1290
= 23.343 T Kontrol
Vs terpasang 23.3432900532
> > OK
Vs perlu 15.409919
d 10000 1290 10000
qu DL
*
L 2 16 2
*
x
-
qu DL
= 5.8254
*
*
0
-
5.8254
-
1
*
-
1
L 2 16 2
Pu BGT =
1.9404
=
0 T.m
= =
Mu q DL 0 0
Mu q DL =
= Mu pDL = = =
n diafragma 2 4 2 0 T.m *
= 0.3564
*
= Mu LL =
Mu total =
x²
Pu diafragma
*
x
*
2.798081
*
0
*
x
-
qu LL
x²
*
0
-
0.3564
* 2 * 2
*
L
x
*
x
*
16
L 16
0
*
0
+ +
Mu qLL 0
0
0 T.m
qu LL
Mu qLL =
* 2 * 2
0
0 T.m
+ + T.m
Mu pDL 0
+ +
Mu LL 0
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 2642.1 mm²
3.1416
*
T
= = =
As * fy 2642.1 * 320 845465.414934 N
a
=
T 0.85 * fc' * 845465.414934085 0.85 * 25 * 49.733 mm
= = Mu terpasang
841
4 *
n
*
4
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
845465.414934
*
1290
-
= =
Kontrol
29 sejumlah π d² *
855701207.792 N. Mm 85.5701207792 T.m
Mu terpasang 85.5701207792
> >
Mu perlu (Mu total) 0
DESAIN OK
a 2 49.733 2
kontrol tulangan rangkap Mu = 0.000 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
0.000 0.8
0
ξ cu ξ cu + 0.003 0.003 + 0.0016 841.3 mm
T.m
ξy
=
ξ cu
= =
x max = 75% a max = β1 C max = 0.85
xb x max fc'
= = b
75% 0.85 a max
As tul tunggal As = Cmax fy
=
9E+06 320
=
Mu max = Cmax
d
-
a max 2
kontrol
=
x x =
841.3 630.98 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
9E+06
> >
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
1400
-
Mn perlu 0
536.33 2
=
0
fy E
=
320 200000
=
0.0016
800
x
536.33
=
9117635.86957 N
=
10319652457 N.mm
tidak diperlukan tulangan rangkap
9m
9m
P dia
P BGT q DL
Rva
Ra
Segmen (8- 9) m Jarak x= 9m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra = q LL x L P BGT x L 9 2 L + = 0.875 x 16 6.0025 x 16 9 2 16 = 9.6261 T
Rb =
= 0.875
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
6.0025
L
+
Pu BGT
16
+
10.805
x L x 16
= 10.3764 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Ra u= qu LL x L Pu BGT x L 9 2 L + = 1.575 x 16 10.805 x 16 9 2 16 = 17.327 T Menghitung Vu DL Vu DL = Ruva = -5.8838 T
q LL
Pu dia
Rb u=
qu LL = 1.575 = 18.6775 T
x 2 x 2
x L x 16
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 18.678 T Menghitung Vu total Vu total = Vu DL + = 12.794 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
51.6 T
φ*Vs perlu = Vu total = 12.79373125 = 38.806 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 300
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
300 d 1290
= 23.343 T Kontrol
Vs terpasang 23.3432900532
> > OK
Vs perlu 38.80626875
d 10000 1290 10000
qu DL
*
= 5.8254
*
Mu q DL =
= Mu pDL =
L 2 16 2
*
x
-
qu DL
*
9
-
5.8254
-
1
*
Pu diafragma
*
x
-
1
*
2.798081
*
9
L 2 16 2
*
x
-
qu LL
x²
*
9
-
0.3564
* 2 * 2
Pu BGT
*
L
x
*
x
1.9404
*
16
L 16
9
*
9
+ +
Mu pDL 25.182729
+ +
Mu qLL 11.2266
x² 81
183.5 T.m
n diafragma 2 = 4 2 = 25.183 T.m qu LL
*
= 0.3564
*
Mu qLL =
* 2 * 2
81
= 11.227 T.m Mu LL = =
= 7.6403 T.m Mu total = = =
Mu q DL 183.501045 227.550699
T.m
+ +
Mu LL 7.640325
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 10568 mm²
3.1416
*
T
= = =
As * fy 10568 * 320 3381861.659736 N
a
=
T 0.85 * fc' * 3381861.65973634 0.85 * 25 * 198.93 mm
= = Mu terpasang
16 d²
*
n
841
*
16
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
3381861.65974
*
1290
-
= =
Kontrol
29 sejumlah π *
3220975626.128 N. Mm 322.0975626128 T.m
Mu terpasang 322.097562613
> >
Mu perlu (Mu total) 227.550699
DESAIN OK
a 2 198.93 2
kontrol tulangan rangkap Mu = 227.551 Mn perlu = Mu φ xb d xb 1290 xb
=
T.m =
ξ cu + 0.003 0.003 + 841.3 mm ξ cu
= =
227.551 0.8
284.43837375 T.m
ξy
=
ξ cu
=
2844383737.5
fy E
=
320 200000
=
0.0016
800
x
536.332
=
9117635.86957 N
0.0016
x max = 75% a max = β1 C max = 0.85
xb x max fc'
= = b
75% 0.85 a max
As tul tunggal As = Cmax fy
=
9117636 320
=
Mu max = Cmax
d
-
a max 2
kontrol
=
x x =
841.3043 630.9783 0.85
28493 mm²
=
Mu tulangan tunggal 10319652457.0977
= = x
630.98 mm 536.33 mm 25 x
=
284.93 cm²
9117636 1400
> >
-
Mn perlu 2844383737.5
536.33 2
=
10319652457.1 N.mm
tidak diperlukan tulangan rangkap
q LL
9 9
9 9
Segmen (m) Jarak x (m)
( 0 - 2) 2
(2 - 4) 4
Rekapitulasi Penulangan Girder Tepi per segmen (4 - 6) (6 - 8) (8 - 10) 6 8 8
Tulangan geser D 12 - 300 mm D 12 - 300 mm D 12 - 300 mm D 12 - 300 mm D 12 - 300 mm Tulangan Longitudinal Tulangan Rangkap
6 D 29
10 D 29
14 D 29
16 D 29
16 D 29
tidak perlu tulangan rangkap
tidak perlu tulangan rangkap
tidak perlu tulangan rangkap
tidak perlu tulangan rangkap
tidak perlu tulangan rangkap
er Tepi per segmen (10 - 12) 6
(12 - 14) 4
(14 - 16) 2
(16 -18) 0
D 12 - 300 mm D 12 - 300 mm D 12 - 300 mm D 12 - 200 mm 14 D 29
10 D 29
6 D 29
4 D 29
tidak perlu tulangan rangkap
tidak perlu tulangan rangkap
tidak perlu tulangan rangkap
tidak perlu tulangan rangkap
PERENCANAAN GIRDER A. Pembebaban Gelagar Bentang jembatan Tinggi girder Lebar girder
L= h= bw =
Mutu Beton Tulangan utama Tulangan sengkang
fc' = fy = fy =
1. Beban Mati Berat Plat
16000 mm 1400 mm 800 mm
d' d
= =
25 320 240
= = =
ts x 0.25 x 0.57 T/m'
(s-bw) 0.95
x x
BJ Beton 2.4
Berat Aspal
= = =
ta x 0.07 x 0.2695 T/m'
s 1.75
x x
BJ Aspal 2.2
Berat Girder
= = =
h girder x 1.4 x 2.688 T/m'
bw 0.8
x x
BJ Beton 2.4
= =
3.22175 T/m' 3.22175 x
1.3
=
4.188275 T/m'
b diafragma 0.3
x x
(s-bw) 0.95
q DL qu DL
P diafragma
= h diafragma = 0.5 = 0.43125 T
110 mm 1290 mm
x x
x x
BJ Beton 2.4
Pu diafragma
x x
Ku 1.3
= = =
BTR x 0.9 x 1.575 T/m'
s 1.75
Beban air hujan
= = =
ts x 0.05 x 0.08575 T/m'
s 1.75
x x
q LL qu LL
= =
1.575 T/m' 1.575 x
1.8
=
P BGT
= = =
BGT 4.9 12.005 T
x x
s 1.75
x x
Pu BGT
= = =
P BGT 12.005 21.609 T
x x
Ku 1.8
2. Beban Hidup Beban merata BTR
= P diafragma = 0.43125 = 0.560625 T
BJ air 0.98
2.835 T/m'
KD 1.4
BEBAN MATI (DL) Menghitung Rva dan Rvb akibat beban merata q DL
=
2.939 T/m'
A
B
L= Rva =
q DL = 2.939
x 2 x 2
L
Rvb =
16
q DL = 2.939
= 23.512 T
16 m x 2 x 2
L
Segmen Jarak Menghitung Ra dan Ra =
16
= 23.512 T =
Menghitung Rva dan Rvb akibat beban terpusat Pdia = A
Rva =
P dia = 0.342 =
Rva =
x 2 x 2
n dia
B
Rvb =
5
= 0.342
0.855 T 23.512 T 0.855 T 24.367 T
P dia
= Rvb =
0.855 T 23.512 T 0.855 T 24.367 T
x 2 x 2
0.342 T
=
Menghitung Ra u da Ra u=
n dia
=
5
= Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL =
Menghitung Ruva dan Ruvb akibat beban merata qu DL =
3.8207 T/m'
A
B
L= Ruva = qu DL = 4.1883
x 2 x 2
L
Ruvb = qu DL
16
= 4.1883
= 33.506 T
Menghitung Vu total Vu total =
16 m x 2 x 2
L 16
= 33.506 T φ*Vs perlu =
Menghitung Ruva dan Ruvb akibat beban terpusat Pu dia = 0.4446 T A
B
Dipasang sengk φ*Vs pasang =
Ruva = Pu dia = 0.5606 = 1.4016 T
x 2 x 2
n dia 5
Rivb =
Pu dia
= 0.5606
x 2 x 2
n dia 5
= 1.4016 T Kontrol
Ruva = 33.506 T 1.4016 T 34.908 T
Ruvb = 33.506 T 1.4016 T 34.908 T
Mu q DL =
Mu pDL =
Mu qLL =
Mu LL =
Mu total
=
Dipasang tulangan m As terpasang
Mu terpasang
Kontrol
P dia
P BGT q DL
Rva
q LL
Ra
Segmen
0m x= 0m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 0 2 L + 1.6625 x 16 12.005 x 16 0 2 16 25.305 T Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 0 2 L + 2.9925 x 16 21.609 x 16 0 2 16 45.549 T Menghitung Vu DL Vu DL = Ruva = = 34.908 T
Ruvb
Rb =
q LL = 1.6625 =
Rb u=
L
+
P BGT
16
+
12.005
x L x 16
0
13.3 T
qu LL = 2.9925 =
x 2 x 2
Segmen Jarak Menghitung Ra dan R 0 Ra =
23.94 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 0 Ra u= 0
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 45.549 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 80.457 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 80.4567625 = 28.857 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 225
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
φ*Vs perlu =
225 d
Dipasang sengk φ*Vs pasang =
1290
= 31.124 T Vs terpasang 31.1243867376
> > OK
Vs perlu 28.8567625
Kontrol
qu DL
*
L 2 16 2
*
x
-
qu DL
= 4.1883
*
*
0
-
4.1883
-
1
*
-
1
L 2 16 2
Pu BGT =
21.609
=
0 T.m
= = =
Mu q DL 0 0
Mu q DL =
= Mu pDL = = =
= 2.835
*
Mu LL =
Mu total
n diafragma 2 4 2 0 T.m *
=
x²
Pu diafragma
*
x
*
0.560625
*
0
*
x
-
qu LL
x²
*
0
-
2.835
* 2 * 2
*
L
x
*
x
*
16
L 16
0
*
0
+ +
Mu qLL 0
Mu q DL =
0
0 T.m
qu LL
Mu qLL =
* 2 * 2
Mu pDL =
Mu qLL =
0
0 T.m
+ + T.m
Mu pDL 0
Mu LL =
+ +
Mu LL 0
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 2642.1 mm²
29 sejumlah π d² * 3.1416
*
T
= = =
As * fy 2642.1 * 320 845465.414934 N
a
=
T 0.85 * fc' * 845465.414934085 0.85 * 25 * 49.733 mm
= = Mu terpasang
841
4 *
n
*
4
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
845465.414934
*
1290
-
= =
Dipasang tulangan m As terpasang
a 2 49.733 2
Mu terpasang
855701207.792 N. Mm 85.5701207792 T.m
Mu terpasang 85.5701207792
> >
Mu perlu (Mu total) 0
DESAIN OK
Kontrol
2m
2m P BGT
P dia q DL
q LL
Rva
Ra
Segmen
( 0 - 2) m x= 2m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 2 2 L + 1.6625 x 16 12.005 x 16 2 2 16 23.804 T
Rb =
= 1.6625
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
12.005
x L x 16
2
= 14.801 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L 16 2 2 L + 2.9925 x 16 21.609 x 16 2 2 16 42.848 T Menghitung Vu DL Vu DL = Ruva = 25.971 T
q LL
Segmen Jarak Menghitung Ra dan R 2 Ra =
Pu dia
Rb u=
qu LL = 2.9925 = 26.641 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 2 Ra u= 2
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 42.848 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 68.818 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 68.8184625 = 17.218 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 300
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
φ*Vs perlu =
300 d
Dipasang sengka φ*Vs pasang =
1290
= 23.343 T Vs terpasang 23.3432900532
> > OK
Vs perlu 17.2184625
Kontrol
qu DL
*
= 4.1883
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
2
-
4.1883
-
1
*
-
1
L 2 16 2
Pu BGT 21.609
* 2 * 2
x²
Pu diafragma
*
x
*
0.560625
*
2
*
x
-
qu LL
x²
*
2
-
2.835
* 2 * 2
*
L
x
*
x
*
16
L 16
2
*
2
+ +
Mu qLL 39.69
Mu q DL =
4
= 58.636 T.m Mu pDL =
n diafragma 2 = 4 2 = 1.1213 T.m qu LL
*
= 2.835
*
Mu qLL =
= Mu LL = =
Mu pDL =
Mu qLL =
4
39.69 T.m Mu LL =
= 37.816 T.m Mu total = = =
Mu q DL 58.63585 137.26285
+ + T.m
Mu pDL 1.12125
+ +
Mu LL 37.81575
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 5284.2 mm²
29 sejumlah π d² * 3.1416
*
T
= = =
As * fy 5284.2 * 320 1690930.82987 N
a
=
T 0.85 * fc' * 1690930.82986817 0.85 * 25 * 99.467 mm
= = Mu terpasang
841
8 *
n
*
8
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
1690930.82987
*
1290
-
= =
Dipasang tulangan m As terpasang
a 2 99.467 2
Mu terpasang
1677764214.74 N. Mm 167.776421474 T.m
Mu terpasang 167.776421474
> >
Mu perlu (Mu total) 137.26285
DESAIN OK
Kontrol
4m
4m P BGT
P dia q DL
q LL
Rva
Ra
Segmen
(2 - 4) m x= 4m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 4 2 L + 1.6625 x 16 12.005 x 16 4 2 16 22.304 T
Rb =
= 1.6625
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
12.005
x L x 16
4
= 16.301 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 4 2 L + 2.9925 x 16 21.609 x 16 4 2 16 40.147 T Menghitung Vu DL Vu DL = Ruva = 17.594 T
q LL
Segmen Jarak Menghitung Ra dan R 4 Ra =
Pu dia
Rb u=
qu LL = 2.9925 = 29.342 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 4 Ra u= 4
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 40.147 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 57.741 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 57.7407875 = 6.1408 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 300
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
φ*Vs perlu =
300 d
Dipasang sengka φ*Vs pasang =
1290
= 23.343 T Vs terpasang 23.3432900532
> > OK
Vs perlu 6.1407875
Kontrol
qu DL
*
= 4.1883
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
4
-
4.1883
-
1
*
Pu diafragma
*
x
-
1
*
0.560625
*
4
L 2 16 2
*
x
-
qu LL
x²
*
4
-
2.835
* 2 * 2
Pu BGT
*
L
x
*
x
21.609
*
16
L 16
4
*
4
+ +
Mu qLL 68.04
* 2 * 2
x²
Mu q DL =
16
= 100.52 T.m Mu pDL =
n diafragma 2 = 4 2 = 2.2425 T.m qu LL
*
= 2.835
*
Mu qLL =
= Mu LL = =
Mu pDL =
Mu qLL =
16
68.04 T.m Mu LL =
= 64.827 T.m Mu total = = =
Mu q DL 100.5186 235.6281
+ + T.m
Mu pDL 2.2425
+ +
Mu LL 64.827
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 9247.3 mm²
29 sejumlah π d² * 3.1416
*
T
= = =
As * fy 9247.3 * 320 2959128.95227 N
a
=
T 0.85 * fc' * 2959128.9522693 0.85 * 25 * 174.07 mm
= = Mu terpasang
841
14 *
n
*
14
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
2959128.95227
*
1290
-
= =
Dipasang tulangan m As terpasang
a 2 174.07 2
Mu terpasang
2847787098.6 N. Mm 284.77870986 T.m
Mu terpasang 284.77870986
> >
Mu perlu (Mu total) 235.6281
DESAIN OK
Kontrol
6m
6m
P dia
P BGT q DL
Rva
Ra
Segmen
(4 - 6) m x= 6m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 6 2 L + 1.6625 x 16 12.005 x 16 6 2 16 20.803 T
q LL Rb =
= 1.6625
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
12.005
x L x 16
6
= 17.802 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 6 2 L + 2.9925 x 16 21.609 x 16 6 2 16 37.446 T Menghitung Vu DL Vu DL = Ruva = 8.6569 T
q LL
Segmen Jarak Menghitung Ra dan R 6 Ra =
Pu dia
Rb u=
qu LL = 2.9925 = 32.043 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 6 Ra u= 6
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 37.446 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 46.102 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 46.1024875 = -5.4975 T Dipasang sengkang φ*Vs pasang =
fc'
12
As
φ*Vc 51.6
-
jarak
* s = 226.19 * -1250 = -5.6024 T
fy * 240 *
Vs terpasang -5.6023896128
> > OK
* 10000 * 10000
φ*Vs perlu =
-1250 d
Dipasang sengka φ*Vs pasang =
1290
Vs perlu -5.4975125
Kontrol
qu DL
*
= 4.1883
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
6
-
4.1883
-
1
*
Pu diafragma
*
x
-
1
*
0.560625
*
6
L 2 16 2
*
x
-
qu LL
x²
*
6
-
2.835
* 2 * 2
Pu BGT
*
L
x
*
x
21.609
*
16
L 16
6
*
6
+ +
Mu qLL 85.05
* 2 * 2
x²
Mu q DL =
36
= 125.65 T.m Mu pDL =
n diafragma 2 = 4 2 = 3.3638 T.m qu LL
*
= 2.835
*
Mu qLL =
= Mu LL = =
Mu pDL =
Mu qLL =
36
85.05 T.m Mu LL =
= 81.034 T.m Mu total = = =
Mu q DL 125.64825 295.09575
+ + T.m
Mu pDL 3.36375
+ +
Mu LL 81.03375
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 11889 mm² T
= = =
a
=
3.1416
*
841
18 *
n
*
18
= =
0.8
*
T
*
d
-
=
0.8
*
3804594.3672
*
1290
-
= =
Dipasang tulangan m As terpasang
As * fy 11889 * 320 3804594.3672 N T 0.85 * fc' * 3804594.36720338 0.85 * 25 * 223.8 mm
=
Mu terpasang
29 sejumlah π d² *
bw 800
a 2 223.8 2
Mu terpasang
3585754603.45 N. Mm 358.575460345 T.m
Mu terpasang 358.575460345
> >
Mu perlu (Mu total) 295.09575
DESAIN OK
Kontrol
8m
8m
P dia
P BGT q DL
q LL
Rva
Ra
Segmen
(6 - 8) m x= 8m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 8 2 L + 1.6625 x 16 12.005 x 16 8 2 16 19.303 T
Rb =
= 1.6625
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
12.005
x L x 16
8
= 19.303 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 8 2 L + 2.9925 x 16 21.609 x 16 8 2 16 34.745 T Menghitung Vu DL Vu DL = Ruva = 0.2803 T
q LL
Segmen Jarak Menghitung Ra dan R 8 Ra =
Pu dia
Rb u=
qu LL = 2.9925 = 34.745 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 8 Ra u= 8
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 34.745 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 35.025 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 35.0248125 = -16.575 T Dipasang sengkang φ*Vs pasang =
fc'
As
12
jarak
* s * -400
fy * 240 *
Vs terpasang -17.50746754
> > OK
= 226.19
φ*Vc 51.6
-
* 10000 * 10000
φ*Vs perlu =
-400
Dipasang sengkang
d
φ*Vs pasang =
1290
= -17.507 T Vs perlu -16.5751875
Kontrol
qu DL
*
= 4.1883
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
8
-
4.1883
-
1
*
Pu diafragma
*
x
-
1
*
0.560625
*
8
L 2 16 2
*
x
-
qu LL
x²
*
8
-
2.835
* 2 * 2
Pu BGT
*
L
x
*
x
21.609
*
16
L 16
8
*
8
+ +
Mu qLL 90.72
* 2 * 2
x²
Mu q DL =
64
= 134.02 T.m Mu pDL = = =
n diafragma 2 4 2 4.485 T.m qu LL
*
= 2.835
*
Mu qLL =
= Mu LL = =
Mu pDL =
Mu qLL =
64
90.72 T.m Mu LL =
= 86.436 T.m Mu total = = =
Mu q DL 134.0248 315.6658
+ + T.m
Mu pDL 4.485
+ +
Mu LL 86.436
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 13210 mm²
29 sejumlah π d² * 3.1416
*
T
= = =
As * fy 13210 * 320 4227327.07467 N
a
=
T 0.85 * fc' * 4227327.07467043 0.85 * 25 * 248.67 mm
= = Mu terpasang
841
20 *
n
*
20
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
4227327.07467
*
1290
-
= =
Dipasang tulangan m As terpasang
a 2 248.67 2
Mu terpasang
3942124030.56 N. Mm 394.212403056 T.m
Mu terpasang 394.212403056
> >
Mu perlu (Mu total) 315.6658
DESAIN OK
Kontrol
8m
8m P dia
P BGT q DL
q LL
Rva
Ra
Segmen
(8 - 10) m x= 8 m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 8 2 L + 1.6625 x 16 12.005 x 16 8 2 16 19.303 T
Rb =
= 1.6625
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
12.005
x L x 16
8
= 19.303 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 8 2 L + 2.9925 x 16 21.609 x 16 8 2 16 34.745 T Menghitung Vu DL Vu DL = - Ruva = -0.2803 T
q LL
Segmen Jarak Menghitung Ra dan R 8 Ra =
Pu dia
Rb u=
qu LL = 2.9925 = 34.745 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 8 Ra u= 8
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = -34.745 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 35.025 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 35.0248125 = -16.575 T Dipasang sengkang φ*Vs pasang =
fc'
12 As
jarak
* s * -400
fy * 240 *
Vs terpasang -17.50746754
> > OK
= 226.19
φ*Vc 51.6
-
* 10000 * 10000
φ*Vs perlu =
-400 d
Dipasang sengk φ*Vs pasang =
1290
= -17.507 T Vs perlu -16.5751875
Kontrol
qu DL
*
= 4.1883
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
8
-
4.1883
-
1
*
Pu diafragma
*
x
-
1
*
0.560625
*
8
L 2 16 2
*
x
-
qu LL
x²
*
8
-
2.835
* 2 * 2
Pu BGT
*
L
x
*
x
21.609
*
16
L 16
8
*
8
+ +
Mu qLL 90.72
* 2 * 2
x²
Mu q DL =
64
= 134.02 T.m Mu pDL = = =
n diafragma 2 4 2 4.485 T.m qu LL
*
= 2.835
*
Mu qLL =
= Mu LL = =
Mu pDL =
Mu qLL =
64
90.72 T.m Mu LL =
= 86.436 T.m Mu total = = =
Mu q DL 134.0248 315.6658
+ + T.m
Mu pDL 4.485
+ +
Mu LL 86.436
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 13210 mm²
29 sejumlah π d² * 3.1416
*
T
= = =
As * fy 13210 * 320 4227327.07467 N
a
=
T 0.85 * fc' * 4227327.07467043 0.85 * 25 * 248.67 mm
= = Mu terpasang
841
20 *
n
*
20
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
4227327.07467
*
1290
-
= =
Dipasang tulangan m As terpasang
a 2 248.67 2
Mu terpasang
3942124030.56 N. Mm 394.212403056 T.m
Mu terpasang 394.212403056
> >
Mu perlu (Mu total) 315.6658
DESAIN OK
Kontrol
6m
6m P dia
P BGT q DL
q LL
Rva
Ra
Segmen
(10 - 12) m x= 6 m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 6 2 L + 1.6625 x 16 12.005 x 16 6 2 16 20.803 T
Rb =
= 1.6625
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
12.005
x L x 16
6
= 17.802 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 6 2 L + 2.9925 x 16 21.609 x 16 6 2 16 37.446 T Menghitung Vu DL Vu DL = - Ruva = -8.6569 T
q LL
Segmen Jarak Menghitung Ra dan R 6 Ra =
Pu dia
Rb u=
qu LL = 2.9925 = 32.043 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 6 Ra u= 6
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = -37.446 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 46.102 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 46.1024875 = -5.4975 T Dipasang sengkang φ*Vs pasang =
fc'
12
As
φ*Vc 51.6
-
jarak
* s = 226.19 * -1250 = -5.6024 T
fy * 240 *
Vs terpasang -5.6023896128
> > OK
* 10000 * 10000
φ*Vs perlu =
-1250 d
Dipasang sengka φ*Vs pasang =
1290
Vs perlu -5.4975125
Kontrol
qu DL
*
= 4.1883
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
6
-
4.1883
-
1
*
Pu diafragma
*
x
-
1
*
0.560625
*
6
L 2 16 2
*
x
-
qu LL
x²
*
6
-
2.835
* 2 * 2
Pu BGT
*
L
x
*
x
21.609
*
16
L 16
6
*
6
+ +
Mu qLL 85.05
* 2 * 2
x²
Mu q DL =
36
= 125.65 T.m Mu pDL =
n diafragma 2 = 4 2 = 3.3638 T.m qu LL
*
= 2.835
*
Mu qLL =
= Mu LL = =
Mu pDL =
Mu qLL =
36
85.05 T.m Mu LL =
= 81.034 T.m Mu total = = =
Mu q DL 125.64825 295.09575
+ + T.m
Mu pDL 3.36375
+ +
Mu LL 81.03375
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 11889 mm² T
= = =
a
=
3.1416
*
841
18 *
n
*
18
= =
0.8
*
T
*
d
-
=
0.8
*
3804594.3672
*
1290
-
= =
Dipasang tulangan m As terpasang
As * fy 11889 * 320 3804594.3672 N T 0.85 * fc' * 3804594.36720338 0.85 * 25 * 223.8 mm
=
Mu terpasang
29 sejumlah π d² *
bw 800
a 2 223.8 2
Mu terpasang
3585754603.45 N. Mm 358.575460345 T.m
Mu terpasang 358.575460345
> >
Mu perlu (Mu total) 295.09575
DESAIN OK
Kontrol
4m
4m P BGT
P dia q DL
q LL
Rva
Ra
Segmen
(12 - 14) m x= 4 m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 4 2 L + 1.6625 x 16 12.005 x 16 4 2 16 22.304 T
Rb =
= 1.6625
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
12.005
x L x 16
4
= 16.301 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 4 2 L + 2.9925 x 16 21.609 x 16 4 2 16 40.147 T Menghitung Vu DL Vu DL = - Ruva = -17.594 T
q LL
Segmen Jarak Menghitung Ra dan R 4 Ra =
Pu dia
Rb u=
qu LL = 2.9925 = 29.342 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 4 Ra u= 4
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = -40.147 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 57.741 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 57.7407875 = 6.1408 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 300
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
φ*Vs perlu =
300 d
Dipasang sengka φ*Vs pasang =
1290
= 23.343 T Vs terpasang 23.3432900532
> > OK
Vs perlu 6.1407875
Kontrol
qu DL
*
= 4.1883
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
4
-
4.1883
-
1
*
Pu diafragma
*
x
-
1
*
0.560625
*
4
L 2 16 2
*
x
-
qu LL
x²
*
4
-
2.835
* 2 * 2
Pu BGT
*
L
x
*
x
21.609
*
16
L 16
4
*
4
+ +
Mu qLL 68.04
* 2 * 2
x²
Mu q DL =
16
= 100.52 T.m Mu pDL =
n diafragma 2 = 4 2 = 2.2425 T.m qu LL
*
= 2.835
*
Mu qLL =
= Mu LL = =
Mu pDL =
Mu qLL =
16
68.04 T.m Mu LL =
= 64.827 T.m Mu total = = =
Mu q DL 100.5186 235.6281
+ + T.m
Mu pDL 2.2425
+ +
Mu LL 64.827
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 9247.3 mm²
29 sejumlah π d² * 3.1416
*
T
= = =
As * fy 9247.3 * 320 2959128.95227 N
a
=
T 0.85 * fc' * 2959128.9522693 0.85 * 25 * 174.07 mm
= = Mu terpasang
841
14 *
n
*
14
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
2959128.95227
*
1290
-
= =
Dipasang tulangan m As terpasang
a 2 174.07 2
Mu terpasang
2847787098.6 N. Mm 284.77870986 T.m
Mu terpasang 284.77870986
> >
Mu perlu (Mu total) 235.6281
DESAIN OK
Kontrol
2m
2m P BGT
P dia q DL
q LL
Rva
Ra
Segmen
(14 - 16) m x= 2 m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 2 2 L + 1.6625 x 16 12.005 x 16 2 2 16 23.804 T
Rb =
= 1.6625
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
12.005
x L x 16
2
= 14.801 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 2 2 L + 2.9925 x 16 21.609 x 16 2 2 16 42.848 T Menghitung Vu DL Vu DL = - Ruva = -25.971 T
q LL
Segmen Jarak Menghitung Ra dan R 2 Ra =
Pu dia
Rb u=
qu LL = 2.9925 = 26.641 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 2 Ra u= 2
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = -42.848 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 68.818 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 68.8184625 = 17.218 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 300
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
φ*Vs perlu =
300 d
Dipasang sengka φ*Vs pasang =
1290
= 23.343 T Vs terpasang 23.3432900532
> > OK
Vs perlu 17.2184625
Kontrol
qu DL
*
= 4.1883
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
2
-
4.1883
-
1
*
-
1
L 2 16 2
Pu BGT 21.609
* 2 * 2
x²
Pu diafragma
*
x
*
0.560625
*
2
*
x
-
qu LL
x²
*
2
-
2.835
* 2 * 2
*
L
x
*
x
*
16
L 16
2
*
2
+ +
Mu qLL 39.69
Mu q DL =
4
= 58.636 T.m Mu pDL =
n diafragma 2 = 4 2 = 1.1213 T.m qu LL
*
= 2.835
*
Mu qLL =
= Mu LL = =
Mu pDL =
Mu qLL =
4
39.69 T.m Mu LL =
= 37.816 T.m Mu total = = =
Mu q DL 58.63585 137.26285
+ + T.m
Mu pDL 1.12125
+ +
Mu LL 37.81575
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 5284.2 mm²
29 sejumlah π d² * 3.1416
*
T
= = =
As * fy 5284.2 * 320 1690930.82987 N
a
=
T 0.85 * fc' * 1690930.82986817 0.85 * 25 * 99.467 mm
= = Mu terpasang
841
8 *
n
*
8
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
1690930.82987
*
1290
-
= =
Dipasang tulangan m As terpasang
a 2 99.467 2
Mu terpasang
1677764214.74 N. Mm 167.776421474 T.m
Mu terpasang 167.776421474
> >
Mu perlu (Mu total) 137.26285
DESAIN OK
Kontrol
P dia
P BGT q DL
q LL
Rva (16 -18) m x= 0 m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 0 2 L + 1.6625 x 16 12.005 x 16 0 2 16 25.305 T
Ra
Segmen
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 0 2 L + 2.9925 x 16 21.609 x 16 0 2 16 45.549 T Menghitung Vu DL Vu DL = - Ruvb = -34.347 T
Rb =
q LL = 1.6625 =
Rb u=
L
+
P BGT
16
+
12.005
x L x 16
0
13.3 T
qu LL = 2.9925 =
x 2 x 2
Segmen Jarak Menghitung Ra dan R 0 Ra =
23.94 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 0 Ra u= 0
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = -45.549 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 79.896 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 79.8961375 = 28.296 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
12 * s * 225
φ*Vc 51.6
-
jarak fy * 240 *
* 10000 * 10000
φ*Vs perlu =
225 d
Dipasang sengka φ*Vs pasang =
1290
= 31.124 T Vs terpasang 31.1243867376
> > OK
Vs perlu 28.2961375
Kontrol
qu DL
*
L 2 16 2
*
x
-
qu DL
= 4.1883
*
*
0
-
4.1883
-
1
*
-
1
L 2 16 2
Pu BGT =
21.609
=
0 T.m
= =
Mu q DL 0 0
Mu q DL =
= Mu pDL = = =
n diafragma 2 4 2 0 T.m *
= 2.835
*
= Mu LL =
Mu total =
x²
Pu diafragma
*
x
*
0.560625
*
0
*
x
-
qu LL
x²
*
0
-
2.835
* 2 * 2
*
L
x
*
x
*
16
L 16
0
*
0
+ +
Mu qLL 0
Mu q DL =
0
0 T.m
qu LL
Mu qLL =
* 2 * 2
Mu pDL =
Mu qLL =
0
0 T.m
+ + T.m
Mu pDL 0
Mu LL =
+ +
Mu LL 0
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 2642.1 mm²
29 sejumlah π d² * 3.1416
*
T
= = =
As * fy 2642.1 * 320 845465.414934 N
a
=
T 0.85 * fc' * 845465.414934085 0.85 * 25 * 49.733 mm
= = Mu terpasang
841
4 *
n
*
4
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
845465.414934
*
1290
-
= =
Dipasang tulangan m As terpasang
a 2 49.733 2
Mu terpasang
855701207.792 N. Mm 85.5701207792 T.m
Mu terpasang 85.5701207792
> >
Mu perlu (Mu total) 0
DESAIN OK
Kontrol
9m
9m
P dia
P BGT q DL
q LL
Rva
Ra
Segmen
(6 - 8) m x= 9m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 9 2 L + 1.6625 x 16 12.005 x 16 9 2 16 18.552 T
Rb =
= 1.6625
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
12.005
L
+
Pu BGT
16
+
21.609
x L x 16
9
x L x 16
9
9
= 20.053 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 9 2 L + 2.9925 x 16 21.609 x 16 9 2 16 33.394 T Menghitung Vu DL Vu DL = Ruva = -4.4686 T
q LL
Pu dia
Rb u=
qu LL = 2.9925 = 36.095 T
x 2 x 2
9
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 36.095 T Menghitung Vu total Vu total = Vu DL + = 31.626 T φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
51.6 T
φ*Vs perlu = Vu total = 31.626475 = 19.974 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 226.19
φ*Vc 51.6
-
12 * s * 300
jarak fy * 240 *
* 10000 * 10000
300 d 1290
= 23.343 T Vs terpasang 23.3432900532
> > OK
Vs perlu 19.973525
d 10000 1290 10000
qu DL
*
= 4.1883
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
9
-
4.1883
-
1
*
Pu diafragma
*
x
-
1
*
0.560625
*
9
L 2 16 2
*
x
-
qu LL
x²
*
9
-
2.835
* 2 * 2
Pu BGT
*
L
x
*
x
21.609
*
16
L 16
9
*
9
Mu pDL 5.045625
+ +
Mu qLL 89.3025
* 2 * 2
x² 81
= 131.93 T.m Mu pDL =
n diafragma 2 = 4 2 = 5.0456 T.m qu LL
*
= 2.835
*
Mu qLL =
81
= 89.303 T.m Mu LL = =
= 85.085 T.m Mu total =
Mu q DL + = 131.9306625 + = 311.364225 T.m
+ +
Mu LL 85.0854375
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 14531 mm²
29 sejumlah π d² * 3.1416
*
T
= = =
As * fy 14531 * 320 4650059.78214 N
a
=
T 0.85 * fc' * 4650059.78213747 0.85 * 25 * 273.53 mm
= = Mu terpasang
841
22 *
n
*
22
bw 800
=
0.8
*
T
*
d
-
=
0.8
*
4650059.78214
*
1290
-
= =
4290083907.46 N. Mm 429.008390746 T.m
Mu terpasang 429.008390746
> >
Mu perlu (Mu total) 311.364225
DESAIN OK
a 2 273.53 2
Penulangan Torsi Girder Tepi fc' fy Tulangan lentur Tulangan geser Tebal selimut (dc) d = h -dc-1/2 ( dia tul. geser) Tinggi balok (h) Lebar balok (bw) Luas tul geser Luas tul lentur
D φ
= = = = = = = = = =
25 Mpa 400 Mpa 29 mm 12 mm 40 mm 1354 mm 1400 mm 800 mm 113.097 mm² 660.52 mm²
1320
GAMBAR CONG
Momen yang mengakibatkan puntir pada girder 1. M DL akibat beban sendiri balok + trotoar Mu A = p tiang sandaran x s + q trotoar x s + q kerb x s = Mu B = =
2.0566 T.m q plat lantai x s
+
q aspal x s
+
q LL pejalan kaki x s
0.8364 T.m
2. M LL akibat beban hidup trotoar Mu A = q LL air hujan x s =
0.2938 T.m
Mu B =
0 T.m
3. M LL akibat beban roda "T" Mu A = 0 T.m Mu B = =
+
M roda "T" beban truk x s 13.86 T.m
q kantilever x s
∆Mu= Tu =
Mu B
-
Mu A
=
14.6964
-
2.3504
=
12.346 T.m
T* =
Tu = 12.346 = 16.461 T.m = 164613853.333 N.mm φ 0.75 = 164.613853333 kN.m Perhitungan modulus puntir BMS, BDM hal 5:106 bw² x=bw = 800 mm Jt = 0.4 x x y=h = 1400 mm = 0.4 x 640000 x = 358400000 mm³ Batas kehancuran badan Vu max = 0.2 x = 0.2 x = 5600000 Tu max =
fc' 25
bw 800
x x
x x
Jt 358400000
h 1400
N
0.2 x fc' 0.2 x 25 1792000000 N.mm 1792 kN.m
= = =
x x
h 1400
Kontrol T* 164.613853333
<
Mu perlu
OK
NO
NO
NO
0 180.9454 310.5098 388.6929
NO
OK
OK
OK
415.495 389.8044 311.6213 182.0569
OK
OK
1.1115 -231.215
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
8.1614 3.57565
-1.0101
V
v ???
45.2920 35.2313 31.09015 26.5044 21.91865 17.3329 12.74715
11 11
12 12
13 13
14 14
15 15
16 16
17 17
18 18
-5.59585 -10.1816 -14.7674 -19.3531 -23.9389 -28.5246 -33.1104 -37.6961
PERENCANAAN GIRDER A. Pembebaban Gelagar Bentang jembatan Tinggi girder Lebar girder
L= h= bw =
Mutu Beton Tulangan utama Tulangan sengkang
fc' = fy = fy =
1. Beban Mati Berat Plat
16000 mm 1400 mm 800 mm
d' d
= =
25 320 240
= = =
ts x 0.25 x 0.57 T/m'
(s-bw) 0.95
x x
BJ Beton 2.4
Berat Aspal
= = =
ta x 0.07 x 0.2695 T/m'
s 1.75
x x
BJ Aspal 2.2
Berat Girder
= = =
h girder x 1.4 x 2.688 T/m'
bw 0.8
x x
BJ Beton 2.4
= =
3.5275 T/m' 3.5275 x
q DL qu DL
P diafragma
= h diafragma = 0.5 = 0.342 T
110 mm 1290 mm
x x
1.3
=
4.58575 T/m'
b diafragma 0.3
x x
(s-bw) 0.95
x x
BJ Beton 2.4
Pu diafragma
x x
Ku 1.3
= = =
BTR x 0.9 x 1.575 T/m'
s 1.75
Beban air hujan
= = =
ts x 0.05 x 0.08575 T/m'
s 1.75
x x
BJ air 0.98
q LL qu LL
= =
1.66075 T/m' 1.66075 x
1.8
=
2.98935 T/m'
x x
2. Beban Hidup Beban merata BTR
= P diafragma = 0.342 = 0.4446 T
P BGT
= = =
BGT 4.9 12.005 T
x x
s 1.75
Pu BGT
= = =
P BGT 12.005 21.609 T
x x
Ku 1.8
KD 1.4
BEBAN MATI (DL) Menghitung Rva dan Rvb akibat beban merata q DL
=
3.5275 T/m'
A
B
L= Rva =
q DL = 3.5275 =
x 2 x 2
L
Rvb =
16
q DL = 3.5275
28.22 T
=
16 m x 2 x 2
L
Segmen Jarak Menghitung Ra dan Ra =
16
28.22 T =
Menghitung Rva dan Rvb akibat beban terpusat Pdia = A
Rva =
P dia = 0.342 =
Rva =
x 2 x 2
n dia
B
Rvb =
5
= 0.342
0.855 T 28.22 T 0.855 T 29.075 T
P dia
= Rvb =
0.855 T 28.22 T 0.855 T 29.075 T
x 2 x 2
0.342 T
=
Menghitung Ra u da Ra u=
n dia
=
5
= Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL =
Menghitung Ruva dan Ruvb akibat beban merata qu DL =
4.5858 T/m'
A
B
L= Ruva = qu DL = 4.5858
x 2 x 2
L
Ruvb = qu DL
16
= 4.5858
= 36.686 T
Menghitung Vu total Vu total =
16 m x 2 x 2
L 16
= 36.686 T φ*Vs perlu =
Menghitung Ruva dan Ruvb akibat beban terpusat Pu dia = 0.4446 T A
B
Dipasang sengk φ*Vs pasang =
Rva =
Pu dia = 0.4446 = 1.1115 T
x 2 x 2
n dia 5
Rvb =
Pu dia = 0.4446
x 2 x 2
n dia 5
= 1.1115 T Kontrol
Ruva = 36.686 T 1.1115 T 37.798 T
Ruvb = 36.686 T 1.1115 T 37.798 T
Mu q DL =
Mu pDL =
Mu qLL =
Mu LL =
Mu total =
Dipasang tulangan m As terpasang
Mu terpasang
Kontrol
P dia
P BGT q DL
Rva
q LL
Ra
Segmen
0m x= 0m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 0 2 L + 1.6608 x 16 12.005 x 16 0 2 16 25.291 T Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L L 0 2 L + 2.9894 x 16 21.609 x 16 0 2 16 45.524 T Menghitung Vu DL Vu DL = Ruva = = 37.798 T
Ruvb
Rb =
q LL = 1.6608
x 2 x 2
L
+
P BGT
16
+
12.005
x L x 16
Segmen Jarak Menghitung Ra dan R 0 Ra = 0
= 13.286 T
Rb u=
qu LL = 2.9894 = 23.915 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 0 Ra u= 0
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 45.524 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 83.321 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 83.3213 = 31.721 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 157.08
φ*Vc 51.6
-
10 * s * 150
jarak fy * 240 *
* 10000 * 10000
φ*Vs perlu =
150 d
Dipasang sengk φ*Vs pasang =
1290
= 32.421 T Vs terpasang 32.421236185
> > OK
Vs perlu 31.7213
Kontrol
qu DL
*
L 2 16 2
*
x
-
qu DL
= 4.5858
*
*
0
-
4.5858
-
1
*
-
1
*
L 2 16 2
*
x
-
qu LL
*
0
-
2.9894
Pu BGT
*
L
x
*
x
=
21.609
*
16
L 16
0
*
0
=
0 T.m
= =
Mu q DL 0 0
+ +
Mu qLL 0
Mu q DL =
= Mu pDL = = =
n diafragma 2 4 2 0 T.m *
= 2.9894
*
= Mu LL =
Mu total =
x²
Pu diafragma
*
x
0.4446
*
0
* 2 * 2
x²
Mu q DL =
0
0 T.m
qu LL
Mu qLL =
* 2 * 2
Mu pDL =
Mu qLL =
0
0 T.m
+ + T.m
Mu pDL 0
Mu LL =
+ +
Mu LL 0
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 1963.5 mm² T
= = =
a
=
3.1416
*
625
4 *
n
*
4
= =
0.8
*
T
*
d
-
=
0.8
*
628318.530718
*
1290
-
= =
Dipasang tulangan m As terpasang
As * fy 1963.5 * 320 628318.530718 N T 0.85 * fc' * 628318.530717959 0.85 * 25 * 36.96 mm
=
Mu terpasang
25 sejumlah π d² *
bw 800
a 2 36.96 2
Mu terpasang
639135684.265 N. Mm 63.9135684265 T.m
Mu terpasang 63.9135684265
> >
Mu perlu (Mu total) 0
DESAIN OK
Kontrol
2m
2m P BGT
P dia q DL
q LL
Rva
Ra
Segmen
( 0 - 2) m x= 2m Menghitung Ra dan Rb akibat beban merata dan BGT yg berjalan dari kiri ke kanan + q LL x L P BGT x L 2 2 L + 1.6608 x 16 12.005 x 16 2 2 16 23.79 T
Rb =
= 1.6608
qu DL
*
x
-
n
*
x 2 x 2
L
+
P BGT
16
+
12.005
x L x 16
2
= 14.787 T
Menghitung Ra u dan Rb u akibat beban merata dan BGT yg berjalan dari kiri ke kanan + Pu BGT x qu LL x L 16 2 2 L + 2.9894 x 16 21.609 x 16 2 2 16 42.823 T Menghitung Vu DL Vu DL = Ruva = 28.181 T
q LL
Segmen Jarak Menghitung Ra dan R 2 Ra =
Pu dia
Rb u=
qu LL = 2.9894 = 26.616 T
= =
x 2 x 2
L
+
Pu BGT
16
+
21.609
x L x 16
Menghitung Ra u dan 2 Ra u= 2
= = Menghitung Vu DL Vu DL =
Menghitung Vu LL Vu LL = diambil nilai paling besar diantara Ra u dan Rb u = 42.823 T
Menghitung Vu LL Vu LL =
Menghitung Vu total Vu total = Vu DL + = 71.004 T
Menghitung Vu total Vu total =
φ *Vc=
0.6
*
=
0.6
*
=
Vu LL
1 6 1 6
*
bw
*
25
*
800
*
d 10000 1290 10000
51.6 T
φ*Vs perlu = Vu total = 71.004075 = 19.404 T Dipasang sengkang φ*Vs pasang =
fc'
As
= 157.08
φ*Vc 51.6
-
10 * s * 150
jarak fy * 240 *
* 10000 * 10000
φ*Vs perlu =
250 d
Dipasang sengka φ*Vs pasang =
1290
= 32.421 T Vs terpasang 32.421236185
> > OK
Vs perlu 19.404075
Kontrol
qu DL
*
= 4.5858
*
Mu q DL =
L 2 16 2
*
x
-
qu DL
*
2
-
4.5858
-
1
*
-
1
*
L 2 16 2
*
x
-
qu LL
*
2
-
2.9894
Pu BGT
*
L
x
*
x
21.609
*
16
L 16
2
*
2
+ +
Mu qLL 41.8509
* 2 * 2
x²
Pu diafragma
*
x
0.4446
*
2
* 2 * 2
x²
Mu q DL =
4
= 64.201 T.m Mu pDL =
n diafragma 2 = 4 2 = 0.8892 T.m qu LL
*
= 2.9894
*
Mu qLL =
Mu pDL =
Mu qLL =
4
= 41.851 T.m Mu LL = =
Mu LL =
= 37.816 T.m Mu total = = =
Mu q DL 64.2005 144.75635
+ + T.m
Mu pDL 0.8892
+ +
Mu LL 37.81575
Mu total =
Dipasang tulangan memanjang As terpasang = 1 * 4 = 1 * 4 = 3927 mm² T
= = =
a
=
3.1416
*
625
8 *
n
*
8
= =
0.8
*
T
*
d
-
=
0.8
*
1256637.06144
*
1290
-
= =
Dipasang tulangan m As terpasang
As * fy 3927 * 320 1256637.06144 N T 0.85 * fc' * 1256637.06143592 0.85 * 25 * 73.92 mm
=
Mu terpasang
25 sejumlah π d² *
bw 800
a 2 73.92 2
Mu terpasang
1259693289.66 N. Mm 125.969328966 T.m
Mu terpasang 125.969328966
<
>
Mu perlu (Mu total) 0
DESAIN OK
a 2 36.96 2
PERENCANAAN GELAGAR A. Pembebaban Gelagar Bentang jembatan Tinggi girder Lebar girder
L= h= bw =
Mutu Beton Tulangan utama Tulangan sengkang
fc' = fy = fy =
1. Beban Mati Berat Plat
Berat Aspal
Berat Girder
q DL qu DL
P diafragma
16000 mm 1400 mm 800 mm
d' d
= =
25 320 240
= = =
ts x 0.25 x 0.57 T/m'
(s-bw) 0.95
x x
BJ Beton 2.4
= = =
ta x 0.07 x 0.2695 T/m'
s 1.75
x x
BJ Aspal 2.2
= h girder x = 1.4 x = 2.688 T/m'
bw 0.8
x x
BJ Beton 2.4
= =
4.6725 T/m' 4.6725 x
= h diafragma
110 mm 1290 mm
x
1.3
=
6.07425 T/m'
b diafragma
x
(s-bw)
x
BJ Beton
= =
0.5 0.603362 T
x
0.3
=P diafragma = 0.603362 = 0.7843706 T
x x
Ku 1.3
= = =
BTR x 0.9 x 1.575 T/m'
s 1.75
= = =
ts x 0.05 x 0.08575 T/m'
= =
0.875 T/m' 0.875 x
P BGT
= = =
BGT 4.9 6.0025 T
Pu BGT
= = =
P BGT 6.0025 10.8045 T
Pu diafragma
2. Beban Hidup Beban merata BTR
Beban air hujan
q LL qu LL
x
0.95
s 1.75
x x
BJ air 0.98
1.8
=
x x
s 1.75
x x
x x
Ku 1.8
x
1.575 T/m'
KD 1.4
2.4
P BGT qLL
P diafragma
P diafragma
P diafragma
P diafragma
P diafragma
q DL
segment (m)
0
2
4
6
8
10
12
14
16
18
segmen ke
0
1
2
3
4
5
6
7
8
9
BEBAN MATI Rva dan Rvb (ton)
38.586724
38.586724
Ruva dan Ruvb (ton)
50.1627
50.1627
BEBAN HIDUP Ra (ton)
8.500625 7.7503125
7 6.2496875
8.500625 9.2509375
10.00125 10.7515625 11.501875 12.2521875
13.0025 13.7528125
Ra u (ton)
23.4045 22.0539375 20.703375 19.3528125
18.00225 16.6516875 15.301125 13.9505625
12.6 11.2494375
Rb u (ton)
12.6 13.9505625 15.301125 16.6516875
18.00225 19.3528125 20.703375 22.0539375
23.4045 24.7550625
Rb (ton
13.0025 12.2521875 11.501875 10.7515625 7 7.7503125
Vu DL (ton)
50.1627
Vu LL (ton)
23.4045 22.0539375 20.703375 19.3528125
Vu total (ton)
37.2299
25.0814
12.9329
10.00125 9.2509375
0.7844
-0.7844
-12.9329
-25.0814
18.00225 -19.352813 -20.703375 -22.053938
73.5672412 59.2838081 45.7847456 32.2856831 18.7866206
20.1372
33.6362
47.1353
-37.2299
-50.1627
-23.4045 -24.755063 60.6344
74.9178
f.Vc = 0,6.1/6.sqrt(fc').bw.d/10000
(ton)
f. Vs perlu = Vutotal - φVc
(ton)
Dipasang sengkang
51.6
kontrol Vs terpasang > Vs perlu
51.6
51.6
51.6
51.6
51.6
51.6
51.6
51.6
21.9672412 7.6838081 -5.8152544 -19.314317 -32.813379 -31.462817 -17.963754 -4.4646919 9.0343706 23.3178037
f 10 - 200
φ. Vs terpasang = Av.fy d/ sa /10000 (ton)
51.6 300
-825
-250
-125
-150
-250
-1075
300
200
24.3159271 16.2106181 -5.8947702 -19.452742 -38.905483 -32.421236 -19.452742 -4.5238934 16.2106181 24.3159271 OK
OK
NO
NO
85.0395
145.782
NO
OK
145.782
85.0395
OK 0
-109.3365
Mu PDL (t-m)
0 1.5687412 3.1374824 4.7062236 6.2749648 6.2749648 4.7062236 3.1374824 1.5687412
0
Mu qLL (t-m)
0
Mu LL (t-m)
0 18.907875
Mu total (t-m)
0 127.566116 219.132982 274.700599 294.268965 276.26934 220.701724 129.134857 1.5687412 -161.99663
37.8
47.25
50.4
182.2275
NO
0
32.4135 40.516875
194.376
NO
Mu qDL (t-m)
22.05
182.2275
NO
47.25
43.218 40.516875
37.8
22.05
0
32.4135 18.907875
-28.35
0 -24.310125
Dipasang Tulangan memanjang bawah D25 sejumlah
4
8
14
18
22
22
18
14
8
4
As terpasang 1963.49541 3926.99082 6872.23393 8835.72934 10799.2247 10799.2247 8835.72934 6872.23393 3926.99082 1963.49541 T = As.fy
(N) 628318.531 1256637.06 2199114.86 2827433.39 3455751.92 3455751.92 2827433.39 2199114.86 1256637.06 628318.531
a = T/(0,85.fc'.bw) (mm) 36.9599136 73.9198271 129.359698 166.319611 203.279525 203.279525 166.319611 129.359698 73.9198271 36.9599136 Mu terpasang = 0,8T (d-a/2)/1E7 (t-m)
Kontrol Mu terpasang > Mu perlu
63.9135684 125.969329 215.56958 272.980821 328.534254 328.534254 272.980821 215.56958 125.969329 63.9135684 OK
NO
NO
NO
OK
OK
OK
OK
OK
OK
0 159.4576 273.9162 343.3757 367.8362 345.3367 275.8772 161.4186 1.960927 -202.496
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
V
v ???
50.1627 36.4455 31.15562 25.08137 19.00712 12.93287 6.858621 0.784371 -5.28988 -11.3641
11 11
12 12
13 13
14 14
15 15
16 16
17 17
18 18
-17.4384 -23.5126 -29.5869 -35.6611 -41.7354 -47.8096 -53.8839 -59.9581
PERENCANAAN GELAGAR A. Pembebaban Gelagar Bentang jembatan Tinggi girder Lebar girder
L= h= bw =
Mutu Beton Tulangan utama Tulangan sengkang
fc' = fy = fy =
1. Beban Mati Berat Plat
Berat Aspal
Berat Girder
q DL qu DL
P diafragma
16000 mm 1400 mm 800 mm
d' d
= =
25 320 240
= = =
ts x 0.25 x 0.57 T/m'
(s-bw) 0.95
x x
BJ Beton 2.4
= = =
ta x 0.07 x 0.2695 T/m'
s 1.75
x x
BJ Aspal 2.2
= h girder x = 1.4 x = 2.688 T/m'
bw 0.8
x x
BJ Beton 2.4
= =
3.5275 T/m' 3.5275 x
= h diafragma
110 mm 1290 mm
x
1.3
=
4.58575 T/m'
b diafragma
x
(s-bw)
x
BJ Beton
= = Pu diafragma
2. Beban Hidup Beban merata BTR
Beban air hujan
q LL qu LL
0.5 0.342 T
x
0.3
=P diafragma = 0.342 = 0.4446 T
x x
Ku 1.3
= = =
BTR x 0.9 x 1.575 T/m'
s 1.75
= = =
ts x 0.05 x 0.08575 T/m'
= 1.66075 T/m' = 1.66075 x
x
0.95
s 1.75
x x
BJ air 0.98
1.8
=
2.98935 T/m'
x x
P BGT
= = =
BGT 4.9 12.005 T
x x
s 1.75
Pu BGT
= = =
P BGT 12.005 21.609 T
x x
Ku 1.8
KD 1.4
x
2.4
P BGT qLL
P diafragma
P diafragma
P diafragma
P diafragma
P diafragma
q DL
segment (m)
0
2
4
6
8
10
12
14
16
18
segmen ke
0
1
2
3
4
5
6
7
8
9
BEBAN MATI Rva dan Rvb (ton)
28.904
28.904
Ruva dan Ruvb (ton)
37.5752
37.5752
BEBAN HIDUP Ra (ton)
25.291 23.790375
22.28975 20.789125
19.2885 17.787875
16.28725 14.786625
13.286 11.785375
Rb (ton
13.286 14.786625
16.28725 17.787875
19.2885 20.789125
22.28975 23.790375
25.291 26.791625
Ra u (ton)
45.5238 42.822675
40.12155 37.420425
34.7193 32.018175
29.31705 26.615925
23.9148 21.213675
Rb u (ton)
23.9148 26.615925
29.31705 32.018175
34.7193 37.420425
40.12155 42.822675
45.5238 48.224925
Vu DL (ton)
37.5752
Vu LL (ton)
45.5238 42.822675
40.12155 37.420425
34.7193 -37.420425
Vu total (ton)
83.099 70.781775
58.90915 47.036525
35.1639
27.9591
18.7876
9.6161
0.4446
-0.4446 37.8650
-9.6161
-18.7876
-40.12155 -42.822675 49.7377
61.6103
-27.9591
-37.5752
-45.5238 -48.224925 73.4829
85.8001
f.Vc = 0,6.1/6.sqrt(fc').bw.d/10000
(ton)
f. Vs perlu = Vutotal - φVc
(ton)
Dipasang sengkang
51.6
51.6
51.6
51.6
31.499 19.181775
7.30915
-4.563475
f 10 - 150
φ. Vs terpasang = Av.fy d/ sa /10000 (ton)
kontrol Vs terpasang > Vs perlu
250
300
-1050
51.6
51.6
-16.4361 -13.734975 -275
-350
51.6
51.6
51.6
-1.86235 10.010275 -2600
300
51.6
21.8829 34.200125 200
125
32.4212362 19.4527417 16.2106181 -4.6316052 -17.684311 -13.894816 -1.8704559 16.2106181 24.3159271 38.9054834 OK
OK
OK
NO
NO
NO
NO
OK
OK
OK
Mu qDL (t-m)
0
64.2005
110.058
137.5725
146.744
137.5725
110.058
64.2005
0
-82.5435
Mu PDL (t-m)
0
0.8892
1.7784
2.6676
3.5568
3.5568
2.6676
1.7784
0.8892
0
Mu qLL (t-m)
0
41.8509
71.7444
89.6805
95.6592
89.6805
71.7444
41.8509
0
-53.8083
Mu LL (t-m)
0
37.81575
64.827
81.03375
86.436
81.03375
64.827
37.81575
0
-48.62025
Mu total (t-m)
0 144.75635
248.4078 310.95435
332.396 311.84355
249.297 145.64555
0.8892 -184.97205
Dipasang Tulangan memanjang bawah D25 sejumlah
4
8
14
18
22
22
18
14
8
4
As terpasang 1963.49541 3926.99082 6872.23393 8835.72934 10799.2247 10799.2247 8835.72934 6872.23393 3926.99082 1963.49541 T = As.fy
(N) 628318.531 1256637.06 2199114.86 2827433.39 3455751.92 3455751.92 2827433.39 2199114.86 1256637.06 628318.531
a = T/(0,85.fc'.bw) (mm) 36.9599136 73.9198271 129.359698 166.319611 203.279525 203.279525 166.319611 129.359698 73.9198271 36.9599136 Mu terpasang = 0,8T (d-a/2)/1E7 (t-m)
Kontrol Mu terpasang > Mu perlu
63.9135684 125.969329 215.56958 272.980821 328.534254 328.534254 272.980821 215.56958 125.969329 63.9135684 OK
NO
NO
NO
0 180.9454 310.5098 388.6929
NO
OK
OK
OK
415.495 389.8044 311.6213 182.0569
OK
OK
1.1115 -231.215
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
0.4446 -4.14115
-8.7269
V
v ???
37.5752 27.5145 23.37335 18.7876 14.20185
9.6161 5.03035
11 11
12 12
13 13
14 14
15 15
16 16
17 17
18 18
-13.3127 -17.8984 -22.4842 -27.0699 -31.6557 -36.2414 -40.8272 -45.4129
Perencanaan Girder Tepi P dia
P BGT q DL
q LL
Rva
Ra
Segmen 1 Jarak x= 0 m Va = Vb akibat q DL L x q DL = 2
16 2
x
4.355
=
34.84 T
Va = Vb akibat p DL n dia x p DL 2
=
4
x 2
0.5516
=
1.1031 T
Va = Vb akibat UDL L x q LL 2
=
16 2
x
0.875
=
7T
Va = Vb akibat KEL L x p LL L
=
16
x 16
6.0025
=
6.0025 T
V DL akibat q DL Va q DL 34.84 4.355
x x
jarak 0
=
0T
V DL akibat p DL Va pDL 1.1031 0.5516
x x
n dia 1
=
0.5516 T
M DL akibat q DL Va x jarak 4.355 x 0
-
0.5 0.5
x x
q DL 4.355
M DL akibat p DL Va x jarak 1.1031 x 0
-
p DL 0.5516
x x
jarak 0
q LL
x
jarak
0.875
x
0
V akibat UDL (q LL) q LL x L 2 0.875 x 16 -
x x
jarak 0
=
0 T.m
=
0 T.m
=
7T
2 V akibat KEL (p LL) L jarak L x p LL M akibat UDL (q LL) 0.5 x q LL 0.5 x 0.875
=
16 16
x
0 6.0025
x x
L 16
x x
jarak 0
=
-
jarak ² 0
M akibat KEL (p LL) jarak ² L x jarak L x p LL 16 x 0 0 16 x 6.0025 Tabel rekap perhitungan V DL akibat q DL V DL akibat p DL M DL akibat q DL M DL akibat p DL V akibat UDL (q LL) V akibat KEL (p LL) M akibat UDL (q LL) M akibat KEL (p LL)
= = = = = = = =
0T 0.5516 T 0 T.m 0 T.m 7T 0.1666 T 0 T.m 0 T.m
V DL total V LL total M DL total M LL Total Vu = 1.3 V DL + 2 V LL Mu = 1.3 M DL + 2 M LL
= = = = = =
0.5516 T 7.1666 T 0 T.m 0 T.m 15.05 T 0 T.m
0.1666 T
=
0 T.m
=
0 T.m
Analisa tulangan lentur Mu = 0 T.m
fc' = limut =
25 MPa 30 mm
φ sengkang = φ tul pokok =
12 mm 22 mm
; ;
fy = fy =
240 MPa 400 MPa
2m
2m P BGT
P dia q DL
q LL
Rva
Ra
Segmen 2 Jarak x= 2 m Va = Vb akibat q DL L x q DL = 2
16 2
x
4.355
=
34.84 T
Va = Vb akibat p DL n dia x p DL 2
=
4
x 2
0.5516
=
1.1031 T
Va = Vb akibat UDL L x q LL 2
=
16 2
x
Err:509
=
### T
Va = Vb akibat KEL L x p LL L
=
16
x 16
6.0025
=
6.0025 T
V DL akibat q DL Va q DL 34.84 4.355
x x
jarak 2
=
60.97 T
V DL akibat p DL Va pDL 1.1031 0.5516
x x
n dia 1
=
0.5516 T
M DL akibat q DL Va x jarak 4.355 x 2
-
0.5 0.5
x x
q DL 4.355
M DL akibat p DL Va x jarak 1.1031 x 2
-
p DL 0.5516
x x
jarak 2
q LL
x
jarak
0.875
x
2
V akibat UDL (q LL) q LL x L 2 0.875 x 16 -
x x
jarak 2
=
4.355 T.m
=
1.1031 T.m
=
5.25 T
2 V akibat KEL (p LL) L jarak L x p LL M akibat UDL (q LL) 0.5 x q LL 0.5 x 0.875
=
16 16
x
2 6.0025
x x
L 16
x x
jarak 2
M akibat KEL (p LL) jarak ² L x jarak L x p LL 16 x 2 4 16 x 6.0025 Tabel rekap perhitungan V DL akibat q DL V DL akibat p DL M DL akibat q DL M DL akibat p DL V akibat UDL (q LL) V akibat KEL (p LL) M akibat UDL (q LL) M akibat KEL (p LL)
= = = = = = = =
60.97 T 0.5516 T 4.355 T.m 1.1031 T.m 5.25 T 0.1458 T 12.25 T.m 0.2915 T.m
=
-
jarak ² 4
0.1458 T
=
12.25 T.m
=
0.2915 T.m
Perencanaan Girder Tepi P dia
P BGT q DL
q LL
Rva
Ra
Segmen 1 Jarak x= 0 m Va = Vb akibat q DL L x q DL = 2
16 2
x
4.355
=
34.84 T
Va = Vb akibat p DL n dia x p DL 2
=
4
x 2
0.5516
=
1.1031 T
Va = Vb akibat UDL L x q LL 2
=
16 2
x
0.875
=
7T
Va = Vb akibat KEL L x p LL L
=
16
x 16
6.0025
=
6.0025 T
V DL akibat q DL Va q DL 34.84 4.355
x x
jarak 0
=
0T
V DL akibat p DL Va pDL 1.1031 0.5516
x x
n dia 1
=
0.5516 T
M DL akibat q DL Va x jarak 4.355 x 0
-
0.5 0.5
x x
q DL 4.355
M DL akibat p DL Va x jarak 1.1031 x 0
-
p DL 0.5516
x x
jarak 0
(q LL) L -
q LL
x
jarak
16
0.875
x
0
V akibat UDL q LL x 2 0.875 x
-
x x
jarak 0
=
0 T.m
=
0 T.m
=
7T
2 V akibat KEL (p LL) L jarak L x p LL M akibat UDL (q LL) 0.5 x q LL 0.5 x 0.875
=
16 16
x
0 6.0025
x x
L 16
x x
jarak 0
=
-
jarak ² 0
M akibat KEL (p LL) jarak ² L x jarak L x p LL 16 x 0 0 16 x 6.0025 Tabel rekap perhitungan V DL akibat q DL V DL akibat p DL M DL akibat q DL M DL akibat p DL V akibat UDL (q LL) V akibat KEL (p LL) M akibat UDL (q LL) M akibat KEL (p LL)
= = = = = = = =
0T 0.5516 T 0 T.m 0 T.m 7T 0.1666 T 0 T.m 0 T.m
V DL total V LL total M DL total M LL Total Vu = 1.3 V DL + 2 V LL Mu = 1.3 M DL + 2 M LL
= = = = = =
0.5516 T 7.1666 T 0 T.m 0 T.m 15.05 T 0 T.m
0 = 0.75
0 T.m
Analisa tulangan lentur Mu = 0 T.m Mn = Mu = φ Rencanakan d= = = Ast = =
D
22
h 1400 1286 mm 1 4 1 4
n=
decking 40
-
x
π
x
D²
x
3.1416
x
484
10 φ sengkang 12
0.1666 T
=
0 T.m
=
0 T.m
fy =
400 MPa
-
D tul lentur 22
-
jarak tulangan 40
= 380.1327 mm² T=
Ast
x
fy
x
T fc'
a= 0.85
= 380.13
x =
x
bw =
Mn* =
T
= 152053.1
x
d
-
x
1286
-
= 194.8603 T.m
400
a 2 8.9443 2
0.85 x 8.9443 mm
= 152053 N 152053 25
= x
800
2m
2m P BGT
P dia q DL
q LL
Rva
Ra
Segmen 2 Jarak x= 2 m Va = Vb akibat q DL L x q DL = 2
16 2
x
4.355
=
34.84 T
Va = Vb akibat p DL n dia x p DL 2
=
4
x 2
0.5516
=
1.1031 T
Va = Vb akibat UDL L x q LL 2
=
16 2
x
Err:509
=
### T
Va = Vb akibat KEL L x p LL L
=
16
x 16
6.0025
=
6.0025 T
V DL akibat q DL Va q DL 34.84 4.355
x x
jarak 2
=
60.97 T
V DL akibat p DL Va pDL 1.1031 0.5516
x x
n dia 1
=
0.5516 T
M DL akibat q DL Va x jarak 4.355 x 2
-
0.5 0.5
x x
q DL 4.355
M DL akibat p DL Va x jarak 1.1031 x 2
-
p DL 0.5516
x x
jarak 2
q LL
x
jarak
0.875
x
2
V akibat UDL (q LL) q LL x L 2 0.875 x 16 -
x x
jarak 2
=
4.355 T.m
=
1.1031 T.m
=
5.25 T
2 V akibat KEL (p LL) L jarak L x p LL M akibat UDL (q LL) 0.5 x q LL 0.5 x 0.875
=
16 16
x
2 6.0025
x x
L 16
x x
jarak 2
M akibat KEL (p LL) jarak ² L x jarak L x p LL 16 x 2 4 16 x 6.0025 Tabel rekap perhitungan V DL akibat q DL V DL akibat p DL M DL akibat q DL M DL akibat p DL V akibat UDL (q LL) V akibat KEL (p LL) M akibat UDL (q LL) M akibat KEL (p LL)
jarak tulangan 40
= = = = = = = =
60.97 T 0.5516 T 4.355 T.m 1.1031 T.m 5.25 T 0.1458 T 12.25 T.m 0.2915 T.m
=
-
jarak ² 4
0.1458 T
=
12.25 T.m
=
0.2915 T.m
PERENCANAN ABUTMENT
12 1 6 10
7 10 2
10 8
3 3 4
11 9
5 Diketahui : γ tanah = 1.59 t/m³ Tinggi abutment = 6m Sudut geser dalam tanah = 14.9 ° q urugan tanah = 0.6 t/m² Lebar abutment = 9.4 m Gaya rem bentang < 50 m = 25 t Kegempaan C = 0.35 faktor wilayah gempa (zona 3) I= 1 faktor kepentingan bangunan R= 1.5 faktor jenis struktur
Beban mati akibat beban bangunan atas No
Jenis Material 1 Pelat lantai kendaraan 3 Balok Girder 4 Balok diafragma 5 Kerb 6 Trotoar 7 Railing /Pipa Sandaran 8 Tiang sandaran
tebal lebar panjang jumlah volume BJ Berat m³ kN/m³ kN m m m unit 0.25 9.4 18 1 42.3 2.5 105.8 1.5 0.5 0.25 0.25
0.6 0.35 0.2 1
0.2
0.2
18 9.4 18 18 18 2
Σ
5 5 2 2 36 20
81 2.5 202.5 8.225 2.5 20.56 1.8 2.5 4.5 9 2.4 21.6 648 1E-06 0.001 1.6 2.5 4 358.9 35.89
Beban lalu lintas a. Beban Terbagi Rata (UDL) Beban terbagi lalu (UDL) dengan intensitas q Kpa dengan q tergantung pada panjang yang dibebani total (L) sebagai berikut L < 30 m q = 8 kPa L < 30 m q= 8 0.5 + 15 kPa L ket : 1 Kpa = 1 kN/m² = 0.1 t/m² Untuk jembatan dengan lebar lantai kendaraan lebih besar dari 5.5 m, beban "D" sepenuhnya 100% dibebankan pada lebar jalur 5.5 m sedang selebihnya dibebani hanya separuh beban "D" (PPPJL PU hal. 7) b. Beban truk "T" Beban truk atau beban garis sebesar P kN/m, ditempatkan dalam kedudukan sembarang sepanjang jembatan dan tefak lurus pada arah lalu lintas P = 49 kN/m P total = ((5.5 P) + (b - 5.5)) 0.5 P c. Beban rem Pengaruh rem dan percepatan lalu lintas harus dipertimbangkan sebagai gaya memanjang. Gaya ini tidak tergantung pada lebar jembatan Dimana panjang jembatan bentang pinggir (L) adalah = 18 m Panjang Bentang (m) ≤ L 80 80 < L < 180 ≥ L 180 Gaya rem yang terjadi =
Gaya rem (kN) 250 2.5 L + 50 500 250 kN
=
25 t
Perhitungan beban lalu lintas Diketahui panjang jembatan lebar pekerasan jembatan beban KEL Beban UDL DLA (Dynamic Load)
L= b= P= q= =
Total beban KEL = ((5.5 P) + (b - 5.5)) 0.5 P = 5.5 x 4.9 + = 69.703 ton Total Beban UDL = ((5.5 q) + (b - 5.5)) 0.5 q x L = 5.5 x 0.8 + = 42.48 ton
18 m 7m 4.9 t/m 0.8 t/m² 0.4
7
-
5.5
x
0.5
x
4.9
7
-
5.5
x
0.5
x
0.8
n
=
2
=
x x
A 21.6
Beban Pedestrian Beban hidup merata, q Untuk 10 m2 < A ≤ 5 -0,033 x (A – 10) Lebar trotoar b= 1.2 m Jumlah trotoar n= 2 Luas bidang yang didukukng abutment A= b x L x 2 A= 1.2 x 18 x 2 Jadi, q = = =
5 5 4.6172 kPa
0.033 0.033
PTP
A x 21.6 x 99.732 kN 9.9732 ton
q 4.6172
= = = =
Beban Angin Kecepatan angin rencana Panjang jembatan Lebar jembatan Tinggi samping jembatang yg terkena angin
Vw L b ha
21.6 m²
-
= = = =
10 10
30 m/s 18 m 9.4 m 2.8 m
x
18
L koef bagian samping jembatan Koef. Seret Gaya angin Tew = 0.0006 x Cw = 0.0006 x 1.2 = 32.659 kN = 3.2659 ton Tekanan tanah aktif Tinggi timbunan Lebar jembatan Berat Jenis tanah Sudut geser tanah q tanah
h= b= γt= Φ= =
Ab Cw x x
= =
L 1.2
Vw² 900
x x
Ab 50.4
x
ha
5.85 m 9.4 m 1.59 t/m³ 14.9 ° 0.6 t/m
Koef tekanan tanah aktif tan² Ka = 45
-
Ka =
tan²
-
Ka =
0.5909
Pa 1
= = =
q x 0.6 x 19.497 t
ka 0.5909
x x
h 5.85
x x
b 9.4
Pa 2
=
γt
x
ka
x
h²
x
b
1.59
x
0.591
x
34.223
x
9.4
=
1 x 2 1 x 2 151.13 t
Pa total = = =
Pa 1 + 19.497 + 170.62 t
Pa1
x
0.5 h
x
0.3 h
19.497
x
+ Pa2 Pa tot 2.925 + 151.13 170.62
x
1.755
=
45
Titik berat terhadap O Σ M Pa = z = Σ Pa = = Beban Gempa Koef geser Faktor tipe bangunan Faktor kepentingan Kh
C= S= I= =
Φ 2 14.9 2
Pa 2 151.13
1.8887 m
0.18 1 1 C
wilayah gempa zona 3
x
S
=
50.4
m²
Teq
=
Kh x I x W = C x S x I x W
Beban gempa bangunan atas Teq 1 = 0.18 x = 3.2302 ton
1
x
1
x
17.946
Beban gempa sendiri abutment Teq 2 = 0.18 x = 14.678 ton
1
x
1
x
81.545
x
Tt 170.62
Beban gempa akibat tekanan tanah dinamis Teq 2 = C x S x = 0.18 x 1 x = 30.712 ton
I
x 1
Pembebanan Abutment
No
Beban sendiri abutment
Plat injak Wing wall
Tanah Urugan
b (m)
1 2 3 4 5 6 7 11 12 13 8 9 10
0.3 0.6 0.3 1 3.6 1.9 0.35 0.85 1.95 1.1 0.3 0.6 0.2
L (m) 9.4 9.4 9.4 9.4 9.4 9.4 9.4 0.6 0.6 0.6 8.2 8.2 8.2
t (m)
BJ Berat (t/m³) (T)
0.7 1 0.5 3.8 1 0.2 0.4 2.25 1.7 2.25 0.5 2.25 1.9
Σ
2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 1.8 1.8 1.8
4.935 5.64 1.41 35.72 33.84 3.572 1.316 1.148 1.989 1.485 1.23 11.07 3.116
Titik Berat thdp Momen (T.m) titik O (m) X 0.65 0.8 0.7 0 0 1.94 0.81 1.38 1.93 2.17 0.75 0.65 1.95
106.5
Y 5.65 4.8 4.14 2.9 0.5 4.75 4.64 1.83 3.81 2.2 3.12 1.83 4.75
X 3.2078 4.512 0.987 0 0 6.9297 1.066 1.5836 3.8388 3.2225 0.9225 7.1955 6.0762
39.541 256.22
Titik Berat Abutment terhadap titik "O" x=
Σ Mx ΣW
y=
Σ My ΣW
x=
39.541 106.47
y=
256.2 106.5
x=
0.37138 m
y=
2.406 m
ganti titik berat
Y 27.883 27.072 5.8374 103.59 16.92 16.967 6.1062 2.0999 7.5781 3.267 3.8376 20.258 14.801
abut tanah
x y 0.4343 2.3867 0.9207 2.5231
Kombinasi Pembebanan Abutment
Tegangan yang dinyatakan dalam (%) terhadap tegangan ijin keadaan elastis
Kombinasi Pembebanan dan Gaya 1. MS + MA + TA + TD +TP 2. MS + MA + TA+ TD + TP + TB + EW 3. MS + MA + TA + TD + TP + TB + FB 4. MS + MA + TA + TD + TP + TB + ET + FB 5. MS + MA + EQ 1 Air Hujan 2 Perkerasan (aspal + overlay)
0.05 0.1
100 % 125 % 125 % 140 % 150 % 9.4 7
18 18
1 1
8.46 12.6
0.98 8.2908 2.2 27.72 36.011
Tekanan tanah aktif 12 7 2 10 8
Ka =
tan²
45
-
Ka =
tan²
45
-
4
Ka =
0.591
9
5 Pesegi Pa1
= = =
Segitiga Pa2 = = =
q x 0.6 x 20 t
ka 0.591
x x
h 6
x x
b 9.4
1 x 2 1 x 2 159 t
γt
x
ka
x
h²
x
b
1.59
x
0.591
x
36
x
9.4
W
Z
ton 91.05 15.42
m
Beban Gempa Gaya Berat Struktur abutment Berat Tanah Total beban gempa
14.9 °
1 0
6 10
sdt geser Φ=
1
6 6
Beban gempa = CxIxWxZ/R ton.m 127.4763 21.5824 149.0587
Φ 2 14.9 2
Tanah
Penjabaran gaya yang diterima oleh abutment Gaya Bang. Atas/Girder (Rva) Beban sendiri abutment Wt Pa1 Pa2 Gaya rem Gaya gempa Jumlah
V H ton ton 25.31 91.05 15.42
x y Mx = V.x My = H.y m m ton .m ton .m 0.434 10.988958424 0.434 39.54136 2.523 0 20 3 59.990383872 159 2 317.94903452 25 0.434 10.856509014 149.1 0.434 64.730284806
131.8
353
Kesatbilan abutment thdp guling Σ Mx SF = = 50.53031842 = Σ My 453.5262122
50.530318424 453.52621221
0.111
Abutment Guling
Sebaiknya menggunakan pondasi tiang pancang
`
b (m)
No 1 2 3 4
1 0.7 0.6 1.3
Titik Berat BJ Berat thdp titik O L (m) t (m) (m) (t/m³) (T) X Y 8.2 0.7 1.59 9.127 1.3 5.65 8.2 1.5 1.59 13.69 1.45 4.55 8.2 0.5 1.59 3.911 0.9 3.97 8.2 2.8 1.59 47.46 1.15 2.4 74.19
x=
Σ Mx ΣW
y=
Σ My ΣW
x = 89.81 74.19
y = 243.3 74.19
x=
y=
1.211
3.279
Momen (T.m) X Y 11.865 51.565 19.85 62.289 3.5203 15.528 54.577 113.9 89.812 243.28
165.24
Rekapitulasi Gaya dan Momen thdp O V ton I. Beban Tetap a. Beban Atas/Gelagar (Rva) b. Abutment c. Tekanan Tanah Aktif II. Pengaruh Beban Hidup a. UDL + KEL b. Angin c. Rem III. Pengaruh Kegempaan a. Ekuivalen bangunan Atas b. Ekuivalent Abutment c. Tekanan tanah akibat gempa
Hx ton
24.37 106.5 179 25.31
Hy ton
x m
y m
z m
Mx My ton.m ton.m
Kombinasi 1
Gaya No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Beban MS MS MS MA TA TD TP TB ET EW EQ EQ EQ FB ∑ 100%
Bagian abutment bangunan atas tanah timbunan di belakang abutment beban mati tambahan tekanan tanah aktif beban lajur D + KEL beban pejalan kaki )pedestrian) gaya rem suhu beban angin beban gempa bangunan atas beban gempa abutment beban gempa tekanan tanah aktif gesekan pada perletakan TOTAL
V 165.241 17.946 74.190 36.011 112.183 9.973
Jarak terhadap titik 0 Momen H x y Mv Mh 0.107 17.643 0 0.000 3.279 243.295 0 0.000 170.622 3.279 0.000 559.529 0 0.000 0 0.000
415.543 170.622 415.543 170.622
260.938 559.529 260.938 559.529
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Gaya Beban MS MS MS MA TA TD TP TB ET EW EQ EQ EQ FB ∑ 125%
Bagian abutment bangunan atas tanah timbunan di belakang abutment beban mati tambahan tekanan tanah aktif beban lajur D beban pejalan kaki gaya rem suhu beban angin beban gempa bangunan atas beban gempa abutment beban gempa tekanan tanah aktif gesekan pada perletakan TOTAL
V 165.241 17.946 74.190 36.011 112.183 9.973
Jarak terhadap titik 0 Momen H x y Mv Mh 0 17.643 0 0 3.279 243.295 0 0 170.622 3.279 559.529 0 0 0 0 25.000 6.000 150.000 3.266
415.543 198.888 519.429 248.610
0
0
260.938 709.529 326.173 886.912
12 1 6
7
10
10 2 10 8
3 3 4
11 9
5
atas bawah
cos^2
=
0.999643419
=
0.968616655
=
0.003695593
=
0.984183243
0.916294
1 0.984183
1 0.984183
PERENCANAAN ELASTOMER/BEARING PAD Perletakan balok girder pada abutment menggunakan bantalan elastomer dengan acuan spesifikasi Freyssinet Elastomeric bearings. Elastomer mampu memberikan reaksi terhadap pembebanan vertikal, horizontal dan geseran. Beban yang bekerja pada elastomer a. Gaya vertikal yang bekerja Beban Mati Aspal = ts x b x L x 0.1 x 1.6 x 17 x
BJ 2.2
=
5.984
kN
Air hujan ts x 0.05 x
b 1.6
x x
L 17
x x
BJ 0.98
=
1.3328
kN
Pelat lantai ts x 0.25 x
b 1.6
x x
L 17
x x
BJ 2.5
=
17
kN
Diafragma b x 0.3 x
jumlah diafragma 5
x x
h 0.5
x x
L 17
x x
BJ 2.5
=
31.875
kN
Girder b x 0.8 x
jumlah gelagar 5
x x
h 1.4
x x
L 17
x x
BJ 2.5
=
238
kN
=
78.4
kN
=
2.24
kN
Beban Hidup Beban Garis 49 kN/m x 49 kN/m x
b 1.6
Beban Merata 9 kN/m² x 9 kN/m² x
b 1.6
x x
L 1.4
Total Total beban vertikal = Vtot/2 b. Gaya horizontal yang bekerja akibat angin akibat rem dan traksi H total
= =
187.4159 kN
= =
53.31744 kN 25 kN
=
78.31744 kN
Untuk tiap tumpuan menahan gaya horisontal setengahnya H= 0.5 x H tot = 39.15872 kN
374.8318 kN
Pemilihan elastomer (freyssynet) direncanakan a. Panjang elastomer = 305 mm b. Lebar elastomer = 305 mm c. Tebal pelat baja elastomer = 5 mm d. Tebal lapis elastomer = 9 mm e. Tebal selimut atas dan bawah = 6 mm f. Daya dukung (V max) = 641 kN g. Rasio geser = 17.51 kips/inch h. Perpendekan elastis = 0.02 inch Kebutuhan elastomer n = V tot = 187.4159 V max 640.512 tebal total
=
=
0.293
~
1
30.5 30.5
x
lapis elastomer
20 mm
Cek terhadap kebutuhan elastomer Terhadap gaya dukung V tot ≤ V max 187 ≤ 641 x 2 187 ≤ 1281.024
OK
Terhadap gelincir H tot > 0.2 Vtot
s=
39.16 187
>
0.2
0.209
>
0.2
NOT OK
Terhadap dimensi a.b = 2(a+b)te 2
30.5 30.5
≥ ≥
4 4
syarat
s 8.472
x +
Terhadap bearing σ = V tot = 187.4159 a.b 305 x 305 syarat
σ 2.015
≤ ≤
fc' 22.83
=
8.472
0.9
OK
=
OK
0.002 kN/mm²
=
2.015 MPa
PERENCANAAN ABUTMENT Data -data : γ tanah = H abutment = Lebar abutment = Sudut Geser tanah = Panjang bentang jembatan = Perhitungan abutment 1. Beban vertikal Beban mati struktur atas Plat lantai ts x B 0.25 x 9.4 Air hujan th x B 0.05 x 9.4 Aspal ta x B 0.1 x 7 Trotoar t x B 0.25 x 1.2 Tiang sandaran P x n 0.19 x 9 Girder P x n 23.8 x 5 Diafragma P x n 3.19 x 5
1.59 t/m³ 6m 9.4 m 14.9 ° 16 m
x x
L 16
x x
BJ 2.4
=
90.24
t
x x
L 16
x x
BJ 0.98
=
7.3696
t
x x
L 16
x x
BJ 2.2
=
24.64
t
x x
L 16
x x
BJ 2.4
=
11.52
t
=
1.6848
t
=
119
t
P total P untuk abutment Beban sendiri abutment
=
15.9375 t
= = =
270.3919 t 135.19595 t 1352 kN
No 1 2 3 4 5
lebar (m) 0.3 0.6 0.3 1 3.6
tinggi (m) 0.7 1 0.5 3.8 1
lebar abut Volume Berat Jenis m³ t/m³ (m) 9.4 1.974 2.5 9.4 5.64 2.5 9.4 1.41 2.5 9.4 35.72 2.5 9.4 33.84 2.5
Titik Berat Abutment thdp O x=
Σ Momen 16.95525 = Σ Berat 196.46
0.0863038 m
Beban tanah timbunan di belakang abutment
Berat t 4.935 14.1 3.525 89.3 84.6
Jarak X Momen X (m) t.m 0.65 3.20775 0.8 11.28 0.7 2.4675 0 0 0 0
196.46
16.95525
No 1 2 3 4
lebar (m) 1 0.7 0.3 1.3
tinggi (m) 0.7 1.5 0.5 2.8
lebar abut Volume Berat Jenis m³ t/m³ (m) 9.4 6.58 1.59 9.4 9.87 1.59 9.4 1.41 1.59 9.4 34.216 1.59
Berat Jarak X t (m) 10.4622 1.3 15.6933 1.45 2.2419 0.9 54.40344 1.15
Momen X t.m 13.60086 22.75529 2.01771 62.56396
82.80084
100.9378
Titik Berat Abutment thdp O x=
Σ Momen 100.93781 = Σ Berat 82.80084
1.22 m
Beban Lalu Lintas (PEL dan KEL) Beban kendaraan yang berupa beban lajur D terdiri dari beban terbagi rata (BTR), dan beban garis (BGT ) BTR memiliki nilai q (kPa) yang besarnya tergantung pada panjang total L yang dibebani lalu lintas atau dinyatakan dengan rumus sebagai berikut: q= 8 kPa q = 8 x (0.5 + 15/L) kPa
untuk L ≤ 30 m untuk L > 30 m
Untuk panjang bentang jembatan, L = q= 8 kPa
16 m
BGT mempunyai intensitas, p = 40 kN/m Faktor beban dinamis (Dinamic Load Allowance) untuk BGT diambil sebagai berikut: DLA = DLA = DLA =
untuk L ≤ 50 m 0.4 0.4 - {0.0025 x (L-50)untuk 50 < L < 90 m untuk L ≥ 90 m 0.3
Sehingga DLA =
0.4
WTD = q x L x (5,5 + b) / 2 + p x DLA x (5,5 + b) / 2 Ket : q = beban merata L = bentang jembatan b = lebar jalur WTD =
q
x
L
x
5.5
=
8
x
16
x
5.5
=
844
+ 2 + 2
b
+
p
x DLA x
5.5
7
+
40
x
5.5
0.4
x
+ 2 + 2
b 7
kN
Beban pada abutment akibat beban lajur D PTD = 0.5 x WTD = 0.5 x 844 = 422 kN = 42.2 t Beban Pejalan kaki (PTD) A = luas bidang trotoar yang dibebani pejalan kaki (m 2) Beban hidup merata q : q = q = q =
5 kPa 5 - {0.033 x (A-10)} kPa 2 kPa
Bentang jembatan Lebar trotoar Jumlah trotoar A= b
x
A = 1.2
x
L 2 16 2
L= b= n=
untuk A ≤ 10 m² untuk 10 m² < L ≤ 100 m² untuk A > 100 m²
16 m 1.2 m 2
x
n
x
2
A = 19.2 m² Sehingga q =
4.99 kPa
Beban pada abutment akibat pejalan kaki Ptp= A x q = 19.2 x 4.99
=
95.712
kN
=
9.5712 t
2. Beban hprizontal Beban rem Pengaruh rem dan percepatan lalu lintas harus dipertimbangkan sebagai gaya memanjang. Gaya ini
tidak tergantung pada lebar jembatan Dimana panjang jembatan bentang pinggir (L) adalah
=
18 m
Panjang Bentang Gaya rem (m) (kN) ≤ 80 L 250 80 < L < 180 2.5 L + 50 ≥ 180 L 500 Gaya rem yang te=
250 kN =
25 t
Beban Angin Kecepatan angin rencana Panjang jembatan Lebar jembatan Tinggi samping jembatang yg terkena angin L koef bagian samping jembatan Koef. Seret Gaya angin Tew = 0 x Cw x Vw² x Ab = 0 x 1.2 x 900 x 50.4 = 32.7 kN = 3.27 ton
Vw L b ha Ab Cw
= = = = = =
30 m/s 18 m 9.4 m 2.8 m L x 1.2
Tekanan tanah aktif Tinggi timbunanh= 5.85 m Lebar jembatan b= 9.4 m Berat Jenis tanahγt= 1.59 t/m³ Sudut geser tanaΦ= 14.9 ° q tanah = 0.6 t/m² Koef tekanan tanah aktif Ka = tan² 45 Φ 2 Ka = tan² 45 - 14.9 2 Ka = 0.59 Pa 1
= = =
Pa 2
= =
q x 0.6 x 19.5 t 1 2 1 2
ka 0.59
x x
h 5.85
x x
b 9.4
x
γt
x
ka
x
h²
x
b
x
1.59
x
0.59
x
34.22
x
9.4
ha =
50.4 m²
Pa total
=
151 t
= = =
Pa 1 + 19.5 + 171 t
Titik berat terhadap O Σ M Pa = z = Σ Pa =
Pa 2 151
Pa1
x 0.5 h + Pa2 Pa tot x 2.93 + 151 171
19.5
=
x 0.3 h x
1.76
1.89 m
Beban Gempa Koef geser Faktor tipe bangunan Faktor kepentingan Kh Teq
C = 0.18 wilayah gempa zona 3 S= 1 I= 1 = C x S = Kh x I x W = C x S x I x W
Beban gempa bangunan atas Teq 1 = 0.18 x 1 = 24.335271 ton
x
1
x
135.19595
Beban gempa sendiri abutment Teq 2 = 0.18 x 1 = 35.3628 ton
x
1
x
196.46
Beban gempa akibat tekanan tanah dinamis Teq 2 = C x S x I x Tt = 0.18 x 1 x 1 x 171 = 30.711965 ton
Beban akibat gesekan pada perleakan Menurut PPPJJR 1987 gaya gesekan pada peletakan adalah 5 % dikalikan total beban mati struktur atas (DL yang membebani abutment. Beban tersebut yaitu : F= 5% x FB = 5% x
DL MA
+
MS
MA= 32.0096 t MS= 196.46 t FB = 5% x
32.0096
+
196.46
= =
11.42348 t 114 kN
Kombinasi 1
MS + MA + TA + TD + TP
No.
Beban
Bagian
1 2 3 4 5 6 7 8 9 10 11 12 13 14
MS MS MS MA TA TD TP TB ET EW EQ EQ EQ FB
abutment bangunan atas tanah timbunan di belakan abutment beban mati tambahan tekanan tanah aktif beban lajur D beban pejalan kai gaya rem suhu beban angin beban gempa bangunan ats beban gempa abutment beban gempa tekana tanah aktif gesekan pada perletakan TOTAL 100%
Σ
Kombinasi 2 Beban
Bagian
1 2 3 4 5 6 7 8 9 10 11 12 13 14
MS MS MS MA TA TD TP TB ET EW EQ EQ EQ FB
abutment bangunan atas tanah timbunan di belakan abutment beban mati tambahan tekanan tanah aktif beban lajur D beban pejalan kai gaya rem suhu beban angin beban gempa bangunan ats beban gempa abutment beban gempa tekana tanah aktif gesekan pada perletakan TOTAL 125%
Kombinasi 3 No.
Beban
V 196.460 135.196 82.801 32.010
H
170.622 42.200 9.571
498.238 498.238
Jarak thdp O X Y 0.086 5.500 1.219 5.500 1.889 5.500 5.500
170.622 170.622
MS + MA + TA + TD + TP + TB + EW
No.
Σ
Gaya
Gaya
25.000
Jarak thdp O X Y 0.086 5.500 1.219 5.500 1.889 5.500 5.500 6.000
3.266
6.000
V 196.460 135.196 82.801 32.010
H
170.622 42.200 9.571
498.238 622.797
198.888 248.610
MS + MA + TA + TD + TP + TB + FB Bagian
Gaya V
H
Jarak thdp O X Y
1 2 3 4 5 6 7 8 9 10 11 12 13 14
MS MS MS MA TA TD TP TB ET EW EQ EQ EQ FB Σ
Kombinasi 4
abutment bangunan atas tanah timbunan di belakan abutment beban mati tambahan tekanan tanah aktif beban lajur D beban pejalan kai gaya rem suhu beban angin beban gempa bangunan ats beban gempa abutment beban gempa tekana tanah aktif gesekan pada perletakan TOTAL 125%
Beban
Bagian
1 2 3 4 5 6 7 8 9 10 11 12 13 14
MS MS MS MA TA TD TP TB ET EW EQ EQ EQ FB
abutment bangunan atas tanah timbunan di belakan abutment beban mati tambahan tekanan tanah aktif beban lajur D beban pejalan kai gaya rem suhu beban angin beban gempa bangunan ats beban gempa abutment beban gempa tekana tanah aktif gesekan pada perletakan TOTAL 140%
Kombinasi 5
0.086 5.500 1.219 5.500 170.622
42.200 9.571
498.238 622.797
1.889 5.500 5.500
25.000
6.000
11.423 207.046 258.807
6.000
MS + MA + TA + TD + TP + TB + ET + FB
No.
Σ
196.460 135.196 82.801 32.010
Gaya V 196.460 135.196 82.801 32.010
H
170.622 42.200 9.571 25.000
498.238 697.533
11.423 207.046 289.864
Jarak thdp O X Y 0.086 5.500 1.219 5.500 1.889 5.500 5.500 6.000
6.000
MS + MA + EQ
No.
Beban
Bagian
1 2 3 4
MS MS MS MA
abutment bangunan atas tanah timbunan di belakan abutment beban mati tambahan
Gaya V 196.460 135.196 82.801 32.010
H
Jarak thdp O X Y 0.086 5.500 1.219 5.500
5 6 7 8 9 10 11 12 13 14
TA TD TP TB ET EW EQ EQ EQ FB
tekanan tanah aktif beban lajur D beban pejalan kai gaya rem suhu beban angin beban gempa bangunan ats beban gempa abutment beban gempa tekana tanah aktif gesekan pada perletakan TOTAL 150%
Σ
24.335 35.363 30.712 446.466 669.700
5.500 1.200 1.500
90.410 135.615
YANG DIPAKAI ADALAH HASIL KOMBINASI TERBESAR (kombinasi5) Σ V = 697.533 t Σ H = 289.864 t
Σ Mh = Σ Mv =
Kontrol Abutment dan beban garis (BGT K ) ontrol terhadap guling ≥ 2.2 bebani lalu lintas SF = Σ MV Σ MH SF = 1851.171 = 2.45 757.111
Σ M total =
757.111 t.m 1851.171 t.m
≥
2.2
OK
V ΣH 697.533 289.864
Kontrol terhadap geser SF = C
x
Bx
x
By
+
SF = 0.22
x
3.6
x
9.4
+
SF = 1.56 ≥
1.1 OK
x tan θ x
1
+
k
x
1
+
1.4
0.27
x
anjang. Gaya ini
an mati struktur atas (DL)
arak thdp O Y
1.889
Momen Mv Mh 16.955 743.578 100.938 176.053 322.253 232.100 52.642
1322.265 322.253 1322.265 322.253
arak thdp O Y
6.000
Momen Mv Mh 16.955 743.578 100.938 176.053 322.253 232.100 52.642 150.000
6.000
19.596
1.889
arak thdp O Y
1322.265 491.849 1652.831 614.811
Momen Mv Mh
16.955 743.578 100.938 176.053 1.889
322.253 232.100 52.642
6.000
150.000
6.000
68.541 1322.265 540.794 1652.831 675.992
arak thdp O Y
1.889
6.000
6.000
arak thdp O Y
Momen Mv Mh 16.955 743.578 100.938 176.053 322.253 232.100 52.642 150.000
68.541 1322.265 540.794 1851.171 757.111
Momen Mv Mh 16.955 743.578 100.938 176.053
5.500 1.200 1.500
133.844 42.435 46.068 0.000 1037.524 222.347 1556.285 333.521
2608.283 t.m
≥
1.1
PENULANGAN ABUTMENT Penulangan Back Wall Data -data γ tanah H abutment Sudut geser tanah,θ Ws Lebar abutment Koef tanah aktif, Ka Tekanan tanah H = 1.2
No. 1 2
1.59 t/m³ 6m 14.9 ° 1.59 t/m³ 9.4 m 0.591
= = = = = =
=
T ta 1 T ta 2 JUMLAH
No 1 2
lebar (m) 0.6 0.6
tinggi (m) 0.7 0.5
Beban Ultimit Back Wall Gaya geser ultimit Vu = K x T
= =
400 MPa 30 MPa
1.2 m
Gaya akibat tekanan tanah
Beban Gempa Statik Ekivalen Kh = C x S = Teq= Kh x I x
fy fc'
0.18 W
T ta ton 6.359 6.359 12.718
x =
1 0.18
Lengan m 0.6 0.4 1.000
Momen ton.m 3.815 2.544 6.359
= x
0.18 1 x
lebar abut Volume m³ (m) 9.4 3.948 9.4 2.82 JUMLAH
Berat Jenis t/m³ 2.5 2.5
W Berat t 9.87 7.05
= T eq t 1.7766 1.269 3.0456
Momen ultimit Mu = K x
M
K = faktor beban ultimit Jenis Beban (m²) Tekanan 1 tanah Gempa 2 statik ekivalen
Faktor Beban 1.25 1 JUMLAH
No
Penulangan a. Tulangan Utama Decking (d') = d = m
50 mm H -
=
d
T t 12.718 3.046
M t.m 6.359 0.000
=
-
0.85
fy x
ρ min =
25%
x
1.4 fy
=
1.4 400
=
ρb
0.85
x
fc' fy 30 400
x
β1
x
ρb
=
= = =
0.85
x
0.75
Mu
=
7.949 t.m
Mn
=
Mu 0.85
Rn
=
=
0.85
=
0.85
15.686
30
0.000875
600 x
1150 mm
x 600
600 + 600 +
fy 400
x
=
0.75
x
79487259 N.mm = 0.85
0.024
93514421.918 N.mm
d²
1 m
x
1
-
1
-
2
x
m fy
x
Rn
1 15.686
x
1
-
1
-
2
x
15.686 400
x
0.07
0.0002
=
0.032513 =
Mn x
b
=
fc'
400 x
50 =
Mu t.m 7.949 0.000 7.949
0.033
ρ max =
ρ perlu =
=
1200
Vu t 15.897 3.046 18.943
93514421.9175044 1000 x 1322500
=
0.070710338
Syarat,
ρ min 0.0009
< >
ρ perlu 0.00018
Sehingga dipakai
As perlu = = =
ρ 0.000875 1006.25
x b x 1000 mm²
Direncanakan tulangan S
0.25
x
=
0.25
x
=
199.81
ρ min 0.000875
x x
d 1150
π
D² x As perlu π x 256 1006.25
x
b
x
1000
x
1000
x
1000
x
b
x
1000
175 mm
As pasang =
0.25
x
π
=
0.25
x
π
=
ρ maks 0.024
16
=
Dipakai jarak
<
ρ perlu 0.00073
<
150634.956
perlu tulangan geser
Geser pada beton sepenuhnya dipikul oleh tulangan geser Vs = Vu = 150634.956 = 188293.69 N Φ 0.8 Untuk tulnagan geser digunakan besi
Asv
= = =
Sx
b x Sy 1000 x 300 442.441 mm²
D Jarak π 4 π 4
13 300 x
d²
x
169
d Vs 900 188293.69
=
Asv
x
fy
x
=
442.441
x
400
x
=
845.9059 ~
Digunakan tulagan geser D
300 mm 13 dengan jarak
300
tinggi (m) 0.7 1 0.5 3.8
lebar abut (m) 9.4 9.4 9.4 9.4
Volume m³ 1.974 5.64 1.41 35.72
truktur atas
Berat Jenis Berat t/m³ t 2.5 4.935 2.5 14.1 2.5 3.525 2.5 89.3 135.196 247.056
= = = = = = =
Lengan m 3 2
1.59 t/m³ 6m 14.9 ° 1.59 t/m³ 9.4 m 0.5909 6m
fy fc'
= =
400 MPa 30 MPa
Momen ton.m 95.385 317.949 413.334
0.18 1 x Berat Jenis t/m³ 1.59 1.59 1.59 1.59
W
=
Berat t 3.13866 8.9676 2.2419 56.7948 196.46
0.18 W T eq t 0.5649588 1.614168 0.403542 10.223064 35.3628
Jarak X (m) 0.65 0.8 0.7 0 0.086304
Momen t.m 2.040129 7.17408 1.56933 0 16.95525
32.0096
5.761728
5.5
299.61256
0.18 x
1x
Gaya geser V ux V uy ton ton
203.7916
190.769 =
413.334
50 299.613 34.338 14.850524
300.000 203.791589 103.01548718 22.275786
Momen M ux M uy ton.m ton.m
238.462
413.334
50
300.000
288.462
0
Gaya geser V ux V uy ton ton
238.462
34.338 ton
Momen M ux M uy ton.m ton.m
238.462
Gaya geser V ux V uy ton ton
176.0528
713.334
0
Momen M ux M uy ton.m ton.m
413.334
50
300.000
34.338 322.800
22.275786 735.610
0
Gaya geser V ux V uy ton ton
Momen M ux M uy ton.m ton.m
238.462
413.334
50
300.000
34.338 322.800
22.275786 735.610
0
Gaya geser V ux V uy ton ton
413.334
50
300.000
0
Gaya geser V ux V uy ton ton
238.462
0
Momen M ux M uy ton.m ton.m
238.462
288.462
0
713.334
0
Momen M ux M uy ton.m ton.m
413.334
300.000 203.791589 103.01548718
299.613 34.338 572.413
0
1020.141
V uy (ton) M ux (ton.m) M uy (ton.m) 0 713.334 0 0 735.610 0 0 735.610 0 0 713.334 0 0 1020.141 0
V uy (ton) M ux (ton.m) M uy (ton.m) 0 71.333 0 0 73.561 0 0 73.561 0 0 71.333 0 0 102.014 0
400
100 = =
900 mm 15.686
30 0.0035
600 600
600 + 600 +
fy 400
0
0.0325
=
0.024
673426861 N.mm
426860.726758 8E+05
=
0.83139119
2
x
m fy
x
Rn
2
x
15.686 400
x
0.83139
ρ maks 0.024
b 1000
1000 1000
b 1000
100 d 900
=
900
5E+06 =
3E+06
900 = 2000
0.95
b
x
h
1000
x
1000
43402310
mm
OK!!!
ρ perlu 0.00001
Sehingga dipakai ρ min As perlu = = =
ρ 0.0035 1750
x b x 1000 mm²
Direncanakan tulangan S
22
=
0.25
x
π
=
0.25
x
π
=
217
Dipakai jarak
x x
x As perlu x 1750
200 mm
As pasang =
0.25
x
π
=
0.25
x
π
=
1901 mm²
x S x 200
b. Tulangan Bagi Direncanakan As perlu = = = S
13 20% x As perlu 20% x 1750 350 mm²
=
0.25
x
π
=
0.25
x
π
=
379
Dipakai jarak c. Tulangan Geser Gaya geser ultimit
x As perlu x 350
300 mm
Vu
=
456572.311591
Vc
= = =
Φ Vc = Φ Vs = Vs
=
1 x 6 1 x 6 456435.46 N 0.6 Vu
fc'
x
b
x
30
x
1000
x
x Vc = - Φ Vc =
273861.28 456572.31
228388.79 N
Untuk tulnagan geser digunakan besi
Asv
π 4 π 4
=
b x Sy 1000 x 300 442 mm²
=
Asv
x
fy
x
=
442
x
400
x
= =
Sx
D Jarak
=
387 ~
Digunakan tulagan geser
D
x x
300 mm 13 dengan jarak
Hy Hx t ww
= = =
6m 2.8 m 0.6 m
BJ
=
2.5 t/m³
Mx
=
My
=
=
1 2 1 2
2.2
x
M
jepit arah X
x
M
jepit arah Y
x
0.6
=
ton 13.1042824344 74.4561501953
wall akibat tekanan tanah Lengan x = Hx/2 x = Hx/2
x (m) My (ton.m) Mx (ton.m) 1.4 39.3128473 18.34599541 1.4 148.9123004 104.2386103 188.2251477 122.5846057
BJ 2.5
1.32 t/m²
x x
Wt 25.2
y=
-
0.59
=
Hy 2
=
3m
0.1
Teq (ton) 12.9878498047 0.8658566536
wall akibat tekanan tanah dinamis Lengan x = Hx/2 x = Hx/2
x (m) My (ton.m) Mx (ton.m) 1.4 51.95139922 18.18298973 1.4 2.597569961 1.212199315 54.54896918 19.39518904
My (ton.m) Mx (ton.m) Faktor Beban Vu (ton) Muy (ton) Mux (ton) 188.225147694 122.5846057 1.25 109.4505 235.2814 153.2308 6.804 3.1752 1 4.536 6.804 3.1752
54.5489691799 19.39518904
1
13.85371 54.54897 19.39519 127.8402 296.6344 175.8011
=
0.85
600 400 x
1.4 400
=
β1
x
-
=
N.mm
15.686
0.0035
x 600
0.75
500 mm
30
600 0.85
100 =
600 + 600 +
fy 400
x
0.03251 =
=
1246363.041 N.mm
1246363.04116359 1000 x 250000
0.024
= 0.004985452
1
-
2
x
m fy
x
Rn
1
-
2
x
15.686 400
x
0
<
