Post on 08-Aug-2018
8/22/2019 Perencanaan Gelagar Prategang
1/18
NIM akhir 4
Diketahui:
A. Material
= 20 m
Beton
f'c = 40.4 MPa
f'ci = 30.4 MPa
Eci = 30000 MPa 3 hariEc = 40000 MPa 28 hari
Baja
fpu = 1860 MPa
fpy = 1450 MPa
Eps = 200000 MPa
dps = 12.7 mm
n strand = 7 (kabel seven wire strand)
1- = 0.15
= 0.85
B. Pembebanan
=
=
Ditanya:
Bentuk & Dimensi Penampang
Gaya Prategang & n kabel perlu
Posisi Kabel
Tulangan Geser Perlu
Penyelesaian:
1. Perhitungan Tegangan Izin
Saat Transfer:
fci = -0,6. f'ci
= -0,6 x 30.4
= -18.24 MPa
fti =
= 0,25 x ( 30.4^0,5)
= 1.378404875 MPa (di tengah bentang)
fti =
= 0,5 x (30.4^0,5)
= 2.75680975 MPa (di tumpuan)
Saat Layan:
fc = -0,45. f'c
= -0,45 x 40.4
= -18.18 MPa
ft =
= 0,5 x (40.4^0,5)
= 3.178049716 MPa
Area = 178064.1600
Centroid x = 203.2000 mm
Centroid y = 319.7700 mm
Moments Inertia x = 9.4668E+09 mm^4
Moments Inertia y = 1.3953E+09 mm^4
2
Ct = 391.4300 mm
Cb = 319.7700 mm
h = 711.2000 mm
b1 = 304.8000 mm
b2 = 406.4000 mm
a. Momen Lentur
qdl = Ac x beton
= 0.1781 x 2.4
= 0.4274 t/m
qsidl = 0.2 t/m
qLL = 0.34 t/m
=
= 1/8 x 0.4274 x 20
= 21.3677 t.m
=
= 1/8 x 0.2 x 20
= 10.0000 t.m
=
= 1/8 x 0.34 x 20
= 17.0000 t.m
Hasil:
Md = 21.3677 t.m
= 213676992.0000 N.mm
Msidl + MLL = 27.0000 t.m
= 270000000.0000 N.mm
3. Perhitungan St dan Sb perlu
a. St dan Sb perlu (akibat pembebanan dan sifat material)
St 15,608,573
St 14,717,503 mm (di tumpuan)
Sb 16,168,009 mm
b. St dan Sb tersedia dari penampang
St = Ic / Ct
= 9466821164.642 / 391.43
= 24,185,221 mm
Sb = Ic / Cb
= 9466821164.642 / 319.77
= 29,605,095 mm
Hasil:
= 24,185,221 > St perlu = ######## (di tengah bentang) OK
= 24,185,221 > St perlu = ######## (di tumpuan) OK
= 29,605,095 > Sb perlu = ######## OK
4. Gaya Prategang Awal
= 1.3785 - ((391.43 / 711.2) x (1.3785-18.24))
= -9.4192 MPa (di tengah bentang)
= 2.7569 - ((391.43 / 711.2) x (2.7569-18.24))
= -8.7994 MPa (di tumpuan)
Pi =
= 178064. 16 x 9.41916573826548
= 1,677,215.8351 N (di tengah bentang)
Pi =
= 178064. 16 x 8.79940684211027
= 1,566,858.9878 N (di tumpuan)
5. Eksentrisitas Maksimum
e
e ((1.3785 - -9.4192) x (24185221.2775/1677215.8351)) + (213676992/1677215.8351)
e 283.0992986 mm (di tengah bentang)
e
e ((2.7569--8.7995) x (24185221.2775/1566858.9879)) + (213676992/1677215.8351)
e 305.7755732 mm (di tumpuan)
*dipakai e = 200
6. Hitung Batas Pi
Di tengah Bentang
Saat Awal
Pi 3,848,953.6312
Pi 2,057,751.9138
Saat akhir
Pi -3,110,653
Pi 565,054
Di tumpuan
Saat Awal
Pi 1,197,655
Pi 1,474,351
Saat akhir
Pi 1,409,006
Pi 1,728,825
Rekap batas
Tengah Bentang
Saat Awal Saat Akhir
Tumpuan
Saat Awal Saat Akhir
7. Luas Baja Prategang
Pi = 2,057,751.9138 N
Pe = 0.85 x 2057751.9138
= 1,749,089.1267 N
= 2057751.9138 / 1450
= 1419.1393
n kabel =
= 1.599760173
2
dp = h - e= 711.2 - 200
= 511.2000 mm
a = n x Aps x fps
0,85 x f'c x b
= 3299993.4
12211.304
= 270.2408686 mm
Mn = n x Aps x fps x (dp- a/2)
= (((0,25 x (22/7) x (12.7^2))) x 7) x 2 x 1860 x (511.2-(270.2409/2))
= 1.2411E+09
0,8. Mn > +
> 213676992 + 270000000
> 4.8368 x 10^8 N.mm
2 bu ah tendo n deng an P i = 205 7751 .9138 N , menimbulkan Mn = 9 .9285 x 10^8 N.mm > Mu = MD + MT = 4.8368 x 10^8 N .mm, OK!
8. Kontrol Tegangan Izin
8.a) Saat transfer
Tengah Bentang
ft = -3.374655756 MPa < 1.378405
fb = -18.24 MPa < -18.24
Tumpuan
ft = 5.460367482 MPa > 2.75681
fb = -25.457575 MPa < -18.24
8.b) Saat layan
Tengah Bentang
ft = -6.522530092 MPa < 3.17805
fb = -12.51888688 MPa > -18.18
Tumpuan
ft = 4.641312359 MPa > 3.17805
fb = -21.63893875 MPa < -18.18
9. Perhitungan Batas Aman Tendon
9.a) Nilai Momen Per Pias Bentang
Akibat MD Akibat MT
Ra = Rb = 4.2735 t Ra = Rb = 5.4000 t
qdl = 0.4274 t/mqsidl = 0.2 t/m
qLL = 0.34 t/m
kt =2
= -(53165.2252 / 319.77)
= -166.2608 mm
kb =2
= (53165.2252 / 391.43)
= 135.8231 mm
Pi = 2,057,751.9138 N
Pe = 1,749,089.1267 N
Di atas Tumpuan 0.0000 m
Batas bawah
=
e5 = 135.8231 mm
0 8 x 1.2411 x 10^9
.9285 x 10^8 N.mm
=
=
akibat LL
Momen tengah bentang
akibat DL
Momen tengah bentang
akibat SIDL
Momen tengah bentang
t/m0.54
0.15 x 213676992 + 270000000
0.85 x 1.37840487520902 - -18.18
St
+
0.85 x 2.75680975041804 - -18.18
St
0.15 x 213676992 + 270000000
3.17804971641414 - 0.85 x -18.24
Sb
cti
LSDDt
ff
MMMS
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LSDDb
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76.
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304.800
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127.
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127.
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319.
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391.
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fcci
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)/.1(
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2rce
ASMfP
tc
tDti
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)/.1(
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2rce
ASMfP
b
cbDcii
)/.1(
)/(
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ASMfP
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)/.1(
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8/22/2019 Perencanaan Gelagar Prategang
2/18
Batas atas
=
e5 = -166.2608 mm
1/8 Bentang 2.5000 m
=
= 9.3484 t.m
Batas bawah
=
= 93483684 / 2057751.9138
= 45.4300 mm
e4 =
= 135.8231 + 45.4301
= 181.2531 mm
+ = ############## N.mm
= 11.8125 t.m
Batas atas
=
= 118125000 / 1749089.12673
= 67.5352 mm
e4 = -
= 67.5352 - -166.2609
= 233.7960 mm
1/4 Bentang 5.0000 m
=
= 16.0258 t.m
Batas bawah
=
= 160257744 / 2057751.9138
= 77.8800 mm
e3 =
= 135.8231 + 77.8801
= 213.7031 mm
+ = ############## N.mm
= 20.2500 t.m
Batas atas
=
= 202500000 / 1749089.12673
= 115.7745 mm
e3 = -
= 115.7746 - -166.2609
= 282.0354 mm
3/8 Bentang 7.5000 m
=
= 20.0322 t.m
Batas bawah
=
= 200322180 / 2057751.9138
= 97.3500 mm
e2 =
= 135.8231 + 97.3501
= 233.1731 mm
= ############## N.mm
= 25.3125 t.m
Batas atas
=
= 253125000 / 1749089.12673
= 144.7182 mm
e2 = -
= 144.7182 - -166.2609
= 310.9790 mm
1/2 Bentang 10.0000 m
=
= 21.3677 t.m
Batas bawah
=
= 213676992 / 2057751.9138
= 103.8400 mm
e1 =
= 135.8231 + 103.8401
= 239.6631 mm
= ##############
= 27.0000 t.m
Batas atas
=
= 270000000 / 1749089.12673
= 154.3661 mm
e1 = -
= 154.3661 - -166.2609
= 320.6269 mm
10. Perencanaan Balok Prategang
10.a) Perhitungan Tulangan Utama
qdl = 0.4274 t/m
L = 4.0000 m *(1 segmen 4 m)
Mu = 0.8547 t.m
= 8,547,079.6800 N.mm
= 13 mm
= 10 mm
= 30 mm
fy = 400 MPa
f'c = 40.4 MPa
h = 711.2000 mm
b1 = 304.8000 mm
b2 = 406.4000 mm
d = h p - sengkang tul. Utama
= 711.2 30 - 10 ( .13)
= 664.7 mm
Ac' = 153883.36
'
a = 186.2970297
b = -320
c = 0.0836
dengan rumus abc diperoleh akar2 persamaan:
x1 = 1.718
x2 = -0.0002612
= 0.0002612
min = 1,4 / fy
= 1,4 / 400
= 0.0035
= 0.0035000
As = . b. D
= 0.0035 x ((304.8 + 406.4) / 2) x 664.7
= 827.28562
10.b) Perhitungan Tulangan Geser
*Pengaruh Beban Mati
= 0.6274 t/m
L = 20 m
= 20000 mm
Vu = 1/2. q. L
= 0,5 x 0.627353984 x 20
= 6.27353984 t
= 62,735.3984 N
d = 664.7000 mm
Vc = gaya lintang yang ditahan oleh beton
Untuk perhitungan Vc ini, harus dilihat dari dua hal yaitu
-retak akibat geseran pada badan penampang (Vcw)
-retak miring akibat lentur (Vci)
-nilai Vc adalah nilai terkecil dari Vcw dan Vci
Vcw = '0,5
Vp = komponen vertikal dari gaya prategang
Vp = 27,949.0187 N
Bw = 250 mm *Separuh Elastomer
fpc = Pe / Ac
= 1749089.1268 / 178064.16
= 9.822802785
Vcw = '0,5
= (((0,29 x (40.4^0,5)) + (0,3 x 9.8229)) x 250 x 664.7) + 27949.0187
= 823,945.4933 N
Mcr = ' '0,5
= (9466821164.642 / 391.43) x ((0,5 x (40.4^0,5)) + 9.8229)
= ############## N.mm
Tegangan terbesar terdapat pada jarak x atau 0,25.L dari tumpuan, maka:
x = 0,25 x L
= 0,25 x 20 m
= 5000 mm
Mmax / Vt =
= ((20000. 5000) - 5000) / (20000 - 2.5000)
= 7500 mm
Vci = '0,5
= (0,05 x 250 x 664.7 x (40.4^0,5)) + (314428494.5389 / 7500)
= 52,811.2412 + 41923.79927
= 94,735.0404 N
dipakai = 94,735.0404 N
= 104,558.9973 N
Vs =
= (62735.3984 / 0, 6) - 94735.0405
= 9,823.9569 N
0,5.Vc = 0,5 x 94735.0404343639
= 47,367.5202 N
Dibutuhkan Tulangan Geser, (Vu / ) > 0,5.Vc
Av / S = Vs / (fy.d)
Av / S = 9823.95689896942 / (400 x 664.7)
Av / S = 0.036948837
Av = 78.57142857
0.03695 = 78.5714285714286 / S
S = Av / (Av / S)
= 78.5715 / 0.037
= 2126.492578 mm
= 212.6492578 cm
S = 0,75 x h
= 533.4 mm
= 53.34 cm
S = 24 inch
= 60.96 cm
S = 53.34 *(Dipakai yg terkecil)
40 *Sesuaikan dengan bentang
Mu / Ac' x d
Mu / Ac' x d
0.0836
tulan an utama
tulan an sen kan
Mu / Ac' x d
0.0836
8/22/2019 Perencanaan Gelagar Prategang
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angan Beton Prategang
NIM akhir 4
iketahui:
. MaterialPanjang bentang :
L = 20 m
Beton
Mutu beton pada umur 28 hari :
f'c = 40.4 MPa
Mutu beton pada umur 3 hari :
f'ci = 30.4 MPa
Modulus elastisitas beton pada umur 3 hari :
Eci = 30000 MPa
Modulus elastisitas beton pada umur 28 hari :
Ec = 40000 MPa
Berat jenis beton :
beton = 2.4 t/m
Baja
Mutu baja prategang ultimit :
fpu = 1860 MPa
Mutu baja prategang leleh :
fpy = 1450 MPa
Modulus elastisitas baja prategang :
Eps = 200000 MPa
Diameter baja prategang :dps = 12.70 mm (1 strand)
Jumlah Strand (dalam 1 stendon):
n strand = 7 (kabel seven wire strand)
Kehilangan prategang :
1- = 0.15 (prategang residual)
= 0.85
. Pembebanan
Beban berat sendiri balok :
qdl = - t/m
Beban mati :
qsidl = 0.20 t/m
Beban hidup :
qLL = 0.34 t/m
itanya:
Bentuk & Dimensi Penampang
Gaya Prategang & n kabel perlu
Posisi Kabel
Tulangan Geser Perlu
BAB 3
PERHITUNGAN
Anggen
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4/18
angan Beton Prategang
enyelesaian:
. Perhitungan Tegangan Izin
Saat Transfer:
Tegangan tekan ijin saat awal :
fci = -0,6. f'ci
= -0,6 x 30.4
= -18.24 MPa
Tegangan tarik ijin saat awal di tengah bentang :
fti =
= 0,25 x ( 30.4^0,5)
= 1.3784 MPa
Tegangan tarik ijin saat awal di tumpuan :
fti =
= 0,5 x (30.4^0,5)
= 2.7568 MPa
Saat Layan:
Tegangan tekan ijin saat akhir :
fc = -0,45. f'c
= -0,45 x 40.4
= -18.1800 MPa
Tegangan akhir ijin saat akhir :
ft =
= 0,5 x (40.4^0,5)
= 3.1780 MPa
. Perhitungan Momen Yang Terjadi
Anggen
8/22/2019 Perencanaan Gelagar Prategang
5/18
angan Beton Prategang
Data Penampang :
Luas = 178064.1600 mm
Moments Inertia x = 9.4668E+09 mm^4
Moments Inertia y = 1.3953E+09 mm^4
R2
= 53165.2252 mm
Ct = 391.4300 mm
Cb = 319.7700 mm
h = 711.2000 mm
b1 = 304.8000 mm
b2 = 406.4000 mm
. Momen Lentur
Beban berat sendiri balok :
qdl = Ac x beton
= 0.1781 x 2.4
= 0.4274 t/m
Beban mati :
qsidl = 0.20 t/m
Beban hidup :
qLL = 0.34 t/m
= 1/8.qdl.l
= 1/8 x 0.4274 x 20
= 21.3677 t.m
= 1/8.qsidl.l
= 1/8 x 0.2 x 20
= 10.0000 t.m
= 1/8.qLL.l
= 1/8 x 0.34 x 20
= 17.0000 t.m
Hasil perhitungan momen :
Md = 21.3677 t.m
= 2.1368E+08 N.mm
Msidl + MLL = 27.0000 t.m
= 2.7000E+08 N.mm
. Perhitungan Modulus Penampang Serat Atas (St) dan Modulus Penampang Serat Bawah (Sb) perlu
. Modulus Penampang St dan Modulus Sb perlu (akibat pembebanan dan sifat material)
Perhitungan Modulus Penampang Serat Atas (St) perlu di tengah bentang :
St 15,608,573 mm
(akibat LL )
Momen tengah bentang
St ((0.15 x 213676992) + 270000000)
((0.85 x 1.37840487520902) - -18.18)
(akibat DL )
Momen tengah bentang
(akibat SIDL )
Momen tengah bentang
Anggen
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angan Beton Prategang
Perhitungan Modulus Penampang Serat Atas (St) perlu di tumpuan :
St 14,717,503 mm
Perhitungan Modulus Penampang Serat Bawah (Sb) :
Sb 16,168,009 mm
. Modulus Penampang Serat Atas (St) dan Modulus Penampang Serat Bawah (Sb) tersedia dari penamp
Modulus Penampang Serat Atas (St) tersedia :
St = Ic / Ct
= 9466821164.642 / 391.43
= 24,185,221 mm
Modulus Penampang Serat Bawah (Sb) tersedia :
Sb = Ic / Cb
= 9466821164.642 / 319.77
= 29,605,095 mm
Hasil perhitungan Modulus Penampang Serat Atas (St) dan Modulus Penampang Serat Bawah (Sb) :
t tersedia = 24,185,221 > St perlu = 15,608,573 mm OK
t tersedia = 24,185,221 > St perlu = 14,717,503 mm OK
b tersedia 29,605,095 > Sb perlu = 16,168,009 mm OK
. Gaya Prategang Awal
= 1.3785 - ((391.43 / 711.2) x (1.3785-18.24))
= -9.4192 MPa (di tengah bentang)
= 2.7569 - ((391.43 / 711.2) x (2.7569-18.24))
= -8.7994 MPa (di tumpuan)
((0.15 x 213676992) + 270000000)
(3.17804971641414 - (0.85 x -18.24))
=
Modulus Penampang Serat Atas (St) :
Modulus Penampang Serat Bawah (Sb) :
=
St ((0.15 x 213676992) + 270000000)
((0.85 x 2.75680975041804) - -18.18)
Sb
Anggen
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angan Beton Prategang
Gaya Prategang Awal di tengah bentang :
Pi = Ac x fcci
= 178064.16 x 9.41916573826548
= 1,677,215.8351 N
Gaya Prategang Awal di tumpuan :
Pi = Ac x fcci
= 178064.16 x 8.79940684211027
= 1,566,858.9878 N
. Eksentrisitas Maksimum
Eksentrisitas Maksimum di tengah bentang :
e
e ((1.3785 - -9.4192) x (24185221.2775/1677215.8351)) + (213676992/1677215.8351)
e 283.0992986 mm
Eksentrisitas Maksimum di tumpuan :
e
e ((2.7569--8.7995) x (24185221.2775/1566858.9879)) + (213676992/1677215.8351)
e 305.7755732 mm
Asumsi eksentrisitas kurang dari eksentrisitas maksimum di tengah bentang, maka dipakai :
e = 200 mm
. Mencari Batas - batas Gaya Prategang
Batas - batas Gaya Prategang Di tengah Bentang
Saat Awal
Pi
Pi 3,848,953.6312 N
Pi
Pi 2,057,751.9138 N
((1.3785 + (213676992 / 24185221.2775)) x 178064.16)
(-1 + ((200 x 391.43) / 53165.2252))
((--18.24 + (213676992 / 29605094.8014)) x 178064.16)
(1 + ((200 x 319.77) / 53165.2252))
Anggen
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8/18
angan Beton Prategang
Saat akhir
Pi
Pi -3,110,653 N
Pi
Pi 565,054 N
Batas - batas Gaya Prategang Di tumpuan
Saat Awal
Pi
(-1 + ((200 x 391.43) / 53165.2252))
Pi 1,197,655 N
Pi
(1 + (200 x 319.77) / 53165.2252)
Pi 1,474,351 N
Saat akhir
Pi
Pi 1,409,006 N
Pi
Pi 1,728,825 N
(3.1781 x 178064.16)
(--18.24 x 178064.16)
(3.1781 x 178064.16)
((-1+((200 x 391.43) / 53165.2252)) x 0.85)
((-1+((200 x 391.43) / 53165.2252)) x 0.85)
((-3.1781 + (270000000 / 29605094.8014)) x 178064.16)
((1+((200 x 319.77) / 53165.2252)) x 0.85)
((-18.18 + (270000000 / 24185221.2775)) x 178064.16)
(--18.18 x 178064.16)
((1+((200 x 319.77) / 53165.2251898529)) x 0.85)
Anggen
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9/18
angan Beton Prategang
Rekapitulasi Hasil Batas - batas Gaya Prategang :
Tengah Bentang
Saat Awal Saat Akhir
Pi 3,848,953.6313 N Pi -3,110,652.8725 N
Pi 2,057,751.9138 N Pi 565,053.8796 N
Tumpuan
Saat Awal Saat Akhir
Pi 1,197,655.2692 N Pi 1,409,006.1991 N
Pi 1,474,350.7547 N Pi 1,728,824.6079 N
. Luas Baja Prategang
Maka batas prategang yang memenuhi persyaratan ( Pi) adalah :
Pi = 1,197,655.2692 N
Gaya Prategang Efektif (Pe)
Pe = . Pi
= 0.85 x 1197655.2692
= 1,018,006.9788 N
Luas Baja Prategang (Apsperlu)
Apsperlu = Pi / fpsi
= 1197655.2692 / 1450
= 825.9692 mm
Jumlah kabel (n)
n = Apsperlu / Aps
= 825.9692 / (((0,25 x (22/7) x (12.7^2))) x 7)
= 0.93109436
1 Tendon
Gaya Prategang Aktual (Pi)
Pi = Pi . n
= 1197655.2692 x 1
= 1,197,655.2692 N
Gaya Prategang Aktual Efektif (Pe)
Pe = Pe . n
= 1018006.97882 x 1
= 1,018,006.9788 N
Luas Baja Prategang Aktual (Apsaktual)
Apsaktual = Jumlah tendon . Luas satu tendon
= n . 1/4 D2
= 1 x (0,25 x (22/7) x (12.7^2) x 7)
= 887.095 mmJarak dari serat tekan terluar :
dp = h - e'
= 711.2 - (319.77 - 200)
= 591.4300 mm
. Anggen
8/22/2019 Perencanaan Gelagar Prategang
10/18
cangan Beton Prategang
Tinggi blok tegangan persegi panjang ekivalen :
a = n x Aps x fps
0,85 x f'c x b
=
= 1649996.712211.304
= 135.1204343 mm
Kuat momen nominal :
Mn = n x Aps x fps x (dp- a/2)
= (((0,25 x (22/7) x (12.7^2))) x 7) x 1 x 1860 x (591.43-(135.1205/2)
= 8.6438E+08 N.mm
Faktor reduksi dikali Momen nominal
0,8. Mn > MD + MT
> 213676992 + 270000000
> 4.8368 x 10^8 N.mm
1 buah tendon dengan Pi = 1197655.2692 N, menimbulkan Mn = 6.9151 x 10^8 N.mm > Mu = MD + MT = 4.8368 x 10^8 N.mm, OK!
Momen tahanan tendon > momen akibat beban sehingga tulangan non-prategang secara teoritis tidak diperlukan,
namun tetap dipasang sebagai tulangan pembentuk.
8. Kontrol Tegangan Izin
8.a) Saat transfer
Tegangan serat di tengah bentang
Tepi atas :
ft = -1,197,655.2692 -213676992.0000178,064.1600 24,185,221
ft = -5.656973521 < 1.378404875 MPa
Tepi bawah :
fb = -1,197,655.2692 213676992.0000
178064.1600 29,605,095
fb = -7.599273736 > -18.24 MPa
Tegangan serat di tumpuanTepi atas :
ft = -1,197,655.2692
178064.1600
ft = 3.178049716 > 2.75680975 MPa
(1 - 1.4726)
(1 + 1.203)
(1 - 1.4726)
0,85 x 40.4 x ((304.8 + 406.4) / 2)
1 x 887.095 x 1860
0,8 x 0.8644 x 10^9
6.9151 x 10^8 N.mm
S. Anggen
8/22/2019 Perencanaan Gelagar Prategang
11/18
angan Beton Prategang
Tepi bawah :
fb = -1,197,655.2692
178064.1600
fb = -14.81684873 > -18.24 MPa
.b) Saat layan
Tegangan serat di tengah bentang
Tepi atas :
ft = -1,018,006.9788 -270000000.0000
178064.1600 24,185,221
ft = -8.462500193 < 3.178049716 MPa
Tepi bawah :
fb = -1,018,006.9788 270000000.0000
178064.1600 29,605,095
fb = -3.474269559 > -18.18 MPa
Tegangan serat di tumpuan
Tepi atas :
ft = -1018006.979
178064.1600
ft = 2.701342259 < 3.178049716 MPa
Tepi bawah :
fb = -1,018,006.9788
178064.1600
fb = -12.59432142 > -18.18 MPa
. Perhitungan Batas Aman Tendon
.a) Nilai Momen Per Pias Bentang
Beban yang Bekerja :
Akibat MD
Ra = Rb = 4.2735 t
Akibat MT
Ra = Rb = 5.40 t
(1 + 1.203)
(1 + 1.203)
(1 - 1.4726)
(1 + 1.203)
(1 - 1.4726)
Anggen
8/22/2019 Perencanaan Gelagar Prategang
12/18
angan Beton Prategang
Beban yang bekerja :
qdl = 0.4274 t/m
qsidl = 0.2 t/m
qLL = 0.34 t/m
Posisi kern atas (diatas garis netral)
kt = -(r2
/ Cb)
= -(53165.2252 / 319.77)= -166.2608 mm
Posisi kern bawah (dibawah garis netral)
kb = (r2
/ Ct)
= (53165.2252 / 391.43)
= 135.8231 mm
Gaya prategang
Pi = 1,197,655.2692 N
Gaya prategang efektif
Pe = 1,018,006.9788 N
Di atas Tumpuan 0.0000 m
Batas bawah
amin = 0 mm
e5 = 135.8231 mm
Batas atas
amax = 0 mm
e5 = -166.2608 mm
1/8 Bentang 2.5000 m
MD = 93,483,684.0000 N.mm
= 9.3484 t.m
Batas bawah
amin = MD /Pi
= 93483684 / 1197655.2692
= 78.0556 mm
e4 = kb + amin= 135.8231 + 78.0556
= 213.8787 mm
MSD + MLL = ############## N.mm
= 11.8125 t.m
Batas atas
amax = MT /Pe
= 118125000 / 1018006.97882
= 116.0356 mm
e4 = amax - kt
= 116.0356 - -166.2609
= 282.2964 mm
0.54 t/m
. Anggen
8/22/2019 Perencanaan Gelagar Prategang
13/18
cangan Beton Prategang
1/4 Bentang 5.0000 m
MD = ############## N.mm
= 16.0258 t.m
Batas bawah
amin = MD /Pi= 160257744 / 1197655.2692
= 133.8096 mm
e3 = kb + amin= 135.8231 + 133.8096
= 269.6326 mm
MSD + MLL = ############## N.mm
= 20.2500 t.m
Batas atas
amax = MT /Pe
= 202500000 / 1018006.97882= 198.9181 mm
e3 = amax - kt
= 198.9181 - -166.2609
= 365.1789 mm
3/8 Bentang 7.5000 m
MD = ############## N.mm
= 20.0322 t.m
Batas bawah
amin = MD /Pi
= 200322180 / 1197655.2692
= 167.2620 mm
e2 = kb + amin= 135.8231 + 167.262
= 303.0850 mm
MSD + MLL = ############## N.mm
= 25.3125 t.m
Batas atas
amax = MT /Pe
= 253125000 / 1018006.97882
= 248.6476 mm
e2 = amax - kt
= 248.6477 - -166.2609
= 414.9084 mm
S. Anggen
8/22/2019 Perencanaan Gelagar Prategang
14/18
angan Beton Prategang
1/2 Bentang 10.0000 m
MD = ############## N.mm
= 21.3677 t.m
Batas bawah
amin = MD /Pi= 213676992 / 1197655.2692
= 178.4128 mm
e1 = kb + amin= 135.8231 + 178.4128
= 314.2358 mm
MSD + MLL = ##############
= 27.0000 t.m
Batas atas
amax = MT /Pe
= 270000000 / 1018006.97882
= 265.2241 mm
e1 = amax - kt
= 265.2242 - -166.2609
= 431.4849 mm
0. Perencanaan Balok Prategang
0.a) Perhitungan Tulangan Geser
Pengaruh Beban Mati dan tambahan beban luar
qdl + qsd = 0.6274 t/m
Panjang bentang (L)
L = 20 m= 20000 mm
Gaya geser terfaktor (Vu)
Vu = 1/2. q. L
= 0,5 x 0.627354 x 20
= 6.2735 t
= 62,735.3984 N
Jarak dari serat tekan terluar ke pusat berat tulangan tarik
d = 664.7000 mm
Vc = gaya lintang yang ditahan oleh beton
Untuk perhitungan Vc ini, harus dilihat dari dua hal yaitu
-retak akibat geseran pada badan penampang (Vcw)-retak miring akibat lentur (Vci)
-nilai Vc adalah nilai terkecil dari Vcw dan Vci
Kuat geser badan (Vcw)
Vcw = (0,29. (f 'c)0,5
+ 0,3.fpc).bw.d + Vp
Komponen vertikal dari gaya prategang di penampang (Vp)
Vp = komponen vertikal dari gaya prategang
Vp = 16,266.9218 N
. Anggen
8/22/2019 Perencanaan Gelagar Prategang
15/18
angan Beton Prategang
Lebar badan (Bw)
Bw = 350 mm
Tegangan tekan beton akibat gaya prategang dari beban luar (fpc)
fpc = Pe / Ac
= 1018006.9789 / 178064.16
= 5.717079612 N/mm
Vcw = (0,29. (f 'c)0,5 + 0,3.fpc).bw.d + Vp
= (((0,29 x (40.4^0,5)) + (0,3 x 5.7171)) x 350 x 664.7) + 16266.9219
= 844,109.1960 N
Momen akibat beban hidup yang bekerja menimbulkan retak
Mcr = (Ic' / Yt).((0,5.f'c0,5
) + fpc)
= (9466821164.642 / 391.43) x ((0,5 x (40.4 0,5)) + 5.7171)
= ############## N.mm
Tegangan terbesar terdapat pada jarak x atau 0,25.L dari tumpuan, maka:
x = 0,25 x L
= 0,25 x 20 m
= 5000 mm
Mmax / Vt = ((L. x) - x) / (L - 2.x)= ((20000. 5000) - 5000) / (20000 - 2.5000)
= 7500 mm
Kekuatan lentur geser
Vci = 0,05.bw.d.(f'c)0,5
+ (Vt.Mcr) / Mmax
= (0,05 x 350 x 664.7 x (40.4 0,5)) + (215130671.1071 / 7500)
= 73,935.7376 + 28684.08948
= 102,619.8271 N
ipakai Vc = Vci = 102,619.8271 N
Kekuatan geser nominal
Vu / = 62735.3984 / 0,6
= 104,558.9973 N
Kuat geser nominal tulangan geser (Vs)
Vs = (Vu / ) - Vc
= (62735.3984 / 0,6) - 102619.8272
= 1,939.1702 N
0,5 kuat geser nominal beton
0,5.Vc = 0,5 x 102619.8272
= 51,309.9136 N
Dibutuhkan Tulangan Geser, (Vu / ) > 0,5.Vc
Mencari kebutuhan luas sengkang per milimeter panjang
Av / S = Vs / (fy.d)
Av / S = 1939.1703 / (400 x 664.7)
Av / S = 0.007293 mm/mm
Luas 1 tulangan sengkang dengan diameter 10 mm
Av = 78.5714 mm tulangan sengkang 10 m
idapatkan 0.0072934 = 78.5715 / S
S = Av / (Av / S)
= 78.5715 / 0.0073
= 10772.9436 mm
= 1077.2944 cm
Anggen
8/22/2019 Perencanaan Gelagar Prategang
16/18
angan Beton Prategang
S = 0,75 x h
= 533.4 mm
= 53.34 cm
S = 24 inch
= 60.96 cm
S = 53.34 *(Dipakai yg terkecil)
40 *Sesuaikan dengan bentang
Anggen
8/22/2019 Perencanaan Gelagar Prategang
17/18
Wandrianto S. Anggen
I 1111 094
NIM akhir 4
Diketahui:
A. Material
= 20 m
Betonf'c = 40.4 MPa
f'ci = 30.4 MPa
Eci = 30000 MPa 3 hari
Ec = 40000 MPa 28 hari
Baja
fpu = 1860 MPa
fpy = 1450 MPa
Eps = 200000 MPa
dps = 12.7 mm
n strand = 7 (kabel seven wire strand)
1- = 0.15
= 0.85
B. Pembebanan
= -
=
Ditanya:
Bentuk & Dimensi Penampang
Gaya Prategang & n kabel perlu
Posisi Kabel
Tulangan Geser Perlu
Penyelesaian:
1. Perhitungan Tegangan Izin
Saat Transfer:
fci = -0,6. f'ci
= -0,6 x 30.4
= -18.24 MPa
fti =
= 0,25 x ( 30.4^0,5)
= 1.378404875 MPa (di tengah bentang)
fti =
= 0,5 x (30.4^0,5)= 2.75680975 MPa (di tumpuan)
Saat Layan:
fc = -0,45. f'c
= -0,45 x 40.4
= -18.18 MPa
ft =
= 0,5 x (40.4^0,5)
= 3.178049716 MPa
2. Perhitungan Momen Yang Terjadi
Area = 178064.1600
Centroid x = 203.2000 mm
Centroid y = 319.7700 mm
Moments Inertia x = 9.4668E+09 mm^4
Moments Inertia y = 1.3953E+09 mm^4
2
Ct = 391.4300 mm
Cb = 319.7700 mm
h = 711.2000 mm
b1 = 304.8000 mm
b2 = 406.4000 mm
a. Momen Lentur
qdl = Ac x beton
= 0.1781 x 2.4
= 0.4274 t/m
qsidl = 0.2 t/m
qLL = 0.34 t/m
=
= 1/8 x 0.4274 x 20
= 21.3677 t.m
=
= 1/8 x 0.2 x 20= 10.0000 t.m
=
= 1/8 x 0.34 x 20
= 17.0000 t.m
Hasil:
Md = 21.3677 t.m
= 213676992.0000 N.mm
Msidl + MLL = 27.0000 t.m
= 270000000.0000 N.mm
3. Perhitungan St dan Sb perlu
a. St dan Sb perlu (akibat pembebanan dan sifat material)
St 15,608,573
St 14,717,503 mm (di tumpuan)
Sb 16,168,009 mm
b. St dan Sb tersedia dari penampang
St = Ic / Ct
= 9466821164.642 / 391.43
= 24,185,221 mm
Sb = Ic / Cb
= 9466821164.642 / 319.77
= 29,605,095 mm
Hasil:
St tersedia = 24,185,221 > St perlu = ######## (di tengah bentang) OK
St tersedia = 24,185,221 > St perlu = ######## (di tumpuan) OK
Sb tersedia = 29,605,095 > Sb perlu = ######## OK
4. Gaya Prategang Awal
= 1.3785 - ((391.43 / 711.2) x (1.3785-18.24))
= -9.4192 MPa (di tengah bentang)
= 2.7569 - ((391.43 / 711.2) x (2.7569-18.24))
= -8.7994 MPa (di tumpuan)
Pi =
= 178064. 16 x 9. 41916573826548
= 1,677,215.8351 N (di tengah bentang)
Pi =
= 178064. 16 x 8. 79940684211027
= 1,566,858.9878 N (di tumpuan)
5. Eksentrisitas Maksimum
e
e ((1.3785 - -9.4192) x (24185221.2775/1677215.8351)) + (213676992/1677215.8351)
e 283.0992986 mm (di tengah bentang)
e
e ((2.7569--8.7995) x (24185221.2775/1566858.9879)) + (213676992/1677215.8351)
e 305.7755732 mm (di tumpuan)
*dipakai e = 200
6. Hitung Batas Pi
Di tengah Bentang
Saat Awal
Pi
Pi 3,848,953.6312
Pi
Pi 2,057,751.9138
Saat akhir
Pi
Pi -3,110,653
Pi
Pi 565,054
Di tumpuan
Saat Awal
Pi
(-1 + ((200 x 391.43) / 53165.2252))
Pi 1,197,655
Pi
(1 + (200 x 319.77) / 53165.2252)
Pi 1,474,351
Saat akhir
Pi
Pi 1,409,006
Pi
Pi 1,728,825
Rekap batas
Tengah Bentang
Saat Awal Saat Akhir
Tumpuan
Saat Awal Saat Akhir
7. Luas Baja Prategang
Pi = 1,197,655.2692 N
Pe = 0.85 x 1197655.2692
= 1,018,006.9788 N
= 1197655.2692 / 1450
= 825.9692
n kabel =
= 0.93109436
1
Pi baru = 1,197,655.2692 N
Pe baru = 1,018,006.9788 N
Aps baru = 887.095 mm
dp = h - e'
= 711.2 - (319.77 - 200)
= 591.4300 mm
a = n x Aps x fps
0,85 x f'c x b
= 1649996.7
12211.304
= 135.1204343 mm
Mn = n x Aps x fps x (dp- a/2)
= (((0,25 x (22/7) x (12.7^2))) x 7) x 1 x 1860 x (591.43-(135.1205/2))
= 8.6438E+08
0,8. Mn >
> 213676992 + 270000000
> 4.8368 x 10^8 N.mm
1 buah tendo n deng an Pi = 1197 655 .2692 N , menimbulkan Mn = 6 .9151 x 10^8 N.mm > Mu = MD + MT = 4.8368 x 10^8 N .mm, OK!
8. Kontrol Tegangan Izin
8.a) Saat transfer
Tengah Bentang
ft = -5.656973521 MPa < 1.378405
fb = -7.599273736 MPa > -18.24
Tumpuan
ft = 3.178049716 MPa > 2.75681
fb = -14.81684873 MPa > -18.24
8.b) Saat layan
Tengah Bentang
ft = -8.462500193 MPa < 3.17805
fb = -3.474269559 MPa > -18.18
Tumpuan
ft = 2.701342259 MPa < 3.17805
fb = -12.59432142 MPa > -18.18
9. Perhitungan Batas Aman Tendon
9.a) Nilai Momen Per Pias Bentang
Akibat MD Akibat MT
3.1781 x 178064.16
-1+ 200 x 391.43 / 53165.2252 x 0.85
--18.18 x 178064.16
1+ 200 x 319.77 / 53165.2251898529 x 0.85
0 8 x 0.8644 x 10 9
6.9151 x 10^8 N.mm
+
3.17804971641414 - 0.85 x -18.24
=
1.3785 + 213676992 / 24185221.2775 x 178064.16
-1 + 200 x 391.43 / 53165.2252
--18.24 + 213676992 / 29605094.8014 x 178064.16
1 + 200 x 319.77 / 53165.2252
-18.18 + 270000000 / 24185221.2775 x 178064.16
-1+ 200 x 391.43 / 53165.2252 x 0.85
- +
1+ 200 x 319.77 / 53165.2252 x 0.85
3.1781 x 178064.16
--18.24 x 178064.16
0.15 x 213676992 + 270000000
0.85 x 1.37840487520902 - -18.18
St 0.15 x 213676992 + 270000000
0.85 x 2.75680975041804 - -18.18
akibat LL
Momen tengah bentang
akibat DL
Momen tengah bentang
akibat SIDL
Momen tengah bentang
=
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MMMS
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2rce
ASMfP
tc
tDti
i
)/.1(
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2rce
ASMfP
b
cbDcii
)/.1(
)/(
2rce
ASMf
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tTc
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)/.1(
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ASMfP
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AfP
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M
r
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Ptf )1(2
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Db
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r
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Pbf )1( 2
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cci
8/22/2019 Perencanaan Gelagar Prategang
18/18
Ra = Rb = 4.2735 t Ra = Rb = 5.4000 t
qdl = 0.4274 t/m
qsidl = 0.2 t/m
qLL = 0.34 t/m
kt = 2
= -(53165.2252 / 319.77)
= -166.2608 mm
kb =2
= (53165.2252 / 391.43)
= 135.8231 mm
Pi = 1,197,655.2692 N
Pe = 1,018,006.9788 N
Di atas Tumpuan 0.0000 m
Batas bawah
=
e5 = 135.8231 mm
Batas atas
=
e5 = -166.2608 mm
1/8 Bentang 2.5000 m
=
= 9.3484 t.m
Batas bawah
=
= 93483684 / 1197655.2692
= 78.0556 mm
e4 =
= 135.8231 + 78.0556
= 213.8787 mm
= ############## N.mm
= 11.8125 t.m
Batas atas
=
= 118125000 / 1018006.97882
= 116.0356 mm
e4 = -
= 116.0356 - -166.2609
= 282.2964 mm
1/4 Bentang 5.0000 m
=
= 16.0258 t.m
Batas bawah
=
= 160257744 / 1197655.2692
= 133.8096 mm
e3 =
= 135.8231 + 133.8096
= 269.6326 mm
+ = ############## N.mm
= 20.2500 t.m
Batas atas
=
= 202500000 / 1018006.97882
= 198.9181 mm
e3 = -
= 198.9181 - -166.2609
= 365.1789 mm
3/8 Bentang 7.5000 m
=
= 20.0322 t.m
Batas bawah
=
= 200322180 / 1197655.2692
= 167.2620 mm
e2 =
= 135.8231 + 167.262
= 303.0850 mm
+ = ############## N.mm
= 25.3125 t.m
Batas atas
=
= 253125000 / 1018006.97882
= 248.6476 mm
e2 = -
= 248.6477 - -166.2609
= 414.9084 mm
1/2 Bentang 10.0000 m
=
= 21.3677 t.m
Batas bawah
=
= 213676992 / 1197655.2692
= 178.4128 mm
e1 =
= 135.8231 + 178.4128
= 314.2358 mm
+ = ##############
= 27.0000 t.m
Batas atas
=
= 270000000 / 1018006.97882
= 265.2241 mm
e1 = -
= 265.2242 - -166.2609
= 431.4849 mm
10. Perencanaan Balok Prategang
10.a) Perhitungan Tulangan Utama
qdl = 0.4274 t/mL = 4.0000 m *(1 segmen 4 m)
Mu = 0.8547 t.m
= 8,547,079.6800 N.mm
= 13 mm
= 10 mm
= 30 mm
fy = 400 MPa
f'c = 40.4 MPa
h = 711.2000 mm
b1 = 304.8000 mmb2 = 406.4000 mm
d = h p - sengkang tul. Utama
= 711.2 30 - 10 ( .13)
= 664.7 mm
Ac' = 153883.36
'
a = 186.2970
b = -320
c = 0.0836
dengan rumus abc diperoleh akar2 persamaan:
x1 = 1.718
x2 = -0.0002612
= 0.0002612
min = 1,4 / fy
= 1,4 / 400
= 0.0035
= 0.0035000
As perlu = . b. D
= 0.0035 x ((304.8 + 406.4) / 2) x 664.7
= 827.28562
= 18 buah
As tersedia = 2390.1429 mm > As perlu = 827.28562 mm
10.b) Perhitungan Tulangan Geser
*Pengaruh Beban Mati
= 0.6274 t/m
L = 20 m
= 20000 mm
Vu = 1/2. q. L
= 0,5 x 0.627353984 x 20
= 6.27353984 t
= 62,735.3984 N
d = 664.7000 mm
Vc = gaya lintang yang ditahan oleh beton
Untuk perhitungan Vc ini, harus dilihat dari dua hal yaitu
-retak akibat geseran pada badan penampang (Vcw)
-retak miring akibat lentur (Vci)
-nilai Vc adalah nilai terkecil dari Vcw dan Vci
Vcw = '0,5
Vp = komponen vertikal dari gaya prategang
Vp = 16,266.9218 N
Bw = 350 mm
fpc = Pe / Ac
= 1018006.9789 / 178064.16
= 5.717079612
Vcw = '0,5
= (((0,29 x (40.4^0,5)) + (0,3 x 5.7171)) x 350 x 664.7) + 16266.9219
= 844,109.1960 N
Mcr = ' '0,5
= (9466821164.642 / 391.43) x ((0,5 x (40.4^0,5)) + 5.7171)= ############## N.mm
Tegangan terbesar terdapat pada jarak x atau 0,25.L dari tumpuan, maka:
x = 0,25 x L
= 0,25 x 20 m
= 5000 mm
Mmax / Vt =
= ((20000. 5000) - 5000) / (20000 - 2.5000)
= 7500 mm
Vci = '0,5
= (0,05 x 350 x 664.7 x (40.4^0,5)) + (215130671.1071 / 7500)= 73,935.7376 + 28684.08948
= 102,619.8271 N
dipakai = 102,619.8271 N
= 104,558.9973 N
Vs =
= (62735.3984 / 0, 6) - 102619.8272
= 1,939.1702 N
0,5.Vc = 0,5 x 102619.8272
= 51,309.9136 N
Dibutuhkan Tulangan Geser, (Vu / ) > 0,5.Vc
Av / S = Vs / (fy.d)
Av / S = 1939.1703 / (400 x 664.7)
Av / S = 0.007293
Av = 78.5714
didapatkan 0.00729 = 78.5715 / S
S = Av / (Av / S)
= 78.5715 / 0.0073
= 10772.9436 mm= 1077.2944 cm
S = 0,75 x h
= 533.4 mm
= 53.34 cm
S = 24 inch
= 60.96 cm
S = 53.34 *(Dipakai yg terkecil)
40 *Sesuaikan dengan bentang
Mu / Ac' x d
Mu / Ac' x d
0.0836
Di akai tulan an okok
t/m
tulan an utama
tulan an sen kan
Mu / Ac' x d
0.54