Tinjauan Ultimit Balok Prestress_revisi.docx

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Tinjauan Ultimit Balok Prestress  Kapasitas Momen Ultimit Balok Tulangan Tambahan Serat Bawah Girder Modulus elastis baja prategang (strands) :

Es = 193000 MPa

Jumlah total strands :

ns = 41 buah

Luas tampang nominal satu strands

Ast = 0,00009871 m2

Tegangan leleh tendon baja prategang

fpy = 1580 MPa

Luas tampang tendon baja prategang

Aps = ns x Ast = 41 x 0,00009871 = 0,00404711 m2

Kuat tekan beton

fc' slab = 28,45 MPa , fc' girder = 40,71 MPa

Kuat leleh baja prestress (fps) pada keadaan ultimit, ditetapkan sebagai berikut : Untuk nilai L / H ≤ 35 :

fps = feff + 150 + [fc'/(100 ρp)] MPa fps harus ≤ feff + 400 MPa dan harus ≤ 0,8 fpy

dengan L = panjang bentang dan H = tinggi balok

Panjang bentang balok prategang (L)

= 32,8 m

Gaya prestress efektif (setelah loss of prestress), Peff = 3535,90321 + 1012,6037 = 4548,50691 kN Tegangan efektif baja prestress, feff

= (Peff / Aps) x 10-3 = 1123,89 MPa

Luas penampang balok prategang komposit, Ac

= 1,140762 m2

Rasio luas penampang baja prestress, ρp

= Aps / Ac = 0,00404711 / 1,140762 = 0,0035

Tinggi total balok prategang, H = h + h0

= 1,7 + 0,24 = 1,94 m

L/H

= 32,8 / 1,94 = 16,90722 < 35 (OK)

fps = feff. +150 + fc'/(100 ρp)

= 1123,89 + 150 + [28,45 / (100 x 0,0035)] = 1355,17 MPa

fps = feff. + 400

= 1123,89 + 400 = 1523,89 MPa

fps = 0,8 fpy

= 0,8(1580) = 1264 MPa

maka, dipilih fps = 1264 MPa Asumsi a ≤ h0 , maka : β1

= 0,85

z0

= 260 mm = 0,26 m diukur dari dasar girder

d

= h + h0 - z0 = 1,68 m

fps

= 1264000 kPa

Ts

= Aps x fps = 0,00404711 x 1264000 = 5115,55 kN

h0

= 0,24 m

Cc

= 0,85 fc' . a . beff

Cc = T s

𝑎=

𝑇𝑠 5115,55 = = 0,11502 𝑚 0,85 . 𝑓𝑐 ′ . 𝑏𝑒𝑓𝑓 (0,85)(28450)(1,839134)

a < h0 , 0,11502 < 0,24 (OK) c = a / β1 = 0,11502 / 0,85 = 0,1353 m εps = 0,003 (d - c) / c = 0,003 (1,68 - 0,1452) / (0,1452) = 0,0317

Cc = 0,85 . fc' . a . beff = 0,85 (28450) (0,11502) (1,839134) = 5115,5 kN

Mn = Cc . y = Cc (d - a/2) = (5115,5) (1,68 - 0,11502/2) = 8299,85 kN.m

ΦMn = (0,8) (8299,85) = 6639,88 kN.m

Mu = 4940,96 kN.m

ΦMn > Mu , maka tidak diperlukan tulangan tambahan pada serat bawah girder.

Tulangan Tambahan Serat Atas Girder Modulus elastis baja prategang (strands) :

Es = 193000 MPa

Jumlah total strands :

ns = 10 buah

Luas tampang nominal satu strands

Ast = 0,00009871 m2

Tegangan leleh tendon baja prategang

fpy = 1580 MPa

Luas tampang tendon baja prategang

Aps = ns x Ast = 10 x 0,00009871 = 0,0009871 m2

Kuat tekan beton

fc' slab = 28,45 MPa , fc' girder = 40,71 MPa

Kuat leleh baja prestress (fps) pada keadaan ultimit, ditetapkan sebagai berikut : Untuk nilai L / H ≤ 35 :

fps = feff + 150 + [fc'/(100 ρp)] MPa fps harus ≤ feff + 400 MPa dan harus ≤ 0,8 fpy

dengan L = panjang bentang dan H = tinggi balok

Panjang bentang balok prategang (L)

= 32,8 m

Gaya prestress efektif (setelah loss of prestress), Peff = 1012,6037 kN Tegangan efektif baja prestress, feff

= (Peff / Aps) x 10-3 = 1025,84 MPa

Luas penampang balok prategang komposit, Ac

= 1,140762 m2

Rasio luas penampang baja prestress, ρp

= Aps / Ac = 0,0009871 / 1,140762 = 0,00087

Tinggi total balok prategang, H = h + h0

= 1,7 + 0,24 = 1,94 m

L/H

= 32,8 / 1,94 = 16,90722 < 35 (OK)

fps = feff. +150 + fc'/(100 ρp)

= 1025,84 + 150 + [28,45 / (100 x 0,00087)] = 1502,85 MPa

fps = feff. + 400

= 1175,32 + 400 = 1575,32 MPa

fps = 0,8 fpy

= 0,8(1580) = 1264 MPa

maka, dipilih fps = 1264 MPa Asumsi a ≤ h5 , maka : β1

= 0,85 - (0,05 . (fc' - 30) / 7) = 0,85 - (0,05 . (40,71 - 30) / 7) = 0,7735

z0

= 490 mm = 0,49 m diukur dari sisi paling luar atas girder komposit

d

= h + h0 - z0 = 1,45 m

fps

= 1264000 kPa

Ts

= Aps x fps = 0,0009871 x 1264000 = 1247,6944 kN

h5+6 = 0,5 m Cc

= 0,85 fc' . a . b

Cc = T s 𝑎=

𝑇𝑠 1247,6944 = = 0,05151 𝑚 0,85 . 𝑓𝑐 ′ . 𝑏 (0,85)(40710)(0,7)

a < h5+6 , 0,05151 < 0,5 (OK) c = a / β1 = 0,05151 / 0,7735 = 0,06659 m εps = 0,003 (d - c) / c = 0,003 (1,45 - 0,06659) / (0,06659) = 0,0623

Cc = 0,85 . fc' . a . b = 0,85 (40710) (0,05151) (0,7) = 1247,7 kN

Mn = Cc . y = Cc (d - a/2) = (1247,7) (1,45 - 0,05151/2) = 1777,03 kN.m

ΦMn = (0,8) (1777,03) = 1421,624 kN.m

Mu = 9253,58 kN.m

ΦMn < Mu , maka diperlukan tulangan tambahan pada serat atas girder komposit. ΔM = Mu - ΦMn = 9253,58 – 1421,624 kN.m = 7831,956 kN.m.

Penulangan 𝑘=

𝜌𝑝𝑒𝑟𝑙𝑢 =

𝑀𝑢 7831,956 𝑥 106 = = 3,87 2 (0,8)(700)(1900)2 ∅𝑏𝑑

0,85𝑓𝑐′ 2𝑘 0,85(40,71) 2(3,87) [1 − √1 − ]= [1 − √1 − ] = 0,0103 𝑓𝑦 0,85𝑓𝑐′ 400 0,85(40,71)

𝜌𝑚𝑖𝑛 =

𝜌𝑚𝑎𝑘𝑠. =

1,4 1,4 = = 0,0035 𝑓𝑦 400

0,85𝑓𝑐′𝛽1 600 0,85(28,8)(0,85) 600 [ ]= [ ] = 0,0312 𝑓𝑦 600 + 𝑓𝑦 400 600 + 400

ρmin < ρperlu < ρmaks. , gunakan nilai ρ = 0,0103 As = ρ . b . d = (0,0103) (700) (1900) = 13699 mm2 Jika digunakan D16 = 200,96 mm2, maka jumlah tulangan butuh adalah = 13699 / 200,96 = 68,17 ≈ 69 buah Maka digunakan tulangan D16-205.

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