Contoh Perhitungan Turap
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Transcript of Contoh Perhitungan Turap
PERKUATAN LERENG (Revetments) dan Turap
Perkuatan lereng (revetments) adalah bangunan yang ditempatkan
pada permukaan suatu lereng guna melindungi suatu tebing aIur sungai atau
permukaan lereng tanggul dan secara keseluruhan berperan meningkatkan
stabilitas alur sungai atau tubuh tanggul yang dilindunginya.
Perhitungan
Profil 6
Parameter:
γ' = 1,11 t/m3
γb = 1,62 t/m3
γwater = 1 t/m3
ϴ = 18 o
γbeton = 2,4 kg/m3
γ pasangan batu 2,2 kg/m3
Kedalaman sungai
(x) 2,1 m
cohesi = 0,3
Tinggi muka air = 1,23 meter
Rumus2 : Ka = tg2 (45 - Ø/2)
Kp = tg2 (45 + Ø/2)Pa 1 = 2.c.ka^0,5Pa 2 = q.ka.(D+2,1)Pa 3 = 0.5.ϒb.h2^2.kaPa 4 = ϒ'.h2.Ka.(D+2,1)
Pa 5 =0.5.ϒ'.Ka.(D+2,1)^2
Pa 6 = 0.5.ϒw.(D+2,1)^2Pp1 = 2.c.kpPp2 = 0.5.ϒ'.kp.DPp3 = 0.5.ϒwater.DSF = ƩPp/Ʃpa
I. Analisis Gaya yang bekerja pada turap
Ka = 0,528
Kp = 1,894
Vol. beton = (0.3*0.3*(2,709+2)) = 0,424 m3
Vol. pas.batu = (0.3*2,709) = 0,813 m3
Vol.tanah = (2,2032 + 3,2604) = 1,101 m3
q Revetments = (0,424*2.4)+(0,813*2.2) = 2,805 t/m
q tanah = (1,62*5,46) = 1,783 t/m
q.sinα = (2,805 x sin 45) = 2,661 ton
q.cosα = (2,805 x cos 45) = 0,887 ton
Profil Beton Pasangan Batu Tanah berat
(t/m)Volume Revetment tanah q sin q cos
3 0.404 0.746 0.928 2.611 1.504 2.477 0.8264 0.432 0.841 1.179 2.888 1.910 2.740 0.9135 0.409 0.762 0.968 2.657 1.568 2.521 0.8406 0.424 0.813 1.101 2.805 1.783 2.661 0.887
II. Tekanan Tanah
Pa1 = (Q x Ka x 0,3) + (Q x Ka x h air) + (Q x Ka x d)
= 4,190 + 2,739 d
Pa2 = (γtnh x Ka x 0,3 x h air) + (γtnh x Ka x 0,3 x d)
= 0,316 + 0,257 d
Pa3 = 1/2 x γtnh x 0,32 x Ka
= 0,5 x 1,62 x 0,32 x 0,528
= 0,038
Pa4 = (1/2*γsat*ka*h air2)+(1/2*γsat*ka*2*h air*d)+(1/2*γsat*ka*d2)
= 6,060 + 4,179 d + 0,721 d2
Profil Pa 1 = (Q x Ka x 0,3) + (Q x Ka x h air) + (Q x Ka x d)
3 6.251 + 2.671 d4 5.094 + 2.769 d5 5.078 + 2.687 d6 4.190 + 2.739 d
Profil Pa 2 = (γtnh x Ka x 0,3 x h air) + (γtnh x Ka x 0,3 x d)
3 0.523 + 0.257 d4 0.395 + 0.257 d5 0.408 + 0.257 d6 0.316 + 0.257 d
Profil Pa 3 = 1/2 x γtnh x 0,32 x Ka3 0.0384 0.0385 0.0386 0.038
ProfilPa 4 = (1/2 x γsat x ka x h air2)+(1/2 x γsat x ka x 2 x h air x
d)+(1/2 x γsat x ka x d2)
3 2.999 + 2.940 d + 0.721 d2
4 1.709 + 2.219 d + 0.721 d2
5 1.822 + 2.291 d + 0.721 d2
6 1.090 + 1.773 d + 0.721 d2
III. Persamaan Momen Aktif
∑Pa = 5,634 + 4,768 d + 0,721 d2
Profil ∑Pa3 9.811 + 5.868 d + 0.721 d2
4 7.237 + 5.244 d + 0.721 d2
5 7.346 + 5.235 d + 0.721 d2
6 5.634 + 4.768 d + 0.721 d2
Ma = ∑Pa x 1/3 x (h air + 0,3)
= 2,873 + 2,432 d + 0,367 d2
Profil ∑Pa x 1/3 x (h air + 0,3)3 7.653 + 4.577 d + 0.562 d2
4 4.438 + 3.217 d + 0.442 d2
5 4.628 + 3.298 d + 0.454 d2
6 2.873 + 2.432 d + 0.367 d2
Ma = ∑Pa x 1/3 d
= 1,878 + 1,589 d2 + 0,240 d3
Profil ∑Pa x 1/3 d3 3.270 d + 1.956 d2 + 0.240 d3
4 2.412 d + 1.748 d2 + 0.240 d3
5 2.449 d + 1.745 d2 + 0.240 d3
6 1.878 d + 1.589 d2 + 0.240 d3
Ma = ( ∑ Pa x 1/3 x (h air + 0,3)) + ( ∑ Pa x 1/3 d )
= 2,873 + 4,310 d + 1,957 d2 + 0,240 d3
Profil Ma3 7.653 + 7.847 d + 2.518 d2 + 0.240 d3
4 4.438 + 5.629 d + 2.190 d2 + 0.240 d3
5 4.628 + 5.747 d + 2.199 d2 + 0.240 d3
6 2.873 + 4.310 d + 1.957 d2 + 0.240 d3
IV. Persamaan Momen Pasif
Pp = d2/2 x γsat x Kp
= 0,5 x 2,73 x 1,894
= 2,586
Mp = Pp x 1/3 d
= 2,586 d2 x 1/3 d
= 0,862 d3
V. Perhitungan Momen Total
Momen total = Momen Aktif – Momen Pasif
Mtotal = (2,873 + 4,310 d + 1,957 d2 + 0,240 d3) + (0,862 d3)
= 2,873 + 4,310 d + 1,957 d2 + (-0,622 d3)
Profil Ma-MP=03 7.653 + 7.847 d + 2.518 d2 + -0.622 d3
4 4.438 + 5.629 d + 2.190 d2 + -0.622 d3
5 4.628 + 5.747 d + 2.199 d2 + -0.622 d3
6 2.873 + 4.310 d + 1.957 d2 + -0.622 d3
Untuk mendapatkan nilai D dilakukan Trial and Error
D1 = 4,780 meter
D2 = 4,790 meter
(Ma-Mp)1 = 2,873 + 4,310 d + 1,957 d2 + (-0,622 d3)
= 2,873 + 4,310 (4,78)+ 1,957 (4,78)2 + (-0,622 (4,78)3)
= 0,272
(Ma-Mp)2 = 2,873 + 4,310 d + 1,957 d2 + (-0,622 d3)
= 2,873 + 4,310 (4,79) + 1,957 (4,79)2 + (-0,622 (4,79)3)
= 0,075
Trial ErorProfil d1 d2 (Ma - Mp)1 (Ma - Mp)2 d ∑Pa ∑Pp SF L Turap
3 6.330 6.340 0.507 0.156 6.344 76.041 104.087 1.369 8.6844 5.420 5.430 0.281 0.025 5.431 56.971 76.273 1.339 7.2715 5.460 5.470 0.348 0.089 5.473 57.585 77.469 1.345 7.363
6 4.780 4.790 0.272 0.075 4.794 45.048 59.426 1.319 6.324
Nilai D profil 6
D = {((D2- D1) x (Ma-Mp)2) / ((Ma-Mp)1 - (Ma-Mp)2))} + D2
= {(0,01 x 0,075) / 0.197} + 4,790
= 4,794 meter
∑Pa = 5,634 + (4,678 x 4,794) + (0,721 x (4,7942)) = 45,048
∑Pp = 2,586 x (4,7942) = 59,426
SF = ∑Pp / ∑Pa = 59,426 / 45,048 = 1,319 > 1,2
L Turap = D + 0,3 + Muka Air
L Turap = 4,794 + 0,3 + 1,23 = 6,324 meter
Dari persamaan diatas didapat nilai D = 4,794 meter.
Jadi tinggi Turap yang dibutuhkan untuk profil 6 adalah
4,794 meter