irbang 2

Bendung Tebanah

Momen tahan dan Guling Terhadap Titik 12 Perhitungan lengan

Segmen Panjang TinggiG1 2.00 2.90G2 4.76 2.90G3 6.76 0.85G4 2.00 1.00G5 2.26 1.50G6 2.00 3.28G7 1.54 2.78G8 2.00 3.28G9 2.00 0.58

G10 2.00 1.72

Momen Tahanan dan Guling Kh(koef. gempa) = 0.15

Segmen ƔbetonGaya (ton)

V H1 2 3 4

G1 5.800 2.200 12.760 1.914G2 6.902 2.200 15.184 2.278G3 5.746 2.200 12.641 1.896G4 2.000 2.200 4.400 0.660G5 3.390 2.200 7.458 1.119G6 6.560 2.200 14.432 2.165G7 4.281 2.200 9.419 1.413

Luas (m2)

G8 6.560 2.200 14.432 2.165G9 0.580 2.200 1.276 0.191

G10 1.720 2.200 3.784 0.568∑ 95.786 14.368

Keterangan : V = Gaya Vertikal /H = Gaya Horizontal /

SF = ∑MT = 13.098∑MG

13.098 > 1.5 OK!!

Perhitungan lengan

Segmen X yG1 11.30 5.44G2 8.71 5.44G3 8.92 3.57G4 11.30 2.64G5 6.67 2.39G6 4.54 1.64G7 2.77 1.39G8 1.00 1.64G9 4.87 3.57

G10 0.67 4.14

Lengan (m) Momen (ton.m)X Y V H

5 611.300 5.440 144.188 10.4128.713 5.440 132.307 12.3908.920 3.565 112.760 6.760

11.300 2.640 49.720 1.7426.670 2.390 49.745 2.6744.540 1.640 65.521 3.5502.770 1.390 26.090 1.964

6.89

1.000 1.640 14.432 3.5504.873 3.570 6.218 0.6830.667 4.140 2.523 2.350

∑ 603.503 46.076

Gaya TahananGaya Guling / akibat gempa

Rembesan/ Uplift

Kondisi Setinggi MercuƔbeton = 2.2

No.Panjang Rembesan

LV (m) LH (m) 1/3 LH (m)1 3 4 5

A0 0.00 0.00 0.00A1 1.50 0.00 0.00A2 1.50 0.50 0.17A3 0.50 1.00 0.33A4 0.50 4.50 1.50A5 1.50 4.50 1.50A6 1.50 5.00 1.67A7 0.50 5.00 1.67A8 0.50 8.50 2.83

No. ΔH (m) Panjang RembesanLV (m) LH (m) 1/3 LH (m)

1 2 3 4 50 3.860 0.000 0.000 0.0001 3.860 3.000 0.000 0.0002 3.860 3.000 2.000 0.6673 3.860 2.000 2.000 0.6674 3.860 2.000 4.500 1.5005 3.860 3.500 4.500 1.5006 3.860 3.500 6.670 2.2237 3.860 5.000 6.670 2.2238 3.860 5.000 8.670 2.8909 3.860 4.500 8.670 2.89010 3.860 4.500 10.030 3.34311 3.860 5.000 10.300 3.43312 3.860 5.000 12.300 4.10013 3.860 0.000 12.300 5.100

UpliftSegmen Gaya Jarak Terhadap Titik 12 Momen Terhadap Titik 12

ton/m x y ton.mu1v 8.492 11.300 95.960u3v 10.097 9.050 91.375u5v 8.987 6.670 59.941u7v 8.452 4.540 38.371u9v 7.064 2.770 19.568

u11v 7.867 1.000 7.867∑v 50.958 ∑v 313.081u0v 6.662 3.500 23.317u2v -7.464 2.500 -18.661u4v 6.354 2.250 14.297u6v 6.087 0.750 4.565u8v -5.332 0.500 -2.666

u10v 5.450 0.250 1.362u12v -4.340 2.500 -10.849∑h 7.417 ∑h 11.366

Kondisi Saat Muka Air BanjirNo. ΔH (m) Panjang Rembesan

LV (m) LH (m) 1/3 LH (m)1 2 3 4 50 2.570 0.000 0.000 0.0001 2.570 3.000 0.000 0.0002 2.570 3.000 2.000 0.6673 2.570 2.000 2.000 0.6674 2.570 2.000 4.500 1.5005 2.570 3.500 4.500 1.5006 2.570 3.500 6.670 2.223

7 2.570 5.000 6.670 2.2238 2.570 5.000 8.670 2.8909 2.570 4.500 8.670 2.89010 2.570 4.500 10.030 3.34311 2.570 5.000 10.300 3.43312 2.570 5.000 12.300 4.10013 2.570 0.000 12.300 5.100

UpliftSegmen Gaya Jarak Terhadap Titik 12 Momen Terhadap Titik 12

ton/m x y ton.mu1v 11.066 11.300 125.046u3v 14.340 9.050 129.778u5v 13.601 6.670 90.719u7v 12.510 4.540 56.794u9v 11.586 2.770 32.093

u11v 13.223 1.000 13.223∑v 76.325 ∑v 447.652u0v 12.421 3.500 43.473u2v -14.058 2.500 -35.145u4v 13.319 2.250 29.968u6v 12.773 0.750 9.580u8v -12.271 0.500 -6.135

u10v 12.717 0.250 3.179u12v -11.977 2.500 -29.944∑v 12.924 ∑h 14.976

Panjang RembesanHx (m) Ux

Lx (m) ∑L (m)(ΔH.Lx)/∑L (t/m2)

6 = 3 + 5 7 8 = (6x2)/7 9 = (2+3) 10 = (9-8)0.000 5.100 0.000 3.860 3.8603.000 5.100 2.271 6.860 4.5893.667 5.100 2.775 6.860 4.0852.667 5.100 2.018 5.860 3.8423.500 5.100 2.649 5.860 3.2115.000 5.100 3.784 7.360 3.5765.723 5.100 4.332 7.360 3.0287.223 5.100 5.467 8.860 3.3937.890 5.100 5.972 8.860 2.8887.390 5.100 5.593 8.360 2.7677.843 5.100 5.936 8.360 2.4248.433 5.100 6.383 8.860 2.4779.100 5.100 6.887 8.860 1.9735.100 5.100 3.860 3.860 0.000

Panjang RembesanHx (m) Ux

Lx (m) ∑L (m)6 = 3 + 5 7 8 = (6x2)/7 9 = (2+3) 10 = (9-8)

0.000 5.100 0.000 5.030 5.0303.000 5.100 1.512 8.030 6.5183.667 5.100 1.848 8.030 6.1822.667 5.100 1.344 7.030 5.6863.500 5.100 1.764 7.030 5.2665.000 5.100 2.520 8.530 6.0105.723 5.100 2.884 8.530 5.646

(ΔH.Lx)/∑L (t/m2)

7.223 5.100 3.640 10.030 6.3907.890 5.100 3.976 10.030 6.0547.390 5.100 3.724 9.530 5.8067.843 5.100 3.952 9.530 5.5788.433 5.100 4.250 10.030 5.7809.100 5.100 4.586 10.030 5.4445.100 5.100 2.570 5.030 2.460

Tekanan Air AktifKondisi Setinggi Mercu

= 1 = 3.86

= 0.7895 = 3

Segmen Deskripsi Gaya (ton)

Ha1 x x 1 m 7.4498

Ha2 x x 1 m 11.58

Ha3 x x 1 m 3.55275

∑HHa 22.58255

Kondisi Saat Muka Air Banjir

= 1 = 1.61

= 0.7895 = 3.86

Tekanan Air AktifSegmen Deskripsi Gaya (ton)

Ha1 x x 1 m 6.2146

Ha2 x x 1 m 7.4498

Ha3 x x 1 m 16.41

Ha4 x x 1 m 3.55275

∑HHa 27.41255Tekanan Air Pasif

= 1 = 1.74

= 0.7895 = 2.2


Hp1 x x 1 m 1.5138

Hp2 x x 1 m 3.828

Hp3 x x 1 m 1.91059

∑HHa 7.25239Tekanan Tanah Aktif

Kondisi Setinggi MercuKa = = 0.33Ø = 27


Pa1 x x Ka 1.1724075

∑HHa 1.1724075Kondisi Saat Muka Air Banjir

Ɣw h1

Ɣsub h2

0,5Ɣw h12

Ɣw h1h2

0,5Ɣsub h22

Ɣw h1'

Ɣsub h2'

Ɣw h1'.h2'

0,5Ɣw h2'

Ɣw (h1'+ h2').h2

0,5Ɣsub h22

Ɣw h1''

Ɣsub h2''

0,5Ɣw h1''2

Ɣw h1''.h2''

0,5Ɣsub h2''2

(1-sinØ)((1+sinØ)

0,5Ɣsub h12


Pa1 x x Ka 1.1724075

∑HHa 1.1724075

Tekanan Lumpur

Kondisi Setinggi Mercu


Ps1 x x Ka 2.458434

∑HHa 2.458434Kondisi Saat Muka Air Banjir


Ps1 x x Ka 2.050818

Ps1 x x Ka 2.458434

∑HHa 4.509252

0,5Ɣsub h12

0,5Ɣw h12

Ɣw h1'.h2'

0,5Ɣw h12

Jarak Pada Titik 12 Momen Pada Titik 12 (ton.m)

6.28 46.784744

3.5 40.53

3 10.65825

∑MHa 97.972994


6.93 43.067178

6.28 46.784744

3.5 57.435

3 10.65825

∑MHa 157.945172


3.71 5.616198

1.64 6.27792

1.1 2.101649

∑MHp 13.995767


3 3.5172225

∑Mpa 3.5172225


3 3.5172225

∑Mpa 3.5172225


6.28 15.43896552

∑Ha 15.43896552


6.93 14.21216874

6.28 15.43896552

∑Mps 29.65113426

Berat Air

Kondisi Saat Muka Air Banjir

Y1 = 1.18 sin 45 = 0.707107Y2 = 1.07 L1 = 2Y3 = 1.74 L2 = 4.76Y4 = 2.16 L3 = 3.14

Y5 = 2.37 = 1

Y6 = 2.5Segmen Deskripsi

PW1 0.5 x (Y1+Y2) x L1 x 1 m x

PW2V 0.5 x (Y2+Y3) x L2 x 1 m x (sin 45) x

PW2H 0.5 x (Y2+Y3) x L2 x 1 m x (sin 45) x

PW3 0.5 x (Y4+Y5) L2 x 1 m x

PW4 6.79 x Y5 x 1 m x

PW5 0.5 x x 1 m x

Ɣw

Ɣw

Ɣw

Ɣw

Ɣw

Ɣw

Y62 Ɣw

Gaya (ton) Jarak Pada Titik 12 (x) Jarak Pada Titik 12 (y) Momen Pada Titik 12 (ton.m)

2.25 5.76 12.96

4.7289887312194 2.4 11.3495729549265

-4.728988731219 4.64 -21.942507712858

2.265 7.51 17.01015

16.0923 3.4 54.71382

24.53125 3.43 84.1421875

∑MpW -21.942507712858 180.175730454927

Kondisi Setinggi MercuSegmen ∑v ∑h ∑Mp ∑Mg

Tekanan Air Aktif 22.58255 97.972994Tekanan Tanah Aktif 1.1724075 3.5172225Tekanan Lumpur 2.458434 15.43896552Uplift 50.957751634 7.41693333333 313.080797908 11.3661058824Berat Sendiri 95.78624 603.503055467

∑ 146.743991634 33.6303248333 916.583853375 128.295287902

Kontrol Guling : Kontrol geser:∑Mp

≥ Sf∑H

∑Mg ∑V916.583853375164

≥ 1.533.6303248333

128.295287902353 44.828488366

7.14432983752908 ≥ 1.5 OK !!!! 0.75019984075

Kontrol Eksentrisitas :

e =∑M

-B

∑V 2

=1044.87914128

-12.3

146.743991634 2

e 0.9704219651

Kontrol Tegangan Tanah :

σ ∑Vx

B

σmax 146.744x 1.47337656834

12.3

σmax 17.5779803918

σmax 17.5779803918 ≤ 40

σmin 146.744x 0.52662343166

12.3

σmin 6.28283125605

(1 ± 6e/B)

σmin 6.28283125605

σmin 6.28283125605 ≥ 0

≥fS

0.652

≥ 0.325 OK !!!!

≤ B6

≤ 12.36

≤ 2.05 OK !!!!

Kondisi Saat Muka Air BanjirSegmen ∑v ∑h ∑Mp ∑Mg

Tekanan Air Aktif 27.41255 157.945172Tekanan Air Pasif 7.25239 13.995767Tekanan Tanah Aktif 1.1724075 3.5172225Tekanan Lumpur 4.509252 29.65113426Uplift 76.3254771242 12.9235333333 447.652149281 14.9759176471Berat Sendiri 95.78624 603.503055467

∑ 172.111717124 53.2701328333 1051.15520475 220.085213407Kontrol Guling : Kontrol geser:

∑Mp≥ Sf

∑H∑Mg ∑V

1051.15520474771≥ 1.5

53.2701328333220.085213407059 19.4607628758

4.77612824812336 ≥ 1.5 OK !!!! 2.73730958921

Kontrol Eksentrisitas :

e =∑M

-B

∑V 2

=1271.24041815

-12.3

172.111717124 2

e 1.23613523469

Kontrol Tegangan Tanah :

σ ∑Vx

B

σmax 172.112x 1.60299279741

12.3

σmax 22.4303937317

σmax 22.4303937317 ≤ 40

σmin 172.112x 0.39700720259

12.3

σmin 5.55525132911

(1 ± 6e/B)

≥fS

0.652

≥ 0.325 OK !!!!

≤ B6

≤ 12.36

≤ 2.05 OK !!!!

Perhitungan Beban VertikalSegmen Deskripsi W

Wc1 0.50 x 8.50 x 2.20 9.35Wc2 0.50 x 8.00 x 2.00 x 2.20 17.60Wc3 6.50 x 2.00 x 2.20 28.60Wc4 0.50 x 1.00 x 2.00 x 2.20 2.20We1 2.00 x 0.50 x 1.70 1.70We2 0.50 x 2.00 x 8.00 x 1.70 13.60We3 3.00 x 8.50 x 1.70 43.35

q 1.00 x 5.00 5.00Total 121.40

Perhitungan Beban Horizontal

Ka = 0.33 q = 100Kp = 0.01 = 1.65

qa1 = Ka x q x = 10.89qa2 = Ka x H x =qp1 = Kp x h1 x =

Segmen Deskripsi H X W x X

Ɣsoil

Ɣsoil

Ɣsoil

Pa1 0.33 x 10.50 3.47 5.25 18.19Pa2 0.50 x 6.94 x 10.50 36.46 3.50 127.60Pp -0.50 x 12.02 x 2.00 -12.02 0.67 -8.05

Total 27.90 137.73

Perhitungan Beban VertikalSegmen Deskripsi W

Wc1 0.50 x 8.50 x 2.20 9.35Wc2 0.50 x 8.00 x 2.00 x 2.20 17.60Wc3 6.50 x 2.00 x 2.20 28.60Wc4 0.50 x 1.00 x 2.00 x 2.20 2.20We1 2.00 x 0.50 x 1.70 1.70We2 0.50 x 2.00 x 8.00 x 1.70 13.60We3 3.00 x 8.50 x 1.70 43.35

q 1.00 x 5.00 5.00Total 121.40


Ka = 0.33 q = 100Kp = 0.01 = 1.65

qa1 = Ka x q x = 10.89qa2 = Ka x H x =

Ɣsoil

Ɣsoil

qp1 = Kp x h1 x =

Segmen Deskripsi H X W x XPa1 0.33 x 10.50 3.47 5.25 18.19Pa2 0.50 x 6.94 x 10.50 36.46 3.50 127.60Pp -0.50 x 12.02 x 2.00 -12.02 0.67 -8.05

Total 27.90 137.73

Ɣsoil

Perhitungan Beban VertikalX W x X Segmen

2.25 21.04 Wc13.17 55.79 Wc23.25 92.95 Wc36.83 15.03 Wc43.50 5.95 We13.83 52.09 We26.00 260.10 We35.00 25.00 q

527.94 Total


KaKp

qa1qa2qp1

Segmen

Pa1Pa2Pp

Total

X W x X2.25 21.043.17 55.793.25 92.956.83 15.033.50 5.953.83 52.096.00 260.105.00 25.00

527.94

Perhitungan Beban VertikalDeskripsi W X

0.50 x 8.50 x 2.20 9.35 2.250.50 x 8.00 x 2.00 x 2.20 17.60 3.176.50 x 2.00 x 2.20 28.60 3.250.50 x 1.00 x 2.00 x 2.20 2.20 6.832.00 x 0.50 x 1.70 1.70 3.500.50 x 2.00 x 8.00 x 1.70 13.60 3.833.00 x 8.50 x 1.70 43.35 6.001.00 x 5.00 5.00 5.00

Total 121.40


= 0.33 q = 100= 0.01 = 1.65

= Ka x q x = 10.89= Ka x H x == Kp x h1 x =

Deskripsi H X W x X

Ɣsoil

Ɣsoil

Ɣsoil

0.33 x 10.50 3.47 5.25 18.190.50 x 6.94 x 10.50 36.46 3.50 127.60-0.50 x 12.02 x 2.00 -12.02 0.67 -8.05

Total 27.90 137.73

W x X21.0455.7992.9515.035.95

52.09260.1025.00

527.94

irbang 2

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