bab iii stabilitas bendung

PERANCANGAN IRIGASI BANGUNAN AIR

45

BAB III

ANALISA STABILITAS BENDUNG

Gaya-gaya yang bekerja pada tubuh bendung, akibat:

1. Tekanan air

2. Tekanan lumpur

3. Tekanan berat sendiri bendung

4. Gaya gempa

5. Gaya angkat (uplift pressure)

3.1. Tekanan Air

3.1.1 Tekanan Air Normal

Gambar 3.1 Diagram tekanan akibat air normal

air = 1 ton/m3

Pa1 = ..h.2

1 2air = .3,85.1.

2

1 2 = 7,411 ton


46

Tabel 3.1 Perhitungan Tekanan Akibat Air Normal

Bagian Gaya (t) Lengan (m) Momen (tm)

V H X Y Mr M0

Pa1 - 7,411 - 5,905 - 43,763

JUMLAH 7,411 43,763

3.1.2 Tekanan Air Banjir

Gambar 3.2 Diagram tekanan akibat air banjir

Pf1 = 2

air h..2

1 = 23,85.1.

2

1 = 7,411 ton

Pf2 = b . h . air = 1,851.(3,85).(1) = 7,126 ton

Pf3 = 2

air h . .2

1 = 22,634.1.

2

1 = - 3,469 ton

Pf4 = 2

air h..2

1 = 22,634.1.

2

1 = 3,469 ton


47

Tabel 3.2 Perhitungan Tekanan Akibat Air Banjir

Bagian Berat (ton) Lengan (m) Momen

V H x y Mr Mo

Pf1 7,411 5,663 41,972

Pf2 7,411 6,305 46,728

Pf3 -3,469 4,756 -16,498

Pf4 3,469 0,892 3,094

JUMLAH 3,469 11,354 3,904 72,202

3.2. Tekanan Lumpur

lumpur = 0,6 ton/m3

= 300

Ka = tan2 (450 /2)

= tan2 (450 30o/2)

= 0,333

Keterangan :

lumpur = berat volume lumpur (t/m3)

= sudut gesek dalam

Ka = tekanan lumpur aktif (0,333)

Gambar 3.3 Diagram tekanan akibat lumpur


48

PL1 = 2

1. Ka . lumpur . h

2

= 2

1.(0,333).(0,6).(3,85)2

= 1,481 ton

Tabel 3.3 Perhitugan Tekanan Akibat Lumpur

Bagian Gaya (t) Lengan (m) Momen (tm)

V H x Y Mr M0

PL1 - 0,888 - 5,663 - 5,031

JUMLAH 0,888 5,301

3.3. Tekanan Berat Sendiri Bendung

Berat volume pasangan batu pas batu = 2,2 t/m2

Ditinjau 1 m lebar bendung

Gambar 3.4 Diagram tekanan berat sendiri bendung

W1 = b . h . pasangan = 2,0 . 2,0 . 2,2 = 8,800 ton

W2 = b . h . pasangan = 1,649 . 3,848 . 2,2 = 13,960 ton

W3 = b . h . pasangan = 1,0 . 4,0 . 2,2 = 8,800 ton

W4 = b . h . pasangan = 1,5 . 3,5 . 2,2 = 11,550 ton


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W5 = b . h . pasangan = 2,5 . 3,0 . 2,2 = 16,500 ton

W6 = 2/3 . b. h . pasangan = 2/3 . 1,5 . 1,5 . 2,2 = 3,300 ton

W7 = 1/2 . b. h . pasangan = 1/2 . 3,0 . 2,5 . 2,2 = 8,250 ton

Tabel 3.4 Perhitungan Tekanan Berat Sendiri Bendung

Bagian Gaya (ton)

Vertikal

Lengan (m) Momen (tm)

x y Mr M0

W1 8,800 6,000 3,000 52,800 26,400

W2 13,960 5,825 5,924 81,311 82,701

W3 8,800 4,500 5,000 39,600 44,000

W4 11,550 3,250 3,750 37,538 43,313

W5 16,500 1,250 1,500 20,625 24,750

W6 3,300 3,500 6,000 11,550 19,800

W7 8,250 1,667 3,833 13,750 31,625

71,160 257,174 272,588

Pada badan bendung yang berbentuk parabola, luas penampang digunakan pendekatan :

A = 2/3 . L . H

Didapat: W = 71,160 ton

Mo = 272,588 tm

Mr = 257,174 tm

3.4. Gaya Gempa

3.4.1 Gempa Horisontal

Gaya Gempa Horisontal (H) = Kh. W

= 0,10. 71,160

= 7,116 ton

Momen akibat H = Kh. Mo

= 0,10. 272,588

= 27,259 tm


50

Keterangan:

Kh = Koefisien gempa horisontal (diambil: Kh = 0,10)

W = Total berat sendiri bendung (t)

Mo = Momen guling akibat berat sendiri bendung (tm)

3.4.2 Gempa Vertikal

Gaya Gempa Vertikal (V) = Kv. W

= 0,05. 71,160

= 3,558 ton

Momen akibat V = Kv. Mr

= 0,05. 257,174

= 12,859 tm

Keterangan :

Kv = Koefisien gempa vertikal (diambil: Kv = 0,005)

Mr = Momen tahanan akibat berat sendiri

3.5. Gaya Angkat (Uplift Pressure)

3.5.1 Tekanan Air Normal

L = Lh + Lv

= 19,15 + 10,62

= 29,77 m

H (air normal) = elev. MAN elev. Dasar sungai

= 168,85 165,00

= 3,85 m

=

.

=

29,77. 3,2

= 0,107

Keterangan :

Hx = tinggi muka air dari titik yang dicari (m)

Lx = panjang rayapan (m)

L = total rayapan (m)


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H = tinggi muka air normal dari lantai dasar bendung (m)

Ux = uplift pressure di titik x (t/m2)

Gambar 3.5 Rayapan gaya angkat akibat muka air normal

Tabel 3.5 Perhitungan Tinggi Air Normal Terhadap Muka Bendung

Titik Hx (m) Lx (m) Ux (t/m2)

A 5.23 29..77 1.380

B 8.23 26.77 4.768

C 8.23 24.27 5.091

D 6.23 22.27 3.350

E 6.23 20.77 3.544

F 5.23 19.77 2.673

G 5.23 18.77 2.803

H 6.23 17.77 3.932

I 6.23 15.77 4.191

J 4.23 13.77 2.449


52

1.3800

3.0000

4.7680

A

B

c

U1

U2

RL

=

2(1 + 2)

=(21 + 2)

3(1 + 2)

Keterangan: R = Resultante Uplift Pressure (ton)

L = Lengan momen (m)

U1 = Uplift Pressure terendah di setiap bagian (ton)

U2 = Uplift Pressure tertinggi di setiap bagian (ton)

Tabel 3.6 Perhitungan Uplift Pressure Akibat Air Normal

Bagian Gambar Gaya angkat per 1 m panjang (t)

A - B

H = xH

UU

2

21

= - 32

768,4380,1x

= - 9,222 t

y =ba

bah

2

3

=

768,4380,1

768,4)380,12(

3

3 x

= 1,224 m

Ytotal = 1,224 m


53

BC 2.5000

5.09104.7680

C

D

5.0910

2.0000

3.3500

DE 1.5000

3.35003.5440

B - C

V = xHUU

2

21

V = - 5,22

091.5768,4x

= -12,324 t

x = cb

cbh

2

3

=

091,5768,4

091,5)768,42(

3

5,2 x

= 1,236 m

X total = 3 1,236 = 1,764 m

C D

H = xHUU

2

21

H = 0,22

350,3091,5x

= 8,441 t

y = dc

dch

2

3

=

350,3091,5

350,3)091,52(

3

0,2 x

= 1,069 m

Ytotal = 1,069 m

D E

V = xH

UU

2

21

V = - 5,12

544,3350,3x

= - 5,170 t

x =ed

edh

2

3

=

544,3350,3

544,3)350,32(

3

5,1 x = 0,743 m

X total = (2,5 0,743) + 1,5 = 3,257 m


54

FG

2.67302.8030

1.0000

G

1.0000

2.8030

3.9320H

E

F

3.5440

1.0000

2.6730

E F

H = xH

UU

2

21

H = 12

673,2544,3x

= 3,109 t

y = fe

feh

2

3

=

673,2544,3

673,2)544,32(

3

1 x

= 0,523 m

Ytotal = 0,523 + 1,0 = 1,523 m

F G

V = xH

UU

2

21

V = - 12

803,2673,2x

= - 2,738 t

x = gf

gfh

2

3

=

803,2673,2

803,2)673,22(

3

1 x = 0,496 m

X total = (1 - 0,496) + 2,5 + 1,5 = 4,504 m

G - H

H = xH

UU

2

21

H = - 0,12

932,3803,2x

= - 3,367 t

y =hg

hgh

2

3

=

932,3803,2

932,3)803,22(

3

0,1 x

= 0,472 m

Ytotal = 0,472 + 1,0 = 1,472 m


55

2.0000

3.93204.1910

HI

I

J

2.0000

2.4490

4.1910

H - I

V = xH

UU

2

21

V = - 22

191,4932,3x

= - 8,122 t

x =hg

hgh

2

3

=

191,4932,3

191,4)932,32(

3

2 x

= 0,989 m

Xtotal = (2 0,989) + 2,5 + 1,5 + 1

= 6,011 m

I - J

H = xH

UU

2

21

H = 22

449,2191,4x

= 6,640 t

y =hg

hgh

2

3

=

449,2191,4

449,2)191,42(

3

2 x

= 1,087 m

Ytotal = 1,087 + 1 = 2,087 m

Tabel 3.7 Gaya Angkat Air Normal

Titik Hx

(m)

Lx

(m)

Ux

(t/m2)

Uplift Force (t) Lengan (m) Lengan (m) Momen

V H x y x

(total)

y

(total) Mr Mo

A 5.23 29.77 1.380

-9.222 1.224 1.224 11.292

B 8.23 26.77 4.768

-12.324 1.236 1.764 21.740

C 8.23 24.27 5.091

8.441 1.069 1.069 9.022

D 6.23 22.27 3.350

-5.170 0.743 3.257 16.840

E 6.23 20.77 3.544


56

3.109 0.523 1.523 4.734

F 5.23 19.77 2.673

-2.738 0.496 4.504 12.332

G 5.23 18.77 2.803

-3.367 0.472 1.472 4.957

H 6.23 17.77 3.932

-8.122 0.989 6.011 48.824

I 6.23 15.77 4.191

6.640 1.087 2.087 13.857

J 4.23 13.77 2.449

(JUMLAH) - 28.355 5.600 30.106 113.491

Catatan : Searah jarum jam (+)

Berlawanan arah jarum jam (-)

Gaya Angkat Akibat Air Normal :

1. Tekanan Vertikal

V = fu x V = 0,5 x (- 28,355) = - 14,178 ton

2. Tekanan Horizontal

H = fu x H = 0,5 x 5,600 = 2,800 ton

3. Momen

Mr = 0.5 x Mr = 0,5 x (30,106) = 15,053 t.m

Mo = 0.5 x Mo = 0,5 x (113,491) = 56,746 t.m

Dimana : fu = koefisien reduksi untuk jenis tanah keras (50 %)

3.5.2 Tekanan Air Banjir

L = 29,77 m

H (air banjir) = elev. M.A.B elev. Dasar sungai

= 170,701 165,000

= 5,701 m

=

. =

29,77. 5,701 = 0,192

Keterangan:

Hx = tinggi muka air dari titik yang dicari (m)

Lx = panjang rayapan (m)

L = total rayapan (m)


57

H = tinggi muka air banjir dari lantai dasar bendung (m)

Ux = uplift pressure di titik x (t/m2)

Gambar 3.6 Rayapan gaya angkat akibat muka air banjir

Tabel 3.8 Perhitungan Tinggi Air Banjir Terhadap Muka Bendung

Titik Hx (m) Lx (m) Ux (tm)

A 7.08 29.77 1.380

B 10.08 26.77 4.995

C 10.08 24.27 5.433

D 8.08 22.27 3.816

E 8.08 20.27 4.104

F 7.08 19.77 3.295

G 7.08 18.77 3.487

H 8.08 17.77 4.678

I 8.08 15.77 5.061

J 6.08 13.77 3.444


58

A1.3800

3.0000

4.9550B

2.5000

4.95505.4330

BC

3.8160

2.0000

5.4330

C

D

Tabel 3.9 Perhitungan Uplift Pressure Akibat Air Banjir

Bagian Gambar Gaya angkat per 1 m panjang (t)

A-B

H = xHUU

2

21

= - 0,32

955,4380,1x

= - 9,502 t

y =ba

bah

2

3

=

955,4380,1

955,4)380,12(

3

0,3 x

= 1,218 m

Ytotal = 1,218 m

B-C

V = xHUU

2

21

V = - 5,22

433,5955,4x

= - 12,985 t

x = cb

cbh

2

3

=

433,5955,4

433,5)955,42(

3

5,2 x

= 1,231 m

X total = 2,5 1,231 = 1,269 m

C-D

H = xH

UU

2

21

H = 0,22

816,3433,5x

= 9,250 t

y = dc

dch

2

3

=

816,3433,5

816,3)433,52(

3

0,2 x = 1,058 m

Ytotal = 1,058 m


59

1.5000

3.81604.1040

DE

4.1040 E

F

1.0000

3.2950

1.0000

3.29503.4870

FG

D-E

V = xHUU

2

21

V = - 5,12

104,4816,3x

= - 5,940 t

x = ed

edh

2

3

=

104,4816,3

104,4)816,32(

3

5,1 x

= 0,741 m

X total = (1,5 - 0,741) + 2,5 = 3,259 m

E-F

H = xHUU

2

21

H = 12

295,3104,4x

= 3,699 t

y = fe

feh

2

3

=

295,3104,4

295,3)104,42(

3

1 x

= 0,518 m

Ytotal = 0,518 + 1,0 = 1,518 m

F-G

V = xHUU

2

21

V = - 0,12

487,3295,3x

= - 3,391 t

x = gf

gfh

2

3

=

487,3295,3

487,3)295,32(

3

0,1 x

= 0,495 m

X total = (1,0-0,495)+2,5+1,5 = 4,505 m


60

1.0000

4.6780

3.4870G

H

2.0000

4.67805.0610

HI

2.0000

5.0610

3.4440

I

J

G-H

H = xHUU

2

21

H = - 0,12

678,4487,3x

= - 4,082 t

y =hg

hgh

2

3

=

678,4487,3

678,4)487,32(

3

0,1 x

= 0,476 m

Ytotal = 0,476 + 1,0 = 1,476 m

H-I

V = xHUU

2

21

V = - 0,22

061,5678,4x

= - 9,739 t

x =hg

hgh

2

3

=

061,5678,4

061,5)678,42(

3

0,2 x

= 0,987 m

Xtotal = (2 0,987) + 2,5 + 1,5 + 1,0

= 6,013 m

I-J

H = xHUU

2

21

H = 0,22

444,3061,5x

= 8,505 t

y =hg

hgh

2

3

=

444,3061,5

444,3)061,52(

3

0,2 x = 1,063 m

Ytotal = 1,063 + 2 = 3,063 m


61

Tabel 3.10 Gaya Angkat Akibat Air Banjir

Titik Hx

(m)

Lx

(m)

Ux

(t/m2)

Uplift Force (t) Lengan (m) Lengan (m) Momen

V H x y x

(total)

y

(total) Mr Mo

A 7.08 29.77 1.380

-9.502 1.214 1.218 11.572

B 10.08 26.77 4.955

-12.985 1.231 1.269 16.478

C 10.08 24.27 5.433

9.250 1.058 1.058 9.789

D 8.08 22.27 3.816

-5.940 0.741 3.259 19.358

E 8.08 20.77 4.104

3.699 0.518 1.518 5.615

F 7.08 19.77 3.295

-3.391 0.495 4.505 15.275

G 7.08 18.77 3.487

-4.082 0.476 1.476 6.025

H 8.08 17.77 4.678

-9.739 0.987 6.031 58.736

I 8.08 15.77 5.061

8.505 1.063 3.063 26.051

J 6.08 13.77 3.444

(JUMLAH) - 32.054 7.870 43.648 125.251

Catatan : Searah jarum jam (+)

Berlawanan arah jarum jam (-)

Gaya Angkat Akibat Air Banjir :

1. Tekanan Vertikal

V = fu x V = 0,5 x (-32.054) = - 16.027 ton

2. Tekanan Horizontal

H = fu x H = 0,5 x (7.870) = 3.935 ton

3. Momen

Mr = 0.5 x Mr = 0,5 x (43.648) = 21.824 t.m

Mo = 0.5 x Mo = 0,5 x (125.251) = 62.626 t.m

Dimana : fu = koefisien reduksi untuk jenis tanah keras (50 %)


62

Tabel 3.11 Akumulasi Beban Beban Pada Bendung

3.6. Kontrol Stabilitas Bendung

Ketentuan :

1. Tegangan tanah dasar yang diijinkan () = 2,0 kg/cm2 = 20 t/m2

2. Over Turning safety factor (guling) = 1,5 kg/cm2

3. Sliding safety factor (geser) = 1,2 kg/cm2

Kombinasi gaya gaya yang bekerja pada bendung :

3.6.1 Tanpa Pengaruh Gempa

1. Keadaan Normal dengan Uplift Pressure

H = a(4) + c(4) + g(4)

= 7,411 + 0,888 + 2,800 = 11,100 t

V = a(3) + c(3) + d(3) + g(3)

= 0,000 + 0,000 + 71,160 14,177 = 56,983 t

Mr = a(5) + c(5) + d(5) + g(5)

= 0,000 + 0,000 + 257,174 + 15,053 = 272,226 tm

M0 = a(6) + c(6) + g(6)

= 43,763 + 5,031 + 56,746 = 105,540 tm

Kontrol:

a. Terhadap Guling (Over Turning)

=

=

272,226

105,540= 2,579 1,5 ()

No. Keterangan Gaya (ton) Momen (ton.meter)

Vertikal Horizontal Mr Mo

1 2 3 4 5 6

Tekanan Air

a Air Normal 0.000 7.411 0.000 43.763

b Air Banjir 3.469 11.354 3.094 72.202

c Tekanan Lumpur 0.000 0.888 0.000 5.031

d Berat Sendiri

Bendung 71.160 - 257.174 -

Gaya Gempa

e Gempa Horisontal - 7.116 27.259 27.259

f Gempa Vertikal 3.558 - 12.859 12.859

Gaya Angkat

g Air Normal -14.177 2.800 15.053 56.746

h Air Banjir -16.027 3.935 21.824 62.626


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b. Terhadap Geser (Sliding)

=f .

=

0,7 . 56,983

11,100= 3,594 1,2 ()

Dimana, f = koefisien geser (diambil f= 0,7)

c. Terhadap Daya Dukung Tanah (Over Stressing)

Resultante beban vertikal bekerja sejarak a dari titik O

=

=

272,226 105,540

56,983= 2,925

Resultante beban vertikal bekerja sejarak e dari pusat berat bendung

=

2 =

7

2 2,925 = 0,575

Jarak e masih terletak didalam Bidang Kern

bab iii stabilitas bendung

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