BAB III Analisa Stabilitas Bendung Rev

JURUSAN TEKNIK SIPIL FAKULTAS TEKNIK UNIVERSITAS UDAYANA

Tugas Irigasi dan Bangunan Air BAB III

ANALISA STABILITAS STABILITAS BENDUNG BENDU NG

Gaya–gaya yang bekerja pada tubuh bendung, akibat : 1.

Tekanan air.

2.

Tekanan lu lumpur.

3.

Tekana kanan n bera beratt sen sendi diri ri bend bendun ung. g.

4.

Gaya gempa.

5.

Gaya angkat (uplift pressure. pressure.

3.1 Tekanan Air Air 3.1.1 Te Tekanan kanan Air Air Normal

Pa2

4,"" m 1

Pa1

1

1(3 ) 4,"" * 1,33 m

!

1,5 m 1,5" m

s

1,#4 m

1," m

u

r

1," m

n

k

1," m

1," m

'

t

",#5 m

2," m

& p

1," m

m

1," m

1,5" m

j

g

1," m

1," m

i

l

1," m

a

1,5" m

$

1," m

h 3,5" m

2,#3+ m 1,5" m

2,5" m

d

e 1," m

%

1,5" m

b

,53 m

Gambar 3.1 -iagram Tekanan kibat kibat ir /&rmal

0 air * 1 t&nm3 1 2

a1 *

1

.0air .h .h 2

2

*

.(1).( 4,")

2

* # t&n

4+


Tugas Irigasi dan Bangunan Air

0 air a2 * b . h .

* (1,5.(4,".(1 (1,5.(4,".(1 *  t&n

Tabel. Tabel. 3.1 erhitungan erhit ungan Tekanan ir /&rmal Gaya (t

agian

 7  

a1 a2 96

engan (m ) y 7 4,1+" ,53 7

6 # 7 #

&men (tm " r 7 33,3 38,21 7 38,21 33,3

3.1. Te Tekanan kanan Air Air Ban!ir "Flood "Flood #

Pf4 1,"8 m

Pf3 Pf2

4," m

Pf5 1

Pf1

1

1,85 m 1(3 )4," * 1,33 m

Pf6

!

4," m

s

1,#4 m

1,5" m

1," m

u

r

&

'

p

1," m

t

",#5 m

1,"8 m

2," m

1," m

n

k

m

l

1," m

1," m

1,5 m

1,5" m

1," m

1,"13 m

j

g

i

h

1," m

1," m

1," m

a

1,5" m

3,5" m

$

1," m

2,#3+ m

1,5" m

2,5" m

d

e 1," m

%

1,5" m

b

5,523 m ,53 m

Gambar 3.2 -iagram Tekanan kibat kibat ir anjir

1 2

1

. 0air . h 2

$ 1 *

2

.(1).( 4," )

2

*

* # t&n

* (1, (1,"8 "8. .(4 (4," ,". .(1 (1

* ,43 ,43  t&n t&n

0 air $ 2 * b . h .

4#



0 air a2 * b . h .

* (1,5.(4,".(1 (1,5.(4,".(1 *  t&n

Tabel. Tabel. 3.1 erhitungan erhit ungan Tekanan ir /&rmal Gaya (t

agian

 7  

a1 a2 96

engan (m ) y 7 4,1+" ,53 7

6 # 7 #

&men (tm " r 7 33,3 38,21 7 38,21 33,3

3.1. Te Tekanan kanan Air Air Ban!ir "Flood "Flood #

Pf4 1,"8 m

Pf3 Pf2

4," m

Pf5 1

Pf1

1

1,85 m 1(3 )4," * 1,33 m

Pf6

!

4," m

s

1,#4 m

1,5" m

1," m

u

r

&

'

p

1," m

t

",#5 m

1,"8 m

2," m

1," m

n

k

m

l

1," m

1," m

1,5 m

1,5" m

1," m

1,"13 m

j

g

i

h

1," m

1," m

1," m

a

1,5" m

3,5" m

$

1," m

2,#3+ m

1,5" m

2,5" m

d

e 1," m

%

1,5" m

b

5,523 m ,53 m

Gambar 3.2 -iagram Tekanan kibat kibat ir anjir

1 2

1

. 0air . h 2

$ 1 *

2

.(1).( 4," )

2

*

* # t&n

* (1, (1,"8 "8. .(4 (4," ,". .(1 (1

* ,43 ,43  t&n t&n

0 air $ 2 * b . h .

4#



0 air $ 3 * b . h .

* ( 1, 1,5.(4,".(1

*  t&n

0 air $ 4 * b . h .

1 2

. 0air . h

* (2,513.(1,"8.(1 * 4,"43 4,"43 t&n

1

2

2

$ 5 *

2

.(1,85) .1

*

− 1 . 0air . h 2

− 1 .(1).(1,85) 2

2

$  *

* 1,8 t&n 2

*

* 7 1,8 t&n

Tabel.3.2 erhitungan Tekanan ir anjir

Gaya (t

agian $ 1 $ 2 $ 3 $ 4 $ 5 $ 

 7 7  4,"43 1,8 7

6 # ,43 7 7 7 71,8

96

11,843

12,53

engan (m ) y 7 4,1+" 7 4,#3+ +,2# 7 ,+# 7 ",5 7 7 3,15

&men (tm r " 7 33,3 7 31,131 43,+1 7 2+,412 7 1,235 7 7 75,8#5 +2,33

5#,5"

3. Te Tekanan kanan L$m%$r γ lumpur

* ", t&nm 3 ;

* 3""

* tan2 (45" – ;2 * tan2 (45" – 3"&2 * ",333

48



0lumpur

* berat !&lume lumpur (tm 3

;

* sudut gesek dalam

* tekanan lumpur akti$

Pa2

4,"" m 1

Pa1

1

1(3 ) 4,"" * 1,33 m

!

1,5 m

s

1,#4 m

1,5" m

1," m

u

r

&

'

p

1," m

t

2," m

k

1," m

1," m

",#5 m

n

1," m

m

1," m

1,5" m

j

g

i

h

1," m

l

1," m

a

1,5" m

1," m

3,5" m

$

1," m

2,#3+ m 1,5" m

2,5" m

d

e 1," m

%

1,5" m

b

,53 m

Gamb ar 3.3 -iagram Tekanan kibat umpur

1

γ lumpur

2

.< a.h2.

1 * 1 2

*

.(",333. (4," 2.(",.

* 1, t&n γ lumpur

2 * b.h. * (1,5.(4,". ", * 3, t&n

Tabel. 3.3 erhitungan Tekanan umpur agian

Gaya (t 

6

engan (m ) y

&men (tm r " 5"



1 2 96

7 3, 3,

1, 7 1,

7 ,53

4,1+" 7

7 23,53" 23,53"

,+2 7 ,+2

3.3 Tekanan Bera& Sen'iri Ben'$n( γ pas ang an

* 2,2 tm2

erat !&lume pasangan batu W7 W8 W9

y

W10 W2

W3

W4 W11 W5

W1 1,5" m

W6 2,5" m

1".13""

14.+1+

3,5" m

1".1524

1,5" m

x 1,5" m

Gambar 3.4 -iagram Tekanan kibat erat =endiri endung

ada badan bendung yang berbentuk parab&la, luas penampang digunakan pendekatan :

 * 23 .  . 6

51



γ pas ang an

>1

* b. h.

* 1,4+2 . 1,#4 . 2,2

* 5,858 t&n

* 1,"13 . 5,3# . 2,2

* 11,88" t&n

* 1,"15 . 5,1 . 2,2

* 12,52+ t&n

* 1,5" . 3,5 . 2,2

* 11,55" t&n

* 1,5" . 3," . 2,2

* 8,8"" t&n

* 1,5" . 2,5 . 2,2

* #,25" t&n

* 23 . 1,"13 . ",45 . 2,2

* ",8 t&n

* 23 . 1,"15 . ",23 . 2,2

* ",342 t&n

* 23 . 1,5" . 1,1 . 2,2

* 2,42" t&n

* 23 . 1,5" . 1,5 . 2,2

* 3,3"" t&n

* 23 . 1,5" . 1,5" . 2,2

* 3,3"" t&n

γ pas ang an

>2

* b. h. γ pas ang an

>3


>4


>5


>


>+

* 23 . b. h . γ pas ang an

>#


>8


>1"


>11

* 23 . b. h .

Tabel 3.4 erhitungan Tekanan erat =endiri endung Ba(ian

>1

B "m#

1,4+2

) "m#

1,#4

Ga*a "&on#

Len(an "m#

+omen "&m#

Ver&ikal

,

*

+r

+-

5,858

+,24

1,82

43,2#4

11,441 52



>2

1,"13

5,3#

11,88"

,"23

3,8

+2,215

44,243

>3

1,"15

5,1

12,52+

5,""#

3,#"5

2,+3

4+,

>4

1,5

3,5

11,55"

3,+5

3,+5

43,313

43,313

>5

1,5

3

8,8""

2,25

2,5

22,2+5

24,+5"

>

1,5

2,5

#,25"

",+5

1,25

,1##

1",313

>+

1,"13

",45

",8

5,#85

,548

3,841

4,3+8

>#

1,"15

",23

",342

5,134

,82

1,+5#

2,281

>8

1,5

1,1

2,42"

3,83#

5,813

8,53"

14,3"8

>1"

1,5

1,5

3,3""

2,43#

4,53

#,"45

15,"5#

>11

1,5

1,5

3,3""

",83#

3,"3

3,"85

1",1"#

2+,3+8

22+,#8

+",2"+

?

3. Ga*a Gem%a 3..1 Gempa 6&ri@&ntal • Gaya 6&ri@&ntal (6

* < h . A1 * ",1" . +",2"+ * +,"21 t&n

•

&men akibat gempa h&ri@&ntal : " * r * < h . A"1 * ",1" . 22+,#8 * 22,+#+ tm

* gaya gempa h&ri@&ntal (t

< h

* k&e$isien gempa h&ri@&ntal, (&ndasi batu : < h * ",1"

1

* berat sendiri bendung (t

"1 * m&men guling akibat berat sendiri (tm

3..

Gempa ertikal • Gaya ertikal (

* < ! . A> * ","5 .( +",2"+  * 3,51 t&n

53



• &men akibat gempa !ertikal :

r * < ! . Ar1 * ","5. (2+,3+8 * 13,#2 tm

* gaya gempa !ertikal (t

< !

* k&e$isien gempa !ertikal, (&ndasi batu : < ! * ","5

r1

* m&men tahanan akibat berat sendiri (tm

3./ Ga*a An(ka& "Uplift Pressure# 3./.1

Air Normal

A

*

h B !

*

15,#5 B 13,4+

*

28,32 m

C6 (air n&rmal * ele!. / – ele!. -asar sungai * 45,5" – 41,5" * 4,"" m )

Σ ) *

6) –

. C6

) 28,32 ) *

6) –

.(4,""

) *

6) – ",13  )

* tinggi muka air dari titik yang di%ari (m

)

* panjang rayapan (m

A

* t&tal rayapan (m

C6

* tinggi muka air n&rmal (m 54



)

* uplift pressure di titik ) (tm 2

 h  2U 1 + U 2    3  U 1 + U 2 e *

U 1 + U 2 xH 2 D *

Gambar 3.5 Dayapan Gaya ngkat

../ B 45,5" m

y

6) B 41,5" m a j

g

$

i

h

e

d %

)

Titik Guling yang -itinjau b

) Gamb ar 3. Gaya ngkat kibat ir /&rmal

Tabel 3.5 erhitungan Tinggi air n&rmal terhadap muka bendung Titik

6) (m

) (m

) (tm2

a

4,33+

28,18"

",+4+

b

,#3+

2,8"

3,554

55



%

,#3+

25,18"

3,+38

d

5,#3+

24,18"

2,#2

e

5,#3+

22,8"

3,"4

$

4,#3+

21,8"

2,18

g

4,#3+

2",18"

2,354

h

5,#3+

18,18"

3,4++

i

5,#3+

15,8"

3,8"+

j

4,#3+

14,8"

3,"3"

Tabel 3. erhitungan Gaya ngkat kibat ir /&rmal

agia

Gambar

n a7b

a

Gaya angkat per 1 m panjang (t

U 1 + U 2 xH 2 6* ",+4+ + 3,554 2

x 2,5

*7 * 75,3+ t

b

 h  2a + b    3  a + b y *

2,5  (2 x ",+4+ + 3,554  3

 

",+4+ + 3,554

 

* * ",8+# m 5



Et&tal * ",8+# m

U 1 + U 2 xH 2 * 3,554 + 3,+38 %

2 b

x1,5

* * 5,4+" t

 h  2b + c    3  b + c

b 7 % ) *

1,5  (2 x3,554 + 3,+38  3

 

3,554 + 3,+38

 

* * ",+44 m F t&tal * 1,5" – ",+44 * ",+5 m U 1 + U 2 xH 2 6* 3,+38 + 2,#2 2

x1,"

6* * 3,3" t %–d

%

 h  2c + d    3  c + d y*

1,"  (2 x3,+38 + 2,#2  3

 

3,+38 + 2,#2

*

  * ",522 m

Et&tal * ",522 m

5+


Tugas Irigasi dan Bangunan Air U 1 + U 2 2

xH

* 2,#2 + 3,"4

e

2

d

x1,5

* * 4,431 t

 h  2d + e    3  d + e

d–e ) *

1,5  (2 x 2,#2 + 3,"4  3

 

 

2,#2 + 3,"4

* * ",+42 m F t&tal * (1,5 – ",+42 B 1,5 * 2,25# m U 1 + U 2 xH 2 6* 3,"4 + 2,18

$

2

x1

6* * 2,"# t

e – $

 h  2e + f    3  e + f e

y *

1  (2 x3,"4 + 2,18 



3  3,"4 + 2,18 *

  * ",52# m

Et&tal * ",52# B 1," * 1,52# m

5#



xH

*

g

2,18 + 2,354

$

2

x1,5

* * 3,382 t $–g

 h  2 f + g    3  f + g ) *

1,5  (2 x2,18 + 2,354  3

 

2,18 + 2,354

*

  * ",+4" m

F t&tal * (1,57",+4"B1,5B1,5 * 3,+ m U 1 + U 2 xH 2 6* 2,354 + 3,4++ 2

g

x1,"

6 *7 * 72,815 t

 h  2 g + h    3  g + h

g7h y *

h

1,"  (2 x 2,354 + 3,4++  3

 

2,354 + 3,4++

 

* * ",4# m Et&tal * ",4# B 1," * 1,4# m

58



xH

* i

3,4++ + 3,8"+

h

2

x3,5

* * 12,822 t h7i

 h  2 g + h    3  g + h ) *

3,5  (2 x3,4++ + 3,8"+  3

 

3,4++ + 3,8"+

 

*

* 1,+1 m

Ft&tal *(3,571,+1B1,5B1,5B1,5*,2#4 m U 1 + U 2 xH 2 6* 3,8"+ + 3,"3"

j

2

x1,"

6* * 3,48 t

 h  2 g + h    3  g + h

i7j

i

y *

1,"  (2 x3,8"+ + 3,"3"  3

 

3,8"+ + 3,"3"

 

* * ",521 m Et&tal * ",521 B 1 * 1,521 m Tabel 3.+ Gaya ngkat kibat ir /&rmal

"



atatan : =earah jarum jam (B erlaHanan arah harum jam (7 

Gaya ngkat kibat ir /&rmal : 1. Tekanan ertikal  * $u ) A * ",5 ) (2,214 * 13,1"+ t&n 2. Tekanan 6&ri@&ntal 6 * $u ) A6 * ",5 ) (1,"#5 * ",543 t&n 3. &men r * ".5 ) Ar * ",5 ) (71,+14 * 7",#5+ tm & * ".5 ) A& * ",5 ) (32,1" * 1,"53 tm

-imana :

3./.

$u * k&e$isien reduksi untuk jenis tanah keras (5" I

Air Ban!ir

A

*

28,18 m

C6 (air banjir * ele!. .. – ele!. -asar sungai

1



* 4+,535 – 41,5" * ,"35 m L x

Σ L ) * 6) 7

. C6 ) 28,18

) * 6) 7

. ,"35

) * 6) 7 ",2"+ )

* tinggi muka air banjir dari titik yang di%ari (m

)

* panjang rayapan (m

A

* t&tal rayapan (m

C6

* beda tinggi .. dengan muka air di hilir (m

)

* uplift pressure di titik ) (tm2

.. B 4+,535 m

../ B 45,5" m

y

6) B 22","" m a j

g

$

i

h

e

)

d %

Titik Guling yang -itinjau b

) Gambar 3.+ Gaya ngkat kibat ir anjir

2



Tabel 3.# erhitungan Tinggi ir anjir Terhadap uka endung Titik

6) (m

) (m

) (tm2

a

,3+2

28,18"

",843

b

#,#+2

2,8"

3,8"#

%

#,#+2

25,18"

4,1#+

d

+,#+2

24,18"

3,3+3

e

+,#+2

22,8"

3,52

$

,#+2

21,8"

2,#3#

g

,#+2

2",18"

3,11+

h

+,#+2

18,18"

4,3"3

i

+,#+2

15,8"

4,854

j ,#+2 14,8" Tabel 3.8 erhitungan Gaya ngkat kibat ir anjir

4,14"

agia n

Gambar

Gaya angkat per 1 m panjang (t

3



xH

6* ",843 + 3,8"#

a

2

x 2,5

*7 * 7,"3 t

 h  2a + b    3  a + b

a7b y *

2,5  (2 x",843 + 3,8"# 

b

3

 

 

",843 + 3,8"#

* * ",885 m Et&tal * ",885 m U 1 + U 2 xH 2 *

%

3,8"# + 4,1#+

b

2

x1,5

* * ,"+1 t

 h  2b + c    3  b + c

b 7 % ) *

1,5  (2 x3,8"# + 4,1#+  3

 

3,8"# + 4,1#+

 

* * ",+41 m F t&tal * 1,5" – ",+41 * ",+58 m

4



xH

6* 4,1#+ + 3,3+3

d

2

x1,"

6* * 3,+# t %–d

%

 h  2c + d    3  c + d y*

1,"  (2 x 4,1#+ + 3,3+3  3

 

4,1#+ + 3,3+3

*

  * ",51# m

Et&tal * ",51# m U 1 + U 2 xH 2 * 3,3+3 + 3,52

e

d

2

x1,5

* * 5,2# t

 h  2d + e    3  d + e

d–e ) *

1,5  ( 2 x 3,3+3 + 3,52  3

 

3,3+3 + 3,52

 

* * ",+4" m F t&tal * (1,5 – ",+4" B 1,5 * 2,2 m

5



xH

6* 3,52 + 2,#3#

$

2

x1

6* * 3,245 t

e – $

 h  2e + f    3  e + f e

y *

1  (2 x3,52 + 2,#3# 



3  3,52 + 2,#3# *

  * ",521 m

Et&tal * ",521 B 1," * 1,521 m U 1 + U 2 xH 2 *

g

2,#3# + 3,11+

$

2

x1,5

* * 4,4 t $–g

 h  2 f + g    3  f + g ) *

1,5  (2 x 2,#3# + 3,11+  3

 

2,#3# + 3,11+

* g7h

g

  * ",+3# m

F t&tal * (1,57",+3#B1,5B1,5 * 3,+2 m U 1 + U 2 xH 2 6* 3,11+ + 4,3"3 2

x1,"

6 *7

h

* 73,+1" t





 h  2 g + h    3  g + h y *

1,"  (2 x3,+11 + 4,3"3  3

 

3,+11 + 4,3"3

 

* * ",4+3 m Et&tal * ",4+3 B 1," * 1,4+3 m U 1 + U 2 xH 2 * i

4,3"3 + 4,854

h

2

x3,5

* * 1,188 t h7i

 h  2 g + h    3  g + h ) *

3,5  (2 x 4,3"3 + 4,854  3

 

4,3"3 + 4,854

 

*

* 1,+"8 m

Ft&tal *(3,571,+"8B1,5B1,5B1,5*,281 m U 1 + U 2 xH 2 6* 4,854 + 4,14" 2 j

x1,"

6* * 4,54+ t

i7j i

 h  2 g + h    3  g + h y *

1,"  (2 x 4,854 + 4,14"  3

 

4,854 + 4,14"

 

* * ",515 m +



Et&tal * ",515 B 1 * 1,515 m

Tabel 3.1" Gaya ngkat kibat ir anjir

atatan : =earah jarum jam (B erlaHanan arah harum jam (7 

Gaya ngkat kibat ir anjir : 1. Tekanan ertikal  * $u ) A * ",5 ) (32,""3 * 1,""2 t&n 2. Tekanan 6&ri@&ntal 6 * $u ) A6 * ",5 ) (1,+8# * ",#88 t&n 3. &men r * ".5 ) Ar * ",5 ) (2," * 1,33 tm #



& * ".5 ) A& * ",5 ) (135,218 * +,1" tm

-imana :

$u * k&e$isien reduksi untuk jenis tanah keras (5" I

Tabel 3.11 kumulasi eban7eban pada endung No

Ke&eran(an

1

 Tekanan Air ir /&rmal ir anjir Tekanan umpur erat =endiri endung Ga*a Gem%a Gempa 6&ris&ntal Gempa ertikal Ga*a An(ka& ir /&rmal ir anjir

a b % d e $ g h

Ga*a "&# Ver&ikal )ori0on&al 3 

+omen "&on me&er# +r +o / 

,""" 11,843 3, +",2"+

#,""" 12,53 1, 7

38,21 +2,33 23,53 2+,3+8

33,3 5#,5" ,+2 7

7 3,51

+,"21 7

22,+#+ 13,#2

22,+#+ 13,#2"

13,1"+ 1,""2

",543 ",#88

7",#5+ 1,33

1,"53 +,1

3. Kon&rol S&a2ili&a0 Ben'$n(

* 2," kg%m2 * 2" tm2

2. L!er Turning sa$ety $a%t&r (guling

* 1,5 kg %m2

3. =liding sa$ety $a%t&r (geser

* 1,2 kg%m2

<&mbinasi gaya7gaya yang bekerja pada bendung : 3..1

Tan%a Gem%a

Tegangan ijin tanah JK* 2" tm2 1.

Keadaan Air Normal dengan Uplift Pressure



A6



A



Ar

* a(4 B %(4 B g(4 * # B 1, B ",543 * 1",143 t * a(3 B %(3 B d(3 B g(3 *  B 3, B +",2"+ B 13,1"+ * 82,814 t * a(5 B %(5 B d(5 B g(5 * 38,21 B 23,53 B 2+,3+8 – ",#5+ * 33#,2# tm 8





A"

* a( B %( B g( * 33,3 B ,+2 B 1,"53 5,"#5 tm =

<&ntr&l : a Terhadap guling (over turning 

∑  r ∑ " =M *

33#,2# 5,"#5

= ,"31

*

.............. N 1,5"

(L
b Terhadap geser ( sliding 

",+" . ( 82,814)

f ∑ V ∑ H =M *

1",143

= ,412

*

.......N 1,2" (L
keterangan : $ * k&e$isien geser

% Terhadap daya dukung tanah (over stressing 

+"



b*#," m

Gambar 3.11. Jarak e dalam bidang Kern •

Desultante beban !ertikal bekerja sejarak a dari titik L.

33#,2# − 5,"#5

∑  r − ∑ " ∑ a * •

= 3,"3+ m

*

Desultante beban !ertikal bekerja sejarak e dari pusat berat bendung.  2

#,"

−a

e * •

82,814

2

− 3,"3+ = ",83 m

*

9arak e masih terletak di dalam P idang
B 

e Q #," 

e * ",83 m Q •



",##8 m Q 1,333 m

(L
Tegangan yang terjadi pada tanah akibat beban – beban pada bendung :

∑ V A

±

M . ) Ry

J*

+1



∑ b ) . b y

±

∑  . e . ",5 . b ) 1 12

3

. b ) . b y

*

∑ b ) . b y

±

.∑.e 2

b ) . b y

*

 ∑ V  1 ±  . e  b x . b y  b )   * Tegangan i@in tanah dasar (JK * 2," kg%m 2 * 2" tm 2 •

Tegangan tanah dik&ntr&l per 1 meter panjang bendung :

 ∑ V  1 ±  . e  b x . b y  b )   J

*

Jmin

82,814   . ( ",83)  1 −  #,". (1)  #,"  * * 3,22 tm2

Jma)

82,814   . ( ",83)  1 +  #,". (1)  #,"  * * 18,+1# tm 2 Q JK* 2" tm2

2.    

S "

(L
(L
Keadaan Banjir dengan Uplift Pressure

A6 A Ar A"

* b(4 B %(4 B h(4 * 12,53 B 1, B ",#88 * b(3 B %(3 B d(3 B h(3 * 11,843 B 3, B +",2"+ B 1,""2 * b(5 B %(5 B d(5 B h(5 * +2,33 B 23,53 B 2+,3+8 B1,33 * b( B %( B h( * 5#,5" B ,+2 B +,1

* 15,"2 t * 1"1,+52 t * 3+3,"2 tm * 132,+## tm

<&ntr&l : a Terhadap guling (over turning 

∑  r ∑ " =M *

3+3,"2 132,+## *

= 2,#14 N 1,5"

(L< O +2



b Terhadap geser ( sliding  $ ∑ 

",+ . (1"1,+52)

∑6

15,"2

=M *

= 4,+28

*

N 1,2"

(L< O


% Terhadap daya dukung tanah (over stressing  •


3+3,"2 − 132,+##

∑  r − ∑ " ∑ a * •

= 2,#+ m

*


e * •

1"1,+52

#,"

−a

2

− 2,#+ = 1,133 m

*

9arak e masih terletak di dalam P idang
B 

e Q #," 

e * 1,133 m Q •



1,133 m Q 1,333 m

(L
Tegangan pada tanah dasar

 ∑   1 ±  . e  b ) . b y  b )   J

*

Jmin

1"1,+52   . (1,133)  1 −  #," . (1)  #,"  * * 1,811 tm2

S "

Jma)

1"1,+52   . (1,133)  1 +  #," . (1)  #,"  * * 18,8+3 tm 2

Q JK* 2" tm2 (L< O

(L
+3



3..

Den(an Gem%a )orion&al

Tegangan ijin tanah (dengan gempa JK* 2" tm 2 ) 1,3 * 2 tm 2 1.
* 1+,14 t

A * a(3 B %(3 B d(3 B g(3 *  B 3, B +",2"+ B13,1"+

* 82,814 t

Ar * a(5 B %(5 B d(5 Bg(5 * 38,21 B 23,53 B 2+,3+8 – ",#5+

* 33#,2# tm

A" * a( B %( B e( B g( * 33,3 B ,+2 B 22,+#+ B 1,"53

* +#,#+2 tm

<&ntr&l : a. Terhadap guling (over turning 

∑ r ∑ " =M *

33#,2# +#,#+2

= 4,2#8

*

N 1,5"

(L< O

b. Terhadap geser ( sliding  $ ∑ 

",+ . ( 82,814)

∑6

1+,14

=M *

= 3,#

*

N 1,2"

(L< O

keterangan : $ * k&e$isien geser %. Terhadap daya dukung tanah (over stressing  •


33#,2# − +#,#+2

∑ M − ∑ M " ∑ V r

a * •

82,814

= 2,+81m

*


e *

#,"

−a

2



− 2,+8 = 1,21 m

*



Q

* 1,333 m


+4



 ∑ V  1 ±  . e  b x . b y  b )   J

*

Jmin

82,814   . (1,21)  1 −  #," . (1)  #,"  * * 1,"+4 tm2

S"

(L< O

Jma)

82,814   . (1,21)  1 +  #," . (1)  #,"  * * 22,154 tm 2

Q JK* 2 tm2

(L< O

2.
* 1,21 t

A * a(3 B %(3 B d(3 *  B 3, B +",2"+

* +8,#"+ t

Ar * a(5 B %(5 B d(5 * 38,21 B 23,53 B 2+,3+8

* 338,125 tm

A" * a( B %( B e( * 33,3 B ,+2 B 22,+#+

* 2,#18 tm


∑  r ∑ " =M *

338,125 2,#18

= 5,38#

*

N 1,5"

(L< O

N 1,2"

(L< O

b. Terhadap geser ( sliding 

=M *

$ ∑ 

",+ . ( +8,#"+ )

∑6

1,21

= 3,31

*



+5



338,125 − 2,#18

∑  r − ∑ " ∑ a * •

+8,#"+

= 3,42 m

*

Desultante beban !ertikal bekerja sejarak e dari pusat berat bendung.  2

e *

#,"

−a

2



− 3,42 = ",53# m

*



Q

* 1,333 m


 ∑   1 ±  . e  b ) . b y  b )   J

*

Jmin

+8,#"+   . ( ",53#)  1 −  #," . (1)  #,"  * * 5,85 tm2

Jma)

+8,#"+   . ( ",53#)  1 +  #," . (1)  #,"  * * 14,""1 tm 2

S"

Q JK* 2 tm2

(L< O

(L< O

3.
* 22,"5 t

A * b(3 B %(3 B d(3 B h(3 * 11,843 B 3, B +",2"+ B 1,""2

* 1"1,+52 t

Ar * b(5 B %(5 B d(5 B h(5 * +2,33 B 23,53 B 2+,3+8 B 1,33

* 3+3,"2 tm

A" * b( B %( B e( B h( * 5#,5" B ,+2 B 22,+#+ B +,1

* 155,5+5tm +




∑ r ∑ " =M *

3+3,"2 155,5+5

= 2,4"1

*

N 1,5"

(L< O

N 1,2"

(L< O


",+ . (1"1,+52)

∑6

22,"5

=M *

= 3,23

*



3+3,"2 − 155,5+5

∑  r − ∑ " ∑ a * •

1"1,"5

= 2,+25m

*


e *

#,"

−a

2

B 

− 2,+25 = 1,2+5 m

*

Q

* 1,333 m


 ∑   1 ±  . e  b ) . b y  b )   J

*

Jmin

1"1,+52   . (1,2+5)  1 −  #," . (1)  #,"  * * ",55 tm 2

Jma)

1"1,+52   . (1,2+5)  1 +  #," . (1)  #,"  * * 24,##1 tm2 Q JK* 2 tm2

S"

(L< O

(L< O

4.
* 21,15+ t

A * b(3 B %(3 B d(3

++



* 11,843 B 3, B +",2"+

* #5,+5 t

Ar * b(5 B %(5 B d(5 B e(5 * +2,33 B 23,53 B 2+,3+8 B 22,+#+

* 38,"58 tm

A" * b( B %( B e( * 5#,5" B ,+2 B 22,+#+

* #+,85 tm


∑ r ∑ " =M *

38,"58 #+,85

= 4,5"2

*

N 1,5"

(L< O

N 1,2"

(L< O


",+ . ( #5,+5)

∑6

21,15+

=M *

= 2,#3+

*



38,"58 − #+,85

∑  r − ∑ " ∑ a * •

#5,+5

= 3,583 m

*


e *

#,"

−a

2



− 3,583 = ",4"+ m

*



Q

* 1,333 m


 ∑   1 ±  . e  b ) . b y  b )   J

*

 1 −  . ( ",4"+)    #," . (1)  #,"  #5,+5

Jmin *

* 1",1+3

S"

(L< O

+#



 1 +  . ( ",4"+ )    #," . (1)  #,"  #5,+5

* 11,24 tm 2 Q JK* 2 tm2

Jma) * 3..3

(L< O

Den(an Gem%a Ver&ikal

Tegangan ijin tanah (dengan gempa JK* 2" tm 2 ) 1,3 * 2 tm 2

1.
* 1",143 t

A * a(3 B %(3 B d(3 B $(3 – g(3 *  B 3, B +",2"+ B 3,51 – 13,1"+

* +",21 t

Ar * a(5 B %(5 B d(5 B $(5 B g(5 * 38,21 B 23,53 B 2+,3+8 B 13,#2 7",#5+

* 352,"## tm

A" * a( B%( B $( B g( * 33,3 B ,+2 B 13,#2" B 1,"53

* 8,8"5 tm


∑ r ∑ " =M *

352,"## 8,8"5

= 18,342

*

N 1,5"

(L< O

N 1,2"

(L< O


",+ . ( +",21)

∑6

1",143

=M *

= 4,#45

*



352,"## − 8,8"5

∑ M − ∑ M " ∑ V r

a * •

+",21

= 4,"18 m

*

Desultante beban !ertikal bekerja sejarak e dari pusat berat bendung.

+8



 2

#,"

−a

e *

2



− 4,"18 = −","18 m

*



Q

* 1,333 m


 ∑   1 ±  . e  b ) . b y  b )   J

*

 1 −  . ( − ","18)    #," . (1)  #,"  +",21

* #,+8+ tm2

Jmin *

S"

(L< O

 1 +  . ( 7 ","18)    #," . (1)  #,"  +",21

* #,+55 tm2 Q JK* 2 tm2

Jma) *

(L< O

2.
* 8, t

A * a(3 B %(3 B d(3 B $(3 *  B 3, B +",2"+ B 3,51

* #3,3+1 t

Ar * a(5 B %(5 B d(5 B $(5 * 38,21 B 23,53 B 2+,3+8 B 13,#2

* 352,845 tm

A" * a( B %( * 33,3 B ,+2

* 4","32 tm


∑  r ∑ " =M *

352,845 4","32

= #,#1+

*

N 1,5"

(L< O

b. Terhadap geser ( sliding 

#"



$ ∑ 

",+ . ( #3,3+1)

∑6

8,

=M *

= ,"+8

*

N 1,2"

(L< O



352,845 − 4","32

∑  r − ∑ " ∑ a * •

#3,3+1

= 3,+53 m

*


e *

#,"

−a

2



− 3,+53 = ",24+ m

*



Q

* 1,333 m


 ∑   1 ±  . e  b ) . b y  b )   J

* #3,3+1   . ( ",24+ )  1 −  #," . (1)  #," 

* #,481 tm2

Jmin *

S"

(L< O

#3,3+1   . ( ",24+ )  1 +  #," . (1)  #," 

Jma) *

* 12,352 tm 2 Q JK* 2 tm 2

(L< O

3.
* 15,"35 t

A * b(3 B %(3 B d(3 B $(3 – h(3 * 11,843 B 3,B +",2"+ B 3,51 – 1,""2

* +3,25# t

Ar * b(5 B %(5 B d(5 B h(5 * +2,33 B 23,53 B 2+,3+8 B 1,33

* 3+3,"2 tm

A" * b( B %( B $( B h(

#1



* 5#,5" B .+2 B 13,#2" B +,1

* 14,"# tm


∑ r ∑ " =M *

3+3,"2 14,"#

= 2,54#

*

N 1,5"

(L< O

N 1,2"

(L< O


",+ . ( +3,25# )

∑6

15,"35

=M *

= 3,411

*



3+3,"2 − 14,"#

∑  r − ∑ " ∑ a *

•

+3,25#

= 3,"88 m

*


e *

#,"

−a

2



− 3,"88 = ",8"1 m

*



Q

* 1,333 m


 ∑   1 ±  . e  b ) . b y  b )   J

*

Jmin

+3,25#   . ( ",8"1)  1 −  #," . (1)  #,"  * * 2,88 tm2

Jma)

+3,25#   . ( ",8"1)  1 +  #," . (1)  #,"  * * 15,345 tm 2 Q JK* 2 tm2

S"

(L< O

(L< O

#2



4.
* 14,13 t

A * b(3 B %(3 B d(3 B $(3 * 11,843 B 3, B +",2"+ B 3,51

* #8,2 t

Ar * b(5 B %(5 B d(5 B $(5 * +2,33 B 23,53 B 2+,3+8 B 13,#2

* 3#,"82 tm

A" * b( B %( * 5#,5" B ,+2

* 5,1+# tm


∑ r ∑ " =M *

3#,"82 5,1+#

= 5,824"

*

N 1,5"

(L< O

N 1,2"

(L< O


",+ . ( #8,2)

∑6

14,13

=M *

= 4,42

*


%. Terhadap daya dukung tanah (over stressing  •


3#,"82 − 5,1+#

∑  r − ∑ " ∑ a * •

#8,2

= 3,585 m

*


e *

#,"

−a

2



− 3,585 = ",4"5 m

*



Q

* 1,333 m


#3

BAB III Analisa Stabilitas Bendung Rev

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