Rekayasa Pondasi(3)

Rekayasa Pondasi

Diketahui konstruksi tembok penahan tipe Gravity wall dengan data-data sebagai berkut :

- Beban merata permukaan q = t/m2

- Tinggi tembok penahan H = m

- Tebal lapisan tanah 1 H1 = m

- Kedalaman muka air dari puncak Ha = m

- Tinggi tanah didepan tembok H2 = m

- Sudut kemiringan permukaan tembok b = o

- Sudut gesek antara tembok dengan tanah d = o

- Berat isi tanah lapisan 1 g1 = t/m3

- Berat isi tanah terendam lapisan 1 g'1 = t/m3

- Berat isi tanah terendam lapisan 2 g'2 = t/m3

- Sudut gesek dalam tanah lapisan 1 f'1 = o

- Sudut gesek dalam tanah lapisan 2 f'2 = o

- Berat isi pasangan batu g'p = t/m3

- Berat isi beton bertulang g'b = t/m3

1. Merencanakan dimensi pondasi sesuai persyaratan yang ada

2.50

2.20

1.76

0.85

0.89

20.00

PENYELESAIAN

III. Tembok Penahan

3.00

5.00

3.50

1.50

2.50

5.55

25.00

29.00

H

H2

H1

Ha

2 2

3

3 1

1

B

Created by ANCHA 08

Rekayasa Pondasi

b = o

a = o

d = o

g1 = t/m3

g'1 = t/m3

g'2 = t/m3

f'1 = o

f'2 = o

g'b = t/m3

Keterangan :

H = Tinggi tembok penahan = m

Ha = Kedalaman muka air dari puncak = m

H1 = Tebal lapisan tanah 1 = m

H2 = Tinggi tanah didepan tembok = m

Hb = H1 - Ha = m

B = = m

d = = m

Hc = H - H1 - d = m

a = = m

x = ( H - d ) . tan a = m

k = d = m

e = B - ( x + a + k ) = m

H0 = ( e + x ) . tan b = m

g = Ha . tan a = m

i = ( H1 - Ha ) . tan a = m

j = Hb . tan a = m

2. Menghitung tekanan tanah secara analitis

0.83

1.35

2/3 . H

1/6 . H

2.00

0.42

0.36

0.67

0.17

0.13

0.17

0.06

20.00

29.00

2.20

1/12 . H

5.00

1.50

3.50

2.50

3.33

0.83

5.55

25.00

1.76

0.85

5.00

0.89H

H2

H1

Ha

d

B

k x a x e

Ho

Hc

g i j

Hb

Created by ANCHA 08

Rekayasa Pondasi

a. Menghitung koefisien tekanan tanah

1. Koefisien tekanan tanah aktif

- Untuk lapisan 1

Diketahui : a = o

f1 = o

d = o

b = o

- Untuk lapisan 2

Pada bagian yang miring

Diketahui : a = o

f2 = o

d = o

b = o

Pada bagian yang tegak

Diketahui : a = o

f2 = o

d = o

b = o

Ka2 =

Ka1 =

25.00

5.55

5.55

5.00

25.00

29.00

5.00

20.00

25.000.5335

5.55

0.4102

0.00

29.00Ka3 = 0.3782

H

H2

H1

Ha

d

B

Ho

Hc

Hb

Pa1

Pa2

Pa3

Pa4

Pa5

Pa6 Pa7

Pa8 Pa9

Pp

22

2

a

)cos().cos(

)sin().sin(1).cos(.cos

)(cosK

bada

bfdfdaa

af

Created by ANCHA 08

Rekayasa Pondasi

2. Koefisien tekanan tanah pasif

Diketahui : a = o

f2 = o

d = o

b = o

b. Menghitung tekanan tanah aktif

akibat pengaruh beban (q) terhadap tanah setinggi H0

s1 =

s1 = t/m2

- Akibat beban (q) terhadap tanah setinggi Ha

s2 =

s2 = t/m2

- Akibat tanah setinggi Ha

s3 =

s3 = t/m2

- Akibat beban (q) dan tanah setinggi Ha terhadap tanah setinggi Hb

s4 =

s4 = t/m2

- Akibat tanah setinggi Hb

s5 = g'1 . Hb . Ka1 + gw . Hb

s5 = t/m2

- Akibat beban (q), tanah setinggi ha, tanah setinggi Hb terhadap tanah

setinggi Hc

s6 = ( q + g1 . Ha + g'1 . Hb ) . Ka2

s6 = t/m2

- Akibat tanah setinggi Hc

s7 = g'2 . Hc . Ka2 + gw . Hc

s7 = t/m2

0.907

3.0109

0.2434

1.6006

g1 . Ha . Ka1

1.4085

Kp =

3.0091

( q + g1 . Ha ) . Ka1

q . Ka1

0.00

29.00

0.00

q . Ka1

1.6006

8.243525.00

22

2

)cos().cos(

)sin().sin(1).cos(.cos

)(cosKp

bada

bfdfdaa

af

Created by ANCHA 08

Rekayasa Pondasi

- Akibat beban (q), tanah setinggi ha, tanah setinggi Hb, tanah setinggi Hc

terhadap tanah setinggi d

s8 = ( q + g1 . Ha + g'1 . Hb + g'2 . Hc ) . Ka3

s8 = t/m2

- Akibat tanah setinggi d

s9 = g'2 . d . Ka3 + gw . d

s9 = t/m2

b. Menghitung tekanan tanah pasif

sp = g'2. H2 . Kp

sp = t/m2

c. Menghitung gaya tekanan tanah aktif

Pa1= 0,5 x s1 x H0 Pa1= t/m

Pa2= s2 x Ha Pa2= t/m

Pa3= 0,5 x s3 x Ha Pa3= t/m

Pa4= s4 x Hb Pa4= t/m

Pa5= 0,5 x s5 x Hb Pa5= t/m

Pa6= s6 x Hc Pa6= t/m

Pa7= 0,5 x s7 x Hc Pa7= t/m

Pa8= s8 x d Pa8= t/m

Pa9= 0,5 x s9 x d Pa9= t/m

d. Menghitung gaya tekanan tanah pasif

Pp = 0,5 x sp x H2 Pp = t/m

e. Menghitung lengan momen tekanan tanah aktif

za1= (1/3) . H0 + H = m

za2= (1/2) . Ha + Hb + Hc + d = m

za3= (1/3) . Ha + Hb + Hc + d = m

za4= (1/2) . Hb + Hc + d = m

za5= (1/3) . Hb + Hc + d = m

za6= (1/2) . Hc + d = m

za7= (1/3) . Hc + d = m

za8= (1/2) . d = m

za9= (1/3) . d = m

3.0003

0.2805

6.0182

0.907

2.0073

0.0811

18.342

0.1337

2.4009

1.0564

4.250

4.000

2.500

2.167

2.5003

0.1169

22.927

5.056

0.417

0.278

1.167

1.056

Created by ANCHA 08

Rekayasa Pondasi

f. Menghitung lengan momen tekanan tanah pasif

zp = (1/3) . H2 = m

4. Menghitung berat tanah dan konstruksi

a. Menghitung luas irisan

F1 = (1/2) . H0 . ( x + e ) = m2

F2 = Ha . ( i + j + e ) = m2

F3 = (1/2) . Ha . g = m2

F4 = Hb . ( j + e ) = m2

F5 = (1/2) . Hb . i = m2

F6 = Hc . e = m2

F7 = (1/2) . Hc . j = m2

F8 = ( H - d ) . a = m2

F9 = (1/2) . ( H - d ) . x = m2

F10= F9 = m2

F11= B . d = m2

b. Menghitung berat irisan

0.759

0.759

2.778

0.175

0.903

0.8333

0.144

2.381

0.019

1.736

0.098

2.825

H

H2

H1

Ha

d

B

k x a x e

Ho

Hc

g i j

Hb

1

2

4

6

11

8

9 10

3

5

7

12

A

Created by ANCHA 08

Rekayasa Pondasi

G1 = F1 . g1 = t/m G7 = F7 . g'2 = t/m

G2 = F2 . g1 = t/m G8 = F8 . gb = t/m

G3 = F3 . g1 = t/m G9 = F9 . gb = t/m

G4 = F4 . g'1 = t/m G10= F10 . gb = t/m

G5 = F5 . g'1 = t/m G11= F11 . gb = t/m

G6 = F6 . g'2 = t/m G12= q . ( x + e ) . sec b = t/m

c. Menghitung lengan momen berat tanah dan konstruksi

x1 = (2/3) . ( x + e ) + a + x + k = m

x2 = (1/2) . ( i + j + e ) + g + a + x + k = m

x3 = (2/3) . g + a + x + k = m

x4 = (1/2) . ( j + e ) + i + g + a + x + k = m

x5 = (2/3) . i + g + a + x + k = m

x6 = (1/2) . e + 2x + a + k = m

x7 = (2/3) . j + i + g + a + x + k = m

x8 = (1/2) . a + x + k = m

x9 = (1/3) . x + a + x + k = m

x10= (2/3) . x + k = m

x11= (1/2) . B = m

x12= (1/2) . ( e + x ) + a + x + k = m

5. Menghitung momen akibat tekanan tanah

Mpa1 = = tm' Mpa6 = = tm'




Mpa5 = = tm' Mpp = = tm'

- = tm'

6. Menghitung momen akibat berat tanah dan konstruksi

Mg1 = = tm' Mg7 = = tm'

Mg2 = = tm' Mg8 = = tm'

Mg3 = = tm' Mg9 = = tm'

Mg4 = = tm' Mg10 = = tm'

Mg5 = = tm' Mg11 = = tm'

Mg6 = = tm' Mg12 = = tm'

tm'

10.185

12.817

S Mg = 53.461

0.295

6.309

G9 . x9

G10 . x10

2.901

1.798

0.034

5.371

0.697

10.644

G7 . x7

G8 . x8

G1 . x1

G2 . x2

G3 . x3

G4 . x4

G11 . x11

G12 . x12

G5 . x5

G6 . x6

0.277

2.134

19.106

2.342

S Mp = S Mpa - S Mpp = 35.617 19.106 16.511

Pp . zp

0.676 Pa6 . za6

Pa7 . za7 0.086

1.042

0.032

10.204

4.226

15.045

Pa2 . za2

Pa3 . za3

Pa4 . za4

Pa8 . za8

Pa9 . za9

Pa5 . za5 1.965

1.406

1.736

1.076

1.667

2.474

Pa1 . za1

2.540

1.702

2.627

1.862

2.656

1.950

6.111

5.181

4.191

0.173

2.401

2.760

0.149

1.671

0.253

0.804

0.017

3.819

1.671

Created by ANCHA 08

Rekayasa Pondasi

7. Menghitung kestabilan konstruksi

a. Kontrol terhadap guling

b. Kontrol terhadap geser

c. Kontrol terhadap eksentrisitas

e' = (1/6) . B = 0.6

< 0.6 (OK!!!)

d. Kontrol terhadap daya dukung tanah

smax = t/m2

smin = t/m2

qult

Sf

=

D

B

dg = 1.0

( SG + Pa sinb ).tand

S Pa cos b

(OK!!!)

4.0884

0.2692

s ijin tanah =qult = cNcscdcic + qNqsqdqiq + 0,5gBNgsgdgig

( diambil Sf = 3 )

Ng = ( Ng - 1 ) . tan ( 1,4 . f )

e < e'

= 0.2692

2.3162

smax < sijin tanah

11.776

35.257

15.222

> 1.5

(OK!!!)

> 1.5

> 1.5

3.2378 > 1.5

> 1.5

S Mg

S Mp

> 1.553.461

16.511

16.443 ( untuk f = f'2 )

13.237

dq = 1 + 2 tan f(1 - sin f)2 = 1.0676

G

MM

2

Be

pg

S

SS

Ss

B

e.61

B

G

f f

245taneN 2tan

g

Created by ANCHA 08

Rekayasa Pondasi

= t/m2

< (OK!!!)

9. Menghitung Momen, gaya geser, gaya normal dan tegangan pada potongan

- Potongan 1 - 1

a. Momen lentur

G1 ((2/3). (e+x)+a+x) + G2 ((1/2). (e+x-g)+g+a+x) + G3 ((2/3).g+a+x)

+ G4 ((1/2). (e+j)+i+g+a+x) + G5 ((2/3).i+g+a+x) + G6 ( (1/2).e+2x+a)

+ G7 ( (2/3) . j+i+g+a+x ) + G8 ( (1/2) . a+x ) + G9 ( (1/3) . x+a+x )

+ G10((2/3).x) + G11((1/2).B-k) + G12((1/2).(e+x)+a+x)

tm'M 1 - 1 = 31.427

16.409 t/m2

0.7122

0.597

=

=

smax < sijin tanah 11.776 16.409

M 1 - 1 =

qult = cNcscdcic + qNqsqdqiq + 0,5gBNgsgdgig 49.227

s ijin tanah =49.227

3.0=

H

H2

H1

Ha

d

Ho

Hc

Hb

Pa1

Pa2

Pa3

Pa4

Pa5

Pa6 Pa7

Pa8 Pa9

Pp

2 2

3

3 1

1

G2

G4

G6

G3

G5

G7

G1

G8

G9

G10

G11

G12

B

k x a x e

g i j

5

afq cot.c.AQ

H.5.01i

f

5

af cot.c.AQ

H.7.01i

fg

Created by ANCHA 08

Rekayasa Pondasi

b. Gaya geser

D = Pa1 + Pa2 + Pa3 + Pa4 + Pa5 + Pa6 + Pa7 + Pa8 + Pa9 - Pp

D = ton

c. Gaya normal

N = G1 + G2 + G3 + G4 + G5 + G6 + G7 + G8 + G9 + G10 + G11 + G12

N = ton

d. Tegangan lentur

Momen inersia permeter panjang pondasi :

b = 1

h = 12

e. Tegangan geser

f. Tegangan normal

N

A

- Potongan 2 - 2

a. Momen lentur

Pa1 ((1/3).H0 +H1+Hc) + Pa2 ((1/2).Ha+Hb+Hc) + Pa3 ((1/3).Ha+Hb+Hc)

+ Pa4((1/2).Hb+Hc) + Pa5((1/3).Hb+Hc) + Pa6((1/2).Hc) + Pa7((1/3).Hc)

- Pa8( (1/2).d ) - Pa9( (2/3).d ) - Pp( (H2 - d) - (2/3).H2 )

tm'

b. Gaya geser

D = G1 + G2 + G3 + G4 + G5 + G6 + G7 + G8 + G9 + G10 + G12

D = ton

M 2 - 2 =

t = -66.58 t/m2

sN = sN = 31.729

1.00 mIx =

t/m2

t =D . s

b . Ix

m4

s = 271.53 t/m2

b . h3 =

s =M . y

Ix

0.04820.83 m

-7.705

26.441

M 2 - 2 = 22.465

20.330

Created by ANCHA 08

Rekayasa Pondasi

c. Gaya normal

N = Pa1 + Pa2 + Pa3 + Pa4 + Pa6 + P7

N = ton

d. Tegangan lentur


b = 1

h = 12

e. Tegangan geser

f. Tegangan normal

N

A

- Potongan 2 - 2

a. Momen lentur

G1 ( (2/3) . (e+x)-x ) + G2 ( (1/2) . (e+x-g)-i-j ) - G3 ( (1/3) . g+i+j )

+ G4 ( (1/2). (e+j)-j ) - G5 ( (1/3).i+j ) + G6 ( (1/2).e ) - G7 ( (1/3).j )

- G8 ((1/2) . a+x) - G9 ((2/3).x) - G10((1/3).x+a+x) - G11((1/2).B-e)

+ G12((1/2).(e+x)-x)

tm'

b. Gaya geser

D = Pa1 + Pa2 + Pa3 + Pa4 + Pa5 + Pa6 + Pa7 + Pa8 + Pa9 - Pp

D = ton

c. Gaya normal

b . h3 = 0.1253

12.605

m4

1.15 m

s =M . y

s = 74.682 t/m2

Ix

1.00 mIx =

t/m2

b . Ix

sN = sN = 11.001 t/m2

t =D . s

t = 67.584

M 3 - 3 =

M 3 - 3 = 1.1331

-7.705

Created by ANCHA 08

Rekayasa Pondasi

N = G1 + G2 + G3 + G4 + G5 + G6 + G7 + G8 + G9 + G10 + G11 + G12

N = ton

d. Tegangan lentur


b = 1

h = 12

e. Tegangan geser

f. Tegangan normal

N

A

26.441

1.00 mIx = b . h3 = 0.0482 m4

0.83 m

s =M . y

s = 9.7902 t/m2

Ix

t/m2

b . Ix

sN = sN = 31.729 t/m2

t =D . s

t = -66.58

Created by ANCHA 08

Rekayasa Pondasi(3)

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