Post on 07-May-2017
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'
Mpa2 = = tm' Mpa7 = = tm'
Mpa3 = = tm' Mpa8 = = tm'
Mpa4 = = tm' Mpa9 = = 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
Momen inersia permeter panjang pondasi :
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
Momen inersia permeter panjang pondasi :
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