rekayasa pondasi(3)
TRANSCRIPT
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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