pondasi

PERHITUNGAN KEKUATAN TIANG PANCANG

[C]2010 : M. Noer Ilham

A. DATA TANAH

DATA HASIL PENGUJIAN LABORATORIUM (DATA BOR TANAH) SONDIR SPT

No Kedalaman Jenis g j Nilai SPT

Tanah ( ... ▫ ) N

1 0.00 5.00 lempung 23.00 9.962 0 5.60 5

2 5.00 10.00 lempung 30.00 9.962 0 12.30 12

3 10.00 15.00 lempung 52.00 9.962 0 18.40 27

4 15.00 20.00 lemp. padat 61.00 10.372 0 22.60 35

5 20.00 25.00 lemp. pasir 63.00 11.683 12 27.30 42

B. DATA BAHAN

Jenis tiang pancang : Beton bertulang tampang lingkaran

Diameter tiang pancang, D = 0.40 m

Panjang tiang pancang, L = 17.00 m

Kuat tekan beton tiang pancang, 25 MPa

Berat beton bertulang, 24

C. TAHANAN AKSIAL TIANG PANCANG

1. BERDASARKAN KEKUATAN BAHAN

Luas penampang tiang pancang, 0.1257

Berat tiang pancang, 51.27 kN

Kuat tekan beton tiang pancang, 25000 kPa

Kapasitas dukung nominal tiang pancang,

881 kN

Faktor reduksi kekuatan, 0.60

Tahanan aksial tiang pancang, 528.57 kN

cu qf

z1 (m) z2 (m) (kN/m2) (kN/m3) (kN/m2)

fc' =

wc = kN/m3

A = p / 4 * D2 = m2

Wp = A * L * wc =

fc' =

Pn = 0.30 * fc' * A - 1.2 * Wp =

f =

f * Pn =

2. BERDASARKAN DATA BOR TANAH (SKEMPTON)

a. Tahanan ujung

Tahanan ujung nominal dihitung dengan rumus :

Faktor daya dukung.


Luas tampang tiang pancang, 0.1257

Kohesi tanah di sekitar dasar tiang, 55.00

Faktor daya dukung menurut Skempton, 9

Tahanan ujung nominal tiang pancang : 62.204 kN

b. Tahanan gesek

Tahanan gesek nominal menurut Skempton :

faktor adhesi

Faktor adhesi untuk jenis tanah lempung pada tiang pancang yang nilainya tergantung dari

nilai kohesi tanah, menurut Skempton, diambil : →Diameter tiang pancang, D = 0.400 m

Luas permukaan dinding segmen tiang,

panjang segmen tiang pancang yang ditinjau (m).

Perhitungan tahanan gesek nominal tiang

No Kedalaman

(m) (kN)

1 0.00 5.00 5.0 6.2832 23.00 0.83 119.707

2 5.00 10.00 5.0 6.2832 30.00 0.75 140.520

3 10.00 15.00 5.0 6.2832 52.00 0.55 179.617

4 15.00 17.00 2.0 2.5133 55.00 0.53 73.149

Tahanan gesek nominal tiang, 512.993

512.993 kN

c. Tahanan aksial tiang pancang

Tahanan nominal tiang pancang, 575.20 kN

Pb = Ab * cb * Nc

Ab = Luas penampang ujung bawah tiang (m2),

cb = Kohesi tanah di bawah dasar tiang (kN/m2),

Nc =

Ab = p / 4 * D2 = m2

cb = kN/m2

Nc =

Pb = Ab * cb * Nc =

Ps = S [ ad * cu * As ]

ad =

cu = Kohesi tanah di sepanjang tiang (kN/m2)

As = Luas permukaan dinding tiang (m2).

ad = 0.2 + [ 0.98 ] cu

As = p * D * L1

L1 =

L1 As cu ad Ps

z1 (m) z2 (m) (m2) (kN/m2)

Ps = S ad * cu * As =

Pn = Pb + Ps =



3. BERDASARKAN HASIL UJI SONDIR (BAGEMANN)

a. Tahanan ujung


faktor reduksi nilai tahanan ujung nominal tiang,

tahanan penetrasi kerucut statis yang merupakan nilai rata-rata dihitung dari 8.D di



Tahanan penetrasi kerucut statis rata-rata dari 8.D di atas dasar s.d. 4.D di bawah dasar

tiang pancang, 42 → 4200

Faktor reduksi nilai tahanan ujung nominal tiang, 0.50


b. Tahanan gesek

Tahanan gesek nominal menurut Skempton dihitung dg rumus :

tahanan gesek kerucut statis rata-rata (kN/m).

No Kedalaman

(m) (kN)

1 0.00 5.00 5.0 6.2832 5.60 35.19

2 5.00 10.00 5.0 6.2832 12.30 77.28

3 10.00 15.00 5.0 6.2832 18.40 115.61

4 15.00 17.00 2.0 2.5133 19.50 49.01

277.09




Tahanan aksial tiang pancang, → 324.59 kN

4. BERDASARKAN HASIL UJI SPT (MEYERHOFF)

Kapasitas nominal tiang pancang secara empiris dari nilai N hasil pengujian SPT

f =

f * Pn =

Pb = w * Ab * qc

w =

Ab = luas ujung bawah tiang (m2),

qc =

atas dasar tiang sampai 4.D di bawah dasar tiang (kN/m2),

Ab = p / 4 * D2 = m2

qc = kg/cm2 qc = kN/m2

w =Pb = w * Ab * qc =

Ps = S [ As * qf ]

Af = Luas permukaan segmen dinding tiang (m2). As = p * D * L1

qf =

L1 As qf Ps

z1 (m) z2 (m) (m2) (kN/m2)

Ps = S [ As * qf ] =

Pn = Pb + Ps =

f =

f * Pn =

menurut Meyerhoff dinyatakan dengan rumus :

(kN)

(kN)

nilai SPT di sekitar dasar tiang, dihitung dari 8.D di atas dasar tiang s.d 4.D di bawah

dasar tiang,

Ň = nilai SPT rata-rata di sepanjang tiang,

Berdasarkan hasil pengujian SPT diperoleh data sbb.

No Kedalaman Nilai SPT

N (m)

1 0.00 5.00 5 5.0 25.0

2 5.00 10.00 12 5.0 60.0

3 10.00 15.00 27 5.0 135.0

4 15.00 17.00 30 2.0 60.0

17.0 280.0

Nilai SPT rata-rata di sepanjang tiang, 16.47

Nilai SPT di sekitar dasar tiang (8.D di atas dasar tiang s.d 4.D di bawah dasar tiang),

30.00



Luas dasar tiang pancang, 0.1257

Luas selimut tiang pancang, 21.3628

502.6548246 kN

< 786.51 kN

Kapasitas nominal tiang pancang, 502.65 kN



5. REKAP TAHANAN AKSIAL TIANG PANCANG

No Uraian Tahanan Aksial Tiang Pancang

1 Berdasarkan kekuatan bahan 528.57

2 Berdasarkan data bor tanah (Skempton) 345.12

3 Berdasarkan hasil uji sondir (Bagemann) 324.59

4 Berdasarkan hasil uji SPT (Meyerhoff) 301.59

Pn = 40 * Nb * Ab + Ň * As

dan harus £ Pn = 380 * Ň * Ab

Nb =

Ab = luas dasar tiang (m2)

As = luas selimut tiang (m2)

L1 L1 * N

z1 (m) z2 (m)

Ň = S L1*N / S L1 =

Nb =

Ab = p / 4 * D2 = m2

As = p * D * L = m2

Pn = 40 * Nb * Ab + Ň * As =

Pn 380 * Ň * Ab =

Pn =

f =

f * Pn =

f * Pn

Daya dukung aksial terkecil, 301.59 kN

Diambil tahanan aksial tiang pancang, → 300.00 kN

D. TAHANAN LATERAL TIANG PANCANG

1. BERDASARKAN DEFLEKSI TIANG MAKSIMUM (BROMS)

Tahanan lateral tiang (H) kategori tiang panjang, dapat dihitung dengan persamaan :

dengan,

D = Diameter tiang pancang (m), D = 0.40 m

L = panjang tiang pancang (m), L = 17.00 m

26720

23500000

0.001257

e = Jarak beban lateral terhadap muka tanah (m), e = 0.20 m

defleksi tiang maksimum (m). 0.006 m

b = koefisien defleksi tiang, 0.548453335 m

9.32 > 2.5 maka termasuk tiang panjang (OK)

Tahanan lateral nominal tiang pancang,

52.68 kN


Tahanan lateral tiang pancang, → 31.61 kN

2. BERDASARKAN MOMEN MAKSIMUM (BRINCH HANSEN)

Kuat lentur beton tiang pancang, 10000

Tahanan momen, 0.00628

Momen maksimum, 62.83 kNm

Kohesi tanah rata-rata di sepanjang tiang

No Kedalaman

(m)

1 0.00 5.00 5.0 23.00 115.00

2 5.00 10.00 5.0 30.00 150.00

3 10.00 15.00 5.0 52.00 260.00

f * Pn =

f * Pn =

H = yo * kh * D / [ 2 * b * ( e * b + 1 ) ]

b = [ kh * D / ( 4 * Ec * Ic ) ]0.25

kh = modulus subgrade horisontal (kN/m3), kh = kN/m3

Ec = modulus elastis tiang (kN/m2), Ec = 4700 * Ö fc' * 103 = kN/m2

Ic = momen inersia penampang (m4), Ic = p / 64 * D4 = m4

yo = yo =

b = [ kh * D / ( 4 * Ec * Ic ) ]0.25 =

b * L =

H = yo * kh * D / [ 2 * b * ( e * b + 1 ) ] =

f =

f * Hn =

fb = 0.40 * fc' * 103 = kN/m2

W = Ic / (D/2) = m3

My = fb * W =

L1 cu cu * L1

z1 (m) z2 (m) (kN/m2)

4 15.00 17.00 2.0 63.00 126.00

17.0 651.00

Kohesi tanah rata-rata, 38.29411765

pers.(1)

g = L - ( f + 1.5 * D ) pers.(2)

pers.(3)

pers.(4)

Dari pers.(1) : f = 0.0072538

Dari pers.(2) : g = 16.40 -0.007254

0.000053 -0.237925 268.96

34.465

Dari pers.(3) : 0.800 0.00363

0.00363 0.80000

Dari pers.(4) : 0.0018134 -8.2000 9269.627

Pers.kuadrat : 0 = 0.00181 9.0000 -9269.627

Dari pers. kuadrat, diperoleh tahanan lateral nominal, 875.510 kN

f = 6.351 m

3480.488 kNm

> → Termasuk tiang panjang (OK)

Dari pers.(3) : 0.800 0.00363

62.83 = 0.00363 0.80000

Pers.kuadrat : 0 = 0.00363 0.80000 -62.83




3. REKAP TAHANAN LATERAL TIANG

No Uraian Tahanan Lateral Tiang Pancang

1 Berdasarkan defleksi tiang maksimum (Broms) 31.61

2 Berdasarkan momen maksimum (Brinch Hansen) 36.86

Tahanan lateral tiang terkecil, 31.61 kN

Diambil tahanan lateral tiang pancang, → 30.00 kN

S L1 = Scu*L1 =ču = S [ cu * L1 ] / S L1 = kN/m2

f = Hn / [ 9 * ču * D ]

My = Hn * ( e + 1.5 * D + 0.5 * f )

My = 9 / 4 * D * ču * g2

* Hn

* Hn

g2 = * Hn2 * Hn +

9 / 4 * D * cu =

My = Hn * ( * Hn )

My = * Hu2 * Hn

My = * Hu2 * Hn

* Hu2 * Hn

Hn =

Mmax = Hn * ( e + 1.5 * D + 0.5 * f ) =

Mmax My

My = Hn * ( * Hn )

* Hn2 * Hu

* Hn2 + * Hn

Hn =

f =

f * Hn =

f * Hn

f * Hn =

f * Hn =

PERHITUNGAN KEKUATAN FONDASI

KODE FONDASI : F4

DATA BAHAN PILECAP

Kuat tekan beton, 20 MPa

390 MPa

240 MPa


DATA DIMENSI FONDASI

Lebar kolom arah x, 0.40 m

Lebar kolom arah y, 0.40 m

Jarak tiang pancang tepi terhadap sisi luar beton, a = 0.40 m

Tebal pilecap, h = 0.40 m

Tebal tanah di atas pilecap, z = 0.90 m

Berat volume tanah di atas pilecap, 18.00

Posisi kolom (dalam = 40, tepi = 30, sudut = 20) 40

fc' =

Kuat leleh baja tulangan deform ( Æ > 12 mm ), fy =

Kuat leleh baja tulangan polos ( Æ ≤ 12 mm ), fy =

wc = kN/m3

bx =

by =

ws = kN/m3

as =

DATA BEBAN FONDASI

Gaya aksial kolom akibat beban terfaktor, 600.00 kN

Momen arah x akibat beban terfaktor. 120.00 kNm

Momen arah y akibat beban terfaktor. 100.00 kNm

Gaya lateral arah x akibat beban terfaktor, 70.00 kN

Gaya lateral arah y akibat beban terfaktor, 50.00 kN


Tahanan lateral tiang pancang, 30.00 kN

DATA SUSUNAN TIANG PANCANG

Susunan tiang pancang arah x : Susunan tiang pancang arah y :

No. Jumlah x No. Jumlah y

n (m) n (m)

1 2 0.50 0.50 1 2 0.50 0.50

2 2 -0.50 0.50 2 2 -0.50 0.50

n = 4 1.00 n = 4 1.00

Lebar pilecap arah x, 1.80 m

Lebar pilecap arah y, 1.80 m

1. GAYA AKSIAL PADA TIANG PANCANG

Berat tanah di atas pilecap, 52.49 kN

Berat pilecap, 31.10 kN

Total gaya aksial terfaktor, 700.31 kN

Lengan maksimum tiang pancang arah x thd. pusat, 0.50 m

Lengan maksimum tiang pancang arah y thd. pusat, 0.50 m

Lengan minimum tiang pancang arah x thd. pusat, -0.50 m

Lengan minimum tiang pancang arah y thd. pusat, -0.50 m

Gaya aksial maksimum dan minimum pada tiang pancang,

285.08 kN

65.08 kN

Syarat : ≤285.08 < 300.00 → AMAN (OK)

2. GAYA LATERAL PADA TIANG PANCANG

Puk =

Mux =

Muy =

Hux =

Huy =

f * Pn =

f * Hn =

n * x2 n * y2

(m2) (m2)

S x2 = S y2 =

Lx =

Ly =

Ws = Lx * Ly * z * ws =

Wc = Lx * Ly * h * wc =

Pu = Puk + 1.2 * Ws + 1.2 * Wc =

xmax =

ymax =

xmin =

ymin =

pumax = Pu / n + Mux* xmax / Sx2 + Muy* ymax / Sy2 =

pumin = Pu / n + Mux* xmin / Sx2 + Muy* ymin / Sy2 =

pumax f * Pn

Gaya lateral arah x pada tiang, 17.50 kN

Gaya lateral arah y pada tiang, 12.50 kN

Gaya lateral kombinasi dua arah, 21.51 kN

Syarat : ≤21.51 < 30.00 → AMAN (OK)

3. TINJAUAN GESER ARAH X

Jarak pusat tulangan terhadap sisi luar beton, d' = 0.100 m

Tebal efektif pilecap, d = h - d' = 0.300 m

Jarak bid. kritis terhadap sisi luar, 0.550 m

Berat beton, 9.504 kN

Berat tanah, 16.038 kN

Gaya geser arah x, 544.613 kN

Lebar bidang geser untuk tinjauan arah x, 1800 mm

Tebal efektif pilecap, d = 300 mm

Rasio sisi panjang thd. sisi pendek kolom, 1.0000

1207.477 kN

1744.133 kN

hux = Hux / n =

huy = Huy / n =humax = Ö ( hux

2 + huy2 ) =

humax f * Hn

cx = ( Lx - bx - d ) / 2 =

W1 = cx * Ly * h * wc =

W2 = cx * Ly * z * ws =

Vux = 2 * pumax - W1 - W2 =

b = Ly =

bc = bx / by =

Kuat geser pilecap arah x, diambil nilai terkecil dari Vc yang diperoleh dari pers.sbb. :

Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

804.984 kN

Diambil, kuat geser pilecap, ® 804.984 kN

Faktor reduksi kekuatan geser, 0.75

Kuat geser pilecap, 603.738 kN

Syarat yang harus dipenuhi,

≥603.738 > 544.613 ® AMAN (OK)

4. TINJAUAN GESER ARAH Y






Gaya geser arah y, 544.613 kN

Lebar bidang geser untuk tinjauan arah y, 1800 mm



Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux

cy = ( Ly - by - d ) / 2 =

W1 = cy * Lx * h * wc =

W2 = cy * Lx * z * ws =

Vuy = 2 * pumax - W1 - W2 =

b = Lx =

bc = bx / by =

Kuat geser pilecap arah y, diambil nilai terkecil dari Vc yang diperoleh dari pers.sbb. :

1207.477 kN

1744.133 kN

804.984 kN





≥603.738 > 544.613 ® AMAN (OK)

5. TINJAUAN GESER DUA ARAH (PONS)



Lebar bidang geser pons arah x, 0.700 m

Lebar bidang geser pons arah y, 0.700 m

Gaya geser pons akibat beban terfaktor pada kolom, 600.000 kN

Luas bidang geser pons, 0.840

Lebar bidang geser pons, 2.800 m


2.236 MPa

Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux

Bx = bx + d =

By = by + d =

Puk =

Ap = 2 * ( Bx + By ) * d = m2

bp = 2 * ( Bx + By ) =

bc = bx / by =

Tegangan geser pons, diambil nilai terkecil dari fp yang diperoleh dari pers.sbb. :

fp = [ 1 + 2 / bc ] * √ fc' / 6 =

2.343 MPa

1.491 MPa

Tegangan geser pons yang disyaratkan, 1.491 MPa

Faktor reduksi kekuatan geser pons, 0.75

Kuat geser pons, 939.15 kN

Syarat : ≥939.149 > 600.000 ® AMAN (OK)

6. PEMBESIAN PILECAP

6.1. TULANGAN LENTUR ARAH X

Jarak tepi kolom terhadap sisi luar pilecap, 0.700 m

Jarak tiang thd. sisi kolom, 0.300 m



Momen yang terjadi pada pilecap,

159.669 kNm

Lebar pilecap yang ditinjau, 1800 mm

Tebal pilecap, h = 400 mm

fp = [ as * d / bp + 2 ] * √ fc' / 12 =

fp = 1 / 3 * √ fc' =

fp =

f =

f * Vnp = f * Ap * fp * 103 =

f * Vnp Puk

cx = ( Lx - bx ) / 2 =

ex = cx - a =

W1 = cx * Ly * h * wc =

W2 = cx * Ly * z * ws =

Mux = 2 * pumax * ex - W1 * cx / 2 - W2 * cx / 2 =

b = Ly =

Jarak pusat tulangan thd. sisi luar beton, d' = 100 mm

Tebal efektif plat, d = h - d' = 300 mm


Kuat leleh baja tulangan, 390 MPa

Modulus elastis baja, 2.00E+05 MPa

Faktor distribusi teg. beton, 0.85

0.022455322

Faktor reduksi kekuatan lentur, 0.80

5.299

199.586 kNm

1.23201

< ® (OK)

Rasio tulangan yang diperlukan,

0.0033

Rasio tulangan minimum, 0.0025

Rasio tulangan yang digunakan, ® 0.0033

Luas tulangan yang diperlukan, 1772.61

Diameter tulangan yang digunakan, D 16 mm

Jarak tulangan yang diperlukan, 204 mm

Jarak tulangan maksimum, 200 mm

Jarak tulangan yang digunakan, ® s = 200 mm

Digunakan tulangan, D 16 - 200

Luas tulangan terpakai, 1809.56

6.2. TULANGAN LENTUR ARAH Y

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Mux / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2

s = p / 4 * D2 * b / As =

smax =

As = p / 4 * D2 * b / s = mm2






159.669 kNm









0.022455322


5.299

199.586 kNm

1.23201

< ® (OK)


0.0033










3. TULANGAN SUSUT

cy = ( Ly - by ) / 2 =

ey = cy - a =

W1 = cy * Lx * h * wc =

W2 = cy * Lx * z * ws =

Muy = 2 * pumax * ey - W1 * cy / 2 - W2 * cy / 2 =

b = Lx =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Muy / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2

s = p / 4 * D2 * b / As =

smax =

As = p / 4 * D2 * b / s = mm2

Rasio tulangan susut minimum, 0.0014

Luas tulangan susut arah x, 756

Luas tulangan susut arah y, 756

Diameter tulangan yang digunakan, Æ 12 mm

Jarak tulangan susut arah x, 269 mm

Jarak tulangan susut maksimum arah x, 200 mm

Jarak tulangan susut arah x yang digunakan, ® 200 mm

Jarak tulangan susut arah y, 269 mm

Jarak tulangan susut maksimum arah y, 200 mm

Jarak tulangan susut arah y yang digunakan, ® 200 mm

Digunakan tulangan susut arah x, Æ 12 - 200

Digunakan tulangan susut arah y, Æ 12 - 200


KODE FONDASI : F3

DATA BAHAN PILECAP


390 MPa

240 MPa










rsmin =

Asx = rsmin* b * d = mm2

Asy = rsmin* b * d = mm2

sx = p / 4 * Æ2 * b / Asx =

sx,max =

sx =

sy = p / 4 * Æ2 * b / Asy =

sy,max =

sy =

fc' =



wc = kN/m3

bx =

by =

ws = kN/m3

as =

DATA BEBAN FONDASI











n (m) n (m)

1 1 0.50 0.25 1 1 0.60 0.36

2 1 0.00 0.00 2 2 -0.30 0.18

3 1 -0.50 0.25

n = 3 0.50 n = 3 0.54










Puk =

Mux =

Muy =

Hux =

Huy =

f * Pn =

f * Hn =

n * x2 n * y2

(m2) (m2)

S x2 = S y2 =

Lx =

Ly =

Ws = Lx * Ly * z * ws =

Wc = Lx * Ly * h * wc =

Pu = Puk + 1.2 * Ws + 1.2 * Wc =

xmax =

ymax =

xmin =



271.97 kN

76.97 kN

Syarat : ≤271.97 < 300.00 → AMAN (OK)





Syarat : ≤16.67 < 30.00 → AMAN (OK)






ymin =



pumax f * Pn

hux = Hux / n =


2 + huy2 ) =

humax f * Hn

cx = ( Lx - bx - d ) / 2 =

W1 = cx * Ly * h * wc =






760.263 kN

849.706 kN

506.842 kN





≥380.132 > 247.112 ® AMAN (OK)




W2 = cx * Ly * z * ws =

Vux = pumax - W1 - W2 =

b = Ly =

bc = bx / by =


Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux








804.984 kN

864.613 kN

536.656 kN





≥402.492 > 241.438 ® AMAN (OK)




cy = y1 + a - ( by + d ) / 2 =

W1 = cy * Lx * h * wc =

W2 = cy * Lx * z * ws =

Vuy = pumax - W1 - W2 =

b = Lx =

bc = bx / by =


Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux







2.236 MPa

2.101 MPa

1.491 MPa




Syarat : ≥491.935 > 400.000 ® AMAN (OK)



Bx = bx + d =

By = by + d =

Puk =

Ap = 2 * ( Bx + By ) * d = m2

bp = 2 * ( Bx + By ) =

bc = bx / by =


fp = [ 1 + 2 / bc ] * √ fc' / 6 =

fp = [ as * d / bp + 2 ] * √ fc' / 12 =

fp = 1 / 3 * √ fc' =

fp =

f =

f * Vnp = f * Ap * fp * 103 =

f * Vnp Puk






77.937 kNm









0.022455322


5.299

97.421 kNm

1.43267

< ® (OK)


0.0038











cx = ( Lx - bx ) / 2 =

ex = cx - a =

W1 = cx * Ly * h * wc =

W2 = cx * Ly * z * ws =

Mux = pumax * ex - W1 * cx / 2 - W2 * cx / 2 =

b = Ly =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Mux / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2

s = p / 4 * D2 * b / As =

smax =

As = p / 4 * D2 * b / s = mm2






101.255 kNm









0.022455322


5.299

126.569 kNm

1.75791

< ® (OK)


0.0048




cy = y1 + a - by / 2 =

ey = cy - a =

W1 = cy * Lx * h * wc =

W2 = cy * Lx * z * ws =

Muy = pumax * ey - W1 * cy / 2 - W2 * cy / 2 =

b = Lx =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Muy / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2







3. TULANGAN SUSUT














KODE FONDASI : F2

DATA BAHAN PILECAP


390 MPa

240 MPa






s = p / 4 * D2 * b / As =

smax =

As = p / 4 * D2 * b / s = mm2

rsmin =



sx = p / 4 * Æ2 * b / Asx =

sx,max =

sx =

sy = p / 4 * Æ2 * b / Asy =

sy,max =

sy =

fc' =



wc = kN/m3

bx =

by =





DATA BEBAN FONDASI











n (m) n (m)

1 1 0.50 0.25 1 1 0.00 0.00

2 1 -0.50 0.25

n = 2 0.50 n = 1 0.00



ws = kN/m3

as =

Puk =

Mux =

Muy =

Hux =

Huy =

f * Pn =

f * Hn =

n * x2 n * y2

(m2) (m2)

S x2 = S y2 =

Lx =

Ly =








201.25 kN

141.25 kN

Syarat : ≤201.25 < 300.00 → AMAN (OK)





Syarat : ≤11.18 < 30.00 → AMAN (OK)

3. TINJAUAN TERHADAP GESER

Ws = Lx * Ly * z * ws =

Wc = Lx * Ly * h * wc =

Pu = Puk + 1.2 * Ws + 1.2 * Wc =

xmax =

xmin =

pumax = Pu / n + Mux* xmax / Sx2 =

pumin = Pu / n + Mux* xmin / Sx2 =

pumax f * Pn

hux = Hux / n =


2 + huy2 ) =

humax f * Hn










447.214 kN

1080.766 kN

298.142 kN





≥223.607 > 188.954 ® AMAN (OK)


cx = ( Lx - bx - d ) / 2 =

W1 = cx * Ly * h * wc =

W2 = cx * Ly * z * ws =

Vux = pumax - W1 - W2 =

b = Ly =

bc = bx / by =


Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux






135.343 kNm









0.022455322


5.299

169.179 kNm

3.38358

< ® (OK)


0.0098









cx = ( Lx - bx ) / 2 =

ex = cx - a =

W1 = cx * Ly * h * wc =

W2 = cx * Ly * z * ws =


b = Ly =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Mux / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2

s = p / 4 * D2 * b / As =

smax =


Tulangan bagi diambil 50% tulangan pokok, 1005.31

Jarak tulangan bagi yang diperlukan, 160 mm





3. TULANGAN SUSUT


Luas tulangan susut, 280


Jarak tulangan susut, 323 mm

Jarak tulangan susut maksimum, 200 mm



As = p / 4 * D2 * b / s = mm2

Asb = 50% * As = mm2

s = p / 4 * D2 * b / Asb =

smax =

As = p / 4 * D2 * b / s = mm2

rsmin =

As = rsmin* b * d = mm2

s = p / 4 * Æ2 * b / As =

smax =

s =

PERHITUNGAN KEKUATAN TIANG PANCANG


A. DATA TANAH

DATA HASIL PENGUJIAN LABORATORIUM (DATA BOR TANAH) SONDIR SPT

No Kedalaman Jenis g j Nilai SPT

Tanah ( ... ▫ ) N

1 0.00 5.00 lempung 23.00 9.962 0 5.60 5

2 5.00 10.00 lempung 30.00 9.962 0 12.30 12

3 10.00 15.00 lempung 52.00 9.962 0 18.40 27

4 15.00 20.00 lemp. padat 61.00 10.372 0 22.60 35

5 20.00 25.00 lemp. pasir 63.00 11.683 12 27.30 42

B. DATA BAHAN

Jenis tiang pancang : Beton bertulang tampang lingkaran



Kuat tekan beton tiang pancang, 25 MPa


C. TAHANAN AKSIAL TIANG PANCANG

1. BERDASARKAN KEKUATAN BAHAN

Luas penampang tiang pancang, 0.1257

Berat tiang pancang, 51.27 kN

Kuat tekan beton tiang pancang, 25000 kPa

Kapasitas dukung nominal tiang pancang,

881 kN



cu qf

z1 (m) z2 (m) (kN/m2) (kN/m3) (kN/m2)

fc' =

wc = kN/m3

A = p / 4 * D2 = m2

Wp = A * L * wc =

fc' =

Pn = 0.30 * fc' * A - 1.2 * Wp =

f =

f * Pn =

2. BERDASARKAN DATA BOR TANAH (SKEMPTON)

a. Tahanan ujung


Faktor daya dukung.



Kohesi tanah di sekitar dasar tiang, 55.00

Faktor daya dukung menurut Skempton, 9


b. Tahanan gesek

Tahanan gesek nominal menurut Skempton :

faktor adhesi

Faktor adhesi untuk jenis tanah lempung pada tiang pancang yang nilainya tergantung dari

nilai kohesi tanah, menurut Skempton, diambil : →Diameter tiang pancang, D = 0.400 m

Luas permukaan dinding segmen tiang,

panjang segmen tiang pancang yang ditinjau (m).

Perhitungan tahanan gesek nominal tiang

No Kedalaman

(m) (kN)

1 0.00 5.00 5.0 6.2832 23.00 0.83 119.707

2 5.00 10.00 5.0 6.2832 30.00 0.75 140.520

3 10.00 15.00 5.0 6.2832 52.00 0.55 179.617

4 15.00 17.00 2.0 2.5133 55.00 0.53 73.149

Tahanan gesek nominal tiang, 512.993

512.993 kN



Pb = Ab * cb * Nc

Ab = Luas penampang ujung bawah tiang (m2),

cb = Kohesi tanah di bawah dasar tiang (kN/m2),

Nc =

Ab = p / 4 * D2 = m2

cb = kN/m2

Nc =

Pb = Ab * cb * Nc =

Ps = S [ ad * cu * As ]

ad =

cu = Kohesi tanah di sepanjang tiang (kN/m2)

As = Luas permukaan dinding tiang (m2).

ad = 0.2 + [ 0.98 ] cu

As = p * D * L1

L1 =

L1 As cu ad Ps

z1 (m) z2 (m) (m2) (kN/m2)

Ps = S ad * cu * As =

Pn = Pb + Ps =



3. BERDASARKAN HASIL UJI SONDIR (BAGEMANN)

a. Tahanan ujung


faktor reduksi nilai tahanan ujung nominal tiang,

tahanan penetrasi kerucut statis yang merupakan nilai rata-rata dihitung dari 8.D di



Tahanan penetrasi kerucut statis rata-rata dari 8.D di atas dasar s.d. 4.D di bawah dasar

tiang pancang, 42 → 4200

Faktor reduksi nilai tahanan ujung nominal tiang, 0.50


b. Tahanan gesek

Tahanan gesek nominal menurut Skempton dihitung dg rumus :

tahanan gesek kerucut statis rata-rata (kN/m).

No Kedalaman

(m) (kN)

1 0.00 5.00 5.0 6.2832 5.60 35.19

2 5.00 10.00 5.0 6.2832 12.30 77.28

3 10.00 15.00 5.0 6.2832 18.40 115.61

4 15.00 17.00 2.0 2.5133 19.50 49.01

277.09





4. BERDASARKAN HASIL UJI SPT (MEYERHOFF)

Kapasitas nominal tiang pancang secara empiris dari nilai N hasil pengujian SPT

f =

f * Pn =

Pb = w * Ab * qc

w =

Ab = luas ujung bawah tiang (m2),

qc =

atas dasar tiang sampai 4.D di bawah dasar tiang (kN/m2),

Ab = p / 4 * D2 = m2

qc = kg/cm2 qc = kN/m2

w =Pb = w * Ab * qc =

Ps = S [ As * qf ]

Af = Luas permukaan segmen dinding tiang (m2). As = p * D * L1

qf =

L1 As qf Ps

z1 (m) z2 (m) (m2) (kN/m2)

Ps = S [ As * qf ] =

Pn = Pb + Ps =

f =

f * Pn =

menurut Meyerhoff dinyatakan dengan rumus :

(kN)

(kN)

nilai SPT di sekitar dasar tiang, dihitung dari 8.D di atas dasar tiang s.d 4.D di bawah

dasar tiang,

Ň = nilai SPT rata-rata di sepanjang tiang,

Berdasarkan hasil pengujian SPT diperoleh data sbb.

No Kedalaman Nilai SPT

N (m)

1 0.00 5.00 5 5.0 25.0

2 5.00 10.00 12 5.0 60.0

3 10.00 15.00 27 5.0 135.0

4 15.00 17.00 30 2.0 60.0

17.0 280.0

Nilai SPT rata-rata di sepanjang tiang, 16.47

Nilai SPT di sekitar dasar tiang (8.D di atas dasar tiang s.d 4.D di bawah dasar tiang),

30.00



Luas dasar tiang pancang, 0.1257

Luas selimut tiang pancang, 21.3628

502.6548246 kN

< 786.51 kN

Kapasitas nominal tiang pancang, 502.65 kN



5. REKAP TAHANAN AKSIAL TIANG PANCANG

No Uraian Tahanan Aksial Tiang Pancang

1 Berdasarkan kekuatan bahan 528.57

2 Berdasarkan data bor tanah (Skempton) 345.12

3 Berdasarkan hasil uji sondir (Bagemann) 324.59

4 Berdasarkan hasil uji SPT (Meyerhoff) 301.59

Pn = 40 * Nb * Ab + Ň * As

dan harus £ Pn = 380 * Ň * Ab

Nb =

Ab = luas dasar tiang (m2)

As = luas selimut tiang (m2)

L1 L1 * N

z1 (m) z2 (m)

Ň = S L1*N / S L1 =

Nb =

Ab = p / 4 * D2 = m2

As = p * D * L = m2

Pn = 40 * Nb * Ab + Ň * As =

Pn 380 * Ň * Ab =

Pn =

f =

f * Pn =

f * Pn

Daya dukung aksial terkecil, 301.59 kN

Diambil tahanan aksial tiang pancang, → 300.00 kN

D. TAHANAN LATERAL TIANG PANCANG

1. BERDASARKAN DEFLEKSI TIANG MAKSIMUM (BROMS)

Tahanan lateral tiang (H) kategori tiang panjang, dapat dihitung dengan persamaan :

dengan,

D = Diameter tiang pancang (m), D = 0.40 m

L = panjang tiang pancang (m), L = 17.00 m

26720

23500000

0.001257

e = Jarak beban lateral terhadap muka tanah (m), e = 0.20 m

defleksi tiang maksimum (m). 0.010 m

b = koefisien defleksi tiang, 0.548453335 m

9.32 > 2.5 maka termasuk tiang panjang (OK)

Tahanan lateral nominal tiang pancang,

87.81 kN



2. BERDASARKAN MOMEN MAKSIMUM (BRINCH HANSEN)

Kuat lentur beton tiang pancang, 10000

Tahanan momen, 0.00628

Momen maksimum, 62.83 kNm

Kohesi tanah rata-rata di sepanjang tiang

No Kedalaman

(m)

1 0.00 5.00 5.0 23.00 115.00

2 5.00 10.00 5.0 30.00 150.00

3 10.00 15.00 5.0 52.00 260.00

f * Pn =

f * Pn =

H = yo * kh * D / [ 2 * b * ( e * b + 1 ) ]

b = [ kh * D / ( 4 * Ec * Ic ) ]0.25

kh = modulus subgrade horisontal (kN/m3), kh = kN/m3

Ec = modulus elastis tiang (kN/m2), Ec = 4700 * Ö fc' * 103 = kN/m2

Ic = momen inersia penampang (m4), Ic = p / 64 * D4 = m4

yo = yo =

b = [ kh * D / ( 4 * Ec * Ic ) ]0.25 =

b * L =

H = yo * kh * D / [ 2 * b * ( e * b + 1 ) ] =

f =

f * Hn =

fb = 0.40 * fc' * 103 = kN/m2

W = Ic / (D/2) = m3

My = fb * W =

L1 cu cu * L1

z1 (m) z2 (m) (kN/m2)

4 15.00 17.00 2.0 63.00 126.00

17.0 651.00

Kohesi tanah rata-rata, 38.29411765

pers.(1)

g = L - ( f + 1.5 * D ) pers.(2)

pers.(3)

pers.(4)

Dari pers.(1) : f = 0.0072538

Dari pers.(2) : g = 16.40 -0.007254

0.000053 -0.237925 268.96

34.465

Dari pers.(3) : 0.800 0.00363

0.00363 0.80000

Dari pers.(4) : 0.0018134 -8.2000 9269.627

Pers.kuadrat : 0 = 0.00181 9.0000 -9269.627


f = 6.351 m

3480.488 kNm

> → Termasuk tiang panjang (OK)

Dari pers.(3) : 0.800 0.00363

62.83 = 0.00363 0.80000

Pers.kuadrat : 0 = 0.00363 0.80000 -62.83




3. REKAP TAHANAN LATERAL TIANG

No Uraian Tahanan Lateral Tiang Pancang

1 Berdasarkan defleksi tiang maksimum 52.68

2 Berdasarkan momen maksimum 36.86

Tahanan lateral tiang terkecil, 36.86 kN

Diambil tahanan lateral tiang pancang, → 30.00 kN

S L1 = Scu*L1 =ču = S [ cu * L1 ] / S L1 = kN/m2

f = Hn / [ 9 * ču * D ]

My = Hn * ( e + 1.5 * D + 0.5 * f )

My = 9 / 4 * D * ču * g2

* Hn

* Hn

g2 = * Hn2 * Hn +

9 / 4 * D * cu =

My = Hn * ( * Hn )

My = * Hu2 * Hn

My = * Hu2 * Hn

* Hu2 * Hn

Hn =

Mmax = Hn * ( e + 1.5 * D + 0.5 * f ) =

Mmax My

My = Hn * ( * Hn )

* Hn2 * Hu

* Hn2 + * Hn

Hn =

f =

f * Hn =

f * Hn

f * Hn =

f * Hn =


KODE FONDASI : F9

DATA BAHAN PILECAP


390 MPa

240 MPa










fc' =



wc = kN/m3

bx =

by =

ws = kN/m3

as =

DATA BEBAN FONDASI











n (m) n (m)

1 3 1.00 3.00 1 3 1.00 3.00

2 3 0.00 0.00 2 3 0.00 0.00

3 3 -1.00 3.00 3 3 -1.00 3.00

n = 9 6.00 n = 9 6.00












274.48 kN

117.81 kN

Syarat : ≤274.48 < 300.00 → AMAN (OK)


Puk =

Mux =

Muy =

Hux =

Huy =

f * Pn =

f * Hn =

n * x2 n * y2

(m2) (m2)

S x2 = S y2 =

Lx =

Ly =

Ws = Lx * Ly * z * ws =

Wc = Lx * Ly * h * wc =

Pu = Puk + 1.2 * Ws + 1.2 * Wc =

xmax =

ymax =

xmin =

ymin =



pumax f * Pn




Syarat : ≤22.05 < 30.00 → AMAN (OK)











2504.396 kN

3219.938 kN

hux = Hux / n =


2 + huy2 ) =

humax f * Hn

cx = ( Lx - bx - d ) / 2 =

W1 = cx * Ly * h * wc =

W2 = cx * Ly * z * ws =

Vux = 3 * pumax - W1 - W2 =

b = Ly =

bc = bx / by =


Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

1669.597 kN





≥1252.198 > 752.371 ® AMAN (OK)











Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux

cy = ( Ly - by - d ) / 2 =

W1 = cy * Lx * h * wc =

W2 = cy * Lx * z * ws =

Vuy = 3 * pumax - W1 - W2 =

b = Lx =

bc = bx / by =


2504.396 kN

3219.938 kN

1669.597 kN





≥1252.198 > 752.371 ® AMAN (OK)










2.236 MPa

Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux

Bx = bx + d =

By = by + d =

Puk =

Ap = 2 * ( Bx + By ) * d = m2

bp = 2 * ( Bx + By ) =

bc = bx / by =


fp = [ 1 + 2 / bc ] * √ fc' / 6 =

2.236 MPa

1.491 MPa




Syarat : ≥1788.854 > 1500.000 ® AMAN (OK)








528.634 kNm



fp = [ as * d / bp + 2 ] * √ fc' / 12 =

fp = 1 / 3 * √ fc' =

fp =

f =

f * Vnp = f * Ap * fp * 103 =

f * Vnp Puk

cx = ( Lx - bx ) / 2 =

ex = cx - a =

W1 = cx * Ly * h * wc =

W2 = cx * Ly * z * ws =


b = Ly =







0.022455322


5.299

660.792 kNm

1.47498

< ® (OK)


0.0040











fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Mux / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2

s = p / 4 * D2 * b / As =

smax =

As = p / 4 * D2 * b / s = mm2






528.634 kNm









0.022455322


5.299

660.792 kNm

1.47498

< ® (OK)


0.0040










3. TULANGAN SUSUT

cy = ( Ly - by ) / 2 =

ey = cy - a =

W1 = cy * Lx * h * wc =

W2 = cy * Lx * z * ws =


b = Lx =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Muy / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2

s = p / 4 * D2 * b / As =

smax =

As = p / 4 * D2 * b / s = mm2














KODE FONDASI : F6

DATA BAHAN PILECAP


390 MPa

240 MPa










rsmin =



sx = p / 4 * Æ2 * b / Asx =

sx,max =

sx =

sy = p / 4 * Æ2 * b / Asy =

sy,max =

sy =

fc' =



wc = kN/m3

bx =

by =

ws = kN/m3

as =

DATA BEBAN FONDASI











n (m) n (m)

1 2 1.00 2.00 1 3 0.50 0.75

2 2 0.00 0.00 2 3 -0.50 0.75

3 2 -1.00 2.00

n = 6 4.00 n = 6 1.50










Puk =

Mux =

Muy =

Hux =

Huy =

f * Pn =

f * Hn =

n * x2 n * y2

(m2) (m2)

S x2 = S y2 =

Lx =

Ly =

Ws = Lx * Ly * z * ws =

Wc = Lx * Ly * h * wc =

Pu = Puk + 1.2 * Ws + 1.2 * Wc =

xmax =

ymax =

xmin =



295.93 kN

77.59 kN

Syarat : ≤295.93 < 300.00 → AMAN (OK)





Syarat : ≤22.42 < 30.00 → AMAN (OK)






ymin =



pumax f * Pn

hux = Hux / n =


2 + huy2 ) =

humax f * Hn

cx = ( Lx - bx - d ) / 2 =

W1 = cx * Ly * h * wc =






1609.969 kN

2921.795 kN

1073.313 kN





≥804.984 > 544.898 ® AMAN (OK)




W2 = cx * Ly * z * ws =

Vux = 2 * pumax - W1 - W2 =

b = Ly =

bc = bx / by =


Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux








2504.396 kN

3219.938 kN

1669.597 kN





≥1252.198 > 854.219 ® AMAN (OK)




cy = ( Ly - by - d ) / 2 =

W1 = cy * Lx * h * wc =

W2 = cy * Lx * z * ws =

Vuy = 3 * pumax - W1 - W2 =

b = Lx =

bc = bx / by =


Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux







2.236 MPa

2.315 MPa

1.491 MPa




Syarat : ≥1699.412 > 950.000 ® AMAN (OK)



Bx = bx + d =

By = by + d =

Puk =

Ap = 2 * ( Bx + By ) * d = m2

bp = 2 * ( Bx + By ) =

bc = bx / by =


fp = [ 1 + 2 / bc ] * √ fc' / 6 =

fp = [ as * d / bp + 2 ] * √ fc' / 12 =

fp = 1 / 3 * √ fc' =

fp =

f =

f * Vnp = f * Ap * fp * 103 =

f * Vnp Puk






396.971 kNm









0.022455322


5.299

496.213 kNm

1.72296

< ® (OK)


0.0047











cx = ( Lx - bx ) / 2 =

ex = cx - a =

W1 = cx * Ly * h * wc =

W2 = cx * Ly * z * ws =


b = Ly =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Mux / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2

s = p / 4 * D2 * b / As =

smax =

As = p / 4 * D2 * b / s = mm2






184.328 kNm









0.022455322


5.299

230.410 kNm

0.51431

< ® (OK)


0.0013




cy = ( Ly - by ) / 2 =

ey = cy - a =

W1 = cy * Lx * h * wc =

W2 = cy * Lx * z * ws =


b = Lx =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Muy / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2







3. TULANGAN SUSUT














KODE FONDASI : F5

DATA BAHAN PILECAP


390 MPa

240 MPa






s = p / 4 * D2 * b / As =

smax =

As = p / 4 * D2 * b / s = mm2

rsmin =



sx = p / 4 * Æ2 * b / Asx =

sx,max =

sx =

sy = p / 4 * Æ2 * b / Asy =

sy,max =

sy =

fc' =



wc = kN/m3

bx =

by =





DATA BEBAN FONDASI











n (m) n (m)

1 2 0.70 0.98 1 2 0.70 0.98

2 1 0.00 0.00 2 1 0.00 0.00

3 2 -0.70 0.98 3 2 -0.70 0.98

n = 5 1.96 n = 5 1.96



ws = kN/m3

as =

Puk =

Mux =

Muy =

Hux =

Huy =

f * Pn =

f * Hn =

n * x2 n * y2

(m2) (m2)

S x2 = S y2 =

Lx =

Ly =










290.61 kN

54.90 kN

Syarat : ≤290.61 < 300.00 → AMAN (OK)





Syarat : ≤24.76 < 30.00 → AMAN (OK)


Ws = Lx * Ly * z * ws =

Wc = Lx * Ly * h * wc =

Pu = Puk + 1.2 * Ws + 1.2 * Wc =

xmax =

ymax =

xmin =

ymin =



pumax f * Pn

hux = Hux / n =


2 + huy2 ) =

humax f * Hn










1967.740 kN

3041.052 kN

1311.827 kN





≥983.870 > 544.005 ® AMAN (OK)


cx = ( Lx - bx - d ) / 2 =

W1 = cx * Ly * h * wc =

W2 = cx * Ly * z * ws =

Vux = 2 * pumax - W1 - W2 =

b = Ly =

bc = bx / by =


Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux










1967.740 kN

3041.052 kN

1311.827 kN





≥983.870 > 544.005 ® AMAN (OK)


cy = ( Ly - by - d ) / 2 =

W1 = cy * Lx * h * wc =

W2 = cy * Lx * z * ws =

Vuy = 2 * pumax - W1 - W2 =

b = Lx =

bc = bx / by =


Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux









2.236 MPa

2.236 MPa

1.491 MPa




Syarat : ≥1788.854 > 700.000 ® AMAN (OK)



Bx = bx + d =

By = by + d =

Puk =

Ap = 2 * ( Bx + By ) * d = m2

bp = 2 * ( Bx + By ) =

bc = bx / by =


fp = [ 1 + 2 / bc ] * √ fc' / 6 =

fp = [ as * d / bp + 2 ] * √ fc' / 12 =

fp = 1 / 3 * √ fc' =

fp =

f =

f * Vnp = f * Ap * fp * 103 =

f * Vnp Puk






212.639 kNm









0.022455322


5.299

265.798 kNm

0.75511

< ® (OK)


0.0020







cx = ( Lx - bx ) / 2 =

ex = cx - a =

W1 = cx * Ly * h * wc =

W2 = cx * Ly * z * ws =


b = Ly =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Mux / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2

s = p / 4 * D2 * b / As =

smax =










212.639 kNm









0.022455322


5.299

As = p / 4 * D2 * b / s = mm2

cy = ( Ly - by ) / 2 =

ey = cy - a =

W1 = cy * Lx * h * wc =

W2 = cy * Lx * z * ws =


b = Lx =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

265.798 kNm

0.75511

< ® (OK)


0.0020










3. TULANGAN SUSUT













Mn = Muy / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d = mm2

s = p / 4 * D2 * b / As =

smax =

As = p / 4 * D2 * b / s = mm2

rsmin =



sx = p / 4 * Æ2 * b / Asx =

sx,max =

sx =

sy = p / 4 * Æ2 * b / Asy =

sy,max =

sy =

PERHITUNGAN FONDASI FOOTPLAT BENTUK EMPAT PERSEGI PANJANG


A. DATA FONDASI FOOT PLAT

DATA TANAH

Kedalaman fondasi, 2.50

Berat volume tanah, 17.60

Sudut gesek dalam, 34.00

Kohesi, c = 0.00

Tahanan konus rata-rata (hasil pengujian sondir), 95.00

DIMENSI FONDASI

Lebar fondasi arah x, 2.20

Lebar fondasi arah y, 1.80

Tebal fondasi, h = 0.40

Lebar kolom arah x, 0.40

Lebar kolom arah y, 0.30

Df =

g =

f =

qc =

Bx =

By =

bx =

by =


BAHAN KONSTRUKSI

Kuat tekan beton, 20.0

Kuat leleh baja tulangan, 390


BEBAN RENCANA FONDASI

Gaya aksial akibat beban terfaktor, 850.000

Momen arah x akibat beban terfaktor, 155.000

Momen arah y akibat beban terfaktor, 136.000

B. KAPASITAS DUKUNG TANAH

1. MENURUT TERZAGHI DAN PECK (1943)

Kapasitas dukung ultimit tanah menurut Terzaghi dan Peck (1943) :

c = c = 0.00

Kedalaman fondasi (m) 2.50

17.60

B = lebar fondasi (m) 1.80

L = panjang fondasi (m) 2.20

Sudut gesek dalam, 34.00

0.59341195

4.01140898

72.4763059

Faktor kapasitas dukung tanah menurut Terzaghi :

52.637

36.504

35.226

Kapasitas dukung ultimit tanah menurut Terzaghi :

1632.71

Kapasitas dukung tanah, 544.24

as =

fc' =

fy =

gc =

Pu =

Mux =

Muy =

qu = c * Nc * (1 + 0.3 * B / L) + Df * g * Nq + 0.5 * B * Ng * (1 - 0.2 * B / L)

kohesi tanah (kN/m2)

Df = Df =

g = berat volume tanah (kN/m3) g =

B = By =

L = By =

f = f = f / 180 * p =a = e(3*p / 4 - f/2)*tan f =

Kpg = 3 * tan2 [ 45° + 1/2*( f + 33°) ] =

Nc = 1/ tan f * [ a2 / (2 * cos2 (45 + f/2) - 1 ] =

Nq = a2 / [ (2 * cos2 (45 + f/2) ] = Nc * tan f + 1 =

Ng = 1/2 * tan f * [ Kpg / cos2 f - 1 ] =

qu = c*Nc*(1+0.3*B/L) + Df*g*Nq + 0.5*B*Ng*(1-0.2*B/L) =

qa = qu / 3 =

2. MENURUT MEYERHOF (1956)

Kapasitas dukung tanah menurut Meyerhof (1956) :

dengan,

B = lebar fondasi (m) 1.80

Kedalaman fondasi (m) 2.50

1.45833333

® diambil, 1.33

Tahanan konus rata-rata hasil sondir pada dasar fondasi, 95.00

5.211

Kapasitas dukung ijin tanah, 521.14

3. KAPASITAS DUKUNG TANAH YANG DIPAKAI

Kapasitas dukung tanah menurut Terzaghi dan Peck : 544.24

Kapasitas dukung tanah tanah menurut Meyerhof : 521.14

Kapasitas dukung tanah yang dipakai : 521.14

C. KONTROL TEGANGAN TANAH

qa = qc / 33 * [ ( B + 0.3 ) / B ]2 * Kd ( dalam kg/cm2)

Kd = 1 + 0.33 * Df / B harus £ 1.33

qc = tahanan konus rata-rata hasil sondir pada dasar fondasi ( kg/cm2 )

B = By =

Df = Df =

Kd = 1 + 0.33 * Df / B =

Kd =

qc =

qa = qc / 33 * [ ( B + 0.3 ) / B ]2 * Kd =

qa =

qa =

qa =

qa =

Luas dasar foot plat, 3.9600

Tahanan momen arah x, 1.4520

Tahanan momen arah y, 1.1880

Tinggi tanah di atas foot plat, 2.10

Tekanan akibat berat foot plat dan tanah, 46.560

Eksentrisitas pada fondasi :

0.1824 m < 0.3667 m

0.1600 m < 0.3000 m

Tegangan tanah maksimum yang terjadi pada dasar fondasi :

482.434

< ® AMAN (OK)

Tegangan tanah minimum yang terjadi pada dasar fondasi :

39.979

> 0 ® tak terjadi teg.tarik (OK)

D. GAYA GESER PADA FOOT PLAT


Jarak pusat tulangan terhadap sisi luar beton, d' = 0.075

Tebal efektif foot plat, d = h - d' = 0.325

A = Bx * By =

Wx = 1/6 * By * Bx2 =

Wy = 1/6 * Bx * By2 =

z = Df - h =

q = h * gc + z * g =

ex = Mux / Pu = Bx / 6 =

ey = Muy / Pu = By / 6 =

qmax = Pu / A + Mux / Wx + Muy / Wy + q =

qmax qa

qmin = Pu / A - Mux / Wx - Muy / Wy + q =

qmin

Jarak bid. kritis terhadap sisi luar foot plat, 0.738

Tegangan tanah pada bidang kritis geser arah x,

334.111

Gaya geser arah x, 480.173

Lebar bidang geser untuk tinjauan arah x, 1800

Tebal efektif footplat, d = 325


1090.083

2010.598

872.067

Diambil, kuat geser foot plat, ® 872.067


Kuat geser foot plat, 654.050


≥654.050 > 480.173 ® AMAN (OK)




Jarak bid. kritis terhadap sisi luar foot plat, 0.593

Tegangan tanah pada bidang kritis geser arah y,

ax = ( Bx - bx - d ) / 2 =

qx = qmin + (Bx - ax) / Bx * (qmax - qmin) =

Vux = [ qx + ( qmax - qx ) / 2 - q ] * ax * By =

b = By =

bc = bx / by =

Kuat geser foot plat arah x, diambil nilai terkecil dari Vc yang diperoleh dari pers.sbb. :

Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux

ay = ( By - by - d ) / 2 =

336.793

Gaya geser arah y, 473.240

Lebar bidang geser untuk tinjauan arah y, 2200

Tebal efektif footplat, d = 315


1291.329

1995.691

1033.063

Diambil, kuat geser foot plat, ® 1033.063


Kuat geser foot plat, 774.798


≥774.798 > 473.240 ® AMAN (OK)




Lebar bidang geser pons arah x, 0.715

Lebar bidang geser pons arah y, 0.615

qy = qmin + (By - ay) / By * (qmax - qmin) =

Vuy = [ qy + ( qmax - qy ) / 2 - q ] * ay * Bx =

b = Bx =

bc = bx / by =

Kuat geser foot plat arah y, diambil nilai terkecil dari Vc yang diperoleh dari pers.sbb. :

Vc = [ 1 + 2 / bc ] * √ fc' * b * d / 6 * 10-3 =

Vc = [ as * d / b + 2 ] * √ fc' * b * d / 12 * 10-3 =

Vc = 1 / 3 * √ fc' * b * d * 10-3 =

Vc =

f =

f * Vc =

f * Vc Vux

cx = bx + 2 * d =

cy = by + 2 * d =

Gaya geser pons yang terjadi,

755.615


Lebar bidang geser pons, 2.660


1.863

2.511

1.491

Tegangan geser pons yang disyaratkan, 1.491


Kuat geser pons, 936.80

Syarat : ≥936.801 > 755.615 ® AMAN (OK)

≥936.801 > 850.000 ® AMAN (OK)

E. PEMBESIAN FOOTPLAT

1. TULANGAN LENTUR ARAH X

Jarak tepi kolom terhadap sisi luar foot plat, 0.900

Tegangan tanah pada tepi kolom,

Vup = ( Bx * By - cx * cy ) * [ ( qmax + qmin ) / 2 - q ] =

Ap = 2 * ( cx + cy ) * d =

bp = 2 * ( cx + cy ) =

bc = bx / by =


fp = [ 1 + 2 / bc ] * √ fc' / 6 =

fp = [ as * d / bp + 2 ] * √ fc' / 12 =

fp = 1 / 3 * √ fc' =

fp =

f =

f * Vnp = f * Ap * fp * 103 =

f * Vnp Vup

f * Vnp Pu

ax = ( Bx - bx ) / 2 =

301.430

Momen yang terjadi pada plat fondasi akibat tegangan tanah,

273.768

Lebar plat fondasi yang ditinjau, 1800

Tebal plat fondasi, h = 400

Jarak pusat tulangan thd. sisi luar beton, d' = 75

Tebal efektif plat, d = h - d' = 325

Kuat tekan beton, 20


Modulus elastis baja, 2.00E+05


0.02245532


5.299

342.210

1.79992

< ® (OK)


0.0049




Diameter tulangan yang digunakan, D 16

Jarak tulangan yang diperlukan, 127

Jarak tulangan maksimum, 200

Jarak tulangan yang digunakan, ® s = 127



2. TULANGAN LENTUR ARAH Y

qx = qmin + (Bx - ax) / Bx * (qmax - qmin) =

Mux = 1/2 * ax2 * [ qx + 2/3 * ( qmax - qx ) - q ] * By =

b = By =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Mux / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d =

s = p / 4 * D2 * b / As =

smax =

As = p / 4 * D2 * b / s =

Jarak tepi kolom terhadap sisi luar foot plat, 0.750

Tegangan tanah pada tepi kolom,

298.078

Momen yang terjadi pada plat fondasi akibat tegangan tanah,

231.674

Lebar plat fondasi yang ditinjau, 2200

Tebal plat fondasi, h = 400

Jarak pusat tulangan thd. sisi luar beton, d' = 85

Tebal efektif plat, d = h - d' = 315

Kuat tekan beton, 20


Modulus elastis baja, 2.00E+05


0.02245532


5.299

289.592

1.32661

< ® (OK)


0.0035




Diameter tulangan yang digunakan, D 16

Jarak tulangan yang diperlukan, 180

ay = ( By - by ) / 2 =

qy = qmin + (By - ay) / By * (qmax - qmin) =

Muy = 1/2 * ay2 * [ qy + 2/3 * ( qmax - qy ) - q ] * Bx =

b = Bx =

fc' =

fy =

Es =

b1 =

rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) =

f =

Rmax = 0.75 * rb * fy * [1-½*0.75* rb * fy / ( 0.85 * fc’ ) ] =

Mn = Muy / f =

Rn = Mn * 106 / ( b * d2 ) =

Rn Rmax

r = 0.85 * fc’ / fy * [ 1 - Ö {1 – 2 * Rn / ( 0.85 * fc’ ) } ] =

rmin =

r =

As = r * b * d =

s = p / 4 * D2 * b / As =

Jarak tulangan maksimum, 200

Jarak tulangan yang digunakan, ® s = 180



3. TULANGAN SUSUT


Luas tulangan susut arah x, 819.000

Luas tulangan susut arah y, 970.200

Diameter tulangan yang digunakan, Æ 12

Jarak tulangan susut arah x, 249

Jarak tulangan susut maksimum arah x, 200

Jarak tulangan susut arah x yang digunakan, ® 200

Jarak tulangan susut arah y, 256

Jarak tulangan susut maksimum arah y, 200

smax =

As = p / 4 * D2 * b / s =

rsmin =

Asx = rsmin* d * Bx =

Asy = rsmin* d * By =

sx = p / 4 * Æ2 * By / Asx =

sx,max =

sx =

sy = p / 4 * Æ2 * Bx / Asy =

sy,max =

Jarak tulangan susut arah y yang digunakan, ® 200



sy =

m

°

kPa

m

m

m

m

m

kN/m3

kg/cm2

MPa

MPa

kN

kNm

kNm

°

m

m

m

°

rad

kN/m3

* (1 - 0.2 * B / L)

kN/m3

kN/m2

kN/m2

m

m

> 1.33

kg/cm2

kg/cm2

kN/m2

kN/m2

kN/m2

kN/m2

m

(OK)

(OK)

tak terjadi teg.tarik (OK)

m

m

m2

m3

m3

kN/m2

kN/m2

kN/m2

m

kN

mm

mm

kN

kN

kN

kN

kN

m

m

m

kN/m2

kN

mm

mm

kN

kN

kN

kN

kN

m

m

m

m

kN/m2

kN

m

MPa

MPa

MPa

MPa

kN

m

m2

kNm

mm

mm

mm

mm

MPa

MPa

MPa

kNm

mm

mm

mm

mm

kN/m2

mm2

mm2

m

kNm

mm

mm

mm

mm

MPa

MPa

MPa

kNm

mm

mm

kN/m2

mm2

mm

mm

mm

mm

mm

mm

mm

mm

mm2

mm2

mm2

pondasi

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