Daya Dukung (Bearing Capacity)
Tanah kuat batuan (rock) SIVA
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Pondasi Dangkal ~ untuk melimpahkan beban ke lapisan di bawahnya ~ utamanya untuk tanah kuat atau beban ringan
Tanah kuat batuan (rock) 2
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Footing Performance Vertical Load
Vertical movement
safe load
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Elastic maximum tolerable settlement
maximum service ultimate capacity load
Plastic
Ultimate Limit State Serviceability Limit State Maximum allowable load = min [safe load, max service load ] Copyright 2001
Plunging Failure
Limit States
Serviceability
Ultimate 4
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Bearing Pressure Definitions Allowable Safe Bearing Pressure qasb < /uA/ ψ =q φF.q s (settlement) F
Plan Area, A
Ultimate Bearing Capacity qu = Ffail / A SIVA
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Foundation Failure
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Rotational Failure
Force
Soil Heave
Resistance
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Pola Keruntuhan
General Failure
Local Shear Failure
Punching Shear Failure 7
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General Failure
Local Shear Failure
Punching Shear Failure
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FOUNDATION FAILURE 1.Generalized Shear Failure q
Soil Failure Lines Settlement passive
rigid radial shear SIVA
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log spiral
2. Local Shear Failure q
minor surface heave only Settlement
Medium dense or firm soils SIVA
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3. Punching Shear Failure q
No surface heave
Settlement
Loose or Soft Soils SIVA
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Perhitungan Daya Dukung Untuk menghitung daya dukung dapat dilakukan dengan analisisis berdasarkan :
Data Uji Laboratorium: Teori Terzaghi Teori Meyerhof Teori Brinch Hansen Teori Vesic
Data Uji Lapangan : Plate Bearing Test Cone Penetration Test/CPT (Sondir Standard Penetration Test/SPT 12
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Aplikasi Teori Daya Dukung KEMIRINGAN
TERZAGHI
MEYERHOF
HANSEN
VESIC
BEBAN
0
θ
θ
θ
MUKA TANAH
0
0
β
β
DASAR PONDASI
0
0
δ
δ
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Daya Dukung Terzaghi Anggapan-anggapan: 1. 2. 3. 4. 5. 6. 7. 8.
Tanah homogen isotropik Mode keruntuhan pondasi adalah adalah general shear failure Pondasi adalah strip dengan permukaan bawah kasar Bidang keruntuhan geser diatas permukaan tanah diabaikan Permukaan tanah adalah horizontal Tidak terdapat gaya horizontal, momen dan eksentrisitas Pondasi terletak pada kedalaman D
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Keseimbangan Gaya
Keseimbangan gaya-gaya yang bekeja pada baji tanah (soil wedge) adalah: Qu.(2b).1 = - W + 2.CsinΦ + 2.Pp 15
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1 q f = cN c + γ 1 DN q + Bγ 2 Nγ 2 Strip footing
1 qf =cNc +γ1DNq + Bγ2Nγ 2
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Faktor Daya Dukung Tanah Menurut Terzaghi dan Berbagai Nilai Nγγ yang Berbeda
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Terzaghi Bearing Equation qu nett = c.Nc + p'o (Nq - 1) + 0.5B 0.5Bγ'Nγ applies to strip footing Nc, Nq and Nγ are functions of φ, and are usually given in graphical form c, φ and γ' refer to soil properties in the failure zone below the footing p'o is the effective overburden pressure at the founding level shear strength contribution above footing level is ignored : conservative for deeper footings
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Terzaghi Bearing Equation qu nett = c.Nc + p'o (Nq - 1) + 0.5B 0.5Bγ'Nγ
Overburden
p'o = γ'o D B
Failure Zone (depth ≈ 2B) Generalized soil strength : c, φ Soil unit weight : γ' (total or effective as applicable) (drainage as applicable) SIVA
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Adopt weighted average values !
Bearing Capacity Factors
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Faktor daya dukung Terzaghi a = e N
q
(
φ 3π − ) tg φ 4 2
a
= 2
2 cos
2
( 45 +
φ
− 1 ). ctg φ
2
)
N
c
= (N
N
c
= 5 , 7 jika : φ = 0
N
γ
= 2(N
q
q
+ 1 ). tg φ 21
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Faktor daya dukung Terzaghi Nq = e
π .tg φ
tg ( 45 + 2
N c = ( N q − 1).ctg φ
φ 2
)
N c = 5,7 jika : φ = 0 N γ = 2 ( N q + 1).tg φ 22
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Faktor Daya Dukung
Bearing capacity factors 23
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Rumus Umum Daya Dukung Secara umum daya dukung dapat ditulis sbb:
qu = ζc.c Nc + ζq.γ D.Nq + ζγ.0,5 γ B.Nγ dimana:
ζc, ζq, ζγ = faktor koreksi yang tergantung pada bentuk,kedalaman,kemiringan: beban, muka tanah, dasar pondasi 24
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Faktor Daya Dukung Bearing Capacity Factor
1000
100
Nc Nq Nγ
Nq = 33 Nc = 10
10
1
0.1 SIVA
Nγ = 250
14o 0
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10
46o
35o 20
30
Friction Angle (deg)
40
50
Persamaan Daya Dukung Meyerhof
qu = c.N c. c.N Ncscdcic + q.N q q..N Nqsqdqiq + 0.5γ 0.5γBN BNγsγdγiγ Bearing Capacity for soil •• Correction factors Factors for footing shape (s), φ cohesion, surcharge and weight footing depth (d) and load inclination (i ). Dfof friction angle, φ q = γ.Df • functions • determine from appropriate equations c • determine by equation B or from graph soil density, γ, (kN/m3) SIVA
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Faktor daya dukung Meyerhof Nq = e
π . tg φ
tg ( 45 + 2
N c = ( N q − 1). ctg φ
φ 2
)
N c = 5 ,14 jika : φ = 0 N γ = ( N q − 1).tg (1, 4 .φ ) 27
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Faktor daya dukung Hansen Nq = e
π .tgφ
φ
tg ( 45 + ) 2 N c = ( N q − 1).ctgφ 2
N c = 5,14 jika : φ = 0 N γ = 1,5( N q − 1).tgφ 28
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Faktor daya dukung Vesic Nq = e
π .tg φ
φ
tg ( 45 + ) 2 N c = ( N q − 1).ctg φ 2
N c = 5,14 jika : φ = 0 N γ = 2( N q − 1).tg φ 29
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Pengaruh Muka air
30
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Pondasi dengan Beban Momen M P e
P
e=M P ekivalen eksentrisitas beban SIVA
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Cara Meyerhof menentukan eksentrisitas beban L
e B
P 2e
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L' = L- 2e
Eksentrisitas 2 arah L 2e2
B
e2
P
2e1 SIVA
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L' = L- 2e1
B' = B- 2e2
e1
Daya Dukung Berdasar Data Uji Lapangan (In Situ Test)
Plate Bearing Test (Uji Pembebanan Pelat) Standard Penetration Test (SPT) Cone Penetration Test/CPT (Sondir)
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Plate Load Tests
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Plate Bearing Test (Uji Pembebanan Pelat)
Tanah dengan kekuatan konstan qu = qu , p B < 4 Bp
Tanah Dengan Kekuatan Meningkat Secara Linear Thd Kedalaman B < 4 Bp
qu = qu , p
Ekstrapolasi Hasil Uji Penurunan Terzaghi & Peck. q q1 = ρi 1,5
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B Bp
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Standard Penetration Test (SPT)
PONDASI TELAPAK (FOOTING) MEYERHOF (1956,1974) N B ≤ 4 ft → qa,1 = n Kd F1 N B + F3 B > 4 ft → qa,1 = n F2 B
2
Dimana : qa,1 = daya dukung ijin utk penurunan 1 inchi Kd = 1+0,33 D/B≤1,33 Nn = SPT yang dikoreksi F = faktor tergantung energi pukulan SPT
PONDASI PELAT (MAT/RAFT) N q a ,1 = n K d F3
q a = ρ q a ,1 37
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Cone Penetration Test/CPT (Sondir) SCHMERTMANN (1978) DAYA DUKUNG BATAS PADA TANAH NON KOHESIF MENERUS : qu = 28 – 0,0052(300-qc)1,5 BUJUR SANGKAR : qu = 48 – 0,0090(300-qc)1,5
DAYA DUKUNG BATAS PADA TANAH KOHESIF MENERUS : qu = 2 + 0,28 qc BUJUR SANGKAR : qu = 5 + 0,34 qc qu dan qc dalam tsf atau kg/cm2 38
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Belajar
Jangan tunggu sampai menit terakhir. 39
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Exams
My mama always said, “Exam is like a box of chocolates; you never know what you are gonna get”
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