daya dukung (bearing capacity) - universitas...
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Daya Dukung (Bearing Capacity)
SIVA1
batuan (rock)
Tanah
kuat
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Pondasi Dangkal
~ untuk melimpahkan beban ke lapisan di bawahnya
~ utamanya untuk tanah kuat atau beban ringan
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batuan (rock)
Tanah
kuat
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Footing PerformanceFooting Performance
Vertical LoadVertical LoadV
ertic
al m
ovem
ent
Ver
tical
mov
emen
t
ElasticElastic
PlasticPlasticmaximum tolerablemaximum tolerable
settlementsettlement
maximum servicemaximum serviceloadload
ultimateultimatecapacitycapacity
safe loadsafe load
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Ver
tical
mov
emen
tV
ertic
al m
ovem
ent
PlasticPlastic
PlungingPlungingFailureFailure
Serviceability Limit StateServiceability Limit State
settlementsettlement
Ultimate Limit StateUltimate Limit State
Maximum allowable load =Maximum allowable load =min min [[safe load, max service load safe load, max service load ]]
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Limit States
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ServiceabilityServiceabilityServiceabilityServiceability UltimateUltimateUltimateUltimate
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Bearing Pressure DefinitionsBearing Pressure Definitions
FFFF Plan Area, APlan Area, A
Bearing PressureBearing Pressure qqbb == F / AF / ASafeSafe qqss = = φφφφφφφφ.q.quu / / ψψψψψψψψAllowableAllowable qqaa < q< qss (settlement)(settlement)
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FFFF Plan Area, APlan Area, A
Ultimate Bearing CapacityUltimate Bearing Capacity qquu == FFfailfail / A/ A
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Foundation FailureFoundation Failure
ForceForceRotational FailureRotational Failure
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Soil HeaveSoil Heave ResistanceResistance
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Pola Keruntuhan
General Failure
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Local Shear Failure
Punching Shear Failure
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General Failure
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Local Shear Failure
Punching Shear Failure
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FOUNDATION FAILURE1.Generalized Shear FailureFOUNDATION FAILURE1.Generalized Shear Failure
Soil FailureSoil Failure
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Soil FailureSoil FailureLinesLines
rigidrigidradialradialshearshear
passivepassive
log spirallog spiral
SettlementSettlement
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2. Local Shear Failure2. Local Shear Failure
minor surfaceminor surface
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Medium denseMedium denseor firm soilsor firm soils
minor surfaceminor surfaceheave onlyheave only
SettlementSettlement
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3. Punching Shear Failure3. Punching Shear Failure
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Loose orLoose orSoft SoilsSoft Soils
No surfaceNo surfaceheaveheave SettlementSettlement
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Perhitungan Daya Dukung
Untuk menghitung daya dukung dapat dilakukan dengan analisisis berdasarkan :
� Data Uji Laboratorium:Teori TerzaghiTeori Meyerhof
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Teori MeyerhofTeori Brinch HansenTeori Vesic
� Data Uji Lapangan :Plate Bearing TestCone Penetration Test/CPT (SondirStandard Penetration Test/SPT
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Aplikasi Teori Daya Dukung
KEMIRINGAN TERZAGHI MEYERHOF HANSEN VESIC
BEBAN 0 θ θ θ
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MUKA TANAH
0 0 β β
DASAR PONDASI
0 0 δ δ
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Daya Dukung Terzaghi
Anggapan-anggapan:
1. Tanah homogen isotropik2. Mode keruntuhan pondasi adalah
adalah general shear failure3. Pondasi adalah strip dengan
permukaan bawah kasar4. Bidang keruntuhan geser diatas
permukaan tanah diabaikan
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permukaan tanah diabaikan5. Permukaan tanah adalah
horizontal6. Tidak terdapat gaya horizontal,
momen dan eksentrisitas7. Pondasi terletak pada kedalaman
D<B8. Daerah elastis mempunyai sudut
batas yang lurus dengan bid. horizontal
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Keseimbangan Gaya
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Keseimbangan gaya-gaya yang bekeja pada baji tanah (soil wedge) adalah:
Qu.(2b).1 = - W + 2.CsinΦ + 2.Pp
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1 2
1
2 γγ γ= + +f c qq cN DN B N
Strip footing
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1 2
1
2 γγ γ= + +f c qq cN DN B N
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Faktor Daya Dukung Tanah Menurut Terzaghidan Berbagai Nilai Nγγγγ yang Berbeda
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Terzaghi Bearing EquationTerzaghi Bearing Equation
� applies to strip footing� Nc, Nq and Nγ are functions of φ, and are
usually given in graphical form
qqu nettu nett = c.N= c.Nc c + p'+ p'o o ((NNqq -- 1) + 0.51) + 0.5BBγγγγγγγγ'N'Nγγγγγγγγ
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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 EquationTerzaghi Bearing Equation
qqu nettu nett = c.N= c.Nc c + p'+ p'o o ((NNqq -- 1) + 0.51) + 0.5BBγγγγγγγγ'N'Nγγγγγγγγ
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Bp'p'o o = = γγγγγγγγ''oo DD
Generalized soil strength : c, Generalized soil strength : c, φφφφφφφφ(drainage as applicable)(drainage as applicable)
Soil unit weight : Soil unit weight : γγγγγγγγ'' (total or(total oreffective as applicable)effective as applicable)
Overburden
Failure Zone (depth ≈≈≈≈ 2B)
Adopt weighted average values !Adopt weighted average values !
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Bearing Capacity Factors
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Faktor daya dukung Terzaghi
φ
φφπ
aN
ea
q
tg
)45(cos2 2
2
)24
3(
+=
=−
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φφ
φ
φ
γ tgNN
jikaN
ctgNN
q
c
qc
).1(2
0:7,5
).1(
)2
45(cos2 2
+===
−=
+
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Faktor daya dukung Terzaghi
φ
φφπ
ctgNN
tgeN
qc
tgq
).1(
)2
45(2.
−=
+=
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φφ
φ
γ tgNN
jikaN
ctgNN
q
c
qc
).1(2
0:7,5
).1(
+===
−=
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Faktor Daya Dukung
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Bearing capacity factors
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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
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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
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Faktor Daya DukungFaktor Daya Dukung
10001000
100100
Bea
ring
Cap
acity
Fac
tor
Bea
ring
Cap
acity
Fac
tor
NcNcNqNq
NNqq = 33= 33 NNγγγγγγγγ
NNγγγγγγγγ = 250= 250
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1010
11
0.10.100 1010 2020 3030 4040 5050
Bea
ring
Cap
acity
Fac
tor
Bea
ring
Cap
acity
Fac
tor
Friction Angle (deg)Friction Angle (deg)
1414oo
NNcc = 10= 10
3535oo 4646oo
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Persamaan Daya Dukung MeyerhofPersamaan Daya Dukung Meyerhof
qquu = c.N= c.Nccssccddcc ii cc + q.N+ q.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBNBNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = = cc.N.Nccssccddcc ii cc + q.N+ q.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBNBNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = c.N= c.Nccssccddcc ii cc + q.N+ q.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBNBNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = c.N= c.Nccssccddcc ii cc + q.N+ q.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBBNNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = c.N= c.Nccssccddcc ii cc + + qq.N.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBNBNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = c.= c.NNccssccddcc ii cc + q.+ q.NNqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBBNNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = c.N= c.Nccssccddcc ii cc + q.N+ q.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBNBNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγ
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cc
φφφφφφφφ
soil density, soil density, γγγγγγγγ, , ((kN/mkN/m33))BB
DDff q = q = γγγγγγγγ.D.Dff
•• Bearing Capacity Factors for soilBearing Capacity Factors for soil
cohesion, surcharge and weightcohesion, surcharge and weight
•• functions of friction angle, functions of friction angle, φφφφφφφφ•• determine by equation or from graphdetermine by equation or from graph
•• Correction factors for footing shape Correction factors for footing shape ((ss )),,
footing depth footing depth ((dd) ) and load inclination and load inclination ((i i ).).
•• determine from appropriate equationsdetermine from appropriate equations
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Faktor daya dukung Meyerhof
).1(
)2
45(2.
φ
φφπ
ctgNN
tgeN
qc
tgq
−=
+=
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).4,1().1(
0:14,5
).1(
φφ
φ
γ tgNN
jikaN
ctgNN
q
c
qc
−===
−=
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Faktor daya dukung Hansen
φ
φφπ
ctgNN
tgeN
qc
tgq
).1(
)2
45(2.
−=
+=
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φφφ
γ tgNN
jikaN
ctgNN
q
c
qc
).1(5,1
0:14,5
).1(
−===
−=
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Faktor daya dukung Vesic
φ
φφπ
ctgNN
tgeN
qc
tgq
).1(
)2
45(2.
−=
+=
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φφφ
γ tgNN
jikaN
ctgNN
q
c
qc
).1(2
0:14,5
).1(
−===
−=
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Pengaruh Muka air
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Pondasi dengan Beban MomenPondasi dengan Beban Momen
P
M
eP
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e
e = MPekivalen eksentrisitas beban
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Cara Meyerhof menentukan eksentrisitas beban
Cara Meyerhof menentukan eksentrisitas beban
ee
L
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PP
ee
2e LL' = LL -- 22ee
B
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Eksentrisitas 2 arahEksentrisitas 2 arah
ee11
LL
22ee22
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PP
ee11
22ee11 LL' = LL -- 22ee11
BB ee2 2
BB' =
BB--
22ee22
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Daya Dukung Berdasar Data Uji Lapangan (In Situ Test)
� Plate Bearing Test (Uji Pembebanan Pelat)Standard Penetration Test (SPT)
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� 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 konstanB < 4 Bp
� Tanah Dengan Kekuatan Meningkat puu qq ,=
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� Tanah Dengan Kekuatan Meningkat Secara Linear Thd Kedalaman
B < 4 Bp
� Ekstrapolasi Hasil Uji Penurunan Terzaghi & Peck.
ppuu B
Bqq ,=
i
qq ρ
5,11 =
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Standard Penetration Test (SPT)
� PONDASI TELAPAK (FOOTING)MEYERHOF (1956,1974)
Dimana :qa,1 = daya dukung ijin utk penurunan 1 inchi
dn
a KF
NqftB
11,4 =→≤
2
3
21,4
+=→>B
FB
F
NqftB n
a
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qa,1 = daya dukung ijin utk penurunan 1 inchiKd = 1+0,33 D/B≤1,33Nn = SPT yang dikoreksiF = faktor tergantung energi pukulan SPT
� PONDASI PELAT (MAT/RAFT)
dn
a KF
Nq
31, =
1,aa qq ρ=
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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
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u cBUJUR SANGKAR : qu = 48 – 0,0090(300-qc)1,5
� DAYA DUKUNG BATAS PADA TANAH KOHESIF
MENERUS : qu = 2 + 0,28 qcBUJUR SANGKAR : qu = 5 + 0,34 qc
qu dan qc dalam tsf atau kg/cm2
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Belajar
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Jangan tunggu sampai menit terakhir.
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Exams
My mama always said, “Exam is like a box of chocolates; you never know what you
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of chocolates; you never know what you are gonna get”
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