Data Sondir
S1 S2 S3
0.2 20 0.2 10 0.2 100.4 10 0.4 6 0.4 80.6 10 0.6 6 0.6 80.8 5 0.8 5 0.8 121 5 1 5 1 12
1.2 5 1.2 5 1.2 101.4 5 1.4 5 1.4 101.6 8 1.6 10 1.6 101.8 8 1.8 10 1.8 182 10 2 8 2 25
2.2 8 2.2 12 2.2 222.4 25 2.4 10 2.4 252.6 35 2.6 15 2.6 202.8 40 2.8 15 2.8 173 47 3 19 3 20
3.2 10 3.2 15 3.2 153.4 15 3.4 20 3.4 103.6 35 3.6 25 3.6 103.8 40 3.8 40 3.8 104 45 4 40 4 10
4.2 40 4.2 58 4.2 204.4 38 4.4 45 4.4 204.6 38 4.6 37 4.6 204.8 40 4.8 43 4.8 205 40 5 37 5 22
5.2 70 5.2 54 5.2 605.4 85 5.4 60 5.4 455.6 90 5.6 60 5.6 505.8 90 5.8 120 5.8 426 90 6 112 6 57
6.2 80 6.2 100 6.2 506.4 60 6.4 87 6.4 406.6 50 6.6 80 6.6 426.8 70 6.8 85 6.8 377 102 7 90 7 39
7.2 128 7.2 100 7.2 457.4 160 7.4 100 7.4 387.6 215 7.6 110 7.6 40
7.8 120 7.8 37
Kedalaman (m)
Konus (kg/cm2)
Kedalaman (m)
Konus (kg/cm2)
Kedalaman (m)
Konus (kg/cm2)
8 130 8 488.2 145 8.2 508.4 150 8.4 708.6 167 8.6 1098.8 215 8.8 130
9 215
S4 S5
0.2 10 0.2 50.4 3 0.4 50.6 5 0.6 20.8 5 0.8 51 8 1 5
1.2 7 1.2 51.4 8 1.4 101.6 7 1.6 81.8 5 1.8 52 5 2 5
2.2 7 2.2 82.4 20 2.4 202.6 25 2.6 452.8 60 2.8 503 5 3 130
3.2 105 3.2 1703.4 62 3.4 2153.6 403.8 304 20
4.2 234.4 304.6 324.8 255 30
5.2 405.4 405.6 405.8 356 33
6.2 656.4 806.6 576.8 507 40
7.2 457.4 477.6 507.8 52
Kedalaman (m)
Konus (kg/cm2)
Kedalaman (m)
Konus (kg/cm2)
8 608.2 1008.4 1078.6 1508.8 1809 215
STRATIFIKASI DAN PARAMETER TANAH
Water Table :
Soil Sample (m)Log Symbol
General Soil Description
1.50 ~ 1.95 6 12
3.00 ~ 3.45 7 34
4.50 ~ 4.95 9 56
6.00 ~ 6.45 23 78
7.50 ~ 7.95 26 910
9.00 ~ 9.45 32 11
10.50 ~ 10.95 Pasir campur gravel,padat, abu-abu 41
12.00 ~ 12.45 Pasir campur gravel,padat, abu-abu 45
13.50 ~ 13.73 50
15.00 ~ 15.45 55
16.50 ~ 16.75 50
18.00 ~ 18.36 50
19.50 ~ 19.85 50
21.00 ~ 21.45 58
22.50 ~ 22.95 Pasir, padat, hitam 43
24.00 ~ 24.45 Pasir, padat, hitam 47
25.50 ~ 25.95 Pasir, padat, hitam 49
27.00 ~ 27.45 Pasir, padat, hitam 46
28.50 ~ 28.95 55
30.00 ~ 30.45 55
Nilai NsptLapisan Tanah
Lanau kelempungan, konsistensi sedang, abu-abu kecoklatan
Lanau kelempungan, konsistensi sedang, abu-abu kecoklatan
Lanau kelempungan, teguh, abu-abu kecoklatan
Lanau kelempungan, sangat teguh, abu-abu kehitaman
Lanau kelempungan, sangat teguh, abu-abu kehitaman
Lanau kelempungan, keras, abu kehitaman
Pasir, sangat padat, abu-abu kehitaman
Pasir campur gravel, sangat padat, hitam dan coklat
Pasir campur gravel, sangat padat, hitam dan coklat
Pasir campur gravel, sangat padat, hitam dan coklat
Pasir, sangat padat, hitam dan coklat
Pasir, sangat padat, hitam dan coklat
Pasir, sangat padat, hitam dan coklat
Pasir, sangat padat, hitam dan coklat
30.00 ~ 30.45 55Pasir, sangat padat, hitam dan coklat
STRATIFIKASI DAN PARAMETER TANAH
Water Table : 5.5 m
Kedalaman (m) Jenis Tanahσ σ'
φcu
0.00 ~ 0.70 Timbunan 1.00 1.38 1.52 0.97 0.48 0 0.710.70 ~ 3.60 Lanau 6.00 1.54 1.69 5.43 3.20 0 0.713.60 ~ 5.50 Lanau 9.00 1.58 1.74 8.44 6.93 0 2.865.50 ~ 8.50 Lanau 23.00 1.63 1.80 13.34 11.14 0 5.00
8.50 ~ 9.70 Lanau 32.00 1.66 1.82 15.33 11.44 0 15.369.70 ~ 12.50 Pasir 41.00 1.75 1.93 20.24 13.83 45 0
12.50 ~ 15.00 Pasir 50.00 1.83 2.02 24.82 15.76 47.5 015.00 ~ 18.65 Pasir 50.00 1.85 2.04 31.58 19.04 47.5 018.65 ~ 22.00 Pasir 50.00 1.94 2.13 38.07 22.00 47.5 022.00 ~ 27.50 Pasir 43.00 1.96 2.15 48.83 27.49 45.5 027.45 ~ 30.45 Pasir 46.00 1.97 2.17 54.75 30.14 46 0
Nilai Nspt
ϒn ϒsat
(t/m3) (t/m3) (t/m2) (t/m2) (kg/cm2)
Tabel Hubungan Shear Strain dan G/Su
Tabel Korelasi N Value Dengan Kuat Geser Tanah
STRATIFIKASI DAN PARAMETER TANAH
E Su
7.60 0.35 0.7145.60 0.34 0.7168.40 0.33 2.86
174.80 0.31 5.00
243.20 0.29 15.36311.60 0.27 1.00380.00 0.25 1.09380.00 0.25 1.09380.00 0.25 1.09326.80 0.26 1.02349.60 0.26 1.04
Poisson's Ratio (ν)
Shear Strain(ton/m2) (kg/cm2)
Tabel Hubungan Shear Strain dan G/Su
BAB IIIANALISIS PONDASI DINAMIS
STRATIFIKASI DAN PARAMETER TANAH
Data Titik Sondir 5
Jenis Tanah σ σ' φ cu E Su
1 0.20 Timbunan 5.00 1.36 1.50 0.27 0.14 0 0.36 10.00 0.35 0.36 0.001 1600 0.035 571.42862 0.40 Timbunan 5.00 1.37 1.51 0.55 0.55 0 0.36 10.00 0.35 0.36 0.001 1600 0.035 571.42863 0.60 Timbunan 2.00 1.37 1.51 0.82 0.82 0 0.14 4.00 0.35 0.14 0.001 1600 0.035 228.57144 0.80 Lanau 5.00 1.40 1.54 1.10 1.10 0 0.36 10.00 0.35 0.36 0.001 1600 0.035 571.42865 1.00 Lanau 5.00 1.43 1.57 1.39 1.39 0 0.36 10.00 0.35 0.36 0.001 1600 0.035 571.42866 1.20 Lanau 5.00 1.46 1.61 1.68 1.68 0 0.36 10.00 0.35 0.36 0.001 1600 0.035 571.42867 1.40 Lanau 10.00 1.47 1.62 1.97 1.97 0 0.71 20.00 0.35 0.71 0.001 1600 0.035 1142.8578 1.60 Lanau 8.00 1.49 1.64 2.27 2.27 0 0.57 16.00 0.35 0.57 0.001 1600 0.035 914.28579 1.80 Lanau 5.00 1.50 1.65 2.57 2.57 0 0.36 10.00 0.35 0.36 0.001 1600 0.035 571.4286
10 2.00 Lanau 5.00 1.57 1.73 2.88 2.88 0 0.36 10.00 0.35 0.36 0.001 1600 0.035 571.428611 2.20 Lanau 8.00 1.68 1.85 3.22 3.22 0 0.57 16.00 0.35 0.57 0.001 1600 0.035 914.285712 2.4 Lanau 20 1.68 1.85 3.56 3.56 0 1.43 40.00 0.35 1.43 0.002 1600 0.035 2285.71413 2.6 Lanau 45 1.71 1.88 3.90 3.90 0 3.21 90.00 0.35 3.21 0.003 1600 0.035 5142.85714 2.8 Lanau 50 1.73 1.90 4.24 4.24 0 3.57 100.00 0.34 3.57 0.003 1500 0.035 5357.14315 3 Lanau 130 1.77 1.95 4.60 4.60 0 9.29 260.00 0.33 9.29 0.006 1300 0.035 12071.4316 3.2 Lanau 170 1.78 1.958 4.95 4.95 0 12.14286 340 0.33 12.14286 0.006 1300 0.035 15785.7117 3.4 Lanau 215 1.78 1.958 5.31 5.31 0 15.35714 430 0.25 15.35714 0.006 1300 0.035 19964.29
Lapisan Tanah
Kedalaman (m)
qc ϒn ϒsat Poisson's Ratio (ν)
Shear Strain Dumping
Ratio
Shear Modulus(kg/cm2) (t/m3) (t/m3) (t/m2) (t/m2) (kg/cm2) (ton/m2) (kg/cm2)
𝐺/𝑆𝑢
TR-51ECNC TAPPING CENTER SPECIFICATION
SPECIFICATION
A. Trial Dimensi Pondasi1. Dimensi "Badan" Pondasi
Panjang : 98 cm
Lebar : 39 cm
Tinggi : 110 cm
2. Dimensi "Kaki" Pondasi
Panjang : 109 cmLebar : 328 cmTinggi : 58 cm
3. Kontrol Berat Pondasi
Berat Badan = 1009.008 KgBerat Kaki = 4976.6784 KgBerat Total = 5985.6864 Kg
Berat Mesin = 42300 kg
Kontrol : Berat Pondasi > 3 x Berat Mesin
5985.6864 >0.142
B. Perhitungan Pondasi Statis
1. Peritungan Daya Dukung (Metode Terzaghi)0.98 m
0.39 m Pondasi diletakan pada kedalaman 2.4 m
1.1 m Maka, parameter tanahnya didapat :
φ
1.09 m 03.28 m0.58 m
Rumus Daya Dukung Tanah Metode Terzaghi :
qu = 1.3 C. Nc + q. Nq + 0.4 γm . B. Nγ
BJ Beton = 2400 qu = DD =
Kontrol :
Berat Pondasi > 3 x Berat Mesin
Kg/m3
423000.142 Kali Berat Mesin Cek
B. Perhitungan Pondasi Statis
1. Peritungan Daya Dukung (Metode Terzaghi)
Pondasi diletakan pada kedalaman 2.4 m
Maka, parameter tanahnya didapat :
cNc Nq
1.43 1.68 1.85 5.70 1.00 0.00
Rumus Daya Dukung Tanah Metode Terzaghi :
qu = 1.3 C. Nc + q. Nq + 0.4 γm . B. Nγ
3890.0013907.53 ton
DD > Berat Mesin + Pondasi13907.53 > 48.28569 OK!!
ϒn ϒsatNϒ
kg/cm2 kg/m3 kg/m3
t/m2
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
(t/m2
)
(m)
C. Resume1. Parameter Tanah dan Pondasi 3. Data Peralatan Mesin
Daya Dukung Tanah 3890.00 Weight of Table 250
Modulus Geser (G) 898990.00 Weight of Tools 3
Internal Damping Ratio 0.049 Weight of Machines 423000.39 Total Weight 42300
Berat Jenis Tanah 16.80
Berat Jenis Beton 2.4
2. Data Pondasi 4. Data Mesin
"Badan Pondasi" Kecepatan blower 3890Panjang (P) 0.98 m Kecepatan motor 1589Lebar (l) 0.39 m Unbalanced Force 0.089
Tinggi (t) 1.1 m"Kaki Pondasi"
Panjang (P) 1.09 mLebar (l) 3.28 mTinggi (t) 0.58 m
t/m2
t/m2
Poisson's Ratio (ν)t/m3
t/m3
3. Data Peralatan Mesin
kg
kg
kgkg
4. Data Mesin
rpmrpmton
3.245 kN 1.000 tm0.325 ton
0.261 tm0.847 kN0.085 ton
3. Geometri Pondasi 4. Geometri Mesin
B = 1.55 m0.39 m L = 2.52 m0.98 m H = 2.8 m1.1 m
3.28 m1.09 m0.58 m
h = 1.68 m
5. Spek Mesin
Kecepatan Spindle : 3890 rpmKecepatan Tapping : 1589 rpm
Berat Total Mesin 42.3 ton
6. Parameter Tanah
Daya Dukung Tanah 3890.00
Modulus Geser (G) ###Damping Ratio 0.05
0.39
Berat Jenis Tanah 16.80
Berat Jenis Beton 2.40
1. Centrifugal Force 2. Rocking Dynamic Moment
a. For Spindle a. For Spindle
F0 = 0.001 x W x (rpm/1000)1.5 Mr = Fo x (h + hC.G Machine)F0 = Mr =F0 = b. For Tappingb. For Tapping Mr = Fo x (h + hC.G Machine)
F0 = 0.001 x W x (rpm/1000)1.5 Mr =F0 =F0 =
"Badan Pondasi"Bp =Lp =Hp =
"Kaki Pondasi"Bk =Lk =Hk =
t/m2
t/m2
Poisson's Ratio (ν)
t/m3
t/m3
L/B Koefisien
0.3 2.190.3 10.3 0.5
7. Koefisien βv, βh, βr 8. Vertical Excitation Analysis
βv =βh =βr =
8.1 Spring Constant 8.2 Damping Ratio
2.329
1.067 m
0.3621.474
βv = 2.191.646
0.05
8982051.183 t/m
1.695
8. Vertical Excitation Analysis
a. Radius Equivalent (rov) for Rectangular Foundation a. Effect of Depth of Embedment on Damping Ratio
αv =
rov =b. Mass Ratio
b. Embedment Factor for Spring Constant
Bv = (1-ν)/4 x W/(ϒ x rov3)ηv = 1 + 0.6 x (1-ν) x (h/rov) Bv = ηv =
c. Geometrical Damping Ratioc. Spring Constant Coefficient
Dv =d. Equivalent Spring Constant for Rectangular Foundation
d. Internal Damping
Dvi =
Kv = d. Total Damping Ratio
Dvt = Dv + Di
Dvt =
𝑟_𝑜𝑣= √((𝐵_𝑘 𝑥 𝐿_𝑘)/𝜋)
𝐾_𝑣=𝐺/((1−𝑣)) . 𝛽_(𝑣 ). √(𝐵 𝑥 𝐿) . 𝑛_𝑣
𝛼_𝑣= [1+1.9.(1−𝑣). ℎ/𝑟_𝑜𝑣 ]/√(𝑛_𝑣 )
𝐷_𝑣=0.425/√(𝐵_𝑣 ).𝛼_𝑣
8.3 Frequency Check
### rpm
#NUM! # 3.390428 RESONANCE NOT POSSIBLE !!!
0.302 0.123
7.31E-01 OK
9.35E-01 OK
e. Transmissibility Factor
1.045
1.013
1.17E-07 m
Effect of Depth of Embedment on Damping Ratio a. Natural Frequency
Fnv =
b. Resonance Frequency (rpm)
Frv = 2 x Dvt =
c. Frequency Ratio
rv (spindle) = rv (tapping) =
d. Magnification Factor
Mv(spindle) =
Mv(tapping) =
Tv(spindle) =
Tv(tapping) =
f. Vibration Amplitude
V(spindle) = Mv(spindle) + Fo(spindle) / Kv Vrocking(spindle) =V(spindle) = Vrocking(spindle) =
𝛼_𝑣= [1+1.9.(1−𝑣). ℎ/𝑟_𝑜𝑣 ]/√(𝑛_𝑣 ) 𝐹_𝑛𝑣=60/(2𝑥𝜋)𝑥√((𝐾_𝑣/𝑚))
𝐹_𝑟𝑣= 𝐹_𝑛𝑣 𝑥√([1−[2𝑥𝐷_𝑣𝑡^2 ]] )
〖𝑟𝑣〗 _𝑠𝑝𝑖𝑛𝑑𝑙𝑒= 𝑓_𝑣/𝐹_𝑛𝑣 〖𝑟𝑣〗 _𝑡𝑎𝑝𝑝𝑖𝑛𝑔= 𝑓_𝑣/𝐹_𝑛𝑣
𝑀_(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=1/√((1−𝑟_(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))^2 )^2+〖 (2 _ _( (𝐷 𝑣𝑡 𝑥𝑟 𝑣 𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗 ^2 )𝑀_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=1/√((1−𝑟_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))^2 )^2+〖 (2 _ _( (𝐷 𝑣𝑡 𝑥𝑟 𝑣 𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗 ^2 )
𝑇_(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=𝑀_(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 𝑥√(1+〖 (2 _ _( (𝐷 𝑣𝑡 𝑥𝑟 𝑣 𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗 ^2 )𝑇_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=𝑀_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 𝑥√(1+〖 (2 _ _( (𝐷 𝑣𝑡 𝑥𝑟 𝑣 𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗 ^2 )
1.14E-07 m
2.31E-07 m
V(tapping) = Mv(tapping) + Fo(tapping) / Kv Vrocking(tapping) =V(tapping) = Vrocking(tapping) =
g. Vtotal
Vtotal = (V(spindle) + Vrocking(spindle))+ (V(tapping) + Vrocking(tapping))Vtotal =
RESONANCE NOT POSSIBLE !!!
0.00E+00 mR(spindle) x (l/2)
0.00E+00 mR(tapping) x (l/2)
Vrocking(tapping))
3.245 kN 1.000 tm0.325 ton
0.261 tm0.847 kN0.085 ton
4. Geometri Pondasi 5. Geometri Mesin
B = 1.55 m0.39 m L = 2.52 m0.98 m H = 2.8 m1.1 m
3.28 m1.09 m0.58 m
h = 1.68 m
6. Spek Mesin
Kecepatan Spindle : 3890 rpmKecepatan Tapping : 1589 rpm
Berat Total Mesin 42.3 ton
7. Parameter Tanah
Daya Dukung Tanah 3890.00
Modulus Geser (G) ###Damping Ratio 0.05
0.39
Berat Jenis Tanah 16.80
Berat Jenis Beton 2.40
1. Centrifugal Force 2. Rocking Dynamic Moment
a. For Spindle a. For Spindle
F0 = 0.001 x W x (rpm/1000)1.5 Mr = Fo x (h + hC.G Machine)F0 = Mr =F0 = b. For Tappingb. For Tapping Mr = Fo x (h + hC.G Machine)
F0 = 0.001 x W x (rpm/1000)1.5 Mr =F0 =F0 =
"Badan Pondasi"Bp =Lp =Hp =
"Kaki Pondasi"Bk =Lk =Hk =
t/m2
t/m2
Poisson's Ratio (ν)
t/m3
t/m3
L/B Koefisien
0.3 2.20.3 10.3 0.52
3. Koefisien βv, βh, βr 9. Horizontal Excitation Analysis
βv =βh =βr =
𝐾_ℎ=2𝑥(1+𝑣).𝐺 . 𝛽_(ℎ ). √(𝐵 𝑥 𝐿) . 𝑛_ℎ
9.1 Spring Constant 9.2 Damping Ratio
3.761
1.067 m
0.4712.395
βh = 11.579
0.0511311275.126 t/m
1.628
9. Horizontal Excitation Analysis
a. Radius Equivalent (rov) for Rectangular Foundation a. Effect of Depth of Embedment on Damping Ratio
αh =
roh =b. Mass Ratio
b. Embedment Factor for Spring Constant
Bh = (7-8ν)/(32x(1-ν))x W/(ϒ x roh3)ηh = 1 + 0.55 x (2-ν) x (h/roh) Bh = ηh =
c. Geometrical Damping Ratioc. Spring Constant Coefficient
Dh =d. Equivalent Spring Constant for Rectangular Foundation
d. Internal Damping
Dhi =Kv =
d. Total Damping Ratio
Dht = Dv + Di
Dht =
𝐾_ℎ=2𝑥(1+𝑣).𝐺 . 𝛽_(ℎ ). √(𝐵 𝑥 𝐿) . 𝑛_ℎ
𝛼_ℎ= [1+1.9.(2−𝑣). ℎ/𝑟_𝑜ℎ ]/√(𝑛_ℎ )
𝐷_ℎ=0.288/√(𝐵_ℎ ).𝛼_ℎ
𝑟_𝑜ℎ= √((𝐵_𝑘 𝑥 𝐿_𝑘)/𝜋)
9.3 Frequency Check
### rpm
#NUM! # 3.255032 RESONANCE NOT POSSIBLE !!!
0.269 0.110
7.84E-01 OK
9.52E-01 OK
e. Transmissibility Factor
1.042
1.011
9.80E-08 m
Effect of Depth of Embedment on Damping Ratio a. Natural Frequency
Fnh =
b. Resonance Frequency (rpm)
ν)/(32x(1-ν))x W/(ϒ x roh3)Frh = 2 x Dvt =
c. Frequency Ratio
rh (spindle) = rh (tapping) =
d. Magnification Factor
Mh(spindle) =
Mh(tapping) =
Th(spindle) =
Th(tapping) =
f. Vibration Amplitude
V(spindle) = Mh(spindle) + Fo(spindle) / Kh Vrocking(spindle) =V(spindle) = Vrocking(spindle) =
𝛼_ℎ= [1+1.9.(2−𝑣). ℎ/𝑟_𝑜ℎ ]/√(𝑛_ℎ ) 𝐹_𝑛ℎ=60/(2𝑥𝜋)𝑥√((𝐾_ℎ/𝑚))
𝐹_𝑟ℎ= 𝐹_𝑛ℎ 𝑥√([1−[2𝑥𝐷_ℎ𝑡^2 ]] )
ℎ〖𝑟 〗 _𝑠𝑝𝑖𝑛𝑑𝑙𝑒= 𝑓_ℎ/𝐹_𝑛ℎ ℎ〖𝑟 〗 _𝑡𝑎𝑝𝑝𝑖𝑛𝑔= 𝑓_ℎ/𝐹_𝑛ℎ
𝑀_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=1/√((1−𝑟_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))^2 )^2+〖 (2𝐷_ℎ𝑡 𝑥𝑟_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗 ^2 )𝑀_(ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=1/√((1−𝑟_(ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))^2 )^2+〖 (2 _𝐷 ℎ _(𝑡 𝑥𝑟 ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗 ^2 )
𝑇_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=𝑀_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 𝑥√(1+〖 (2 _𝐷 ℎ _(𝑡 𝑥𝑟 ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗 ^2 )𝑇_(ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=𝑀_(ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 𝑥√(1+〖 (2 _𝐷 ℎ _(𝑡 𝑥𝑟 ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗 ^2 )
9.16E-08 m
1.90E-07 m
V(tapping) = Mh(tapping) + Fo(tapping) / Kh Vrocking(tapping) =V(tapping) = Vrocking(tapping) =
g. Vtotal
Vtotal = (V(spindle) + Vrocking(spindle))+ (V(tapping) + Vrocking(tapping))Vtotal =
RESONANCE NOT POSSIBLE !!!
0.000 mR(spindle) x (h+C.G)
0.000 mR(tapping) x (l/2)
Vrocking(tapping))
3.245 kN 1.000 tm0.325 ton
0.298 tm0.967 kN
0.097 ton
4. Geometri Pondasi 5. Geometri Mesin
B = 1.55 m
0.39 m L = 2.52 m
0.98 m H = 2.8 m1.1 m
3.28 m1.09 m
0.58 m
h = 1.68 m
6. Spek Mesin
Kecepatan Spindle : 3890 rpmKecepatan Tapping : 1589 rpm
Berat Total Mesin 42.3 ton
7. Parameter Tanah
Daya Dukung Tanah 3890.00
Modulus Geser (G) ###Damping Ratio 0.05
0.39
Berat Jenis Tanah 16.80
Berat Jenis Beton 2.40
1. Centrifugal Force 2. Rocking Dynamic Moment
a. For Spindle a. For Spindle
F0 = 0.001 x W x (rpm/1000)1.5 Mr = Fo x (h + hC.G Machine)F0 = Mr =F0 = b. For Tappingb. For Tapping Mr = Fo x (h + hC.G Machine)
F0 = 0.001 x W x (rpm/1000)1.5 Mr =F0 =
F0 =
"Badan Pondasi"
Bp =
Lp =Hp =
"Kaki Pondasi"Bk =Lk =
Hk =
t/m2
t/m2
Poisson's Ratio (ν)
t/m3
t/m3
L/B Koefisien
0.3 2.20.3 10.3 0.54
3. Koefisien βv, βh, βr 10. Rocking Excitation Analysis
βv =βh =βr =
𝐾_𝑟=𝐺/((1−𝑣) ) 𝑥 〖 〗𝛽 _𝑟 𝑥 𝐿 𝑥 𝐵^3 𝑥 𝑛_𝑟
10.1 Spring Constant 10.2 Damping Ratio
1.020 m 3.153
3.646 401.27472
6.2745194692βr = 0.54
407.549239469
5.028111415421.972 t/m
1.010
0.030
10. Rocking Excitation Analysis
a. Radius Equivalent (rov) for Rectangular Foundation a. Effect of Depth of Embedment on Damping Ratio
ror = αr =
b. Embedment Factor for Spring Constant b. Mass Ratio
ηr = 1 + 1.2 x (1-ν) x (h/ror) + 0.2 x (2-ν) x (h/ror)3 Imachine = W x (h + C.G)2
ηr = Imachine =
c. Spring Constant Coefficient Ifoundation = Σ(Wf /12.(a2+b2) + Wf.k2)
Ifoundation =
Io= Imachine + Ifoundation
d. Equivalent Spring Constant for Rectangular Foundation Io=
Br = 3 x (1-ν)/8 x Io /(ϒ x ror5)Br =
Kr =
c. Effective Damping Coefficient
ηr =
d. Geometrical Damping Ratio
Dr =
e. Internal Damping
𝑟_𝑜𝑟= [(𝐿_𝑘 𝑥 𝐵_𝑘^3 )/(3 𝑥 𝜋)]^(1/4)
𝐾_𝑟=𝐺/((1−𝑣) ) 𝑥 〖 〗𝛽 _𝑟 𝑥 𝐿 𝑥 𝐵^3 𝑥 𝑛_𝑟
𝛼_𝑟= (1+0.7 𝑥 (1−𝑣)𝑥 (ℎ/𝑟_𝑜𝑟 )+0.6 𝑥 (2−𝑣)𝑥 (ℎ/𝑟_𝑜𝑟 )^3)/√(𝑛_𝑟 )
𝐷_𝑟=0.15 𝑥 𝛼_𝑟/[(1+ 𝑛_𝑟+ 𝛽_𝑟 )𝑥 √((𝑛_𝑟 𝑥 𝛽_𝑟))]
0.05
0.079
Dri =
d. Total Damping Ratio
Drt = Dr + Di
Drt =
10.3 Frequency Check
4992.913 rpm
4961.7951 RESONANCE NOT POSSIBLE !!!
0.779 0.318
2.43E+00 cek
1.11E+00 OK
e. Transmissibility Factor
2.45E+00
1.11E+00
Moment Arm =
Effect of Depth of Embedment on Damping Ratio a. Natural Frequency
Fnr =
b. Resonance Frequency (rpm)
t/m2 Frr=
/12.(a2+b2) + Wf.k2) c. Frequency Ratio
t/m2
machine + Ifoundation
t/m2 rr(spindle) = rr (tapping) =
3 x (1-ν)/8 x Io /(ϒ x ror5) d. Magnification Factor
Effective Damping Coefficient
Mr(spindle) =
Mr(tapping) =
Tr(spindle) =
Geometrical Damping Ratio
Tr(tapping) =
f. Vibration Amplitude
R(spindle) = Mr(spindle) + Fr(spindle) / Kr
𝛼_𝑟= (1+0.7 𝑥 (1−𝑣)𝑥 (ℎ/𝑟_𝑜𝑟 )+0.6 𝑥 (2−𝑣)𝑥 (ℎ/𝑟_𝑜𝑟 )^3)/√(𝑛_𝑟 )
𝐷_𝑟=0.15 𝑥 𝛼_𝑟/[(1+ 𝑛_𝑟+ 𝛽_𝑟 )𝑥 √((𝑛_𝑟 𝑥 𝛽_𝑟))]
𝐹_𝑛𝑟=60/((2𝑥𝜋) ) 𝑥 √(𝐾_𝑟/𝐼_0 )
𝐹_𝑟𝑟= 𝐹_𝑛𝑟 𝑥√([1−[2𝑥𝐷_𝑟𝑡^2 ]] )
𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))= 𝑓_𝑟/𝐹_𝑛𝑟 𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))= 𝑓_𝑟/𝐹_𝑛𝑟
𝑀_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=1/√((1−𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))^2 )^2+〖 (2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗 ^2 )𝑀_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=1/√((1−𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))^2 )^2+〖 (2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗 ^2 )
𝑇_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=𝑀_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 𝑥√(1+〖 (2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗 ^2 )𝑇_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=𝑀_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 𝑥√(1+ 〖 (2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗 ^2 )
2.43E+00 rad Moment Arm =
1.11E+00 rad
R(spindle) =
R(tapping) = Mr(tapping) + Fr(tapping) / Kr
R(tapping) =
11. Amplitudo Check
2.31E-07 m0.000 cm
RESONANCE NOT POSSIBLE !!! 1.90E-07 m0.000 cm
0.00001 in
Moment Arm = (h + C.G)
11.1 Total Amplitudoa. Vertical Amplitudo
Vtotal = Vertical Vibration Amplitude + Rocking Vibration Amplitude x (B/2)Vtotal =Vtotal =
b. Horizontal Amplitude
Htotal = Horizontal Vibration Amplitude + Rocking Vibration Amplitude x (h + C.G)
Htotal =Htotal =
Htotal =
c. Maximum Velocity
𝑀_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=1/√((1−𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))^2 )^2+〖 (2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗 ^2 )𝑀_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=1/√((1−𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))^2 )^2+〖 (2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗 ^2 )
𝑇_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=𝑀_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 𝑥√(1+〖 (2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗 ^2 )𝑇_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=𝑀_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 𝑥√(1+ 〖 (2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗 ^2 )
Moment Arm = 3.080 m
Velocity = 0.01 in/secVelocity = 0.00025 m/sec
6.14E-07
Vertical Velocity
4.79E-05
1.89E-05
At(spindle) =
At(spindle) =
c. Vibration Velocity
Vv(spindle) = (V(spindle) + Vrocking(spindle)) x (2 x π x f/60)Vv(spindle) =
Vv(tapping) = (V(tapping) + Vrocking(tapping)) x (2 x π x f/60)Vv(tapping) =
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦/(2.𝜋.𝑚𝑎𝑐ℎ𝑖𝑛𝑒(𝑟𝑝𝑚))
√( 〖𝑉 _(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 〗 ^2+ 〖𝑉_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 〗 ^2 )
5.15E-05
Horizontal Velocity
3.99E-05
1.52E-05
4.27E-05
Vv(total) =Vv(total) =
Vh(spindle) = (H(spindle) + Hrocking(spindle)) x (2 x π x f/60)Vh(spindle) =
Vh(tapping) = (H(tapping) + Hrocking(tapping)) x (2 x π x f/60)Vh(tapping) =
Vh(total) =Vh(total) =
√( 〖𝑉 _(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 〗 ^2+ 〖𝑉_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 〗 ^2 )
√( 〖𝑉 _(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 〗 ^2+ 〖𝑉 _(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 〗 ^2 )
0.3392613 ton
0.09798289 ton
0.43724419 ton
0.33815314 ton
0.09776211 ton
0.43591525 ton
7.18E+00
9.32370151 ton m
12. Soil Bearing Check12.1 Transmissibility Forcea. Transmissibility Vertical Force
Rocking Vibration Amplitude x (B/2) Pv (spindle) = (Tv(spindle) x F0(spindle))Pv (spindle) =
Pv (tapping) = (Tv(tapping) x F0(tapping))Pv (tapping) =
Rocking Vibration Amplitude x (h + C.G) Pv (total) = Pv (spindle) + Pv (tapping)
Pv (total) =
b. Transmissibility Horizontal Force
Ph (spindle) = (Th(spindle) x F0(spindle))
Ph (spindle) =
Ph (tapping) = (Th(tapping) x F0(tapping))
Ph(tapping) =
Ph (total) = Ph(spindle) + Ph (tapping)
Ph (total) =
c. Transmissibility Moment
Pr = (Tr(spindle) x Mr(spindle)) + (Tr(tapping) x Mr(tapping))
Pr =
12.2 Total Transmissibility Moment
Ptr = Pr + (Pv(total) x (PL/2 + Edx) + (Ph(total) x (C.G + h))Ptr =
6.00963E-05
cek
cek
At(motor) =
At(motor) =
) x (2 x π x f/60)
) x (2 x π x f/60)
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦/(2.𝜋.𝑚𝑎𝑐ℎ𝑖𝑛𝑒(𝑟𝑝𝑚))
cek
cek
cek
cek
) x (2 x π x f/60)
) x (2 x π x f/60)
(ξ) = 1.5
0.75 x qu
2917.5
20.23
6.78
19.20
7.81
Qall = 2917.5
20.23
Qall > Psta+dyn Ok !!
12.3 Soil Bearing Preassure (Static + Dynamic,Static)a. Fatigue Factor (ξ)
b. Qall
Qall =
Qall = t/m2
c. Psta+dyn
Psta+dyn (+) = t/m2
Psta+dyn (-) = t/m2
Psta+dyn (+) = t/m2
Psta+dyn (-) = t/m2
x Mr(spindle)) + (Tr(tapping) x Mr(tapping)) t/m2
Psta+dyn = t/m2
x (PL/2 + Edx) + (Ph(total) x (C.G + h))
𝑃_(𝑠𝑡𝑎+𝑑𝑦𝑛)= 𝑊_𝑡/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_(𝑣(𝑡𝑜𝑡𝑎𝑙)))/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_(ℎ(𝑡𝑜𝑡𝑎𝑙)) 𝑥 (𝐶.𝐺_𝑠ℎ𝑎𝑓𝑡+ℎ)𝑥 6)/(𝐵 𝑥 𝐿^2 ) ± ("ξ" 𝑥 𝑃_𝑟 𝑥 6)/(𝐵 𝑥 𝐿^2 )
𝑃_(𝑠𝑡𝑎+𝑑𝑦𝑛)= 𝑊_𝑡/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_(𝑣(𝑡𝑜𝑡𝑎𝑙)))/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_𝑡𝑟 𝑥 6)/(𝐵 𝑥 𝐿^2 )
𝑃_(𝑠𝑡𝑎+𝑑𝑦𝑛)= 𝑊_𝑡/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_(𝑣(𝑡𝑜𝑡𝑎𝑙)))/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_(ℎ(𝑡𝑜𝑡𝑎𝑙)) 𝑥 (𝐶.𝐺_𝑠ℎ𝑎𝑓𝑡+ℎ)𝑥 6)/(𝐵 𝑥 𝐿^2 ) ± ("ξ" 𝑥 𝑃_𝑟 𝑥 6)/(𝐵 𝑥 𝐿^2 )
𝑃_(𝑠𝑡𝑎+𝑑𝑦𝑛)= 𝑊_𝑡/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_(𝑣(𝑡𝑜𝑡𝑎𝑙)))/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_𝑡𝑟 𝑥 6)/(𝐵 𝑥 𝐿^2 )
A. Trial Dimensi Pondasi1. Dimensi "Badan" Pondasi
Panjang : 262 cm 2.62 mLebar : 165 cm 1.65 mTinggi : 180 cm 1.8 m
2. Dimensi "Kaki" Pondasi
Panjang : 1500 cm 15 mLebar : 1500 cm 15 mTinggi : 60 cm 0.6 m
3. Kontrol Berat Pondasi
Berat Bada 18675.36 Kg BJ Beton = 2400 Kg/m3Berat Kaki 324000 KgBerat Total 342675.36 Kg
Berat Mesi 3200 kg
Kontrol : Berat Pondasi > 3 x Berat Mesin342675.36 > 3200
107 Kali Berat Mesin OK!!
B. Perhitungan Pondasi Statis
1. Peritungan Daya Dukung (Metode Terzaghi)
Pondasi diletakan pada kedalaman 2.4 mMaka, parameter tanahnya didapat :
φ c ϒn ϒsat Nc Nq Nϒkg/cm2 kg/m3 kg/m3
0 1.43 1.68 1.85 5.70 1.00 0.00
Rumus Daya Dukung Tanah Metode Terzaghi :
qu = 1.3 C. Nc + q. Nq + 0.4 γm . B. Nγqu = 451.73 t/m2DD = 101639.81 ton
Kontrol : DD > Berat Mesin + Pondasi101639.81 > 345.8754 OK!!
2. Distribusi Tegangan Metode 2 : 1
h (m)
0.00 1.5370.10 1.517
0.20 1.497
0.30 1.478
0.40 1.458
0.50 1.440
0.60 1.421
0.70 1.403
0.80 1.385
0.90 1.368
1.00 1.351
1.10 1.334
1.20 1.318
1.30 1.302 Rumus :1.40 1.286
1.50 1.270
1.60 1.255 Dimana : Q = Beban Kerja (ton)1.70 1.240 B = Lebar Pondasi (m)1.80 1.225 L = Panjang Pondasi (m)1.90 1.211 z = Kedalaman (m)2.00 1.197
2.10 1.183
2.20 1.169
2.30 1.156
2.40 1.142
2.50 1.129
2.60 1.117
2.70 1.104
2.80 1.092
2.90 1.079
3.00 1.068
3.10 1.056
3.20 1.044
3.30 1.033
3.40 1.022
Δσv' (t/m2)
0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.0000.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
3. Perhitungan Settlement
Dimana ; B = 15.00 m Df/B = 0.16 q = 1.54 t/m2L = 15.00 m h/B = 0.07 Es = 100 kg/cm2Df = 2.40 m L/B = 1.00h = 1.00 m µ1 = 0.99
µ2 = 0.36Df/B µ1 Mencari µ2
0 1h/B Circle L/B
2 0.9 1 2 5 104 0.88 1.00 0.36 0.36 0.36 0.36 0.366 0.875 2.00 0.47 0.53 0.63 0.64 0.648 0.87 4.00 0.58 0.63 0.82 0.94 0.94
10 0.865 6.00 0.61 0.67 0.88 1.08 1.1412 0.863 8.00 0.62 0.68 0.9 1.13 1.2214 0.86 10.00 0.63 0.7 0.92 1.18 1.316 0.856 20.00 0.64 0.71 0.93 1.26 1.4718 0.854 30.00 0.66 0.73 0.95 1.29 1.5420 0.85
Rumus Penurunan :Penurunan Primer : Penurunan Seketika :Sc = mv * Δσ * Δh Si = μ1 x μ2 (q.B/Es)Δh = 3.40 m Si = 0.008235 m
Sc (m)
2.4 40.00 0.0025 1.14 0.0068542.6 90.00 0.0011 1.12 0.0002482.8 100.00 0.0010 1.09 0.0002183 260.00 0.0004 1.07 8.212E-05
3.2 340.00 0.0003 1.04 6.142E-053.4 430.00 0.0002 1.02 4.752E-05
Total 0.007512
Penurunan Total (S) : 0.015747 m1.575 cm
C. Resume1. Parameter Tanah dan Pondasi 3. Data Peralatan Mesin
Daya Dukung Tanah 451.73 t/m2 Weight of Table 250 kgModulus Geser (G) 228.57 t/m2 Weight of Tools 3 kgInternal Damping Ratio 0.035 Weight of Machines 3200 kgPoisson's Ratio (ν) 0.35 Total Weight 3453 kgBerat Jenis Tanah 1.68 t/m3
Berat Jenis Beton 2.4 t/m3
2. Data Pondasi 4. Data Mesin
"Badan Pondasi" Kecepatan Spindle 8000 rpmPanjang (P) 2.62 m Kecepatan Tapping 3000 rpmLebar (l) 1.65 mTinggi (t) 1.8 m
"Kaki Pondasi"Panjang (P) 15 mLebar (l) 15 mTinggi (t) 0.6 m
Kedalaman (m) E (kg/cm2)
mv (m2/ton)
Δσ (ton/m2)
1. Centrifugal Force 2. Rocking Dynamic Moment
a. For Spindle a. For SpindleF0 = 0.001 x W x (rpm/1000)1.5 Mr = Fo x (h + hC.G Machine)F0 = 0.781 kN Mr = 0.297 tmF0 = 0.078 ton b. For Tapping
b. For Tapping Mr = Fo x (h + hC.G Machine)F0 = 0.001 x W x (rpm/1000)1.5 Mr = 0.068 tmF0 = 0.179 kNF0 = 0.018 ton
3. Geometri Pondasi 4. Geometri Mesin
"Badan Pondasi" B = 1.55 mBp = 1.65 m L = 2.52 mLp = 2.62 m H = 2.8 mHp = 1.8 m
"Kaki Pondasi"Bk = 15 m 7. Koefisien βv, βh, βrLk = 15 mHk = 0.6 m L/B Koefisienh = 2.4 m βv = 1.0 2.19
βh = 1.0 1βr = 1.0 0.5
5. Spek Mesin
Kecepatan Spindle : 8000 rpmKecepatan Tapping : 3000 rpm
Berat Total Mesin 3.453 ton
6. Parameter Tanah
Daya Dukung Tanah 451.73 t/m2Modulus Geser (G) 228.57 t/m2Damping Ratio 0.04Poisson's Ratio (ν) 0.35Berat Jenis Tanah 1.68 t/m3
Berat Jenis Beton 2.40 t/m3
8. Vertical Excitation Analysis8.1 Spring Constant 8.2 Damping Ratio 8.3 Frequency Checka. Radius Equivalent (rov) for Rectangular Foundation a. Effect of Depth of Embedment on Damping Ratio a. Natural Frequency
Fnv = 180.749 rpmαv = 1.290
rov = 8.463 m b. Resonance Frequency (rpm)b. Mass Ratio
b. Embedment Factor for Spring Constant Bv = (1-ν)/4 x W/(ϒ x rov3)
ηv = 1 + 0.6 x (1-ν) x (h/rov) Bv = 0.055 Frv = #NUM! # 2 x Dvt = 4.731708 RESONANCE NOT POSSIBLE !!!ηv = 1.097
c. Geometrical Damping Ratio c. Frequency Ratioc. Spring Constant Coefficient
βv = 2.19Dv = 2.331 rv (spindle) = 44.260 rv (tapping) = 16.598
d. Equivalent Spring Constant for Rectangular Foundationd. Internal Damping d. Magnification Factor
Dvi = 0.04
Kv = 12644.594 t/m d. Total Damping Ratio Mv(spindle) = 5.08E-04 OK
Dvt = Dv + DiDvt = 2.366
Mv(tapping) = 3.50E-03 OK
e. Transmissibility Factor
Tv(spindle) = 0.106
Tv(tapping) = 0.275
f. Vibration Amplitude
V(spindle) = Mv(spindle) + Fo(spindle) / Kv Vrocking(spindle) = R(spindle) x (l/2)V(spindle) = 6.22E-06 m Vrocking(spindle) = 0.00E+00 m
V(tapping) = Mv(tapping) + Fo(tapping) / Kv Vrocking(tapping) = R(tapping) x (l/2)V(tapping) = 1.70E-06 m Vrocking(tapping) = 0.00E+00 m
g. Vtotal
Vtotal = (V(spindle) + Vrocking(spindle))+ (V(tapping) + Vrocking(tapping))Vtotal = 7.92E-06 m
𝑟_𝑜𝑣= √((𝐵_𝑘 𝑥 𝐿_𝑘)/𝜋)
𝐾_𝑣=𝐺/((1−𝑣)) . 𝛽_(𝑣 ). √(𝐵 𝑥 𝐿) . 𝑛_𝑣
𝛼_𝑣= [1+1.9.(1−𝑣). ℎ/𝑟_𝑜𝑣 ]/√(𝑛_𝑣 )
𝐷_𝑣=0.425/√(𝐵_𝑣 ).𝛼_𝑣
𝐹_𝑛𝑣=60/(2𝑥𝜋)𝑥√((𝐾_𝑣/𝑚))
𝐹_𝑟𝑣= 𝐹_𝑛𝑣 𝑥√([1−[2𝑥𝐷_𝑣𝑡^2 ]] )
𝑀_(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=1/√((1−𝑟_(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))^2 )^2+〖(2𝐷_𝑣𝑡 𝑥𝑟_(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗̂ 2 )𝑀_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=1/√((1−𝑟_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))^2 )^2+〖(2𝐷_𝑣𝑡 𝑥𝑟_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗̂ 2 )
𝑇_(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=𝑀_(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 𝑥√(1+〖(2𝐷_𝑣𝑡 𝑥𝑟_(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗̂ 2 )𝑇_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=𝑀_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 𝑥√(1+〖(2𝐷_𝑣𝑡 𝑥𝑟_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗̂ 2 )
〖 〗𝑟𝑣 _𝑠𝑝𝑖𝑛𝑑𝑙𝑒= 𝑓_𝑣/𝐹_𝑛𝑣 〖 〗𝑟𝑣 _𝑡𝑎𝑝𝑝𝑖𝑛𝑔= 𝑓_𝑣/𝐹_𝑛𝑣
9. Horizontal Excitation Analysis9.1 Spring Constant 9.2 Damping Ratio 9.3 Frequency Checka. Radius Equivalent (rov) for Rectangular Foundation a. Effect of Depth of Embedment on Damping Ratio a. Natural Frequency
Fnh = 173.342 rpmαh = 1.685
roh = 8.463 m b. Resonance Frequency (rpm)b. Mass Ratio
b. Embedment Factor for Spring Constant Bh = (7-8ν)/(32x(1-ν))x W/(ϒ x roh3)
ηh = 1 + 0.55 x (2-ν) x (h/roh) Bh = 0.069 Frh = #NUM! # 2 x Dvt = 3.775443 RESONANCE NOT POSSIBLE !!!ηh = 1.258
c. Geometrical Damping Ratio c. Frequency Ratioc. Spring Constant Coefficient
βh = 1Dh = 1.853 rh (spindle) = 46.151 rh (tapping) = 17.307
d. Equivalent Spring Constant for Rectangular Foundationd. Internal Damping d. Magnification Factor
Dhi = 0.04Kv = 11629.452 t/m
d. Total Damping Ratio Mh(spindle) = 4.68E-04 OK
Dht = Dv + DiDht = 1.888
Mh(tapping) = 3.27E-03 OK
e. Transmissibility Factor
Th(spindle) = 0.082
Th(tapping) = 0.214
f. Vibration Amplitude
V(spindle) = Mh(spindle) + Fo(spindle) / Kh Vrocking(spindle) = R(spindle) x (h+C.G)V(spindle) = 6.76E-06 m Vrocking(spindle) = 0.000 m
V(tapping) = Mh(tapping) + Fo(tapping) / Kh Vrocking(tapping) = R(tapping) x (l/2)V(tapping) = 1.82E-06 m Vrocking(tapping) = 0.000 m
g. Vtotal
Vtotal = (V(spindle) + Vrocking(spindle))+ (V(tapping) + Vrocking(tapping))Vtotal = 8.58E-06 m
𝐾_ℎ=2𝑥(1+𝑣).𝐺 . 𝛽_(ℎ ). √(𝐵 𝑥 𝐿) . 𝑛_ℎ
𝛼_ℎ= [1+1.9.(2−𝑣). ℎ/𝑟_𝑜ℎ ]/√(𝑛_ℎ )
𝐷_ℎ=0.288/√(𝐵_ℎ ).𝛼_ℎ
𝐹_𝑛ℎ=60/(2𝑥𝜋)𝑥√((𝐾_ℎ/𝑚))
𝐹_𝑟ℎ= 𝐹_𝑛ℎ 𝑥√([1−[2𝑥𝐷_ℎ𝑡^2 ]] )
ℎ〖𝑟 〗 _𝑠𝑝𝑖𝑛𝑑𝑙𝑒= 𝑓_ℎ/𝐹_𝑛ℎ ℎ〖𝑟 〗 _𝑡𝑎𝑝𝑝𝑖𝑛𝑔= 𝑓_ℎ/𝐹_𝑛ℎ
𝑀_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=1/√((1−𝑟_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))^2 )^2+〖 (2𝐷_ℎ𝑡 𝑥𝑟_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗 ^2 )𝑀_(ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=1/√((1−𝑟_(ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))^2 )^2+〖 (2𝐷_ℎ𝑡 𝑥𝑟_(ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗 ^2 )
𝑇_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=𝑀_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 𝑥√(1+〖 (2𝐷_ℎ𝑡 𝑥𝑟_(ℎ(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗 ^2 )𝑇_(ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=𝑀_(ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 𝑥√(1+ 〖 (2𝐷_ℎ𝑡 𝑥𝑟_(ℎ(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗 ^2 )
𝑟_𝑜ℎ= √((𝐵_𝑘 𝑥 𝐿_𝑘)/𝜋)
10. Rocking Excitation Analysis10.1 Spring Constant 10.2 Damping Ratio 10.3 Frequency Checka. Radius Equivalent (rov) for Rectangular Foundation a. Effect of Depth of Embedment on Damping Ratio a. Natural Frequency
Fnr = 375.843 rpmror = 1342.870 m αr = 1.000
b. Resonance Frequency (rpm)b. Embedment Factor for Spring Constant b. Mass Ratio
ηr = 1 + 1.2 x (1-ν) x (h/ror) + 0.2 x (2-ν) x (h/ror)3 Imachine = W x (h + C.G)2ηr = 1.001 Imachine = 49.86132 t/m2 Frr= #NUM! #NUM!
c. Spring Constant Coefficient Ifoundatio Σ(Wf /12.(a2+b2) + Wf.k2) c. Frequency RatioIfoundatio 6151.17236 t/m2
βr = 0.54Io= Imachine + Ifoundation
d. Equivalent Spring Constant for Rectangular Foundation Io= 6201.03368 t/m2 rr(spindle) = 21.285 rr (tapping) = 7.982
Br = 3 x (1-ν)/8 x Io /(ϒ x ror5) d. Magnification FactorBr = 0.000
Kr = 9605802.627 t/mc. Effective Damping Coefficient
Mr(spindle) = 1.44E-07 OKηr = 1.010
Mr(tapping) = 3.83E-07 OK
e. Transmissibility Factor
Tr(spindle) = 1.00E+00
d. Geometrical Damping Ratio
Tr(tapping) = 1.00E+00
Dr = 163458.025 f. Vibration Amplitude
e. Internal Damping R(spindle) = Mr(spindle) + Fr(spindle) / Kr Moment Arm = (h + C.G)R(spindle) = 5.47E-07 rad Moment Arm = 3.800 m
Dri = 0.04R(tapping) = Mr(tapping) + Fr(tapping) / Kr
d. Total Damping Ratio R(tapping) = 9.66E-07 rad
Drt = Dr + DiDrt = 163458.060
𝑟_𝑜𝑟= [(𝐿_𝑘 𝑥 𝐵_𝑘^3 )/(3 𝑥 𝜋)]^(1/4)
𝐾_𝑟=𝐺/((1−𝑣) ) 𝑥 〖 〗𝛽 _𝑟 𝑥 𝐿 𝑥 𝐵^3 𝑥 𝑛_𝑟
𝛼_𝑟= (1+0.7 𝑥 (1−𝑣)𝑥 (ℎ/𝑟_𝑜𝑟 )+0.6 𝑥 (2−𝑣)𝑥 (ℎ/𝑟_𝑜𝑟 )^3)/√(𝑛_𝑟 )
𝐷_𝑟=0.15 𝑥 𝛼_𝑟/[(1+ 𝑛_𝑟+ 𝛽_𝑟 )𝑥 √((𝑛_𝑟 𝑥 𝛽_𝑟))]
𝐹_𝑛𝑟=60/((2𝑥𝜋) ) 𝑥 √(𝐾_𝑟/𝐼_0 )
𝐹_𝑟𝑟= 𝐹_𝑛𝑟 𝑥√([1−[2𝑥𝐷_𝑟𝑡^2 ]] )
𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))= 𝑓_𝑟/𝐹_𝑛𝑟 𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))= 𝑓_𝑟/𝐹_𝑛𝑟
𝑀_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=1/√((1−𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))^2 )^2+〖(2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗̂ 2 )𝑀_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=1/√((1−𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))^2 )^2+〖(2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗̂ 2 )
𝑇_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))=𝑀_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 𝑥√(1+〖(2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑠𝑝𝑖𝑛𝑑𝑙𝑒))) 〗̂ 2 )
𝑇_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))=𝑀_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 𝑥√(1+〖(2𝐷_𝑟𝑡 𝑥𝑟_(𝑟(𝑡𝑎𝑝𝑝𝑖𝑛𝑔))) 〗̂ 2 )
11. Amplitudo Check11.1 Total Amplitudoa. Vertical Amplitudo
Vtotal = Vertical Vibration Amplitude + Rocking Vibration Amplitude x (B/2)Vtotal = 7.92E-06 mVtotal = 0.001 cm
b. Horizontal Amplitude
Htotal = Horizontal Vibration Amplitude + Rocking Vibration Amplitude x (h + C.G)Htotal = 8.58E-06 mHtotal = 0.001 cmHtotal = 0.00034 in
c. Maximum Velocity
Velocity = 0.01 in/secVelocity = 0.00025 m/sec
At(spindle) = At(motor) =
At(spindle) 2.98E-07 At(motor) 3.183E-05
c. Vibration Velocity
Vertical Velocity
Vv(spindle)(V(spindle) + Vrocking(spindle)) x (2 x π x f/60)Vv(spindle) 5.21E-03 cek
Vv(tapping(V(tapping) + Vrocking(tapping)) x (2 x π x f/60)Vv(tapping 5.33E-04 cek
Vv(total) =Vv(total) = 5.24E-03 cek
Horizontal Velocity
Vh(spindle)(H(spindle) + Hrocking(spindle)) x (2 x π x f/60)Vh(spindle) 5.66E-03 cek
Vh(tapping(H(tapping) + Hrocking(tapping)) x (2 x π x f/60)Vh(tapping 5.73E-04 cek
Vh(total) =Vh(total) = 5.69E-03 cek
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦/(2.𝜋.𝑚𝑎𝑐ℎ𝑖𝑛𝑒(𝑟𝑝𝑚)) 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦/(2.𝜋.𝑚𝑎𝑐ℎ𝑖𝑛𝑒(𝑟𝑝𝑚))
√( 〖𝑉 _(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 〗̂ 2+ 〖𝑉_(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 〗̂ 2 )
√( 〖𝑉 _(𝑣(𝑠𝑝𝑖𝑛𝑑𝑙𝑒)) 〗̂ 2+ 〖𝑉 _(𝑣(𝑡𝑎𝑝𝑝𝑖𝑛𝑔)) 〗̂ 2 )
12. Soil Bearing Check12.1 Transmissibility Force 12.3 Soil Bearing Preassure (Static + Dynamic,Static)a. Transmissibility Vertical Force a. Fatigue Factor (ξ)
Pv (spindle(Tv(spindle) x F0(spindle)) (ξ) = 1.5Pv (spindle 0.00831 ton
b. QallPv (tapping(Tv(tapping) x F0(tapping))Pv (tapping 0.49479 ton Qall = 0.75 x qu
Qall = 338.7994 t/m2Pv (total) =Pv (spindle) + Pv (tapping)Pv (total) = 0.503099 ton c. Psta+dyn
b. Transmissibility Horizontal Force
Ph (spindle(Th(spindle) x F0(spindle))Ph (spindle 0.006373 ton Psta+dyn (+ 1.54 t/m2
Psta+dyn (- 1.53 t/m2Ph (tapping(Th(tapping) x F0(tapping))Ph(tapping)0.384602 ton
Ph (total) =Ph(spindle) + Ph (tapping)Ph (total) = 0.390976 ton Psta+dyn (+ 1.54 t/m2
Psta+dyn (- 1.53 t/m2c. Transmissibility Moment
Pr = (Tr(spindle) x Mr(spindle)) + (Tr(tapping) x Mr(tapping)) Qall = 338.7994 t/m2Pr = 5.27E-07 Psta+dyn = 1.54 t/m2
12.2 Total Transmissibility Moment Qall > Psta+dyn Ok !!
Ptr = Pr + (Pv(total) x (PL/2 + Edx) + (Ph(total) x (C.G + h))Ptr = 5.67401 ton m
𝑃_(𝑠𝑡𝑎+𝑑𝑦𝑛)= 𝑊_𝑡/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_(𝑣(𝑡𝑜𝑡𝑎𝑙)))/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_(ℎ(𝑡𝑜𝑡𝑎𝑙)) 𝑥 (𝐶.𝐺_𝑠ℎ𝑎𝑓𝑡+ℎ)𝑥 6)/(𝐵 𝑥 𝐿^2 ) ± ("ξ" 𝑥 𝑃_𝑟 𝑥 6)/(𝐵 𝑥 𝐿^2 )
𝑃_(𝑠𝑡𝑎+𝑑𝑦𝑛)= 𝑊_𝑡/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_(𝑣(𝑡𝑜𝑡𝑎𝑙)))/𝐴𝑟𝑒𝑎 ± ("ξ" 𝑥 𝑃_𝑡𝑟 𝑥 6)/(𝐵 𝑥 𝐿^2 )
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