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Contoh desain pondasi beban dinamis / pondasi mesin, perhitungan pondasi beban dinamis, mulai dari perhitungan statik sampai dinamis.
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1.0 GENERAL
1.1 Scope ----------------------------------------------------------------------------------------
1.2 Definitions ----------------------------------------------------------------------------------------
2.0 REFERENCE CODES, STANDARD AND PROJECT DOCUMENTS
2.1 Industry Codes and Standards ------------------------------------------------------------------
2.2 Company References ------------------------------------------------------------------
2.3 Saudi Arabian Standard Organization ------------------------------------------------------------------
2.4 Project Documents ------------------------------------------------------------------
2.5 Reference Document ------------------------------------------------------------------
3.0 MATERIALS AND UNITS
3.1 Materials ----------------------------------------------------------------------------------
3.2 Units of Measurements ----------------------------------------------------------------------------------
4.0 DYNAMIC FOUNDATION REQUIREMENTS
4.1 Foundation Grouping for Vibrating Machinery -------------------------------------------------------
4.2 General Design Requirements -------------------------------------------------------
5.0 BLOWER FOUNDATION
5.1 General Sketch -----------------------------------------------------------------------
5.2 The Soil and Foundation Paramete-----------------------------------------------------------------------
5.3 Foundation Data -----------------------------------------------------------------------
5.4 Equipment Data -----------------------------------------------------------------------
5.5 Machine Data -----------------------------------------------------------------------
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TABLE OF CONTENTS
DECRIPTION
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6.0 CHECK FOR BLOWER FOUNDATION DESIGN
6.1 The Mass Ratio of Blower Foundation -------------------------------------------------------
6.2 The Minumum Thickness of Concrete Foundati -------------------------------------------------------
6.3 The Width of Concrete Foundation -------------------------------------------------------
6.4 Allowable Soil Bearing Pressure -------------------------------------------------------
6.5 Allowable Eccentricities for Concrete Foundatio-------------------------------------------------------
6.6 Rebar Check -------------------------------------------------------
ATTACHMENT (1)- Dynamic Analysis
ATTACHMENT (2)- Engineering Data
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1.0 GENERAL
1.1 Scope
1.2 Definitions
Project :Company : SATORP(Saudi Aramco Total Refining and Petrochemical Company)Contractor :Location : Industrial Site of Jubail 2, The West Coast of Arabian Gulf, Saudi
2.0 REFERENCE CODES, STANDARD AND PROJECT DOCUMENTS
2.1 Industry Codes and Standards
ACI-318-02 Building Code Requirements for Reinforced ConcreteMinimum Design Loads for Buildings and Other Structures
2.2 Company References
JERES-M-001 Civil and Structural Design CriteriaJERES-Q-001 Criteria for Design and Construction of Concrete StructuresJERES-Q-005 Concrete FoundationsJERES-Q-007 Foundations and Supporting Structure for Heavy MachineryJERES-Q-010 Cement Based, Non-Shrink Grout for Structural and Equipment GroutingJERES-Q-011 Epoxy Grout for Machinery SupportJERMS-H-9106 Epoxy Coating of Steel Reinforcing Bars
2.3 Saudi Arabian Standard Organization
SASSO SSA 2 Steel Bars for the Reinfocement of ConcreteSASSO SSA 224 Steel Fabric for Reinforcement of Concrete
This calculation report is relevant to the design of C.A.BLOWER Foundation (551-B-1001/2001/3001/4001)
ASCE 7-05
2.4 Project Documents
SA-JER-PUAAA-SKEC-468002 Design Criteria for Civil and StructureSA-JER-PUAAA-SKEC-588001 Geotechnical Investigation ReportSA-JER-PUAAA-SKEC-468001 Geotechnical & Foundation Design Basis
2.5 Reference Document
Design of Structures and Foundations for Vibrating Machines by Suresh C. Arya
3.0 MATERIALS AND UNITS
3.1 Materials
3.1.1 Concrete
- Cement
1) Below Grade (up to 150 mm above grade)Type - V Portland cement (JERES-Q-001 and ASTM 150) orType - I Portland cement (JERES-Q-001 and ASTM 150) + Silica Fume 7%
2) Above Grade (from 150 mm above grade)Type - I Portland cement (JERES-Q-001 and ASTM 150)
- Specified Compressive Cylinder Strength at 28 Days
1) f'c = 35 Mpa for basins and water retaining structures2) f'c = 28 Mpa for foundations, walls and pavings
- Unit Weight for Reinforced Concrete
1) Wc = 24 kN/m³
- Modulus of elasticity
1) Ec = (f'c = 28 Mpa)2) Ec = (f'c = 35 Mpa)
24800 Mpa27800 Mpa
3.1.2 Reinforcing Bar
1) Reinforcing steel bars shall conform to SASO SSA 2, hot-rolled, high tensile, deformed steel.2) Characteristic Strength (ACI 318M)
= 422 Mpa
3) Modulus of Elasticity- Es = 200,000 Mpa
3.1.3 Anchor Bolt
1) Threaded Anchor Bolts : ASTM A36/A36M or ASTM F1554, Gr. 36 - Headed Bolts : ASTM A307 Grade A - Washers : ASTM F436/F436M - Nuts : ASTM A563 Grade A, Heavy Hex or ASTM A 563M2) High Strength Anchor Bolts - Anchor Bolts : ASTM A193/A193M Gr. B7 or ASTM F1554, Gr. 105 - Washers : ASTM F436/F436M - Heavy Hex Nuts : ASTM A194/A194M or ASTM A563, DH3) Min. Anchor Bolt Diameter : 20 mm4) For Corrosion Allowance : Anchor Bolt Diameter + 3 mm.
3.1.4 Grout for Machinery Support
When type of grout is not specified by the equiment Manufacturer,cenmentitious grout shall be used for any of the following
1) Non-Shrink Grout for Structural and Equipment- Equipment with driver horsepower < 500 (373 kW)- RPM of Equipment < 3600 RPM- Total weight of Equipment < 2270 kg
2) Epoxy Grout for Machinery Support- Equipment with driver horsepower ≥ 500 (373 kW)- RPM of Equipment ≥ 3600 RPM- Total weight of Equipment ≥ 2270 kg
- fy
3.2 Units of Measurements
The Metric units shall be used :
- Force : kN- Length : meter- Temperature : Degree centigrade
4.0 PUMP FOUNDATION DESIGN ASSUMPTION
4.1 Foundation Grouping for Vibrating Machinery
4.1.1 Centrifugal Rotating Machinery
1) Horsepower ≥ 500 The foundatiom shall be designed for the expected dynamic forces using dynamic analysis procedures
2) Horsepwoer < 500 The foundation weight shall be 3 times the total machinery weight
4.2 General Design Requirements
4.2.1 Clean, simple outlines shall be used for foundations. Beams and columns shall be of a uniform rectangular shape. Block foundations should be rectangular.
4.2.2 The height of the machine support above grade shall be the minimum to accommodate suction and discharge piping arrangements.
4.2.3 The minimum thickness of the concrete foundations
- 0.60 + L / 30 (meters)
Where, L = Length of foundation parallel to the machine bearing axis in meters
ITEMS
551-B-1001/2001/3001/4001
UNIT FDN. TYPEMACHINE
TYPERATING
(JERES-Q-007 Section 5.1.1)
POWERDYNAMIC ANALYSIS
1587 HP YESUNIT 551 Rigid Block Rotating 1167 kW
4.2.4 The width of the foundation
- B ≥ 1.5 × Vertical distance from the base to the machine centerline
Where, B = Width of foundation in meters
4.2.5 For deformed bars
1) The reinforcement in each direction shall not be less than 0.0018 times the gross area perpendicular to the direction of reinforcement
2) Minimum tie size in pers shall be 12 mm
4.2.6 Allowable Eccentricities for Concrete Foundations with Horizontal Shaft Machinery
1) The horizontal perpendicular to the machine bearing axis, between of gravity of the machine foundation system and the centroid of the cosil contact area ( < 0.05 × B)
2) The horizontal parallel to the machine bearing axis, between of gravity of the machine foundation system and the centroid of the cosil contact area ( < 0.05 × L)
4.2.7 Allowable Soil Bearing Pressures
1) For High-tuned foundatio: Soil bearing pressures shall not exceed 50% of the allowable bearing pressure permitted for static loads
2) For Low-tuned foundatio: Soil bearing pressures shall not exceed 75% of the allowable bearing pressure permitted for static loads
Where,High-tuned System = A high-tuned system is a machine support/foundation system
in which the operating frequency (range) of the machinery is below all natural frequencies of the system
Low-tuned System = A low-tuned system is a machine support/foundation systemin which the operating frequenct (range) of the machinery is aboveall natural frequencies of the system
4.2.8 Permissible Frequency Ratios
To avoid the danger of excessive vibration, the ratio between the operating frequency of the machif, and each natural frequency of the machine foundation system, f(n) shall not lie in the range of 0.7 to 1.3.
4.2.9 Permissible Vibration
If Manufacturer's vibration criteria are not available, the maximum velocity of movement during steady-state normal operation shall be limited to 0.12 inch per second for centrifugal machi
5.0 BLOWER FOUNDATION (551-B-1001/2001/3001/4001)
5.1 General SketchCombined C.G
X direction
Y direction
C.G of Machine
[ unit : m ]
200
Z direction G.L
X direction [ unit : m ]
1.406
0.00
0
3.000
3.000
P L A N
1.945
0.000
10.0
00
TOG EL.+100,
3.645
1.784
0.294
5.34
6
1.443
10.0
00
0.000
5.06
9
1.216
AX
IS O
F R
OC
KIN
G
0.00
0
3.550
S E C T I O N
1.850
0.200
1.000
0.500
5.2 The Soil and Foundation Parameters
Allowable Soil Beraing
Shear Modulus, G
Soil Internal damping Ratio
Poisson's Ratio, υ
Unit Weight (Soil)
Unit Weight (Con'c)
5.3 Foundation Data
Height (h)
Thickness of Grout
5.4 Equipment Data
=
=
=
=
=
5.5 Machine Data
(1) For values for Equipment
R.P.M F
Rotor Weight
Unbalanced Force
ton
C.A.BLOWER - 2242
C.A.BLOWER - 3.670
C.A.BLOWER - 0.072
ton
rpm
ton
MOTOR - 1490
m
m
0.040
17.000
m
kN/m²
0.321
Pedestal Height (PH)
rpm
kN
m
m
Weight of Motor (Wm)
1.200
0.025
m
25.506
0.500
ton
ton
ton6.000
m
304.110 kN
kN
kN
58.860 kN
200.000
24.000
82579.233
kN/m²
Item No.
Footing Width (FL)
551-B-1001/2001/3001/4001
m
kN/m³kN/m³
3.000
ton
Ground Level (G.L.)
Footing Length (FB)
Footing Height (FH)
Pedestal Width (PL)
Pedestal Length (PB)
Weight of C.A.BLOWER (Wc) 127.530
92.214
Total Weight (Wt) 31.000 ton
Weight of Base Plate (Wb)
Weight of Silencer (Ws)
ton
10.000
3.000
0.200
1.700
m10.000
13.000
2.600
9.400
(2) For dimensions of Equipment & Foundation
C.G from machines bottom to Machine center
C.G of Shaft from machines bottom (C.Gshaft)
C.G from Pedestal Edge to Machine Center (X-direction) (Edx)
C.G from Pedestal Edge to Machine Center (Y-direction) (Edy)
6.0 CHECK FOR BLOWER FOUNDATION DESIGN
6.1 The Mass Ratio of Blower Foundation
(1) Foundation Weight Pedestal (Wcp)
Footing (Wcf)
= [(FL × FB × FH) + (PL × PB × PH)] × Unit Weight (Con'c)
= [(3.000 m × 10.000 m × 0.500 m) + (3.000 m × 10.000 m × 1.200 m)] × 24.000
= kN
(2) Machine Weight
= Weight of Blower + Weight of Motor + Weight of Base Plate + Weight of Silencer
= 127.530 + 92.214 + 25.506 + 58.860
= kN
(3) Mass Ratio
= / >
= / >
= >
6.2 The Minumum Thickness of Concrete Foundation
- Thickness (= FH + PH) ≥ 0.6 + FB / 30 (m)
0.933
OK!!
Wc
360.000 kN
OK!!
0.6 + FB / 30 (m)Length ( = FB)
(m)
Thickness ( = FH + PH)
(m)
1.700
3.0
864.000 kN
Item No.
551-B-1001/2001/3001/4001 10.000
(m)
3.0
4.025
R
304.110
Wm
1.850
3.0
Wc
m
m
m
1.945 m
5.346
Wm
304.110
1224.000
1224.000
1.216
6.3 The Width of Concrete Foundation
- FL ≥ 1.5 × Vertical Distance from The Base to the Machine Centerline
6.4 Allowable Soil Bearing Pressure (Static)
[kN/m²]
= 1,528.110 / 30.000
= kN/m²
Where,
= × [kN/m²]= 0.750 × 200.000
= kN/m²
= Allowable soil capacity for static case.
= kN/m²
= + [kN]
= 1,224.000 + 304.110
= kN
= 0.25 Wm × (FH + PH + G.L[kN-m]
= 0.250 × 304.110 × (0.500 + 1.200 + 1.850)
= kN-m
= FB × FL [m²]= 10.000 × 3.000
= m²
OK!!
OK!!
1.5 × C.G
2.775
QItem No.
Q = 0.750 × Qa
(kN/m²)
Q =Wt
Area
551-B-1001/2001/3001/4001 50.937
551-B-1001/2001/3001/4001
150.000
269.898
(kN/m²)
Length ( = FL)
(m)Item No.
(m)
A
30.000
3.000
150.000
1528.110
50.937
Wm
Qas
Mx
Qa 0.750
Wt
200.000
Qas
Wc
(JERES-Q-007 Section 9.3)
Low-tuned Foundations
6.5 Allowable Eccentricities for Concrete Foundations
= + = kN
= [(304.110 × 1.216) + (864.000 × 1.500) + (360.000 × 1.500)] / 1,528.110 = m
Eccentricity(X-dir) = (1.500 - 1.443) ×100 / 3.00 = < %
= [(304.110 × 5.346) + (864.000 × 5.000) + (360.000 × 5.000)] / 1,528.110 = m
Eccentricity(Y-dir) = (5.000 - 5.069) ×100 / 10.0 = < %
= [(304.110 × 3.645) + (864.000 × 1.100) + (360.000 × 0.250)] / 1,528.110 = m
6.6 Rebar Check
a = @ 200
c = @ 200
b = @ 200
5.069
1.443
1.884
OK!!
5.000
Y'
Wt 1528.110Wc
X'
a (mm²)cb Top (mm²) Bottom (mm²)Rebar Dia.
Wm
Z' 1.406
D20 D20 D12 1350.000
Use AS
5.000
OK!!
Req'd AS = 0.0018 × b × (H / 2)
OK!!
1350.000 5024.000
0.689
Item No.
551-B-1001/2001/3001/4001
"Dynamic Analysis.xls"
Job Name: Subject:
Job Number: Originator: TYP Checker:
1.0 Machine Data
Blower Blower =
Motor Motor =
Unbalanced Force Blower = Motor =
Moment by U.F Blower = Motor =
1.1 Centrifugal Force (Fo)
1) F0 = (Wr / g) × e × w² = (Wr / g) × e × w²
= 64,750.000 / 981.0 × 0.00588 × 234.78 = 0.000 / 981.0 × 0.00721 × 234.780²
= N = N
= kN = kN
Where,
g = cm/sec² = cm/sec²
w = (RPM × 2 × π / 60) = (RPM × 2 × π / 60)
= 2,242 × 2 × π / 60 = 1,490 × 2 × π / 60
= rad/sec = rad/sec
e = α × (12000 / RPM) × 0.0025 (cm) = α × (12000 / RPM) × 0.0 (cm)
(Maximum) = α × (12000 / RPM) (mil) = α × (12000 / RPM) (mil)
= 1.000 × (12000 / 2,242) = 1.000 × (12000 / 1,490)
= (mil) = (mil)
= cm = cm
Weight of Rotor of Blower Weight of Rotor of Motor
Wr = 1.000 = 0.000
= ton = ton
= kN = kN
Wc = Weight of C.A.BLOWER = 13.000 ton = kN
Wm = Weight of Motor = 9.400 ton = kN
Wb = Weight of Base Plate = 2.600 ton = kN
Ws = Weight of Silencer = 6.000 ton = kN
2) F0 = Factor × W × (rpm / 1000)1.5 = Factor × W × (rpm / 1000)1.5
= 0.001 × 600.408 × (2242 / 1000)^1 = 0.001 × 0.000 × (1490 / 1000)^1.5
= kN = kN
= ton = ton
R.P.M Rotor Weight
0.405 ton
0.600 ton
0.000 ton
For Motor
0.205
0.000
For Motor
0.205
0.000
92.214
25.506
0.000
For Blower
981
234.780
2.314
1490 rpm
For Blower
234.780
0.000 ton
DYNAMIC ANALYSIS
Design of Structures and Foundations for Vibrating Machines
981
64.750
For Block Foundation (Centrifugal Machinery)
127.530
58.860
2.016
1.000 (mil)
2.838
0.000
0.000
0.00721
2242 rpm
21384.054
21.384
0.00588
6.600
1.437 ton-m 0.000 ton-m
(Wc(rotor) + Ws) × (Wm(rotor)) ×
"Dynamic Analysis.xls"
Where,
Factor = 0.001 for SI units W = Total mass of the rotating
= 0.1 for imperial units FD = Steady state dynamic force
3) F0 = kg = kg
= ton = ton
= kN = kN
Vertical Dynamic Force kN
kN
kN
Horizontal Dynamic Force kN
kN
kN
Rocking Dynamic moment [Verti. Force(blower)]× (From Base to C.G) = FV(blower) × (h + C.G.
[3.970]× (1.700 + 1.850)
kN-m
[Verti. Force(motor)]× (From Base to C.G) = FV(motor) × (h + C.G.)
[0.000]× (1.700 + 1.850)
kN-m
1.2 Calculation of center of gravity of machine & fdn.
Wp = =
Wm = =
Wb = =
Ww = =
WE = = WE / g kN-sec²/mWcp = = Wcp / g kN-sec²/mWcb = = Wcb / g kN-sec²/mWF = = WF / g kN-sec²/m
W = = W / g kN-sec²/m
Io = I (Machine) + I (Foundation)
= We k²M + ∑ [WF / 12 (a²i + b²i) + WF k²Fi]
= [31.000 × (1.700 + 1.945)²] + [(88.073) / 12 × (3.000² + 1.200²)]
+ [(88.073) × (0.600 + 0.500)²] + [(36.697) / 12 × (3.000² + 0.500²)] + [(36.697) × (0.250)²]
= kN-m²
Fv(motor) =
Fh(blower) =
Fh(motor) =3.970
0.000
3.970Fv(blower + motor) =
Mr(blower) =
= 88.073
= 36.697
= 155.771
= 124.771
13.000 ton
9.400 ton
2.600 ton
6.000 ton
3.970
Apply for → 3) Fо
For Blower For Motor
31.000 ton
124.771 ton
88.073 ton
14.094
0.405
3.970
360.000 kN
58.860 kN
Fh(blower + motor) =
92.214 kN
Mr(motor) =
0.000
Fv(blower) =
0.000
3.970
36.697 ton
404.689
1224.000 kN
25.506 kN
1528.110 kN
864.000 kN
127.530 kN
304.110 kN
155.771 ton
625.640
= 31.000
"Dynamic Analysis.xls"
Where,
WE = Total Machine Weight
WF = Foundation Weight
W = Total Static Load (Total Machine Weight + Foundation Weight)
g = cm/sec²
Io = SUM [mi (Ai² + Bi²) / 12 + miKi²]
1.3 Coefficients Bv, Bh, and Br for Rectangular Footings
L = 3.000 m
B = 10.000 m
Coefficents βv, βh and βr for rectangular footings
2.0 Vertical Excitation Analysis
2.1 Spring Constant
(1) Equivalent radius (r0v) for Rectangular Foundation
rov = (FB × FL / π)
= m
(2) Embedment factor for Spring Constant
Effective Embedment height
ηv = 1 + 0.6 × (1 - υ) × (h / rov) = Height(h) - Ground Level(G.L.)
= 1 + 0.6 × (1 - 0.321) × (1.500 / 3.090) = 1.700 - 0.200
= = 1.500
(3) Spring Constant Coefficient
βv =
L / B
0.300Roking (βr)
0.300
2.150
981.000
1.198
3.090
2.150
π=
10.000 × 3.000
Horizontal (βh) 1.017
0.408
0.300
Coefficients
Vertical (βv)
AX
ISO
FR
OC
KIN
G
L
B
B
L
β
β
L/B
β
"Dynamic Analysis.xls"
(4) Equivalent Spring Constant for Rectangular Foundation
Kv = G / (1 - υ) × βv × FB × FL × ηv
= kN/m
2.2 Damping Ratio
(1) Effect of Depth of Embedment on Damping Ratio
αv = [1 + 1.9 (1 - υ) × h / rov] / ηv
= [1 + 1.9 × (1 - 0.321) × 1.500 / 3.090] / 1.198
=
(2) Mass Ratio
Bv = (1 - υ) / 4 × W / (γ × rov³)
=
(3) Effective Damping Coefficient
This is not available for Vertical Mode
(4) Geometrical Damping Ratio
Dv = 0.425 / Bv × αv
= 0.425 / 0.517 × 1.486
=
(5) Internal Damping
Dvi =
(6) Total Damping Ratio
Dvt =
=
=
155.771
Consider the Internal Damping
1 - 0.321=
×
Dv + Dvi
(1 - 0.321)
0.040
=
1715667.000
1.486
1.733 × 3.090³
10.000 × 3.000 × 1.198
0.918
82579.2332.150
0.878 + 0.040
0.878
×
4
0.517
×
"Dynamic Analysis.xls"
2.3 Frequency Check
(1) Natural Frequency
Fnv = 60 / (2 × π) × ( Kv / m)
= 60 / (2 × π) × (1,715,667.000 / 155.771)
= rpm
(2) Resonance Frequency (rpm)
Frv = Fnv × [1 - (2 × Dvt²)]
= 1,002.178 × [1 - ( 2 × 0.918²)]
∴ 2 × Dvt²
= 2 × 0.918²
= 1.685 > 1.00
(3) Frequency Ratio (JERES-Q-007, Section 10.1)
When f / f(n) < 0.7, f / f(n) > 1.3, O.K!!!
= =
(4) Magnification Factor
For Blower
Mv(blower) = 1 / (1 - rv(blower)²)² + (2 Dvt × rv(blower))²
= 1 / (1 - 2.237²)² + (2 × 0.918 × 2.237)² =
= < 1.500
For Motor
Mv(motor) = 1 / (1 - rv(motor)²)² + (2 Dvt × rv(motor))²
= 1 / (1 - 1.487²)² + (2 × 0.918 × 1.487)² =
= < 1.500
For Blower For Motor
rv(motor) =
=
0.335
0.335 OK!!!
fv(motor)
2242.000
Fnv
1490.000
0.174
1.487
OK!!!
RESONANCE NOT POSSIBLE!!! (There is no need to analysis Vibration)
=rv(blower)
0.174
=1002.178
fv(blower)
1002.178
2.237
Not Apply
1002.178
OK!!!
Fnv
OK!!!
"Dynamic Analysis.xls"
(5) Transmissibility Factor
For BlowerTv(blower) = Mv(blower) × 1 + (2 Dvt × rv)²
= 0.174 × 1+ (2 × 0.918 × 2.237)²
=
For MotorTv(motor) = Mv(motor) × 1 + (2 Dvt × rv)²
= 0.335 × 1+ (2 × 0.918 × 1.487)²
=
(6) Vibration Amplitude
For Blower(For the normal operating speed - 2242 rpm) (For the normal operating speed - 1490 rpm)
V(blower) = Mv(blower) × Fv(blower) / Kv Vrocking(blower)
= R(blower) × (FL / 2)
= 0.0000005 × (3.000 / 2)
= m = m
For Motor(For the normal operating speed - 2242 rpm) (For the normal operating speed - 1490 rpm)
V(motor) = Mv(motor) × Fv(motor) / Kv Vrocking(motor)
= R(motor) × (FL / 2)
= 0.0000000 × (3.000 / 2)
= m = m
Total Vertical Amplitude
Vtotal = V(blower) + Vrocking(blower) + V(motor) + Vrocking(motor)
= m
=
7.714E-07
0.000E+00
0.335 × 0.000
0.736
1715667.000
4.026E-07
=
1715667.000
0.000E+00
1.174E-06
0.974
0.174 × 3.970
"Dynamic Analysis.xls"
3.0 Horizontal Excitation Analysis
3.1 Spring Constant
(1) Equivalent radius (r0h) for Rectangular Foundation
roh = (FB × FL / π)
= m
(2) Emebedment factor for Spring Constant
Effective Embedment height
ηh = 1 + 0.55 × (2 - υ) × (h / roh) = Height(h) - Ground Level(G.L.)
= 1 + 0.55 × (2 - 0.321) × (1.500 / 3.090) = 1.700 - 0.200
= = 1.500
(3) Spring Constant Coefficient
βh =
(4) Equiavelent Spring Constant for Rectangular Foundation
Kh = 2 × (1 + υ) × G × βh × FB × FL × ηh
= 2 × (1 + 0.321) × 82,579.233 × 1.017 × 10.000 × 3.000 × 1.448
= kN/m
3.2 Damping Ratio
(1) Effect of Depth of Embedment on Damping Ratio
αh = [1 + 1.9 (2 - υ) × h / roh] / ηh
= [ 1 + 1.9 × (2 - 0.321) × 1.500 / 3.090] / 1.448
=
(2) Mass Raito
Bh = (7 - 8υ) / [32 × (1 - υ)] × W / (γ × roh³)
=
=π
1760211.961
0.621
2.118
=
1.017
1.448
3.090
×
10.000 × 3.000
32 × (1 - 0.321)
(7 - 8 × 0.321)
1.733 × 3.090³
155.771
AX
ISO
FR
OC
KIN
G
L
B
"Dynamic Analysis.xls"
(3) Effective Damping Coefficient
This is not avilable for Horizontal Mode
(4) Geometrical Damping Ratio
Dh = 0.288 / Bh × αh
= 0.288 / 0.621 × 2.118
=
(5) Internal Damping
Dhi =
(6) Total Damping Ratio
Dht =
=
=
3.3 Frequency Check
(1) Natural Frequency
Fnh = 60 / (2 × π) × (Kh / m)
= 60 / (2 × π) × 1,760,211.961 / 155.771
= rpm
(2) Resonance Frequency (rpm)
Frh = Fnh × [1 - (2 × Dht²)]
= 1,015.000 × [1 - (2 × 0.814²)]
∴ 2 × Dht²
= 2 × 0.814²
= 1.325 > 1.0
0.774
RESONANCE NOT POSSIBLE!!! (There is no need to analysis Vibration)
0.814
0.040 Consider the Internal Damping
Dh + Dhi
0.774 + 0.040
1015.000
Not Apply
"Dynamic Analysis.xls"
(3) Frequency Ratio (JERES-Q-007, Section 10.1)
When f / f(n) < 0.7, f / f(n) > 1.3, O.K!!!
= =
(4) Magnification Factor
For Blower
Mh(blower) = 1 / (1 - rh(blower)²)² + (2 Dht × rh(blower))²
= 1 / (1 - 2.209²)² + (2 × 0.814 × 2.209)² =
= < 1.50
For Motor
Mh(motor) = 1 / (1 - rh(motor)²)² + (2 Dht × rh(motor))²
= 1 / (1 - 1.468²)² + (2 × × 1.468)² =
= < 1.50
(5) Transmissibility Factor
For BlowerTh(blower) = Mh(blower) × 1 + (2 Dht × rh(blower))²
= 0.189 × 1 + ( 2 × 0.814 × 2.209)²
=
For MotorTh(motor) = Mh(motor) × 1 + (2 Dht × rh(motor))²
= 0.377 × 1 + ( 2 × 0.814 × 1.468)²
=
0.377
0.377
OK!!!
0.977
For Motor
rh(blower)
1490.000
rh(motor) =fh(motor)
Fnh
fh(blower)
Fnh
2242.000
1015.000
2.209
=1015.000
1.468
OK!!!
=
0.189
OK!!!
=
0.189 OK!!!
For Blower
0.705
"Dynamic Analysis.xls"
(6) Vibration Amplitude
For Blower
(For the normal operating speed - 2242 rpm) (For the normal operating speed - 1490 rpm)
H(blower) = Mh(blower) × Fh(blower) / Kh Hrocking(blower)
= R(blower) × (h + C.G.)
= 0.0000005 × (1.700 + 1.850)
= m = m
For Motor(For the normal operating speed - 2242 rpm) (For the normal operating speed - 1490 rpm)
H(motor) = Mh(motor) × Fh(motor) / Kh Hrocking(motor)
= R(motor) × (h + C.G.)
= 0.0000000 × (1.700 + 1.850)
= m = m
Total Horizontal Amplitude
Htotal = H(blower) + Hrocking(blower) + H(motor) + Hrocking(motor)
= m
4.0 Rocking Excitation Analysis
4.1 Spring Constant
(1) Equivalent (r0r) for Rectangular Foundation
ror = [(FB × FL³) / (3 × π)]^(¼)
^(¼)
= m
(2) Embedment factor for Spring Constant
ηr = 1 + 1.2 × (1 - υ) × (h / ror) + 0.2 × (2 - υ) × (h / ror)³= 1 + 1.2 × (1 - 0.321) × (1.500 / 2.314) + 0.2 × (2 - 0.321) × (1.500 / 2.314)³
=
Effective Embedment height
= Height(h) - Ground Level(G.L.)
= 1.700 - 0.200
= 1.500
=0.377 × 0.000
1760211.961
=[ (10.000 × 3.000³) ]
1.826E-06
0.000E+00
2.252E-06
0.000E+00
0.189 × 3.970=
1760211.961
3 × π
2.314
4.263E-07
1.620
AX
ISO
F
RO
CK
ING
L
B
"Dynamic Analysis.xls"
(3) Spring Constant Coefficient
βr =
(4) Equivalent Spring Constant for Rectangular Foundation
Kr = G / (1 - υ) × βr × FB × FL² × ηr
= kN/m
4.2 Damping Ratio
(1) Effect of Depth of Embedment on Damping Ratio
=
(2) Mass Ratio
Br = 3 × (1 - υ) / 8 × Io / (ρ × ror5)
=
(3) Effective Damping Coefficient
nr =
(4) Geometrical Damping Ratio
Dr = 0.15 × αr / [(1 + nr × Br) × (nr × Br) ]
=
(5) Internal Damping
Dri =
7234608.000
ηr
1 + 0.7 × (1 - 0.321) × (1.500 / 2.314) + 0.6 × (2 - 0.321) × (1.500 / 2.314)³
1.620
×
1.387
1.244
=
=
0.052
8=
(1 - 0.321)× 0.408 × 10.000 × 3.000² × 1.620
3 × (1 - 0.321) 625.640
1.251
0.040
82579.233
0.408
αr
1.733 × 66.277
=
(1 + 1.251 × 1.387) × (1.251 × 1.387)
1 + 0.7 × (1 - υ) × (h / ror) + 0.6 × (2 - υ) × (h / ror)³
0.15 × 1.244
=
"Dynamic Analysis.xls"
(6) Total Damping Ratio
Drt =
=
=
4.3 Frequency Check
(1) Natural Frequency
Fnr = 60 / (2 × π) × (Kr / I0)
= 60 / (2 × π) × [7,234,608.000 / 625.640]
= rpm
(2) Resonance Frequency
Frr = Fnr × [1 - (2 × Drt²)]
= 1,027.000 × [1 - (2 × 0.092²)]
= rpm
∴ 2 × Drt²
= 2 × 0.092²
= 0.017 < 1.00
(3) Frequency Ratio (JERES-Q-007, Section 10.1)
When f / f(n) < 0.7, f / f(n) > 1.3, O.K!!!
= =
1490.000
fr(motor)
OK!!!
For Blower
Fnr
For Motor
rr(motor) =
=1027.000
2.183
=1027.000
1.451
RESONANCE COULD BE POSSIBLE!!! (It is necessary to analysis Vibration)
OK!!!
0.092
1027.000
1018.270
0.052 + 0.040
Dr + Dri
rr(blower) =fr(blower)
Fnr
2242.000
"Dynamic Analysis.xls"
(4) Magnification Factor
For BlowerMr(blower) = 1 / (1 - rr(blower)²)² + (2 Drt × rr(blower))²
= 1 / (1 - 2.183²)² + (2 × 0.092 × 2.183)² =
= < 1.500
For MotorMr(motor) = 1 / (1 - rr(motor)²)² + (2 Drt × rr(motor))²
= 1 / (1 - 1.451²)² + (2 × 0.092 × 1.451)² =
= < 1.500
(5) Transmissibility Factor
For BlowerTr(blower) = Mr(blower) × 1 + (2 Drt × rr(blower))²
= 0.264 × 1 + (2 × 0.092 × 2.183)²
=
For MotorTr(motor) = Mr(motor) × 1 + (2 Drt × rr(motor))²
= 0.880 × 1 + (2 × 0.092 × 1.451)²
=
(6) Vibration Amplitude
For Blower Moment Arm = (h + C.G.)
R(blower) = Mr(blower) × Fr(blower) / Kr = (1.700 + 1.850)
= 3.550
= rad
For MotorR(motor) = Mr(motor) × Fr(motor) / Kr
= rad
OK!!!
0.880
0.911
=0.880 × (0.000 × 3.550)
7234608.000
7234608.000
0.880
0.264 × (3.970 × 3.550)
0.285
0.264
0.264 OK!!!
0.000E+00
5.143E-07
=
"Dynamic Analysis.xls"
5.0 Amplitude Check
5.1 Total Amplitude
(1) Vertical Amplitude
Vtotal = Vertical Vibration Amplitude + Rocking Vibration Amplitude × (FL / 2)
= m
= cm
= in
(2) Horizontal Amplitude
Htotal = Horizontal Vibration Amplitude + Rocking Vibration Amplitude × (h + C.G.)
= m
= cm
= in
(3) Maximum Velocity
Where,
Velocity = in/sec
= m/sec
"Machine" is the imposed frequency of the rotating equipment.
RPM = (For Pump)
= (For Motor)
= cm = cm
= in = in
∴ <
2 × π × 24.833
0.0020
0.00077
OK!!!
2 × π × 37.367
At
0.003
Blower
=Velocity
Motor
=
Velocity
0.000089
0.000046
1490
Max(Vtotal, Htotal)
2242
0.003 m/sec
=
0.0013
=
0.120
0.00012
1.174E-06
2 × π × Machine(rpm)2 × π × Machine(rpm)
2.252E-06
0.003 m/sec
0.00051
0.00023
"Dynamic Analysis.xls"
5.2 Vibration Velocity
Vmax = 2 × π × f × (Amplitude)
(1) Vertical Velocity
For BlowerVv(blower) = [V(blower) + Vrocking(blower)] × [2 × π × (Fv(blower) / 60)]
= [0.00000040 + 0.00000077] × [2 × π × (2,242 / 60)]= m/s
For MotorVv(motor) = [V(motor) + Vrocking(motor)] × [2 × π × (Fv(motor) / 60)]
= [0.00000000 + 0.00000000] × [2 × π × (1,490 / 60)]= m/s
Vv(total) =
=
= m/s
(2) Horizontal Velocity
For BlowerVh(blower) = [H(blower) + Hrocking(blower)] × [2 × π × (Fh(blower) / 60)]
= [0.00000043 + 0.00000183] × [2 × π × (2,242 / 60)]= m/s
For MotorVh(motor) = [H(motor) + Hrocking(motor)] × [2 × π × (Fh(motor) / 60)]
= [0.00000000 + 0.00000000] × [2 × π × (1,490 / 60)]= m/s
Vh(total) =
=
= m/s
OK!!!
OK!!!
OK!!!
OK!!!
5.287E-04
OK!!!
OK!!!
2.756E-04
5.287E-04
0.000E+00
Vv(blower)² + Vv(motor)²
0.00052873² + 0.00000000²
2.756E-04
0.000E+00
Vv(blower)² + Vv(motor)²
0.00027565² + 0.00000000²
"Dynamic Analysis.xls"
6.0 Soil Bearing Check (Static + Dynamic)
6.1 Transmissibility Force
(1) Transmissibility Vertical Force
Pv(blower) = [Tv(blower) × Fv(blower)]
= [0.736 × 3.970]
= kN
Pv(blower) = [Tv(motor) × Fv(motor)]
= [0.974 × 0.000]
= kN
Pv(total) = [Tv(blower) × Fv(blower)] + [Tv(motor) × Fv(motor)]
= [0.736 × 3.970] + [0.974 × 0.000]
= kN
(2) Transmissibility Horizontal Force
Ph(blower) = [Th(blower) × Fh(blower)]
= [0.705 × 3.970]
= kN
Ph(motor) = [Th(motor) × Fh(motor)]
= [0.977 × 0.000]
= kN
Ph(total) = [Th(blower) × Fh(blower)] + [Th(motor) × Fh(motor)]
= [0.705 × 3.970] + [0.977 × 0.000]
= kN
(3) Transmissibility Moment
Pr = [Tr(blower) × Mr(blower)] + [Tr(motor) × Mr(motor)]
= [0.285 × 14.094] + [0.911 × 0.000]
= kN-m
6.2 Total Transmissibility Moment
Ptr = Pr + [Pv(total) × (PL / 2 - Edx)] + [Ph(total) × (C.Gshaft + h)]
= 4.010 + [2.922 × (3.000 / 2 - 1.216)] + [2.801 × 3.550]
= kN-m
2.801
2.922
4.010
14.782
2.922
0.000
0.000
2.801
"Dynamic Analysis.xls"
6.3 Soil Beraing Pressure (Static + Dynamic, Static)
(1) Fatigue Factor (ξ) [Foundations and Supporting Structures for Heavy Machinery]
Design of Structures and Foundations for Vibrating M (8)
(2) Qall = = kN/m²
= or kN/m²
= or ton/m2
= or kN/m²
= or ton/m2
= kN/m²
= kN/m²
∴ >
(3) Psta+dyn
Psta+dyn 52.561
Qall Pdyn OK!!!
±1.500 × 2.922
3.000 × 10.000 3.000 × 10.000
150.000
1528.110
5.086 5.299
±
Qall
0.750 × Qa
49.893
=
=Wt
51.981
Area
±ξ × Ph(total) × (C.Gshaft + h) × 6
B × L²
Area±
ξ × Pv(total)
1.500
150.000
ξ × Pr × 6
B × L²
1.500 × 2.801 × (3.550) × 3.000±
10.000 × 3.000²
±
1.500 × 4.010 × 6
10.000 × 3.000²
=Wt
±ξ × Pv(total)
Area Area
3.000 × 10.000
±ξ × Ptr × 6
B × L²
±1.500 × 14.782 × 6
10.000 × 3.000²
=1528.110
±1.500 × 2.922
3.000 × 10.000
52.561 49.313
5.358 5.027