Bảng tính toán móng thiết bị (Móng động )

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 Paramet
e

5.3 Foundation Data
5.4 Equipment Data

5.5 Machine Data
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PAGE
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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 Foundati

o

-
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 Concrete
Minimum Design Loads for Buildings and Other Structures
2.2 Company References
JERES-M-001 Civil and Structural Design Criteria
JERES-Q-001 Criteria for Design and Construction of Concrete Structures
JERES-Q-005 Concrete Foundations

JERES-Q-007 Foundations and Supporting Structure for Heavy Machinery
JERES-Q-010 Cement Based, Non-Shrink Grout for Structural and Equipment Grouting
JERES-Q-011 Epoxy Grout for Machinery Support
JERMS-H-9106 Epoxy Coating of Steel Reinforcing Bars
2.3 Saudi Arabian Standard Organization
SASSO SSA 2 Steel Bars for the Reinfocement of Concrete
SASSO 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 Structure
SA-JER-PUAAA-SKEC-588001 Geotechnical Investigation Report
SA-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) or
Type - 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 structures
2) f'
c

= 28 Mpa for foundations, walls and pavings
- Unit Weight for Reinforced Concrete
1) W
c
= 24 kN/m³
- Modulus of elasticity
1) E
c
= (f'c = 28 Mpa)
2) E
c
= (f'c = 35 Mpa)
24800 Mpa
27800 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
- E
s
= 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 563M
2) 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, DH
3) Min. Anchor Bolt Diameter : 20 mm
4) 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
- f
y
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 weigh
t

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
5
51-B-1001/2001/3001/400
1
UNIT FDN. TYPE
MACHINE
TYPE
RATING
(JERES-Q-007 Section 5.1.1)
POWER
DYNAMIC
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 foundati
o
:
Soil bearing pressures shall not exceed 50% of
the allowable bearing pressure permitted for static loads
2) For Low-tuned foundati
o
:
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 system
in which the operating frequenct (range) of the machinery is above
all 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 mach
i
f, 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 mach
i

5.0 BLOWER FOUNDATION (551-B-1001/2001/3001/4001)
5.1 General Sketch
Combined C.G
X direction
Y direction
C.G of Machine
[ unit : m ]
200
Z direction
G.L
X direction
[ unit : m ]
1.406
0.000
3.000
3.000
P L A N
1.945
0.000
10.000
TOG EL.+100,
3.645
1.784
0.294
5.346
1.443
10.000
0.000
5.069
1.216

AXIS OF ROCKING
0.000
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 (W
m
)
1.200
0.025
m
25.506
0.500
ton
ton

ton
6.000
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/m³
kN/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 (W
c
)
127.530
92.214
Total Weight (W

t
)
31.000
ton
Weight of Base Plate (W
b
)
Weight of Silencer (W
s
)
ton
10.000
3.000
0.200
1.700
m
10.000
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.G
shaft
)
C.G from Pedestal Edge to Machine Center (X-direction) (E
dx
)
C.G from Pedestal Edge to Machine Center (Y-direction) (E
dy

)
6.0 CHECK FOR BLOWER FOUNDATION DESIGN
6.1 The Mass Ratio of Blower Foundation
(1) Foundation Weight
Pedestal (W
cp)
Footing (W
cf
)
= [(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!!
W
c
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
W
m
1.850
3.0
W
c
m
m
m
1.945
m
5.346
W
m
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 W
m
× (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
Q
Item No.
Q = 0.750 × Qa
(kN/m²)
Q=
W
t
Area
5
51-B-1001/2001/3001/400
1
50.937
5
51-B-1001/2001/3001/400
1
150.000
269.898
(kN/m²)
Length ( = FL)
(m)
Item No.
(m)
A
30.000

3.000
150.000
1528.110
50.937
W
m
Q
as
M
x
Q
a
0.750
W
t
200.000
Q
as
W
c
(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 / 3.0
0
=<%
= [(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'
W
t
1528.110
W
c
X'
a
(mm²)
cb
Top (mm²) Bottom (mm²)
Rebar Dia.
W
m
Z' 1.406
D20 D20 D12 1350.000
Use A
S

5.000
OK!!
Req'd A
S
= 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 Centrifu
g
al Force (F
o
)
1) F
0
=
(W
r

/ g) × e × w²
=
(W
r
/ g) × e × w²
= 64,750.000 / 981.0 × 0.00588 × 234.7
8
= 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) × 0.002
5
(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
W
r

= 1.000 = 0.000
= ton = ton
=kN=kN
W
c
= Weight of C.A.BLOWER = 13.000 ton = kN
W
m
= Weight of Motor = 9.400 ton = kN
W
b
= Weight of Base Plate = 2.600 ton = kN
W
s
= Weight of Silencer = 6.000 ton = kN
2) F
0
=
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
(W
c(rotor)
+ W
s
) × (W
m(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) F
0
=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) = F
V(blower)
× (h + C.G
.
[3.970]× (1.700 + 1.850)
kN-m
[Verti. Force
(motor)
]× (From Base to C.G) = F
V(motor)
× (h + C.G.)
[0.000]× (1.700 + 1.850)
kN-m
1.2 Calculation of center of gravity of machine & fdn.
W
p
==
W
m
==
W
b
==
W
w
==
W
E
==

W
E
/ g
kN-sec²/m
W
cp
==
W
cp
/ g
kN-sec²/m
W
cb
==
W
cb
/ g
kN-sec²/m
W
F
==
W
F
/ g
kN-sec²/m
W = = W / g
kN-sec²/m
I
o
= I (Machine) + I (Foundation)

=
W
e
k²
M
+ ∑ [W
F
/ 12 (a²
i
+ b²
i
) + W
F
k²
F
i
]
= [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
F
v(motor)
=
F
h(blower)
=
F
h(motor)
=
3.970

0.000
3.970
F
v(blower + motor)
=
M
r(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
F
h(blower + motor)
=

92.214 kN
M
r(motor)
=
0.000
F
v(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,
W
E
= Total Machine Weight
W
F
= Foundation Weight
W = Total Static Load (Total Machine Weight + Foundation Weight)

g = cm/sec²
I
o
=
SUM [m
i
(A
i
² + B
i
²) / 12 + m
i
K
i
²]
1.3 Coefficients B
v
, B
h
, and B
r
for Rectangular Footings
L = 3.000 m
B = 10.000 m
Coefficents β
v
, β
h
and β
r

for rectangular footings
2.0 Vertical Excitation Analysis
2.1 Spring Constant
(1) Equivalent radius (r
0v
) for Rectangular Foundation
r
ov
=
(FB × FL / π)
=m
(2) Embedment factor for Spring Constant
Effective Embedment height
η
v
=
1 + 0.6 × (1 - υ) × (h / r
ov
)
= 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
β
v
=
L / B
0.300
Roking (β
r

)
0.300
2.150
981.000
1.198
3.090
2.150
π
=
10.000 × 3.000
Horizontal (β
h
)
1.017
0.408
0.300
Coefficients
Vertical (β
v
)
AXIS OF
ROCKING
L
B
B
L
β
β
L/B
β

"Dynamic Analysis.xls"
(4) Equivalent Spring Constant for Rectangular Foundation
K
v
=
G / (1 - υ) × β
v
× FB × FL × η
v
= kN/m
2.2 Damping Ratio
(1) Effect of Depth of Embedment on Damping Ratio
α
v
=
[1 + 1.9 (1 - υ) × h / r
ov
] / η
v
= [1 + 1.9 × (1 - 0.321) × 1.500 / 3.090] / 1.198
=
(2) Mass Ratio
B
v
=
(1 - υ) / 4 × W / (γ × r
ov
³)
=
(3) Effective Damping Coefficient

This is not available for Vertical Mode
(4) Geometrical Damping Ratio
D
v
=
0.425 / B
v
× α
v
= 0.425 / 0.517 × 1.486
=
(5) Internal Damping
D
vi
=
(6) Total Damping Ratio
D
vt
=
=
=
155.771
Consider the Internal Damping
1 - 0.321
=
×
D
v
+ D
vi

(1 - 0.321)
0.040
=
1715667.000
1.486
1.733 × 3.090³
10.000 × 3.000 × 1.198
0.918
82579.233
2.150
0.878 + 0.040
0.878
×
4
0.517
×
"Dynamic Analysis.xls"
2.3 Frequency Check
(1) Natural Frequency
F
nv
=
60 / (2 × π) × ( K
v
/ m)
= 60 / (2 × π) × (1,715,667.000 / 155.771)
= rpm
(2) Resonance Frequency (rpm)
F
rv

=
F
nv
× [1 - (2 × D
vt
²)]
= 1,002.178 × [1 - ( 2 × 0.918²)]
∴
2 × D
vt
²
= 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
M
v
(
blower
)
=
1 / (1 - r
v(blower)
²)² + (2 D
vt
× r

v(blower)
)²
= 1 / (1 - 2.237²)² + (2 × 0.918 × 2.237)² =
= < 1.500
For Motor
M
v
(
motor
)
=
1 / (1 - r
v(motor)
²)² + (2 D
vt
× r
v(motor)
)²
= 1 / (1 - 1.487²)² + (2 × 0.918 × 1.487)² =
= < 1.500
For Blower For Motor
r
v(motor)
=
=
0.335
0.335
OK!!!
f
v(motor)

2242.000
F
nv
1490.000
0.174
1.487
OK!!!
RESONANCE NOT POSSIBLE!!! (There is no need to analysis Vibration)
=
r
v(blower)
0.174
=
1002.178
f
v(blower)
1002.178
2.237
Not Apply
1002.178
OK!!!
F
nv
OK!!!
"Dynamic Analysis.xls"
(5) Transmissibility Factor
For Blower
T
v(blower)
=

M
v(blower)
× 1 + (2 D
vt
× r
v
)²
= 0.174 × 1+ (2 × 0.918 × 2.237)²
=
For Motor
T
v(motor)
=
M
v(motor)
× 1 + (2 D
vt
× r
v
)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)
=
M
v(blower)

× F
v(blower)
/ K
v
V
rocking(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)
=
M
v(motor)
× F
v(motor)
/ K
v
V
rocking(motor)
=
R
(motor)
× (FL / 2)
= 0.0000000 × (3.000 / 2)

=m =m
Total Vertical Amplitude
V
total
=
V
(blower)
+ V
rocking(blower)
+ V
(motor)
+ V
rocking(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 (r
0h
) for Rectangular Foundation
r
oh
= (FB × FL / π)
=m
(2) Emebedment factor for Spring Constant
Effective Embedment height
η
h
=
1 + 0.55 × (2 - υ) × (h / r
oh
)
= 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
β
h
=
(4) Equiavelent Spring Constant for Rectangular Foundation
K
h
=
2 × (1 + υ) × G × β
h
× FB × FL × η
h

= 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
α
h
=
[1 + 1.9 (2 - υ) × h / r
oh
] / η
h
= [ 1 + 1.9 × (2 - 0.321) × 1.500 / 3.090] / 1.448
=
(2) Mass Raito
B
h
=
(7 - 8υ) / [32 × (1 - υ)] × W / (γ × r
oh
³)
=
=
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
AXIS OF
ROCKING
L
B
"Dynamic Analysis.xls"
(3) Effective Damping Coefficient
This is not avilable for Horizontal Mode
(4) Geometrical Damping Ratio
D
h
=
0.288 / B
h
× α
h
= 0.288 / 0.621 × 2.118
=
(5) Internal Damping
D
hi
=
(6) Total Damping Ratio
D
ht

=
=
=
3.3 Frequency Check
(1) Natural Frequency
F
nh
=
60 / (2 × π) × (K
h
/ m)
= 60 / (2 × π) × 1,760,211.961 / 155.771
= rpm
(2) Resonance Frequency (rpm)
F
rh
=
F
nh
× [1 - (2 × D
ht
²)]
= 1,015.000 × [1 - (2 × 0.814²)]
∴
2 × D
ht
²
= 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
D
h
+ D
hi
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
M
h
(
blower
)
=
1 / (1 - r
h(blower)
²)² + (2 D
ht
× r
h(blower)
)²
= 1 / (1 - 2.209²)² + (2 × 0.814 × 2.209)² =

= < 1.50
For Motor
M
h
(
motor
)
=
1 / (1 - r
h(motor)
²)² + (2 D
ht
× r
h(motor)
)²
= 1 / (1 - 1.468²)² + (2 × × 1.468)² =
= < 1.50
(5) Transmissibility Factor
For Blower
T
h(blower)
=
M
h(blower)
× 1 + (2 D
ht
× r
h(blower)
)²
= 0.189 × 1 + ( 2 × 0.814 × 2.209)²

=
For Motor
T
h(motor)
=
M
h(motor)
× 1 + (2 D
ht
× r
h(motor)
)²
= 0.377 × 1 + ( 2 × 0.814 × 1.468)²
=
0.377
0.377
OK!!!
0.977
For Motor
r
h(blower)
1490.000
r
h(motor)
=
f
h(motor)
F
nh
f

h(blower)
F
nh
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)
=
M
h(blower)
× F
h(blower)

/ K
h
H
rocking(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)
=
M
h(motor)
× F
h(motor)
/ K
h
H
rocking(motor)
=
R
(motor)
× (h + C.G.)
= 0.0000000 × (1.700 + 1.850)
=m =m
Total Horizontal Amplitude

H
total
=
H
(blower)
+ H
rocking(blower)
+ H
(motor)
+ H
rocking(motor)
=m
4.0 Rocking Excitation Analysis
4.1 Spring Constant
(1) Equivalent (r
0r
) for Rectangular Foundation
r
or
=
[(FB × FL³) / (3 × π)]^(¼)
^(¼)
=m
(2) Embedment factor for Spring Constant
η
r
=
1 + 1.2 × (1 - υ) × (h / r
or
) + 0.2 × (2 - υ) × (h / r

or
)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
AXIS OF
ROCKING
L
B
"Dynamic Analysis.xls"
(3) Spring Constant Coefficient

β
r
=
(4) Equivalent Spring Constant for Rectangular Foundation
K
r
=
G / (1 - υ) × β
r
× FB × FL² × η
r
= kN/m
4.2 Damping Ratio
(1) Effect of Depth of Embedment on Damping Ratio
=
(2) Mass Ratio
B
r
=
3 × (1 - υ) / 8 × I
o
/ (ρ × r
or
5
)
=
(3) Effective Damping Coefficient
n
r
=

(4) Geometrical Damping Ratio
D
r
=
0.15 × α
r
/ [(1 + n
r
× B
r
) × (n
r
× B
r
) ]
=
(5) Internal Damping
D
ri
=
7234608.000
η
r
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
α
r
1.733 × 66.277
=
(1 + 1.251 × 1.387) × (1.251 × 1.387)
1 + 0.7 × (1 - υ) × (h / r
or
) + 0.6 × (2 - υ) × (h / r
or
)³
0.15 × 1.244
=
"Dynamic Analysis.xls"
(6) Total Damping Ratio
D
rt
=
=

=
4.3 Frequency Check
(1) Natural Frequency
F
nr
=
60 / (2 × π) × (K
r
/ I
0
)
= 60 / (2 × π) × [7,234,608.000 / 625.640]
= rpm
(2) Resonance Frequency
F
rr
=
F
nr
× [1 - (2 × D
rt
²)]
= 1,027.000 × [1 - (2 × 0.092²)]
= rpm
∴
2 × D
rt
²
= 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
f
r(motor)
OK!!!
For Blower
F
nr
For Motor
r
r(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
D
r
+ D
ri

r
r(blower)
=
f
r(blower)
F
nr
2242.000