Blower Foundation

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)) ×


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


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


(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

×


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!!!


(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


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


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


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


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



This is not avilable for Horizontal Mode


Dh = 0.288 / Bh × αh

= 0.288 / 0.621 × 2.118

=


Dhi =


Dht =

=

=

3.3 Frequency Check


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



When f / f(n) < 0.7, f / f(n) > 1.3, O.K!!!

= =


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


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



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

=


= 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



βr =

(4) Equivalent Spring Constant for Rectangular Foundation

Kr = G / (1 - υ) × βr × FB × FL² × ηr

= kN/m

4.2 Damping Ratio


=

(2) Mass Ratio

Br = 3 × (1 - υ) / 8 × Io / (ρ × ror5)

=


nr =


Dr = 0.15 × αr / [(1 + nr × Br) × (nr × Br) ]

=


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

=



Drt =

=

=

4.3 Frequency Check


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


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



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


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

=


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

=


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


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


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


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

Blower Foundation

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