Pump+Turbine_ foundation design spreadsheet

FOR CONSTRUCTION

0A

10.10.25

MVR

0

09.09.18

MVR

Rev

Date

Prepared

P.C

S.B

ISSUED FOR CONSTRUCTION

P.C

H.B.J

ISSUED FOR CONSTRUCTION

Checked

Approved

Details of Revision

Owner

Owner’s Engineer Contractor

Sub-Supplier

Project

PC

1 x 660 MW CIREBON COAL FIRED POWER PLANT

T07119 UAS Code VE04

Date

Name

Scale

Unit Code

Title

KKS Code

P1 Prepared Checked Approved Dept.

09.09.18

MVR

09.09.18

P.C

09.09.18

S.B

UMA

ANALYSIS & DESIGN OF BOILER FEED PUMPTURBINE DRIVEN(A)

Reg. No. 161008 Rev. 0A

CIVIL

Document No.

Page-No.

T07119-VE04-P1UMA-161008

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION

Designed By

Checked By

Approved By

M V REDDY

P.CHATTOPADHYAY

S.B

CONTENTS SECTION

PAGE NO.

1

SCOPE

2

2

DESIGN PHILOSOPHY

2

3

DATA

2

4

STATIC DESIGN OF PUMP FOUNDATION & DYNAMIC LOADS INPUT & DESIGN LIMITS

3

5

ECCENTRICITY CHECK

7

6

PRELIMINARY PILE CAPACITY CHECK

7

CALCULATION OF SPRING CONSTANTS & DAMPING RATIOS

9

8

CALCULATION OF FREQUENCIES & AMPLITUDES

13

9

PILE CAPACITY CHECK

16

REINFORCEMENT CALCULATION

18

10

8

APPENDIX-A

LOAD INPUT

A

APPENDIX-B

REFERENCES

B

2 of 17

3 of 17

CIREBON (695 MW x1 DESIGN OF Boiler Feed Pump - Turbine Driven

Designed By

Checked By

Approved By

M V REDDY

P.Chattopadyay

S.B

1.0 SCOPE: This document covers the Static & Dynamic analysis for Boiler Feed Pump Foundation (Turbine Driven) of the Project 660 MW Coal Fired Power Plant at Cirebon, Indonesia.

2.0 DESIGN PHILOSOPHY: The pump and turbine are mounted on acommon rectangular block foundation resting on piles. The block foundation is designed for the pump and turbine weight as per vendor drawing.

3.0 DATA: 3.1 Material Data Concrete Design Compr. Strength of concrete F'c

=

27.5

N/mm2

Grade of concrete for Spun Pile

=

27.5

N/mm2 (Cylindrical strength)

c w

=

25

KN/m3

Unit weight of water

=

10

KN/m3

Concrete cover for foundations

Cc

=

75

mm

fy

=

410

N/mm2

=

78.5

KN/m3

=

19

KN/m3

Unit weight of concrete

Reinforcement Yield Strength of steel unit weight of steel

3.2 Soil Data Unit weight of soil

s

(From Geo tech report )

3.3 Ground water table: Water level is assumed to be at finished grade elevation for critical effect.

4 of 17

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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Approved By

M V REDDY

4.0 STATIC DESIGN OF PUMP FOUNDATION 4.1. DESIGN DATA 4.1.1 Block Dimensions: LB

Length in X-direction Length in Z-direction Height of the Block Above HPP Depth of Foundation from HPP Total Height of Block

BB HB_AG D HB

= =

7.90 3.00

m m

= =

0.1 1.20

m m

=

1.3

m

4.1.2 Pump Data: Length of the skid in X-direction Width of the skid in Z-direction

LS BS

= =

3.771 m 2.34 m

286 91.9

Ht.of the skid in Y-direction

HS

= =

0.27 m 18

10.5

= = =

25 2.946 m 2.20 m

31 83

=

1.21 m

48

No. of anchor bolts Anchor Bolts Dia C/c distance bet. far end bolts along length,L a C/C distance bet. far end bolts along width,B a

Mz Z

hS

CL of Discharge

Height of shaft from u/s of skid

4.13

Y CL of Pump hs

BB

Ba Bs

Hs HB_AG HPP

HB

LS LB

La

D

X

X Mx

PLAN VIEW

SECTION VIEW

4.1.3 Motor Data: Length of block in X-direction Width of the block in Z-direction Ht.of the Shaft from u/s of skid

Lt Bt Htb

= = =

2.985 m 2.34 m 1.21 m

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ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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Approved By

M V REDDY 4.1.4 Unit Weights: Unit weight of concrete

c

=

25 kN/m³

Unit weight of Water Unit weight of soil(Saturated)

w s

= =

10 kN/m³ 18 kN/m³

4.2 STATIC LOADS 4.2.1 Pump Weight: Pump Weight,

Pp

=

8165 kg Ppr = 2450 = 4414 kg = 363 kg Total weight of pump, W P = Pp + Pb + Po W cf1 Weight of concrete fill inside the skid Pump rotor Weight, Pb Base Weight, Po Other

kg

=

80.10 kN

= =

24.03 kN 43.30 kN 3.56 kN

=

= 150.99 kN > 22.27 KN = 3.771 x 2.335 x 0.267 x 2 = 58.8 KN

4.2.2Motor Weight: Pp Turbine Package We Turbine rotor Weight,

=

Gear Box rotor Weight,

8392 kg Ppr = 2517 Ppr = 0

kg

= =

82.33 kN 24.69 kN

kg

=

0.00

=

100

mm =

0.1

m

=

50

mm =

0.05

m

kN

4.3 PRELIMINARY FOUNDATION CHECK: 4.3.1 Check for Plinth Size: Minimum bolt edge distance, Dmin Minimum edge of skid to concrete,Cmin Therefore Min. plinth length required Min. plinth length required

= ( 2 x Dmin ) + La+ Lt = ( 2 x 0.1 ) + 9.116 = 6.131 m ( 2 x C ) + L = = ( 2 x 0.05 ) + 6.756 = m 6.856 min s+Lt = Max of the above = 6.856 m <

7.9

m

3

m

Hence O.K Min. plinth width required Min. plinth width required

= ( 2 x Dmin ) + W a = ( 2 x Cmin ) + Bs

= ( 2 x 0.1 ) + 2.2 = ( 2 x 0.05 ) + 2.335

= Max of the above

= = =

2.4 2.435

m m

m < 2.435 Hence O.K

4.3.2 Check for Foundation Depth: Min. foundation depth

= 0.60 + L/30 = 0.863 m

( Where L is greater of length or width in meters ) < 1.3 m Hence O.K

5 of 17

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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M V REDDY 4.3.3 Check for Foundation Weight: WP

Total weight (Pump+Turb) Foundation weight, W f

= 233.32 kN = (7.9 x 3 x 1.3 x 25 ) = 770.25 KN > 3 times the pump weight+Turb. Fdn Block Wt.) 3.30126

Total Vertical force

FY

Hence O.K

= W P + W cf1 + W f + W t = 150.99 + 58.8 + 770.25 +82.33

=

1062.37

KN

=

1158.45

KN

= Mx_I = Σ'0.25 x 150.99 x (1.21 + 0.1 + 1.2 ) = Mz_I

=

145.38

KNm

= Σ'0.25 x 150.99 x (1.21 + 0.1 + 1.2 )

=

145.38

KNm

Total Vertical force with 50% impact load = FY + 50% W P+25% WT Fyi

= 1062.37 + 0.5 x 150.99 +0.25 x 82.33

Moment due to impact load (i.e.25% of (pump +turbine) weight acting at shaft level) Total Mom in Long. Direction at Bottom of base Total Mom in Tran. Direction at Bottom of base

MX Mz

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ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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M V REDDY 4.4 DYNAMIC LOADS INPUT & DESIGN LIMITS 4.4.1 Pump data: Dynamic forces from vendor data** S.No Description Rotor weight kN 1 2

Pump Shaft

24.03 0.00

Speed (rpm)

Dynamic force* kN

Vertical Fy (kN)

Longitudinal Fx (kN)

Lateral Fz (kN)

Rocking T (kNm)

1780 0

7.13 0.00

0 0

0 0

0 0

0 0

0

0

0

0

3 Motor 24.69 1800 7.41 * Dynamic force (kN) = (Rotor weight )x(Rotor speed,r.p.,m) / 6000

4.4.2 Soil & Pile parameters for Dynamic loads

(From Geo tech report Table 1)

Soil Dynamic Shear Modulus( G ) Dynamic Shear Modulus( Gf ) for embedment Poisson ratio of soil,

=

368732

= =

121437 0.35

Soil internal damping ratio (D)

=

0.03

Pile Type of Pile

=

KN/m2 KN/m2

Drilled Concrete end bearing

Diameter of pile Number of piles considered

d n

= =

0.45 8

m

Length of Piles Spacing between piles, X-dir Spacing between piles, Z-dir

l ax az

= =

m m m

Edge Distance from Central Line of Pile Allowable Compression load

e

= =

15 2.4 2.3

m

P T

= =

0.35 445

L

=

Allowable Tension load Allowable lateral load

> 3 Dp - OK > 3 Dp - OK

kN kN

289 222

kN

4.4.3 Alloawable limits for design

of LB

Allowable eccentricity of C.G.in X-direction,x Allowable eccentricity of C.G.in Z-direction,z

= =

5% 5%

C.G.in Y-direction,y

=

Below TOC

Damped Natural Frequencies shall be less than or more than

= =

0.8 1.2

Allowable peak-to-peak amplitude

=

Range of shear modulus (G) values to consider

=

of BB

 

16 microns 0.5

to

= =

0.05 x 7.9 0.05 x 3

= =

0.395 0.15

m m

=

1.3

=

1.3

m

= =

0.8 x 1780 1.2 x 1780

= =

1424 2136

rpm rpm

Fig 3.7 of Arya, Neil & Pincus 1

7 of 17

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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Approved By

M V REDDY

5 ECCENTRICITY CHECK (Eccentricity of C.G. of machine+foundation system to be checked in all 3 directions w.r.t. C.G of foundation) 5.1 COMPUTATION OF CG OF BASE BLOCK

Elements pump

Area (m2) Ai

Dimensions(m) Lxi Lzi Lyi -

Coordinates of CG of elements xi(m) zi(m) yi(m)

-

-

2.23

1.42

2.42

-

-

5.61 3.95

1.50 1.50

2.53 1.60

3.00

1.30

23.7

3.95

1.50

23.7

15.74 5.917

C.G. of Foundation ,x dir-, X

=

C.G. of Foundation ,z dir-, Z C.G. of Foundation ,y dir-, Y

= =

AiXi/Ai AiZi/Ai

Motor Base Plate Foundation Block 7.90

Total

Static moment of area Ai*Xi Ai*Zi Ai*Yi -

-

-

0.65

93.6

35.6

15.4

7.19

93.6

35.55

15.4

AiYi/Ai

=

93.615 / 23.7

=

3.950

m

= =

35.55 / 23.7 15.405 / 23.7

= =

1.500 0.650

m m

5.1 COMPUTATION OF CG OF MACHINE & FOUNDATION BLOCK

Elements Pump

Mass mi Wi (kN) kNsec2/m 80.10 8.17

Coordinates of CG Static moment of mass of elements (kNSec2) xi zi yi mixi mizi miyi 2.23 1.42 2.42 18.219 11.58 19.76

Weight

Base Plate Motor

43.30 82.33

4.41 8.39

3.95 5.61

1.50 1.50

1.60 2.53

17.42 47.093

6.62 12.6

7.04 21.18

Foundation Block

770.25

78.52

3.95

1.50

0.65

310.15

117.8

51.04

Total

975.98

99.49

15.74

5.92

7.19

393

149

99

Combined C.G. in X direction,xo Combined C.G. in Z direction,zo Combined C.G. in Y direction,yo

= =

mi.xi/mi mi.zi/mi

=

mi.yi/mi

=

392.88567/99.49

=

3.95

m

= =

148.55689/99.49 99.02058/99.49

= =

1.49 1.00

m m

5.2 ECCENTRICITY OF CG OF FOUNDATION SYSTEM W.R.T. PILE GROUP (check with limits in 4.4.3)

C.G. OF Pile group in X-direction, Xp

=

C.G. OF Pile group in Z-direction, Zp

=

Eccentricity in X direction (x-x0)

Eccentricity in Z direction (z-z0)

in Y direction, y0

3.950 1.500 = =

3.95 - 3.95 0.00

m

<

0.395

m

Hence OK

= =

1.5 - 1.49 0.01

m

<

0.15

m

Hence OK

=

1.00

<

1.3

m

Hence OK

8 of 17

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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6 PRELIMINARY PILE CAPACITY CHECK 6.1 PILE GROUP CONFIGURATION Pile No

X-coord of Z-coord of pile from pile from origin, x(m) origin, z(m)

Distance b/w pile & pile group C.G

Xg2

Zg2

Xg2+Zg2

xg

zg

1 2

0.35 2.75

0.35 0.35

-3.600 -1.200

-1.150 -1.150

12.96 1.44

1.3 1.3

14.28 2.76

3 4

5.15 7.55

0.35 0.35

1.200 3.600

-1.150 -1.150

1.44 12.96

1.3 1.3

2.76 14.28

5 6 7

0.35 2.75 5.15

2.65 2.65 2.65

-3.600 -1.200 1.200

1.150 1.150 1.150

12.96 1.44 1.44

1.3 1.3 1.3

14.28 2.76 2.76

8 9

7.55

2.65

3.600

1.150

12.96

1.3

14.28

31.60

12.00

57.60

10.58

10 11 12 13 14 15 16 17 Total

C.G of pile group in x-direction w.r.t origin

x1

=

Σx/n

C.G of pile group in Z-direction w.r.t origin Distance b/w pile and pile group C.G

z1 xg zg

= = =

Σz/n x-x1 z-z1

M.I of pile group about C.G x-x M.I of pile group about C.G y-y Section modulus of pile group abt X axis

Ixp Izp

= =

Iyp zxp

=

Section modulus of pile group abt Z axis

zzp

Distance b/w pile and pile group C.G M.I of pile group about C.G z-z

6.2 PILE CAPACITIES Max. compression load on each pile (Due to Mxi)

Max. compression load on each pile (Due to Mzi)

Max. Tension load on each pile (Due to Mxi)

Max. Tension load on each pile (Due to Mzi)

Max Lateral Load

= =

=

12 / 8

Σxg2 Σzg2

= =

57.60

m2

Σxg2+Σzg2 Σxg2/xg, max

= =

10.580 68.18 57.6 / 3.6

m2 m2

Σzg2/zg, max

=

10.58 / 1.15

m

= 16.000 = 9.200

m m

m

m

Fyi / n + MXi / ZXp

= = =

Fyi / n + Mzi / Zzp

= =

Fyi / n - MXi / ZXp

=

135.72

= =

Fyi / n - Mzi / ZXp

=

129.00

=

= 3.950 = 1.500

m

= = =

= =

68.18 = 31.6 / 8

1158.45 / 8 + 145.38295 / 16 153.89 < 445x50% = kN

223 kN Safe

1158.45 / 8 + 145.38295 / 9.2 160.61 < 445x50% = kN

223 kN Safe

1158.45 / 8 - 145.38295 / 16 <

kN

-289.00

kN

Safe

-289.00

kN

Safe

1158.45 / 8 - 145.38295 / 9.2 <

kN

25% of (Pump weight +Turbine Weight +Foundation Weight) 0.25 x (312.94 + 667+4310 )/17 31.36

<

kN

222 kN Safe

7 CALCULATION OF SPRING CONSTANTS & DAMPING RATIOS 7.1 PILE PROPERTIES Young's modulus of the pile material

Area of cross section of pile

Ep

Ap

=

4700 (fck)0.5

=

2.46.E+07

= =

3.1416 / 4 x (0.45^2) 0.159

kN/m2

m2 9 of 17

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Designed By

Checked By

Approved By

M V REDDY

10 of 17

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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Approved By

M V REDDY ro

The equivalent radius of pile

= = =

Moment of inertia of the pile

= =

Ip

Shear wave velocity of soil, (From Geo tech report Table 1)

(Ap/)0.5 (0.159 / 3.1416)^0.5 0.225 m d4)/64 3.1416 / 64 x (0.45^4)

=

0.0008

=

448

25.0 kN/m3

Unit weight of pile material

p

=

Compression wave velocity in pile

Vc

= =

L/ro

= =

dependant factor for coeffieicients

a0

= = = =

fx,i

Pile stifness factor

m/sec

(EP *g/P)0.5 (24647008 x 9.81 / 25 )^0.5

= Pile slenderness

m4

3109.9 m/sec (15)/(0.23) 66.67 2* f * ro / (G*g/s)0.5 2x3.1415x1780x0.225 / (448.284 ) 5.61 Table below (Appendix-B at pile tip) Fig.5-1a &Table 5-2 of Arya, Neil & Pincus f11,1 f11,2 f7,1 f7,2

G



L/ro

Vs/Vc

f18,1

f18,2

f9,1

f9,2

1.00G 0.50G

0.35 0.35 0.35

66.67 66.67

0.1441 0.1019

0.035 0.023

0.05 0.03

0.0291 0.0185

0.069 0.0438

0.399 0.3490

0.2785 0.2430

-0.077 -0.0582

-0.112 -0.0848

66.67 66.67

0.1144 0.1257

0.0290 0.035

0.0400 0.05

0.0238 0.0291

0.0564 0.069

0.3740 0.399

0.2608 0.2785

-0.0676 -0.077

-0.0984 -0.112

0.89G 66.67 0.1360 1.00G 0.35 66.67 0.1441 Pile cap stiffness factor

0.0365 0.038

0.055 0.06 Sx,i

0.0344 0.0816 0.4245 0.29625 0.0397 0.0942 0.45 0.314 = Table below (Appendix-B at pile tip)

-0.087 -0.097

-0.1265 -0.141

0.63G 0.76G

0.35 0.35



S1

S2

Su1

Su2

0.350

2.7

6.7

4.1

10.5

Table 5-1 of Arya, Neil & Pincus S S2 2.5

1.8

7.1.1 Individual Pile Spring constants & Damping constants (Equations 5-5, 5-6, 5-12, 5-13, 5-18, 5-19, 5-21 & 5-24 of Arya et al. - Refer Appendix-B) Mode of Vibration Vertical Y

Horizontal, X,Z

Rocking 

Cross stiffness 

Individual Pile Spring constant K

Individual Pile Damping constant C

1

1 y

y

= (Ep*Ap/ro)*f18,1 = 24647008 x 0.159 / 0.225 x 0.035

= =

= 609602.66 K1x

= 437.1 C1x

kN/m

(Ep*Ap/Vs)*f18,2 24647008 x 0.159 / 448.284 x 0.05

= (Ep* Ip/ro3)* f11,1 = 24647008x0.0008 / 0.225^3 x 0.0291

= =

= 50373.21 K1 = (Ep*Ip/ro)*f 7,1

= 59.95 C1 = (Ep*Ip/Vs)*f7,2

kN/m

(Ep*Ip/ro2*Vs)*f11,2 (24647008x0.0008 /(0.225^2x448.284))x0.069

= 24647008x0.0008 / 0.225 x 0.399

=

= 34965.89 K1x = (Ep*Ip/ro2)*f 9,1

= 12.25 C1xθ

kNm/radian

kN-sec/m

(24647008 x 0.0008 / 448.284) x 0.2785

= =

(Ep*Ip/roVs)*f

= 24647008x0.0008 / 0.225^2 x -0.077 = -29990.24

=

-21.89

kNm/radian

kN-sec/m

kNm-sec 9,2

(24647008x0.0008 /(0.225x448.284))x-0.112 kNm-sec

11 of 17

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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M V REDDY 7.2 PILECAP PROPERTIES Area of pile cap

A

= =

7.9 X 3 23.70

m2

Effective depth of pilecap below FGL

h

= =

1.2 - 75/1000 1.125

m

The Equivalent radius of pilecap

rc

= =

(A/)0.5 (23.7 / 3.1416)^0.5

Depth to radius ratio

h/rc

= =

2.75 1.125 / 2.75

= 0.409 7.2.1 Pilecap Spring constant & Damping constant (Equations 5-10, 5-11, 5-16, 5-17, 5-122 & 5-25 of Arya et al. - Refer Appendix-B) Mode of vibration Vertical, Y Kfy = Gf*h*S1

Pilecap Damping constant Cfy =

=

= 121437 x 1.125 x 4.1 = 560128.16 Kf = Gf rc2 h SØ1+

(h*rc)*(Gfxf/g)0.5 *S2

= 1.125x2.75 x (121437x18/9.81)^0.5 x6.7 = 9784 kN.sec/m Cfx

kN/m

(h*rc)*(Gf*f/g)0.5 * Su2

= 1.125x2.75 x (121437x18/9.81)^0.5 x10.5 = 15334 kN.sec/m Cf

kN/m

=

Gf rc2 h [(h/rc)2/3+(Yc/rc)2-(h/rc)*(Yc/rc)] Su1

h rc3 (Gf f/g)0.5 * {S2+[(h/rc)2/3+(Yc/rc)2-(h/rc)*(Yc/rc)] Su2}

= 121437x2.75^2 x 1.125x2.5+ 121437x2.75^2"x1.125x

= 1.125x2.75^3x(121437x18/9.81)^0.5x (1.8+(0.409^2/3+(1/2.75)^2-0.409x(1/2.75))x10.5)

[(0.409^2/3+(1/2.75)^2-0.409x(1/2.75)]x4.1 = 2749231.13 kNm/radian

=

7.3 MASS MOMENTS OF INERTIA AND INERTIA RATIOS Elements

m

Pilecap Spring constant

= 121437 x 1.125 x 2.7 = 368864.89 f horizontal K x X,Z = Gf*h*Su1

Rocking 

m

mass mi

mass moment of inertia of individual elements abt its own axis

kNsec2/m

Ix = mi /12 *(Lyi2+Lzi2)

Iy = mi /12 *(Lxi2+Lzi2)

Iz = mi /12 *(Lxi2+Lyi2)

PUMP

8.17

-

-

BP Turbine

4.41 8.39

-

-

-

Foundation Block

78.52

69.948

Total

99.49

69.948

24432.47

kNm-sec

(Table 4.6 of Arya, Neil & Pincus) Distance between common C.G. & C.G. of individual elements (m) xoi zoi yoi

Mass moment of inertia of whole system about common CG Ix = mi* (yoi2+zoi2)

Iy = mi* (xoi2+zoi2)

Iz = mi* (xoi2+yoi2)

-1.418

16.47

24.214

40.598

1 -1.525

14.201 19.513

78.598 23.204

73.217 42.715

0.35

9.627

0.01

9.619

59.81

126.02

166.15

xo - xi

zo - zi

yo - yi

1.72

0.073

-

3.95 -1.663

1.49 -0.01

467.259

419.428

0

-0.01

467.259

419.43

12 of 17

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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Mass Moment of Inertia of the whole system about each Mass Moment of Inertia of the whole system about axis passing through the common C.G. & perpendicular each axis passing through the centroid of the base to the plane of vibration area & perpendicular to the plane of vibration Iox

Ioz

Ioy

=

1/12 x mi(lyi2+lzi2)+mi(yoi2+zoi2)

= =

69.948 + 59.812 129.8 kN sec2-m 2 1/12 x mi(lxi +lyi2)+mi(xoi2+yoi2)

= = = = =

= =

129.76 + 99.49 x 1^2 kN sec2-m 229.3 2 Ioz + m.yo

419.428 + 166.149

=

585.6 kN sec2-m 2 1/12 x mi(lxi +lzi2)+mi(xoi2+zoi2)

=

585.577 + 99.49 x 1^2 kN sec2-m 685.1

Iz =

Iy =

467.259 + 126.024

x = Iox/Ix = 129.76 / 229.25 = 0.566 z = Ioz/Iz = 585.577 / 685.067

Iox + m.yo2

Ix =

=

0.855

Ioy =

kN sec2-m

593.28

= 593.28 kN sec2-m Mass moment of inertia effective against rocking excitation , I

=

229.25

kN sec2-m

Mass moment of inertia effective against cross excitation ,I

=

593.28

kN sec2-m

Effective Mass for translation (both Vertical and Horizontal) excitation ,m c

=

99.49

kN sec2/m

7.4 PILEGROUP PROPERTIES (Equations 5-8, 5-9, 5-20 & 5-23 of Arya et al. - Refer Appendix-B) A Interaction factor for piles =

3.78

Mode of vibration

Ratio between moments of inertia



=

6.31

Pile group - Spring constants, Damping constants & Damping ratios k Spring constant

Vertical, Y

Damping constant Damping ratio Spring constant

horizontal X,Z

Damping constant Damping ratio

g y

1 f = n ky /αA+ky

=

(8x609602.66) /3.78 + 368864.89

= Cyg 1 0.5 f = n cy /αA +cy Dyg = (cyg) / [2(kygmc)0.5]

1290164.36

kN/m

= =

(8x437.1) /(3.78)^0.5 + 9784.47 1798.56 kN.sec/m

=

1798.56 /(2x1290164.36x99.49)^0.5 0.11

=

<

0.150

*

kxg 1 f = n kx /αB+kx

= =

(8x50373.21) /6.31 + 560128.16 63864.61 kN/m

=

(8x59.95) /(6.31)^0.5 + 15333.87 190.93 kN.sec/m

Cxg 1 0.5 f = n cx /αB +cx

= Dxg = (cxg) / [2(kxgmc)0.5]

190.93 /(2x63864.61x99.49)^0.5

= =

0.05

<

0.150

*

kg

Spring constant

= ΣN (K1+Ky1zr2+Kx1Yc2-2 Yc K1x)+Kf Zr1 = 1.49 - 0.35 = 1.140 m Zr2 = 3 - 1.49 - 0.35 = 1.160 m = 8x34965.89 + 8x609602.66x(10.58) + 8x50373.21x1^2 - 8x2x1x-29990.24 + 2749231.13 = Cg

Rocking 

55508556.91

kNm/radian

Damping constant

= ΣN (C1ψ+Cy1zr2+Cx1Yc2-2 Yc C1xψ)+Cfψ = 8x12.25+8x437.1x(10.58)+8x59.95x1^2-8x2x1x-21.89+24432.47 kNm-sec = 62356.5 Dg

Damping ratio

= (cg) / [2(kgI)0.5] = 62356.45 /(2x55508556.91x229.25)^0.5 =

0.39

>

0.100

* 13 of 17

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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7.5 SUMMARY OF SPRING CONSTANTS AND DAMPING RATIOS Mode of vibration Vertical Y (kN/m)

Spring constant 1290164.36

Damping ratio* 0.11

Horizontal X(kN/m) Rocking (kN/m/rad)

63864.61 55508556.91

0.05 0.10

8 CALCULATION OF FREQUENCIES & AMPLITUDES 8.1 CALCULATION OF DYNAMIC FORCES (if vendor data is not available) Location No Description

Rotor weight kN

Speed w(rpm)

Dynamic force kN

1 2

PUMP G BOX

24.03 0.00

1780 0

7.129 0.000

3

Turb

24.69

1800

7.407

Point of Application at Shaft Combined C.G of machine and Location foundation X(m) Y(m) Z(m) Xo (m) Yo (m) Zo(m) 2.230 2.418 1.417 3.950 1.000 1.490 5.61 2.525 1.500 3.950 1.490 1.000 5.61

2.525

1.500

3.950

1.000

1.490

8.1.1 Dynamic forces Rocking (Due to Rocking (due Lateral translation) to shaft ecentricity)

No

Description

Lateral translation Fz(kN)

Longitudinal translation* Fx(kN)

Vertical translation Fy(kN)

Mψ1 (kNm)

Mψ2 -kNm

1 2

PUMP G BOX

7.129 0.000

0.000 0.000

7.129 0.000

10.629 0.000

0.520 0.000

7.407 14.536

0.000 0.000

7.407 14.536

11.370 21.999

0.074 0.594

3 Turb Total transmitted force =

* Longitudinal translation not considered since it is usually lesser than that of Lateral translation 8.2 CALCULATION OF NATURAL FREQUENCIES Resonance frequency  mr [n (1-2D2)0.5]

Undamped Natural frequency,  n [ (60/2π)x(K/m)0.5]

Mode of Vibration Vertical Horizontal

(60/(2x3.14))x(1290164.36/99.49)^0.5 (60/(2x3.14))x(63864.61/99.49)^0.5

= =

1087 242

(1087x(1-2x0.112252932901 = (242x(1-2x0.053559846919 =

1073 241

Rocking

(60/(2x3.14))x(55508556.91/229.25)^0.5

=

4699

(4699x(1-2x0.1^2)^0.5

4652

=

8.3 CALCULATION OF FREQUENCY RATIO ,MAGNIFICATION FACTOR ,DISPLACEMENT,AMPLITUDE , TRANSMISSIBLITY FACTOR AND TRANSMITTED FORCE (Table 1.4 of Arya, Neil & Pincus) (Since the machine will operate at constant speed, formulae associated with sinusoidal force of constant amplitude are used in the dynamic analysis) Mode of Vibration

Frequency ratio, r

Magnification factor, M

Transmissiblity factor, Tr

Transmitted force/moment

Displacement response, Ax

n

1/((1-r2)2+(2Dr)2)0.5

(1+(2Dr)2)0.5 / [(1-r2)2+(2Dr)2]0.5

FtrTrFo

M(Fo/K)

Vertical,Y Horizontal,X

1.638 7.355

0.589 0.019

0.604 0.019

8.782 kN 0.000 kN

7 Micron 0 Micron

Horizontal,Z

7.355 0.379

0.019 1.137

0.019 1.159

0.275 kN 26.196 kNm

4 Micron 4.6E-07 radians

Rocking,

14 of 17

ANALYSIS & DESIGN CALCULATION FOR PUMP + TURBINE FOUNDATION Checked By

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8.4 FORCES & AMPLITUDES FOR VARIOUS ROTOR POSITIONS 8.4.1 Dynamic loads - In-phase & 180 degrees out-of-phase Rotor Position

Load Case

Lateral Translation

Longitudinal Translation

Vertical Translation

Rocking (Due to Translation Force)

Rocking (Due to shaft eccentricity)

Pitching

Twisting

Fz(kN)

Fx(kN)

Fy(kN)

MØ' (kNm)

MØ2 (kNm)

Mψ1 (kNm)

M1 (kNm)

In Phase In Phase

1 2

14.536 -

-

14.536

21.999 -

0.594487

0.000

-

Out of Phase Out of Phase

3 4

7.129 -

-

7.129

10.109 -

0.520417

12.260

12.262 -

8.4.2 Transmitted Force (Ftr) on Foundation due to various Rotor positions Rotor Position

Load Case

Lateral Translation

Longitudinal Translation

Vertical Translation

Rocking (Due to Translation Force)

Rocking (Due to shaft eccentricity)

Fz(kN)

Fx(kN)

Fy(kN)

MØ' (kNm)

MØ2 (kNm)

In Phase In Phase

1 2

0.275 -

-

8.782

25.507 -

0.689

Out of Phase Out of Phase

3 4

0.135 -

-

4.307

11.721 -

0.603

-

8.4.3 Amplitudes Translation Displacement Due to Fz Due to Fx Due to Fy ( micron ) ( micron ) ( micron )

Rotational Displacement

Rotor Position

Load Case

In Phase

1

4

-

-

4.51E-07

Due to M2 (Rad) -

In Phase Out of Phase

2 3

2

-

7 -

2.07E-07

1.20E-08 -

Out of Phase

4

-

-

3

-

0

Due to M1 (Rad)

8.4.4 Total Amplitudes Calculation Mode of Vibration

Phase

Amplitude Calculations

Vertical Ky

In phase

AY+Ø*X/2

= 7+0E-06x7.9/2

=

7

<

Horizontal Kx

Out of phase In phase

AY+Ø*X/2 AX

= 3+0x7.9/2 = 0

= =

3 0.00

< <

Horizontal Kz

Out of phase In phase

AX Az+ψYC Az+ψYC

= 0 = 4+0.5E-06x (2.418-1)

= =

0.00 4

= 2+0.2E-06x (2.418-1)

=

2

Out of phase

16 microns 16 microns

SAFE SAFE

< <

16 microns 16 microns 16 microns

SAFE SAFE

<

16 microns

SAFE SAFE

8.4.5 Summary of Frequncies and Amplitudes

S.No

Mode of Vibration

Natural Frequency fn, rpm

Allowable frequency,f m,rpm

Check for Frequency

Total Amplitude, (micron)

Check for Amplitude

1

Vertical Translation-Y

1087

-20% 1424

20% 2136

SAFE

7

SAFE

2 3

Longitudinal Translation -X Lateral Translation -Z

242 242

1424 1424

2136 2136

SAFE SAFE

0 4

SAFE SAFE

4

Rocking about z-axis

4870

1424

2136

SAFE

15 of 17

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8.5 CHECK FOR VARIOUS SHEAR MODULUS VALUES =

Shear Modulus values considered

0.50G

0.63G

0.76G

0.89G

1.00G

8.5.1 Individual Pile Spring Constants for Various G Values G

Vertical Ky KN/m

Horizontal kx KN/m

Translational kz KN/m

Rocking KØ1

0.50G 0.63G 0.76G

400596.04 505099.35 609602.66

32024.21 41198.71 50373.21

32024.21 41198.71 50373.21

30584.2 32775.04 34965.89

0.89G 1.00G

635728.49 661854.32

59547.71 68722.21

59547.71 68722.21

37200.55 39435.21

kNm/radian

8.5.2 Pile group Spring Constants for Various G Values G

Vertical Ky KN/m

Horizontal kx KN/m

Translational kz KN/m

Rocking KØ1

0.50G 0.63G

1032254.75 1301378.21

347840.19 440073.78

347840.19 440073.78

35781931.67 45075414.6

0.76G 0.89G

1570501.68 1673746.87

532307.37 624540.96

532307.37 624540.96

54368897.6 57028861.18

1.00G

1769614.77

705571.99

705571.99

59633840.13

kNm/radian

8.5.3 Summary of Frequencies for various 'G' values with check for Frequency Range Rocking, Vertical,Y Horizontal,X Horizontal,Z G 0.50G

rpm 973

Check