Block foundation - Dynamic analysis

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ANALYSIS & DESIGN CALCULATION FOR BFP FOUNDATION Designed by

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TABLE OF CONTENTS SECTION 1

GENERAL DESCRIPTION

PAGE NO. 2 2

2

DESIGN PHILOSOPHY

2

3

DATA

2

4

STATIC DESIGN OF PUMP FOUNDATION

3

5

ECCENTRICITY CHECKS & INERTIA CALCULATIONS

7

6

CALCULATION OF SPRING CONSTANTS & DAMPING RATIOS 10

7

CHECK FOR VARIOUS SHEAR MODULUS VALUES

13

8

STABILITY CHECKS

15

9

REINFORCEMENT CALCULATION

16

APPENDIX-A

LOAD INPUT

APPENDIX-B

EXTRACT FROM REFERENCES

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ANALYSIS & DESIGN CALCULATION FOR BFP FOUNDATION Designed by

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1.0 GENERAL DESCRIPTION: 1.1 SCOPE The purpose of this calculation is to design the foundation of the centrifugal pump (6 HDX 24A).

1.2 STANDARDS

vendor drawing.

Flowserve Drawing NO 50015HE0673

Refer Appendix -A

Arya, S., O'Neil, M., & Pincus, G. (1981). Design of Structures and Foundations for Vibrating Machines. Gulf Publishing Company. ACI 351.3R-04

Foundations for dynamic equipment

DEP 34.00.01.30-GEN

Standard design and engineering of onshore structures

DEP 34.11.00.12-GEN

Geotechnical and foundation engineering onshore

2.0 DESIGN PHILOSOPHY: The pump and motor are mounted on an common skid which is supported by a rectangular block foundation resting on soil. The block foundation is designed for the pump and motor weight as per vendor drawing.

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

=

27.5

N/mm2

Unit weight of concrete c w Unit weight of water

=

24

kN/m

=

10

kN/m3

Concrete cover for foundationsCc

=

50

mm

=

410

N/mm2

=

78.5

KN/m

(4000 psi)

3

Reinforcement Yield Strength of steel unit weight of steel

fy

3

(60000 psi)

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3.2 Soil Data Unit weight of soil

s

=

18.87 KN/m3

Coefficient of friction



=

0.35

(From Geo tech report )

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

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4.0 STATIC DESIGN OF PUMP FOUNDATION 4.1. DESIGN DATA 4.1.1 Block Dimensions: Length in X-direction Length in Z-direction Height of the Block Above FGL Depth of Foundation from FGL Total Height of Block Length in Z-direction(Motor/BP Area) 4.1.2 Pump Data: Length of the skid in X-direction Width of the skid in Z-direction Ht.of the skid in Y-direction

LB BB HB_AG D HB Bm

LS BS HS

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 hS Height of shaft from u/s of skid

Mz Z

5.4 2.3 0.3 1.70 2.00 2.30

m m m m m m

= = = = = = = = =

4.50 2.00 0.25 12 42 3.84 1.64 0.95 0.05

m m m

m m m m

CL of Discharge

Depth of grouting considered

= = = = = =

Y CL of Pump BB

hs

Ba Bs

Hs HB_AG FGL

HB

LS LB

La

D

X Mx

PLAN VIEW

4.1.3 Motor & BFBP Data: Length of the skid in X-direction Width of the skid in Z-direction Ht.of the block in Y-direction

SECTION VIEW

Lm Bm Hmb

= = =

5.00 2.00 0.25

m m m

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

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4.1.4 Unit Weights: Unit weight of concrete Unit weight of Water Unit weight of soil Co-eff of friction bet. Soil & Concrete 4.1.5 Stability Limits: Finished Ground Level Elevation =

c w s

= = = =

µ

100.0 m 98.3 m Allowable Soil Bearing Pressure at Elevation

Approved by

24 10 18.87 0.35

kN/m³ kN/m³ kN/m³

=

100 kN/m²

(Note: Bottom of lean concrete El. is 98.3 m.) Depth from finished ground to bottom of the foundation, d = 1.70 m 0.00 m Required depth of lean concrete, t = = 100 kN/m² Allowable bearing pressure at base of mat, F FOS against Sliding = 1.5 Sliding FOT FOS against Overturning = 2 FBUO FOS against Buoyancy = 1.25 4.2 STATIC LOADS 4.2.1 Pump, Motor & BFBP Weight: Pp Pump Weight, Ppr Pump rotor Weight, Pm Motor Weight, Pmr Motor rotor Weight, Pb Base Weight of BFP, Pbp BP Weight Pbpr BP rotor Weight Pbp Base Weight of BP, Po Other

= = = = = = = = =

1900 570 2517 755.1 2520 0 0 0

kg kg kg kg kg kg kg kg kg

= = = = = = = = =

Total weight of pump, WP=Pp+ Pm + Pb+Pbp+Pbp+Po = Weight of concrete fill inside the skid

W cf1 W cf2

18.64 5.59 24.69 7.41 24.72 0.00 0.00 0.00 0.00

kN kN kN kN kN kN kN kN kN

68.05

kN

= 4.5x 2 x 0.25 x 24 = 5x 2 x 0.25 x 24

(if no vendor data, assume 30% of Pump wt)

(if no vendor data, assume 30% of motor wt)

(if no vendor data, assume 30% of motor wt)

= =

54 60

KN KN

4.2.2 Buoyancy Force: Buoyancy Force

Fb

4.3 PRELIMINARY FOUNDATION CHECK: 4.3.1 Check for Plinth Size:

= =

LB x BB x D x w 5.4x2.3x1.7x10

=

211.14 KN

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

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Minimum bolt edge distance, Dmin Minimum edge of skid to concrete,Cmin Therefore Min. plinth length required Min. plinth length required

Min. plinth width required Min. plinth width required

= =

150 75

mm mm

= =

Approved by

0.15 m 0.075 m

= (2 xDmin)+La+Lm = (2 x 0.15 ) + (3.84+5) = 4.14 m = ( 2 x Cmin ) + Ls+Lm = (2x0.075 ) + (4.5+5) = m 4.65 = Max of the above = 4.65 m < 5.4 Hence O.K = ( 2 x Dmin ) + W a = ( 2 x 0.15 ) + 1.64 ( 2 x C ) + B = = ( 2 x 0.075 ) + 2 min s = Max of the above

= = =

1.94 m 2.15 m 2.15 m <

2.3

Hence O.K 4.3.2 Check for Foundation Depth: Min. foundation depth

= 0.60 + L/30 = 0.780 m

( Where L is greater of length or width in meters ) < 2 m Hence O.K

4.3.3 Check for Foundation Weight: Foundation weight should be greater than 3 times the total weight of the pump, Machine or Pump total weight, W P = 68.05 kN Foundation weight, W f = (5.4 x 2.3 x 2 x 24 ) = 596.16 KN > 3 times the pump weight Hence O.K 4.3.4 Preliminary Check for Bearnig pressure: Total Vertical force

FY

= W P + W cf1 +Wcf2+ W f = 68.05 + 54 + 60 + 596.16

=

718.21

KN

=

752.24

KN

0.25 x 68.05 x (0.95 + 0.3 + 1.7 ) Mz_I

=

50.19

KNm

0.25 x 68.05 x (0.95 + 0.3 + 1.7 )

=

50.19

KNm

Total Vertical force with 50% impact load = FY + 50% W P Fyi = 718.21 + 0.5 x 68.05 Moment due to impact load (i.e.25% of pump weight acting laterally at shaft level) Total Mom in Long. Direction at Bottom of base Total Mom in Tran. Direction at Bottom of base

MX

Maximum Base Pressure at founding depth below HPP

PMAX

Mz

= = = =

Mx_I

= P / A + MX / ZX

m

m

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

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Approved by

= (752.24 / (4.5 x 2.3 + 5 x 2.3 )) + (50.19 x 6 / (4.5 x 2.3^2 + 5 x 2.3^2 )) = 40.42 KN/m2 < 80 KN/m2 (80% of allowable) Hence O.K P / A + M / Z = Z Z = (752.24 / (4.5 x 2.3 + 2.3 x 5 )) + (50.19 x 6 / (2.3 x 4.5^2 + 2.3 x 5^2 )) = 37.32 KN/m2 < 80 KN/m2 PMAX

Hence O.K

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

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4.4 DYNAMIC LOADS INPUT 4.4.1 Pump data:

Location No Description 1 2 3

Rotor weight kN 5.59 7.41 0.00

Pump Motor BP

Speed (rpm)

Dynamic forces from vendor data

Dynamic force*

Vertical

kN 1.68 2.22 0.00

Fy (kN) 0 0 0

1800 1800 0

Longitudinal Lateral

Rocking Pitching Fz (kN) T (kNm) T (kNm) 0 0 0 0 0 0 0 0 0

Fx (kN) 0 0 0

* Dynamic force (kN) = (Rotor weight )x(Rotor speed,r.p.,m) / 6000 ACI 351.3R-04 eq. 3.7 Cl. 3.2.2.1d

4.4.2 Soil & Foundation parameters for Dynamic loads

(From Geo tech report )

Dynamic Shear Modulus( Gdyn )

=

Poisson ratio, Soil internal damping ratio (D)

= =

117877 0.35 0.02

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

= = =

5% of LB 5% of BB Below TOC

= = =

0.05 x 5.4 0.05 x 2.3 2

= = =

0.27 0.115 2

m m m

Damped Natural Frequencies shall be less than or more than

= =

0.8  1.2 

= =

0.8 x 1800 1.2 x 1800

= =

1440 2160

rpm rpm

Allowable peak-to-peak amplitude

=

Range of shear modulus (G) values to consider

=

KN/m2

4.4.3 Alloawable limits for design

16 microns 0.5

to

Fig 3.7 1

5 ECCENTRICITY CHECK & INERTIA CALCULATIONS (Eccentricity of C.G. of machine+foundation system to be checked in all 3 directions w.r.t. C.G of foundation)

Z

Y CL of Pump

C.G C.G HB

origin

D

X

X

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

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X

origin

X

5.1 COMPUTATION OF CG OF BASE BLOCK

Elements

Dimensions(m) Lxi Lzi Lyi* -

Area Coordinates of CG (m2) of elements Ai xi(m) zi(m) yi(m) 1.23 1.28 3.00 3.14 1.20 3.00

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

Pump Motor BP Skid1 Skid2 Mat_BFP Motor/pump 5.00 2.30 2 11.5 2.50 1.15 1.00 28.8 13.2 11.5 Total 11.50 6.86 3.63 7.00 28.8 13.2 11.5 * Concrete fill in skid and grout thickness included in height of block for CG Calculation = = =

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 AiYi/Ai

= = =

28.75 / 11.5 13.225 / 11.5 11.5 / 11.5

= = =

2.500 m 1.150 m 1.000 m

= = =

2.49 1.16 1.15

5.2 COMPUTATION OF CG OF MACHINE & FOUNDATION BLOCK Mass mi Elements Weight Wi (kN) kNsec2/m BFP 18.64 1.9 Motor 24.69 2.52 BP 0.00 0 Skid1 0 0 Skid2 0 0 Mat_BFP 0 0 Mat_Motor 552 56.27 Total 595.33 60.69

Coordinates of CG of elements xi 1.23 3.14 0.00 0.00 0.00 0.00 2.50 6.86

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

zi 1.28 1.20 0.00 0.00 0.00 0.00 1.15 3.63

Static moment of mass (kNSec2)

yi mixi mizi miyi 3.00 2.33 2.42 5.70 3.00 7.91 3.02 7.56 0.00 0 0.00 0.00 0.00 0 0.00 0.00 0.00 0 0.00 0.00 0.00 0 0.00 0.00 1.00 141 64.71 56.27 7.00 151 70 70

mi.xi/mi mi.zi/mi mi.yi/mi

= = =

150.91154/60.69 70.157/60.69 69.53/60.69

m m m

5.3 ECCENTRICITY OF CG OF FOUNDATION SYSTEM W.R.T. BASE BLOCK(check with limits in 4.4.3) Eccentricity in X direction (x-x0)

= =

2.5 - 2.49 0.01

m

<

0.27

m

Hence OK

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

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Eccentricity in Z direction (z-z0)

in Y direction, y0

= =

1.15 - 1.16

=

1.15

5.4 MASS MOMENTS OF INERTIA AND INERTIA RATIOS

Elements

mass mi

Ix = mi /12 kNsec /m *(Lyi2+Lzi2)

1.9 2.52 0 0 0 0 56.27 60.69

0.000 0.000 0.000 43.562 43.562

Iy = mi /12 *(Lxi2+Lzi2)

Iz = mi /12 *(Lxi2+Lyi2)

0.000 0.000 0.000 142.035 142.035

0.000 0.000 0.000 135.986 135.99

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

Ioz

Ioy

m

< <

0.115 m 2

Hence OK

m

Hence OK

(Table 4.6 of Arya, Neil & Pincus)

mass moment of inertia of Mass moment of inertia of individual elements abt its own Distance between common C.G. & C.G. whole system about common axis of individual elements (m) CG

2

BFP Motor BP Skid1 Skid2 BFP_Mat Motor_Mat Total

-0.01

Approved by

= = =

1/12 x mi(lyi2+lzi2)+mi(yoi2+zoi2)

= = =

1/12 x mi(lxi2+lyi2)+mi(xoi2+yoi2)

= = =

1/12 x mi(lxi2+lzi2)+mi(xoi2+zoi2)

43.562 + 16.429 kN sec2-m 60.0

135.986 + 20.486 kN sec2-m 156.5

142.035 + 4.126 kN sec2-m 146.16

xoi xo - xi

zoi zo - zi

yoi yo - yi

1.26 -0.65 2.49 2.49 2.49 2.49 -0.01

-0.115 -0.04 1.16 1.16 1.16 1.16 0.01

-1.85 -1.85 1.15 1.15 1.15 1.15 0.15

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

Ix = mi* (yoi2+zoi2)

6.528 8.629 0.000 0.000 0.000 0.000 1.272 16.43

Iy = mi* Iz = mi* (xoi2+zoi2) (xoi2+yoi2)

3.1 1.1 0.0 0.0 0.0 0.0 0.0 4.13

9.5 9.7 0.0 0.0 0.0 0.0 1.3 20.49

Ratio between moments of inertia

Ix = Iox + m.yo2 = 59.991 + 60.69 x 1.15^2 = 140.3 kN sec2-m

x

= Iox/Ix = 59.991 / 140.254 = 0.428

Iz = Ioz + m.yo2 = 156.472 + 60.69 x 1.15^2 = 236.7 kN sec2-m

z

= Ioz/Iz = 156.472 / 236.735 = 0.661

Iy = Ioy = 146.16 kN sec2-m

Mass moment of inertia effective against rocking excitation , I

=

140.25

kN sec2-m

Mass moment of inertia effective against pitching excitation ,I

=

236.74

kN sec2-m

Mass moment of inertia effective against cross excitation ,I

=

146.16

kN sec2-m

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

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

=

60.69

Approved by

kN sec2/m

6 CALCULATION OF SPRING CONSTANTS & DAMPING RATIOS LB = Length in X-direction Average Width in Z-direction Bavg = LB / Bav = L/B Ratio BB / L B = B/L Ratio depth of foundation embedment below grade, h =

5.4 2.3 5.4 / 2.3 2.3 / 5.4 1.70

m m = =

2.35 0.43

m

6.1 SPRING CONSTANTS (Table 4.1 & 4.2 of Arya, Neil & Pincus - Refer Appendix-B) Mode of Vibration

Geometry factors

Equivalent radius r0

Fig4.1(Arya)

Vertical Y y =

###

Embedment coefficients ηy

Ky

= (BL/)0.5 = (2.3x5.4/3.14)^0.5

= 1+0.6(1-)(h/r0) = 1+0.6x(1-0.35)x(1.7/1.988)

=

= ηx

= (G/(1-)) y (B L)0.5 ηy = 117877/(1-0.35)x2.262x (2.3x5.4)^0.5x1.334

(Refer z value in the Fig 4.1)

Horizontal, x = X,Z

###

= (BL/)0.5 = (2.3x5.4/3.14)^0.5 =

Rocking   =

###

###

###

= (BL3/3)0.25 = (2.3x5.4^3/3x3.14)^0.25 =

###

= (B3L/3)0.25 Pitching   =

###

= (2.3^3x5.4/3x3.14)^0.25

(Refer for BB/LB ratio in Fig 4.1)

=

###

Spring Constant

1.334

= 1928524 kN/m Kx

= 1+0.55(2-)(h/r0) = 1+0.55x(2-0.35)x(1.7/1.988)

= =

= η

= 1950600 kN/m K = (G/(1-)) (BL2) ηΦ

1.78

3 = 1+1.2(1-)(h/r0)+0.2(2-)(h/ro) = 1+1.2x(1-0.35)x(1.7/2.49)+ 0.2x(2-0.35)x(1.7/2.49)^3 = 1.638 η 3 = 1+1.2(1-)(h/r0)+0.2(2-)(h/ro) = 1+1.2x(1-0.35)x(1.7/1.625)+ 0.2x(2-0.35)x(1.7/1.625)^3 = 2.194

2(1+)G x(BL)0.5 ηx 2*(1+0.35)x117877x0.977x (2.3x5.4)^0.5x1.78

= 117877/(1-0.35)x0.635x (2.3x5.4^2)x1.638 = K

12650821

kN/m/radian

= (G/(1-))  (B2L) η = (117877/(1-0.35)x0.433x (2.3^2x5.4)x2.194 = 4921411 kN/m/radian

6.2.0 CALCULATION OF DYNAMIC FORCES (in the absence of vendor data) Location No Description 1

Pump

Rotor weight kN 5.59

Speed w(rpm) 1800

Dynamic force kN 1.677

Point of Application at Shaft Location*

Combined C.G of machine and foundation

X(m) 1.227

Xo (m) 2.490

Y(m) 3.000

Z(m) 1.275

Yo (m) 1.150

Zo(m) 1.160

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

2

Motor

Checked by

7.41

1800

2.223

3.14

Approved by

3.000

1.200

2.490

1.150

1.160

*Pump and motor locations assumed at L/4 & 3L/4 in X-direction respectively. 6.2.1 Dynamic forces Lateral Description translation Fz(kN)

No

Longitudinal translation*

Vertical translation

Rocking (Due to Lateral Pitching translation)

Fx(kN)

Fy(kN)

Mψ1 (kNm)

MØ'-kNm

Rocking (due to shaft ecentricity) Mψ2 -kNm

1

Pump

1.677

0.000

1.677

3.295

2.118

0.193

2

Motor

2.223

0.000

2.223

4.201

1.438 3.556

0.2818

Total transmitted force = 3.900 0.000 3.900 7.497 * Longitudinal translation not considered since it is usually lesser than that of Lateral translation

0.089

6.3 CALCULATION OF EQUIVALENT DAMPING RATIO (Tables 4.3 & 4.4 of Arya, Neil & Pincus) Mode of Vibration

Mass (or Inertia) ratio

Embedment factor

y By = (1-) W / (4r03) = = Vertical Y = (1-0.35)x595.33 / (4x18.87x1.988^3) = 0.653 =  Bx x = (7-8) W / (32(1- r03) = Horizontal, = (7-8x0.35)x595.33 / = X,Z (32x(1-0.35)x18.87x1.988^3) = 0.811 =  B 

Damping ratio D

(1+1.9(1-h/r0)) / (ηy)0.5 (1+1.9x(1-0.35)(1.7/1.988))/(1.334)^0.5

=

1.780 (1+1.9(2-h/r0)) / (ηx)0.5 (1+1.9x(2-0.35)x(1.7/1.988))/(1.78)^0.5

= 

0.936

Dx = 0.288 x / (Bx)0.5 = (0.288x2.759)/(0.811)^0.5 =

2.759

3 0.5 = (1+0.7(1-h/r0)+0.6(2-h/ro) ))/(η = (1+0.7x(1-0.35)x(1.7/2.49)+ 0.6x(2-0.35)x(1.7/2.49)^3)/(1.638)^0.5

= 3(1-) I /(8 r05) Rocking  = (3x(1-0.35)x140.254) / (8x(18.87/9.81)x2.49^5) = 0.186 n = ### ** B = 3(1-) I /(8 r05)

Dy = 0.425 y / (By)0.5 = (0.425x1.78)/(0.653)^0.5

1.270

3 0.5 = (1+0.7(1-h/r0)+0.6(2-h/ro) ))/(η = (1+0.7x(1-0.35)x(1.7/1.625)+ 0.6x(2-0.35)x(1.7/1.625)^3)/(2.194)^0.5

0.882

D = 0.15  / ((1+nB (nB0.5) = (0.15x1.27/((1+1.6x0.186)x (1.6x0.186)^0.5) = 0.269 D = 0.15  / ((1+nB (nB0.5)

= (0.15x1.762/((1+1.122x2.65)x Pitching  = (3*(1-0.35)x236.735) / (1.122x2.65)^0.5) 8x(18.87/9.81)x1.625^5) n  = 2.65 ### ** = 0.039 = 1.762  = ** Values for nnfor various values of BTable 4.5 of Arya, Neil & Pincus, reproduced below) B nn

5 1.08

3 1.11

2 1.143

1 1.219

0.8 1.251

0.5 1.378

0.2 1.6

6.3.1 SUMMARY OF DAMPING RATIOS (Final D is 2/3 of Theoritical value + soil internal damping ratio or 0.7 whichever is lesser ) Mode of Vibration Vertical

Soil internal damping ratio 0.02

Total Damping Ratio = Concrete + Soil 2/3 x 0.936 + 0.02

= 0.644

Max. Damping ratio 0.70

Final Damping ratio Dy

=

0.500

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

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Approved by

Horizontal

0.02

2/3 x 0.882 + 0.02

= 0.608

0.70

Dx

=

0.200

Rocking

0.02

2/3 x 0.269 + 0.02

= 0.199

0.70

D

=

0.100

Pitching

0.02

2/3 x 0.039 + 0.02

= 0.046

0.70

D =

0.046

6.4 CALCULATION OF UNDAMPED NATURAL FREQUENCIES Undamped Natural frequency,  n (rpm) [ (60/2π)x(K/m)0.5]

Mode of Vibration Vertical Horizontal Rocking Pitching

(60/(2x3.14))x(1928524/60.69)^0.5 (60/(2x3.14))x(1950600/60.69)^0.5 (60/(2x3.14))x(12650821/140.254)^0.5 (60/(2x3.14))x(4921411/236.735)^0.5

= = = =

1702 1712 2868 1377

Damped Natural frequency  mr [n (1-D2)0.5] (rpm) (1702x(1-0.5^2)^0.5 (1712x(1-0.2^2)^0.5 (2868x(1-0.1^2)^0.5 (1377x(1-0.046^2)^0.5

= = = =

1474 1677 2854 1376

6.5 CALCULATION OF FREQUENCY RATIO , MAGNIFICATION FACTOR , AMPLITUDE , TRANSMISSIBLITY FACTOR AND TRANSMITTED FORCE (Table 1.4 of Arya, Neil & Pincus, Ref.Appendix-B) (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 n

Vertical,Y Horizontal,X Horizontal,Z Rocking, Pitching,

1.058 1.051 1.051 0.628 1.307

Magnification factor, M

Transmissiblity factor, Tr

1/((1-r2)2+(2Dr)2)0.5 0.940 2.306 2.306 1.616 1.391

(1+(2Dr)2)0.5 / [(1-r2)2+(2Dr)2]0.5 1.368 2.502 2.502 1.628 1.401

Transmitted force/moment

Displacement response, Ax

FtrTrFo

M(Fo/K)

5.334 kN 0.000 kN 9.758 kN 12.666 kNm 4.983 kNm

2 Micron 0 Micron 5 Micron 0.00 radians 0.00 radians

6.6 FORCES & AMPLITUDES FOR VARIOUS ROTOR POSITIONS 6.6.1 Dynamic loads (Fo) - In-phase & 180 degrees out-of-phase Rotor Position

In Phase In Phase Out of Phase Out of Phase

Load Case 1 2 3 4

Lateral Translation

Longitudinal Translation

Vertical Translation

Rocking (Due to Rocking (Due to shaft Translation Force) eccentricity)

Fz(kN)

Fx(kN)

Fy(kN)

MØ' (kNm)

MØ2 (kNm)

Mψ1 (kNm)

3.900 0.546 -

-

3.900 0.546

7.497 1.010 -

0.281775 -0.06279

3.556 0.680

Pitching

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

Load Case

Lateral Translation

Longitudinal Translation

Vertical Translation

Fz(kN)

Fx(kN)

Fy(kN)

Rocking (Due to Rocking (Due to shaft Translation Force) eccentricity) MØ' (kNm)

MØ2 (kNm)

Pitching Mψ1 (kNm)

13 of 17

ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

In Phase

1

In Phase Out of Phase Out of Phase

Checked by

9.758

-

-

2

-

-

3 4

1.366 -

-

Approved by

12.207

-

-

5.334

-

0.459

4.983

0.747

1.645 -

-0.102

0.953

6.6.3 Amplitudes (Ay) (Maginfication factor M x Dynamic loads Fo / Spring constants K ) Rotor Position

Load Case

In Phase In Phase Out of Phase Out of Phase

1 2 3 4

Translation Displacement Due to Fz Due to Fx Due to Fy ( micron ) ( micron ) ( micron ) 5 1 -

-

Rotational Displacement Due to M (Rad)

Due to M2 (Rad)

9.57E-07 1.29E-07 -

3.60E-08 0

1

2 0

Due to M' (Rad) 1.01E-06 1.92E-07

6.6.4 Total Amplitudes Calculation (Maginfication factor M x Dynamic loads Fo / Spring constants K ) Mode of Vibration Vertical Ky

Phase

In phase Out of phase Horizontal Kx In phase Out of phase Horizontal Kz In phase Out of phase

Amplitude Calculations AY+ψ/2+Ø*LB/2 AY+ψ/2+Ø*LB/2 AX+ØY-Yo) AX+ØY-Yo) Az+ψY-Yo) Az+ψY-Yo)

= = = = = =

2+0E-06x5.4/2+1E-06x2.3/2 0+0x5.4/2+0.2E-06x2.3/2 0+1E-06x (3-1.15) 0+0.2E-06x (3-1.15) 5+1E-06x (3-1.15) 1+0.1E-06x (3-1.15)

= = = = = =

2 ### ### ### 5 1

< < < < < <

16 microns 16 microns 16 microns 16 microns 16 microns 16 microns

7.0 CHECK FOR VARIOUS SHEAR MODULUS VALUES Shear Modulus values considered

=

7.1 SPRING CONSTANTS FOR VARIOUS G VALUES Vertical Ky Horizontal kx Translational kz G KN/m KN/m KN/m 0.50G 964262 975300 975300 0.63G 1214970 1228878 1228878 0.76G 1465678 1482456 1482456 0.89G 1716386 1736034 1736034 1.00G 1928524 1950600 1950600

0.50G

0.63G

0.76G

Rocking KØ1

Pitching Kψ1

kN/m/radian 6325410 7970017 9614624 11259230 12650821

kN/m/radian 2460706 3100489 3740273 4380056 4921411

0.89G

1.00G

7.2 SUMMARY OF FREQUENCIES FOR VARIOUS 'G' VALUES WITH CHECK FOR FREQUENCY RANGE* Rocking, Pitching,  Vertical,Y Horizontal,X Horizontal,Z G

SAFE SAFE SAFE SAFE SAFE SAFE

14 of 17

ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION Designed by

Checked by

Approved by

G rpm

Check

rpm

Check

0.50G

1042

0.63G

1170

0.76G 0.89G 1.00G

rpm

Check

rpm