block foundation - dynamic analysis

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ANALYSIS & DESIGN CALCULATION FOR BFP FOUNDATIONDesigned by Checked by Approved by

TABLE OF CONTENTS

SECTION PAGE NO.

1 GENERAL DESCRIPTION 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 FOUNDATIONDesigned by Checked by Approved by

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 (4000 psi)

Unit weight of concrete = 24

Unit weight of water = 10

Concrete cover for foundationsCc = 50 mm

Reinforcement

Yield Strength of steel fy = 410 (60000 psi)

unit weight of steel = 78.5

N/mm2

c kN/m3

w kN/m3

N/mm2

KN/m3

3 of 173.2 Soil Data

Unit weight of soil = 18.87 (From Geo tech report )

Coefficient of friction = 0.35

s KN/m3

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ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATIONDesigned by Checked by Approved by

4.0 STATIC DESIGN OF PUMP FOUNDATION4.1. DESIGN DATA

4.1.1 Block Dimensions:

Length in X-direction = 5.4 m

Length in Z-direction = 2.3 m

Height of the Block Above FGL = 0.3 m

Depth of Foundation from FGL D = 1.70 m

Total Height of Block = 2.00 m

Length in Z-direction(Motor/BP Area) Bm = 2.30 m

4.1.2 Pump Data:

Length of the skid in X-direction = 4.50 m

Width of the skid in Z-direction = 2.00 m

Ht.of the skid in Y-direction = 0.25 m

No. of anchor bolts = 12

Anchor Bolts Dia = 42

= 3.84 m

= 1.64 m

Height of shaft from u/s of skid = 0.95 m

Depth of grouting considered = 0.05 m

4.1.3 Motor & BFBP Data:

Length of the skid in X-direction = 5.00 m

Width of the skid in Z-direction = 2.00 m

Ht.of the block in Y-direction = 0.25 m

LB

BB

HB_AG

HB

LS

BS

HS

C/c distance bet. far end bolts along length,La

C/C distance bet. far end bolts along width,Ba

hS

Lm

Bm

Hmb

PLAN VIEW SECTION VIEW

X

Z CL

of

Dis

char

geMz

Mx

LB

LS

La

BB Ba

Bs

FGLH

B_AG

Hs

D

CL of Pump

Y

hs

HB

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4.1.4 Unit Weights:

Unit weight of concrete = 24 kN/m³

Unit weight of Water = 10 kN/m³

Unit weight of soil = 18.87 kN/m³

Co-eff of friction bet. Soil & Concrete µ = 0.35

4.1.5 Stability Limits:

Finished Ground Level Elevation = 100.0 m

Allowable Soil Bearing Pressure at Elevation 98.3 m = 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

Required depth of lean concrete, t = 0.00 m

Allowable bearing pressure at base of mat, = 100 kN/m²

FOS against Sliding = 1.5

FOS against Overturning = 2

FOS against Buoyancy = 1.25

4.2 STATIC LOADS

4.2.1 Pump, Motor & BFBP Weight:

Pump Weight, = 1900 kg = 18.64 kN

Pump rotor Weight, = 570 kg = 5.59 kN (if no vendor data, assume 30% of Pump wt)

Motor Weight, = 2517 kg = 24.69 kN

Motor rotor Weight, = 755.1 kg = 7.41 kN (if no vendor data, assume 30% of motor wt)

Base Weight of BFP, = 2520 kg = 24.72 kN

BP Weight = kg = 0.00 kN

BP rotor Weight = 0 kg = 0.00 kN (if no vendor data, assume 30% of motor wt)

Base Weight of BP, = 0 kg = 0.00 kN

Other = 0 kg = 0.00 kN

Total weight of pump, WP=Pp+ Pm + Pb+Pbp+Pbp+Po = 68.05 kN

Weight of concrete fill inside the skid = 4.5x 2 x 0.25 x 24 = 54 KN

= 5x 2 x 0.25 x 24 = 60 KN

4.2.2 Buoyancy Force:

Buoyancy Force =

= 5.4x2.3x1.7x10 = 211.14 KN

4.3 PRELIMINARY FOUNDATION CHECK:

4.3.1 Check for Plinth Size:

c

w

s

FSliding

FOT

FBUO

Pp

Ppr

Pm

Pmr

Pb

Pbp

Pbpr

Pbp

Po

Wcf1

Wcf2

Fb L

B x B

B x D x

w

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= 150 mm = 0.15 m

= 75 mm = 0.075 m

Therefore

Min. plinth length required = (2 xDmin)+La+Lm = (2 x 0.15 ) + (3.84+5) = 4.14 m

= = (2x0.075 ) + (4.5+5) = 4.65 m

Min. plinth length required = Max of the above = 4.65 m < 5.4 m

Hence O.K

Min. plinth width required = = ( 2 x 0.15 ) + 1.64 = 1.94 m

= = ( 2 x 0.075 ) + 2 = 2.15 m

Min. plinth width required = Max of the above = 2.15 m < 2.3 m

Hence O.K

4.3.2 Check for Foundation Depth:

Min. foundation depth = 0.60 + L/30 ( Where L is greater of length or width in meters )

= 0.780 m < 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, = 68.05 kN

= (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 =

= 68.05 + 54 + 60 + 596.16 = 718.21 KN

Total Vertical force with 50% impact load

=

Fyi = 718.21 + 0.5 x 68.05 = 752.24 KN

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 = 0.25 x 68.05 x (0.95 + 0.3 + 1.7 ) = 50.19 KNm

Total Mom in Tran. Direction =

at Bottom of base = 0.25 x 68.05 x (0.95 + 0.3 + 1.7 ) = 50.19 KNm

Maximum Base Pressure =

at founding depth below HPP

Minimum bolt edge distance, Dmin

Minimum edge of skid to concrete,Cmin

( 2 x Cmin

) + Ls+Lm

( 2 x Dmin

) + Wa

( 2 x Cmin

) + Bs

WP

Foundation weight, Wf

FY

WP + W

cf1 +Wcf2+ W

f

FY + 50% WP

MX

Mx_I

Mz

Mz_I

PMAX

P / A + MX / Z

X

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= (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 < 80 (80% of allowable)

Hence O.K

=

= (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 < 80

Hence O.K

KN/m2 KN/m2

PMAX P / A + MZ / ZZ

KN/m2 KN/m2

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4.4 DYNAMIC LOADS INPUT

4.4.1 Pump data:

Location No Description Speed

Dynamic forces from vendor data

Vertical Longitudinal Lateral Rocking Pitching

kN kN Fy (kN) Fx (kN) Fz (kN)

1 Pump 5.59 1800 1.68 0 0 0 0 0

2 Motor 7.41 1800 2.22 0 0 0 0 0

3 BP 0.00 0 0.00 0 0 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 )

= 117877

= 0.35

= 0.02

4.4.3 Alloawable limits for design

Allowable eccentricity of C.G.in X-direction,x = 5% = 0.05 x 5.4 = 0.27 m

Allowable eccentricity of C.G.in Z-direction,z = 5% = 0.05 x 2.3 = 0.115 m

C.G.in Y-direction,y = Below TOC = 2 = 2 m

Damped Natural Frequencies shall be less than = 0.8 = 0.8 x 1800 = 1440 rpm

or more than = 1.2 = 1.2 x 1800 = 2160 rpm

Allowable peak-to-peak amplitude = 16 microns Fig 3.7

Range of shear modulus (G) values to consider = 0.5 to 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)

Rotor weight

Dynamic force*

(rpm) T (kNm) T (kNm)

Dynamic Shear Modulus( Gdyn

) KN/m2

Poisson ratio,Soil internal damping ratio (D)

of LB

of BB

D

CL of Pump

X

Y

HB

C.G

X

Z

C.G

origin

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5.1 COMPUTATION OF CG OF BASE BLOCK

Elements Dimensions(m)

Lxi Lzi Lyi* xi(m) zi(m) yi(m)

Pump - - - 1.23 1.28 3.00 - - -

Motor - - - 3.14 1.20 3.00 - - -

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 = = 28.75 / 11.5 = 2.500 m

C.G. of Foundation ,z dir-, Z = = 13.225 / 11.5 = 1.150 m

C.G. of Foundation ,y dir-, Y = = 11.5 / 11.5 = 1.000 m

5.2 COMPUTATION OF CG OF MACHINE & FOUNDATION BLOCK

Elements Weight

Wi (kN) xi zi yi mixi mizi miyi

BFP 18.64 1.9 1.23 1.28 3.00 2.33 2.42 5.70

Motor 24.69 2.52 3.14 1.20 3.00 7.91 3.02 7.56

BP 0.00 0 0.00 0.00 0.00 0 0.00 0.00

Skid1 0 0 0.00 0.00 0.00 0 0.00 0.00

Skid2 0 0 0.00 0.00 0.00 0 0.00 0.00

Mat_BFP 0 0 0.00 0.00 0.00 0 0.00 0.00

Mat_Motor 552 56.27 2.50 1.15 1.00 141 64.71 56.27

Total 595.33 60.69 6.86 3.63 7.00 151 70 70

= = 150.91154/60.69 = 2.49 m

= = 70.157/60.69 = 1.16 m

= = 69.53/60.69 = 1.15 m

5.3 ECCENTRICITY OF CG OF FOUNDATION SYSTEM W.R.T. BASE BLOCK(check with limits in 4.4.3)

= 2.5 - 2.49

= 0.01 m < 0.27 m Hence OK

Area(m2)

Coordinates of CG of elements

Static moment of area

Ai

Ai*X

iA

i*Z

iA

i*Y

i

AiXi/Ai

AiZi/Ai

AiYi/Ai

Massmi

Coordinates of CG of elements

Static moment of mass (kNSec2)

kNsec2/m

Combined C.G. in X direction,xo mi.xi/mi

Combined C.G. in Z direction,zo mi.zi/mi

Combined C.G. in Y direction,yo m

i.y

i/m

i

Eccentricity in X direction (x-x0)

XXorigin

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= 1.15 - 1.16

= -0.01 m < 0.115 m Hence OK

= 1.15 < 2 m Hence OK

5.4 MASS MOMENTS OF INERTIA AND INERTIA RATIOS (Table 4.6 of Arya, Neil & Pincus)

Elements

mass

mi

xoi zoi yoi

BFP 1.9 - - - 1.26 -0.115 -1.85 6.528 3.1 9.5

Motor 2.52 - - - -0.65 -0.04 -1.85 8.629 1.1 9.7

BP 0 - - - 2.49 1.16 1.15 0.000 0.0 0.0

Skid1 0 0.000 0.000 0.000 2.49 1.16 1.15 0.000 0.0 0.0

Skid2 0 0.000 0.000 0.000 2.49 1.16 1.15 0.000 0.0 0.0

BFP_Mat 0 0.000 0.000 0.000 2.49 1.16 1.15 0.000 0.0 0.0

Motor_Mat 56.27 43.562 142.035 135.986 -0.01 0.01 0.15 1.272 0.0 1.3

Total 60.69 43.562 142.035 135.99 16.43 4.13 20.49

Iox = Ix = = Iox/Ix

= 43.562 + 16.429 = 59.991 + 60.69 x 1.15^2 = 59.991 / 140.254

= 60.0 = 140.3 = 0.428

Ioz = Iz = = Ioz/Iz

= 135.986 + 20.486 = 156.472 + 60.69 x 1.15^2 = 156.472 / 236.735

= 156.5 = 236.7 = 0.661

Ioy = Iy = Ioy

= 142.035 + 4.126 = 146.16

= 146.16

= 140.25

= 236.74

= 146.16

Eccentricity in Z direction (z-z0)

in Y direction, y0

mass moment of inertia of individual elements abt its own

axisDistance between common C.G. & C.G.

of individual elements (m)

Mass moment of inertia of whole system about common

CG

kNsec2/mIx = mi /12 *(Lyi2+Lzi2)

Iy = mi /12 *(Lxi2+Lzi2)

Iz = mi /12 *(Lxi2+Lyi2)

Ix = mi* (yoi2+zoi2)

Iy = mi* (xoi2+zoi2)

Iz = mi* (xoi2+yoi2)xo - xi zo - zi yo - yi

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

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

Ratio between moments of inertia

1/12 x mi(l

yi2+l

zi2)+m

i(y

oi2+z

oi2) Iox + m.y

o2

x

kN sec2-m kN sec2-m

1/12 x mi(l

xi2+l

yi2)+m

i(x

oi2+y

oi2) Ioz + m.yo

2 z

kN sec2-m kN sec2-m

1/12 x mi(lx

i2+l

zi2)+m

i(x

oi2+z

oi2)

kN sec2-m

kN sec2-m

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

Mass moment of inertia effective against pitching excitation ,I kN sec2-m

Mass moment of inertia effective against cross excitation ,I kN sec2-m

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= 60.69

6 CALCULATION OF SPRING CONSTANTS & DAMPING RATIOSLength in X-direction = 5.4 m

Average Width in Z-direction Bavg = 2.3 m

L/B Ratio / Bav = 5.4 / 2.3 = 2.35

B/L Ratio / = 2.3 / 5.4 = 0.43

depth of foundation embedment below grade, h = 1.70 m

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

Embedment coefficients Spring Constant

Fig4.1(Arya)

Vertical Y

Ky

= = =

= ### = (2.3x5.4/3.14)^0.5 = 1+0.6x(1-0.35)x(1.7/1.988) = 117877/(1-0.35)x2.262x

(2.3x5.4)^0.5x1.334

in the Fig 4.1) = ### = 1.334 = 1928524 kN/mKx

= = =

= ### = (2.3x5.4/3.14)^0.5 = 1+0.55x(2-0.35)x(1.7/1.988) = 2*(1+0.35)x117877x0.977x

(2.3x5.4)^0.5x1.78

= ### = 1.78 = 1950600 kN/m

= = =

= ### = (2.3x5.4^3/3x3.14)^0.25 = 1+1.2x(1-0.35)x(1.7/2.49)+ = 117877/(1-0.35)x0.635x

0.2x(2-0.35)x(1.7/2.49)^3 (2.3x5.4^2)x1.638

= ### = 1.638 = 12650821 kN/m/radian

= = =

= ### = (2.3^3x5.4/3x3.14)^0.25 = 1+1.2x(1-0.35)x(1.7/1.625)+ = (117877/(1-0.35)x0.433x

0.2x(2-0.35)x(1.7/1.625)^3 (2.3^2x5.4)x2.194

ratio in Fig 4.1) = ### = 2.194 = 4921411 kN/m/radian

6.2.0 CALCULATION OF DYNAMIC FORCES (in the absence of vendor data)

Location No Description Speed

kN kN X(m) Y(m) Z(m) Xo (m) Yo (m) Zo(m)

1 Pump 5.59 1800 1.677 1.227 3.000 1.275 2.490 1.150 1.160

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

c kN sec2/m

LB

LB

BB

LB

Mode of Vibration

Geometry factors Equivalent radius r0

ηy

(BL/)0.5 1+0.6(1-)(h/r0) (G/(1-)) y (B L)0.5 η

y

y(Refer z value

Horizontal, X,Z

ηx

(BL/)0.5 1+0.55(2-)(h/r0) 2(1+)G x(BL)0.5 η

x

x

Rocking

η K(BL3/3)0.25 1+1.2(1-)(h/r

0)+0.2(2-)(h/r

o)3 (G/(1-)) (BL2) η

Φ

Pitching

η K(B3L/3)0.25 1+1.2(1-)(h/r0)+0.2(2-)(h/ro)

3 (G/(1-)) (B2L) η

(Refer for BB/LB

Rotor weight

Dynamic force

Point of Application at Shaft Location*

Combined C.G of machine and foundation

w(rpm)

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2 Motor 7.41 1800 2.223 3.14 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

No Description

Pitching

Fz(kN) Fx(kN) Fy(kN)

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 0.089

Total transmitted force = 3.900 0.000 3.900 7.497 3.556 0.2818

* Longitudinal translation not considered since it is usually lesser than that of Lateral translation

Mass (or Inertia) ratio Embedment factor Damping ratio D

Vertical Y

By Dy

= = =

= (1-0.35)x595.33 / = (1+1.9x(1-0.35)(1.7/1.988))/(1.334)^0.5 = (0.425x1.78)/(0.653)^0.5

(4x18.87x1.988^3)

= 0.653 = 1.780 = 0.936

Bx Dx

= = =

= (7-8x0.35)x595.33 / = (1+1.9x(2-0.35)x(1.7/1.988))/(1.78)^0.5 = (0.288x2.759)/(0.811)^0.5

(32x(1-0.35)x18.87x1.988^3)

= 0.811 = 2.759 = 0.882

= = =

= (3x(1-0.35)x140.254) / = (1+0.7x(1-0.35)x(1.7/2.49)+ = (0.15x1.27/((1+1.6x0.186)x

(8x(18.87/9.81)x2.49^5) 0.6x(2-0.35)x(1.7/2.49)^3)/(1.638)^0.5 (1.6x0.186)^0.5)

= 0.186 = ### ** = 1.270 = 0.269

= = =

= (3*(1-0.35)x236.735) / = (1+0.7x(1-0.35)x(1.7/1.625)+ = (0.15x1.762/((1+1.122x2.65)x

8x(18.87/9.81)x1.625^5) 0.6x(2-0.35)x(1.7/1.625)^3)/(2.194)^0.5 (1.122x2.65)^0.5)

= 2.65 = ### ** = 1.762 = 0.039

5 3 2 1 0.8 0.5 0.2

1.08 1.11 1.143 1.219 1.251 1.378 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 )

Final Damping ratio

Vertical 0.02 2/3 x 0.936 + 0.02 = 0.644 0.70 Dy = 0.500

Lateral translation

Longitudinal translation*

Vertical translation

Rocking (Due to Lateral translation)

Rocking (due to shaft ecentricity)

Mψ1

(kNm) MØ'-kNm M

ψ2 -kNm

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

Mode of Vibration

y

(1-) W / (4r0

3) (1+1.9(1-h/r0)) / (η

y)0.5 0.425

y / (B

y)0.5

Horizontal, X,Z

x

(7-8) W / (32(1- r0

3) (1+1.9(2-h/r0)) / (η

x)0.5 0.288

x / (B

x)0.5

Rocking

B D

3(1-) I /(8 r0

5) (1+0.7(1-h/r0)+0.6(2-h/r

o)3))/(η

0.5 0.15 / ((1+nB (nB0.5)

n

Pitching

B D3(1-) I /(8 r

05) (1+0.7(1-h/r

0)+0.6(2-h/r

o)3))/(η0.5 0.15 / ((1+nB (nB0.5)

n** Values for nnfor various values of BTable 4.5 of Arya, Neil & Pincus, reproduced below)

B

nn

Mode of Vibration

Soil internal damping ratio

Total Damping Ratio= Concrete + Soil

Max. Damping ratio

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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 = 0.100

Pitching 0.02 2/3 x 0.039 + 0.02 = 0.046 0.70 = 0.046

6.4 CALCULATION OF UNDAMPED NATURAL FREQUENCIES

Vertical (60/(2x3.14))x(1928524/60.69)^0.5 = 1702 (1702x(1-0.5^2)^0.5 = 1474

Horizontal (60/(2x3.14))x(1950600/60.69)^0.5 = 1712 (1712x(1-0.2^2)^0.5 = 1677

Rocking (60/(2x3.14))x(12650821/140.254)^0.5 = 2868 (2868x(1-0.1^2)^0.5 = 2854

Pitching (60/(2x3.14))x(4921411/236.735)^0.5 = 1377 (1377x(1-0.046^2)^0.5 = 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)

Magnification factor, M Transmissiblity factor, Tr

Vertical,Y 1.058 0.940 1.368 5.334 kN 2 Micron

Horizontal,X 1.051 2.306 2.502 0.000 kN 0 Micron

Horizontal,Z 1.051 2.306 2.502 9.758 kN 5 Micron

0.628 1.616 1.628 12.666 kNm 0.00 radians

1.307 1.391 1.401 4.983 kNm 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 Pitching


In Phase 1 3.900 - - 7.497 - -

In Phase 2 - - 3.900 - 0.281775 3.556

Out of Phase 3 0.546 - - 1.010 - -

Out of Phase 4 - - 0.546 - -0.06279 0.680

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

Rotor Position Pitching


DD

Mode of Vibration

Undamped Natural frequency, n (rpm)

[ (60/2π)x(K/m)0.5]

Damped Natural frequency mr

[n (1-D2)0.5] (rpm)

Mode of Vibration

Frequency ratio, r

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 FtrTrF

oM(F

o/K)

Rocking,Pitching,

Load Case

Lateral Translation

Longitudinal Translation

Vertical Translation

Rocking (Due to Translation Force)

Rocking (Due to shaft eccentricity)

MØ' (kNm) MØ

2 (kNm) Mψ1 (kNm)

Load Case

Lateral Translation

Longitudinal Translation

Vertical Translation

Rocking (Due to Translation Force)

Rocking (Due to shaft eccentricity)

MØ' (kNm) M

Ø2 (kNm) M

ψ1 (kNm)

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In Phase 1 9.758 - - 12.207 - -

In Phase 2 - - 5.334 - 0.459 4.983

Out of Phase 3 1.366 - - 1.645 - -

Out of Phase 4 - - 0.747 - -0.102 0.953

6.6.3 Amplitudes (Ay)

(Maginfication factor M x Dynamic loads Fo / Spring constants K )

Translation Displacement Rotational Displacement

Rotor Position

In Phase 1 5 - - 9.57E-07 - -

In Phase 2 - - 2 - 3.60E-08 1.01E-06

Out of Phase 3 1 - - 1.29E-07 - -

Out of Phase 4 - - 0 - 0 1.92E-07

6.6.4 Total Amplitudes Calculation

(Maginfication factor M x Dynamic loads Fo / Spring constants K )

Phase Amplitude Calculations

Vertical Ky In phase = 2+0E-06x5.4/2+1E-06x2.3/2 = 2 < 16 microns SAFE

Out of phase = 0+0x5.4/2+0.2E-06x2.3/2 = ### < 16 microns SAFE

Horizontal Kx In phase = 0+1E-06x (3-1.15) = ### < 16 microns SAFE

Out of phase = 0+0.2E-06x (3-1.15) = ### < 16 microns SAFE

Horizontal Kz In phase = 5+1E-06x (3-1.15) = 5 < 16 microns SAFE

Out of phase = 1+0.1E-06x (3-1.15) = 1 < 16 microns SAFE

7.0 CHECK FOR VARIOUS SHEAR MODULUS VALUES

Shear Modulus values considered = 0.50G 0.63G 0.76G 0.89G 1.00G

7.1 SPRING CONSTANTS FOR VARIOUS G VALUES

G Vertical Ky Horizontal kx Translational kz

KN/m KN/m KN/m kN/m/radian kN/m/radian

0.50G 964262 975300 975300 6325410 2460706

0.63G 1214970 1228878 1228878 7970017 3100489

0.76G 1465678 1482456 1482456 9614624 3740273

0.89G 1716386 1736034 1736034 11259230 4380056

1.00G 1928524 1950600 1950600 12650821 4921411

7.2 SUMMARY OF FREQUENCIES FOR VARIOUS 'G' VALUES WITH CHECK FOR FREQUENCY RANGE*

G Vertical,Y Horizontal,X Horizontal,Z

Load Case

Due to Fz ( micron )

Due to Fx ( micron )

Due to Fy ( micron )

Due to M1 (Rad) Due to M

2 (Rad) Due to M'

(Rad)

Mode of Vibration

AY+ψ/2+Ø*LB/2

AY+ψ/2+Ø*LB/2

AX+ØY-Yo)

AX+ØY-Yo)

Az+ψY-Yo)

Az+ψY-Yo)

Rocking KØ1 Pitching Kψ

1

Rocking, Pitching,

14 of 17


G

rpm Check rpm Check rpm Check rpm Check rpm Check

0.50G 1042 <20% ok 1186 <20% ok 1186 <20% ok 2018 - 973 <20% ok

0.63G 1170 <20% ok 1331 <20% ok 1331 <20% ok 2265 >20% ok 1092 <20% ok

0.76G 1285 <20% ok 1462 Not ok 1462 Not ok 2488 >20% ok 1199 <20% ok

0.89G 1391 <20% ok 1582 Not ok 1582 Not ok 2692 >20% ok 1298 <20% ok

1.00G 1474 - 1677 - 1677 - 2854 >20% ok 1375 <20% ok

* Frequencies are damped natural frequencies

** Here G is maximum value of G. For clays 88% of this value shall be used. (Ref: Page 66 AOP)

7.3 SUMMARY OF AMPLITUDES FOR VARIOUS 'G' VALUES WITH CHECK FOR AMPLITUDE LIMIT

GCheck

Vertical,Y

0.50G 1.727 0.380 0.759 2.960 2 2 microns SAFE

0.63G 1.538 0.486 0.892 3.479 2 2 microns SAFE

0.76G 1.401 0.588 1.013 3.949 2 2 microns SAFE

0.89G 1.294 0.685 1.121 4.371 2 2 microns SAFE

1.00G 1.221 0.760 1.199 4.677 2 2 microns SAFE

Horizontal,X

0.50G 1.518 0.695 0.813 0.000 0 0 microns SAFE

0.63G 1.352 1.011 1.150 0.000 0 0 microns SAFE

0.76G 1.231 1.403 1.564 0.000 0 0 microns SAFE

0.89G 1.138 1.843 2.025 0.000 0 0 microns SAFE

1.00G 1.073 2.197 2.391 0.000 0 0 microns SAFE

Horizontal,Z

0.50G 1.518 0.695 0.813 3.171 3 3 microns SAFE

0.63G 1.352 1.011 1.150 4.484 3 3 microns SAFE

0.76G 1.231 1.403 1.564 6.099 4 4 microns SAFE

0.89G 1.138 1.843 2.025 7.899 4 4 microns SAFE

1.00G 1.073 2.197 2.391 9.326 4 4 microns SAFE

0.50G 0.892 3.687 3.745 29.129 4.53E-06

0.63G 0.795 2.495 2.526 19.649 2.44E-06

0.76G 0.723 2.005 2.026 15.760 1.62E-06

0.89G 0.669 1.759 1.775 13.807 1.22E-06

1.00G 0.631 1.626 1.639 12.750 1.00E-06

0.50G 1.85 0.412 0.418 1.485 5.95E-07

0.63G 1.648 0.581 0.587 2.088 6.66E-07

0.76G 1.501 0.793 0.801 2.848 7.54E-07

0.89G 1.387 1.072 1.081 3.845 8.71E-07

1.00G 1.309 1.382 1.392 4.950 9.99E-07

Mode of Vibration

Frequency ratio, r

Magnification factor, M

Transmissiblity factor, Tr

Transmitted force/moment

Amplitude(Microns/rad

)

Amplitude, Total

Rocking,

Pitching,

15 of 17


8 STABILITY CHECKS

8.1 SUMMARY OF TRANSMITTED FORCE /MOMENT

S.No Mode of Vibration

1 Vertical Translation 4.677

2 Lateral Translation -Z 9.326

3 Rocking about X-axis 29.129

4 Pitching about Z-axis 4.950

8.1.1 Calculation of additional loads due to Transmitted force /moment

Total Horizontal load in Z-direction = 9.326+29.129/(2+0.25+0.95+0.05)

= 18.29 kN

8.2 CHECK FOR BEARING PRESSURE:

Total Vertical force = 718.21 kN

Total Vertical force(with impact load) = 752.24 kN

Total Mom in Tran. Direction =

at Bottom of base = 50.19+18.29x(2+0.25+0.95+0.05) = 109.63 KNm

Maximum Base Pressure =

at founding depth below HPP = 752.24/(5.4x2.3)+109.63x6/(5.4x2.3^2)

= 83.594 > 80

Revise the size

8.3 CHECK FOR BUOYANCY:

The critical case for buoyancy check is, when the pump is under maintenance condition. So the self weight of

the block itself has to resist the buoyancy force.

Buoyancy Force = 211.14 KN (Cl.4.2.2)

Transmitted Force/Moment

kN / kNm

Thz

FY

FYi

Mx

Mz_I

+ Thz

x distance b/w shaft & bottom of base

PMAX P / A + MX / ZX

KN/m2 KN/m2

Fb

16 of 17


Resisting Force =

= 5.4x2.3x(1.7+0.3)x24 = 596.16 KN

FOS for Buoyancy Check = 596.16 / 211.14

= 2.82 > 1.25

Hence O.K

8.4 CHECK FOR OVERTURNING:

Resisting Moment in Tran. Direction = (718.21 - 211.14) x2.3 / 2 = 583.13 KN-m

FOS against Overturning in Z-axis, = 583.13 / 109.63 = 5.3 > 2

Hence O.K

8.5 CHECK FOR SLIDING

Frictional co-efficient m = = 0.35

Sliding Force along Z-axis = = 35.30 KN

Frictional Resistance = = 0.35x(718.21-211.14) = 273.2 KN

Actual Factor of Safety against Sliding, FOS = 273.163 / 35.3025 = 7.74 > 1.5

Hence O.K

9 REINFORCEMENT CALCULATION:

Provide T 20 @ 200 c/c E/W Top and Bottom of Footing

Provide T 20 @ 200 c/c Sides of Footing

Provide T 12 @ 600 c/c Triaxial Vertical Only for blocks with depth more than 1.0 m

Provide T 12 @ 600 c/c Triaxial Horizontal

9.1 CHECK FOR WEIGHT OF REINFORCEMENT

Weight of reinf. required(footing) = 5.4 x 2.30 x 2.00 x 30 = 745.20 kg

Reinforcement provided :

Footing

Top 28 bars x ( 2.30 + 2.000 ) 2.47 = 297.39 kg

13 bars x ( 5.4 + 2.000 ) 2.47 = 237.61 kg

Bottom same as that in top = 535.00 kg

Sides (horz) 9 bars x 7.7 x 2.47 = 171.17 kg

Fresist L

B x B

B x (D+H

B_AG) x

c

Considering water table at ground level, vertical force will be taken as FY - F

b

MRz

FOSZ

Considering water table at ground level, vertical force will be taken as FY - F

b

FSz

Fz_I

FRr

x (FY - F

b)

As the foundation is designed as a block foundation, a minimum shrinkage reinforcement of 30kg/m3 shall be provided. (ACI 351.3R-04 Cl 4.4)

17 of 17


9 bars x 7.7 x 2.47 = 171.17 kg

Triaxial (Horz) 8 bars x 2.3 x 0.89 = 16.38 kg

3 bars x 5.4 x 0.89 = 14.42 kg

Triaxial (Ver) 16 bars x 2 x 0.89 = 28.48 kg

Total Reinforcement in Foundation = 1471.62 kg > 745.200 kg

Hence O.K

9.2 REINFORCEMENT SKETCH:

T20 - 200 c/c E/W Top and Bottom

SECTIONAL PLAN

18 of 17


T20 - 200 c/c T.O.G EL+100.300

F.G.L EL+100.000

Triaxial 16Nos of T12 - 600 c/c

B.O.F EL+98.300

Triaxial 8Nos of T12 - 600 c/c Triaxial 3Nos of T12 - 600 c/c

SECTIONAL ELEVATION

REINFORCEMENT ARRANGEMENT

19 of 17

ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATIONApproved by

20 of 17


21 of 17


9.5

9.7

0.0

0.0

0.0

0.0

1.3

20.49

Mass moment of inertia of whole system about common

CG

Iz = mi* (xoi2+yoi2)

Ratio between moments of inertia

22 of 17


Spring Constant

117877/(1-0.35)x2.262x

2*(1+0.35)x117877x0.977x

117877/(1-0.35)x0.635x

(117877/(1-0.35)x0.433x

Zo(m)

1.160

Combined C.G of machine and foundation

23 of 17


1.160

0.193

0.089

0.2818

Damping ratio D

Rocking (due to shaft ecentricity)

Mψ2

-kNm

24 of 17


2 Micron

0 Micron

5 Micron

0.00 radians

0.00 radians

Pitching

-

3.556

-

0.680

Pitching

Displacement response, Ax

M(Fo/K)

Mψ1 (kNm)

Mψ

1 (kNm)

25 of 17


-

4.983

-

0.953

Rotational Displacement

-

1.01E-06

-

1.92E-07

Amplitude Calculations

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

Due to M'

(Rad)

26 of 17


Check

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

SAFE

27 of 17


28 of 17


29 of 17


30 of 17


ANALYSIS & DESIGN CALCULATION FOR6 HDX 24A FOUNDATION

Designed by Checked by Approved by



Table 4-1 Ref. Suresh Arya , O'Neill & Pincus - Equivalent Spring Constants for Rigid Circular and Rectangular Footings

Figure 4-1 Ref. Suresh Arya , O'Neill & Pincus - Coefficients for Rectangular footings



Figure 4-2 Ref. Suresh Arya , O'Neill & Pincus - Embedment coefficients for spring constants

Table 4-3 - Ref. Suresh Arya, O'Neil & Pincus -Equivalent Damping Ratio for Rigid Circular and Rectangular Footings



Table 4-4 Ref. Suresh Arya , O'Neill & Pincus - Effect of Depth of Embedment on Damping Ratio

Table 4-5 - Ref. Suresh Arya, O'Neil & Pincus

Table 4-9 Ref. Suresh Arya , O'Neill & Pincus - Typical values for Poisson's Ratio



Table 1-4 Ref. Suresh Arya , O'Neill & Pincus - Freuquency & Amplitude calculations

block foundation - dynamic analysis

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