**ANALYSIS & DESIGN CALCULATION FOR BFP FOUNDATION**

*Designed 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**

**ANALYSIS & DESIGN CALCULATION FOR BFP FOUNDATION**

*Designed 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

**4.0 STATIC DESIGN OF PUMP FOUNDATION**

**4.1. 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

L_{B}
B_{B}
H_{B_AG}
H_{B}
L_{S}
B_{S}
H_{S}

C/c distance bet. far end bolts along length,L_{a}
C/C distance bet. far end bolts along width,B_{a}
h_{S}

L_{m}
B_{m}
H_{mb}

PLAN VIEW SECTION VIEW

X
Z CL
o
f
D
is
ch
ar
ge
M_{z}
M_{x}
L_{B}
L_{S}
L_{a}
B_{B} B_{a} B_{s}
FGL
H_{B_AG}
H_{s}
D
C_{L} of Pump
Y
h_{s}
H_{B}

*Designed by* *Checked by* *Approved by*

**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
F_{Sliding}
F_{OT}
F_{BUO}
P_{p}
P_{pr}
P_{m}
P_{mr}
P_{b}
Pb_{p}
Pb_{pr}
P_{bp}
P_{o}
W_{cf1}
W_{cf2}
F_{b} L_{B} x B_{B} x D x w

= 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, D_{min}
Minimum edge of skid to concrete,C_{min}

( 2 x C_{min} ) + L_{s+Lm}
( 2 x D_{min} ) + W_{a}
( 2 x C_{min} ) + B_{s}
W_{P}
Foundation weight, W_{f}
F_{Y} W_{P} + W_{cf1} +Wcf2+ W_{f }
F_{Y} + 50% W_{P}
M_{X} M_{x_I}
M_{z} M_{z_I}
P_{MAX} P / A + M_{X} / Z_{X}

*Designed by* *Checked by* *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 **<** 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/m}2
P_{MAX} P / A + M_{Z} / Z_{Z}
KN/m2 _{KN/m}2

**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( G_{dyn} ) KN/m2

Poisson ratio,

Soil internal damping ratio (D_{})

of L_{B}
of B_{B}
_{}
_{}
D
CL of Pump
X
Y
HB
C.G
X
Z
C.G
origin

**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}A_{i} A_{i}*X_{i} A_{i}*Z_{i} A_{i}*Y_{i}

AiXi/Ai

AiZi/Ai

AiYi/Ai

**Mass**

**mi** **Coordinates of CG of elements** **Static moment of mass (kNSec2 _{)}**
kNsec2

_{/m}Combined C.G. in X direction,x

_{o}m

_{i}.x

_{i}/m

_{i}Combined C.G. in Z direction,z

_{o}m

_{i}.z

_{i}/m

_{i}Combined C.G. in Y direction,y

_{o}m

_{i}.y

_{i}/m

_{i}Eccentricity in X direction (x-x

_{0}) X X origin

= 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-z_{0})
in Y direction, y_{0}

mass moment of inertia of individual elements abt its own

axis Distance between common C.G. & C.G. of individual elements (m)

Mass moment of inertia of whole system about common

CG

kNsec2_{/m} _{*(Lyi}Ix = mi /12 2_{+Lzi}2_{)} _{*(Lxi}Iy = mi /12 2_{+Lzi}2_{)} _{*(Lxi}Iz = mi /12 2_{+Lyi}2_{)} x_{o} - x_{i} z_{o} - z_{i} y_{o} - y_{i} _{(yoi}Ix = mi* 2_{+zoi}2_{)} _{(xoi}Iy = mi* 2_{+zoi}2_{)} _{(xoi}Iz = mi* 2_{+yoi}2_{)}

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 m_{i}(l_{yi}2_{+l}
zi2)+mi(yoi2+zoi2) Iox + m.yo
2 _{}
x
kN sec2_{-m} _{kN sec}2_{-m}
1/12 x m_{i}(l_{xi}2_{+l}
yi2)+mi(xoi2+yoi2) Ioz + m.yo2 z
kN sec2_{-m} _{kN sec}2_{-m}
1/12 x m_{i}(lx_{i}2_{+l}
zi2)+mi(xoi2+zoi2)
kN sec2_{-m}
kN sec2_{-m}

Mass moment of inertia effective against

rocking excitation , I_{} _{kN sec}2_{-m}

Mass moment of inertia effective against pitching

excitation ,I_{} _{kN sec}2_{-m}

Mass moment of inertia effective against cross

= 60.69

**6 CALCULATION OF SPRING CONSTANTS & DAMPING RATIOS**

Length 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/m Kx = = = = ### = (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 sec}2_{/m}

L_{B}
L_{B}
B_{B} L_{B}
**Mode of **
**Vibration**
**Geometry **

**factors** **Equivalent radius r _{0}**

η_{y}
(BL/)0.5 1+0.6(1-)(h/r
0) (G/(1-)) y (B L)0.5 ηy
y
(Refer z value
Horizontal,
X,Z
η_{x}
(BL/)0.5 1+0.55(2-)(h/r
0) 2(1+)G x(BL)0.5 ηx
x
Rocking
η_{} _{K}_{}
(BL3_{/3}_{}_{)}0.25 1+1.2(1-)(h/r
0)+0.2(2-)(h/ro)3 (G/(1-)) (BL2) ηΦ
Pitching
η_{} _{K}_{}
(B3_{L/3}_{)}0.25 1+1.2(1-)(h/r
0)+0.2(2-)(h/ro)
3
(G/(1-)) (B2_{L) η}_{}
(Refer for BB/LB
Rotor

weight Dynamic force Point of Application at Shaft Location* Combined C.G of machine and foundation w(rpm)

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) shaft ecentricity)Rocking (due to

M_{ψ1} (kNm) M_{Ø}'-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 / (4r_{0}3_{)} (1+1.9(1-h/r
0)) / (ηy)0.5 0.425 y / (By)0.5
Horizontal,
X,Z
x
(7-8) W / (32(1-r_{0}3_{)} (1+1.9(2-h/r
0)) / (ηx)
0.5
0.288 x / (Bx)0.5
Rocking
B_{} D
3(1-) I_{} /(8 r_{0}5_{)} (1+0.7(1-h/r
0)+0.6(2-h/ro)
3_{))/(η}
0.5 0.15 _{} / ((1+n_{}B_{} (n_{}B_{}0.5)
n_{}
Pitching
B_{} D
3(1-) I_{} /(8 r_{0}5_{)} (1+0.7(1-h/r
0)+0.6(2-h/ro)3))/(η0.5 0.15 _{} / ((1+n_{}B_{} (n_{}B_{}0.5)
n_{}

** Values for n_{}n_{}for various values of B_{}_{}Table 4.5 of Arya, Neil & Pincus, reproduced below)

B_{}_{}

n_{}n_{}

**Mode of **

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

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

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

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

D

D

**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 force/moment Transmitted Displacement response, Ax

_{}_{n} 1/((1-r2_{)}2_{+(2Dr)}2_{)}0.5 _{(1+(2Dr)}2_{)}0.5 _{/ [(1-r}2_{)}2_{+(2Dr)}2_{]}0.5 _{Ftr}_{T}

rFo M(Fo/K)

Rocking,

Pitching,

Load

Case TranslationLateral Longitudinal Translation TranslationVertical Translation Force)Rocking (Due to Rocking (Due to shaft eccentricity)

M_{Ø}' (kNm) _{M}

Ø2 (kNm) Mψ

1_{ (kNm)}

Load

Case TranslationLateral Longitudinal Translation TranslationVertical Translation Force)Rocking (Due to Rocking (Due to shaft eccentricity)

M_{Ø}' (kNm) _{M}

Ø

2_{ (kNm)} M

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 M

1 _{(Rad)} _{Due to M}
2 (Rad) Due to M'
(Rad)
Mode of
Vibration
A_{Y}+ψ_{}/2+Ø*L_{B}/2
A_{Y}+ψ_{}/2+Ø*L_{B}/2
A_{X}+ØY-Yo)
A_{X}+ØY-Yo)
A_{z}+ψY-Yo)
A_{z}+ψY-Yo)
Rocking K_{Ø}1 _{Pitching K}
ψ
1
Rocking, Pitching,

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**
G
Check
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 force/moment Transmitted

Amplitude (Microns/rad ) Amplitude, Total Rocking, Pitching,

**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**
T_{hz}
F_{Y}
F_{Yi}

M_{x} M_{z_I} + T_{hz} x distance b/w shaft & bottom of base

P_{MAX} P / A + M_{X} / Z_{X}

KN/m2 _{KN/m}2

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

F_{resist} L_{B} x B_{B} x (D+H_{B_AG}) x _{c}

Considering water table at ground level, vertical force will be taken as F_{Y} - F_{b}

**M _{Rz}**

FOS_{Z}

Considering water table at ground level, vertical force will be taken as F_{Y} - F_{b}

**F _{Sz}** F

_{z_I}

**F _{Rr}** x (F

_{Y}- F

_{b)}

As the foundation is designed as a block foundation, a minimum shrinkage reinforcement of 30kg/m3_{ shall be }

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

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**

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_{+yoi}2_{)}

Ratio between moments of inertia

**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

1.160
0.193
0.089
0.2818
**Damping ratio D**
Rocking (due to
shaft ecentricity)
M_{ψ2} -kNm

2 Micron
0 Micron
5 Micron
0.00 radians
0.00 radians
Pitching
-3.556
-0.680
Pitching
Displacement
response, Ax
M(F_{o}/K)
M_{ψ}1_{ (kNm)}
M_{ψ}1_{ (kNm)}

-4.983
-0.953
Rotational Displacement
-1.01E-06
-1.92E-07
Amplitude Calculations
SAFE
SAFE
SAFE
SAFE
SAFE
SAFE
Due to M_{}'
(Rad)

Check SAFE SAFE SAFE SAFE SAFE SAFE SAFE SAFE SAFE SAFE SAFE SAFE SAFE SAFE SAFE

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

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

**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**