3. 1. INTRODUCTION
The analysis and design of structure or foundation subjected to vibratory
loading is a complex problem as it involves interaction of three domains viz.
Structural Engineering, Geotechnical Engineering and Structural dynamics.
The machines used in Oil and Gas industry are usually supported on a
concrete block or a concrete frame and occasionally on steel frames. In
majority of the cases the machines are supported on a simple concrete block.
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4. Types of Machines in Oil and Gas Industry
1.Centrifugal Machines ( Rotating)
Fig-1
2. Reciprocating Machines
Fig-2
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5. Centrifugal Machine ( Rotating)
Fig-3
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7. Classification of rotating machines based on
Frequency/speed
•Very low speed machines < 100 rpm
•Low speed machines 100 rpm to 500 rpm
•Medium Speed machines 500 rpm to 1500 rpm
•Moderately high speed machines 1500 rpm to 3000 rpm
•High speed machines >3000 rpm
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8. Various Types of Machine Foundations
MACHINE
CONCRETE CONCRETE/ST
BLOCK EEL FRAME
CONCRETE BASE
RAFT
SOIL
SOIL
1.Block (Concrete) 2. Frame ( Concrete or Steel)
Type Type
Fig-5
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9. MACHINE
CONCRETE CONCRETE/ST
BLOCK EEL FRAME
SOIL
SOIL
1.Block (Concrete) 2. Frame ( Concrete or Steel)
Supported by piles supported by Piles
Fig-6
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10. 2. INPUTS
What inputs are needed for foundation design?
The inputs are broadly categorized as
Project Design basis for Machine foundation
Soil Parameters for foundation Design
Machine vendor inputs
The above are elaborated in the subsequent slides
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11. What inputs are available in Project Design
basis?
The following are the major inputs to be extracted from the project
design basis:
•Criteria for Dynamic Analysis
•Permissible Amplitudes of Displacements and rotation of the foundation in
the absence of Vendor data.
•Grade of Material ( Concrete/Steel ) to be used for the construction of
Machine foundation
•Permissible % of bearing pressures for dynamic loading.
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12. What are the Soil Parameters required?
Primary parameters
1. Dynamic Shear Modulus
2. Poisson’s Ratio
3. Damping factor
Secondary Parameters
1. Coefficient of Elastic uniform compression Cz
2. Coefficient of Elastic uniform shear Cτ
3. Coefficient of Elastic non uniform compression Cθ
4. Coefficient of Elastic non uniform shear Cψ
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13. How to determine the Soil Parameters?
Field Tests :
•Cross Hole Test ( CHT).
•Down hole test (DHT).
•Spectral Analysis of Shear wave ( SASW)
•Block Vibration Tests
Laboratory tests:
•Resonant Column test
•Cyclical Tri axial Test
The above test are conducted usually by a Geotechnical Contractor and
appropriate values are recommended by him in the Geotechnical report
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19. Machine Vendor Input
The following input is required from the machine vendor:
•Geometric configuration of the Machine
•Loads from the Machine: Mass of the stationary as well as rotating parts of
the machine and load transfer mechanism from machine to the foundation
•Critical Machine performance parameters: Critical speeds of rotors, balance
grades and acceptable levels of amplitudes of vibration
•Dynamic forces generated by the Machine: forces generated under various
operating conditions and their transfer mechanism to the foundation for
dynamic response analysis.
•Additional forces generated under emergency or faulted conditions, Test
condition, Erection condition & Maintenance condition of the machine, forces
due to bearing failure ( if applicable) for strength analysis of the foundation.
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20. Typical Vendor Input ( Machine GAD):
Fig-12
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21. 3.ANALYSIS & DESIGN
The Analysis of the Machine foundation is done in two stages:
•Dynamic Analysis : Includes determination of the the natural frequencies
of the Machine foundation system and calculation of amplitudes of
displacements and rotations of the foundation under dynamic loading.
•Static Analysis: Includes check for strength of the foundation, stability of
the foundation and check for soil bearing capacity.
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22. The process of evaluating the critical soil properties that influence soil
structure interaction is probably the most difficult part of the machine
foundation design- Dr. K.G.Bhatia
The significant aspects of soil properties which influence soil-structure
interactions are:
•Energy transfer mechanism- Not quantifiable
•Soil mass participation in vibration of the foundation- Not quantifiable
•Effect of embedment of foundation- Approximately quantifiable
•Applicability of Hooke’s law to soil- To some extent
•Dynamic soil parameters-Approximately quantifiable
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23. Deformation modes of soil
Based on above deformable modes of foundation, the following deformable
modes can be anticipated for Soil beneath the block foundation:
• Uniform Compression
•Uniform Shear
•Non Uniform compression
•Non Uniform shear
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24. In the context of Machine foundation design, a Machine would necessarily
include:
•A drive machine
•A driven machine
•A coupling device
Schematically:
coupling Driven
Drive
machine machine
Fig-13
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25. A typical data set required for each of the components shown in the previous
schematic is:
For dynamic response analysis of foundation:
•Total mass of machine ( including rotating parts), Radius of gyration and its over
all centroid location.
•Mass of rotating parts of the machine, operating speed, height of the centre of the
rotor from machine base frame, etc
•Foot print of machine base frame, details of holding down bolts
•Dynamic forces generated by the machine under operating conditions
For strength design of foundation:
• Static loads from machine
•Equivalent static forces i.e. dynamic forces converted to equivalent static forces
•Forces generated under emergency and faulted conditions eg: bearing failure,
loss of blade, short circuit etc.
•Forces during erection, maintenance and test conditions of the machine.
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26. Parameters for rotary ( centrifugal) machines:
Balancing of rotating machine
Centre of Mass
Centre of Rotation
Balanced condition
Fig-14
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27. Centre of Mass ‘m’
e
Centre of Rotation
Un- Balanced condition
Force Generated due to unbalanced condition F= meω2
The above force is called unbalanced force
Fig-15
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28. Unbalanced forces along the shaft with multiple supports
Fig-16
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31. In every rotating machine there will be certain amount of unbalance(
eccentricity) which is inevitable.
ISO/ Machine manufacturer has set standards for the allowable eccentricity
based on:
•Function of the machine
•Speed of the machine and
•Rotating mass
Many rotating machines are balanced to an initial balance quality as per ISO
standards. This is called the balance quality grade.
Fig-19
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32. Critical speeds: Correspond to flexural frequencies of the rotor. These are
supplied by the vendor. High vibration can occur on account of resonance of
foundation with critical speeds
Forces due to Emergency conditions:
Bearing Failure: Grinding halt of machine due to failure of bearings. Difficult to
quantify and can be taken as an static force equivalent to 3 to 5 times the
rotor weight.
Short circuit force: Furnished by Machine vendor
Loss of parts like blade: Furnished by Machine vendor
Fig-20
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33. Parameters for reciprocating machines:
Typical arrangement for single cylinder reciprocating system
Fig-21
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34. Dynamic forces transferred at C.G of machine at base frame level
Fig-22
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35. Foundation Parameters
Under tuned foundation:
The vertical vibration frequency is < operating frequency of the machine
Preferred for Medium to High speed Machines
Over tuned foundation:
The vertical vibration frequency is > Operating frequency of the machine
Preferred for very low to low speed machines
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36. Vibration Limits in Machine Foundation design
Rotary type machines
Machine Operating speed Permissible amplitude in
in rpm Microns
100 to 500 200 to 80
500 to 1500 80 to 40
1500 to 3000 40 to 20
3000 to 10000 20 to 5
Reciprocating type machines
Machine Operating speed Permissible amplitude in
in rpm Microns
300 to 1500 1000 to 20
100 to 300 1000
The above are only approximate values. Actual permissible should be
given by the Machine Vendor/Manufacturer
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37. Foundation Sizing ( Block foundation):
Foundation should be dimensioned in such a way that the derived
eccentricity, in both lateral and longitudinal directions is bare minimum.
In no case it should not exceed 5% of the base dimension in the respective
direction
Foundation should extend by at least 150 mm on all sides of machine base
frame
The pressure developed in the soil loads due to static loads should not
exceed 75% of the allowable safe bearing capacity.
Though from strength point of view it may appear adequate to keep
foundation mass slightly above the machine mass, a higher mass ratio
helps to keep the eccentricity of loading within limits.
For rotary machines: foundation mass = 2.5 to 3 times of machine mass
For reciprocating machines: foundation mass= 5 to 8 times of machine
mass
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38. Foundation Stiffness:
Foundation parameters that govern the dynamic response are its mass
and its area of contact with the soil. In specific cases projected parts of
foundation having finite stiffness also influence the dynamic response.
The rigidity of foundation is much higher compared to that of soil
supporting it.
In the case of block foundation the rigidity is so high that under the
influence of static and dynamic forces the deformations of the block are
negligible compared to soil. The block foundation is therefore considered
as rigid body consisting of mass only.
In case the foundation of machine is not a solid block but a frame or some
other kind of structure which has stiffness comparable to that of soil, then
elements of those structures shall be considered to have both mass and
stiffness.
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39. Strength Design:
Since the block foundation behaves like a rigid body supported on a soft media like soil,
invariably the block foundations would turn out to be having adequate strength vis-à-vis
forces imparted by machine.
Strength design is done considering the forces and moments on the foundation due to
static loads, dynamic loads, emergency loads and applicable earthquake/wind loads.
Anchor bolts: All anchor bolts should be checked for pullout force caused due to
Dynamic and Emergency loads
Stability Checks:
The foundation shall be checked for sliding and overturning . But these checks are not
compulsory.
Minimum Reinforcement :
•25 to 50 kg/m3
•Minimum dia. of the bar 12 mm
•Two way reinforcement on all the faces and shrinkage reinforcement ( when thickness
of block exceeds 1m)
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40. Dynamic Analysis ( Block Foundation)
THERE ARE SIX MODES OF VIBRATION OF BLOCK FOUNDATION
WITH REFERENCE TO THE X-Y-Z CO-ORDINATE SYSTEM
VERTICAL VIBRATION
HORIZONTAL VIBRATION ( 2 DIRECTIONS) IN SAME PLANE
ROCKING
PITCHING
YAWING OR TWISTING
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41. Possible Movement for Block foundation:
Z
Y
θ
φ
X
ψ
Fig-23
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42. Single Degree Freedom Mathematical Model
Mass of machine and
foundation
Soil Damping
Stiffness of the soil
Fig-24
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43. Lumped Parameter System
Z mz cz z k z z P0 sin( t )
z
k
n
Cz Kz m
Kx
Iψ m X
ψ
Cx
Kψ D c ccr ccr 2 k m
Cψ/2
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Cψ/2
January 2011
Fig-25
44. Lumped Parameter Values
Mode Vertical Horizontal Rocking Torsion
4Gr 8Gr 8Gr 3 16Gr 3
Stiffness k 3(1 )
1 2 3
Mass Ratio m(1 ) m(2 ) 3I (1 ) I
m
mˆ 4 r 3 8r 3 8 r 5 r 5
Damping 0.425 0.288 0.15 0.50
Ratio, D ˆ
m1/ 2 ˆ
m1/ 2 (1 m)m1/ 2
ˆ ˆ 1 2mˆ
Fictitious 0.27m 0.095m 0.24I x 0.24I z
Mass mˆ mˆ mˆ mˆ
D=c/ccr G=Shear Modulus ν=Poisson's Ratio r=Radius ρ=Mass Density
Iψ,Iθ=Mass Moment of Inertia
45. Closed form solution for free and forced vibration of foundation block subjected
to dynamic loads:
Fig-26
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46. FE Models of Block foundation
Fig-27
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47. Model with Soil and Block foundation
Fig-28
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48. Foundation Sizing ( Framed foundation):
Foundation GA and loading diagram is provided by the Machine
vendor/Manufacturer.
Typical Steel Frame foundation for Turbo Generator
Fig-29
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49. Eccentricity:
For Framed foundation there are two connotations to the term eccentricity:
1. Overall eccentricity: it is defined as the distance between the centre of mass
of the over all system ( machine+ foundation) and C.G of the base contact
area of the foundation with soil. This should be restricted to 5%
2. Top deck eccentricity: It is defined as the distance between the centre of the
Mass Cm ( combined C.G of machine mass, top deck mass and 23% percent
of column mass) and centre of stiffness of frames Ck in the transverse and
longitudinal directions. It is desirable to restrict this eccentricity to 1% of the
respective dimension of the top deck.
Top deck sizing:
Top deck comprises of transverse and longitudinal beams, slab connecting these
beams, projections on all sides of the beams, depressions, cutouts, notches etc.
a. The top deck weight > weight of the machine
b. For beams: Span/Depth = 3 to 5; Depth/width = 1 to 1.5
c. Extent of cantilever projections in plan should not be more than half the width
of the corresponding beam
d. Depth of slab should be invariably same as that of the encompassing beams
except at areas where the recess or depressions are provided to accommodate
machine
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50. Columns:
Total weight of the columns should be close to the weight of the machinery. This is
desirable but not essential condition
But the following should be kept in mind while assessing the sizes of columns
•Centre of stiffness of all the frames should coincide with centre of mass of
machine and top deck.
•Lateral natural frequencies of each of the column ( along transverse as well as
longitudinal directions) considering fixed at both ends should not coincide with
Machinery frequency or its harmonics.
Base raft:
• Raft plan dimensions are selected such that the bearing pressure generated is
less than 70% of allowable bearing pressure.
• Base raft thickness should be such that it acts like a rigid block and undergoes
uniform deformation.
•General guide line is weight of the base raft should be about twice the weight of
the machine
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51. Stiffness of frame foundation:
Unlike block members of frame foundation have finite stiffness and are
subjected to considerable elastic deformations.
Framed foundation is considered as elastic body with both mass and stiffness.
Strength design:
For frame foundation the reinforcement is provided as dictated by the strength
design of the structural members i.e. columns, beams and slabs.
Minimum Reinforcement:
• Reinforcement for top deck and columns to be in the range of 100 to 120
kg/m3
•Reinforcement for base raft shall be in the range of 70 to 80 kg/m3
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52. Framed foundation under construction
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January 2011
53. Dynamic Analysis ( Framed Foundations)
Unlike block foundations, framed foundation has many modes of vibration.
Closed form solutions for framed foundation:
Before the advent of computers the framed foundations are analyzed manually.
The manual procedure aims at analyzing the frames of the foundation
independently for free and forced vibrations and algebraically summing up the
response for all frames. ( Refer Handbook of Machine foundations by Srinivasulu
and Vaidyanathan for Manual Analysis of framed foundation).
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54. Modeling Methods for Framed foundation:
There are two acceptable methods
Method 1:the loads are applied to the model of the super structure to
determine the foundation response. The computed reactions at the
base of the columns are then used as input forces on the model of the
mat
Method2: in this method both the superstructure and foundation are
incorporated into a single model. This procedure will yield results for
the entire foundation in one analysis.
For both the above methods the beams and columns are modeled
using 3 dimensional beam elements, shear walls ( if any) and mat are
modeled using plate-bending elements.
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55. Models for Dynamic Analysis ( some major points to remember):
The dynamic model should not be created independently of the static model but
should be created from static model by incorporating the following:
•Enough nodes should be specified along the length of beams and columns so
as to capture frequencies of modes which match with machine frequency.
•The nodal masses can be computed either by lumped mass approach or
consistent mass approach
•It is recommended that 2% of critical damping used for concrete elements and
1% for steel elements.
•The dynamic model of foundation should also include the machine. The simplest
method to model this is modeling the machine as series of mass points lumped
with the foundation.
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56. Loads for which Static Analysis is recommended:
•Dead Load
•Live load
•Normal torque load
•Condenser load
•Thermal loading due to machine expansion/contraction
•Piping loads
Loads for which Pseudo-dynamic Analysis is recommended:
•Normal machine unbalanced load for machines mounted on conventional
foundations
•Seismic loading
Loads for which Pseudo-dynamic analysis is acceptable:
•Short circuit load
•Out of phase synchronization
•Loading due to bowed rotor
•Load due to missing rotor blade
Loads for which dynamic analysis is recommended:
•Normal machine unbalance load for machines mounted on low tuned
foundation
•Seismic loading
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57. Typical Free Vibration Response of FE model of Framed foundation
Fig-31
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58. Typical Response of foundation subjected to Dynamic loading
Fig-32
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59. Miscellaneous Topics
1. Soil- Structure Interaction effects:
•The presence of supporting soil affects the static and dynamic
response of the turbine foundation. These effects are termed as
soil structure interaction effects.
•Usually soil-structure interaction effects are considered
negligible for framed foundation under operating conditions.
However, they can be critical under non-periodic forces like
earthquake, short circuit etc.
•Soil structure interaction effects are more predominant in the
case of block foundations.
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60. 2. Machine foundations on Piles:
Piles are specifically required for machine foundations in the following
circumstances:
• When soil is weak to withstand the loads
•When it is required to increase the natural frequency of the machine
foundation system.
•When dynamic amplitudes are required to be reduced
•When it is required to stiffen the support system on account of seismic
considerations.
Problems associated with Analysis of machine foundations supported on
piles
•Understanding of dynamic behavior of group of piles is still in its infancy.
•As the reliability of dynamic characteristics of group of piles is faced with
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many questions, so shall be January 2011 of computed dynamic response
the status
61. The following are observations by various researchers with regard to
dynamic behavior of piles:
•Dynamic stiffness of the pile is generally found to be greater than static
stiffness
•Both stiffness and damping of pile are found to be frequency dependent
•Damping increases with pile length
•Embedment of pile cap results in increased stiffness. However, its
quantification is not yet established
•Damping of group of piles is more frequency dependent
•Dynamic group effect considerably differs from static group effect.
•Rocking and torsional stiffness of the pile can be safely ignored.
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62. 4.REFERENCES
BOOKS:
1. Barkan D.D.” Dynamics of bases and Foundations”- Mc Grawhill
2. P.Srinivasulu and Vaidyanathan “Hand Book of Machine foundations”- Tata Mc Grawhill
3. “Foundations for Industrial Machines: Hand book for Practicing Engineers”- K.G.Bhatia-
DCAD publishers
4. S.Prakash and V.Kpuri “ Foundation for machines- Analysis and Design”- John Wiley
5. Arya, O Neil and Pincus “ Design of Structure and Foundation for Vibrating Machines”-
Gulf Publishing
6. Indrajit Chowdhury and P.Dasgupta “ Dynamic of Structure and Foundation” –CRC
press
7. “Soil Dynamics and Machine foundations” – Swami Saran- Galgotia
8. “Soil Dynamics “ - Braja M. Das
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63. CODES:
Indian:
IS2974: 5 parts of which parts 1,3 & 4 are for Reciprocating and Rotating machines
IS 5249: Methods of test for determination of Dynamic soil properties
British:
CP 2012
German:
DIN4024 ( Part 1): For framed type ( Flexible) foundations
DIN 4024 ( Part 2): For block type ( Rigid) foundations
American:
ACI 351
Saudi:
SAES-Q-007
ISO:
1S0 10816 ( 7 parts)
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