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Foundations for Dynamic and Sensitive Equipment
University of Minnesota - Structures Seminar October 30, 2015
Carl Nelson, Ph.D., P.E.
Tony Baxter, P.E.
2
ESI’s History Our roots go back to a
group of professors and graduate students at the
U of M in the 1960’s
3
Who We Are Today!
Minnesota based consulting engineering firm since 1970
Provide specialized engineering services
Specialists in high force/shock, vibration and noise control
From small medical devices and consumer products to sensitive buildings and large industrial facilities, ESI helps clients with advanced analysis and design. Our professional
engineering services are focused in the areas of structural dynamics and design, vibration control, noise and acoustics, and monitoring.
4
FEA and Structural Analysis
5
High Force Structures and Foundations
6
Vibration Measurements and Monitoring
Vibration Analysis for Healthcare, Manufacturing and Research
7
Recent Projects at U of M
Rec Center Expansion Cancer and Cardio Research Building
Physics and Nanotechnology Cleanroom Northrop Balconies
SE corner of clean
room floor
soil
drilled piers
(soil not shown)
N
8
What we will talk about today
1. Types of Foundations for Equipment • Foundations for Sources • Foundations for Receivers
2. Vibration Control Methods for Foundations • In ground – Viper Example (Source), Physics & Nanotechnology
Cleanroom Floor Example (Receiver)
• Isolated – Toyota Example
3. Technical Discussion of Dynamic Foundation in Soil • Model, Equations • Example Calculations and Recommendations
4. References – ACI Committee 351, Books
5. Closing & Questions
9
Types of Foundations For Equipment
1. Not Dynamic (Inertial Forces are Not Significant)
2. Foundations for Dynamic Sources a) Isolated b) On ground
3. Foundations for Sensitive Receivers a) Isolated b) On ground
Sources
Receiver
10
?
Foundation Types - not dynamic -
Not Dynamic (Inertial Forces are Not Significant)
Multi-Axial Subassembly Testing (MAST) Laboratory
11
React forces, provide a stable base and maintain alignment
Foundations For Dynamic Sources
12
• React forces • Provide a stable base and maintain alignment • Minimize motion, on and off foundation
13
Sensitive Receiver
K1 C1
M1
X1
Xg
Foundation
Soil
Foundation in Soil
2 MW
Generator
K1 C1
M1
X1
Xg
Foundation
Soil
K1 C1
M1
X1
Xg
Foundation
Soil
K2
M2
C2
X2
K1
K2
M2
C2
C1
M1X1
X2
F2(t)
M3
Press
Tub and Soil
Press and
foundation
Tub and soil
Foundation
Dynamic Source
Fou
nd
atio
n in
Gro
un
d
Iso
late
d F
ou
nd
atio
n
The Concept of Transmissibility
0.00001
0.0001
0.001
0.01
0.1
1
10
100
0 1 10 100
Fo
rce O
ut/
Fo
rce In
f/fn
Force Transmissibility
0
0.01
0.05
0.1
0.2
0.5
1
2
Fraction of Critical Damping
F
Fground
xground
/groundT F F
/ groundT x x
Transmissibility applies (exactly the same equation!) to both source force transmissibility and receiver displacement transmissibility
Receiver
Source
14
Foundations for Dynamic Sources
actuators
Test item
Soil Supported Viper Test Rig at Virginia International Speedway
15
16
Foundations for Dynamic Sources
Soil Supported Viper Test Rig at Virginia International Speedway
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Foundations for Dynamic Sources Air Mount Isolated with Foundation
18
19
High force
Mass
Air Springs
- Attenuated force transmitted to foundation - Minimize motion at actuator base
Foundation Isolation with Air Mounts
Soil Supported Foundations for Sensitive Receiver Overview of Concepts
20
Engineered Fill
Slab
1. Simple Thick Slab on Ground – Wavelength Effect
2. Isolated Slab for Electron Microscopy Center - Shepherd Laboratories
Bedrock
Sand
Thick Slab
Criteria 125 u"/s --- Measured > 300 u"/s
Tall
“Isolated” Caissons
Slab-on-Grade
Typical Wavelength = 50 - 100 ft
Bedrock
Sand Auger
Cast Piles
3. Physics and Nanotechnology Cleanroom – U of M
Air Space
Floor Structure Criteria 125 u"/s --- Measured ~ 100 u"/s
Foundations for Sensitive Equipment Isolated with Various Types of Isolators
Sensitive Equipment Isolation Techniques
Air Mounts (<2 Hz) Steel Springs (2-5 Hz) Resilient Pad or Sheets (>6 Hz)
Entire Building Isolation Drachen-Center Basel Switzerland
21
22
Rigid Foundation on Elastic Halfspace
under harmonic loading
, ,G
,or m
( ) i t
oP t P e
What do all these foundations have in common?
Two Minutes on Elastic Wave Propagation
P Waves – Compression (fastest) S Waves – Shear Rayleigh Waves – Speed close to that of S waves
Amplitude decreases with
Accounts for 2/3 of the energy
(See Figure 3-16 on p. 91 in Richart, Hall, and Woods)
s
G
V
2
P
G
V
1
r
(1 )(1 2 )
E
23
24
24
Predicting Vibration Versus Distance
0 15 30 45 60 75 90 105 1200
0.02
0.04
0.06
0.08
0.1
0.12
LRT Vibration Amplitude vs. Distance
Dista nce - Fe et
Vib
ration
Am
pli
tude
- Inch
es/s
econ
d
.12
0.002
.z( )r 12
.z g( )r 12
.z lim 12
1205 r
Geometric Damping Only: z g( )r .z 1
r 1
r
Geometric & Material Damping: z( )r ..z 1
r 1
rexp . r r 1
Early Boussinesq (1885), Lamb (1904) – static, dynamic load on the surface of elastic halfspace Riessner (1936) – Dynamically loaded, rigid circular foundation on elastic halfspace Lysmer and Richart – “Dynamic Response of Footings to Vertical Loading,” ASCE Journal of the Soil Mechanics and Foundations Division, January 1966. “Lysmer’s Analog” Numerical Methods Many Contributors – FEA, Boundary Element Method Beskos and Co-Workers and the University of Minnesota (1970s-80s)
Some History Development of Techniques
25
Winkler Foundation Plate on Elastic Halfspace Rigid Plate on Elastic Halfspace
Lysmer’s Analogue (1966)
Complicated! Still Complicated!
But…
Approaches to the Dynamic Foundation Problem
26
Lysmer’s Analog
( )i tP
F ek
1 2( ) ( ) ( )iF F F
F is a dimensionless displacement function with real and imaginary parts
2
2 2 2 2
1( )
(1 )
(1 ) (1 )
o o
o o o o
i
i
Ba aF
Ba a Ba a
2 2 2
1
(1 )o o
M FBa a
Textbook so far, but with slightly unfamiliar notation
( ) i t
oP t P e
Magnification Factor
2n
o
ca
k
2
k mB
c
Introducing the dimensionless ratios
27
Model
Static vertical stiffness
Dimensionless frequency
Dimensionless mass
Equation of motion
Lysmer’s Analog
Simple Damped Oscillator
2n
o
ca
k
2 2 2
1
(1 )o o
FBa a
2
k mB
c
4
1
oG rk
, ,G
,or m
Rigid Circular Foundation on Elastic Halfspace
oo o
sG
ra r
V
2
24
1s
o o
Vm mB
k r r
k
( ) i t
oP t P e ( ) i t
oP t P e
1 1s
i too
V
k rm c k k P e
i t
om c k P e
o
s
rck V
o
s
rkc
V
28
Lysmer’s Analog
, ,G
,or m
( ) i t
oP t P e
1 1s
i too
V
k rm c k k P e
29
Magnification Factor vs. Frequency and Mass Ratio
2 2 2(
1
(1 ) 0.85 )o o
M FBa a
oo
s
ra
V
24
1
o
mB
r
0.5B
0B
1B
5B
2B
See Fig. 11 of Lysmer (1966) to see how well this compares to the elastic halfspace solution
30
Sample Calculations Reciprocating Compressor
oo
s
ra
V
2 2 2(
1
(1 ) 0.85 )o o
M FBa a
0.5B
0B
Note that B will generally be in
this range
Soil properties, medium dense silty sand
Vs 750ft
s 115
lbm
ft3
G Vs2
13962psi
Sallowable 2000psf 0.35
Foundation pad properties
L 25 ft b 15 ft rob L
10.925ft t 4.5 ft
Wf ro2
t 150 pcf 2.531 105
lbf
k4 G ro
1 11.26 10
6
lbf
in
Vertical stiffness
Compressor Weight
Wequip 50000lbfWf
Wequip
5.062 >5
Wf Wequip
b L808psf < 0.5Sallowable 1000psf
mWf Wequip
g Total mass of foundation plus equipment
B1
4
m
ro3
0.328Mass ratio
fn1
2
k
m 19.06
1
s Vertical natural frequency
31
Sample Calculations More Plots
20 40 60 80 1000
0.2
0.4
0.6
0.8
1
1
0.036
M i
1001 f i
Hz
1 10 1000.01
0.1
1
M i
f i
Hz
Mi
1
1
fi
fn
2
2
0.85aoi
2
fn 19.06Hz
In terms of actual frequency…
32
Sample Calculations
o
PM
k
Let’s get down to some real numbers. Suppose that the compressor exerts a vertical force of 4500 lb at a frequency of 600 rpm (10 Hz).
P 4500lbfP
k3.99 10
4 in in 10
6in g 10
6g
20 40 60 80 1000
1 104
2 104
3 104
4 104
Displacement vs frequency
Frequency (Hz)
Dis
pla
cem
ent (i
n)
P
kM i
in
f i
Hz
20 40 60 80 1000
10000
20000
30000
40000
Velocity in micro in/sec vs frequency
Vel
oci
ty (
mic
ro in
/sec
)
2 f iP
k M i
in
s
f i
Hz
20 40 60 80 1000
5000
10000
15000
Acceleration in micro g's vs frequency
Acc
eler
atio
n (
mic
ro g
's)
2 f i 2 P
k M i
g
f i
Hz
33
Sample Calculations
Let’s see how this compares to some vibration criteria
34
Sample Calculations
Forces exerted by seismic tables with heavy specimens can be large
The system shown above has a 4m x 4m table with 8 actuators. The four vertical actuators are capable of generating a total of 343 kN (77 kips) at frequencies
from 1 to 30 Hz.
Note the size of the foundation mass reacting the actuator forces..
35
Case Study Foundations for Sensitive Equipment- Soil Supported
Physics and Nanotechnology Clean Floor Design at U of M
Project / Location: P1721- U of M Physics & Nanotech Building Measurement ID: File: TEST004.AE2 Record Date and Time :12/20/2010 1:35:53 PM
Date: 20-Dec-10 Channel 3: Sidewalk NW corner
Conditions: Delivery truck leaving by CH 4 Channel 4: Asphalt SW corner
Setup: 90% overlap, hanning window, delta f = 0.125 Hz Vibration Criteria VC-C (green), VC-D, VC-E
Channel 3 Trigger Channel 4 Trigger
Channel 3 Peakhold Spectrum Channel 4 Peakhold Spectrum
-0.20
-0.10
0.00
0.10
0.20
0 1 2 3 4 5 6 7 8
Acce
lera
tio
n (in
/s2)
Time (s)
-0.2
-0.1
0.0
0.1
0.2
0 1 2 3 4 5 6 7 8
Acce
lera
tio
n (in
/s2)
Time (s)
12.5, 289
10
100
1000
1 10 100
Ve
locit
y (m
icro
-in
/s r
ms)
Freq (Hz)
12.5, 460
10
100
1000
1 10 100
Ve
locit
y (m
icro
-in
/s r
ms)
Freq (Hz)
36
Measurement Locations
Sample of Ground Vibration Measurements Prior to Construction
N
37
Case Study Foundations for Sensitive Equipment- Soil Supported
Physics and Nanotechnology Clean Floor Design at U of M
Auger Cast Pile Placement
Pile Top and Floor Detail
Foundation Plan
1/3 Octave Velocity vs. Frequency
Floor Response at Vistec-E-Beam
0
20
40
60
80
100
120
140
160
180
200
0 5 10 15 20 25 30 35 40
Frequency (Hz)
Ve
loc
ity -
(in
/se
c)
Predicted Response at 75
Predicted Response at 893
Predicted Response at 898
Predicted Response at 4
Predicted Response at 126
VC-E
38
SE corner of clean
room floor
soil
drilled piers
(soil not shown)
N
Case Study Foundations for Sensitive Equipment- Soil Supported
Physics and Nanotechnology Clean Floor Design at U of M
Predicted Velocity on Cleanroom Floor
FEA Model (COSMOS)
ACI Committee 351 – Foundations for Equipment and Machinery
Active Committee Documents: • 351.1R-12: Report on Grouting between Foundations and Bases for Support of Equipment and Machinery • 351.2R-10: Report on Foundations for Static Equipment • 351.3R-04: Foundations for Dynamic Equipment • 351.4-14: Specification for Installation of Cementitious Grouting between Foundations and Equipment Bases • 351.5-15 Specification for Installation of Epoxy Grout between Foundations and Equipment Bases Documents Under Development: • 351.3R: Foundations for Dynamic Equipment • 351.4M-14: Specification for Installation of Cementitious Grouting between Foundations and Equipment Bases • 351.5M-15: Specification for Installation of Epoxy Grouting between Foundations and Equipment Bases
39
Wrap Up
Important Topics We Have Not Talked About Today Rotational and Horizontal Modes Embedment Effects Strength Requirements Anchorage Numerical Methods/Software Questions? Thank you for inviting us!
40