ACI 351.3R-04 Report: Foundation Design for Dynamic Equipment

This report details the design criteria, methods, and construction procedures for dynamic equipment foundations, referencing ACI 351.3R-04. It covers various aspects, including foundation and machine types, design considerations, dynamic soil properties, vibration performance criteria, and concrete performance criteria. The report addresses the importance of collaboration between the owner/operator, geotechnical engineer, structural engineer, and equipment supplier. It further discusses design methods, materials, vibration analysis, structural foundation design, the use of isolation systems, and repair/upgrade strategies for foundations. Construction considerations such as subsurface preparation, placement tolerances, formwork, construction sequence, equipment installation, grouting, and quality control are also highlighted, providing a comprehensive guide for industry practitioners involved in dynamic equipment foundation engineering.

Chapters 1 to 3 have been excerpted for use
with the ACI CEU Online Program.
ACI 351.3R-04

Foundations for Dynamic Equipment
Reported by ACI Committee 351
James P. Lee * Yelena S. Golod *
Chair Secretary
William L. Bounds * Fred G. Louis Abdul Hai Sheikh
William D. Brant Jack Moll Anthony J. Smalley
Shu-jin Fang Ira W. Pearce Philip A. Smith
Shraddhakar Harsh Andrew Rossi * W. Tod Sutton †
Charles S. Hughes Robert L. Rowan, Jr. ‡ F. Alan Wiley
Erick Larson William E. Rushing, Jr.
*Members of the editorial subcommittee.
†Chair of subcommittee that prepared this report.
‡Past chair.

This report presents to industry practitioners the various design criteria
and methods and procedures of analysis, design, and construction applied
to dynamic equipment foundations.
Keywords: amplitude; concrete; foundation; reinforcement; vibration.
CONTENTS
Chapter 1—Introduction, p. 351.3R-2
1.1—Background
1.2—Purpose
1.3—Scope
1.4—Notation
Chapter 2—Foundation and machine
types, p. 351.3R-4
2.1—General considerations
ACI Committee Reports, Guides, Standard Practices, and
Commentaries are intended for guidance in planning,
designing, executing, and inspecting construction. This
document is intended for the use of individuals who are
competent to evaluate the significance and limitations of its
content and recommendations and who will accept
responsibility for the application of the material it contains.
The American Concrete Institute disclaims any and all
responsibility for the stated principles. The Institute shall not
be liable for any loss or damage arising therefrom.
Reference to this document shall not be made in contract
documents. If items found in this document are desired by
the Architect/Engineer to be a part of the contract documents,
they shall be restated in mandatory language for
incorporation by the Architect/Engineer.
It is the responsibility of the user of this document to
establish health and safety practices appropriate to the
specific circumstances involved with its use. ACI does not
make any representations with regard to health and safety
issues and the use of this document. The user must determine
the applicability of all regulatory limitations before applying
the document and must comply with all applicable laws and
regulations, including but not limited to, United States
Occupational Safety and Health Administration (OSHA)
health and safety standards.
2.2—Machine types
2.3—Foundation types
Chapter 3—Design criteria, p. 351.3R-7
3.1—Overview of design criteria 3.2
—Foundation and equipment loads
3.3—Dynamic soil properties 3.4—
Vibration performance criteria 3.5—
Concrete performance criteria
3.6—Performance criteria for machine-mounting systems
3.7—Method for estimating inertia forces from multi-
cylinder machines
Chapter 4—Design methods and materials,
p. 351.3R-26
4.1—Overview of design methods 4.2—
Impedance provided by the supporting media 4.3
—Vibration analysis
4.4—Structural foundation design and
materials 4.5—Use of isolation systems
4.6—Repairing and upgrading foundations
4.7—Sample impedance calculations
Chapter 5—Construction considerations,
p. 351.3R-53
5.1—Subsurface preparation and improvement
5.2—Foundation placement tolerances 5.3—
Forms and shores
5.4—Sequence of construction and construction
joints 5.5—Equipment installation and setting 5.6—
Grouting
5.7—Concrete materials
5.8—Quality control
ACI 351.3R-04 became effective May 3, 2004.
Copyright © 2004, American Concrete Institute.
All rights reserved including rights of reproduction and use in any form or by any
means, including the making of copies by any photo process, or by electronic or
mechanical device, printed, written, or oral, or recording for sound or visual
reproduc-tion or for use in any knowledge or retrieval system or device, unless
permission in writing is obtained from the copyright proprietors.

351.3R-1

351.3R-2 ACI COMMITTEE REPORT

Chapter 6—References, p. 351.3R-57
6.1—Referenced standards and
reports 6.2—Cited references
6.3—Software sources and other references
6.4—Terminology
CHAPTER 1—
INTRODUCTION 1.1—Background
Heavy machinery with reciprocating, impacting, or rotating
masses requires a support system that can resist dynamic
forces and the resulting vibrations. When excessive, such
vibrations may be detrimental to the machinery, its support
system, and any operating personnel subjected to them.
Many engineers with varying backgrounds are engaged in
the analysis, design, construction, maintenance, and repair of
machine foundations. Therefore, it is important that the
owner/operator, geotechnical engineer, structural engineer,
and equipment supplier collaborate during the design process.
Each of these participants has inputs and concerns that are
important and should be effectively communicated with each
other, especially considering that machine foundation design
procedures and criteria are not covered in building codes and
national standards. Some firms and individuals have
developed their own standards and specifications as a result of
research and development activities, field studies, or many
years of successful engineering or construction practices.
Unfortunately, most of these standards are not available to
many practitioners. As an engineering aid to those persons
engaged in the design of foundations for machinery, the
committee developed this document, which presents many
current practices for dynamic equipment foundation
engineering and construction.
1.2—Purpose
The committee presents various design criteria and
methods and procedures of analysis, design, and
construction currently applied to dynamic equipment
foundations by industry practitioners.
This document provides general guidance with reference
materials, rather than specifying requirements for adequate
design. Where the document mentions multiple design
methods and criteria in use, factors, which may influence
the choice, are presented.
1.3—Scope
This document is limited in scope to the engineering,
construction, repair, and upgrade of dynamic equipment
foundations. For the purposes of this document, dynamic
equipment includes the following:
1. Rotating machinery;
2. Reciprocating machinery; and
3. Impact or impulsive machinery.
1.4—Notation
[C] = damping matrix
[K] = stiffness matrix
[K*] = impedance with respect to CG
[k] = reduced stiffness matrix
[kj′ ] = battered pile stiffness matrix
[M] = mass matrix
[m] = reduced mass matrix
[T] = transformation matrix for battered pile
[αir] = matrix of interaction factors between any
two piles with diagonal terms αii = 1
A = displacement amplitude
Ahead, Acrank = head and crank areas, in.2 (mm2)
Ap = cross-sectional area of the pile
a, b = plan dimensions of a rectangular foundation
ao = dimensionless frequency
Bc = cylinder bore diameter, in. (mm)
Bi = mass ratio for the i-th direction
Br = ram weight, tons (kN)
b1, b2 = 0.425 and 0.687, Eq. (4.15d)
cgi = damping of pile group in the i-th direction
ci = damping constant for the i-th direction
ci*(adj) = damping in the i-th direction adjusted for
material damping
cij = equivalent viscous damping of pile j in the
i-th direction
Di = damping ratio for the i-th direction
Drod = rod diameter, in. (mm)
d = pile diameter
dn = nominal bolt diameter, in. (m)
ds = displacement of the slide, in. (mm)
Ep = Young’s modulus of the pile
em = mass eccentricity, in. (mm)
ev = void ratio
F = time varying force vector
F1 = correction factor
Fblock = the force acting outwards on the block from
which concrete stresses should be calcu-
lated, lbf (N)
(Fbolt)CHG = the force to be restrained by friction at the
cross head guide tie-down bolts, lbf (N)
(Fbolt)frame = the force to be restrained by friction at the
frame tie-down bolts, lbf (N)
FD = damper force
FGMAX = maximum horizontal gas force on a throw
or cylinder, lbf (N)
FIMAX = maximum horizontal inertia force on a
throw or cylinder, lbf (N)
Fo = dynamic force amplitude (zero-to-peak),
lbf (N)
Fr = maximum horizontal dynamic force
Fred = a force reduction factor with suggested
value of 2, to account for the fraction of
individual cylinder load carried by the
compressor frame (“frame rigidity
factor”)
Frod = force acting on piston rod, lbf (N)
Fs = dynamic inertia force of slide, lbf (N)
FTHROW = horizontal force to be resisted by each
throw’s anchor bolts, lbf (N)
Funbalance = the maximum value from Eq. (3.18)
applied using parameters for a horizontal
compressor cylinder, lbf (N)

FOUNDATIONS FOR DYNAMIC EQUIPMENT 351.3R-3

fi1, fi2
= dimensionless stiffness and damping
functions for the i-th direction, piles
fm = frequency of motion, Hz
fn = system natural frequency (cycles per second)
fo = operating speed, rpm
G = dynamic shear modulus of the soil
Gave = the average value of shear modulus of the
soil over the pile length
Gc = the average value of shear modulus of the
soil over the critical length
GE = pile group efficiency
Gl = soil shear modulus at tip of pile
GpJ = torsional stiffness of the pile
Gs = dynamic shear modulus of the embedment
(side) material
Gz = the shear modulus at depth z = lc /4
H = depth of soil layer
Ii = mass moment of inertia of the machine-
foundation system for the i-th direction
Ip = moment of inertia of the pile cross section
i = –1
i = a directional indicator or modal indicator,
Eq. (4.48), as a subscript
K2 = a parameter that depends on void ratio and
strain amplitude
Keff = the effective bearing stiffness, lbf/in. (N/mm)
K* = impedance in the i-th direction with respect
ij to motion of the CG in j-th direction
Kn = nut factor for bolt torque
Kuu = horizontal spring constant
Kuψ = coupling spring constant
Kψψ = rocking spring constant
k = the dynamic stiffness provided by the
supporting media
kei* = impedance in the i-th direction due to
embedment
kgi = pile group stiffness in the i-th direction
ki = stiffness for the i-th direction
ki(adj) = stiffness in the i-th direction adjusted for
ki* material damping
= complex impedance for the i-th direction
ki*(adj) = impedance adjusted for material damping
kij = stiffness of pile j in the i-th direction
kj = battered pile stiffness matrix
kr = stiffness of individual pile considered in
isolation
kst = static stiffness constant
kvj = vertical stiffness of a single pile
L = length of connecting rod, in. (mm)
LB = the greater plan dimension of the founda-
tion block, ft (m)
Li = length of the connecting rod of the crank
mechanism at the i-th cylinder
l = depth of embedment (effective)
lc = critical length of a pile
lp = pile length
Mh = hammer mass including any auxiliary
foundation, lbm (kg)
Mr = ram mass including dies and ancillary
parts, lbm (kg)
m = mass of the machine-foundation system
md = slide mass including the effects of any
balance mechanism, lbm (kg)
mr = rotating mass, lbm (kg)
mrec,i = reciprocating mass for the i-th cylinder
mrot,i = rotating mass of the i-th cylinder
ms = effective mass of a spring
(Nbolt)CHG = the number of bolts holding down one
crosshead guide
(Nbolt)frame = the number of bolts holding down the
frame, per cylinder
NT = normal torque, ft-lbf (m-N)
Phead, Pcrank = instantaneous head and crank pressures,
psi (μPa)
Ps = power being transmitted by the shaft at the
connection, horsepower (kilowatts)
R, Ri = equivalent foundation radius
r = length of crank, in. (mm)
ri = radius of the crank mechanism of the i-th
cylinder
ro = pile radius or equivalent radius
S = press stroke, in. (mm)
Sf = service factor, used to account for increasing
unbalance during the service life of the
machine, generally greater than or equal to 2
Si1, Si2 = dimensionless parameters (Table 4.2)
s = distance between piles
T = foundation thickness, ft (m)
Tb = bolt torque, lbf-in. (N-m)
Tmin = minimum required anchor bolt tension
t = time, s
Vmax = the maximum allowable vibration, in. (mm)
Vs = shear wave velocity of the soil, ft/s (m/s)
v = displacement amplitude
v′ = velocity, in./s (cm/s)
vh = post-impact hammer velocity, in./s (mm/s)
vo = reference velocity = 18.4 ft/s (5.6 m/s)
from a free fall of 5.25 ft (1.6 m)
vr = ram impact velocity, ft/s (m/s)
W = strain energy
Wa = equipment weight at anchorage location
Wf = weight of the foundation, tons (kN)
Wp = bolt preload, lbf (N)
Wr = rotating weight, lbf (N)
w = soil weight density
X = vector representation of time-dependent
displacements for MDOF systems
Xi = distance along the crankshaft from the
reference origin to the i-th cylinder
x, z = the pile coordinates indicated in Fig. 4.9
xr, zr = pile location reference distances
yc = distance from the CG to the base support
ye = distance from the CG to the level of
embedment resistance
yp = crank pin displacement in local Y-axis,
in. (mm)

351.3R-4 ACI COMMITTEE REPORT

Zp
zp
α
α′
α1
αh
αi
α*ij
αuf
αuH
αv
αψH
αψM
β
βi
βj
βm
βp
δ
W
εir
ψi
γj
λ
μ
ν
νs
ρ
ρa
ρc
σo
ωi
ωm
ωn
ωo
ωsu, ωsv
= piston displacement, in. (mm)
= crank pin displacement in local Z-axis,
in. (mm)
= the angle between a battered pile and
vertical
= modified pile group interaction factor
= coefficient dependent on Poisson’s ratio
as given in Table 4.1
= ram rebound velocity relative to impact
velocity
= the phase angle for the crank radius of the
i-th cylinder, rad
= complex pile group interaction factor for
the i-th pile to the j-th pile
= the horizontal interaction factor for fixed-
headed piles (no head rotation)
= the horizontal interaction factor due to
horizontal force (rotation allowed)
= vertical interaction coefficient between
two piles
= the rotation due to horizontal force
= the rotation due to moment
= system damping ratio
= rectangular footing coefficients (Richart,
Hall, and Woods 1970), i = v, u, or ψ
= coefficient dependent on Poisson’s ratio
as given in Table 4.1, j = 1 to 4
= material damping ratio of the soil
= angle between the direction of the loading
and the line connecting the pile centers
= loss angle
= area enclosed by the hysteretic loop
= the elements of the inverted matrix [αir]–1
= reduced mode shape vector for the i-th
mode
= coefficient dependent on Poisson’s ratio
as given in Table 4.1, j = 1 to 4
= pile-soil stiffness ratio (Ep /Gl)
= coefficient of friction
= Poisson’s ratio of the soil
= Poisson’s ratio of the embedment (side)
material
= soil mass density (soil weight
density/gravi-tational acceleration)
= Gave/Gl
= Gz /Gc
= probable confining pressure, lbf/ft2 (Pa)
= circular natural frequency for the i-th
mode
= circular frequency of motion
= circular natural frequencies of the system
= circular operating frequency of the
machine (rad/s)
= circular natural frequencies of a soil layer
in u and v directions
CHAPTER 2—FOUNDATION AND MACHINE
TYPES 2.1—General considerations
The type, configuration, and installation of a foundation
or support structure for dynamic machinery may depend on
the following factors:
1. Site conditions such as soil characteristics,
topography, seismicity, climate, and other effects;
2. Machine base configuration such as frame size,
cylinder supports, pulsation bottles, drive mechanisms, and
exhaust ducts;
3. Process requirements such as elevation requirements
with respect to connected process equipment and hold-
down requirements for piping;
4. Anticipated loads such as the equipment static weight,
and loads developed during erection, startup, operation,
shutdown, and maintenance;
5. Erection requirements such as limitations or
constraints imposed by construction equipment,
procedures, techniques, or the sequence of erection;
6. Operational requirements such as accessibility, settle-
ment limitations, temperature effects, and drainage;
7. Maintenance requirements such as temporary access,
laydown space, in-plant crane capabilities, and machine
removal considerations;
8. Regulatory factors or building code provisions such as
tied pile caps in seismic zones;
9. Economic factors such as capital cost, useful or antici-
pated life, and replacement or repair cost;
10. Environmental requirements such as secondary
containment or special concrete coating requirements; and
11. Recognition that certain machines, particularly large
reciprocating compressors, rely on the foundation to add
strength and stiffness that is not inherent in the structure of
the machine.
2.2—Machine types
2.2.1 Rotating machinery—This category includes gas
turbines, steam turbines, and other expanders; turbo-pumps
and compressors; fans; motors; and centrifuges. These
machines are characterized by the rotating motion of impel-
lers or rotors.
Unbalanced forces in rotating machines are created when
the mass centroid of the rotating part does not coincide with
the center of rotation (Fig. 2.1). This dynamic force is a
function of the shaft mass, speed of rotation, and the
magnitude of the offset. The offset should be minor under
manufactured conditions when the machine is well balanced,
clean, and without wear or erosion. Changes in alignment,
operation near resonance, blade loss, and other malfunctions
or undesirable conditions can greatly increase the force
applied to its bearings by the rotor. Because rotating machines
normally trip and shut down at some vibration limit, a real-
istic continuous dynamic load on the foundation is that
resulting from vibration just below the trip level.
2.2.2 Reciprocating machinery—For reciprocating
machinery, such as compressors and diesel engines, a
piston moving in a cylinder interacts with a fluid through
the

FOUNDATIONS FOR DYNAMIC EQUIPMENT 351.3R-5

kinematics of a slider crank mechanism driven by, or
driving, a rotating crankshaft.
Individual inertia forces from each cylinder and each
throw are inherently unbalanced with dominant frequencies
at one and two times the rotational frequency (Fig. 2.2).
Reciprocating machines with more than one piston
require a particular crank arrangement to minimize
unbalanced forces and moments. A mechanical design that
satisfies operating requirements should govern. This leads
to piston/ cylinder assemblies and crank arrangements that
do not completely counter-oppose; therefore, unbalanced
loads occur, which should be resisted by the foundation.
Individual cylinder fluid forces act outward on the
cylinder head and inward on the crankshaft (Fig. 2.2). For a
rigid cylinder and frame these forces internally balance, but
deformations of large machines can cause a significant
portion of the fluid load to be transmitted to the mounts and
into the foundation. Particularly on large reciprocating
compressors with horizontal cylinders, it is inappropriate
and unconservative to assume the compressor frame and
cylinder are sufficiently stiff to internally balance all
forces. Such an assumption has led to many inadequate
mounts for reciprocating machines.
2.2.3 Impulsive machinery—Equipment, such as forging
hammers and some metal-forming presses, operate with
regulated impacts or shocks between different parts of the
equipment. This shock loading is often transmitted to the
foundation system of the equipment and is a factor in the
design of the foundation.
Closed die forging hammers typically operate by dropping a
weight (ram) onto hot metal, forcing it into a predefined shape.
While the intent is to use this impact energy to form and shape
the material, there is significant energy transmission,
particularly late in the forming process. During these final
blows, the material being forged is cooling and less shaping
takes place. Thus, pre-impact kinetic energy of the ram
converts to post-impact kinetic energy of the entire forging
hammer. As the entire hammer moves downward, it becomes a
simple dynamic mass oscillating on its supporting medium.
This system should be well damped so that the oscillations
decay sufficiently before the next blow. Timing of the blows
commonly range from 40 to 100 blows per min. The ram
weights vary from a few hundred pounds to 35,000 lb (156
kN). Impact velocities in the range of 25 ft/s (7.6 m/s) are
common. Open die hammers operate in a similar fashion but
are often of two-piece construction with a separate hammer
frame and anvil.
Forging presses perform a similar manufacturing
function as forging hammers but are commonly
mechanically or hydraulically driven. These presses form
the material at low velocities but with greater forces. The
mechanical drive system generates horizontal dynamic
forces that the engineer should consider in the design of the
support system. Rocking stability of this construction is
important. Figure 2.3 shows a typical horizontal forcing
function through one full stroke of a forging press.
Mechanical metal forming presses operate by squeezing
and shearing metal between two dies. Because this equip-
Fig. 2.1—Rotating machine diagram.
Fig. 2.2—Reciprocating machine diagram.
Fig. 2.3—Forcing function for a forging press.
ment can vary greatly in size, weight, speed, and operation, the
engineer should consider the appropriate type. Speeds can vary
from 30 to 1800 strokes per min. Dynamic forces from the
press develop from two sources: the mechanical balance of the
moving parts in the equipment and the response of the press
frame as the material is sheared (snap-through forces).
Imbalances in the mechanics of the equipment can occur both
horizontally and vertically. Generally high-speed equipment is
well balanced. Low-speed equipment is often not balanced
because the inertia forces at low speeds are small. The
dynamic forces generated by all of these presses can be
significant as they are transmitted into the foundation and
propagated from there.
2.2.4 Other machine types—Other machinery generating
dynamic loads include rock crushers and metal shredders.
While part of the dynamic load from these types of equipment
tend to be based on rotating imbalances, there is also a