Kee H. Lee's Civil & Architectural Engineering Document

Kee H. Lee, P.E. (kee007.lee@samsung.com)
Civil & Architectural Engineering Department
June 23th, 2016

2
I. Overview
II. Basic Concepts of Dynamics
III. Design Requirements
IV. Preliminary Sizing
V. Design Loads
VI. Impedance (Stiffness and Damping)
VII. Dynamic Analysis Using STAAD Pro
Contents

4
Overview
 Tabletop-type foundation
Elevated support is common for large turbine-driven equipment such as
electric generators. Elevation allows for ducts, piping, and ancillary items
to be located below the equipment.
Tabletop structures are considered to be flexible, hence their response to
dynamic loads can be quite complex and depend both on the motion of its
discreet elements (columns, beams, and footing) and the soil upon which
it is supported.

5
Overview
Design Procedure of Tabletop Foundation
Out of Resonance Range?
0.8 fm < f < 1.2 fm
Modal Analysis
(Eigenvalue)
Yes
Amplitude (or Velocity)
Limit, OK?
Time History Analysis
with Harmonic Loads
Yes
No
Unbalanced Forces &
Static Operating Loads
No
Tune upFDN.
Geometry
Preliminary
Foundation Sizing
Allowable Bearing
Capacity, OK?
Shallow Foundation
Detail Sizingwith EQ. Data
Pile Foundation
Pile CapDesign
Calculate Contact
Pressure (qmax, qmin)
Yes
No
75% of the allowable
bearing capacity
Start of Stability Check
End of Stability Check
Impedance:
Stiffness and Damping
Start of Vibration
Dynamic Analysis
DesignLoads and
LC per ASCE 7
Static Structural
Analysis
Modal Response
Spectrum Analysis
Member Sizing
Design Requirements
per ASCE 7, OK?
Yes
No
Design Requirements
per ACI 318, OK?
No
Re-design
Structure
Start of Structural
Analysis & Design
End of Vibration
Dynamic Analysis
Yes
End of Structural
Analysis & Design

6
Codes & Standards
1. ASCE 7-10, American Society of Civil Engineers, "Minimum Design Loads for Buildings
and Other Structures."
2. ACI 318M-14, American Concrete Institute, "Building Code Requirements for Structural
Concrete and Commentary."
3. ACI 351.3R-04, Report on "Foundations for Dynamic Equipment."
4. PIP STC01015, Structural Design Criteria
Reference
1. S. Arya, M. O'Neill, and G. Pincus, "Design of Structures and Foundations for Vibrating
Machines", Gulf Publishing Company, Houston, Texas, May, 1981.
Overview

7
II. Basic Information on Dynamic Analysis

8
 Static Structural Analysis:
Might ensure that the design will withstand steady-state loading conditions, but it may
not be sufficient, especially if the load varies with time.
 Dynamic Structural Analysis:
Used to determine the behavior of structures subjected to loads which vary with time.
Inertia, and possibly damping of the structure play an important role.
Dynamics also include the study of free vibrations, i.e., the oscillations of a structure
after the force causing the motion has been removed.
Basic Information on Dynamic Analysis

9
F
M
V
k
F
Fxk sta 
staS xkF 
F(t)
M(t)
V(t)
Inertia
forces
)(tFxkxcxm dyndyndyn  
Static Loading Condition
Dynamic Loading Condition

10
 Modal Analysis:
Modal analysis is used to determine a
structure’s natural frequencies and mode
shapes.
Allows the design to avoid resonant
vibrations or to vibrate at a specified
frequency.

11
Fundamental and two higher translational modes
of oscillation along X-direction
Two translational and one rotational mode shapes
 Basic Modes of Oscillation
image source: http://www.iitk.ac.in/nicee/IITK-GSDMA/EBB_001_30May2013.pdf

12
 Response Spectrum Analysis:
A response-spectrum analysis can be used to determine how a structure responds to
earthquakes.

13
Equivalent SDOF Structures Corresponding to Each Mode of Oscillation of Building
image source: http://www.iitk.ac.in/nicee/IITK-GSDMA/EBB_001_30May2013.pdf

14
Artificial Time History Acceleration Matched to a Code Spectrum
(Amr S. Elnashai, Fundamentals of Earthquake Engineering)

15
 Response Time History Analysis:
A response time history analysis can be used to calculate a structure’s response
to time varying loads.
This analysis is performed using the modal superposition method used in
STAAD.
A machinery foundation is defined as a structure subjected to harmonic loading,
therefore the analysis is carried out applying unbalancing forces for checking
the vibration performance.

16
Derivation of Elastic Spectra (Amr S. Elnashai, Fundamentals of Earthquake Engineering)

18
Requirements Description
1 Codes & Standard ACI 351.3R
2 Frequency Ratio 0.8 < 𝑓𝑜/ 𝑓𝑛 < 1.2 (per ACI 351.3R)
3 Isolation
The foundation which needs to be designed through a detail dynamic analysis shall be
isolated from the adjacent foundation and/or structure.
4
Exemption Provisions
from Dynamic Analysis
Centrifugal:
Less than 500 HP (375 kW) and 3 times total machine weight
(2.5 times for pile foundation as per ACI 351.3R)
Reciprocating:
Less than 200 HP (150 kW) and 5 times total machine weight
(4 times for pile foundation as per ACI 351.3R)
5
Vibration Performance Criteria
- Vibration Velocity
Centrifugal: 0.12 inch/sec (3.0 mm/sec)
Reciprocating: 0.15 inch/sec (3.8 mm/sec) (per PIP STC01015)
7 Allowable Bearing Capacity
The maximum soil pressure and/or pile reaction due to static and dynamic load combinatio
ns shall not exceed 75% of the allowable soil and/or bearing capacity. (per PIP STC01015)
8 Allowable Settlement
uniform settlement: 1 inch (25 mm)
differential settlement: 3/4 inch (20 mm)
Design Requirements
Design Criteria for Vibrating Equipment Foundations

19
Design Requirements
Resonance Range: 0.7 fe < fs < 1.3 fe
fe : Frequency of Dynamic Force (Operating Speed of Machine)
fs : Frequency of Supporting System (Equipment + Foundation)
Decoupling Mass Ratio: me / ms
me : Mass of Vibrating Machine
ms : Mass of Foundation
☞ Ignore interaction if the condition is satisfied

20
Vibration Criteria for Rotating Machinery
General Limits for Personnel Sensitivity
(Relationship between Displacement Amplitude and Vibration Frequency)
Design Requirements

21
Horizontal Peak Velocity
(in./sec)
Machine Operation
<0.005
0.005-0.010
0.010-0.020
0.020-0.040
0.040-0.080
Extremely smooth
Very smooth
Smooth
Very good
Good
0.080-0.160
0.160-0.315
0.315-0.630
>0.630
Fair
Slightly rough
Rough
Very rough
Acceptance Criteria for Vibrations of Rotating Machinery
R. L. Baxter and D. L. Bernhard, "Vibration Tolerances for Industry",
ASME paper 67- PEM-14, Plant Engineering and Maintenance
Conference, Detroit, Michigan, April,1967.
Design Requirements
General Machinery Vibration Severity Chart
(Baxter and Bernhard 1967).

22
No. Seismic Design Requirement Application Remark (for a Case: Seismic Design Category B)
1 Vertical Seismic Load Effect N/A SDS is less than 0.125
2 Orthogonal Combination of Horizontal Seismic Loads N/A Not Required for Seismic Design Category B
3 Horizontal Structural Irregularities N/A No Irregularity
4 Vertical Structural Irregularities N/A No Irregularity
5 Diaphragm Flexibility N/A Rigid Diaphragm
6 Torsional Effects Applied automatically included in the structural analysis
7 Amplification of Accidental Torsional Moment N/A Not Required for Seismic Design Category B
8 Story Drift N/A Not Required for Seismic Design Category B
9 P-delta Effects Applied checked as per Sect. 12.8.7, ASCE 7-10
Seismic Design Requirements (Chaps. 12 & 15, ASCE 7-10)
Design Requirements

23
Seismic Coefficients for Nonbuilding Structure Similar to Building (Table 15.4-2, ASCE 7-10)
Response Modification Factor (R): 3.0 for ordinary reinforced concrete moment structure
Overstrength Factor (Ω0): 3.0 for ordinary reinforced concrete moment structure (not used in the calculations)
Deflection Amplification Factor (Cd): 2.5 for ordinary reinforced concrete moment structure
Redundancy Factor (ρ): 1.0 for Seismic Design Category B structure
 For more convenient design using STAAD program, the "modal response spectrum analysis" is selected for the
structural analysis.
 The base shear based on ELF (and T = Ta Cu) should be calculated to check if the computed from modal analysis is
less than 85% of the ELF base shear.
Design Requirements

24
Inelastic Force-Deformation Curve
original source:
A Brief Guide to Seismic Design Factors
Design Requirements
 Multiply spectral accelerations by modal
participation factor and by (I/R)
 For determining drift, multiply the results of the
modal analysis (including the I/R scaling but not the
85% scaling) by Cd/I.
It is permitted to be neglected for the Seismic Design
Category B structure not having horizontal
irregularity Type 1a or 1b of table 12.3-1, ASCE 7-10.

25
Basic Strategy of Earthquake Design:
Calculate maximum elastic forces and reduce by a factor to obtain design forces.
Design Requirements
Special Reinforced
Concrete Moment Frames

27
 Preliminary member sizing and geometrical arrangement constitute the initial design phase for
the structural system.
 The vendor will provide a preliminary foundation outline drawing, which can be used in the initial
design phases.
 Deck System/Beams
 Beam depth should be equal to approximately 0.2 times the clear span or 600 mm (2 ft),
whichever is greater.
 The beams should not deflect more than 0.5 mm (0.02") when subjected to static loads.
Preliminary Sizing

28
 Columns
 Locate columns at the intersection of beams where they are stressed approximately equally
under static vertical loads.
 The column dimensions should not be less than one eighth of the unsupported column
length and should not be smaller than 0.14 m2 (1.5 ft2).
 The center of column rigidity for the column group should coincide with the point of dynamic
load application, and should also be compatible (eccentricity less than 5%) with the center of
mass of the equipment including the top half of the structural mass.
Preliminary Sizing

29
Preliminary Sizing
 Mat
 The minimum thickness of mat shall not be less than the following.
tmin = 0.6 + L/30 (m) ≥ 750 mm (2.5 ft) , where L is the foundation length.
 The weight of the mat foundation plus soil surcharge should be at least equal to the weight
of the deck plus vibrating equipment.
 The following rule-of-thumb formula proposed by the ASCE task committee (Ref. 9.10) can
also be used for calculating the minimum thickness, t, for soil-supported mat foundation:
tmin = 0.07 L4/3 (ft) , where L is the average of two adjacent spans between columns, in terms
of feet.

31
Load Type Design Loads Check V/P Data Remark
Static
Dead Loads Applied Required
Live Loads Applied Required
personnel, tools, maintenance equipment
and materials
Wind Loads Applied if any
to be calculated in the structural design
(not governing)
Seismic Loads Applied if any to be calculated in the structural design
Static Operating Loads Applied Required
during normal operation
(not time-varying loads by machine)
Special Loads for Elevated-type FDN N/A N/A
Erection and Maintenance Loads Applied if any temporary load
Thermal Loads Applied if any not governing (except under constrained conditions)
Dynamic
Dynamic Loads
due to Unbalanced Masses
Applied Required operating speed, loading point, phase difference
Design Loads for Machinery Foundation (as per ACI 351.3R)
Design Loads

32
Design Loads
 The dynamic loads due to unbalanced masses are generally reflected by loading sinusoidally-varying
loads at the C.O.G in the analysis model including the rigid links and a lumped mass attached at the
dynamic loading point. If dynamic loads are applied at the anchor points, those loads should include the
additional coupled forces.

33
Effective Eccentricity
Design Loads
Balance quality grades for selected groups of representative
rigid rotors excerpted from ANSI/ASA S2.19)

34
Design Loads
 The normal torque (sometimes called drive torque) is generally applied to the foundation as a static force
couple in the vertical direction at the anchor points

35
 Static Loads (Not Time-varing)
 Self-weight of Equipment
 Case 1: All loads are applied to the C.O.G. (Center of Gravity).
 Case 2: All loads are applied to the anchor locations.
Case 2
Wself /2 Wself /2
Wself
Case 1
Design Loads

36
 Static Loads (Not Time-varing)
 Static Operating Loads: Additional Weight
Case 2
Woper
Woper /2 Woper /2
Case 1
Design Loads

37
T
L
 Static Loads
 Static Operating Loads: Torque
L
T/L T/L
Case 1 Case 2
h h
where
NT = normal torque, N·m
Ps = power being transmitted by the shaft
at the connection, kilowatts
f0 = machine operating speed, rpm
NT =
(9550)(Ps)
f0
N ∙ m
Design Loads

38
L
 Dynamic Loads
L
Case 1
h h
F(t)
FX(t)
FY(t)
FX(t)
FY(t)
M(t)
M(t)=FX(t) × h
Case 1-1
 Case 1-1: All loads are applied to the center point between two anchors
Design Loads

39
L
 Dynamic Loads  Case 1: All loads are applied to the C.O.G. (Center of Gravity).
 Case 1-1: All loads are applied to the center point between two anchors
L
Case 2
h h
FX(t) /2
FY(t) /2
FX(t) /2
FY(t) /2
FX(t)×h /L FX(t)×h /L
+
Design Loads

40
 Dynamic Load Sample Calculations (Centrifugal)
Design Loads

41
Design Loads
Because the motion repeats itself over equal intervals of time, it is called
periodic motion. Furthermore, motion that is described in terms of the
circular functions, sine and cosine, is known as harmonic motion. (All
harmonic motion is periodic, but not all periodic motion is harmonic.)
The parameter p is referred to as the (natural) circular frequency, E is called
the amplitude, and α is known as the phase angle. As shown in the figure
above, τ denotes the period of the motion—that is, the time taken by one
complete cycle of the motion.
Dividing it by m,
 Undamped Free Vibrations (vertical motion of the mass-spring system)
Harmonic Loading for Time History Analysis
(STAAD Input)

42
Type Applied Load Loading Point
Rotating
Mass
Force
Operating
Speed (fo)
Remark
Weight
Fcomp = 40,000 kgf COG of Compressor
Fbase = 18,500 kgf Anchor Locations Baseplate
Dynamic Unbalanced Force COG of Compressor 193.68 kg 950 kgf 3055 rpm 1900 kgf
Design Loads Induced by Compressor
Compressor Gear Motor
V/P Data Example (Centrifugal Type): Design Loads Induced by Compressor

43
1. The COG of the motor shall be provided to calculate the seismic load.
2. The phase differences between dynamic forces in three directions shall be
informed to compute the correct response of the foundation.
Type Applied Load Loading Point Rotating Mass
Operating
Speed (fo)
Phase Remark
Weight FMotor = 284.4 kN COG of Motor 47.4×6=284.4
Dynamic
Fv_left = 87.0 kN Anchor Locations 1800 rpm Required Is this a unbalanced force?
Fv_right = 87.0 kN Anchor Locations 1800 rpm Required Is this a unbalanced force?
Fh = 11.0 kN Anchor Locations 1800 rpm Required Is this a unbalanced force?
Faxis = 2.2 kN Anchor Locations 1800 rpm Required Is this a unbalanced force?
Short
Circuit
(Max.)
Fv = 201.4 kN Anchor Locations Required Required Accidental load case
Fh = 82.5 kN Anchor Locations Required Required Same as above
Faxis = 2.2 kN Anchor Locations Required Required Same as above
V/P Data Example (Centrifugal Type): Design Loads Induced by Motor

4444
V/P Data Example (Centrifugal Type): Design Loads Induced by Gear
FGS
Unbalanced
Force 2
Unbalanced
Force 2
The C.O.G. locations shall be shown in the drawing
to apply unbalanced forces due to the pinion and the bull gear.
Type Applied Load Loading Point
Rotating
Mass
Operating
Speed (fo)
Eccentricity Remark
Weight FG = 52,307 N COG of Gear (total)
Static
Operating
Mges =127,605 N·m COG of Gear (total)
Ff = 141,867 N Anchors (bull gear)
FGS = 2,294 N COG of Gear (total)
Fs = 87,266 N Anchors (pinion)
Short Circuit
(Max.)
Mges =127,605 N·m COG of Gear (total) Accidental load case
Ff = 141,867 N Anchors (bull gear) Same as above
FGS = 2,294 N COG of Gear (total) Same as above
Fs = 87,266 N Anchors (pinion) Same as above
Dynamic
Unbalanced Force 1 COG of Bull Gear 1775 kg 1780 rpm e=6.35/f0 mm Estimated per ACI 351.3R
Unbalanced Force 2 COG of Pinion 718 kg 3039 rpm e=6.35/f0 mm Estimated per ACI 351.3R

4545
V/P Data Example (Centrifugal Type)
Equipment Motion Type
Operating
Speed (fo, RPM)
Power
Transmitted (kW)
Rotation Direction
Motor Rotating 1,800 15,000 counterclockwise
Gear
Bull Gear Rotating 1,780 15,000 counterclockwise
Pinion Rotating 3,039 15,000 clockwise
Compressor Rotating 3,055 11,300 clockwise
Equipment
Weight Data Dynamic Loads
Weight of
Equipment (kN)
Weight of
Maintenance (kN)
Weight of
Rotating Part (kN)
Max. Unbalanced
Force (kN)
Operating
Speed (fo, RPM)
Phase Angle
(deg)
Loading Point
Motor
47.40
Ver. ± 87.00
1,800
0.0
Each AnchorHor. ± 11.00 90.0
284.40= 47.40 (6 EA) Axial ± 2.20 0.0
Gear
Bull Gear 52.31 17.41 ± 4.06 1,780 0.0 COGbg
Pinion - 7.04 ± 3.66 3,039 0.0 COGpn
Compressor 392.40 120.66 18.64 ± 9.32 3,055 0.0 COGcomp
Base Plate 181.49 N/A
Dry Gas Seal Console 15.70 N/A
V/P Sheet Applied in the Calculation Document

4646
V/P Data Example (Centrifugal Type)
Equipment
Static Operating Loads (Rated) Short Circuit Loads (Max.)
Loading PointFsuction Fout Torque Vertical left Vertical right Horizontal Axial
(kN)
Motor - - - 201.40 -201.40 82.50 2.20 Each Anchor
Gear - - - 0.83 -0.77 - - Each Anchor
Compressor - - - - - - -
Short Circuit Torque (SCT)
The motor short circuit torque, when provided by the machine manufacturer, should be considered in the
structural design. The torque, which is not a normal occurrence, is a very short-duration loading, and occurs as a
result of a fault within the electrical circuit of the machines. The short circuit torque should not be combined
with wind or earthquake. ACI 351.3R Sec. 3.2.1.5

47
V/P Data Example (Reciprocating Type)

48

49
Equipment Motion
Operating Speed
(fo, RPM)
Power
Transmitted (kW)
Rotation Direction
Motor Rotating 356 1609 clockwise
Compressor Reciprotating See the resultant See the resultant up-down
Equipment
Dynamic Loads
Max. Unbalanced
Force (lbf) & Momemt (lb.ft)
Operating
Speed (fo, RPM)
Phase Angle (deg) Loading Point
Motor
Vertical ± 346
356
0
COGmtHorizontal ± 346 90
Axial 0
Compressor
Resultant
Force (Fv)
1st Ord. ± 5273 356 0
COGcomp
2nd Ord. ± 2755 712 0
Resultant
Moment (Mh)
1st Ord. ± 93569 356 135
2nd Ord. ± 0 0 0
Resultant
Moment (Mv)
1st Ord. ± 257575 356 45.9
2nd Ord. ± 93233 712 180

50
 Dynamic Load Calculations (Reciprocating)

51
VI. Impedance (Stiffness and Damping)

52
Impedance (Stiffness and Damping)

53
 Calculation Procedure to Determine Impedance Provided by Supporting Media
1. Calculate Initial Impedance
2. Incorporate Material Damping into Initial Impedance
3. Add Embedment Effects to Adjusted Impedance
4. Reduce Damping Ratio (20%, 50%, and 12% for horizontal, vertical, and torsional motions)
5. Calculate Amplitudes (or Perform Analysis to Find Amplitudes)

54

55
The complex domain impedance is easier to describe mathematically and is applied in the impedance models
of Veletsos and others (Veletsos and Nair 1974; Veletsos and Verbic 1973; Veletsos and Wei 1971).
Relationship between impedance models and damped stiffness models
(ki and ci are calculated assuming perfect elasticity, and ci includes only geometric damping).
Horizontal impedance
Rocking impedance
Vertical impedance
Torsional impedance
 Initial Impedance

56
 Material Damping
 An approximate approach often used to account for material damping multiplies the complex impedance,
evaluated without regard to material damping, by the complex factor (1+ i2βm) to determine an adjusted
complex impedance
Where, βm = material damping ratio of the soil, and other
terms are as previously defined.

57
 Embedment Effects
 Embedment increases both stiffness and damping, but the increase in damping is more significant.
 The lack of confining pressure at the surface often leads to separation of the soil from the foundation and to the
creation of a gap as indicated on Fig. 4.5
 To find an approximate correction for this effect, the engineer
should consider an effective embedment depth less than the
true embedment.

58
 Embedment Effects
Horizontal impedance
Rocking impedance
Vertical impedance
Torsional impedance

59
 Adjustments to Theoretical Values
 Damping values for large foundations undergoing small vibration amplitudes are typically less than those
analytically predicted values (EPRI 1980; Novak 1970).
 EPRI 1980 recommends the soil damping ratio for use in the design of power plant fan foundations should not
exceed 20% for horizontal motion, 50% for vertical motion, 10% for transverse rocking motion, and 15% for axial
and torsional motions.
 German DIN 4024 recommends that the soil damping ratios used in vibration analysis of rigid block foundations
should not exceed 25%.
 Novak (1970) recommends reducing the analytically determined geometric damping ratios (from elastic half-
space models) by 50% for a dynamic analysis of the foundation.

60
 Calculation of Amplitude

61
VII. Dynamic Analysis Using STAAD.Pro

62
Dynamic Analysis Using STAAD.Pro
 Mass Modeling
 Even if the loading is known to be only in one direction there is usually mass motion in other
directions at some or all joints and these mass directions (applied as loads, in weight units)
must be entered to be correct.
 Masses should be entered in global directions with the same sign as much as possible so that
the representative masses do not cancel each other.
 STAAD uses a diagonal mass matrix of six lumped mass equations per joint. The selfweight or
uniformly loaded member is lumped 50% to each end joint without rotational mass
moments of inertia. The other element types are integrated but—roughly speaking—the
weight is distributed equally amongst the joints of the element.

63
 Damping Modeling
 Composite modal damping permits
computing the damping of a mode from
the different damping ratios for different
materials (steel, concrete, soil). Modes
that deform mostly the steel would have
steel damping ratio, whereas modes that
mostly deform the soil, would have the
soil damping ratio.
 Composite modal damping is based on a weighted average of strain
energies in each material.

64
 For more convenient design using STAAD program, the "modal
response spectrum analysis" is selected for the structural analysis.
 The base shear based on ELF (and T = Ta Cu) should be calculated
to check if the computed from modal analysis is less than 85% of
the ELF base shear.
 Multiply spectral accelerations by modal participation factor and by
(I/R)
 Input Window for Response Spectrum Analysis

65
 Harmonic Loading for Time History Analysis

66
 Input Window for Harmonic Loading (Time History Analysis)

67
 Input Window for Harmonic Loading

68
Finite Element Model for Vibration Dynamic Analysis

70
Rebar Arrangement (Column and Beam)
Excessive reinforcement can create constructibility and quality problems and should be avoided.
Some firms specify a minimum reinforcing of 3.1 lbf/ft3 (50 kg/m3 or 0.64%) for piers (machine
support edestals) and 1.9 lbf/ft3 (30 kg/m3 or 0.38%) for foundation slabs. For compressor
blocks, some firms suggest 1% reinforcing by volume and may post-tension the block.
Appendix - Reinforced Concrete

71
Rebar Arrangement (Column, Beam, and Slab)
Appendix - Reinforced Concrete

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