US Army Corps

of Engineers

Construction Engineering

Research Laboratories

Approved for public release; distribution is unlimited.

USACERL Technical Report 97/58

March 1997

The CERL Equipment Fragility and

Protection Procedure (CEFAPP)

Experimental Definition of Equipment Vulnerability to Transient Support Motions

by

James Wilcoski, James B. Gambill, and Steven J. Smith

This report documents a new test procedure for

defining the vulnerability of critical equipment to

earthquake and other transient support motions. The

CERL Equipment Fragility and Protection Procedure

(CEFAPP) defines the capacity of equipment to

withstand transient support motion in terms of

amplitude versus frequency. The amplitude is the

support motion or response spectrum amplitude at

which failure occurs. Failure may comprise actual

mechanical damage, temporary loss of function,

acceleration or strain levels at critical locations, or any

other user defined criteria. The frequency content of

support motion is critical as it determines the manner

(modes) in which equipment responds and fails.

CEFAPP requires narrow-band random sweep tests.

These tests consist of random motions concentrated

within a narrow frequency range; that sweep across a

wide frequency range over time. Test amplitudes are

increased and tests repeated until the equipment fails.

The amplitude, frequency, and mode of failure are

recorded as single data points for each failure. All

failure data are plotted, and confidence bands may be

plotted across the spectrum if enough failure data is

gathered. CEFAPP was validated through time history,

site specific and design spectra testing of equipment,

demonstrating that the procedure reasonably defines

the vulnerability of the selected equipment.

Design engineers evaluating the installation of

equipment can define predicted motions at equipment

installation locations in terms of response spectrum.

These response spectra, defining the demand, are

overlaid against the experimentally defined equipment

capacity plots to evaluate the adequacy of equipment.

Any number of demand environments may be

compared against the experimentally defined capacity

without need for further expensive—and often overconservative—qualification testing.

Equipment manufacturers can test their equipment

according to CEFAPP as a design aid, because the

test results define improvements needed to withstand

potential demands. Currently, manufacturers primary

goal is to pass a qualification test envelope—often

expressed as a design response spectrum. If their

equipment fails when testing to such an envelop,

CEFAPP can be used as a diagnostic tool to

characterize the failure and guide equipment

improvements, ensuring passage of qualification tests.
USACERL TR 97/58 iii

SF 298

This is a placeholder page for a required form. Leave it as is.

The CERL Equipment Fragility and Protection Procedure (CEFAPP) is a new

testing protocol that defines the capacity of equipment to withstand seismic and

other transient support motion in terms of amplitude versus frequency. The

amplitude is the support motion or response spectrum amplitude at which failure

occurs. Failure may comprise actual mechanical damage, temporary loss of

function, acceleration or strain levels at critical locations, or any other userdefined criteria. The frequency content of support motion is critical as it

determines the manner (modes) in which equipment responds and fails.

CEFAPP uses narrow-band random sweep tests to determine the amplitude,

frequency, and mode of failure, and records these as single data points for each

failure. All failure data are plotted, and confidence bands may be plotted across

the spectrum if enough failure data are gathered. CEFAPP was validated

through time history, site-specific spectra, and design spectra testing of

equipment.

Design engineers can define predicted motions at equipment installation

locations and overlay these data onto the experimentally defined equipment

capacity plots to evaluate the adequacy of equipment. Equipment manufacturers can test their equipment according to CEFAPP as a design aid, because the

test results define improvements needed to withstand potential demands.
iv USACERL TR 97/58

Foreword

This study was conducted for Headquarters, U.S. Army Corps of Engineers under

Project 4A162784AT41, "Military Facilities Engineering Technology"; Work Unit

CA7, "Seismic Protection of Equipment." The technical monitor was Charles

Gutberlet, CEMP-ET.

The work was performed by the Engineering Division (FL-E) of the Facilities

Technology Laboratory (FL), U.S. Army Construction Engineering Research

Laboratories (USACERL). The CEFAPP demonstration presented in Chapter 4 is

based on fragility tests performed on a power transformer bushing supplied at no

cost to USACERL by the Tennessee Valley Authority (TVA). USACERL gratefully

acknowledges TVA's cooperation in making this critical equipment available to the

researchers. Further information about the seismic behavior of the power

transformer bushing is available in the TVA report Earthquake Analysis and Shake

Table Seismic Testing of 500 kV Transformer Bushing/Bus Bar Configuration Used

at TVA Electric Substations, by Husein A. Hasan and Joe V. Peyton (TVA 1997).

Mr. Hasan and Mr. Peyton are members of the Resource Group/Engineering

Services at TVA.

Dale L. Herron is Acting Chief, CECER-FL-E, and Larry M. Windingland is Acting

Operations Chief, CECER-FL. The USACERL technical editor was Gordon L.

Cohen, Technical Information Team.

COL James A. Walter is the Commander of USACERL and Dr. Michael J. O'Connor

is the Director.
USACERL TR 97/58 v

Contents

SF 298 ................................................................ iii

Foreword .............................................................. iv

List of Tables and Figures ................................................ vii

1 Introduction ....................................................... 1

Background ........................................................ 1

Objective .......................................................... 2

Approach ......................................................... 2

Mode of Technology Transfer .......................................... 3

2 The CEFAPP Experimental Procedure .................................. 4

Development of Narrow-Band Random Records ............................ 4

Preparation for Fragility Testing ......................................... 7

Failure Definition .................................................... 8

Conducting and Documenting the Fragility Tests ............................ 9

Development of Equipment Fragility Test Envelopes ........................ 11

3 Seismic and Shock Validation Testing ................................ 12

4 Example Fragility Testing of a Power Transformer Bushing ............... 15

Seismic Design Response Spectra ..................................... 16

Generating Narrow-Band Random Records ............................... 17

Scaling the Narrow-Band Random Records ............................... 19

Evaluating the Quality of the Generated Signals ........................... 21

Increasing Test Levels and Notching the Records .......................... 24

Documenting Failures Based on Response Spectra Amplitude ................ 25

Probability Considerations for Fragility Data .............................. 28

Using the Fragility Data .............................................. 30

5 How to Use the Test Results ........................................ 31

Defining Predicted Equipment Support Motions ............................ 31

Comparing Equipment Capacity and Demand ............................. 38

Guidance for Developing Equipment Protection Systems .................... 39

6 Conclusions ..................................................... 41

References ........................................................... 43
vi USACERL TR 97/58

Figures Referenced in Main Body of Report ................................. 45

Appendix A: Matlab Routine RANSWP.M for Digital Generation of Narrow-Band Random 

Sweep Records ................................................... 119

Appendix B: Numerical Analysis of Single Degree of Freedom (SDOF) Oscillators .... 134

Appendix C: Fragility Test Support Motion Filtering and Integration ............... 139

Appendix D: Development of Single Degree of Freedom (SDOF) Oscillator Envelopes

............................................................... 142

Abbreviations and Acronyms ........................................... 146

Distribution
USACERL TR 97/58 vii

List of Tables and Figures

Tables

1 Time vs center frequency of narrow-band random sweep motions ......... 5

2 Calculated strong motion cycles (SMC) and sweep rate (SR) for SDOF

oscillators .................................................... 7

3 Calculated SR for SDOF oscillators for the Lucerne seismic and shock

records .................................................... 13

4 Narrow-band random signal generation Matlab program parameter ....... 18

5 Scaling relationship for narrow-band random records .................. 20

6 Amplitude of tests conducted on CERL TESS (percent of Figure 18

records) .................................................... 22

7 Bushing primary modes of vibration and associated damping ............ 25

8 Qualification tests conducted on CERL TESS (percent IEEE 693 HP

level and TVA site-specific) ..................................... 27

9 Seismic spectral response maps from NEHRP 1994 and USGS Internet

home page .................................................. 35

B1 Calculation of strong motion cycles for 12.2 hz SDOF oscillator at 2%

damping subjected to the El Centro earthquake record ................ 138

C1 Filters used for narrow-band random data presented in Chapter 2 ....... 140

Figures

1 Example of narrow-band random sweep motions, Test 72 .............. 46

2 Envelope of the USACERL shake table vertical capacity. .............. 46
viii USACERL TR 97/58

3a Response of 12.2 hz SDOF oscillator to El Centro time history, 2%

damping .................................................... 47

3b Response of 12.2 hz SDOF oscillator, identifying strong motion cycles .... 47

4a Configuration of IBM-XT personal computer tested on the USACERL

shaketable .................................................. 48

4b Close-up showing anchorage and some instrumentation of the IBM

computer ................................................... 48

5a Attenuation function for Fragility Test 67 ........................... 49

5b Scaled envelope for Fragility Test 67 .............................. 49

5c Fragility Test 67 narrow band random record and SDOF response

envelope ................................................... 49

6a Test 72 support motion, SDOF oscillator envelope and failure data ....... 50

6b Test 40 support motion, SDOF oscillator envelope and failure data ....... 50

6c Test 41 support motion, SDOF oscillator envelope and failure data ....... 51

6d Test 43 support motion, SDOF oscillator envelope and failure data ....... 51

6e Test 44 support motion, SDOF oscillator envelope and failure data ....... 52

6f Test 60 support motion, SDOF oscillator envelope and failure data ....... 52

6g Test 65 support motion, SDOF oscillator envelope and failure data ....... 53

6h Test 67 support motion, SDOF oscillator envelope and failure data ....... 53

6i Test 76 support motion, SDOF oscillator envelope and failure data ....... 54

6j Test 80 support motion, SDOF oscillator envelope and failure data ....... 54

6k Test 86 support motion, SDOF oscillator envelope and failure data ....... 55

6l Test 101 support motion, SDOF oscillator envelope and failure data ....... 55

6m Test 105 support motion, SDOF oscillator envelope and failure data ....... 56
USACERL TR 97/58 ix

6n Test 107 support motion, SDOF oscillator envelope and failure data ....... 56

7 SDOF envelopes of support motion and failure data .................... 57

8 Equipment fragility data ......................................... 57

9a Lucerne seismic record with failure point ............................ 58

9b SDOF envelope of Lucerne seismic record with failure point ............. 58

10a Shock record ................................................. 59

10b SDOF envelope of shock record with failure point ..................... 59

11 Fragility data with seismic and shock failures ......................... 60

12 TVA power transformer bushing tested on the USACERL triaxial shake

table ........................................................ 61

13 Horizontal and vertical response spectra, IEEE 693 high seismic

performance level ............................................. 62

14a Generated narrow-band random signal, Ran1 ........................ 62

14b Generated narrow-band random signal, Ran2 ........................ 63

14c Generated narrow-band random signal, Ran3 ........................ 63

14d Generated narrow-band random signal, Ran4 ........................ 63

14e Generated narrow-band random signal, Ran5 ........................ 64

14f Generated narrow-band random signal, Ran6 ........................ 64

14g Generated narrow-band random signal, Ran7 ........................ 64

14h Generated narrow-band random signal, Ran8 ........................ 65

14i Generated narrow-band random signal, Ran9 ........................ 65

14j Generated narrow-band random signal, Ran10 ....................... 65

15 IEEE 693 high seismic performance response spectra and unscaled

response spectra .............................................. 66
x USACERL TR 97/58

16 Scaling used for both horizontal (lateral and longitudinal) and vertical

records ..................................................... 67

17a IEEE 693 high seismic performance response spectra and scaled

response spectra .............................................. 69

17b IEEE 693 spectra and selected scaled response spectra ................ 69

18a Lateral narrow-band random scaled signal, Ran8 ...................... 71

18b Longitudinal narrow-band random scaled signal, Ran3 .................. 71

18c Vertical narrow-band random scaled signal, Ran9 ..................... 72

19a Achieved lateral acceleration with input motions at 29% of Figure 18a ...... 72

19b Achieved longitudinal acceleration with input motions at 29% of Figure

18b ........................................................ 73

19c Achieved vertical acceleration with input motions at 29% of Figure 18c ..... 73

20 Test response spectra from 29% Figure 18 motions and 29% IEEE 693

spectra ...................................................... 75

21a Original longitudinal narrow-band random scaled signal, Ran 3 (from

Figure 18b) .................................................. 75

21b First region (Ran31) of narrow-band random scaled signal .............. 77

21c Second region (Ran32) of narrow-band random scaled signal ............ 77

21d Third region (Ran33) of narrow-band random scaled signal .............. 78

22a Approximate attenutation with respect to frequency for the regions of

Figure 21 .................................................... 78

22b Response spectra for Figure 21a and three regions of Figure 21b through

21d ........................................................ 79

23a Narrow-band random record generated by the new Matlab routine scaled

to Bellcore (Bel2) .............................................. 79

23b First region of Bellcore narrow-band random scaled signal (Bel21) ......... 81
USACERL TR 97/58 xi

23c Second region of Bellcore narrow-band random scaled signal (Bel22) ...... 81

23d Third region of Bellcore narrow-band random scaled signal (Bel23) ........ 82

23e Fourth region of Bellcore narrow-band random scaled signal (Bel24) ....... 82

23f Fifth region of Bellcore narrow-band random scaled signal (Bel25) ......... 83

24a Approximate attenuation with respect to frequency for the regions of

Figure 23 .................................................... 83

24b Response spectra for Figure 23a and five regions of Figures 23b through

23f ......................................................... 85

25a Achieved lateral acceleration, 50% of Figure 18a (Frag10) ............... 85

25b Achieved longitudinal acceleration, 50% of Figure 18b with 1.2 hz HP filter

........................................................... 87

25c Achieved vertical acceleration, 50% of Figure 18c ..................... 87

26a Scale with Notch 2 ............................................. 88

26b Lateral achieved acceleration with Notch 2 and 100% of Figure 18a

(Frag17) ..................................................... 88

26c Longitudinal achieved acceleration with Notch 2 and 100% of Figure 18b

(Frag17) ..................................................... 88

26d Vertical achieved acceleration with Notch 2 and 100% of Figure 18c

(Frag17) ..................................................... 89

26e IEEE 693 spectra and TRS for 100% of Figure 18 motions with Notch 2

(Frag17) ..................................................... 89

27a Scale and Notch 1 ............................................. 91

27b Scale and Notch 2 ............................................. 91

27c Scale and Notch 3 ............................................. 91

28a Maximum TRS through Frag23, 220% of Figure 18 .................... 93
xii USACERL TR 97/58

28b Maximum TRS through Frag23 and failure data ....................... 93

28c Maximum TRS without notches ................................... 95

29a IEEE 693 (50% PL) and site-specific spectra, achieved motion response

spectra and leak failures ........................................ 95

29b Failure data from CEFAPP, IEEE 693 and site-specific tests ............. 97

30 Fragility data with site-specific and IEEE 693 design response spectra ..... 97

31 Example of site-specific response spectrum .......................... 98

32a Example response spectrum based on 1994 NEHRP recommended

provisions ................................................... 98

32b Example 1994 NEHRP response spectrum plotted with respect to

frequency .................................................... 99

33a USGS Spectral Acceleration Map, California and Nevada, 2% PE, 0.2 sec

period ..................................................... 101

33b USGS Spectral Acceleration Map, California and Nevada, 2% PE, 0.3 sec

period ..................................................... 103

33c USGS Spectral Acceleration Map, California and Nevada, 2% PE,1.0 sec

period ..................................................... 105

34a USGS Spectral Acceleration Map, Central and Eastern U.S., 2% PE, 0.2

sec period .................................................. 107

34b USGS Spectral Acceleration Map, Central and Eastern U.S., 2% PE, 0.3

sec period .................................................. 109

34c USGS Spectral Acceleration Map, Central and Eastern U.S., 2% PE,1.0

sec period .................................................. 111

35a Example response spectrum based on expected 1997 NEHRP recommended provisions ............................................ 113

35b Example response spectra plotted with respect to frequency ............ 113

36 Shock response spectrum for a floor slab. .......................... 115
USACERL TR 97/58 xiii

37 Seismic and shock response spectra with CERL fragility data ........... 115

38a Fragility Test 72 C hard disk response of test specimen to support

motion. .................................................... 117

38b Fragility Test 72 C support motion ................................ 117

A1 Time sweep rate ratio .......................................... 132

A2 Relationship between the raw random series and final signal length ....... 132

A3 Ideal low-pass filter ........................................... 133

A4 Truncated and windowed low-pass filter. ........................... 133

A5 Definition of filter error ......................................... 133

C1 Filters used for narrow and random data presented in Chapter 2 ......... 140

 D1 SDOF response (X) over harmonic support motion (Y) ................. 145
USACERL TR 97/58 1

*

For example, high-voltage (230 kV and larger) porcelain power transformer bushings have experienced numerous

failures in recent earthquakes (1994 Northridge, in particular). Another example is damage to a well anchored

gamma camera at the Sepulvada Veterans Administration Medical Center in the 1994 Northridge earthquake.

1 Introduction

Background

Earthquakes often cause more costly damage to building contents than to the

buildings themselves (FEMA 1994). Much of this damage can be reduced by

anchoring or bracing equipment to the structure. Some kinds of equipment may

be protected by allowing sufficient "rattle space" between the equipment and other

surfaces. However, sensitive equipment with this problem has been damaged by

even moderate earthquakes because the equipment itself lacks sufficient

strength.*

 Other building motions, created either by accidental or hostile

explosions, can create building vibration that will damage equipment.

Critical equipment must remain operable following either earthquake or explosive

shock induced vibration. Emergency response equipment such as communication

systems, computers, power supplies, and critical medical components must

continue to function. Other critical equipment includes items that support

hazardous material handling or storage operations at facilities such as nuclear

power plants. Some critical systems may include components whose loss would

result in significant financial losses, such as computers and communication

equipment that control large corporate financial and inventory data management

systems.

Critical equipment for facilities such as military command centers and nuclear

power plants often is experimentally qualified on a shake table using motions that

define the worst-case demand. However, existing qualification methods are often

based on either response spectra or acceleration power spectral density (APSD)

testing that does not provide information on the specific frequency of motions that

caused failures. Other current qualification test methods are based on

overconservative sine-sweep or sine-beat testing that produces unrealistic

response at the equipment resonance frequency. Furthermore, these kinds of

qualification tests must be repeated for new demand requirements—for example,

when one type of equipment is to be used at muliple locations that have different
2 USACERL TR 97/58

vibration environments. Repetition of qualification tests is expensive, and the

data they produce do not provide a complete profile of equipment fragility.

As an alternative to blanket qualification of critical equipment against a

worst-case demand, it is proposed that equipment capacity be defined

experimentally as an envelope of support motion or response spectra amplitude

at failure across a frequency spectrum. Then the ability of the equipment to

withstand differing support motions or design response spectra (i.e., vulnerability)

at proposed installation locations and against various dynamic motion hazards

may be analyzed without additional shake table tests. A single CEFAPP test

series will provide all data necessary to evaluate the equipment against any

number of specific demands. This new approach should yield significant cost

savings for vulnerability testing, provide more reliable information for equipment

procurement, and enable owners to optimize equipment protection.

As an alternative to equipment qualification testing, the U.S. Army Construction

Engineering Research Laboratories (USACERL) has developed and tested an

alternative procedure called CEFAPP—the CERL Equipment Fragility and

Protection Procedure.

Objective

This report documents the development and validation of an equipment-fragility

test procedure that may be used as an alternative to conventional equipment

qualification methods, or for diagnostic testing in support of qualification testing.

Approach

Defining equipment fragility using the CERL Equipment Fragility and Protection

Procedure (CEFAPP) requires the following steps:

• development of narrow-band random records

• preparation for fragility testing

• failure definition

• conducting and documenting fragility tests

• development of equipment fragility test envelopes.
USACERL TR 97/58 3

Chapter 2 illustrates the procedure based on the test record generated from

analog random signal and sweeping filters. The fragility amplitude was defined

by support motion spectral velocity.

Chapter 3 presents seismic and shock validation tests that evaluate the example

presented in Chapter 2. 

Chapter 4 presents an example of an actual CEFAPP test based on digital records

generated by a Matlab routine. In this example the fragility amplitude was

defined by response spectrum acceleration. (It is recommended that users of

CEFAPP use the Matlab routine, which is shown in Appendix A.) Chapter 4

includes a section on evaluating the quality of the generated signals and also

illustrates the use of the fragility data by comparing fragility-based capacity

against various seismic design response spectrum demands.

Chapter 5 provides a more generalized discussion of defining seismic or shock

demand in terms of a spectrum and comparing these with equipment capacity

(from Chapter 2) to evaluate the equipment vulnerability and guide protective

systems.

Mode of Technology Transfer

CEFAPP will be disseminiated through the Army Corps of Engineers in an

Engineer Technical Letter. CEFAPP will impact future revisions of Army

Technical Manual (TM) 5-809-10-1, Seismic Design Guidelines for Essential

Buildings, and/or TM 5-809-10-2, Seismic Design Guidelines for Upgrading

Existing Buildings. The contents of ESL-TR-87-57, Protective Constructive Design

Manual, also will be impacted. USACERL will also work with appropriate

technical committees to seek adoption of CEFAPP in industry standards.
4 USACERL TR 97/58

*

All tests were conducted on the USACERL biaxial shake table, which has since been upgraded to a triaxial system

with fully controlled translations and rotations in six directions. The upgrade includes new control and dataacquisition systems.

2 The CEFAPP Experimental Procedure

USACERL developed CEFAPP for defining the vulnerability of equipment by

physical testing on a shake table. Throughout this report the reader is referred

to plots produced from tests on the USACERL shake table*

. These plots and

related figures are presented immediately before Appendix A.

Development of Narrow-Band Random Records

CEFAPP tests equipment using progressively greater narrow-band random sweep

motions. Figure 1 is an example of such test motions. These motions may be in

any direction, but normally testing will be uniaxial to minimize confusion over the

cause of failure. The swept random signal is scaled such that it follows some

predetermined spectrum envelope, such as a design response spectrum. Figure

2 shows the vertical motion envelope of USACERL shake table capacity (prior to

its triaxial upgrade), which was used in the development of this procedure rather

than a design spectrum. Thus the initial shape of the random signal will depend

on this design spectrum. The initial shape of the random signal should not have

an impact on the eventual shape of the fragility envelope for a given equipment

item unless the shake-table motion limits are encountered prior to creating

failures within a particular frequency range. The narrow-band random signal is

created by sweeping the random signal through high- and low-pass filters. This

process creates a random signal with the energy of motion concentrated within

prescribed frequency limits, and the center frequency moves at a defined rate with

respect to time. The record shown in Figure 1 was created by sweeping filters

across the random signal at a rate of 12 octaves/minute. Each octave is a

doubling in frequency, so the center frequency of the record doubles every 5

seconds. Table 1 defines the relationship between time and center frequency.

Figure 1 shows this relationship between center frequency of the record and time,

which are both plotted on the abscissa axis. The energy of the signal at any given

time is concentrated within 1/3 octave by offsetting the high- and low-pass filters

1/6 octave from the center frequency throughout the record. Multiple narrow-
USACERL TR 97/58 5

Frequency Time Octave

Log(f) f t

(Hz) (sec)

0.301 2 -0.833 

0.3512 2.245 0.000 

0.4014 2.52 0.833 1/3 rd Oct

0.4515 2.828 1.667 

0.5017 3.175 2.500 1/3 rd Oct

0.5519 3.564 3.333 

0.6021 4 4.167 Full Oct

0.6522 4.49 5.000 

0.7024 5.04 5.833 1/3 rd Oct

0.7526 5.657 6.667 

0.8027 6.35 7.500 1/3 rd Oct

0.8529 7.127 8.333 

0.9031 8 9.167 Full Oct

0.9533 8.98 10.000 

1.0034 10.08 10.833 1/3 rd Oct

1.0536 11.31 11.667 

1.1038 12.7 12.500 1/3 rd Oct

1.1539 14.25 13.333 

1.2041 16 14.167 Full Oct

1.2543 17.96 15.000 

1.3045 20.16 15.833 1/3 rd Oct

1.3546 22.63 16.667 

1.4048 25.4 17.500 1/3 rd Oct

1.455 28.51 18.333 

1.5051 32 19.167 Full Oct

1.5553 35.92 20.000 

1.6055 40.32 20.833 1/3 rd Oct

1.6557 45.25 21.667 

1.7058 50.8 22.500 1/3 rd Oct

1.756 57.02 23.333 

1.8062 64 24.167 Full Oct

1.8564 71.84 25.000 

1.9065 80.63 25.833 1/3 rd Oct

1.9567 90.51 26.667 

2.0069 101.6 27.500 1/3 rd Oct

2.057 114 28.333 

2.1072 128 29.167 Full Oct

2.1574 143.7 30.000 

2.2076 161.3 30.833 1/3 rd Oct

2.2577 181 31.667 

2.3079 203.2 32.500 1/3 rd Oct

2.3581 228.1 33.333 

2.4082 256 34.167 Full Oct

2.4584 287.4 35.000 

2.5086 322.5 35.833 1/3 rd Oct

2.5588 362 36.667 

2.6089 406.4 37.500 1/3 rd Oct

2.6591 456.1 38.333 

2.7093 512 39.167 Full Oct

2.7594 574.7 40.000 

2.8096 645.1 40.833 1/3 rd Oct

2.8598 724.1 41.667 

2.91 812.7 42.500 1/3 rd Oct

2.9601 912.3 43.333 

3.0103 1024 44.167 Full Oct

Table 1. Time vs center frequency of

narrow-band random sweep motions.

band random records of this type should be

generated. An infinite number of records could

be generated, and they should all have the same

general characteristics of amplitude and

frequency. The frequency range of generated

records will differ depending on the

predetermined spectrum envelope or the

frequency capability of the shake table being

used. The record shown in Figure 1 has a

frequency range of 2 – 512 Hz, which equates to

8 octaves and a test duration of 40 seconds (i.e.,

sweeping 1 octave every 5 seconds). The signal

shown in Figure 1 was created by generating an

analog random signal and sweeping analog

filters across the signal.

Appendix A presents a Matlab routine for

digitally generating narrow-band random sweep

signals (RANSWP.M). This routine allows more

options in signal generation and does not require

the hardware needed for analog signal

generation. RANSWP.M can generate a signal

with a much lower starting center frequency and

a linear varying sweep rate.

Chapter 4 presents a detailed example to

illustrate the development of narrow-band

random sweep records and failure

documentation. These examples are strictly for

earthquake applications, as evidenced by the low

frequency ranges and slow sweep range. The

first has a frequency range of 0.5 – 64 Hz, which

covers 7 octaves and has a sweep rate of 6

octaves/minute, giving a test duration of 70

seconds. The second has a frequency range of

0.2 – 51.2 Hz, covers 8 octaves with a sweep rate

of 6 octaves/minute and a test duration of 80

seconds. This same routine could be used to

generate signals more appropriate for a shockinduced vibration environment, with a higher frequency range and faster sweep

range.
6 USACERL TR 97/58

*

See Appendix B.

SR '

BandWidth

SMC

f

n

'

(1/3octave)

(SMC)

(f

n

)(60sec/min) (1)

A band width of only 1/3 octave was considered as this is a reasonable balance of

concentrating the energy of the signal within a band narrow enough to identify

the frequency of failure and wide enough to preserve some random character to

the signal (i.e., not so narrow as to unrealistically excite the equipment as would

be the case with a sine-sweep signal). The 1/3 octave is also a standard frequency

increment for random experimental testing.

For the analog generated records presented in this chapter, a sweep rate of 12

octaves per minute was chosen based on the numerical analysis of several single

degree of freedom (SDOF) oscillators subjected to various seismic time histories

and narrow-band random records with different sweep rates. A strong-motion

cycle (SMC) was defined as any response in an oscillator that exceeds 50% of the

Maximum oscillator cycle between positive and negative peaks. SDOF oscillators,

at 2 Hz increments (i.e., at 2, 4, 6, 8, 10 and 12.2 Hz) and at 2 and 5% critical

damping, were excited by the seismic time histories. These time histories were

recorded in the El Centro, Park, Taft, and Melendy earthquakes, which contain

a wide range of frequency content and duration of strong-motion shaking. Figure

3a shows the 12.2 Hz, 2% damped SDOF oscillator response to the El Centro time

history. Figure 3b shows the same oscillator response in the strong motion region,

with each SMC labeled (total of 14 SMCs). Table B (in Appendix B) summarizes

the results of this SDOF oscillator for each of the 14 SMCs. Table B1 shows the

cycle time, positive peak, negative peak, difference, and percent of the maximum

for each SMC identified in Figure 3b.

The sweep rate (SR) that would excite an equivalent number of cycles is

calculated for each frequency (fn

). This rate can be expressed by the following

equation*

:

Table 2 presents the number of SMCs and SRs for the El Centro, Park, Taft, and

Melendy earthquakes for 2 and 5% damped oscillators. The results in Table 2

show that the SR needed to give an equivalent number of SMCs generally

increases as frequency increases. A slow SR, such as those shown in Table 2 at

the lower frequencies, is more conservative as it will excite the equipment more

severely. However, the tests presented in this chapter (using surplus desktop

computers) showed that the equipment was most vulnerable to failure at

frequencies above 15 Hz. Table 2 indicates that 6 octaves/minute would be a

conservative and yet reasonable SR assuming equipment vulnerability at the
USACERL TR 97/58 7

Oscillator 

Frequency

(Hz)

El Centro Park Taft Melendy

2% 5% 2% 5% 2% 5% 2% 5%

SMC SR SMC SR SMC SR SMC SR SMC SR SMC SR SMC SR SMC SR

2 9 4.4 5 8 7 5.7 4 10 25 1.6 12 3.3 8 5 5 8

4 8 10 4 20 9 8.8 7 11.4 28 2.8 22 3.6 10 8 5 16

6 24 5 17 7.1 7 17 6 20 23 5.2 14 8.6 10 12 7 17.1

8 24 6.7 14 11 10 16 9 18 35 4.6 24 6.7 16 10 12 13

10 17 12 18 11 11 18 10 20 48 4.2 37 5.4 9 22 6 33

12.2 14 17 8 31 29 8.4 19 13 31 79 17 14 10 24 9 27

Table 2. Calculated strong motion cycles (SMC) and sweep rate (SR) for SDOF oscillators.

higher frequencies of 8 to 12.2 Hz. Earlier SR calculation methods led to a less

conservative SR of 12 octaves/minute, upon which testing reported here is based.

Details on the numerical analysis of SDOF oscillators subjected to time history

and narrow-band random base motion are provided in Appendix B.

The testing reported in this chapter and in Chapter 4 was based on waveforms

with constant sweep rates, of 12 and 6 octaves/minute, respectively. Table 2

indicates that the ideal waveform would begin at a slower sweep rate and end at

a greater rate. The revised Matlab routine RANSWP.M, shown in Appendix A,

satisfies this need with the capability to generate records with linear varying

sweep rates.

A more rigorous method for calculating sweep rate to produce equivalent numbers

of SMCs is needed. The narrow-band random signal produces a Rayleigh

distribution for the absolute value of its peaks (Thomson 1981). Future research

will investigate defining SR based on an improved numerical analysis of narrowband random signals.

Preparation for Fragility Testing

The equipment is fastened to the shake table in the configuration for which the

vulnerability must be defined. A test fixture is often used to accommodate the

normal anchorage configuration of the equipment and the attachment points of

the shake table. This fixture must be very stiff to eliminate any fixture motion

relative to the shake table. This fixture is instrumented with accelerometers near

the attachment points to the equipment. A single accelerometer can be used if it

can be assured that all attachment points move together as a unit. The stiffness
8 USACERL TR 97/58

of the test fixture and possible need for multiple accelerometers to record support

motion should be evaluated in light of the maximum frequency at which fragility

data are to be gathered. For example, if fragility data are to be gathered up to

100 Hz, then the test fixture and fastening system must not be excited by motions

at or below 100 Hz. For large equipment with multiple attachment points, the

motions near each attachment should be measured and they should be plotted

relative to each other to ensure that they are of equivalent magnitude and

frequency. The equipment fragility data are obtained by processing this support

motion data (from a single accelerometer), as described later in this report.

The equipment may also be instrumented with accelerometers or displacement

gages at other locations if equipment response is desired. Equipment response

may be needed for measuring failures, as discussed below under "Failure

Definition," but these data are not required for fragility definition. Modes of

failure can be understood by measuring the amplitude and frequency of motions

at critical locations on the equipment. Low-level modal analysis tests are

recommended to define the natural frequencies and mode shapes of the

equipment. The equipment will be most severely excited at its natural

frequencies, which can lead to failure at relatively low support motions. The

modal analysis results can aid in understanding the fragility test results and can

help guide any required upgrading of the equipment itself or its support

conditions. It is recommended that low-level random or sine-sweep tests be done

to define the natural frequencies and mode shapes both before and after

equipment-fragility testing. Damping should also be measured for each mode

both before and after testing using white noise random or sine decay tests. Modal

testing after the fragility testing is used to determine if the modal characteristics

changed due to yielding or other damage. Changes in modal characteristics are

significant because they change frequency-dependent equipment fragility.

All tests presented in this chapter were conducted in the vertical direction because

of the suspected vulnerability of the equipment being tested, but the identical

procedure could be repeated along either horizontal axis.

Failure Definition

Methods of defining failure must be established. Failure may be loss of function,

actual physical damage, or some measured response that is determined to be

unacceptable. Examples of loss of function include memory loss in a computer

system or a temporary short-circuit in electronic equipment. Actual physical

damage is permanent damage to some portion of the equipment. Measured
USACERL TR 97/58 9

*

IBM Corp., Old Orchard Rd., Armok, NY 10504.

response that is unacceptable might include strains in a material at a particular

location that exceed acceptable limits, or accelerations at a location that may

damage an attached subcomponent. Failures also may occur when rattle space

is inadequate and impact or contact occurs between two components. Measured

response would require the installation of sensors at the critical locations. After

the test, the response data are inspected and, if the limits are exceeded, the time

at which the failure occurs is documented for later recording on fragility

envelopes. An example of measured response that defines failure is strains in the

porcelain at critical measured locations in power transmission components such

as live tank breakers. Currently strain values at critical locations are the

pass/fail criteria for qualification tests of these components. The method for

defining failure in equipment qualification tests could also be used for defining

failure in this test procedure. The time at which failure occurs during the test

must be determined in order to document the corresponding frequency of the

motions that caused failure.

Original development of this procedure was done by testing old IBM*

 XT personal

computers. Figures 4a and 4b show one of these computers on the USACERL

shake table. The commercial computer diagnostic software package Norton

Utilities (Symantec Corp., 10201 Torre Ave., Cupertino, CA 95014) was used to

detect read/write errors to the hard disk. This software was running throughout

testing, and each failure of this type was caused by physical damage to the hard

drive. The head impacted the disk, causing permanent damage to the hard drive

media. The software indicated the time at which this error occurred. The time

of each error was recorded by a hand-held "switch" with its own data channel.

Conducting and Documenting the Fragility Tests

The narrow-band random tests begin at very low amplitudes, with amplitude

gradually increasing for subsequent tests.

Documenting Frequency and Amplitude of Failure

The "switch" data channel recorded the time that failures occurred. The

frequency/time relationship shown in Table 1 and Figure 1 was used to determine

the frequency of failure. The support motion accelerometer record was used to

determine the amplitude of failure. As the amplitude is increased, the equipment

begins to fail. Each failure is documented as a data pair of support-motion
10 USACERL TR 97/58

amplitude versus center frequency of the narrow-band motion at the time of

failure. When possible the mode of each failure should be recorded. After an

initial failure is produced, the test should be repeated at the same amplitude and

then at slightly lower amplitude if failures continue. If no other failures occur, the

tests should be repeated at slightly greater amplitude. The purpose of this is to

begin to populate a failure envelope with data from several failures.

Notching the Support Motion

If multiple failures occur within a fairly narrow frequency range, then the support

motion must be modified to cause failures outside this range. This can be done by

"notching" the support motion frequency spectrum. The notched record is

constructed by multiplying the narrow-band random signal with an attenuation

function that has the same number of data points as the random signal. The

magnitude of the attenuation function varies from 0 to 1.0 to give the desired

notch shape. The notches used in the USACERL tests included flat and sloped

straight line segments. The amplitude is significantly reduced within the notch

range. Then the scale of the notched signal is increased so that failures are

created outside the notched frequency range. Figures 5a through 5c show the

attenuation function for Fragility Test 67 at USACERL—the scaled envelope for

this test in terms of velocity and the actual narrow-band test record that fits this

envelope.

Data Filtering and Integration

Support motion acceleration motions were filtered and integrated as described in

Appendix C to yield the velocity versus frequency records such as those shown in

Figure 1. Support motion and fragility data also may be plotted in terms of

spectral acceleration versus frequency.

Failure Amplitude Based on SDOF Response

The failure amplitude is further refined by defining for each record an envelope

that is intended to approximate the amplitude of the support motion across the

frequency spectra. This is achieved by calculating the maximum response of

SDOF oscillators with 50% damping subjected to the measured support motions.

For each octave of support motion data the response of 10 SDOF oscillators,

spaced equally across this frequency range (at 1/10 octave increments) are

calculated. Figure 5c shows both the support motion time history and the

envelope approximating the support motion for Fragility Test 67. This envelope

for the actual random support motion in Test 67, may be compared to the ideal
USACERL TR 97/58 11

envelope in Figure 5b, from which the random signal was generated. The dots

shown on Figure 5c mark failure points, which are placed on these envelopes at

the frequency causing failure. These failure points are in a format that can be

compared, for validation purposes, with the amplitude generated in a similar

manner from actual earthquake records. This amplitude is also a more accurate

measure of the support motions at that frequency than the ideal envelope used to

generate the random signal. The fragility data are hereinafter referred to as the

amplitude on these SDOF oscillator envelopes at the frequencies where failures

occurred. Appendix D gives the details for the development of these SDOF

oscillator envelopes.

Fragility data presented in Chapter 4 use the recommended and much simpler

method of defining fragility data in terms of response spectra amplitude at the

frequency of failure.

Fragility Data for Tests Conducted at USACERL

Figures 6a through 6n plot all the test data that caused failures in the testing

conducted at USACERL. Each plot includes the support motion records, SDOF

oscillator envelopes approximating amplitude and actual failure data. Figures 6a

and 6h repeat the test records shown in Figure 1 and Figure 5c. Gradually

increasing the width of the notch and the amplitude of the remaining signal

allows the creation of failures across the frequency range being tested, up to the

operating limits of the shake table.

Development of Equipment Fragility Test Envelopes

The amplitude and frequency for each failure described above are plotted

together. Figure 7 shows the SDOF envelopes of support motion and failure data

for tests conducted at USACERL. Figure 8 shows the same failure points plotted

without the support motion envelopes. An equipment fragility test envelope is

created when all failure points from a particular test configuration are plotted

together, as illustrated in Figure 8. The amplitude may be plotted in terms of

spectral velocity or acceleration. For equipment particularly vulnerable at lower

frequencies, spectral displacement could be plotted, because displacement may be

a critical concern due to limitations such as slack in cables or rattle space between

components. When sufficient failure points are generated across the frequency

range, confidence bands could be developed. These bands may indicate for

example, that if predicted support motions fall below the band, the equipment has
12 USACERL TR 97/58

a 95% chance of survival. Multiple bands could be generated to represent various

percentage levels for probability of survival.
USACERL TR 97/58 13

3 Seismic and Shock Validation Testing

Validation tests were conducted using seismic and shock waveforms. The seismic

waveform was recorded in the Lucerne earthquake. The seismic record was

amplified to 251% of the recorded motions (LUC3D5), as this was the minimum

level needed to fail the equipment tested at USACERL. This record and its

corresponding spectrum are plotted in Figures 9a and 9b, respectively. The

seismic spectrum was generated from the time history in the same manner as

from the fragility records, so a valid comparison of amplitude and frequency of

failure could be made. The seismic time history and spectrum, shown in Figures

9a and 9b show the amplitude and time of failure and predominant frequency that

caused failure.

The shock record used was generated as a predicted motion for naval applications.

 This shock record was amplified to 102% of the recorded motions (A12D12), as

this was the minimum level to cause failure. This record and its corresponding

spectrum are plotted in Figures 10a and 10b. The shock spectrum was generated

from the entire shock record. The peak amplitude and corresponding frequency

were chosen as the failure point, as this peak dominates the spectrum. The short

duration of the test did not allow identification of the portion of the signal that

caused the failure.

The modified response spectra are also applied to the seismic and shock records.

This is done without the octave marching as it would not have any meaning in the

context of an arbitrary site record. The spectra for the seismic and shock records

are finally compared to the envelope of the failure ordinates from the fragility

data to determine the suitability of the equipment to the environment.

Figure 11 shows all the failure points plotted on the equipment fragility envelope

shown in Figure 8 plus the seismic and shock validation points shown in Figures

9b and 10b. Figure 11 illustrates that the equipment-fragility test procedure

reasonably predicts the amplitude at which either the seismic or shock records

would produce failure. This figure suggests that a slower sweep rate may have

more conservatively predicted the equipment failure because the seismic record

actually produces failure at a lower level. The earlier discussion on selecting a

sweep rate, based on the calculations summarized in Table 2, indicates that a
14 USACERL TR 97/58

Oscillator

Frequency

(fn)

Lucerne Seismic Record Shock Record

2% 5% 2% 5%

SMC SR SMC SR SMC SR SMC SR

2 15 2.7 10 4.0 0* C 0* C

4 40 2.0 30 2.7 0* C 0* C

6 14 8.6 13 9.2 4 30.0 2 60.0

8 15 10.7 16 10.0 8 20.0 5 32.0

10 24 8.3 25 8.0 7 28.6 5 40.0

12.2 19 12.8 16 15.3 8 30.5 4 61.0

16** 37 8.6 57 5.6 5 64.0 3 106.7

21 24 17.5 25 16.8 6 70.0 4 105.0

32 55 11.6 30 21.3 10 64.0 6 106.7

40 *** C *** C 4 200.0 3 266.7

* The 2 and 4 Hz SDOF oscillator acted as an isolator in responding to the highCfrequency shock record, such

that the response is essentially zero.

** The Lucerne seismic and shock records have a smaller time step than those records in Table 2, allowing the

computation of the response of SDOF oscillators at higher frequencies.

*** The Lucerne record produces very little response in the 40 Hz oscillator because this record has almost no

energy at 40 Hz, causing the oscillator to move as a rigid body.

Table 3. Calculated SR for SDOF oscillators for the Lucerne seismic and shock records.

sweep rate of 6 rather than 12 octaves/minute should have been used. This is

consistent with the results of the validation tests.

The numerical analysis of SDOF oscillators was repeated for the Lucerne seismic

and shock records used here to determine what sweep rates should be used based

on the procedure presented previously for defining an appropriate sweep rate.

Similar to Table 2, Table 3 presents the number of SMCs and SR for the Lucerne

seismic record with 2% damping. This table also gives the SR for Lucerne at 5%

damping and for the shock record at 2 and 5% damping. The results in Table 3

show that the sweep rate needed to give an equivalent number of SMCs generally

increases as frequency increases. This table also indicates that a sweep rate of 6

rather than 12 octaves/minute would have better excited an equivalent number

of strong motion cycles. This is particularly true for the 16 Hz oscillator excited

by the Lucerne seismic record, which yielded equivalent SRs of 8.6 and 5.6

octaves/minute, for 2 and 5% critical damping, respectively. The equipment

failures caused by the Lucerne record were at a frequency close to 16 Hz (12.5 Hz),

which suggests the equipment was vulnerable to support motion in this frequency

range. Had a slower sweep rate been used in the fragility tests, the equipment

response would experience greater amplification such that smaller support
USACERL TR 97/58 15

motions would cause failure. This would have brought the fragility data shown

in Figure 11 into closer agreement with the seismic validation failure. The

calculations summarized in Table 3 indicate that a sweep rate of 12

octaves/minute does reasonably produce an equivalent number of SMCs as the

shock record. Chapter 4 presents further development and validation of CEFAPP,

confirming its potential for defining equipment capacity to withstand support

motions.
16 USACERL TR 97/58

*

Institute of Electrical and Electronics Engineers 693, Recommended Practices for Seismic Design of Substations,

Draft 6 (IEEE, 1997).

4 Example Fragility Testing of a Power

Transformer Bushing

This chapter presents the development of digital test records and their use in

fragility testing of a power transformer bushing. The Tennessee Valley Authority

(TVA) conducted seismic qualification tests on a 500 kV power transformer

bushing using TESS, the Triaxial Earthquake and Shock Simulator at USACERL.

The bushing sustained no permanent damage in these qualification tests, and

TVA subsequently donated the bushing to USACERL for fragility testing. The

use of this bushing provided an opportunity to demonstrate CEFAPP on critical

equipment that may be vulnerable to seismic motions. Figure 12 shows the TVA

bushing mounted on the TESS.

CEFAPP is illustrated by developing records based on seismic design spectra. The

early records were used for fragility testing of the bushing. The starting point for

defining support motions can be based on design response spectra or some other

predetermined spectrum envelope. The examples presented in this chapter are

based on design response spectra. The selected spectrum defines the initial shape

of random signal but should not have an impact on the eventual shape of the

equipment fragility envelope.

All spectrum plots in this chapter are based on response spectra of SDOF

oscillators to the generated support motions. This allows direct comparison of

equipment response spectra capacity with design response spectra demand.

Alternatively, all spectrum plots in Chapter 2 are based on equipment support

motion spectra that are equated to the building response spectra; in that case

equipment support motion spectra capacity would be compared with the building

response spectra demand.

This chapter presents both the development of test waveforms and a method of

documenting failures in order to illustrate the vulnerability evaluation based on

response spectra capacity and demand. The specific example presented here uses

the seismic design spectra from IEEE 693*

 as the basis for its narrow-band
USACERL TR 97/58 17

random sweep motions. The bushing fragility test records that follow were

generated by an early version of the Matlab routine RANSWP.M that is now used

in CEFAPP. However, the current version of this routine generates higherquality records. This quality difference is central to the section entitled

“Evaluating the Quality of Generated Signals,” in which examples of the improved

waveforms are presented. It is appropriate at this point to alert the reader that

these improved waveforms were based not on the IEEE 693 spectra (which were

the basis for the USACERL bushing fragility test data) but on a different seismic

design response spectrum (see Bellcore GR-63-CORE, October 1995). Therefore,

the reader should use the improved waveforms to compare quality only—not the

specific data values.

Seismic Design Response Spectra

Widely accepted design spectra should be used when available for the equipment

being tested. The first set of spectra used in this example (Figure 13) are from

Figure 3 in IEEE 693, which defines the high seismic performance level (PL) with

2% of critical damping. According to section 9.3.1 IEEE 693, "Equipment that is

shown by this practice to perform acceptably in ground shaking up to the High

Seismic Performance Level is said to be seismically qualified to the High Level."

Thus, these spectra provide an industry-recognized starting point for defining the

test motions for electrical power substation equipment. The leakage criteria for

bushings (IEEE 693, sec D.5.1.d) require that the bushing gasket not leak when

subjected to the PL shake table testing that has been adjusted for the influence

of the transformer and local flexibility at the bushing mounting. Section D.4.3 of

IEEE 693 states that the acceleration levels at the bushing flange can be doubled

to account for this amplification of the transformer. Such modification was not

applied to the "starting point" spectra as the fragility data generated could be

used for bushings attached to a variety of transformers. The fragility data

generated from this test procedure will later be compared with design spectra that

should be modified to reflect amplification from the transformer. Testing at the

high seismic PLs allows direct comparison with ultimate strength of porcelain or

other components. Figure 13 shows the spectra for both the horizontal direction

and vertical, where the vertical is simply 80% of horizontal values (IEEE 693,

A.1.1.1).

Later waveform development was based on seismic design spectra from the

Bellcore, Network Equipment–Building System (NEBS) Requirement: Physical

Protection, GR-63-CORE, Issue 1, October 1995. The required response spectrum
18 USACERL TR 97/58

for Zone 4, shown in Figure 5-15 of the Bellcore report, serves as the "starting

point" for the later waveform development.

Generating Narrow-Band Random Records

The next step is to generate random motions that span the full frequency range.

An earlier version of the Matlab routine, "RANSWP.M" (shown in Appendix A),

generated a random signal between 0 and Nyquist frequency (1⁄2 sample rate),

exceeding the entire range of the spectra shown in Figure 13. 

This same routine is used to sweep high- and low-pass filters across this random

signal at a user-defined rate. Figures 14a through 14j are examples of records

(Ran1 through Ran10) generated using RANSWP.M. The variables used to

generate these records are defined below. These are the same variables used in

the improved version of RANSWP.M that also allow a linear varying sweep rate.

The terms in parethese are the variable names that RANSWP.M assigns to each

of the input requests.

Initialization Time (kern). The waveform created by RANSWP.M is based on

pseudo-random numbers generated by Matlab. A default value of zero is used for

the random number generator at the beginning of new Matlab sessions. Using

this default value would lead to the generation of exactly the same signal for each

new session in Matlab. Therefore, the user is prompted to enter the current time,

which is used as the starting point of the random number generation, formatted

as hour.minute (e.g., 11.21 for 11:21 AM).

Sample Rate (aqrate). This is the frequency at which data points are generated

(inverse of time step) in the digitized record. Experience (see Otnes and Enachson

1972) indicates that 2.5 samples per cycle, or a sample rate of at least 2.5 times

the ending frequency, is needed. For the records in Figures 14a through 14j, this

becomes (64 Hz + 1/6th octave) x 2.5 = 180 Hz.

Beginning Sweep Rate (swratelow). This is the rate at which the high- and

low- pass filters sweep across the random record at the beginning of the record.

The basis for defining this rate is presented in Chapter 2 under “Development of

Narrow-Band Random Records,” and in Appendix B.

Ending Sweep Rate (swratehigh). This is the rate at which the high- and lowpass filters sweep across the random record at the end of the record. The sweep
USACERL TR 97/58 19

rate varies linearly with time (and logarithmically with frequency) between the

beginning and ending sweep rates.

Beginning Center Frequency (centerlow). This defines the lower frequency

of interest for which the fragility tests are to be conducted, normally based on the

lower frequency limit of the design response spectra. This frequency should be

chosen at a conservatively low point recognizing that data may later be needed

at frequencies lower than anticipated in the original test program. Additionally,

this value should not be greater than 1⁄2 the lowest natural frequency of the

equipment being tested, recognizing that response amplification will occur near

the natural frequencies.

Ending Center Frequency (centerhigh). This similarly defines the upper

frequency of interest, and also should be chosen at a conservatively high point.

Filter Bandwidth (band). This is the difference in frequency between the highpass and low-pass filter at any point in time during the sweep. This variable is

defined in terms of octaves (doubling of frequency) and remains constant

throughout the record. This variable is held constant at 1/3 octave for all tests

using this procedure, as this width is narrow enough to define the frequency at

which failure occurs, yet wide enough that the signal remains somewhat random

(i.e., not a sine sweep).

Filter Error (error). This quantifies the allowable filter error as defined in

Appendix A.

Table 4 gives the values for these parameters used to generate the records. The

second column gives the values used to generate the record shown in Figure 2,

which was the intial record for all the fragility data presented in Chapter 2. This

record was generated electronically as an analog record and then digitized at the

sample rate shown in Table 4. The third column gives the values used to generate

all the records shown in Figures 14a through 14j.
20 USACERL TR 97/58

Parameter Figure 2

Values

Figure 14a - 14j

Values

Figure 23a*

Values

Sample Rate (Hz) 2000 200 200

Beginning Sweep Rate (octaves/min) 12 6 6

Ending Sweep Rate (octaves/min) 12 6 6

Beginning Center Frequency (Hz) 2 0.5 0.2

Ending Center Frequency (Hz) 512 64 51.2

Filter Bandwidth (octaves) 0.333 0.333 0.333

Filter Error (octaves) 0.2

*The last column of the table gives the values used to generate the record shown in Figure 23a. This

record has already been scaled in the manner described in the following paragraphs. These values were

used in the most recent version of the Matlab routine, which gives the best quality waveforms.

Table 4. Narrow-band random signal generation Matlab program parameters.

Scaling the Narrow-Band Random Records

The amplitude of the records shown in Figures 14a through 14j are unitless. They

are scaled across their frequency range to produce levels consistent with the

baseline design response spectra. This scaling can be illustrated by scaling the

records shown in Figures 14a through 14j to produce response spectrum levels

consistent with Figure 13. This is done by generating a response spectrum for

each record using the same percentage of critical damping used to generate the

baseline design response spectra (e.g., 2% for Figure 13). The response spectra are

plots of the maximum response of SDOF oscillators subjected to support motions

across a frequency range. Response spectra are generated from the unitless

records shown in Figures 14a through 14j using the shake table software. Input

parameters for generating the response spectra include the following:

C Minimum Frequency, which is normally the same as the Beginning

Center Frequency defined above.

C Maximum Frequency, which is normally the same as the Ending Center

Frequency defined above.

C Number of Frequency Points per Octave, which defines the increment

in frequency for the response spectrum calculations, which for the spectra

shown in Figures 15, 17, and 20 is 24, yielding 168 points (SDOF oscillators)

across the 7 octave record.

C Percentage of Critical Damping, which is the same value used for

defining the design response spectra—2% for this example.

Figure 15 shows the unitless response spectrum plots for each of the narrow-band
USACERL TR 97/58 21

Frequency

Range,

fn-1 - fn

(Hz)

Time Range

tn-1 - tn

(seconds)

Scale Number &

Amplitude,

Horizontal 

Scaling, 

SH

(g)

Vertical Scaling, 

SV

 (g)

n An

 (g)

0 12

0.5 - 1.122 0 - 11.67 1 8

1 0

1 0

0 0

A - A

t -t

 (t -t ) + A 0.8 S H

1.122 - 8 11.67 - 40 2 2

2 1

2 1

1 1

A - A

t -t

 (t -t ) + A 0.8 S H

8 - 33.903 40 - 60.833 3 0.25

3 2

3 2

2 2

A - A

t -t

 (t -t ) + A 0.8 S H

33.903 - 64 60.833 - 70 4 0.2 4 3

4 3

3 3

A - A

t -t

 (t -t ) + A 0.8 S H

Table 5. Scaling relationship for narrow-band random records.

random records in Figures 14a through 14j plus the IEEE 693 design spectra from

Figure 13. Next, the narrow-band records are scaled so their response spectra

become equivalent to the amplitude shown in the design spectra. Figure 15 shows

where and to what degree the unitless spectra need to be scaled to produce

response spectra equivalent to the design spectra. Table 5 shows frequency

ranges and expressions (linear in this example) used to scale the unitless spectra.

Figure 16 graphically shows the expressions for scaling the horizontal (lateral and

longitudinal) and vertical narrow-band random records. Figure 16 also includes

the information from Table 5 to provide direct comparison with the plots of Figure

16. Time for the narrow-band random records is directly related to the center

frequency as defined by the sweep rate, with their ranges shown in Table 5. The

dual frequency/time axis for Figure 16 illustrates the center frequency and time

correspondence.

Figure 17a shows the scaled response spectra after multiplying the spectra in

Figure 15 by the expressions shown in both Table 5 and Figure 16. The

amplitudes of the response spectra in Figure 17a vary greatly from the ideal IEEE

693 envelopes. From these records, three are selected that have the smallest

variation from the design spectrum, and these are used for shake table motions.

Each of these records has significant energy across the frequency range of

interest. Ran8, Ran3, and Ran9 are used for lateral, longitudinal, and vertical

motions, respectively. These selected spectra are plotted in Figure 17b. Ran9 was
22 USACERL TR 97/58

*

The TRS are the calculated response spectra that are developed from actual time history motion of the shake table

for the particular test conducted and value of damping. These do not need to envelop the design spectra from IEEE

693, as would be the case for IEEE 693 qualification tests. Still, the eventual maximum TRS from fragility tests will

exceed the design spectra, unless early failures cause notching of the test records, resulting in reduced TRS in the

notch region.

selected for the vertical record because of its relatively small amplitude at the

lower frequencies, so as to avoid the large displacements at low frequencies that

would quickly exceed the vertical displacement capacity of the TESS. Also,

vertical motions at lower frequencies are less important than horizontal because

buildings that house critical equipment will amplify low frequency horizontal

motions at the natural frequencies of the building. The primary modes of a

building will almost always be at lower frequencies in the horizontal directions

than the vertical. Therefore, most equipment will experience greater motions at

the lower frequencies in the horizontal directions than vertical because of the

building amplification. Earlier modal testing of the bushing revealed a dominant

first mode at 6 Hz, particularly in the longitudinal direction. Therefore, Ran3 was

selected for the longitudinal direction as it has a somewhat more uniform

distribution of energy in this frequency range. Ran8 had a similar response

spectrum as Ran3, and was selected for the lateral signal.

The expressions in Table 5 are next used to scale the unitless narrow-band time

histories — Ran8, Ran3, and Ran9 in Figures 14h, 14c, and 14i, respectively —

to give those shown in Figures 18a – 18c. The records shown in Figures 18a – 18c

are plotted with respect to both time and frequency again to illustrate the

time/center frequency correspondence. Finally, these records are used in actual

tests on the shake table, beginning at very low levels. Table 6 shows the percent

amplitude of Figure 18 motions used in preliminary tests on the TESS. Figures

19a – 19c show the achieved TESS motions in the lateral (Y), longitudinal (X), and

vertical (Z) directions at 29% of the input motions (Test File Frag9) shown in

Figures 18a – 18c. The amplitude of these records is great enough so that the

achieved motions are much greater than the noise level measured at the TESS,

but still below levels that could cause failure. From these records, test response

spectra (TRS*

) are generated for each of the three directions. Figure 20 shows the

TRS plotted relative to 29% of the IEEE 693 design response spectra to guide

further revision of the scaling expressions. The expressions shown in Table 5 may

be revised based on the achieved motions so future tests will more closely follow

the ideal design spectra. Then the input motions of Figures 18a – 18c are

adjusted by the revised expressions. In this example these expressions were not

revised because the TRS matched the design response spectra (see Figure 20).
USACERL TR 97/58 23

Evaluating the Quality of the Generated Signals

The frequency content of the record shown in Figure 18b was examined further

to evaluate the effectiveness of the signal generating routine. Three time/center

frequency regions of this record were selected. Figures 21a through 21d show the

orginal record (Figure 18b) and the three selected regions. Each of these regions

contains a 5 second portion (plus 0.42 second ramp up and ramp down) of the

original record, which equates to a 1/2 octave change in center frequency. These

regions of the record were created by multiplying the original time record by an

attenuation function that has values of zero before the region of interest, ramps

up to 100% in 1/24 of an octave, remains constant at 100% for 1/2 octave, ramps

down to zero over 1/24 of an octave, and finally is zero for the remainder of the

record. The quality of the filters may be evaluated by creating approximate

attenuation functions (with respect to frequency) and comparing these with the

response spectrum of each region. These approximate attenuation functions

account for the sweeping of the center frequency across 1/2 octave and the band
24 USACERL TR 97/58

Date of

Test

Test File

Name

Test Level,

% Fig 18

High-Pass (HP)

Filter or Notch Failure or Other Observations

10/11/96 Frag9 29% - None

10/17/96 Frag10 50% 1.2 Hz HP- Long only

10/23/96 Frag11 50% 1.2 Hz HP- Long only Fluid leaked from the Bushing South Side at 36

seconds (6.1 Hz) - documented w/dsl LVDT =0.015"

10/23/96 Frag12

Frag13 60% 1.2 Hz HP Long &Vert

Fluid leaked from both North & South side at 35 sec

(5.7 Hz) - 36.8 sec (6.3 Hz), Porcelain Slippage at 35

sec (5.7 Hz) (dst).

10/28/96 Frag14 60% 1.2 Hz HP - all 3

axes, Notch1 None

10/28/96 Frag15 80% 1.2 Hz HP - all 3

axes, Notch1

Fluid leaked from South side at 32.5 seconds (4.8

Hz)

10/28/96 Frag16 80% 1.2 Hz HP - all 3

axes, Notch2 None

10/28/96 Frag17 100% 1.2 Hz HP - all 3

axes, Notch2 None

10/28/96 Frag18 120%

HP 1.2 Hz Lat. &

Long., 1.8 Hz Vert.,

Notch2

None

10/29/96 Frag19 140%

HP 1.2 Hz Lat. &

Long., 1.8 Hz Vert.,

Notch2

None

10/29/96 Frag20 160%

HP 1.2 Hz Lat. &

Long., 1.8 Hz Vert.,

Notch2

Fluid leaked at 39 seconds (7.55 Hz)

10/29/96 Frag21 180%

HP 1.2 Hz Lat. &

Long., 1.8 Hz Vert.,

Notch2

Fluid leaked at 30 seconds (4.0 Hz) and 39 seconds

(7.55 Hz)

10/30/96 Frag22 200%

HP 1.2 Hz Lat. &

Long., 1.8 Hz Vert.,

Notch3

None

10/30/96 Frag23 220%

HP 1.2 Hz Lat., 1.5

Hz Long. & 1.8 Hz

Vert., Notch3

Fluid leaked at 22 seconds (2.3 Hz), dsl & dtx show

that 2.3 Hz table motion excites the 6 Hz bushing

rocking mode.

10/30/96 Frag24 80% 1.2 Hz HP 3 axes Greater leaks at 32.5 seconds (2.3 Hz)

10/30/96 Frag25 100% 1.2 Hz HP 3 axes Major leaking and dst = 0.018" slip at 35 seconds

(5.6 Hz)

10/31/96 Frag26 120% HP 1.2 Hz Lat& Long,

1.8 Hz Vert

Major leaking and dst = 0.015" slip at 35 seconds

(5.6 Hz) and 0.03" slip at 37.5 seconds (6.7 Hz).

10/31/96 Frag27 140% HP 1.2 Hz Lat& Long,

1.8 Hz Vert Major leaking

10/31/96 Frag28 160% HP 1.2 Hz Lat& Long,

1.8 Hz Vert

Major leaking and det = 0.03" slip at 33 sec (4.9 Hz),

dst = 0.01" slip at 35.8 sec (6.0 Hz) and 0.015" at

37.5 sec. (6.7 Hz).

NOTES: dsl = displacement at the south side of bushing along the longitudinal direction; dst = displacement at south side

of the bushing along the transverse direction; dtx = TESS longitudinal displacement; det = displacement at the east side of

bushing along the transverse direction; LVDT = linear variable differential transformer sensor.

Table 6. Amplitude of tests conducted on CERL TESS (percent of Figure 18 records).
USACERL TR 97/58 25

width of 1/3 octave. The 1/3 octave width means the lower frequency limit (highpass filter) will be 1/6 octave below the center frequency at the begining of the

region and the higher frequency limit (low-pass filter) will be 1/6 octave above the

center frequency at the end of the region. This results in a total width of each

region being 11/12 of an octave (1/6 + 1/24 + 1/2 + 1/24 + 1/6 octave), if the

sweeping filters are perfect. These approximate attenuation functions with

respect to frequency for the three regions are shown in Figure 22a. Response

sprecta were generated for the three regions shown in Figure 21b through 21d,

and are shown in Figure 22b.

The response spectrum for each region (Ran31, Ran32, and Ran33) shown in

Figure 22b should be close to the amplitude of the overall response spectrum

(Ran3 longitudinal) within the frequency regions shown in Figure 22a. Figure

22b shows excellent agreement in frequency content and response spectrum

amplitude for both the 2nd and 3rd regions (Ran32 and Ran33). However the first

region (Ran31) shows the Ran 31 response spectra shifts to lower frequencies

relative to the attenuation function shown in Figure 22a and overall response

spectra (Ran3 longitudinal in Figure 22b). Also, the amplitude of the regional

response spectrum has dropped relative to the overall response spectrum. The

amplitude in individual region spectra are less than the overall spectrum because

the overall spectrum includes response to motions at the oscillator frequencies

that had been set to zero with the attenuation for the regional records but still

contained energy at the oscillator frequency due to imperfections in the filters.

Furthermore as damping increases, the response of oscillators (which makes up

the response spectrum) to support motions away from the oscillator frequency

increases. Figure 22b indicates that the first region amplitude falls below the

overall spectrum by about 33%. Another issue to evaluate is how quickly the

response spectrum for each region drops off outiside the frequency ranges defined

in Figure 22a. Filter imperfections lead to response spectra for each region that

are wider than the 11/12 octave defined above. 

As noted previously, the routine for generating records was improved. The new

records were scaled to the Bellcore Required Response Spectrum for Zone 4, in the

same manner as the Ran 3 record presented earlier. Figure 23a shows one of the

scaled records (Bel2). The parameters for creating this record are shown in Table

4. This record begins at a lower center frequency of 0.2 Hz and sweeps up to 51.2

Hz. The new routine adds a filter error variable (error), which is defined in

Appendix A. Five regions of this record were selected to evaluate the quality of

this revised routine. Figures 23b – 23f show the five selected regions. This signal

can be evaluated using the same attenuation function as Ran3 because the sweep

rate, band width, and sampling rate are the same. This also allows a direct
26 USACERL TR 97/58

comparison of the quality of the signal. The approximate attenuation functions

for this signal are shown in Figure 24a. Response spectra were generated for the

original record (Figure 23a) and the five regions shown in Figure 23b through 23f,

and they are shown in Figure 24b. 

The response spectrum for each region (Bel21, Bel22, Bel23, Bel24, and Bel25)

shown in Figure 24b should be close to the amplitude of the overall response

spectrum (Bel2) within the frequency regions shown in Figure 24a. Figure 24b

shows excellent agreement in frequency content and response spectrum amplitude

for all but the first region. The frequency of the first region (Bel21) is much less

than that of the first region using the earlier routine (Ran31). The lower

frequency regions are more challanging for the routine. The second region using

the revised routine (Bel22) is still at a lower frequency than the first with the old

routine (Ran31), and it produces a better agreement with the overall signal

response spectrum (Bel2). The response spectrum for Bel22 is less than Bel2

because the region of the signal selected by the attenuation function is slightly

greater in frequency (Figure 24a) than the peak in the overall response spectrum

(Bel2). The response spectra for the regions shown in Figure 24b "dropoff" faster

than those based on the earlier routine (Figure 22b). This dropoff reflects the

improved performance of the filters in removing energy outside the desired

frequency range. The new routine also reduces the high-frequency noise seen in

the early portions of the record. This can be seen by comparing the early portions

of the records shown in Figure 21a and 23a. 

Increasing Test Levels and Notching the Records

All remaining presentation and discussion of test waveforms are illustrated using

the old matlab routine that resulted in the scaled signals shown in Figures 18a

– 18c. These records are gradually increased from the levels shown in Figures 19a

– 19c until failures occur. Then the input signals are notched using revisions of

the scaling expressions shown in Table 5, and the amplitudes of subsequent tests

are increased to cause failures at other frequencies. In a similar manner the

signals and expressions in Table 5 may be revised to avoid exceeding the shake

table motion limits. Alternatively, the driving signals in Figure 18 may be

reduced by filtering these records. Table 6 (Test File Name Frag10) shows that

the longitudinal motion in Figure 18b was filtered with a 1.2 Hz high-pass (HP)

filter to avoid exceeding the longitudinal displacement limits of the TESS. An HP

filter removes energy in the signal below the chosen frequency. The resulting

decrease in achieved acceleration is reflected in a reduction of the TRS. Figures
USACERL TR 97/58 27

Mode of Vibration Natural Frequency

(Hz)

Equivalent Viscous Damping

(% Critical)

1st Longitudinal 5.66 Hz 2.5 %

1st Lateral 6.35 Hz 3.0 %

Table 7. Bushing primary modes of vibration and associated damping.

25a – 25c show the achieved TESS motions at 50% of Figures 18a - 18c, but with

the longitudinal motion of Figure 18b filtered at 1.2 Hz.

Figure 26a shows the scale and notch (Notch 2) for Fragility Test Frag17, which

used 100% of the Figure 18 motions. To scale the record, Notch 2 slopes down

from 100% of the original levels at 4.49 Hz to 1% at 4.62 Hz, remains constant at

1% to 6.92 Hz and slopes back up to 100% at 7.13 Hz. Figures 26b – 26d shows

the achieved TESS acceleration in the lateral, longitudinal, and vertical

directions, illustrating the effect of the notch in the time domain. Figure 26e

shows the TRS generated from these motions. The TRS show the effectiveness of

the notch in reducing shake table motions within the desired frequency range by

scaling the time history input motions. Note that further improvements would be

seen if the new Matlab rountine had been used for signal generation. Figure 26e

also includes IEEE 693 spectra for comparison with the TRS. Figures 27a – 27c

are Notches 1 through 3, which were used in the fragility tests as indicated in

Table 6.

Documenting Failures Based on Response Spectra Amplitude

The modal frequency and equivalent viscous damping should be measured for

each significant equipment mode of vibration. This basic information is needed

to understand the response of the equipment to support motions. The primary

transformer bushing modes of vibration (lateral and longitudinal) and associated

damping are given in Table 7. The damping values were calculated from the halfpower band-width of the acceleration transfer functions between the TESS and

top of the bushing, based on low-level sine-sweep tests. The second modes of the

bushing are near 30 Hz and are much less significant than the primary modes

shown in Table 7. However, other types of equipment may have higher modes

that do contribute significantly to the dynamic response of equipment.

For each failure, the time of failure is recorded and the center frequency of motion

at that time is determined. The maximum response of an SDOF oscillator at that
28 USACERL TR 97/58

*

These qualification acceptance criteria state that there shall be no evidence of damage, such as broken, shifted, or

dislodged insulators, visible leakage of oil, or broken support flanges. The visible fluid leaks and shifting seen at the

bushing porcelain/flange connection therefore constitute a type of failure even though the leaks or minor slippage

themselves will not impair bushing performance in the field. The bushing tested at USACERL was filled with 75

gallons of water to represent the weight of oil. Had it been filled with oil the leakage would have lubricated the

connection and the slippage may have been much worse, leading to gasket or porcelain failure.

frequency is calculated, which is the amplitude of the TRS (e.g., Figure 20) at the

frequency of failure. This value of response spectrum amplitude together with the

frequency of failure becomes a failure data point. These same values for each

failure are plotted to produce a failure envelope. This failure envelope can now

be compared directly with site-specific spectra or design spectra, as they represent

the response of SDOF oscillators across a spectrum with the same damping (e.g.,

2% of critical damping in this example).

Normally fragility tests will be uniaxial, and the same tests may be repeated in

all three axes. However, for the IEEE 693 guidelines, tests are to be triaxial, with

the horizontal design response spectrum shown in Figure 13 applied both in the

lateral and longitudinal direction, plus the vertical design spectrum applied

vertically. When triaxial tests are conducted, three independent random signals

are needed for the tests to be truly triaxial. Because the test motions in each of

the three directions are unique, the TRS will also differ, and the test engineer

must determine which amplitude from the three TRS is the dominant cause of

failure. Normally this will be the direction of motion that causes amplified

equipment response at the frequency of failure.

Figure 28a shows the maximum achieved response spectra for all fragility tests

up through Frag23, along with the IEEE 693 design spectra. The amplitude of

these tests went as high as 220% of Figure 18, but with a large notch around the

natural frequency of the bushing. Figure 28b shows all the failure points, the

same maximum achieved TRS, and the IEEE 693 design spectra. The failures are

summarized in Table 6. Each failure comprises either visible fluid leakage or

slippage at the porcelain/flange connection, as defined in IEEE 693, sec D.5.1.*

Note the V-shaped plot of the failures, with the amplitude of motions that cause

failure increasing with distance away from the bushing natural frequency. This

V-shape will be steeper for equipment with low damping due to the sharpness of

resonance. After pushing the test levels very high outside the notch region (i.e.,

220% of Figure 18 motions), further tests were conducted with the notch removed.

The tests without notches caused increased leakage and slippage, but no

additional failure modes were observed. The notch-less tests were conducted up

to 160% of Figure 18 (Frag 24 – Frag 28). The maximum achieved TRS for these

tests can be seen in Figure 28c along with the IEEE 693 design spectra.
USACERL TR 97/58 29

Date of

Test

Test File

Name

Test

Level,

% Fig13

High-Pass (HP) Filter Failure or Other Observations

10/29/96 IEEE2 20% None None

10/29/96 IEEE3 30% 1.0 Hz HP- Long only None

10/29/96 IEEE4 50% 1.0 Hz HP all 3 axes Major fluid leaks

10/29/96 IEEE5 40% 1.0 Hz HP all 3 axes Moderate fluid leaks

10/30/96 IEEE6 35% 1.0 Hz HP all 3 axes Small leaks

10/30/96 IEEE7 32% HP 1.0 Hz Long & Vert Small leak

10/29/96 EQTST31 200%* None Site-Specific Spectra, Small Leak

* The test level of EQTST31 was 200% of the time-histories generated to fit the TVA site-specific spectra.

Table 8. Qualification tests conducted on CERL TESS (percent IEEE 693 HP level and TVA sitespecific).

The fragility data presented in Figure 28b can be compared with design response

spectra or site-specific spectra to evaluate the equipment's (i.e., bushing’s)

vulnerability to other support motion. This use of the fragility data was evaluated

by testing the bushing according to the IEEE 693 high performance level spectra

and particular site-specific spectra. Figure 29a shows the maximum achieved

TRS for IEEE 693 random tests. The TESS motions were generated by the shake

table software to fit the high performance level spectra, with 20 seconds of strong

motion and 5 seconds of ramp-up and ramp-down. The TRS shown in Figure 29a

are based on 50% of the generated test motions and the IEEE 693 spectra

envelopes are plotted at the same 50%. The test levels were reduced to 32%, at

which level leaking was first observed. The TRS amplitude at the 6 Hz natural

frequency of the bushing (i.e., response of an SDOF oscillator at 6 Hz) was 1.28

g. This data point is shown in Figure 29a. Table 8 summarizes these tests.

The IEEE 693 tests require random motions with energy across a broad frequency

range (see Figure 29a). Random motion tests such as these are necessary in

conjuction with fragility tests to confirm that high- and low-frequency modes do

not couple to produce a mode of failure that would not be seen in the sweeping

narrow-band random fragility tests. Thus these tests validate that coupled modes

have not been overlooked in the fragility test procedure.

In a similar manner, the bushing was tested against time histories generated to

fit TVA site-specific spectra. Leaking was first initiated at 200% of these motions

and the resulting TRS are plotted in Figure 29a. The amplitude of the TRS at 6

Hz for the site-specific-spectrum-based test was slightly greater at 1.61 g. This

is because the dominant energy for the site-specific waveform peaks at slightly

greater frequencies than the 6 Hz bushing frequency, whereas IEEE 693 specifies
30 USACERL TR 97/58

a broad distribution of energy across the spectrum. Table 8 also summarizes the

site-specific test.

The magnitude of the TRS at failure and at 6 Hz, from both the IEEE 693 and

site-specific tests, agree well with the magnitude of failure in the fragility tests at

6 Hz. Figure 29b shows the failure points from the fragility, IEEE 693, and sitespecific tests. However, the fragility tests reveal more information in terms of the

equipment's vulnerability to motions away from its own natural frequency — the

sharpness of the V, for example, in Figure 28b. Test data from Frag 23 suggest

that 2.3 Hz motions excited a 6 Hz (first mode) response in the bushing. This

observation is based on comparing the TESS-achieved acceleration and

longitudinal (axis of bushing) displacement from a linear variable differential

transformer (LVDT) around 22 seconds.

All observations made here are based on TESS motions, TESS motion TRS and

limited strain, and LVDT measurements near the bushing flange. Test data could

be analyzed further to evaluate the response of the bushing, but these few

observations are sufficient to illustrate the application of CEFAPP.

There also are other potential modes of failure that may not even be associated

with the equipment's first mode of vibration. Many additional observations can

be made about modes of failure from fragility test data, revealing additional

information about the nature of equipment response and vulnerability. Fragility

testing may also be used to evaluate methods of upgrading vulnerable equipment.

Probability Considerations for Fragility Data

It should be noted that the fragility data shown in Figure 28b are failure points

for only one narrow-band random sweep record (Ran3, which has been scaled, HP

filtered and notched). Other narrow-band random sweep records would create

somewhat different failure data. However, failure is primarily due to a resonant

response of some portion of the equipment, and equipment response is similar to

that of the response of an SDOF oscillator, of which response spectra are made up.

A single failure point on the TRS is the response of an SDOF oscillator, with the

center frequency attributed to failure and the damping for which the response is

calculated. Therefore, a different narrow-band random signal, scaled to produce

the same equipment failure/response would generate a response similar to an

SDOF oscillator at the frequency of failure, resulting in a failure point of

essentially the same magnitude and frequency as that from the original record.

Real-world equipment response will differ somewhat from that of an SDOF
USACERL TR 97/58 31

oscillator, especially for equipment modes of vibration with large damping. The

response of equipment will also be somewhat load-path dependent, especially if

the equipment responds in a nonlinear manner. If the equipment failure causes

significant material or geometric nonlinear response, the modes of vibration and

therefore frequency of failure will shift (normally decreasing because of the

reduced stiffness that damage causes). Such nonlinear response will make the

equipment response and fragility data path dependent. Modal testing should be

conducted both before and after fragility testing to determine if there was a

frequency shift at the modes of vibration responsible for failure. In the case of the

bushing, the frequencies shown in Table 7 did not shift, which confirms that the

bushing failures did not cause permanent mechanical damage and that the

bushing response was not path dependent. Because the primary bushing modes

of vibration have very low damping (2.5 % in the longitudinal direction, as

indicated in Table 7), the bushing failure data from only one record is reasonable.

If other equipment being tested had greater damping, or the failure modes

included significant nonlinear response, testing with multiple narrow-band

random sweep records may be necessary. In the case of significant nonlinear

response, a new undamaged equipment specimen (or the original one with the

damaged components replaced) would have to be tested with the new narrowband random sweep record. 

Variations in equipment construction may lead to variation in the fragility data

if the modes of failure are influenced by properties of the equipment that vary.

For example, if a failure mode is very dependent on a particular welded

connection, then a large tolerance in weld construction or variations in the quality

of the weld will lead to large variation on the resulting fragility. This condition

would require the testing of several specimens in order to build a statistically

significant fragility data set. From these data, confidence bands or probability of

failure lines (drawn across the response spectra data envelope) would be added to

the fragility data. The bushing failure leakage and slippage is dependent on the

flange detailing, porcelain details at this connection, gasket construction, and

tension in the spring-loaded center tension rod. It is assumed that all of these are

standard for this model and manufacturer of bushing, with possible exception in

the prestress of the tension rod. Therefore, it must be understood that the

fragility data presented here are only applicable for the particular bushing tested;

the users of such data would need to investigate whether their bushing varies (in

the construction related to the failure modes) from the one tested here. Again, it

must be emphasized that this fragility test is only intended as a demonstration

of CEFAPP and such details on bushing construction had not been gathered.
32 USACERL TR 97/58

Using the Fragility Data

The fragility data collected in the narrow-band random sweep tests define the

capacity of the equipment tested. Site-specific or IEEE 693 design spectra define

the demand. Equipment vulnerability is determined by comparing the capacity

and demand. For example, Figure 30 shows the bushing fragility data (capacity)

together with site-specific and IEEE 693 spectra (two cases of demand). The

fragility data plot above the site-specific spectrum, indicating that the bushing is

not vulnerable to this seismic demand. However, the fragility data plot below the

IEEE 693 spectrum (between 4 and 7 Hz), indicating a predicted failure to this

seismic demand. In a similar manner the bushing capacity may be compared with

other site-specific or design spectra. As noted previously, the IEEE 693 spectrum

in Figure 30 should be modified to reflect transformer amplification. If the

demand spectra plots above the fragility data (capacity), then the equipment is

vulnerable to the type of failure that the fragility data represents (i.e., bushing

fluid leaking and slippage in this example).

Equipment vulnerability is defined as that region on the spectrum plot where the

demand exceeds the capacity. Multiple regions may define more than one mode

of failure, induced either by different failure mechanisms (e.g., leaking, slippage

or porcelain fracture) or different modes of vibration (e.g., first or second lateral).

Defining this vulnerability will guide equipment retrofit approaches.

If equipment fails qualification tests, CEFAPP also can be used as a diagnostic

procedure to define the mode or modes of failure that prevented passing the

qualification tests. The information gathered on mode of failure and amplitude

and frequency of failure can be used to design a retrofit that will ensure the

equipment passes the qualification test requirements. 

Quantifying equipment dynamic characteristics and modes of failure is essential

to developing equipment protection. Analytical models can be developed, based

on the vulnerability data gathered, that allow the generalization of the

vulnerability data to equipment with similar dynamic characteristics and modes

of failure. Vulnerability of equipment not tested could be defined based on such

models. 
USACERL TR 97/58 33

*

NEHRP: National Earthquake Hazards Reduction Program. ** FEMA: Federal Emergency Management Agency.

5 How to Use the Test Results

Chapter 4 presented a specific example of the use of CEFAPP in the vulnerability

evaluation of a power transformer bushing. This chapter more generally presents

the definition of equipment demand and shows how that demand is compared

with the capacity as defined in Chapter 2 and illustrated in Chapter 4. 

Defining Predicted Equipment Support Motions

These motions may result from vibration of the supporting structure caused by

earthquakes, explosions from accidents or terrorist attack, or heavy vehicle traffic

near the building. The predicted motions will normally be expressed in terms of

design response spectra. Development of site-specific response spectra based on

site conditions and ground motion potential will form the most accurate basis for

defining equipment support motion. In the absence of these data, earthquake

response spectra can be developed following two methods. The first is using the

current guidance in the 1994 NEHRP*

 Recommended Provisions for Seismic

Regulations for New Buildings (comprising FEMA** 222A, Part 1 – Provisions, and

FEMA 223A, Part 2 – Commentary). The second and preferred method will be to

use the 1997 NEHRP Recommended Provisions which according to 1994 NEHRP

FEMA 222A (Appendix to chap 1, p 19) will provide “a new, more rational seismic

design procedure.” This document states that:

unlike the current design procedure, which uses the relatively dated USGS

(U.S. Geological Survey) peak velocity and peak acceleration ground motion

maps, the revised procedure will be based on the USGS spectral response

maps, which are being revised.

Final maps are already available from USGS and preliminary guidance on their

use is available in the 1991 NEHRP Recommended Provisions for the Development

of Seismic Regulations for New Buildings (FEMA 222, Part 1 Provisions),

Appendix to Chapter 1, "Preliminary Spectral Response Maps and Method for

Establishing Design Ground Motions."
34 USACERL TR 97/58

The example seismic design spectra developed in this chapter are based only on

the first mode response of the equipment-supporting structure. These design

spectra provide simple response-spectra-based demand that can be used to

illustrate the demand versus equipment fragility comparison that establishes

equipment vulnerability. However, a more rigorous definition of design response

spectra based on multi-mode dynamics of the structure is recommended. A modal

analysis approach that parallels the modal analysis procedure in Section 2.4 of

NEHRP 1994 is given in Singh, Suarez, Matheu, and Maldonado (1993,

hereinafter referred to as “NCEER-93-0013").

Shock design response spectra are commonly used, based on code guidance or time

history analysis. At this time only brief comments are made on defining predicted

motions based on shock response spectra. However the procedures laid out in

detail for seismic spectra also apply to shock-induced vibration response spectra.

Site-Specific Response Spectra

When sufficient information can be obtained on seismic or shock motion potential,

site-specific response spectra may be developed. This will allow more precise

definition of predicted motions, which will result in potential savings due to less

severe demand on the equipment. Site-specific response spectra will require

detailed knowledge about fault characteristics near the site, geological data,

building construction type, and specific location of equipment to be installed.

Figure 31 is an example of a site-specific response spectrum.

Current Guidance from 1994 NEHRP Recommended Provisions

The seismic response spectrum is developed from FEMA 222A. These provisions

serve as a broadly accepted source document for building design codes. The

response spectrum is developed from these provisions for the building site under

consideration by determining the variables shown below:

1. Effective peak acceleration, Aa

 from Map 1 and Table 1.4.1.1 or Map 3

2. Effective peak velocity-related acceleration, Av

 from Map 2 and Table 1.4.1.1

or Map 4

3. Soil profile type A through F as defined in Section 1.4.2

4. Seismic coefficient, Ca

, from soil profile type and Aa, from Table 1.4.2.4a

5. Seismic coefficient, Cv

, from soil profile type and Av, from Table 1.4.2.4b

6. Response modification coefficient, R, from Table 2.2.2, based on the

structural system and seismic force resisting system of the building

7. Modal period of vibration (in seconds) of the mth mode of the building, Tm
USACERL TR 97/58 35

Csm '

1.2 Cv

RT2/3

m

(2)

CsmMAX '

2.5 Ca

R

(3)

fm'

1

Tm

and v '

a

T

'

386 in/sec2/g Csm

2Bfm

(4)

8. Modal seismic response coefficient, Csm, is determined by (Equation 2.4.5-3):

9. maximum modal seismic response coefficient, CsmMAX, is (Section 2.4.5):

Equations 2 and 3 (for Csm and CsmMax) are plotted to give the seismic response

spectrum. The seismic response spectrum is replotted in terms of spectral

acceleration (Csm and C smmax) versus frequency (Hz); or spectral velocity, V

(inches/second), versus frequency. The spectral velocity and frequency are

calculated from the modal seismic response coefficient, Csm, and modal period, Tm,

as follows: 

Example Response Spectrum Based on 1994 NEHRP Recommended

Provisions

To illustrate this procedure a response spectrum is developed for San Francisco,

CA, soil profile type D (stiff soil) and an ordinary moment frame building of

reinforced concrete:

1. Effective peak acceleration, Aa

, from Map 1 is 0.4g

2. Effective peak velocity-related acceleration, Av

, from Map 2 is 0.4g

3. Soil profile type D, based on section 1.4.2.

4. Seismic coefficient, Ca

, from Table 1.4.2.4a for soil profile type D and Aa =

0.4g is 0.44g.

5. Seismic coefficient, Cv

, from Table 1.4.2.4b, for soil profile type D and Av =

0.4g is 0.64g.

6. Response modification coefficient, R ,from Table 2.2.2, for an ordinary

moment frame building of reinforced concrete is 3.

7. Modal period of vibration (in seconds) of the mth mode of the building is Tm.

8. Modal seismic response coefficient, Csm, is determined by (Equation 2.4.5-3):
36 USACERL TR 97/58

Csm '

1.2 Cv

RT2/3

m

'

(1.2) ( 0.64 g)

3 T

2/3

m

'

0.256 g

T

2/3

m

(5)

CsmMAX '

2.5 Ca

R

'

(2.5) (0.44 g)

3

' 0.367 g (6)

9. Maximum modal seismic response coefficient, CsmMAX, is (Section 2.4.5):

Figure 32a shows the expressions above for Csm and CsmMaxplotted with respect to

period (Tm), giving the seismic response spectrum. Figure 32b re-plots the seismic

response spectrum in terms of spectral acceleration (Csm and CsmMax) versus

frequency.

Future Guidance from 1997 NEHRP Recommended Provisions

The more rational design procedure to be made available in the 1997 NEHRP

Recommended Provisions will use USGS Spectral Acceleration maps. Draft

versions (intended for trial design) of these maps are available in the 1994

NEHRP Recommended Provisions, Maps 5 through 13. Final versions of the

USGS Spectral Acceleration maps are now available from USGS on the Internet

at http://wwwneic.cr.usgs.gov/eq/finmaps.shtml. Table 9 summarizes spectral

maps from both sources that are available as of this writing. Figures 33a, 33b

and 33c show these maps for California/Nevada for 2% probability of exceedence

(PE) in 50 years for spectral acceleration periods of 0.2 seconds, 0.3 seconds, and

1.0 seconds, respectively. Figures 34a, 34b, and 34c show similiar maps for the

2% PE for the Central and Eastern United States.

Defining the seismic threat for such low probabilites is appropriate for critical

facilites and equipment. The 2% PE in 50 years is equivalent to a return period

of 2500 years ( i.e., estimate these levels of seismic motions every 2500 years).

The 5% PE and 10% PE in 50 years equate to return periods of 1000 and 500

years, respectively. For the low probablities of 2% PE, the greatest spectral

accelerations for the New Madrid area in the Central United States are almost as

great as those in California. However, for the higher probabilities (5% and 10%

PE) the seismic threat for the West coast is much greater, because severe motions

are expected much more frequently.
USACERL TR 97/58 37

Region Spectral 

Acceleration

Period

Probability of

Exceedance

in 50 years

Spectral 

Acceleration

Value

Draft 1994

NEHRP Map

No.

Final USGS Map

No. by Region

National 0.2 sec 10% SA(0.2) 4

National 0.2 sec 5% SA(0.2) 5

National 0.2 sec 2% SA(0.2) 6

National 0.3 sec 10% SA(0.3) 5 7

National 0.3 sec 5% SA(0.3) 8

National 0.3 sec 2% SA(0.3) 9 9

National 1.0 sec 10% SA(1.0) 7 10

National 1.0 sec 5% SA(1.0) 11

National 1.0 sec 2% SA(1.0) 11 12

California/Nevada 0.2 sec 10% SA(0.2) 4

California/Nevada 0.2 sec 5% SA(0.2) 5

California/Nevada 0.2 sec 2% SA(0.2) 6

California/Nevada 0.3 sec 10% SA(0.3) 6 7

California/Nevada 0.3 sec 5% SA(0.3) 8

California/Nevada 0.3 sec 2% SA(0.3) 10 9

California/Nevada 1.0 sec 10% SA(1.0) 8 10

California/Nevada 1.0 sec 5% SA(1.0) 11

California/Nevada 1.0 sec 2% SA(1.0) 12 12

Central/Eastern U.S. 0.2 sec 10% SA(0.2) 4

Central/Eastern U.S. 0.2 sec 5% SA(0.2) 5

Central/Eastern U.S. 0.2 sec 2% SA(0.2) 6

Central/Eastern U.S. 0.3 sec 10% SA(0.3) 7

Central/Eastern U.S. 0.3 sec 5% SA(0.3) 8

Central/Eastern U.S. 0.3 sec 2% SA(0.3) 9

Central/Eastern U.S. 1.0 sec 10% SA(1.0) 10

Central/Eastern U.S. 1.0 sec 5% SA(1.0) 11

Central/Eastern U.S. 1.0 sec 2% SA(1.0) 12

Table 9. Seismic spectral response maps from NEHRP 1994 and USGS Internet home page.

Preliminary guidance on developing spectral response maps, using the data

provided in the draft maps from 1994 NEHRP and the USGS Internet site, is

given in the 1991 NEHRP Recommended Provisions (FEMA 222, Part 1, Appendix

to Chapter 1). The method presented in that appendix is modified slightly to

incorporate the new spectral acceleration values for the 0.2 second period

available on the USGS Internet site. Since the USGS Internet maps are final, all

spectral acceleration values will be taken from these maps. The following

variables are determined from these maps, together with 1991 NEHRP and 1994

NEHRP, and are defined below:
38 USACERL TR 97/58

Csm '

SA(1.0)S

RT

n

m

(7)

CsmMAX '

SA(0.2)

R

and CsmMAX '

SA(0.3)

R

(8)

1. Spectral acceleration (0.2), SA(0.2), is the spectral response acceleration

coefficient, at a period of 0.2 second, expressed as a fraction of gravity, from

the USGS locations shown in Table 9.

2. Spectral acceleration (0.3), SA(0.3), is the spectral response acceleration

coefficient, at a period of 0.3 second, expressed as a fraction of gravity, from

the USGS locations shown in Table 9.

3. Spectral acceleration (1.0), SA(1.0), is the spectral response acceleration

coefficient, at a period of 1.0 second, expressed as a fraction of gravity, from

the USGS locations shown in Table 9.

4. Soil coefficient, S, is based on the soil profile types defied in Table 3.2

(Appendix to Chapter 1, 1991 NEHRP).

5. Response modification coefficient R, from Table 3.3, is based on the

structural system and seismic force resisting system of the building.

6. Modal period of vibration (in seconds) of the mth mode of the building is Tm.

7. n = 1 for Tm 1.0 second; or 2/3 for Tm > 1.0 seconds.

8. Modal seismic design coefficient, Csm, is determined by (Equation 5-3):

9. Maximum modal seismic design coefficient, CsmMAX, is (Section 2.4.5):

The equations above for Csm and CsmMAX, are plotted with respect to period (Tm) to

give the seismic response spectrum. If SA(0.2) and SA(0.3) differ, interpolate the

values for CsmMAX between the periods of 0.2 and 0.3 seconds. The seismic

response spectrum is replotted in terms of spectral acceleration versus frequency.

Example Response Spectrum Based on 1997 NEHRP Recommended

Provisions

To illustrate this procedure a response spectrum is developed for San Francisco,

CA, soil profile type S2

 (stiff clay) and an ordinary moment frame building of

reinforced concrete. Critical emergency response equipment is located in the

building and it is determined that the most conservative 2% PE in 50 years should

be used for defining the seismic demand.
USACERL TR 97/58 39

Csm '

SA(1.0)S

RT

n

m

'

(3.0g)(1.0)

2 T

n

m

'

1.5 g

T

n

m

(9)

CsmMAX '

SA(0.3)

R

'

3.2g

2

' 1.6 g (10)

CsmMAX '

SA(0.2)

R

'

3.2 g

2

' 1.6 g (11)

1. Spectral acceleration (0.2), SA(0.2), from USGS California/Nevada Region Map

6 (see Figure 33a) is 3.2 g.

2. Spectral acceleration (0.3), SA(0.3), from USGS California/Nevada Region Map

9 (see Figure 33b) is 3.2 g.

3. Spectral acceleration (1.0), SA(1.0), from USGS California/Nevada Region Map

12 (see Figure 33c) is 3.0 g.

4. Soil coefficient, S, for soil profile type S2

, is 1.0.

5. Response modification coefficient, R, for an ordinary moment frame building

of reinforced concrete is 2.

6. Modal period of vibration (in seconds) of the mth mode of the building is Tm.

7. n = 1 for Tm 1.0 second; or 2/3 for Tm > 1.0 seconds.

8. Modal seismic design coefficient, Csm, determined by (Equation 5-3):

9. Maximum modal seismic design coefficient, CsmMAX is (Section 5.5):

Figure 35a shows the expressions above for Csm and CsmMax plotted with respect to

period (Tm), giving the seismic response spectrum. Figure 35b replots the seismic

response spectrum in terms of spectral acceleration versus frequency.

Shock Motions

A significant threat to equipment is shock-induced building vibration caused by

either accidental or hostile explosions. Shock motions at locations where

equipment is to be installed are commonly defined in terms of a shock response

spectra. Figure 36 is an example of a shock response spectrum for a floor slab in

a building based on a finite element analysis of the building. This spectrum

defines the support motion demand that equipment installed at this location must

withstand.
40 USACERL TR 97/58

Comparing Equipment Capacity and Demand

The equipment fragility (capacity) as defined by this test procedure is next

compared to the predicted support motions (demand). This is illustrated using the

CERL fragility data and the predicted support motions defined by response

spectra whose development was described above. Figure 37 shows the fragility

data (from Figure 8), site-specific response spectrum (from Figure 31), 1994

NEHRP-based earthquake spectrum for San Francisco (from Figure 32b), 1997

NEHRP-based earthquake spectrum for San Francisco (from Figure 35b), 1997

NEHRP-based earthquake spectrum for Memphis, (2%PE) and shock response

spectrum (from Figure 36). The 1997 NEHRP-based spectrum for San Francisco

is much greater than the 1994 NEHRP spectrum; in fact the 1997 spectrum with

10% PE is much greater than the 1994 spectrum. This is because the new USGS

maps provide a degree of micro-zonation. Not only the USGS spectral acceleration

but also peak acceleration maps now provide this micro-zonation such that the

San Francisco location has peak acceleration values for 10% PE of 1.0 g. For the

same location the 1994 NEHRP maps give a 0.4 g effective peak acceleration

value for the same 10% PE in 50 years, based on the broader boundaries of this

most severe seismic zone. All earthquake spectra shown in Figure 37 are based

on soil profile type S2

 (stiff clay) and an ordinary moment frame building of

reinforced concrete.

If the predicted motions, represented by the design response spectra (demand), fall

below the fragility data throughout the frequency range, the equipment is

adequate as long as it is anchored in the same manner as it was during the shake

table testing. The equipment is vulnerable if the response spectra exceed the

fragility data along any portion of the frequency range. This indicates that the

equipment must either be strengthened or protected against the design-spectrabased predicted motions within that frequency range. The earthquake design

spectra shown in Figure 37 fall below the equipment fragility data all across the

frequency range, except for the 1997 NEHRP-based San Francisco spectrum at

2% PE, which falls slightly above in the 4 to 17 Hz range. Had the slower sweep

rate of 6 octaves/minute been used in the fragility testing, as defined based on

later sweep-rate calculations and the validation test results, the equipment would

have failed at lower levels, resulting in greater vulnerability relative to the

spectra shown in Figure 37. All fragility data presented in Chapter 2 and this

chapter are based on vertical support motions only, to which the tested equipment

was particularly vulnerable. While Figure 37 illustrates the use of these data,

actual comparison must be based on support motion demand and capacity in the

same direction.
USACERL TR 97/58 41

The predicted shock spectra shown in Figure 37 exceed the equipment fragility

data for the entire frequency range above 6 Hz; thus the equipment is vulnerable

to the shock motions above 6 Hz.

If a building is analyzed using a time-history analysis rather than a response

spectrum approach, response spectra could be generated from the time histories.

Generated time histories taken from locations where the equipment is to be

installed can be used to generate response spectra using the method explained in

Appendix D for the development of SDOF oscillator envelopes with 50% damping.

Alternatively, response spectra can be generated from the design ground motion

and anticipated damping of the building. From either approach the generated

response spectra can be laid over the equipment fragility data to evaluate the

vulnerability of equipment.

Guidance for Developing Equipment Protection Systems

Appropriate equipment strengthening or stiffening will raise the failure points

above the predicted support motions. Alternatively, if the equipment is

vulnerable to support motions at relatively high frequencies, the equipment may

be protected by mounting the equipment on isolators. In general, the frequency

of the equipment/isolator system should be no greater than the minimal

vulnerable frequency of the unisolated frequency divided by 2. This will reduce

the motions affecting the equipment at any isolator damping. Details on shock

isolation design are provided in the Shock and Vibration Handbook (Harris 1988).

The isolation however, could produce significant amplification of motions

(especially for lightly damped isolators), and thus increase the response spectra

demand near the natural frequency of the isolated system. For the predicted

shock spectra shown in Figure 18, the equipment may be protected by mounting

it on isolators that will result in an isolated system natural frequency at or below

4.2 Hz (6 Hz/ 2).

As was discussed earlier, equipment may be instrumented at key locations to

evaluate the modes of failure. In the testing of desktop computers done at

USACERL, the predominant failure was read-write errors caused by the readwrite head impacting and damaging the hard disk surface. An accelerometer was

attached to the hard disk case to measure the vertical vibration of the hard disk.

Figure 38a shows the response of the hard disk during Fragility Test 72, and

Figure 38b shows the support motion at the base of the computer during the same

test. Comparing the two shows significant amplified motion at the hard disk

relative to the support locations. This amplification occurs between 32 and 90 Hz.
42 USACERL TR 97/58

The computer frame appears to have provided significant attenuation of the

support motion below 32 Hz and isolation above 90 Hz. The amplification is

caused by resonance response in the computer frame and/or hard disk within the

frequency range of amplification. This helps to explain why the computer failed

at relatively low support motions within this range. Methods of protecting this

equipment would naturally focus on this vulnerability.

Quantifying equipment dynamic characteristics and modes of failure is essential

to developing equipment protection. Analytical models can be developed, based

on the vulnerability data gathered, that allow the generalization of the

vulnerability data to equipment with similar dynamic characteristics and modes

of failure. Vulnerability of equipment not tested could be defined based on these

models.
USACERL TR 97/58 43

6 Conclusions

The CERL Equipment Fragility and Protection Procedure (CEFAPP) was

developed to determine if equipment is vulnerable to predicted support

motions.CEFAPP defines the frequency range at which the equipment is

vulnerable and the mode or modes of failure created. The data generated by

CEFAPP can be used to develop methods of protecting equipment, either by

strengthening or isolation of the equipment.

The use of CEFAPP to test a power transformer bushing was presented in

Chapter 4. Validation tests support the accuracy of this procedure for defining the

capacity of equipment. The failure envelopes developed here can effectively be

compared with seismic demand, thereby reducing the need for additional testing

for other seismic hazards (e.g., using the same equipment at other locations). This

is especially true if demand is defined by site-specific spectra, because earthquake

potential is then expressed with respect to its frequency content. Equipment

vulnerability for various locations may be evaluated by comparing various sitespecific spectra with the capacity spectrum defined by the original fragility

testing, thus eliminating need for further testing to accommodate new or

unanticipated demands.

The characterization of equipment vulnerability may also be used to develop

analytical models that would allow generalization to equipment with similar

dynamic characteristics and modes of failure. With such models, the vulnerability

of equipment not tested could be defined.

CEFAPP can be used to evaluate the effectiveness of prototype equipment

protection design. Strengthening methods, isolation techniques, and combinations

of the two may be evaluated by conducting fragility tests on protected equipment.

CEFAPP could be used by equipment manufacturers to define the capability of

their equipment to withstand a variety of dynamic support motions.

Manufacturers could publish such information in their product literature, and the

information could be used by equipment procurement personnel to assess the

adequacy of the equipment for their installation, or to determine what protection

may be needed. CEFAPP could significantly increase reliability and decrease the
44 USACERL TR 97/58

cost of critical equipment by reducing or eliminating the need for expensive

qualification testing.

A more rigorous method for calculating sweep rate to produce equivalent numbers

of strong motion cycles is needed. Future work in this area will investigate how

to define sweep rate based on an improved numerical analysis of narrow-band

random signals.
USACERL TR 97/58 45

References

Bellcore, Network Equpiment-Building System (NEBS) Requirements: Physical Protection, Bell

Communications Research, GR-63-CORE, Issue 1, October 1995.

Drake, J.L, et al., Protective Construction Design Manual, ESL-TR-87-57 (Air Force Engineering

and Service Laboratory, November 1989).

FEMA, NEHRP Recommended Provisions for Seismic Regulations for New Buildings 1994 Edition,

Part 1 Provisions, FEMA 222A, May 1995.

FEMA, NEHRP Recommended Provisions for Seismic Regulations for New Buildings 1994 Edition,

Part 2 Commentary, FEMA 223A, May 1995.

FEMA, NEHRP Recommended Provisions for the Development of Seismic Regulations for New

Buildings 1991 Edition, Part 1 Provisions, FEMA 222, January 1992.

FEMA, NEHRP Recommended Provisions for the Development of Seismic Regulations for New

Buildings 1991 Edition, Part 2 Commentary, FEMA 223, January 1992.

FEMA 74, Reducing the Risks of Nonstructural Earthquake Damage – A Pictoral Guide (Federal

Emergency Management Agency, September 1994), pp 7–12.

Harris, C.M., Shock and Vibration Handbook, 3d ed. (McGraw-Hill, 1988), chap 30–34.

IEEE 693, Recommended Practices for Seismic Design of Substations, draft 6 (Institute of

Electrical and Electronics Engineers, 1997).

Otnes, R.K., and L. Enachson, Digital Time Series Analysis (John Wiley & Sons, 1972).

Rabiner, Lawrence R., and Bernard Gold, AT&T Theory and Practice of Digital Signal Processing,

(Prentice-Hall, Englewood Cliffs, NJ).

Singh, M.P., L.E. Suarez, E.E. Matheu, and G.O. Maldonado, Simplified Procedures for Seismic

Design of Nonstructural Components and Assessment of Current Code Provisions,

NCEER-93-01 (National Center for Earthquake Engineering Research, August 1993).

Sues, R.H., C.E. Murphy, and R.A. Frank, Protective Constrution Design Manual Change 5,

Expedient Hardening Methods for Structures Subjected to the Effects of Non-Nuclear

Munitions (Air Force Engineering and Services Laboratory, ESL-TR-87-57, June 1991).
46 USACERL TR 97/58

Thomson, W.T., Theory of Vibration With Applications (Prentice-Hall, 1981), pp 404–420.
48 USACERL TR 97/58

Figures Referenced in Main Body of Report
46 USACERL TR 97/58

Figure 1. Example of narrow-band random sweep motions, Test 72.

The upgrade of the USACERL shake table, which is now triaxial, included an increase in velocity

capacity to 50 inches/second in the longitudinal and new lateral axes.

Figure 2. Envelope of the USACERL shake table vertical capacity.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

Time (seconds)

0 5 10 15 20 25 30 35 40

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

0

5

10

15

20

25

30

35

Time (seconds)

0 5 10 15 20 25 30 35 40
USACERL TR 97/58 47

Figure 3a. Response of 12.2 hz SDOF oscillator to El Centro time history, 2% damping.

Figure 3b. Response of 12.2 hz SDOF oscillator identifying strong motion cycles.

Time (seconds)

0 5 10 15 20 25 30 35 40 45 50

Acceleration (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Time (seconds)

2 3 4 5 6 7 8 9 10

Acceleration (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

1

14

14

1 2

3-MAX

4 5 6

7 8

9

10

11

12

13

2-MAX

4

5

6

7

8

10

9

11

12

13
48 USACERL TR 97/58

Figure 4a. Configuration of IBM-XT personal computer tested on the USACERL shaketable.

Figure 4b. Close-up showing anchorage and some instrumentation of the IBM computer.
USACERL TR 97/58 49

1 2 4 8 16 32 64 128 256 512 1024

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Attenuation Factor

Frequency (hertz)

Figure 5a. Attenuation function for Fragility Test 67.

1 2 4 8 16 32 64 128 256 512 1024

0

1

2

3

4

5

Velocity (in/sec)

Frequency (hertz)

Figure 5b. Scaled envelope for Fragility Test 67.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-10

0

10

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 5c. Fragility Test 67 narrow-band random record and SDOF response envelope.
50 USACERL TR 97/58

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6a. Test 72 support motion, SDOF oscillator envelope and failure data.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6b. Test 40 support motion, SDOF oscillator envelope and failure data.
USACERL TR 97/58 51

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6c. Test 41 support motion, SDOF oscillator envelope and failure data.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6d. Test 43 support motion, SDOF oscillator envelope and failure data.
52 USACERL TR 97/58

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6e. Test 44 support motion, SDOF oscillator envelope and failure data.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6f. Test 60 support motion, SDOF oscillator envelope and failure data.
USACERL TR 97/58 53

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6g. Test 65 support motion, SDOF oscillator envelope and failure data.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity - in/sec

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6h. Test 67 support motion, SDOF oscillator envelope and failure data.
54 USACERL TR 97/58

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6i. Test 76 support motion, SDOF oscillator envelope and failure data.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6j. Test 80 support motion, SDOF oscillator envelope and failure data.
USACERL TR 97/58 55

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6k. Test 86 support motion, SDOF oscillator envelope and failure data.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6l. Test 101 support motion, SDOF oscillator envelope and failure data.
56 USACERL TR 97/58

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6m. Test 105 support motion, SDOF oscillator envelope and failure data.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-20

-15

-10

-5

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 6n. Test 107 support motion, SDOF oscillator envelope and failure data.
USACERL TR 97/58 57

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

0

5

10

15

20

25

30

Figure 7. SDOF envelope of support motion and failure data.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

0

5

10

15

20

Figure 8. Equipment fragility data.
58 USACERL TR 97/58

Time (seconds)

0 5 10 15 20 25 30

Velocity (in/sec)

-10

-8

-6

-4

-2

0

2

4

6

8

10

Figure 9a. Lucerne seismic record with failure point.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

0

1

2

3

4

Figure 9b. SDOF envelope of Lucerne seismic record with failure point.
USACERL TR 97/58 59

Time (seconds)

0.0 0.5 1.0 1.5 2.0 2.5

Velocity (in/sec)

-10

-8

-6

-4

-2

0

2

4

6

8

10

Figure 10a. Shock record.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

0

1

2

3

4

Figure 10b. SDOF envelope of shock record with failure point.
60 USACERL TR 97/58

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

0

5

10

15

20

Time (seconds)

0 5 10 15 20 25 30 35 40

Seismic Error

Fragility Data

Shock Error

Velocity (in/sec)

Figure 11. Fragility data with seismic and shock failures.
64 USACERL TR 97/58

Figure 12. TVA power transformer bushing tested on the USACERL triaxial shake table.
62 USACERL TR 97/58

Figure 14a. Generated narrow-band random signal, Ran1.

Figure 13. Horizontal and vertical response spectra, IEEE 693 high seismic performance level.

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Horizontal RRS, 2% Damping Vertical RRS, 2% Damping

Time (seconds)

Signal Amplitude (no units)

0 10 20 30 40 50 60 70

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4
USACERL TR 97/58 63

Time (seconds)

Signal Amplitude (no units)

0 10 20 30 40 50 60 70

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 14b. Generated narrow-band random signal, Ran2.

Time (seconds)

Signal Amplitude (no units)

0 10 20 30 40 50 60 70

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 14c. Generated narrow-band random signal, Ran3.

Time (seconds)

Signal Amplitude (no units)

0 10 20 30 40 50 60 70

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 14d. Generated narrow-band random signal, Ran4.
64 USACERL TR 97/58

Time (seconds)

Signal Amplitude (no units)

0 10 20 30 40 50 60 70

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 14e. Generated narrow-band random signal, Ran5.

Time (seconds)

Signal Amplitude (no units)

0 10 20 30 40 50 60 70

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 14f. Generated narrow-band random signal, Ran6.

Time (seconds)

Signal Amplitude (no units)

0 10 20 30 40 50 60 70

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 14g. Generated narrow-band random signal, Ran7.
USACERL TR 97/58 65

Time (seconds)

Signal Amplitude (no units)

0 10 20 30 40 50 60 70

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 14h. Generated narrow-band random signal, Ran8.

Time (seconds)

Signal Amplitude (no units)

0 10 20 30 40 50 60 70

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 14i. Generated narrow-band random signal, Ran9.

Time (seconds)

Signal Amplitude (no units)

0 10 20 30 40 50 60 70

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Figure 14j. Generated narrow-band random signal, Ran10.
66 USACERL TR 97/58

Figure 15. IEEE 693 high seismic performance response spectra and unscaled response

spectra.

0

1

2

3

4

5

6

7

8

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Hor RRS 2% Ver RRS 2% Ran1 Ran2

Ran3 Ran4 Ran5 Ran6

Ran7 Ran8 Ran9 Ran10
USACERL TR 97/58 67

Scaling Relationships for Narrow-Band Random Tests

Scale Number

& Amplitude,

Frequency Range,

fn-1 – fn

(Hz)

Time Range

tn-1 - tn

(seconds) n An

 (g)

Horizontal Scaling, SH

(g)

Vertical

Scaling,Sv

(g)

0 12

0.5 – 1.122 0 – 11.67 1 8 0.8 SH

1.122 – 8 11.67 – 40 2 2 0.8 SH

8 – 33.903 40 – 60.833 3 0.25 0.8 SH

33.903 – 64 60.833 – 70 4 0.2 0.8 SH

Note: This information is reproduced from Table 5, Chapter 4.

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Scale (g)

0

2

4

6

8

10

12

Time (seconds)

0 10 20 30 40 50 60 70

Horizontal Scale

Vertical Scale

Figure 16. Scaling used for both horizontal (lateral and longitudinal) and vertical records.

2 2

3 2

3 2 (t t ) A

t t

A A − + −−

3 3

4 3

4 3 (t t ) A

t t

A A − + −−

1 1

2 1

2 1 (t t ) A

t t

A A − + −−

0 0

1 0

1 0 (t t ) A

t t

A A − + −−
USACERL TR 97/58 69

Figure 17a. IEEE 693 high seismic performance response spectra and scaled response spectra.

0

1

2

3

4

5

6

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Hor RRS 2% Ran1 Ran2 Ran3

Ran4 Ran5 Ran6 Ran7

Ran8 Ran9 Ran10

0

1

2

3

4

5

6

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

 Hor RRS 2% Ver RRS 2% Ran8 Lateral Ran3 Longitudinal Ran9 Vertical

Figure 17b. IEEE 693 spectra and selected scaled response spectra.
USACERL TR 97/58 71

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 18a. Lateral narrow-band random scaled signal, Ran8.

Time (seconds)

0 10 20 30 40 50 60 70

Accleration (g)

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 18b. Longitudinal narrow-band random scaled signal, Ran3.
72 USACERL TR 97/58

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 18c. Vertical narrow-band random scaled signal, Ran9.

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 19a. Achieved lateral acceleration with input motions at 29% of Figure 18a.
USACERL TR 97/58 73

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 19b. Achieved longitudinal acceleration with input motions at 29% of Figure18b.

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 19c. Achieved vertical acceleration with input motions at 29% of Figure18c.
USACERL TR 97/58 75

Figure 20. Test response spectra from 29% Figure 18 motions and 29% IEEE 693 spectra.

Figure 21a. Original longitudinal narrow-band random scaled signal, Ran3 (from Figure 18b).

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Horizontal RRS, 2% Damping Vertical RRS, 2% Damping Lateral Longitudinal Vertical

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Frequency (Hertz)

0.5 1 2 4 8 16 32 64
USACERL TR 97/58 77

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 21b. First region (Ran31) of narrow-band random scaled signal.

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 21c. Second region (Ran32) of narrow-band random scaled signal.
78 USACERL TR 97/58

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 21d. Third region (Ran33) of narrow-band random scaled signal.

Figure 22a. Approximate attenuation with respect to frequency for the regions of Figure 21.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.1 1 10 100

Frequency (hertz)

Approximate Attenuation

Ran31 Ran32 Ran33
USACERL TR 97/58 79

Figure 22b. Response spectra for Figure 21a and three regions of Figure 21b through 21d.

Figure 23a. Narrow-band random record generated by the new Matlab routine scaled to Bellcore

(Bel2).

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Hor RRS 2% Ran3 Longitudinal Ran31 Ran32 Ran33

Time (seconds)

0 10 20 30 40 50 60 70 80

Amplitude (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Frequency (hertz)

0.2 0.4 0.8 1.6 3.2 6.4 12.8 25.6 51.2
USACERL TR 97/58 81

Time (seconds)

0 10 20 30 40 50 60 70 80

Amplitude (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Frequency (hertz)

0.2 0.4 0.8 1.6 3.2 6.4 12.8 25.6 51.2

Figure 23b. First region of Bellcore narrow-band random scaled signal (Bel21).

Time (seconds)

0 10 20 30 40 50 60 70 80

Amplitude (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Frequency (hertz)

0.2 0.4 0.8 1.6 3.2 6.4 12.8 25.6 51.2

Figure 23c. Second region of Bellcore narrow-band random scaled signal (Bel22).
82 USACERL TR 97/58

Time (seconds)

0 10 20 30 40 50 60 70 80

Amplitude (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Frequency (hertz)

0.2 0.4 0.8 1.6 3.2 6.4 12.8 25.6 51.2

Figure 23d. Third region of Bellcore narrow-band random scaled signal (Bel23).

Time (seconds)

0 10 20 30 40 50 60 70 80

Amplitude (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Frequency (hertz)

0.2 0.4 0.8 1.6 3.2 6.4 12.8 25.6 51.2

Figure 23e. Fourth region of Bellcore narrow-band random scaled signal (Bel24).
USACERL TR 97/58 83

Time (seconds)

0 10 20 30 40 50 60 70 80

Amplitude (g)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Frequency (hertz)

0.2 0.4 0.8 1.6 3.2 6.4 12.8 25.6 51.2

Figure 23f. Fifth region of Bellcore narrow-band random scaled signal (Bel25).

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.1 1 10 100

Frequency (hertz)

Approximate Attenuation

Bel21 Bel22 Bel23 Bel24 Bel25

Figure 24a. Approximate attenuation with respect to frequency for the regions of Figure 23.
USACERL TR 97/58 85

Figure 25a. Achieved lateral acceleration, 50% of Figure 18a (Frag10).

0

1

2

3

4

5

6

7

8

9

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Bel2 Bel21 Bel22 Bel23 Bel24 Bel25 Bellcore, Zone 4 Design

Figure 24b. Response spectra for Figure 23a and five regions of Figures 23b through 23f.

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Frequency (hertz)

0.5 1 2 4 8 16 32 64
USACERL TR 97/58 87

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 25b. Achieved longitudinal acceleration, 50% of Figure 18b with 1.2 hz HP filter.

Time (seconds)

0 10 20 30 40 50 60 70

Acceleration (g)

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Frequency (hertz)

0.5 1 2 4 8 16 32 64

Figure 25c. Achieved vertical acceleration, 50% of Figure 18c.
88 USACERL TR 97/58

Time (seconds)

Scale (g)

0 10 20 30 40 50 60 70

0

2

4

6

8

10

12

Figure 26a. Scale with Notch 2.

Time (seconds)

Acceleration (g)

0 10 20 30 40 50 60 70

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Figure 26b. Lateral achieved acceleration with Notch 2 and 100% of Figure 18a (Frag17).

Time (seconds)

Acceleration (g)

0 10 20 30 40 50 60 70

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Figure 26c. Longitudinal achieved acceleration with Notch 2 and 100% of Figure 18b (Frag17).
USACERL TR 97/58 89

Figure 26d. Vertical achieved acceleration with Notch 2 and 100% of Figure 18c (Frag17).

Figure 26e. IEEE 693 spectra and TSR for100% of Figure 18 motions with Notch 2 (Frag17).

Time (seconds)

Acceleration (g)

0 10 20 30 40 50 60 70

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Horiz RRS, 2% Damp Vert RRS, 2% Damp Lateral Long Vertical
USACERL TR 97/58 91

Time (seconds)

Scale (g)

0 10 20 30 40 50 60 70

0

2

4

6

8

10

12

Figure 27a. Scale and Notch 1.

Time (seconds)

Scale (g)

0 10 20 30 40 50 60 70

0

2

4

6

8

10

12

Figure 27b. Scale and Notch 2.

Time (seconds)

Scale (g/unit)

0 10 20 30 40 50 60 70

0

2

4

6

8

10

12

Figure 27c. Scale and Notch 3.
USACERL TR 97/58 93

Figure 28a. Maximum TRS through Frag23, 220% of Figure 18.

0

1

2

3

4

5

6

7

8

9

10

0.1 1 10 100 Frequency (hertz)

Spectral Acceleration (g)

Horz. RRS, 2% Damping Vert. RRS, 2% Damping Lateral Long Vertical

0

1

2

3

4

5

6

7

8

9

10

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Horz. RRS, 2% Damping Vert. RRS, 2% Damping Lateral Long Vertical Leak Failure

Leak & Slippage

Figure 28b. Maximum TRS through Frag23 and failure data.
USACERL TR 97/58 95

0.0

0.5

1.0

1.5

2.0

2.5

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Horz. RRS, 2% Damp Vert. RRS, 2% Damp Lateral

 Long Vert IEEE 693 Leak

Site- Spec Site-Spec Leak

Figure 29a. IEEE 693 (at 50% PL) and site-specific spectra, TRS, and leak failures.

0

1

2

3

4

5

6

7

8

9

0.1 1 10 100 Frequency (hertz)

Spectral Acceleration (g)

Horz. RRS, 2% Damping Vert. RRS, 2% Damping Lateral Long Vertical

Figure 28c. Maximum TRS without notches.
USACERL TR 97/58 97

0

1

2

3

4

5

6

7

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Fragility IEEE 693 Site-Spec

Figure 29b. Failure data from CEFAPP, IEEE 693 and site-specific tests.

0

1

2

3

4

5

6

7

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Horz. RRS, 2% Damp Vert. RRS, 2% Damp Site Specific Fragility

Figure 30. Fragility data with site-specific and IEEE 693 design response spectra.
98 USACERL TR 97/58

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Period, Tm (seconds)

Csm (g)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Figure 31. Example of site-specific response spectrum.

Figure 32a. Example response spectrum based on 1994 NEHRP recommended provisions.
USACERL TR 97/58 99

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Figure 32b. Example 1994 NEHRP response spectrum plotted with respect to frequency.
USACERL TR 97/58 101

Figure 33a. USGS Spectral Acceleration Map, California and Nevada, 2% PE, 0.2 sec. period.
USACERL TR 97/58 103

Figure 33b. USGS Spectral Acceleration Map, California and Nevada, 2% PE, 0.3 sec. period.
USACERL TR 97/58 105

Figure 33c. USGS Spectral Acceleration Map, California and Nevada, 2% PE, 1.0 sec. period.
USACERL TR 97/58 107

Figure 34a. USGS Spectral Acceleration Map, Central and Eastern U.S., 2% PE, 0.2 sec. period.
USACERL TR 97/58 109

Figure 34b. USGS Spectral Acceleration Map, Central and Eastern U.S., 2% PE, 0.3 sec. period.
USACERL TR 97/58 111

Figure 34c. USGS Spectral Acceleration Map, Central and Eastern U.S., 2% PE, 1.0 sec. period.
USACERL TR 97/58 113

Figure 35a. Example response spectrum based on expected 1997 NEHRP recommended

provisions.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Period, Tm (seconds)

Csm (g)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.1 1 10 100

Frequency (hertz)

Spectral Acceleration (g)

Figure 35b. Example response spectra plotted with respect to frequency.
USACERL TR 97/58 115

0.1

1

10

100

1 10 100 1000

Frequency (hertz)

Spectral Acceleration (g) 0.1

1

10

100

0.1 1 10 100 1000

Frequency (hertz)

Spectral Acceleration (g)

Site Specific Spectra 1997 San Franciso, 2%PE 1997 Memphis, 2%PE 1997 San Franciso, 10%PE

1994 San Franciso Shock Spectra CERL Fragility Data

Figure 36. Shock response spectrum for a floor slab.

Figure 37. Seismic and shock response spectra with CERL fragility data.
USACERL TR 97/58 117

Time (seconds)

0 5 10 15 20 25 30 35 40

Velocity (in/sec)

-80

-60

-40

-20

0

20

40

60

80

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Figure 38a. Fragility Test 72  hard disk response of test specimen to support motion.

Frequency (hertz)

1 2 4 8 16 32 64 128 256 512 1024

Velocity (in/sec)

-80

-60

-40

-20

0

20

40

60

80

Time (seconds)

0 5 10 15 20 25 30 35 40

Figure 38b. Fragility Test 72  support motion.
USACERL TR 97/58 121

Appendix A: Matlab Routine RANSWP.M for

Digital Generation of NarrowBand Random Sweep Records

Narrow-band random signals, with a linearly variable sweep rate were generated

digitally using the Matlab routine RANSWP.M.

Requested input for this routine is:

kern: the current time (entered as hour.minute) is used as a kernel for

the pseudo-random number generator. Unless otherwise

instructed, the Matlab routine “rand” is initiated with the same

number each time, thus always generating the same series of

normally distributed pseudo-random numbers. Initiating the

routine with the current time is an effort to ensure the creation of

unique random series.

aqrate: the sample rate (in hertz) at which the input signal should be

created.

swratelow: beginning sweep rate (in octaves per minute).

swratehigh: ending sweep rate (in octaves per minute); the sweep rate varies

linearly with time (and logarithmically with frequency) between

these two limits. 

centerlow: the beginning center frequency (Hz).

centerhigh: the ending center frequency (Hz).

band: the filter bandwidth, in octaves.

error: allowable filter error, in octaves.
122 USACERL TR 97/58

ran(i) ' 2(rand&0.5), i'1...npts. [Eq A1]

outfile: the name of the output file in which to store the generated signal.

The algorithm for generating the test signal is outlined below. The variables used

in the equations presented here correspond to the variables used in the Matlab

routine RANSWP.M.

A series of npts random numbers is generated by

The Matlab function rand generates a series of pseudo-random numbers uniformly distributed in the interval (0,1). The rand output is adjusted to return a

series with 0 mean and unit absolute magnitude. This series is used to represent

a time history containing frequencies ranging from 0 Hz (though, with a zero

mean, there will be no DC component) to the nyquist frequency (aqrate ÷2).

Eventually sweeping filters will be applied to this raw random series to generate

a new narrow band random series with a sweeping center frequency. Before this

is done, certain relationships must be developed to determine the time and

frequency characteristics of the final record.

The time duration of the final record is determined from the sweep rate and the

number of octaves to be generated. The relation between time and sweep rate is

shown in Figure A1, and given by

swr(t) ' swratelow% s(t [Eq A2]

where

s '

swratehigh&swratelow

dur

, [Eq A3]

and dur is the time length of the record. The number of octaves generated by the

record at any time t, is then given by

numoct(t) '

m

swr(t) dt. [Eq A4]

Substituting A2 into A4 and evaluating the integral yields

numoct(t)'swratelow(t%

st 2

2

, [Eq A5]
USACERL TR 97/58 123

where the constant of integration is equal to zero, since at t'0, numoct(t)'0.

Substituting A3 into A5 and evaluating for the limits (0,dur) gives

numoct (t)'dur swratehigh%sratelow

2

, [Eq A6]

which can then be solved to give the total time duration of the record as

dur '

2(60)(numoct)

(swratehigh%swratelow)

. [Eq A7]

The constant of 60 is included to convert dur from minutes to seconds.

Knowing the duration of the record in time and the sampling rate, the number of

data points in the final record is limit'dur(aqrate. Note that there is a difference

between the length of the final record (limit) and the length of the initial, raw

random series (npts); the purpose of this is shown schematically in Figure A2.

The length of the raw random series is equal to that of the final record augmented

by one full bandwidth and a region called a pad (i.e.,

npts ' limit%bandnum%padlength ). The purpose of the addition of an extra

bandwidth is that the beginning and ending points of the final record represent

center frequencies. To be consistent, and to simplify the structure of the program,

the raw random series is extended so that the extreme regions of the final record

operate on the exact same length of data as the interior region. There is a

difference in the length of the bandwidth at the beginning and the end of the

record in terms of data points; for simplicity RANSWP.M always uses the larger

of the two. The purpose of the pad is to protect the record from magnitude loss as

the filters “spool up.” The linear, digital finite impulse response (FIR) filters used

in this routine (and defined shortly) will not return steady state magnitude until

reaching a point in the record equal to one half the filter order. Thus the initial

pad region is equal to one half the beginning filter order. The filter order is

allowed to vary during a run of RANSWP.M. Each time the filter order is updated

the length of the pad is appropriately adjusted.

The operating logic of the main loop of RANSWP.M is to start at the beginning of

the raw random series, treating the first point (offset by the pad length and onehalf the initial bandwidth) as the beginning center frequency and extracting a

region from the raw random series that is equal in length to the bandwidth

centered about the center frequency, plus the pad. This region is filtered, and the

data point that is associated with the center frequency is stored in a separate

vector (ranfilt); the rest of the filtered region is discarded. The loop then repeats

and advances one data point in the raw random series. The new center frequency

associated with this data point is determined and again a region equal in length
124 USACERL TR 97/58

to the bandwidth (centered about the center frequency) plus the pad is extracted.

Once this region is filtered appropriately the data point corresponding to the

present center frequency is stored in the vector ranfilt along with the previously

filtered point. The loop continues in this manner until the ending center

frequency is reached.

To track the center frequency and determine what the filter limits should be at

any point in the record, a relationship must be determined between time (and

thus data points) and frequency. This is developed by first expressing the number

of octaves that have been generated at any particular frequency, f, as

numoct(f) '

log(f) &log(centerlow)

log(2)

. [Eq A8]

Because the distribution of frequency and time must map to the same distinct

number of octaves that have been generated at any point in the record, A8 can be

equated to A5 to yield

log(f) &log(centerlow)

log(2)

' swratelow(t%

st 2

2

. [Eq A9]

Solving for f gives the desired relation:

f ' 10

log(2)[swratelow(t%

st 2

2

]%log(centerlow)

[Eq A10]

At this point, knowing the bandwidth, the center frequency, and the allowable

filter error, the necessary design requirements for the band pass filters have been

specified. FIR (finite impulse response) filters were selected based on their

simplicity, linear phase, and nonrecursive nature (i.e., the filter only operates on

the incoming raw, unfiltered data, as opposed to infinite impulse response filters,

which operate recursively on previously filtered data). For generation of the FIR

filters used by RANSWP.M, first consider the frequency response of the ideal low

pass filter shown in Figure A3. To determine the filter coefficients the impulse

response of the system are calculated by taking the inverse fourier transform of

the frequency response,

h(t) '

1

2B m

&

H(T) e

iTtdT. [Eq A11]

Accounting for the step function nature of H(T), and using Euler’s identity to

express the complex sinusoid in terms of elementary trigonometric functions, A11

becomes

h(t) '

1

2B m

T0

&T0

[cosTt%isin(Tt)] dT. [Eq A12]

Since H(T) is an even function in T,the sin term can be discarded, giving
USACERL TR 97/58 125

h(t) '

1

2B m

T0

&T0

cosTt%dT '

sin(T0t)

Bt

, [Eq A13]

which is a variation of the familiar sin(x)/x,or sinc function. Matlab defines its

sinc function as

sinc(x) '

sin(Bx)

Bx

. [Eq A14]

Substituting x'T into A14 gives 0t/B

sinc(

T0t

B

) '

sin(T0t)

T0t

. [Eq A15]

Therefore, using the Matlab sinc function, the impulse response can be expressed

as

h(t) '

T0

B

sinc(

T0t

B

). [Eq A16]

This approach provides the best least squares approximation to the transfer

function in Figure A3. For digital implementation, the continuous time variable,

t, becomes the discrete integer variable, n, giving

h(n) '

T0

B

sinc(

T0n

B

). [Eq A17]

The development of a band pass filter from the low pass filter given by A17 is

simply achieved by subtracting a low pass filter with a cutoff frequency equal to

the lower cutoff frequency of the band pass filter (Tl), from a low pass filter with

a cutoff frequency equal to the higher cutoff frequency of the band pass filter (T ). h

Thus, the impulse response for the band pass filter would be given by

h(n) '

Th

B

sinc(

Thn

B

) &

Tl

B

sinc(

Tln

B

). [Eq A18]

The series h(n) must be truncated to a finite number of terms for numerical

implementation, the limit of which is the filter order (order). The truncation of

A18 causes a ripple effect about the cutoff frequencies due to Gibb’s phenomenon.

To minimize this effect a Hamming window is applied to the filter, smoothing the

transfer function (Rabiner and Gold 1975, p92). The final, realizable filter is

shown schematically in Figure A4. The effect of the truncation of A18 and

windowing is to smooth the discontinuity at the cutoff frequencies into a

transition region. The filters designed in this manner will always have a

frequency response magnitude, H(T), of 0.5 at the cutoff frequencies.
126 USACERL TR 97/58

To define the filters, lastly it is necessary to relate the filter order to the error in

the transition region. We define filter error as the amount of overshoot allowed

by the filter at the cutoff frequencies, as shown in Figure A5. During each

increment of the main loop, RANSWP.M updates the allowable filter error based

on the present center frequency and the user specified error. This is necessary

since the user- specified error is in octaves, and thus the actual filter error, in

hertz, is a function of the current center frequency. This filter error, in hertz, is

determined from the center frequency and specified error as

errhz ' 10[log(centerfreq)%log(2)error]¢erfreq. [Eq A19]

The filter order/error relationship was determined empirically by observing the

filter transfer functions over a wide range of filter orders. It was found that the

error, normalized to the nyquist frequency, obeys the following relation to filter

order (initorder):

log(errnorm) ' &log(initorder) %0.531, [Eq A20]

where

errnorm ' errhz/nyquist. [Eq A21]

Or, solving for the filter order (initorder):

initorder ' 100.531&log(errnorm) '

100.531

errnorm

. [Eq A22]

For example, if an allowable filter error (error) of 0.1 octave is specified,

RANSWP.M first references this to the current center frequency to convert from

octaves to hertz. Letting the current center frequency be 100 Hz for illustrative

purposes, yields an allowable filter error (errhz) of 7.18 Hz. If the sampling rate

were 400 Hz the nyquist frequency would be 200 Hz, giving a normalized error

(errnorm) of 0.0359. From A21, a filter of order (initorder) 95 is required to satisfy

the error criterion. Since the filter error is specified in terms of octaves, the filter

order will vary with the center frequency. At the beginning of RANSWP.M two

auxiliary m-files are utilized when the user is asked to specify the allowable filter

error. The dialogue box for specifying the error is generated by ERRORBOX.M,

and the computations for relating filter order and error within this box are carried

out by ORDERR.M; both of these m-files are included at the end of this appendix.

After creating the appropriate bandpass filter, the region of the raw random

signal that corresponds to the filter bandwidth (by equating time and frequency)

is read into a separate vector (range) for filtering. All filtering is conducted using

the built-in Matlab function filter. Essentially, filter operates in the time domain

by convolving the filter coefficients (h) with the present region of the raw random

signal. Since FIR filters are being used there is no phase distortion due to the

filtering process, but there is a constant group delay of one-half the filter order
USACERL TR 97/58 127

(i.e., the entire filtered region is shifted order/2 steps). Because the bandpass

filter in RANSWP.M has a variable order, as the filter sweeps through the raw

random signal the group delay is not constant, effectively causing a phase

distortion in the final filtered record. This problem is avoided by forward and

reverse filtering, which negates any group delay in the filtered record. The

process of forward and reverse filtering also generates twice the filter order, so

that the effective order/error relationship for the total filtering process becomes

order ' 100.531&log(2(errnorm) '

100.531

2(errnorm)

. [Eq A23]

So, returning to the previous example, the actual filter order (order) that is used

by RANSWP.M would be 48. After filtering, the data point corresponding to the

current center frequency is stored in ranfilt along with all previous center

frequencies and the loop is incremented.

After filtering, the midpoint in the filtered region, which corresponds to the center

frequency, is extracted and stored in a separate vector that contain all previously

filtered midpoints. Each of these points is scaled by a factor of

sf ' nyquist/(highfreq&lowfreq). This was done because it was found that the

filtered data points had a relative magnitude that was proportional to the inverse

of the filter bandwidth.

At the completion of the main loop, an attenuation function that ramps from zero

to unity is applied to one-half of the first period of the filtered data. This was done

to address the issue of an initial spike that was often experienced in the record

and caused by a lack of rigorous enforcement of a zero initial value.

Finally, the vector ranfiltm is written to the output file (outfile).

Transcripts of the code for RANSWP.M, ERRORBOX.M, and ORDERR.M follow.

RANSWP.M

% Matlab M-file to calculate narrow band random signal

% based on a sweeping center frequency, with a variable sweep rate.

global loworder highorder lowerrhz higherrhz aqrate centerlow centerhigh error

% Request user input

clear all;

kern = input('To initialize random number generator, enter time as hr.min: ');

aqrate = input('Enter the sample rate (Hz): ');

swratelow = input('Enter the beginning sweep rate (oct/min): ');

swratehigh = input('Enter the ending sweep rate (oct/min): ');
128 USACERL TR 97/58

centerlow = input('Enter the beginning center freq. (Hz): ');

centerhigh = input('Enter the ending center freq. (Hz): '); 

band = input('Enter the filter bandwidth (oct): ');

errorbox;

outfile = input ('Select desired error, then enter the name of the signal

output file: ','s');

% initialize random number generator

seed = (kern^3);

rand('seed',seed);

% calculate system parameters: # octaves, duration, # data points

numoct = round((log10(centerhigh) - log10(centerlow))/.30103);

dur = 2*60*numoct/(swratehigh + swratelow);

time_swr_rel = (swratehigh - swratelow)/dur;

limit = dur*aqrate;

datapt_swr_rel = (swratehigh - swratelow)/limit;

% determine length of initial padding as 1/2 the greatest filter order.

% (the order corresponding to the lowest frequency).

% The purpose of the pad is to protect the beginning and end

% of the record from loss as the filter "spools up".

% Also include 1/2 of the ending bandwidth to account for region of record

% greater than the final center frequency at the end of the record.

padlength = round(loworder/2);

bandtime = 60*band/swratelow;

halfband = round(.5*bandtime*aqrate);

bandnum = 2*halfband;

npts = limit + padlength + bandnum;

padoffset = padlength;

bandoffset = halfband;

% Generate random series with unit absolute amplitude

ran = zeros(1,npts);

for n=1:npts

ran(n) = 2*(rand - .5);

%sin(.015*pi*n);

end

% MAIN LOOP for sweeping filter through random signal

cntr=1;

order = loworder;

lowpoint = padoffset;

centpoint = padoffset + halfband;

highpoint = padoffset + bandnum;
USACERL TR 97/58 129

swrate = swratelow;

for i=1:limit

t(i) = i;

% echo % finished

if i/limit > cntr/100

i/limit

cntr=cntr+1;

end 

% filter band parameters

bandtime = 60*band/swrate;

halfband = round(.5*bandtime*aqrate);

bandnum = 2*halfband;

% convert from datapoint to time

% NEGATIVE TIME???? CHECK OFFSET

lowtime = (lowpoint - padoffset - bandoffset)/aqrate;

centtime = (centpoint - padoffset - bandoffset)/aqrate;

hightime = (highpoint - padoffset - bandoffset)/aqrate;

% convert from time to frequency

lowfreq = 10^(((lowtime*swratelow/60 + time_swr_rel*lowtime^2/120)*.30103) +

log10(centerlow));

centfreq = 10^(((centtime*swratelow/60 + time_swr_rel*centtime^2/120)*.30103)

+ log10(centerlow));

highfreq = 10^(((hightime*swratelow/60 + time_swr_rel*hightime^2/120)*.30103)

+ log10(centerlow));

% calculate filter order

nyquist = aqrate/2;

errhz = 10^(log10(centfreq) + .30103*error) - centfreq;

errnorm = errhz/nyquist;

order = round(10^(.531)/(2*errnorm));

% generate band pass filter as via sinc functions with

% hamming window. Filter order (filtlim) is a function

% of the allowable filter error (error) specified in octaves

filtlim = round(order/2);

lowlimit = lowfreq/nyquist;

highlimit = highfreq/nyquist;

highlowpass = highlimit*sinc(highlimit*(-filtlim:filtlim));

lowlowpass = lowlimit*sinc(lowlimit*(-filtlim:filtlim));
130 USACERL TR 97/58

step = highlowpass - lowlowpass;

h = step.*hamming(2*filtlim + 1)';

% read in new piece of raw random series, equal in length to the

% filter band plus pad

padnum = round(order/2);

rangelim = bandnum + padnum;

clear range;

range = zeros(1,rangelim);

for j= 1:rangelim

 range(j) = ran(j+lowpoint - padnum);

end

% filter present region of random signal. Forward and reverse filter

% to return a signal with 0 phase delay and twice the filter order

rantemp = filter(h,1,range);

rantemp = rantemp(length(rantemp):-1:1);

rantemp = filter(h,1,rantemp);

rantemp = rantemp(length(rantemp):-1:1);

% scale factor to be applied to saved data to maintain reasonable bound

% on magnitude

sf = (nyquist/(highfreq - lowfreq));

% combine midpoint of the present filtered region to signal containing

% all previously filtered midpoints

datapoint = halfband;

ranfilt(i) = sf*rantemp(datapoint);

% increment low, center and high data point markers for next loop iteration

lowpoint = lowpoint + 1;

centpoint = centpoint + 1;

highpoint = highpoint + 1;

swrate = swratelow + datapt_swr_rel * i;

% end main loop

end

% attenuate 1/2 of beginning period to enforce 0 initial condition

attentime = 1/(2*centerlow);

 attenpts = round(attentime * aqrate);

for i = 1:attenpts

 atten(i) = i/attenpts;

 end
USACERL TR 97/58 131

 

for i = attenpts + 1: length(ranfilt)

 atten(i) = 1;

 end

 

ranfiltm = atten.*ranfilt;

% write signal to file

fid = fopen(outfile,'w');

 fprintf(fid,'%8.5f\r\n',ranfiltm);

fclose(fid);

ERRORBOX.M

 clf reset;

% set(gcf,'Units','normalized','backingstore','off');

echo off

global loworder highorder lowerrhz higherrhz aqrate centerlow

centerhigh error

 % Create intial signal

 min_err = .01;

 max_err = 1;

 err_dummy = num2str(.5);

 freq_text=uicontrol('Style','text','Position',[.18 .02 .38.

07],..

 'Units','normalized','BackgroundColor','black',...

 'ForegroundColor','white','String','Filter Error (Oct):');

 uicontrol('style','text','pos',[.14 .07 .04 .05],...

 'Units','normalized','BackgroundColor','black',...

 'ForegroundColor','white','String',num2str(min_err));

 uicontrol('style','text','pos',[.79 .07 .02 .05 ],...

 'Units','normalized','BackgroundColor','black',...

 'ForegroundColor','white','String',num2str(max_err));

 err_field=uicontrol('Style','edit','Position',[.59 .02 .12.

07],..

 'Units','normalized','String',err_dummy,...

 

'CallBack',['set(err_slider,''Value'',','str2num(get(err_field,''Stri

ng''))),',...
132 USACERL TR 97/58

'orderr(','get(err_slider,''Val'')',');,',...

'set(order_field1,''String'',','num2str(loworder));,',...

 'set(order_field2,''String'',','num2str(highorder));,',...

'set(error_field1,''String'',','num2str(lowerrhz));,',...

 'set(error_field2,''String'',','num2str(higherrhz));,',...

'error = ','get(err_slider,''Val'');']); 

 err_slider=uicontrol('Style','slider','Position',[.15 .12 .65

.04],...

 

'Units','normalized','Value',str2num(get(err_field,'String')),'Max',m

ax_err,'Min',min_err,...

 

'CallBack',['set(err_field,''String'',','num2str(get(err_slider,''Val

''))),',...

'orderr(','get(err_slider,''Val'')',');,',...

'set(order_field1,''String'',','num2str(loworder));,',...

 'set(order_field2,''String'',','num2str(highorder));,',...

'set(error_field1,''String'',','num2str(lowerrhz));,',...

 'set(error_field2,''String'',','num2str(higherrhz));,',...

'error = ','get(err_slider,''Val'');']); 

%

 close_button=uicontrol('Style','Pushbutton','Position',[.85 .02

.12 .07],...

 

'Units','normalized','Callback','close(gcf)','String','Done');

% * * * * * * * * * * Filter Order Dialogue * * * * * * * * * * * * *

% TITLE

 order_text=uicontrol('Style','text','Position',[.15 .8 .22

.07],..

 'Units','normalized','BackgroundColor','black',...

 'ForegroundColor','white','String','Filter Order (# pts):');

% SUBTITLE

 order_sub1=uicontrol('Style','text','Position',[.15 .72

.38.07],...

 'Units','normalized','BackgroundColor','black',...

 'ForegroundColor','white','String','Beginning Frequency ');

 order_sub2=uicontrol('Style','text','Position',[.5 .72 .38

.07],...

 'Units','normalized','BackgroundColor','black',...

 'ForegroundColor','white','String','Ending Frequency');
USACERL TR 97/58 133

% Order boxes

 order_field1=uicontrol('Style','edit','Position',[.27 .65 .12

.07],...

 'Units','normalized','String',num2str(loworder));

 order_field2=uicontrol('Style','edit','Position',[.63 .65 .12

.07],...

 'Units','normalized','String',num2str(highorder));

% * * * * * * * * * * Filter Error Dialogue * * * * * * * * * * * *

% TITLE

 error_text=uicontrol('Style','text','Position',[.15 .45

.22.07],...

 'Units','normalized','BackgroundColor','black',...

 'ForegroundColor','white','String','Filter Error (+/- Hz):');

% SUBTITLE

 error_sub1=uicontrol('Style','text','Position',[.15 .37

.38.07],...

 'Units','normalized','BackgroundColor','black',...

 'ForegroundColor','white','String','Beginning Frequency ');

 error_sub2=uicontrol('Style','text','Position',[.5 .37 .38

.07],...

 'Units','normalized','BackgroundColor','black',...

 'ForegroundColor','white','String','Ending Frequency');

% Error boxes

 error_field1=uicontrol('Style','edit','Position',[.27 .3 .12

.07],

 'Units','normalized','String',num2str(lowerrhz));

 error_field2=uicontrol('Style','edit','Position',[.63 .3 .12

.07],

 'Units','normalized','String',num2str(higherrhz));

ORDERR.M

function orderr(dummy)

global loworder highorder lowerrhz higherrhz aqrate centerlow

centerhigh error
134 USACERL TR 97/58

Figure A1. Time sweep rate relationship.

Figure A2. Relationship between the raw random series and final signal length.

nyquist = aqrate/2;

low er

rhz =

10^ (l

og1 0(

cen te

rlo w)

+ .3

010 3*

dum my

) - ce

nte rl

ow;

hig he

rrh z

= 10

^(l og

10( ce

nte rh

igh) + .30103*dummy) - centerhigh;

lowerrnorm = lowerrhz/nyquist;

higherrnorm = higherrhz/nyquist;

loworder = round(10^(.531)/(2*lowerrnorm));

hi gho

rd er

= rou

nd (10

^( .53

1) /(2

*h igh

er rno

rm ));
USACERL TR 97/58 135

Figure A3. Ideal low-pass filter.

Figure A4. Truncated and windowed low-pass filter.

Figure A5. Definition of filter error.
136 USACERL TR 97/58

Appendix B: Numerical Analysis of Single

Degree of Freedom (SDOF)

Oscillators

SDOF Time History Analysis

In determining the appropriate sweep rate, it is necessary to calculate the time

history response of single degree of freedom (SDOF) oscillators to base excitation.

The nature of the base motion is governed by the type of fragility testing being

conducted and is thus arbitrary, ranging from shock to seismic input motions.

The method employed for this analysis is to calculate the response of an SDOF

oscillator as the convolution of the SDOF impulse response and the base

excitation. This method is described below in greater detail.

Arbitrary input motion may be viewed as a sequence of impulses

F(t) j F(J) )J *(t&J), [Eq B1]

where *(t&J)is the delta function defined at t'J, and F(J) )Jrepresents the

magnitude of the impulse. It can also be shown that the impulse response of an

oscillator to base excitation is expressed as

I(t) '

1

Td

e

&.Tnt

sin Tdt.

[Eq B2]

where T and are the undamped and damped natural frequencies of the n Td

system. Applying the series of impulsive forces to the impulse response function

yields the system response to general base excitation as

x(t) j F(J))JI(t&J) [Eq B3]

or, if we allow )J 0

x(t) '

m

t

0

F(J) I(t&J) dJ. [Eq B4]

Substituting Equation B2 and differentiating yields an expression for the velocity

of the system:
USACERL TR 97/58 137

x

.

(t) '

m

t

0

F(J)cos Td(t&J)e

&.Tn(t&J)

dJ

&

.Tn

Td

m

t

0

F(J)sin Td(t&J)e

&.Tn(t&J)

dJ.

[Eq B5]

The total acceleration (input plus response) can be found by substituting

(Equations B4 and B5) into the equilibrium expression

x

..

(t) ' &2Tn. x

.

(t) &T

2

n

x(t)

[Eq B6]

yielding,

x

..

(t) ' (2.

2&1)

T

2

n

Td

m

t

0

F(J)sin Td(t&J)e

&.Tn(t&J)

dJ

& 2Tn.

m

t

0

F(J)cos Td(t&J)e

&.Tn(t&J)

dJ.

[Eq B7]

To apply Equation B7 to sampled data we must return to a discrete formulation

expressing B7 as

x

..

(i) '

(2.

2&1)

T

2

n

Td

j

i

j'1

F(j)sin Td(i&j)e

&.Tn(i&j)

)J

& 2Tn.j

i

j'1

F(j)cos Td(i&j)e

&.Tn(i&j)

)J, i'1,...,end.

[Eq B8]

This is the expression used to determine system response in the Matlab routine

SDOF.M (shown below). Vectors g1 and g2 are used to store the trigonometric

and exponential terms of the first and second summation. The Matlab library

convolution routine (conv) is then used to convolve these system vectors with the

forcing vector (F(J))J).

The code for SDOF.M follows:

% Matlab Routine SDOF.M

% Matlab M-file to calculate SDOF response to arbitrary

% base motion.

% request user input 
138 USACERL TR 97/58

% open input file and read in excitation

infile = input ('Enter the name of the excitation file: ','s');

outfile = input ('Enter the name of the SDOF response file: ','s');

freq = input ('Enter the undamped natural frequency: ');

etap = input ('Enter the percentage of critical damping: ');

dt = input('Enter the time step for the input motion: ');

fid = fopen(infile);

f = fscanf(fid,'%e');

fclose(fid);

numpt = length(f)

% calculate system parameters

eta = etap/100;

wn=2*pi*freq;

wd = ((1 - (eta)^2)^.5)*wn;

% Calculate system vector: SDOF response to unit pulse, which is

% equivalent to initial velocity response.

% r is the theoretical response to resonant input- used for

debugging.

for I = 1:numpt

 t = dt*I;

 g1(I) = exp(-(eta*wn*t))*sin(wd*t);

 g2(I) = exp(-(eta*wn*t))*cos(wd*t);

 r(I) = ((exp(-eta*wn*t)-1)*cos(wn*t) +

eta*exp(-eta*wn*t)*sin(wn*t))/(2*eta);

end

% calculate response as the convolution of the forcing 

% vector and the response vector 

% The forcing vector does not have a mass term

% to be consistent with ground motion excitation.

% The response has been integrated twice and represents the

% TOTAL acceleration.

%

y = (2*eta^2 - 1)*(wn^2/wd)*conv(dt*f,g1) - 2*wn*eta*conv(dt*f,g2);

% convolution returns 2n data points for a length n record

% vector temp stores only first n values of y
USACERL TR 97/58 139

N0

2M

' 1 [Eq B9]

SMC '

BandWidth

SR Tn

[Eq B10]

for I = 1:numpt

temp(I) = y(I);

end

x = temp';

fid = fopen(outfile,'w');

fprintf(fid,'%8.3f\r\n',x);

fclose(fid);

SDOF Narrow Band Random Sweep Analysis

SDOF oscillators are excited with narrow band random sweep base motions. A

narrow band random base motion provides a Gaussian normal excitation of the

SDOF oscillator. The signal generated by low pass and high pass filters on a

random signal will have a Rayleigh distribution of the absolute values of its

peaks. For a Rayleigh distribution the distribution of peak values is of interest,

which can be expressed by:

where N0

 is the number of zero crossings and 2M is the sum of positive and

negative peaks.

Figure 1 (immediately following the main body of the report) shows a narrow band

random signal of this type. Sweeping the narrow band random record adds

another variable to calculating the statistical response of SDOF oscillators in the

frequency range of the sweep. Further study of this response is needed.

At this point it is assumed that a SDOF oscillator of frequency, fn

, is excited with

the number of strong motion cycles (SMC) that equal the time required for the

sweep to move across oscillator frequency (band width / sweep rate) divided by the

period, Tn

, of the oscillator.

This may be expressed as follows:

The sweep rate (SR) needed to produce a desired number of SMC for any oscillator

at frequency, fn

, subjected to narrow band random sweep base excitation may then

be expressed as:
140 USACERL TR 97/58

SR '

BandWidth

SMC

f

n

'

1/3octave

SMC

f

n

(60sec/min) [Eq B11]

Figure 3b Time Positive Negative Difference Percentage

Cycle Peak Peak of Max Diff

(#) (sec) (g) (g) (g) (%)

1 2.12 0.369 -0.472 0.841 69%

2 2.42 0.393 -0.771 1.164 95%

3 2.46 0.448 -0.771 1.219 100%

4 2.54 0.355 -0.496 0.851 70%

5 2.62 0.322 -0.588 0.91 75%

6 2.7 0.339 -0.452 0.791 65%

7 2.82 0.276 -0.382 0.658 54%

8 3.34 0.282 -0.483 0.765 63%

9 3.42 0.383 -0.265 0.648 53%

10 4.68 0.301 -0.318 0.619 51%

11 4.8 0.514 -0.139 0.653 54%

12 4.88 0.47 -0.692 1.162 95%

13 4.96 0.126 -0.499 0.625 51%

14 9.54 0.317 -0.299 0.616 51%

Table B1. Calculation of strong motion cycles for 12.2 hz SDOF oscillator

at 2% damping subjected to the El Centro earthquake record.
USACERL TR 97/58 141

Appendix C: Fragility Test Support Motion

Filtering and Integration

Accelerometer data recorded at the equipment attachment locations and on the

equipment were processed to obtain plots of velocity versus time. This required

that the raw data be filtered and integrated as defined below. (Note that these

steps were not needed for the bushing test data presented in Chapter 4.)

Data Filtering

The measured signal from accelerometers is expressed in terms of voltage. These

data are converted to engineering units by multiplying it by the accelerometer's

calibration factor (in g's/volt) and dividing it by the amplifier’s gain factor set in

the data acquisition system for that particular channel at the time the data was

recorded. The voltage data will include certain levels of noise from various

sources (e.g., line current at 60hz, 120 hz etc.). Normally this noise is fairly small

relative to the measured response if the gains have been set properly. The gain

for each channel is normally set as high as possible to achieve maximum

resolution in the recorded data while ensuring that the recording limits are not

exceeded. For the fragility tests conducted at USACERL, a very wide frequency

range was used, which means that the gains had to be set to measure the

relatively large accelerations at higher frequencies while minimizing the relative

magnitude of noise at the lower accelerations at lower frequencies.

Understanding the nature of the recorded data is important to guiding the use of

appropriate filtering procedures.

One advantage of narrow band sine-sweep fragility testing is the knowledge of the

frequency content at any point in the time history. Filtering is facilitated by this

in that response outside of the 1/3 octave band (+/- 1/6 octave about the center

frequency) is known a priori to be noise. Ideally a 1/3 octave band pass filter (+/-

correction factor for singularity at the cutoff frequency) would be applied to the

time history of the response, matching the center frequency. Since the capability

of a continuously varying filter was not available at the time, the record was

divided into four discrete frequency ranges to isolate regions of consistent noise.

Appropriate band pass filters were then applied to each region. Table C1 and

USACERL TR 97/58 143

compromises were made between the numerical rigor and computational

practicality in deciding the number of filtering ranges.

A problem arises when there is suspected error of the same frequency content as

known to exist in the time history because there is no way to filter out the noise

without destroying the valid signal. Knowing the magnitude of the noise at other

frequency ranges it could be assumed that the noise maintains that level in

unfilterable region of the record. One could attempt to apply a suitable

attenuation to the fourier coefficients in that frequency range of the time history,

but such a method was not employed in this analysis. For the present work, the

simplifying assumption was made that in regions where noise and valid signal

overlap, the true signal would be of significantly greater magnitude than the noise

so as to self-limit the induced error. For example, low-frequency noise (2 Hz) was

found in higher frequency regions at an amplitude in physical units of 0.25g, while

the true signal was at an amplitude of similar magnitude. Clearly, in this range,

filtering was necessary to avoid significant error. However, in the low-frequency

region of the record where the application of a 2 Hz filter would not be possible,

magnitudes were of the order of 5g.

Thus, if the 2 Hz noise is still 0.25g in this range, its impact on the overall error

is relatively small.
144 USACERL TR 97/58

Appendix D: Development of Single Degree

of Freedom (SDOF) Oscillator

Envelopes

The purpose of the CEFAPP is to define the levels of motion at which equipment

fails across a broad frequency range. These levels can be defined in terms of

support motion spectral amplitude or response spectral amplitude (the example

in Chapter 4 uses response spectral amplitude). The CEFAPP support motion is

a narrow-band random signal with a center frequency that shifts across the

desired range. An envelope representing spectral support motion, related to the

peaks of this signal is developed by calculating the response of damped SDOF

oscillators that cover the frequency range of the test signal (Appendix B). The

magnitude of this envelope at the frequency of equipment failure is then used as

the definition of support motion magnitude (spectral support motion) that caused

failure at that frequency. The purpose and method of defining support motion in

this way is described below.

Methodology and Assumptions

It is assumed that the equipment being analyzed is responding to the input

motion as an SDOF system. Sustaining the appropriateness of this assumption

may require more complex equipment assemblies to be reduced to simpler

components suitable to a SDOF model.

For the fragility data to be useful in a general sense, a basis for comparison is

needed to extrapolate fragility test results to records of expected site support

motion (i.e., seismic or shock). However, these site records will generally be in the

form of a time history, with the frequency content not being known apriori at

discreet times in the record as it is for the fragility test records. The site record

is thus subjected to the response spectrum analysis for a determination of its

frequency content.
USACERL TR 97/58 145

T '

X

Y

'

k

2 % (Tc)2

(k&mT

2

)

2

% (cT)

2

'

k

2 %(2Bfc)2

(k&(2Bf)

2m)

2

% (2Bfc)

2

. [Eq D1]

The basis for comparison now becomes the response spectrum analysis of the

fragility record and the site record. Two modifications were required of the

response spectrum analysis, as discussed below.

Octave Marching

Given the narrow-band nature of the random sweep input (1

/3 octave) it would not

be consistent to apply the entire fragility record as input to each of the SDOF

systems of the response spectra. Ideally, each SDOF system would only receive

as input that part of fragility record within ± 1/6 octave of its frequency. As a

model less demanding in terms of computerization, the fragility record was

marched through one octave at a time, applying each octave as input only to those

SDOF systems that would have been subjected to that frequency range during the

test procedure. The rationale for this is that lower-frequency input early in the

record could not have excited a high-frequency failure later in the fragility testing,

so any high-frequency failures that occurred were caused only by the highfrequency input at the end of the record. However, in a traditional response

spectrum analysis the maximum response of the high-frequency SDOF systems

may be controlled by the low-frequency input. Octave marching mitigates this

problem. Octave marching is only applied to the fragility input record; there is no

need for it to be applied to the site records.

Damping

For compatibility between the amplitude of equipment capacity defined by the

failure data and the demand defined by design or analysis procedures it was

desired to have magnitudes from the response spectrum analysis of the same

order as the magnitudes of the fragility test signal. In other words, it was desired

to have the ratio of response (X) to input (Y) as close as possible to unity. This

was accomplished by using a damping ratio of 50% in the response spectrum

analysis. The purpose of this is understood easiest by considering

transmissibility. Transmissibility (T) of a damped SDOF oscillator is illustrated

in Figure D1 and expressed as

The transmissibility when the excitation frequency equals the SDOF undamped

natural frequency with 50% damping is 2. Transmissibility is determined from

the ideal steady-state response of an SDOF oscillator to harmonic support motion.

A smaller response is achieved in the narrow band tests conducted here because

the sweep rate does not allow a steady-state response and the excitation is not
146 USACERL TR 97/58

harmonic. For the narrow band random sweep tests it was found that 50%

damping returned magnitudes of comparable values to the recorded signal,

effectively enveloping the support motion across the frequency range of the test

(see Figures 6a through 6n). If later work determines that a different sweep rate

is to be used, an investigation would be needed to determine what level of steadystate response is being excited and thus the appropriate artificial damping for

calculating the envelopes. Care must be taken if the damping is too high to

account for the resulting offset between natural and damped frequency. Critical

damping of 50 percent was applied to the response spectrum analyses for both the

fragility and validation (seismic and shock) records.

These modified response spectra are generated for all fragility records that

produced unique failures. The frequency and spectral magnitude of all failure

points are then assembled into a failure envelope. Finally, this failure envelope

is used for comparison with the response spectrum (with appropriate damping) of

the site records to determine if they contain any failure critical frequency content.

For the seismic validation tests, the Lucerne seismic record was subjected to the

response spectrum analysis to determine its frequency content. The strongest

peaks of the spectrum were located at 2 Hz and 12.5 Hz. A power spectrum

analysis was also run on the portion of the Lucerne record running from 9.2 to

10.2 seconds (failure was documented at 10.2 seconds). The power spectra also

had a strong peak at 12.5 Hz, but showed little frequency content at 2 Hz. It was

thus assumed that the 12.5 Hz peak in the response spectra corresponded to the

failure. A similar procedure was used with the shock verification test. However,

in using the power spectrum analysis to determine which peak of the shock

response spectra was appropriate for defining failure, the entire record was used

(as opposed to a particular time interval of the record). This was required by the

short duration of the shock test, and the resulting inability to define a discrete

time in the record at which failure occurred. The power spectra of the shock

record had a very strong peak near 11 Hz, reinforcing the selection of the

maximum peak of the response spectra (11.1 Hz) to define the frequency at which

failure occurred. There is thus an important difference in the selection of the

response spectra peaks for the seismic and shock tests. For the seismic test we

were able to validate the selection of the failure point from the response spectrum

that was run over the entire test with a power spectrum that was run over only

a limited range of the record (and thus an independent and distinct spectrum from

the response spectrum). The shock record loses that distinction between the two

spectra by calculating them both over the entire record.

Response spectra developed based on time history analyses of a building should

be generated by subjecting SDOF oscillators with 50% damping to the entire
USACERL TR 97/58 147

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

f/fn

X/Y

50% Critical Damping

equipment support location time history predicted motions. These response

spectra may then be compared with equipment fragility in the same manner as

described for the NEHRP-based response spectra.

Figure D1. SDOF response (X) over harmonic support motion (Y).
148 USACERL TR 97/58

Abbreviations and Acronyms

APSD acceleration power spectral density

CEFAPP CERL Equipment Fragility and Protection Procedure

CERL (U.S. Army) Construction Engineering Research Laboratories

FEMA Federal Emergency Management Agency

FIR finite impulse response

HP high pass

LVDT linear variable differential transformer

NEHRP National Earthquake Hazards Reduction Program

PE probability of exceedence

PL performance level

SDOF single degree of freedom

SMC strong-motion cycle

SR sweep rate

TESS Triaxial Earthquake and Shock Simulator

TRS test response spectra

TVA Tennessee Valley Authority

USGS U.S. Geological Survey

USACERL U.S. Army Construction Engineering Research Laboratories
USACERL TR 97/58 149

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