METHODOLOGY FORMITIGATION OF SEISMIC HAZARDS

IN EXISTING UNREINFORCEDMASONRY BUILDINGS

PHASE I

S. A. Adham

R. D. Ewing

March 1978

Prepared under

National Science Foundation Contract No. C~AEN77~19829

AGBABIAN ASSOCIATESEI Segundo, California

I

I q

Methodology for Mitigation of Seismic Hazards in Existing,Unreinforced Masonry Buildings, Phase 1

_c .~""

S~~"tOl

REf?ORT DOCUMENTATION" PAGE

"Title and Subtitle

l,-REPORT NO.

NSF/RA-7801312.

7. Alilhor(s)

'S.A. Adham R.D. EwinB. Performing Organization Rept. No.

!a. Performing Organization Name and Address 10. Project/Task/Work Unit No.

Agbabian Associates'El Se gundo, Cali forn i a 90245 11. Contract(C) Or Grant(G) No.

(C) AEN7719829(G)

14.

13. Type of Report & Period Covered12. Sponsoring Organization Name and Address

Applied Science and Research applications (ASRA)National Science Foundation1800 G Street, N.W.

. Washington, DC 205501-------"-----.:-------------.--------------------1.-

15. Supplementary Notes

1----------------_..--~---~ - - -- -·----~-----------I·1fi.Abstract(Limit:200words) A multiphased program is initiated to develop a methodology for the

_mitigation of seismic hazards in existing unreinforced masonry (URM) buildings. Thepresent research, part of Phase 1, identifies trends in the seismic response of thecomponents of URM buildings and determines what studies and testing are necessary toarrive at a methodology that can be used nationwide. The response of plywood,diagonal-sheathed, and straight-sheathed diaphragms, represented by lumped-mass mathe-·mati cal models, was studied. Experimental data on static loading and unloading wereused. Both local and distant earthquake ground motions were used as inputs. The re­sults show a strong dependence of the diaphragm response on the long-period content ofthe input. The response of masonry walls subjected to in-plane earthquake groundmotion was also studied. The analytical results show that the model used can reasonablypredict the response of the wall as a function of its height-to-width ratio and of thestiffness of the supporting soil. The report evaluates methods for selecting earth­quake ground-motion input at a site in the United States and describes analysis methods,that can be used to determi ne the response of URM buil dings to earthquake forces.

U:.Document Analysis a. Descriptors

'Earthquakes£arthquake resistant structuresSeismology

Mathematical modelsEarth movementsMasonry

Hazards

OPTIONAL FORM 272 (4-77)(Formerly NTlS-35)Department of Commerce

See Instructions on Reverse

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'b. Identifiers/Open-Ended Terms

;;~eismic hazards.;,Vnrei nforced masonry (URM)':'C,,~>:~',

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R-7815-4610

ACKNOWLEDGMENTS

This research effort has been supported by the National Science

Foundation under Contract No. C-AEN77-19829. The support is gratefully

acknowledged.

Primary contributors to this work were R.D. Ewing, Principal

Investigator, and S.A. Adham, Project Engineer. Staff members from

Agbabian Associates who also supported the work were H.S. Ts1ao, K.T. Dill,

and E.M. Dombourian. J.D. Radler edited the final report, and M.S. Agbabian

and R.W. Anderson contributed suggestions throughout the program .

.. .I I I

R-7815-4610

SUMMARY

Existing unreinforced masonry (URM) buildings are considered the

largest single earthquake hazard today. Nevertheless, no nationally accepted

structural engineering standards provide guidelines for retrofitting these

buildings to improve their earthquake resistance. The National Science

Foundation has therefore initiated a multiphased program to develop a

methodology for the mitigation of seismic hazards in existing URM buildings.

The present research, part of Phase I, has concentrated primarily

on identifying trends in the seismic response of the components of URM

buildings; and on determining what studies and testing are necessary to

arrive at a methodology that can be used nationwide.

The response of plywood, diagonal-sheathed, and straight-sheathed

diaphragms, represented by lumped-mass mathematical models, was studied.

Experimental data on static loading and unloading were used. Both local

and distant earthquake ground motions were used as inputs. The results

show a strong dependence of the diaphragm response on the long-period content

of the input.

The response of masonry walls subjected to in-plane earthquake

ground motion was also studied. The analytical results show that the model

used can reasonably predict the response of the wall as a function of its

height-to-width ratio and of the stiffness of the supporting soil.

The report evaluates methods for selecting earthquake ground-motion

input at a site in the United States and describes analysis methods that

can be used to determine the response of URM buildings to earthquake forces.

This part of Phase I, combined with the interrelated studies of two

other investigators, lays a foundation for the more specific experimental

and analytical studies recommended for Phase I I.

iv

Section

R-7815-4610

CONTENTS

2

INTRODUCT ION . . . . . . . . .

1.1 Statement of the Problem

1.2 Purpose and Scope of Research Program.

1.3 Summary of Results

1.4 Report Organization .....

PRIOR STUDIES OF MASONRY BUILDINGS.

1-1

1-1

1-31-4

1-5

2-1

CONSiDERATION LEADING TO CHOICE OF DESIGNEARTHQUAKE AND RELATED BUILDING CAPABILITY.

3

3.1

3.2

3.3

3.43.53.63.73.8

Introduct ion

Earthquakes .

Earthquake Prediction ..

Modes of Earthquake Damage

Earthquake Threat to Buildings

Design Earthquake Event .•\

Earthquake Input Criteria. . •..

Procedure Outl ined by ATC-3 (Ref. 36) forSpecification of Earthquake Ground Shakingand Definition of Seismic Hazard Index

3-1

3-1

3-1

3-33-33-63-9

3-10

3-12

4 SEISMiC ANALYSIS OF UNREINFORCEDMASONRY BU ILD INGS .. . • 4-1

4.1 Methods of Analysis. . . • . 4-1

4.2 Analysis Models. . . . • • . 4-4

4.3 Adequacy of Current Analysis Assumptions.. 4-6

5 EXAMPLE ANALYSES OF ROOF DIAPHRAGMS AND MASONRY­WALL ROCKING DUE TO EARTHQUAKE EXCITATION 5-1

5.1 Analysis of One-Story Building with Wood-Diaphragm Roof Supported on Masonry Walls 5-1

5.2 Analysis of In-Plane Masonry-WallRock i n9 .

v

5-28

Section

6

7

Figure

2-1

2-2

2-3

2-4

2-5

2-6

CONTENTS (CONTINUED)

CONCLUSIONS OF PHASE I STUDY ANDRECOMMENDATIONS FOR PHASE I I STUDY.

6.1 Conclusions of Phase I Study

6.2 Recommendations for Phase I I Study

REFERENCES . . . . .

ILLUSTRATIONS

Typical Transverse Section Used for Analysis-­Symmetric Building .........•

Plan View of Second through Thirteenth Floor ofCondominium--Asymmetric Building.

Masonry Bed-Joint Triplet Specimen and Fixture

Masonry Panel Specimens and Loading Members

Panel Shear Test ..

Diagonal Compression Test

R-7815-4610

6-1

6-1

6-2

7-1

2-3

2-4

2-5

2-6

2-8

2-8

2-7 Diagonal Compression Test:Distribution on the Planes

Principal Stressy = 0 and x = 0 2-3

2-8

2-9

2-10

2-11

3-1

Failure Envelope for Zero Head Joint NormalStress . . . .. ....

Biaxial Strength of Concrete

Typical Panel Dimensions

Types of Shear Walls

Fault Types

vi

2-9

2-9

2-10

2-10

3-2

Figure

3-2

3-3

3-4

3-5

3-6

3-7

3-8

4-1

5-1

5-2

5-3

5-4

5-5

5-6

5-7

5-8

ILLUSTRATIONS (CONTINUED)

Comparison of Richter Scale Magnitude Vs.Equivalent Energy of TNT .

Generation and Transmission of Seismic Waves

(Reference 36)

Effective Peak Acceleration Map

Effective Peak Velocity Map

Average Acceleration Spectra for Different SiteConditions .....

Normalized Spectral Curves Recommended for Usein Building Code. . . .. . ....

Types of Mathematical Models of Structures

One-Story Unreinforced Masonry Building with aWood Di aphragm Roof . . . .

Diaphragm/Wall Configuration and ModelConsidered in Example Analysis.

Lumped Parameter Model (4 Segments--Model 1)

Lumped Parameter Hodel (8 Segments--Half Model,Model 2) • . . . . . . . . . ...

Cyclic Load Deflection Relations atApproximately Constant Deflection

Repetitive Loading at 360 and 720 PLF(12 x 60 ft diaphragm sheathed with 1/2 in.plywood) .

Idealized Load Deflection Relations Used inDiaphragm Models of This Study .....

Response Spectrum of San Fernando Earthquake,9 February 1971: Castaic Old Ridge Route,Comp N69W .

vi i

R-7815-4610

3-4

3-5

3-13

3-15

3-16

3-17

3-18

4-5

5-3

5-4

5-5

5-6

5-3

5-9

5-10

5-14

Figure

5-9

5-10

5-11

5-12

5-13

5-14

5-15

5-16

5-17

5-18

5-19

5-20

5-21

ILLUSTRATIONS (CONTINUED)

Response Spectrum of Imperial Valley Earthquake,18 May 1940: E1 Centro Site, Imperial ValleyIrrigation District, Comp SOOE ........•

Absolute Displacements at Midpoint of DiaphragmModels, Cases 1, 2, 3 . . . . .. . .....

Comparison of Absolute Displacements at Hidpointof Diaphragm Models, Cases 4, 5, 6 .

Comparison of Absolute Displacements at Midpointof Plywood Diaphragm Models, Cases 4 and 8 ...

Comparison of Acceleration Time-HistoryResponses at Midpoint of Plywood DiaphragmModels, Cases 4 and 8 .

Comparison of Absolute Displacements at Midpointof Plywood Di aphragm t10de 1s, Cases 7, 8, and 9 .

Comparison of Acceleration Time-HistoryResponses at Midpoint of Plywood DiaphragmModels, Cases 7 and 9 .

Comparison of Absolute Displacements at Midpointof Plywood and Straight-Sheathed DiaphragmModels, Cases 9 and 11 .

Comparison of Absolute Displacements at Midpointof Plywood and Straight-Sheathed DiaphragmModels, Cases 10 and 12 .

Masonry Wall and Supporting Foundation

Lumped-Parameter Wall Model Considered in Wall-Rocking Analysis .

Soil Spring Characteristics

Comparison of Absolute Displacements of Wall,Case 1 . • . . . . . . . . . . . . . . . . . .

vi i i

R-7815-4610

5-15

5-17

5-19

5-20

5-21

5-22

5-24

5-25

5-27

5-29

5-30

5-32

. 5-36

Figure

5-22

5-23

5-24

5-25

Table

5-1

5-2

5-3

5-4

ILLUSTRATIONS (CONCLUDED)

Lifting of Two Bottom Corners of Wall, Case 1

Comparison of Absolute Displacements of Wall,Case 3 .. . .. .

Lifting of Two Bottom Corners of Wall, Case 3

Comparison of Absolute Displacements of Top ofWall for Cases 1, 2, and 3 .

TABLES

Stiffness of Roof Diaphragm Used in the PresentAna 1ys is. .

Summary of Diaphragm Analysis Results

Lumped Mass Model Prope~ties for SelectedHID Ratios .

Summary of Wall-Rocking Analysis Results

Ix

R-7815-4610

5-37

5-39

5-40

5-41

5-11

5-13

5-34

5-35

R-7815-4610

SECTION 1

INTRODUCT ION

1.1 STATEMENT OF THE PROBLEM

Un~einforced masonry (URM) construction has been widely used

throughout the United States. The majority of such buildings existLng today

were constructed more than 50 years ago, some before the turn of the century.

Evaluation of overall damage from high intensity earthquakes indicates that

existing URM buildings constitute the greatest single-hazard category.

Concern for the safety of these structures in seismically active regions has

been 'increasing as public agencies and the private sector become more

conscious of the potential hazards when such structures are subjected to

earthquake shaking and of the potential liability of injury or loss of life.

The socioeconomic implications of property damage and the resulting disruption

and dislocation are also significant cause for concern.

It was hoped that normal attrition would slowly reduce the hazards

presented by the existing URM buildings. In recent years, however, it has

become apparent that an increase in the salvaging and retrofitting of

existing URM buildings for further use has slowed the attrition rate of

these hazards.

Some of the existing URM buildings have suffered earthquake damage.

Others, experiencing an Identical Intensity of shaking, have been unscathed.

As a result, governing agencies and the building owners differ considerably

in their opinions about the need for increasing the seismic resistance of

such structures.

The formulation of design methods and criteria is needed for

determining (1) which structures actually require hazard mitigation and

(2) what methods of retrofit should be used. Even In areas of the

United States where no mandatory regulations for earthquake protection

exist, the concern is rising for some definition of the minimum level of

1-1

R-7815-4610

protection in zones of differing seismic activity. The City of Long Beach,

California, passed an ordinance that requires evaluation of old concrete

masonry structures and regulation of new concrete masonry construction.

A preliminary survey of existing buildings in the City of Los Angeles

indicates that approximately 10,000 URM buildings need to be evaluated for

seismic hazards.

Research has been conducted on the strength and material behavior

of existing URM construction to develop a better understanding of variations

in strength and stiffness that can be expected in this type of construction.

Research on modeling masonry structures and determining their

dynamic response to high-intensity earthquakes is in its early stages.

Major efforts have been launched by several agencies to establish

criteria for seismic risk and seismic design input for different types of

buildings in various zones of the United States.

Full-scale tests of existing buildings under low-ampl itude vibrations

have been conducted. These tests are being extended to high-ampl itude vibra­

tions. An attempt is being made to correlate the results obtained by analyti­

cal model ing with the response of structures during large shaking tests or

actual earthquake events.

The National Science Foundation (NSF) has initiated a program to

develop methodology for mitigation of seismic hazards in existing unreinforced

masonry buildings. The overall objectives of this multiphase program are

(1) to evaluate the current state of the art for mitigating the seismic

hazards of existing URM buildings, (2) to develop a methodology for mitigation

of these hazards, (3) to evaluate the methodology, and (4) to conduct a

util ization plan for disseminating the information assembled by the total

program effort.

1-2

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1.2 PURPOSE AND SCOPE OF RESEARCH PROGRAM

In October 1977, three of the contracts awarded by the NSF for a

Phase I program were given to Agbabian Associates (AA), S.B. Barnes and

Associates (SB&A), and Kariotis, Kesler, and Allys (KK&A). With NSF's

concurrence, the three firms planned an interactive six-month effort to

fulfill the following tasks:

a. Evaluate the current state of the art for seismic-hazard

mitigation in existing URM buildings.

b. Conduct a nationwide survey of different ~ypes of existing

masonry construction.

c. Determine what studies and testing are necessary to arrive

at a methodology that can be used nationwide for mitigating

seismic hazards in existing URM buildings and to develop

structural and economic criteria for any'required retrofitting

of existing masonry buildings.

The three firms conducted weekly meetings to collaborate in all

studies conducted for Phase I. However, each firm assumed the prime responsi­

bility of some tasks. For example, SB&A developed an experimental and

analytical program for studying selected retrofit methods. KK&A categorized

types of existing URM construction in various seismic zones of the United

States, and investigated material properties, critical building components,

and current structural alteration methods. AA was primarily concerned with

the development of earthquake input ground motions, the selection of seismic­

response analyses methods, and the development of an experimental and

analytical program for studying static and dynamic behavior of critical

components of URM buildings.

Phase I has been essentially an exploratory program. The data

base resulting from this phase will guide the more specific experimental

and analytical work to be proposed for the Phase I I program.

R-7815-4610

1.3 SUMMARY OF RESULTS

During Phase I, the research effort has been primarily directed

towards identifying trends in seismic response of components of URM buildings

and identifying areas that need more experimental and analytical work, therefore

*warranting further studies. It was concluded that ATC-3 provides the

state-of-the-art tool for describing the ground shaking at various sites

in the United States. (However, an ensemble of time-history records, rather

than elastic response spectra, should be selected for sites to be studied

in Phase II of this program.) Earthquake ground-motion input at a site is

discussed and analysis methods used to determine the response of buildings

to earthquake forces are described. It was concluded that the STARS t computer

program should be used for this study.

The response of plywood, diagonal-sheathed, and straight-sheathed

wood diaphragms was studied using a lumped parameter model. Experimental

data on monotonic loading and unloading of wood diaphragms were idealized.

A hysteretic stress/strain relationship was included in the model and viscous

damping was added to the analyses of some cases. Local and distant earthquake

input ground motion were represented by the 1971 Castaic and 1940 El Centro

records, respectively. Both records were scaled to the 0.40 g level specified

for ground shaking in the Los Angeles area and were applied to the model.

The model is described in detail and the analyses results are discussed.

These example analyses show three particularly important trends.

First, the wood diaphragms have relatively long periods. Second, the response

of these diaphragms strongly depends on the long-period content of the input

earthquake motions. Third, straight-sheathed diaphragms tend to attenuate

earthquake motions, as compared to the plywood and diagonal-sheathed diaphragms.

~

"The Applied Technology Council's 1977 report Recommended ComprehensiveSeismic Design Provisions for Buildings.

tSTARS Is a lumped parameter computer program developed by Agbabian Associatesfor the dynamic analysis of nonlinear structural systems (User's Guide forSTARS Code~ R-6823-999, Agbabian-Jacobsen Associates, Los Angeles, 1969).

1-4

R-7815-4610

The response of masonry walls, supported on soil to in-plane

earthquake ground motions was studied using a lumped parameter model. Results

from the analyses, detailed in Section 5, show a particularly important

trend: walls with height-to-width ratios equal to or greater than 1, on

soft soil, would amplify the input earthquake motions.

Phase I represents only the first step in the development of a

general methodology for carrying out analyses and evaluation of various

components of existing URM buildings. Possible subsequent steps of Phase I I

are (1) selecting an ensemble of time histories for the analyses that

relate to ATC-3 standard spectra, (2) extending and refining the diaphragm

and wall-overturning analyses of Phase I, (3) conducting an experimental

program on diaphragms to include both pseudo-static and -dynamic input

(these tests would provide data for correlation with the results of the

analyses of Phases I and I I), (4) studying the effect of out-of-plane forces

on the response of URM walls of different height-to-depth ratios, (5) evalu­

ating the torsional capabil ities of diaphragms, and (6) applying the

methodology to a single and multistory URM building and evaluating the

results.

1.4 REPORT ORGANIZATION

This report is organized in seven sections. Section 2 summarizes

significant studies of masonry buildings. The consideration leading to the

choice of design earthquake and the related capabilities of the buildings

is given in Section 3. The analytical methods used to determine the response

of buildings to earthquake forces are given in Section 4. Example analyses

of diaphragms and masonry-wall rocking due to earthquake excitation are

given in Section 5. Conclusions reached from the Phase 1 study and recom­

mendations for a Phase I I study are given in Section 6. The report concludes

with the references listed in Section 7.

1-5

R-7815-4610

SECTION 2

PRIOR STUDIES OF MASONRY BUILDINGS

Ouring Phase I of this program, a brief review of prior studies

of masonry buildings was conducted to (1) evaluate the current state of

knowledge in this area, and (2) use this information in the planning and

development of the present research program including a Phase I I proposal

and utilization plan. Procedures and results from these studies are briefly

summarized in this section. Comprehensive surveys of the available literature

relevant to the mechanics of concrete masonry assemblies can be found in

References 1 and 2.

Two separate major research programs were recently conducted to

investigate the earthquake response of concrete-masonry buildings. The

first program was conducted as a consortium research effort under the

sponsorship of the National Science Foundation (NSF). The host institution

for this program is the University of California, San Diego (UCSD). Partici­

pating institutions during the first phase were San Diego State University,

Weidlinger Associates, and Agbabian Associates. The second program was

conducted at the University of Cal ifornia, Berkeley (UCB), and was jointly

sponsored by NSF and the Masonry Institute of America.

The prel iminary investigations that preceded the research program

at UCS0 included a study of two multistory concrete-masonry buildings,

constructed in San Diego County (Refs. 3,4). The purpose of the study was

to provide the predicted behavior of these buildings when subjected to

earthquake ground motions and to determine whether these structures would

experience severe damage if subjected to earthquake ground motion of a

strength consistent with that which could reasonably be expected to occur

during the planned life of the structure.

The first building had a relatively symmetric shape while the

second building was highly asymmetric. A large eccentricity existed between

the mass center and the center of rigidity of the asymmetric building. The

2-1

R-7815-4610

transverse section of the first building and the plan of the second building

are shown in Figures 2-1 and 2-2. All walls, with minor exceptions, were

constructed of 8-in. reinforced concrete masonry, generally fully grouted

up to the ninth floor.

A large-capacity digital computer program for two- and three­

dimensional analysis of structural systems using the finite element approach

was used to obtain the dynamic response of the two buildings to earthquake

excitation. The analysis results indicated that the structures are stiff

and walls would be subjected to several cycles of overstress. It was

concluded that these walls would be badly damaged and would probably collapse

if subjected to the seismic loads considered in the study. The results of

this study indicated that more research is needed to provide better under­

standing of the behavior of concrete masonry in highly seismic zones. The

study also indicated that some provisions of the present concrete masonry

codes should be carefully evaluated.

The UCSD program (Refs. 5 and 6) involved a series of laboratory

experiments designed to determine the linear and nonlinear behavior of

reinforced and unreinforced concrete masonry blocks and joints (i.e.,

triplets, Fig. 2-3), and assemblies of blocks (i.e., panels, Fig. 2-4). These

tests include static, quasi-static, and dynamic cyclic load histories and

are intended to yield data that can be used to identify failure modes in

concrete masonry and,to develop constitutive relations.

In this program, a biaxial panel test that provides a globally

homogeneous state of stress was developed. In this test, in contrast to

conventional test methods (Ref. 2), the determination of material properties

is not prejudiced by boundary constraint; further in contrast to the direct

methods (Ref. 1), extraction of biaxial failure states does not necessitate

a conjecture of isotropic linear elastic material behavior prior to macro­

cracking (Ref. 7). The test system shown in Figure 2-5 is capable of creating

simple shear deformation.

2-2

R-7615-4610

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R-7615-4610

UHINUHADING EDGEHBER

HYDRAULICISTONS

-i

~

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r ~r 'r ,IF

.. ~ ~~ ~ ....- --

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FIGURE 2-4. MASONRY PANEL SPECIMENS AND LOADING MEMBERS (Ref. 5)

2-6

R-7815-4610

The diagonal compression test (Fig. 2-6) is actually an indirect

biaxial test (Ref. 1). Under concentrated diagonal compressive loads, the

central portion of the specimen is subjected to a biaxial stress state, which

is reasonably uniform over a characteristic length (area). In this test,

the shear stress on the planes intersecting diagonals vanishes from symmetry.

Failure occurs by induced tensile stresses on the vertical plane of symmetry

(Fig. 2-7).

The curves in Figure 2-8 represent several macroscopic, analytical

failure models considered to date. The dotted curve, shown for batch 6,

is based upon the premise that failure occurs when a principal stress reaches

either the tensile strength or the compressive strength associated with a

uniaxial, 0 deg lay-up test. The solid curves result from the premise that

the failure envelope in principal stress space is linear in the tension­

compression zone, as illustrated in Figure 2-9 for plain concrete under

biaxial stress states. This model is seen to provide a more accurate

description of material behavior. The two solid curves in Figure 2-8 corre­

spond to estimated (from prism tests) compressive strengths, and measured

(from 0 deg lay-up panels) uniaxial tensile strengths for two groups of

specimens. Note that only two experiments are necessary for construction of

this failure model: (1) the uniaxial tensile strength and (2) the uniaxial

compressive strength. The dashed curve represents a modification of the

solid curve for batch 6 to account for the anisotropy discussed below

(Ref. 7). Agbabian Associates participated in the first phase of the work

at UCSD and contributed to the experimental program and analytical studies

(Ref. 6).

The program at UCB (Ref. 8) involved a series of quasi-static and

dynamic tests on double-piered elements (Fig. 2-10). These elements provide

the primary shear resisting capacity for multistory reinforced-masonry

buildings. Understanding the earthquake behavior of these elements would

assist in developing a more realistic model of an entire perforated shear

wall and, in addition, will aid in understanding the behavior of the coupled

2-7

R-761S-4610

!!MMM

WWWW

FI GURE 2-5. PANEL SHEAR TEST (Ref. 7)

Pdt

~2.5 -<. 0 xa h

2.0 '>-t

1.5Pd

a/i-1.0 0. 707Pd Pd

7 =0.5

at = 2iit

x/h0.4 0.8

6 -a /r2

5

a/i- 4

32

~HYDRAULIC 1a1/,r

PRESS y/h00 0.4 0.8

FIGURE 2-6. DIAGONAL COMPRESSIONTEST (Ref. 7)

FIGURE 2-7. DIAGONAL COMPRESSION TEST:PRINCIPAL STRESS DISTRIBUTIONON THE PLANES Y = 0 AND x = 0(Ref. 7)

2-8

R-7615-4610

A MEANS, BATCH 6• MEANS, BATCHES 1-5

----- I NOEPENDENT TENS I LE, COMPRESS I VE STRENGTHS

------- LINEAR VARIATION OF TENSILE, COMPRESSIVE STRENGTHS

---- MODI FI CATION FOR ANISOTROPY

-200 400r·-----. .. __ -30

0-400 SHEAR STRESS, PSI

0;' '-'-

-10~ -/ 30°

/--. / 20°I ../"-100

-1600 -1400 -1200 -1000 -Boo -600 -400 -200 0 200

NORMAL STRESS, PS I

FIGURE 2-8. FAILURE ENVELOPE FOR ZERO HEAD JOINT NORMAL STRESS (Ref. 7)

0"1

f cu

---t---+--+---+--+-·---0.2

-0.8 -0.6 ~-0.2-\ 0'2.

--16fI"----<-. 0 ..~~-"7""'--~--0.2\ '

I (j~-Hf------ ,\~ .---:,f--~--<.?'J,. I

,0 Ii

FIGURE 2-9. BIAXIAL STRENGTH OF CONCRETE (Ref. 7)

2-9

14'-8"

CONNECTION TOTHE ACTUATORS3-'" 10

VERTICAL REINFORCEMENTIN THE JAMOS

R-761S-4610

MATERIAL: HOLLOW CONCRETE BLOCKS 6" WIOE • 0" HIGH. 16" LONG .

. FIGURE 2-10. TYPICAL PANEL DIMENSIONS (Ref. 8)

oooDo

VERTICALCANTILEVER DDDD

c:::J c:::J c:::J CJ

oj--tu 0 0c::J- ~c::J c::J c:::::J

D cn'-o-bo 0'0-0

PERFORATED SHEAR WALL

COUPLEDSHEAR WALL

FIGURE 2-11. TYPES OF SHEAR WALLS (Ref. 8)

2-10

R-7815-4610

and cantilever shear walls (Fig. 2-11). The variables included in these

tests are the frequency of load appl ication, the quantity and distribution

of reinforcement, the vertical bearing stress, and partial grouting. The

ultimate strength, shear mode failure, combined shear and flexure modes of

failure, full and partially grouted, horizontal and vertical reinforcement,

and ductility of these piers were also investigated. It was found that

partial grouting produces elastoplastic force deflection for piers failing

in shear mode. It was also observed that piers which failed in the shear

mode had pseudostatic ultimate strength less than the corresponding dynamic

strength. Piers that failed in the flexural mode had pseudostatic ultimate

strength greater or almost equal to the corresponding dynamic strength.

It was also found that stiffness increased significantly by increasing the

bearing stress. It was concluded from this work that the ultimate shear

strength of masonry assemblages, and the validity of determlning the allowable

UBC strength as a function of the ultimate compressive strength, f', of am

prism must be further evaluated.

A program for testing of half-scale models of typical single-story

masonry dwellings has been completed at UCB. The objective of the program

was to determlne design and construction requirements for such structures in

Seismic Zone 2 of the United States. Shaking table tests were performed

on these models to accomplish this objective. The project was supported

by the Department of Housing and Urban Development.

Currently, a collaborative research program is being supported

by the National Science Foundation to study structural identification, which

includes both damage assessment and system identification. Several dynamic

experiments will be performed on the EERC shake table at UCB, and these test

data will be analyzed for damage assessment and system identification at

Purdue University and UCB, respectively.

2-11

R-7815-4610

The behavior of masonry panels framed by reinforced-concrete

members under alternating loads was studied by Esteva (Ref. 9). Both sol id

and hollow 3 m x 3 m panels were subjected to in-plane loads. These loads

were app1 ied in an alternating form along each diagonal, up to 70 cycles

and reaching strains as high as 0.03 in./in. Elastic, cracking, and post­

cracking behaviors-were studied. Stress/strain curves were developed.

The structural performance of masonry walls under compression and

flexure was studied by Fatta1 and Cattaneo (Ref. 10). Prisms and walls of

brick, concrete block, and composite brick and block masonry construction

were tested under various combinations of compressive and transverse loads.

Constitutive relations for masonry were developed from test results. The

report shows that prism strength can be predicted on the basis of linear

behavior at failure. It was also shown that wall strength can be predicted

on the basis of prism strength when an appropriate allowance is made for

the effect of wall slenderness on sectional capacity.

Mayes and Galambos (Ref. 11) conducted a study of an existing

full-scale contemporary reinforced-concrete building with infi1led brick

walls in St. Louis, Missouri. The test building was an approximately

40 ft x 40 ft square eleven-story tower structure. The building was sub­

jected to large amplitude dynamic excitation. The effect of this excitation

on the behavior of this building was observed. The work consisted of

(1) survey of material and dimensional properties of the building, (2) small

amplitude dynamic excitation to determine the dynamic characteristics of

the structure as it existed before the large amp1 itude tests, (3) large

amplitude dynamic tests to study the change of dynamic characteristics as the

building was progressively damaged. The results indicate that there were

large changes in the period of the building in most of the modes. The

largest changes occurred in the first translational modes. The changes in

the period associated with the large amplitude tests were permanent. The

changes in mode shapes associated with the large changes in period were

generally small. The most significant changes were in the first translational

mode. There was a significant increase in damping as the input force level

increased.

2-12

R-7815-4610

Blume, et al. (Refs. 12, 13) performed a structural dynamic

investigation of 15 school buildings subjected to simulated earthquake

motion. The study included detailed consideration of the short-period

range of the earthquake spectrum. The study concluded that major elements

of school buildings such as roof or floor diaphragms should be designed so

that natural periods of such elements are 0.15 sec or less in order to avoid

dangerous response to peak spectral values, which generally occur at around

0.25 sec. However, these results are limited to ambient vibrations under

low amplitude forcing functions. Lower frequencies and longer periods would

be expected during the inelastic response of the building to actual intensive

earthquake motions.

A dynamic test program was conducted on an old school building by

Rea, et al. (Ref. 14). The building had three basic modes of vibration

that have been designated transverse, longitudinal, and flexure of the roof

diaphragm. The resonant frequencies of transverse and longitudinal modes

ranged from 7 to 10 Hz, and the associated damping capacities from 3% to 4%.

The resonant frequenci es of the fl exure modes of the roof diaphragm ranged

from 6 to 10 Hz and the associated damping capacities from 1% to 3%. These

tests are also I imited to ambient vibrations and would overestimate the

frequencies of the diaphragms during an intensive earthquake shaking.

Static tests of full-scale lumber and plywood sheathed diaphragms

were conducted by several investigators (Refs. 15 to 28). The series of

test programs conducted by Stillinger (Ref. 22) included lumber-sheathed

and plywood sheathed diaphragms 20 ft x 60 ft in size in order to determine

the strength and stiffness at various load levels. The summary of test

results indicates that the strength and stiffness of roof diaphragms can

be appreciably influenced by altering any of the test variables included

in this testing program. However, these tests did not include a load

reversal cyclic loading and unloading.

2-13

R-7815-4610

The previous discussion indicates that most of the research

programs have been directed toward studying masonry for new construction.

Research programs for mitigation of earthquake hazard in existing

unreinforced-masonry buildings are meager and still in the early stages.

The survey conducted in this study revealed that there is a large

number of diaphragms of wood construction (girder-planking system) in older

existing unreinforced-masonry buildings. The effectiveness of these dia­

phragms is an important consideration to how the building is modeled and

analyzed. The response of the supporting masonry walls and foundation wall

to in-plane seismic forces needs further evaluation.

No data are available on the dynamic behavior of diaphragms

under earthquake loading. Low amplitude testing results of full-scale

buildings would not necessarily provide adequate information on the dynamic

properties of these buildings under intensive earthquake excitations.

2-14

R-781S-4610

SECTION 3

CONSIDERATION LEADING TO CHOiCE OF DESIGN EARTHQUAKEAND RELATED BUILDING CAPABILITY

3. 1 INTRODUCT ION

This section provides background information on earthquake hazards

and the current methods for selecting design earthquake motions for structures.

3.2 EARTHQUAKES

Earthquakes are normally caused by the release of stored energy

during sudden displacement in the earth's crustal rock along a specific

fault or by rupture of the rock (Fig. 3-1). This sudden motion of the crustal

rock generates stress waves that propagate outward from the fault length

along which the energy was released J resulting in an earthquake. It is the

ground shaking induced by the passage of the stress wave that causes much

of the earthquake damage J not the actual surface rupture of the fault.

Faults are considered active or potentially active according to

evidence of past geologic activity. Also J an earthquake can occur along

a fault that may have been permanently inactive J or a new fault may be

produced. An example of this is the fault that generated the February 9J 1971

San Fernando earthquake. Few geologists knew of its existence in the

San Gabriel Mountains behind Los Angeles until it ruptured J registering

6.4 to 6.6 magnitude on the logarithmic Richter scale. Parts of the

mountain were vertically displaced eight feet. There was severe ground

shaking in the surrounding area J lasting 10 to 12 sec. The earthquake

resulted in the death of 64 persons; 1000 buildings were demolished or badly

damaged J including 3 hospitals; 5 highway overpasses collapsed; and utilities

were disrupted. It is interesting to compare this earthquake with the

8.3 magnitude earthquake that destroyed San Francisco in 1906. The energy

released in the 1906 earthquake was 350 times the energy generated by the

3-1

R-7815-4610

NORMAL FAULT

LEFT LATERAL FAULT(STRIKE-SLIP)

REVERSE FAULT

(a)

FAULT LINE

LEFT LATERAL NORMAL FAULT(LEFT OBLIQUE NORMAL FAULT)

LEFT LATERAL REVERSE FAULT(LEFT OBLIQUE REVERSE FAULT)

FIGURE 3-1. FAULT TYPES (Ref. 29)

R-7815-4610

1971 San Fernando earthquakes. Figure 3-2 shows the variation of earthquake

magnitude with equivalent energy release expressed in tons of TNT, comparing

the energies released by well-known earthquakes, as well as those released

by nuclear weapons.

3.3 EARTHQUAKE PREDICTION

Earthquake-prediction technology in the United States has acceler­

ated in recent years as more data have been acquired from an expanding

network of instrumentation along active faults, such as is shown in Figure 3-3.

Predictions for the Pacific Coast states, principally Alaska and California,

are being emphasized, since they are especially vulnerable to earthquakes

and related disaster. However, nearly every state in the nation faces some

degree of risk from future earthquakes. Because of limitations on available

moneys to support earthquake-prediction research, it has been necessary to

restrict fault-monitoring activity to only a few locations along active and

'potentially damaging faults.

3.4 MODES OF EARTHQUAKE DAMAGE

Modes of failure associated with seismic events include ground

shaking, ground failure, and water flooding.

3.4.1 GROUND SHAKING

Ground shaking is probably the most damaging effect of an earth­

quake because such a large area is subjected to the shaking.

3.4.2 GROUND FAILURE

Ground failure Is the result of seismic activity on earth materials

and includes landsl iding, surface rupture, liquefaction, and compaction and

subsidence.

a. Landsliding is a common geologic process normally associated

with hilly or mountainous terrain and depends on the inabil ity

R-7815-4610

I­z:I-

X 10

...... .....-:-:-:

1 MEGATON H-BOMB

EL CENTRO

4 5 6 7 8 9 •RICHTER SCALE OF MAGNITUDE

KERN COUNTY (1952)

SAN FRANCISCO (1906)

SAN FERNANDO (1971)

LONG BEACH (1933)HIROSHIMA ATOM BOMB

3

SAN FRANCISCO

FIGURE 3-2. COMPARISON OF RICHTER SCALE MAGNITUDE VS.EQUIVALENT ENERGY OF TNT (Ref. 30)

3-4

CAUSATIVE FAULT

R-7815-4610

FIGURE 3-3. GENERATION AND TRANSMISSION OF SEISMIC WAVES(Adapted from Ref. 31)

3-5

R-7815-4610

of a slope of soil or rock to resist moving downhill. Earth­

quakes can trigger sl ides in areas prone to landsl iding,

depending on the stabil ity of the slope. This will be influ­

enced by rock-type and geologic structure; slope gradient,

precipitation, or moisture penetration: and ground shaking

from earthquakes.

b. Surface rupture (faulting, fissures, cracking, and fracturing)

normally occurs in close proximity to the fault zone as the

result of a seismic event on these faults.

c. Liquefaction is the sudden loss of strength of soils under

saturated conditions, due to earthquake shock. It involves

a temporary transformation of material into a fluid mass.

d. Compaction and subsidence of low-density alluvial material

can result from ground shaking, depending on the physical

properties of the material.

Landsliding could cause serious building damage due to foundation

failure. Liquefaction may cause building foundations to settle or slide.

Compaction of material may cause settlement of the foundations.

3.4.3 FLOODING

Flooding is a potential earthquake hazard at some sites, should

hillside water reservoirs above the sites fail as a result of ground shaking

or ground failure.

3.5 EARTHQUAKE THREAT TO BUILDINGS

3.5.1 EARTHQUAKE DAMAGE

The 1971 San Fernando earthquake occurred on the fringe of the

very large metropolitan area of Los Angeles and provided the first really

3-6

R-7815-4610

comprehensive test of modern U.S. building code provIsions. It occurred

also within the boundary area of a large network of strong-motion accelero­

graphs. These are instruments developed for derivation of engineering data

rather than of seismological data. These instruments (more than 250 in

number), installed in buildings and on the ground, recorded in this one

earthquake more useful data on t~e parameters of strong ground motion and

facil ity response to this motion than the total of all records previously

made by such instruments worldwide.

Seismograms from the San Fernando earthquake indicate a background

acceleration level of from 0.35 to 0.5 g, with a maximum spike of accelera­

tion at one location of more than 1.0 g. Coupled with this high level of

ground acceleration, large ground displacements and surface faulting occurred.

The time duration of violent ground motion lasted only from 10 to 12 sec,

whereas in a magnitude 8.0+ earthquake, it would approximate 30 to 40 sec

in the epicentral area.

3.5.2 EARTHQUAKE-RESISTANT DESIGN

Building codes intend to provide minimum requirements for lateral

force resistance to prevent building collapse under the conditions of the most

probable severe earthquake to which the structure would be subjected.

The damage experienced during the 1971 San Fernando earthquake

demonstrated that, in general, modern structures designed according to the

minimum requirements of the building codes received only architectural damage

in areas where the accelerations were 20% g or less. There was minor-to­

appreciable structural damage in the 20% to 30% g range, and the damage to

buildings of minimum design varied from appreciable damage to collapse in

the area of very strong shaking. Had the shaking endured longer, as it

would have in a larger earthquake, the damage would have been more severe

and more modern structures would have collapsed.

3-7

R-7815-4610

The San Fernando earthquake experience leads to the conclusion

that the building codes of the time could not have been expected to produce

a uniform structural performance or earthquake resistance in all buildings

because of the many variables that influenced design such as architectural

plan, structural system, and engineering judgment. In addition, the qual ity

of design and construction differs greatly from one building to another.

Many of the studies and reports of the San Fernando earthquake have concluded

that improvements should be made in seismic code requirements relating to

building design and construction. Most West coast code agencies and other

advisory and regulatory bodies have already revised their code requirements

or are currently in the process. For example, the 1976 edition of the

Uniform Building Code and the 1974 Recommended Code of Practice of the

Structural Engineering Association of California incorporate new earthquake

design provisions more stringent than those of previous codes.

Building codes that have been revised since the 1971 San Fernando

earthquake are now requiring the use of considerably higher coefficient

values for computing lateral forces. These new values represent lateral

forces that are closer to actual measured earthquake motion loadings deter­

mined from measured records. The direction is also toward the requirement

for an analysis of building response that considers the time variation of

ground motion to validate maximum equivalent static design coefficients.

The importance of the critical "use)) or "occupancy" of a building is now

being recognized in the seismic code requirements. Also, more attention

is being paid to nonstructural building components and systems.

R-7815-4610

3.6 DESIGN EARTHQUAKE EVENT

3.6.1 INTRODUCTION

The earthquake criteria for earthquake-resistant design discussed

in this phase of the study is based on the design philosophy that

a. For moderate intensity earthquakes, I ittle structural damage

should result, but some damage to nonstructural elements In

the building would be allowable.

b. For very high Intensity earthquake ground motion, some struc­

tural damage could occur, but there should be no possibil ity

of structural collapse. These very high intensity earthquake

ground motions would be generated by the design earthquake

event.

3.6.2 DEFINITION OF DESIGN EARTHQUAKE EVENT

A design earthquake event specifies the maximum values of certain

characteristic parameters that may reasonably be expected to occur over the

design life of the struture, or, in the case of a seismic safety plan for

existing buildings, over the remaining I ife of the structure. This design

earthquake generally specifies the maximum ground displacements, velocities,

and accelerations that are likely to occur. Some measure of the time

duration of the ground motions is also included. An important tool used

to represent design earthquake motions is the response spectrum, which

actually represents the peak response of a series of simple (single-degree­

of-freedom) structures to given ground motions. Each earthquake ground-motion

history produces a unique spectrum, and the design spectrum is usually a

composite average, or envelope, of such spectral records that are appropriate

for the site of the proposed facility. Development of criteria for a specific

site generally requires consideration of major geological features; tectonics

for the site, i.e., the types, locations, and arrangement of faults; seismic

R-7815-4610

history including records of intensity and ground motion, if available; and

local soil conditions. Engineering judgment and, in some cases, ground­

motion calculations, provide the basis for selecting the required design

earthquake event.

3.6.3 GOVERNING EARTHQUAKE CONDITIONS AT THE SITE

Earthquake threat to a site may come from different conditions.

In many cases, two earthquake conditions govern the design at the site. The

first corresponds to a nearby earthquake. The second condition corresponds

to a distant event. Frequency content and duration of the record vary from

one condition to the other, and one condition may be more detrimental to a

certain building than the other condition.

3.7 EARTHQUAKE INPUT CRITERIA

3.7.1 INTRODUCTION

The earthquake input ground motion at the site that corresponds

to the design earthquake event can be estimated by different methods. The

geologic features that affect the ground shaking at the site can be related

to the source mechanism, source site transmission path, and local soil

conditions (Ref. 32). These factors are considered in the following methods.

3.7.2 SOIL-RESPONSE ANALYSES

This analysis requires constructing a mathematical model for the

soil profile at the site. Well defined soil properties obtained from the

geotechnical investigation of the site are used to define the material prop­

erties of the model. A selection is made of an ensemble of rock-outcrop

motions for use as input to the computations. This ensemble is selected at

the site to correspond to the intensity level that corresponds to the design

earthquake event developed for the site. The ensemble of rock-outcrop

3-10

R-7815-4610

motions is selected based on the fol lowing: (1) the motions must be taken

from accelerograph stations that are underlain by rock materials; (2) the

earthquake magnitude, source mechanism, and causative-fault distances should

be as close as possible to that of the design earthquake event; and (3) where

possible, the peak acceleration of the rock-outcrop records should be reasonably

close to the peak acceleration specified for the design earthquake event.

The SHAKE code (Ref. 33) is used for the analysis of soil profiles

that can be modeled as infinite horizontal layers. However, for incl ined

layers, a two-dimensional analysis should be used. The results of soil

response analyses are used to develop composite response spectra for the site.

The mean and mean-plus-one standard deviation spectrum can be developed from

these results.

3.7.3 SiTE-MATCHED RECORDS

Site-matched records (Ref. 34) should be selected to represent

conditions comparable to those of the actual site, based on consideration of

such features as magnitude, distance, local soil conditions, tectonic

province, and fault mechanism. These records are scaled to the criterion

for the site, and composite spectra corresponding to the mean statistical

levels can be developed.

3.7.4 SEED-UGAS-LYSMER SPECTRUM SHAPES

Seed et al. (Ref. 35) have developed standardized spectrum shapes

developed from statistical analyses of 106 spectra normalized to a O-period

acceleration of 0.10 9 and categorized according to local soil conditions of

the various accelerograph sites.

3.7.5 COMPARISON OF SPECTRA DEVELOPED BY DIFFERENT METHODS

The spectra developed by using site-soil response analyses, site­

matched ensemble, and the Seed-Ugas-Lysmer method are compared and a final

design spectrum can be selected for the site.

3-11

R-7815-4610

3.8 PROCEDURE OUTLINED BY ATC-3 (REF. 36) FOR SPECIFICATION OF EARTHQUAKEGROUND SHAKING AND DEFINITION OF SEISMiC HAZARD INDEX

3.8.1 INTRODUCTION

Two earthquake ground shaking regionalization maps were developed

by ATC-3. These maps are based on the following: (1) the design lateral force

and the period of a structure should take into account the distance from antici­

pated earthquake sources; (2) the probability of exceeding the design ground

shaking should, as a goal, be roughly the same in all parts of the country;

and (3) the regionalization maps should not attempt to delineate microzones.

Any such microzonation should be done by experts who are familiar with

localized conditions.

3.8.2 DESIGN EARTHQUAKE GROUND MOTIONS

ATC-3 defines the "design ground shaking" for a location as the

ground motion that an architect or engineer should have in mind when he

designs a building that is to give proper protection to life safety. A

smoothed elastic response spectrum for single degree-of-freedom system

(Ref. 37) was proposed.

3.8.3 GROUND MOTION PARAMETERS

The intensity of design ground shaking is represented by two para­

meters. These parameters are called the effective peak acceleration (EPA)

and effective peak velocity (EPV). The EPA is proportional to spectral

ordinates for periods in the range of 0.10 to 0.5 sec, while the EPV is

proportional to spectral ordinates at a period of about 1 sec. The constant

of proportionality (for the 5% damped spectra) is set at a standard value

of 2.5 in both cases.

For a specific actual ground motion of normal duration, EPA and EPV

can be determined as illustrated in Figure 3-4. The 5% damped spectrum for

the actual motion is graphed and fitted by straight lines at the periods

mentioned above. The ordinates of the smoothed spectrum are then divided by

2.5 to obtain EPA and EPV.

>­I-

uo...JlJJ:::>

...Jo::x:0::::I­ulJJa..

,V')

~

o...J

0.1

SEPA = _a_

2.5

5EPV = -:::f-

2.5

0.5

LOG PE RI 00, SEC

R-7815-4610

FIGURE 3-4. (Ref. 36)

3-13 '

3.8.4 DESIGN ELASTiC RESPONSE SPECTRA

R-7815-4610

The EPA and EPV maps are shown in Figures 3-5 and 3-6 (see Ref. 36

for a complete description.of these maps) and have four contours whose associ­

ated values of EPA or EPV are as follows:

Contour

1

2

34

EPA EPV

Map Map 2

0.05g 1.5 in./sec

0.10g 30.20g 6

0.40g 12

For simpl icity in appl ication and to avoid the need for interpre­

tation between contours, the maps for both EPA and EPV have been divided along

county boundaries into seven levels of motion (Ref. 36). A seismic hazard

index, which reflects the ability of different types of construction to

withstand the effects of earthquake motions, was also included.

Spectral shapes representative of the different soil conditions

discussed in Reference 36 were selected on the basis of statistical studies

(Fig. 3-7). These spectra were simplified to a family of three curves by

combining the spectra for rock and stiff soil conditions leading to the

normalized spectral curves shown in Figure 3-8.

Recommended ground motion spectra for 5% damping for the different

map zone levels are thus obtained by multiplying the normalized spectra

values shown in Figure 3-8 by the values of effective peak ground acceleration.

Soil profile factors were also derived for the above response spectra.

ATC-3 represents a .state-of-the-art workable tool for describing

the design ground shaking as a smoothed elastic response spectrum. However,

the smoothed elastic response spectrum is not necessarily the ideal means for

3-14

~I~ \1

1

~OTE

:CO

~TOU

RSSH

OW~ALUE

Of

A1

fI(jU

RE3-

5·

~?\

~.j

-".)

..-

EffE

CTI~

EPE

AK

AC

CEL

ERA

TiO

NM

AP(R

ef.

36)

~I

--.I a:>

-"

\11 I ~ 0'"

-" o

FIGU

RE3-

6EF

FECT

IVE

PEAK

VELO

CITY

MAP

(Ref

.36

)

NO

TE:

CONT

OURS

SHOW

VALU

EO

FA 2

::u I ......

ex> ..... V1 I

.j::

­C

J' ..... o, "

....,..

......."

\/

\.......

.~

""'.O

\.r'

j'--"\,~....

.<.

.-jl!.

·--

-'_

,'7

,.'.\

.,>

.•.l'~

..-

--(--J

"L.-.

~\

..,~~-.~

r...

j

0.2 o.

10

.05

EFFE

CTIV

EPE

AKVE

LOCI

TY

12IN

./SE

C6

IN./S

EC

3IN

./SE

C1.

5IN

./SE

C

VJ I .... CJ'

R-7815-4610

4r----r----r-'----r-------,---~---_TOTAL NUMBER OF RECORDS ANALYZED: 104SPECTRA FOR 5% DAMPING

S 3z!<o a::j::UJ«....Ja:: UJUJU....JUUJ « 2u QU z«::::l....JO«a::a::(,:,I-.~u::::l::::~Vl -

~~

SOFT TO MEDIUM CLAY AND SAND - 15

j DEEP COHESIONLESS SOILS (>250 FT)STIFF SITE CONDITIONS «150 FT) ­ROCK - 28 RECORDS,

~-.........-~~

RECORDS- 30 RECORDS31 RECORDS

3.02.52.0

0~ --..1 _.L. _I_ _'__ __J"__ .....J

0.5 1.0 1.5

PERIOD, SEC

FIGURE 3-7. AVERAGE ACCELERATION SPECTRA FOR DIFFERENT SITE CONDITIONS

3-17

R-7815-4610

4r----~----.----__r---_r----r__--____,

:z0

:z !;( 30- c:::!;( UJ~

c::: UJUJ U~ UUJ <Cuu Cl<C :z 2:::>~ 0<C c:::c::: (.:J

I-u ~UJ :::>0.. ~(/') -

X<C~

. SOFT TO MEDI UM CLAYS AND SANDS

!(SOIL CONDITION 1)

DEEP COHESIONLESS OR STIFF CLAY SOILS(SOIL CONDITION 2)

~----r-~-------, " ROCK AND STIFF SOIL CONDITIONS'" (SOIL CONDITION 3)

'. .' .... ............... .................. .... ......................

-- ...... _--- -------

2.52.01.5PERIOD, SEC

1.00.50l-- -J. ....1- -'- ..l- .L- --'

o

FIGURE 3-8. NORMALIZED SPECTRAL CURVES RECOMMENDED FOR USE IN BUILDING CODE

3-18

R-7815-4610

describing the design ground shaking. A significant deficiency of the

response spectrum is that it does not by itself say anything about duration

of the shaking. It might be better to use a set of four or more accelera­

tion time histories, whose average elastic response spectrum is similar to

the design spectrum. This approach may be desirable for buildings of special

importance or for research studies of the seismic response of buildings.

3-19

R-7815-4610

SECTION 4

SEISMiC ANALYSIS OF UNREINFORCEDMASONRY BUILDINGS

This section describes the analytical methods that can be used

for the seismic analysis of unreinforced masonry (URM) structures and how

these methods can be used to estimate the response of critical elements.

In addition, the adequacy of the analysis methods and corresponding modeling

assumptions are dIscussed.

4.1 METHODS OF ANALYSIS

The analytical methods that are available for the seismic analysis

of URM structures can be divided into three basic categories:

• Static

• Pseudodynamic

• Dynamic

In each of these categories, either linear or nonlinear analyses can be

performed. A description of these methods and some important subcategories

are given in the following subsections.

4.1.1 STATIC ANALYSIS

The response of URM structures to seismic environments is a dynamic

phenomenon, and the use of static methods is only approximate. In the case

of reinforced masonry, building codes have established criteria for the magni­

tude and distribution of seismic forces to be appl ied in static analyses.I

Although the magnitude of these forces is specified as a function of the

structural frequencies, they are only an approximation of the inertial forces

that would result in a dynamic environment.

4-1

R-7815-4610

However» in some cases» relatively stiff or rigid structures

will respond as a rigid body and can be analyzed using equivalent static

forces. In the case of a stiff structure sited on a good soil» the struc­

ture will respond with the free field, and equivalent static forces can be

determined from the structural weight and the peak ground acceleration.

For a stiff structure sited on soft soil» some ampl ifications of the peak

ground acceleration can be expected due to the rocking response.

In general» static analyses are useful only if the dynamic

response of the structure is known.

4.1.2 PSEUDODYIlAHIC ANALYSIS

Pseudodynamic analyses are approximate methods and should be

viewed as a refinement of the equivalent static method. In these analyses,

simple mathematical models are employed to estimate the dynamic response

of the structure. Inertial loads determined from the response are appl ied

as equivalent static loads.

4.1.3 DYNAMIC ANALYSES

There are three subcategories of dynamic analyses methods» as

given below:

1. Response spectrum

2. Modal time history

3. Direct integration time history

Each of these methods can be utilized with one-» two-» or

three-dimensional mathematical models. All three methods can be used for

linear elastic models. However, nonlinearities can be treated in an approxi­

mate way with the first two methods. When nonlinearities are important»

the direct integration method must be employed.

4-2

R-7815-4610

In the response spectrum method, the seismic input is defined in

the form of a response spectrum. The input response spectrum defines the

peak responses to a specific seismic or loading environment of several

linear single-degree-of-freedom (SDOF) oscillators with various values of

equivalent viscous damping. The peak responses are defined as the relative

displacements, pseudorelative velocities, or absolute pseudoaccelerations.

However, the exact time at which the peak responses occur is not specified.

Based on a 1imited number of normal modes of the structure, the peak struc­

tural response in each mode can be obtained from the response spectrum. The

response of the complete structure is determined by combining the contribu­

tions from each mode. The peak modal responses do not necessarily occur

at the same instant of time, and the response spectrum does not provide

information on phase relationships. Accordingly, the complete structural

response is estimated by combining the peak modal responses in a probabi lis­

tie manner. Several procedures are available, such as--

• Square root of the sum of the squares (SRSS)

• Peak (or peaks) plus the SRSS of the rest

• Absolute sum

The procedure selected will depend on the modes obtained.

lent viscous damping can be included to simulate energy dissipation

account for nonlinearities in an approximate way.

Equiva­

and

The modal time-history analysis method uses a time history input

rather than a response spectrum. Based on a limited number of normal modes

of the structure, the structural response time history in each mode is

obtained by direct integration. The response time history of the complete

structure is determined directly by combining the contributions from each

mode. As in the response spectrum method, equivalent viscous damping can

be included to simulate energy dissipation and account for nonl inearities

in an approximate way.

4-3

R-7815-4610

The direct integration time-history method is the most general

method for the seismic analysis of structures. It provides the time­

dependent response to a time-history input. In this scheme, the numerical

integrations are carried out directly on the coupled set of simultaneous

differential equations of motion in the structural system1s physical

coordinates. This method allows for the inclusion of nonlinearities that

can be very important for URM structures.

4.2 ANALYSIS MODELS

A mathematical model is a mathematical representation of a struc­

tural system in terms of its significant characteristics. The type and

complexity of the model selected will depend on the response to be determined

and the importance of structural interactions. There is a wide range of

mathematical models that may be used to represent a structure:

• Simple one-dimensional cantilever beam models

• Two-dimensional frame and shear wall models

• Pseudo-three-dimensional building models

• Three-dimensional structural models

as shown in Figure 4-1. In addition, the soil can be included in each of

these models, either as one-dimensional spring elements or two- and three­

dimensional continuum elements.

Some typical mathematical models for the nonlinear analysis of

diaphragms and wall rocking are given in Section 5. These are very simple

lumped parameter models for the analysis of critical elements of a URM

structure. Depending on the information required, more complex three­

dimensional finite element models can be used.

4-4

~ 0/ ~7

(a) One-dimensional (b) Two-dimensionalsingle frame

RIGID DIAPHRAGM WITHNO OUT-OF-PLANEBENDING

<

/

CALCULATED STI FFNESS OFFLEXIBLE DIAPHRAGM ORRIGID LINK FOR RIGIDDI APHRAGM

A, a,

..

.A, &,.-

hllW ~~ ~!:' ~~

(c) Two-dimensionalmultiple frames Cd) Pseudo-three-dimens ional

(e) Three-dimensional

FIGURE 4-1. TYPES OF MATHEMATICAL MODELS OF STRUCTURES(Source: SEAOC, Electronic Computation Committee, SeismioAnaZysis by Computer~ Los Angeles, 1977.)

4-5

R-7815-4610

4.3 ADEQUACY OF CURRENT ANALYSIS ASSUMPTIONS

The review of the analytical methods and models indicate that the

response of critical elements can be predicted using finite element and

lumped parameter models. In general, the performance prediction of a URM

structure in a seismic environment will require nonl inear analyses, since

these structures are not expected to respond in the elastic range. The

adequacy of these analyses depend on the availability of data on the non­

linear characteristics of the various components of a URM structure.

Analysis of existing test data is necessary to develop criteria

for the nonlinear characteristics of several elements including piers, panels,

and masonry joints. Additional test data are necessary for the out-of-plane

characteristics of walls, the nonlinear properties of diaphragms, masonry

panel strength and stiffness, and anchorage characteristics.

Once these data are available, reasonable upper and lower bound

performance prediction of URM structures can be made using dynamic nonl inear

parameter and finite element models.

4-6

R-7815-4610

SECTION 5

EXAMPLE ANALYSES OF ROOF DIAPHRAGMS AND MASONRY­WALL ROCKING DUE TO EARTHQUAKE EXCITATION

This section represents results obtained by using the STARS computer

program for the analysis of two examples:

a. A simple one-story building with a wood diaphragm roof supported

on masonry walls. The purpose of these calculations was to

demonstrate (1) some basic phenomena and the potential effect

that the energy-absorption capacity of wood diaphragms will

have on the response of existing unreinforced masonry buildings,

(2) the effect that stiffening these diaphragms will have on

the response of masonry buildings to earthquake loading, and

(3) the usefulness of the. STARS computer program as a tool

for studying these effects.

b. In-plane masonry-wall rocking. The purpose of these calcu­

lations was to study (1) whether the wall would detach from

its supporting soil at the response levels used in this study,

(2) the relationship of the HID ratio and supporting soil

stiffness to the rocking of such walls, (3) the effect that

rocking will have on the response of these walls to seismic

excitations, and (4) the usefulness of the STARS computer

program as a tool for studying these effects.

These analyses were performed in close collaboration with the firms of

KK&A and SB&A.

5.1 ANALYSIS OF ONE-STORY BUILDING WITH WOOD-DIAPHRAGM ROOF SUPPORTED ONMASONRY WALLS

5.1.1 SYSTEM DESCRIPTION

The one-story building considered in the following calculations

consists of a wood diaphragm roof supported at four sides by 13-in. solid

5-1

R-7815-4610

masonry walls as illustrated in Figure 5-1. The uniform load of the roof

is assumed to be 30 lb/sq ft and the wall uniform load as 130 lb/sq ft.

The roof diaphragm is· modeled as a deep shear beam (Fig. 5-2a).

This beam is divided into a series of segments, as shown in Figures 5-2b

and 5-2c. The 100-ft-long masonry wall will crack when subjected to

shaking normal to its plane. Therefore, only its weight will be included

in the model.

For the present phase of the analysis the two end walls are assumed

rigid. Earthquake input motions are assumed to be transmitted from the

foundation level (Levels C and D) to the top of the end shear walls (Levels A

and B) without any modification (Fig. 5-2a).

The four-segment model is shown in Figure 5-3; the eight-segment

model is shown in Figure 5-4.

5.1.2 MATERIAL PROPERTIES

From full-scale tests on plywood diaphragms (Ref. 38) it appears

that for cycl ic monotonic loading, the deflection may be expressed by

where

~ = CWL (5-1)

~ = Midpoint diaphragm deflection in inches (Total deflectionis attributed to in-plane shear deformation.)

C = Flexibility coefficient

W = Total load in kips in diaphragm assumed uniformly distributedover diaphragm length

L = Diaphragm span in feet

Use of a single constant C to describe flexibility appears to be appl icable

for diaphragm span/depth ratios of 2 to 4.

5-2

13"

SOLI

DW

ALL

ta:

+~ +~ +~

I.-+~8

'w

10

0'

~;;:

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r-

AGM

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OFDIAPH~

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RNAT

IVES

CONS

IDER

ED:

+-•

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(1"

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8'I

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IGHT

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ITH

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R-781S-4610

System(a)

"O'~EARTHQUAKE I~

MOT ION AT A 1./ A

~t-x.)-A~ ~

/ C 'END ~A'" FOUNDATION WALL~

7 WE I GHT {PARAPET EARTHQUAKEEARTHQUAKE MOT I ON AT BMOTION AT C INCLUDED IN 1/2 WALL \..

DIAPHRAGM HEIGHT ~

MODEL D

~ FOUNDATION

~ EARTHQUAKEconfiguration MOTION AT 0

EARTHQUAKE INPU~TMOTIONS

A

EARTHQUAKEMOTIONS

~EARTHQUAKE INPUTMOTIONS

Four-segment diaphragm model

~ EARTHQUAKE INPUTMOTIONS

(c) Eight-segment diaphragm model AA9133

FIGURE 5-2. DIAPHRAGM/WALL CONFIGURATION AND MODEL CONSIDERED INEXAMPLE ANALYSIS

5-4

R-78l5-4610

!f---------------l001---------------1--r--

50'

~ ~ ~ ~ ~xl . x3 x4 Xs xl

0 EXTERNAL DOF

0 INTERNAL SPRI NG tJ + COMP, o-TENSION

6 INTERNAL DAMPER, + COMPo

FIGURE 5-3. LUMPED PARAMETER MODEL (4 SEGMENTS - MODEL 1)

R-7815-4610

!1f-----l0101-.--_o\I

1-- I.--__---Jl•••• +1 2 3 4 5

It.I

It.

0 EXTERNAL DOF

0 INTERNAL SPRING L::J+ COMPo o-TENSION

6 INTERNAL DAMPER 1+COMPo

0- TENSION

DISPLACEMENT GAGE

FIGURE 5-4. LUMPED PARAMETER MODEL (8 SEGMENTS - HALF MODEL, MODEL 2)

5-6

R-7815-4610

The plot on Figure 5-5 indicates that the diaphragm will cycle

at a constant deflection for repetitions of reloading. This is generally

confirmed by the plots of tests shown in Figure 5-6.

The simple ideal ized load deflection relation, shown in Figure 5-7,

describes a monotonically increasing loading curve in compression and an image

relationship in tension. The hysteretic curve indicates a permanent set of

0.5 ~., This ideal ization was included in the present analysis.

As illustrated in Figure 5-7, the data on plywood was presented

by the relation

t:. = 5 x 10-4 WL (5-2)

for

W = 5 kips

and

L 100 ft

f::. = 0.25 in.

If K represents the stiffness of the plywood diaphragm

K1= cr

or

K = 1

5 x 10-4 L

or

K = 20 kips/in.

5-7

R-7815-4610

30r------r--------,-------r------r-----.----...,

1. 751. 50

,/

//

//

//

1. 000.750.50

0L.- 4=---_-=-__....l..- ...1..- J..- l-- -'

a 0.25

20

10

5

25

IIIa..-~ 15

HIDPOINT DEFLECTION, IN.

FIGURE 5-5. CYCLIC LOAD DEFLECTION RELATIONS AT APPROXlt1ATELYCONSTANT DEFLECTION (Ref. 38)

5-8

~

- -~

80

0,ii'

12

345

6

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C1' o

R-7815-4610

For the four-segment model, the stiffness per segment is

Kk = q = 5 kips/in.

For the eight segment model

Kk = 8 = 2.5 kips/in.

A summary of material properties used for the diaphragms analyzed in this

study is given in Table 5-1.

TABLE 5-1. STIFFNESS OF ROOF DIAPHRAGM USEDIN THE PRESENT ANALYSIS

Stiffness/Segment, k,kips/in.

Diaph ragmRoof Stiffness, Model 1 Model 2

Diaphragm Load-Deflection Relation kips/in. 4 Segments 8 Segments

Plywood !J. = 5 x 10-4 WL 20 5 2.5

Diagonal !J. = 2.5 x 10-3 WL 4 1 0.5

Straight !J. = 10 x 10-3 \·JL 1 0.25 0.125

5-11

R-7815-4610

In addition to the hysteretic damping provided by the hysteretic

cycles of Figure 5-7, a 10% critical damping was used in the analyses of

some cases to account for viscous damping provided by the roofing materials

(viscous damping shown in Table 5-2).

5.1.3 INPUT MOTIONS

The intensity of ground shaking used in this study represents

the level of shaking expected in a highly seismic area such as Los Angeles.

Effective peak acceleration for such an area is 0.40 g (Ref.' 36). Two earth­

quakes can be specified to represent bounding conditions for the earthquake

shaking at the site. The first condition corresponds to a local earthquake

with high-frequency content. The second condition corresponds to a large

earthquake event centered some 40 miles from the site. This earthquake

would have a long duration and a wide band of dominant frequencies.

The N69W component of the 1971 Castaic record was selected for the

nearby event. The time history record was scaled to the 0.40 9 level and used

as the first earthquake input to the diaphragm analysis. The response

spectra for this record are shown in Figure 5-8.

The N-S component of the 1940 El Centro record was selected for

the distant event. The time history record was scaled to the 0.40 g level and

used as input to both diaphragm and wall-overturning models. The response

spectra for this record are shown in Figure 5-9.

For the diaphragm analysis, the critical orientation of earth­

quake input motions is shown in Figure 5-2. In this analysis, the scaled

time-history motions discussed above were applied directly at the ends of

the roof diaphragm (Levels A and B).

5.1.4 DISCUSSION OF RESULTS OF DIAPHRAGM ANALYSES

A number of parametric cases were run as summarized in Table 5-2.

Cases 1, 2, and 3 were subjected to the 1971 Castaic N69W component. A

5-12

\.n I

I.JJ

TABL

E5

-2.

SUM

MAR

YOF

DIAP

HRAG

MAN

ALYS

ISRE

SULT

S

Cal

cula

ted

Acc

eler

atio

nR

elat

ive

Pea

kC

ase

No.

of

Ear

thqu

ake

Mat

eria

lT

ype

of

Per

iod

at

Cen

ter,

Dis

plac

emen

tt

No.

Dia

phra

gmS

egm

ents

Input'~

Pro

per

tyD

ampi

ngT

,se

cg

at

Cen

ter,

In.

1Pl

ywoo

d1

.73

0.1

53

·9C

asta

ic2

Dia

gona

l19

713

.35

0.0

34

.2S

hea

thin

gN6

9WC

ompo

nent

3S

tra

Igh

t9

.30

0.01

6.5

Sh

eath

ing

4Pl

ywoo

d4

Ela

stic

Vis

cous

1.8

00

.20

6.2

EIC

entr

o

5D

iago

nal

1940

3.0

00

.06

7.4

N-S

Sh

eath

ing

Com

pone

nt

6S

traig

ht

9.3

00

.02

12

.0S

hea

thin

g

7Pl

ywoo

dE

last

icNo

2.8

00

.20

11

.0D

ampi

ng

8Pl

ywoo

dEI

ast

IcV

isco

us2

.80

0.1

410

.4

9Pl

ywoo

dEl

Cen

tro

Hy

ster

etic

Hy

ster

etic

3.0

00

.20

8.0

10Pl

ywoo

d8

1940

Hy

ster

etic

Hy

ster

etic

3.0

00

.12

10.7

'1'

N-S

&V

isco

us

11S

traJ

gh

tC

ompo

nent

Hy

ster

etic

Hy

ster

etic

10

.60

0.0

21

1.0

Sh

eath

ing

12S

traig

ht

Hy

ster

etic

Hys

tere

tic

11

.50

0.0

06

9.0

fS

hea

thin

g&

Vis

cous

:::..~

*Ear

thqu

ake

inp

ut

mot

ions

scal

edto

0.4

0g

peak

grou

ndaccele

rati

on

tRela

tiv

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akd

isp

lace

men

tsw

ere

calc

ula

ted

bysu

btr

acti

ng

the

abso

lute

inp

ut

dis

pla

cem

ent

from

the

abso

lute

peak

mid

po

int

dis

pla

cem

ent.

f30

-sec

reco

rdus

edfo

rca

ses

10an

d12

NO

TES:

3-s

ecre

cord

used

for

case

s1

and

21

5-s

ecre

cord

used

for

case

s3

thro

ug

h9

and

case

11.

AA

9070

;0 J

"-J

00 ..... \.n I .t:­

O"\

...... o

R-7815-4610

200

.,....................----""''-1 100

-+-~-¥---<,..L.--l 80

,~,..,.L.~~~=-..j60

20 20

uLLJ(/) 10 10........ 8 8:z

6 6

>-I-

4 4u0-JLLJ;:-

2 2

. I U1.J...w:w....J...l..w.l...:w....:......~u:u.LWu.LUliJl.u.JJ.W..Ll..u.L:u.ll..L..u..J-U.llJ.JI-W..1.U.J.llu.wJJ...l..LW..l-UJ.U..J..U.LU..u.u..w...uJ

.0406 .08 .1 .2 .4.6.8 I 2 4 6 8 10 20

PERIOD, SEC

FI GURE 5-8. RESPONSE SPECTRUM OF SAN FERNANDO EARTHQUAKE, 9 FEBRUARY 1971:CASTAIC OLD RIDGE ROUTE, COMP N69W (Damping values are 0, 2, 5,10 and 20 percent of critical--unscaled)

5-14

R-7815-4610

200

20

~-..,f.->"~ 100

-+-&,-~:....-l,.L---l80

~,."L--+----i>uL-~6 0

8 1042

20

uUJIn....... 10.z: 8

6>-I-u 40...JUJ:>

2

PERIOD» SEC

FIGURE 5-9. RESPONSE SPECTRUM OF IMPERIAL VALLEY EARTHQUAKE» 18 MAY 1940:EL CENTRO SITE» IMPERIAL VALLEY IRRIGATION DISTRICT» COMP SOOE(Damping values are 0, 2, 5, 10 and 20 percent of critical-­unsealed)

5-15

R-7815-4610

3.5 sec record was used for cases 1 and 2, whereas a longer record of 15 sec

was used for the longer-period diaphragm of case 3. The 1940 EI Centro

N-S component was used as input to cases 4 through 12. The length of the

record used for cases 4 through 9, in addition to case 11, was 15 sec. The

length of record used for cases 10 and 12 was 30 sec.

Both elastic and hysteretic material properties were assumed in

the analysis. Viscous and hysteretic damping were included in 11 cases, as

illustrated in Table 5-2. The results of the calculations are presented

in Table 5-2 and Figures 5-10 through 5-17. They are provided at the middle

of the diaphragm (DOF 4 in Fig. 5-3 and DOF 5 in Fig. 5-4). The relative peak

displacements shown in Table 5-2 are determined by calculating the maximum

difference between input displacements and the absolute displacements of the

midpoint of the diaphragm at the same instant of time.

The first set of results corresponds to cases 1 through 3. The

results from the diagonal-sheathing model (case 2) show response periods that

are longer than those of the plywood model (case 1), as was shown in Tab 1e5-2.

As a result, the peak acceleration at the middle of the case 2 diaphragm is

lower than that of the case 1 diaphragm (0.03 g vs. 0.15 g). However, the

relative peak displacement of case 2 is only slightly higher than that of

case 1 (4.2 in. vs. 3.9 in.), as illustrated in Figure 5-10.

The straight-sheathing diaphragm (case 3) has the longest period

among the three diaphragms studied (9.30 sec). Maximum acceleration of

0.01 g (Fig. 5-10) and relative peak displacement of 6.5 in. were calculated

at the mi dpo i nt.

The second set of results corresponds to cases 4 through 6 sub­

jected to the 1940 El Centro input motions with a longer duration (15 sec).

The results of case 4 indicate that the fundamental period is 1.80 sec,

about the same as case 1. The peak acceleration of 0.20 g is slightly

higher than the 0.15 g calculated for case 1. The major differences can

be seen in peak displacements for case 4 as compared to case 1. A peak

5-16

R-781S-4610

___ CASE 1 (PLYWOOO)

____ CASE 2 (OIAGONAL SHEATHING)

--- 6~P~TA~~~:~~~EMENT (AT ENOS

-2

-4o!------:;o:l.;.5,..--..,.Jl,no --'1-";.5,..----;;l2,"";;"O--.2-";.5,..----;;l3."";;"O--'3-";.5,..---74. 0

TIME, SEC

(a) Cases 1 and 2

12,----,----,------r---,---,...--"T"----,-----,

_.__ CASE 3 (STRAIGHT SHEATHING)

81-

I-z

~...~

~

~;;~

:J! -4 I-

-81-

'--'\/ .. \

.'-'" .I \./ "\ / .,/. i \

-

-

-120!----!-----+------!-----,!---~10:------:11::-2-----;!;-14---iI6TIME, ~EC.

(b) Case 3

AA9071

Relative peak displacements were calculated by subtracting theabsolute input displacement from the absolute peak midpointdisplacement.

FIGURE 5-10. ABSOLUTE DISPLACEMENTS AT MIDPOINT OF DIAPHRAGM MODELS,CASES 1, 2, 3

5-17

R-7815-4610

relative displacement of 6,2 in, is shown in Figure 5-11, This higher

displacement is attributed to the strong long-period content of the El Centro

record,

The response time-history for case 5 indicates that the period

of the system is 3,0 sec. The peak acceleration of 0,06 g is slightly higher

than the peak acceleration of case 2, associated with the Castaic input record,

The case 5 relative peak displacement of 7,4 in, (Fig, 5-11) is higher than

that of case 2, However, due to phasing of the response, the peak displacement

appears not much greater than that of case 4,

From the results of cases 1 through 5 and the results of the first

15 sec of case 6, it Is estimated that for case 6 the maximum acceleration

will reach around 0,02 g, The peak displacement is estimated to be 12 in.

(Fig, 5-11), which is the same as the peak displacement of input motions,

The third set of results corresponds to cases 7 through 10, Four

diaphragms of varying material properties and damping were analyzed, Fig-

ure 5-12 and Table 5-2 illustrate how the response of the diaphragm is

affected by increasing the number of segments in the diaphragm model, The

results of case 8 indicate that the second and third natural modes provide a

considerable contribution to the response, The 6,2 in, peak displacement of

case 4 was increased to 10,4 in. in case 8 by including the contribution of

the second mode (Fig. 5-12). This resulted in shifting the response to a

lower acceleration region, The contribution of the higher modes, particularly

the second mode, to the acceleration is minimal; and the final result was

a reduction in peak acceleration from 0.20 g for case 4 to 0,14 g for case 8

(Fig, 5-13), Therefore, the four-segment model behaves like a stiffer struc­

ture with a higher acceleration (0,2 g), shorter period (1.8 sec), and smaller

displacement (6.2 in,); whereas the eight-segment model performs like a more

flexible structure with a lower acceleration (0.14 g), longer period (2,8 sec),

and larger displacement (10,4 in,). It is also observed that the El Centro

input, with its strong long period content, when applied to the eight-segment

model, provides the most interaction with the periods of the plywood diaphragm

(Fig, 5-14),

5-13

16,

II

Ii

iI

II

12

_••

_CA

SE4

(PLY

WO

OD

)

__

__

__

CAS

E5

(DIA

GO

NA

LS

HE

ATH

ING

)

••••

••••

••••

••••

•CA

SE6

(STR

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HT

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EA

THIN

G)

INP

UT

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1940

ELCE

NTRO

N-S

(SC

ALE

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0G

)

~

­III"

.-

-4

""...... o 0"\

-8'

,1

11

I,

,-

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o2

46

810

1214

16

TIM

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SEC

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t.

::0 I "co U1 I~ 0

'

FIGU

RE5-

11.

COM

PARI

SON

OFAB

SOLU

TEDI

SPLA

CEM

ENTS

ATM

IDPO

INT

OFDI

APHR

AGM

MOD

ELS.

CASE

S4.

5.6

0

12I

II

IIIii

j

8

-0

-

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4(4

SEG

MEN

TS)

CASE

8(8

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MEN

TS)

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UT

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CENT

RO19

40N

-S(S

CA

LED

TO0

.40

G)

N ......

o (7\

-I

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!I~

120

24

68

1012

1416

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E,

SEC

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FIGU

RE5-

12.

COM

PARI

SON

OFAB

SOLU

TEDI

SPLA

CEM

ENTS

ATM

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INT

OFPL

YWOO

DDI

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ELS,

CASE

S4

AND

8

:::0 I

'J 00 .... \J1 I .t:­

O' .... o

12

.Iiii

II

i

-0

---

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4(4

SEGM

ENTS

)

CASE

8(8

SEGM

ENTS

)

-..... - -~

8

~

0 ~ N~4

1\t

/:j\!

\l\

.!\

!\/1

-..

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VI

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vIf

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\!

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t-~ .....

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co <:(

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1214

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C;0 I'-

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FIGU

RE5-

13.

COM

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SON

OFAC

CELE

RATI

ONTI

ME-

HIS

TORY

RESP

ON

SES

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IDPO

INT

OFPL

YWOO

DDI

APHR

AGM

MOD

ELS,

CASE

S4

AND

8

V1 I .r:­

0' .... o

12,

I,

II

Ii

ii

~. - -

tJ"

CASE

7(E

LAST

Ic)

CASE

8

CASE

9

INPU

TEL

CENT

RO19

40N

-S(S

CALE

DTO

0.4

0G)

-0

-

-+

--

8 -8

II

\J()'

00 .....

.0 0

'\

-12

'I

II

II

II

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02

46

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1214

16

.4

z - .II

Il- Z w 4 w u « ..

.JQ

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CR

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dis

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ng

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ab

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pu

td

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men

t.

FIGU

RE5

-14

.:CO

MPA

RISO

NOF

ABSO

LUTE

DISP

LACE

MEN

TSAT

MID

POIN

TOF

PLYW

OOD

.DI

APHR

AGM

MOD

ELS.

CASE

S7.

8.9

;:0 .I "<Xl ->

\J1 I

.j::

­

0'

-> o

R-7815-4610

When the diaphragm material is represented by hysteretic character­

istics, as shown in case 9, the structural response corresponds to contribu­

tions from a band of diaphragm frequencies, bounded by values related to

the slopes of the loading and unloading curves (Fig. 5-15). The period of

the diaphragm is lengthened from 2.8 sec (case 7) to 3.0 sec (case 9) for

the plywood diaphragm. Because of the combination of higher damping and

more frequency contribution to the response, the relative peak accelerations

are about the same for cases 7 and 9, as illustrated in Figure 5-16 (0.2 g).

However, the peak displacement for case 9 is 8 in., which is smaller than that

of case 7, due to the damping effect.

The difference between cases 9 and 10 is that the latter has

viscous damping in addition to the hysteretic characteristics. In addition,

case 10 was run to 30 sec, whereas case 9 was run for only 15 sec. The peak

acceleration for case 9 is 0.20 g as compared to 0.12 g for case 10. There­

fore, viscous damping appears to have a considerable effect on attenuating

peak accelerations in these diaphragms. The relative peak displacement for

case 10 is 10.7 in., compared to 8 in. for case 9 (Table 5-2). However,

case 9 may show higher displacements if run for an additional 15 sec.

For the straight sheathing diaphragm, the natural periods are

10.6 and 11.5 sec for cases 11 and 12, respectively. The effect of the

additional viscous damping in case 12 results in a reduction of the response

of the diaphragm from 11.0 in. for case 11 to 9.0 in. for case 12. The

peak acceleration of the midpoint is 0.02 g and 0.006 9 for cases 11 and 12,

respectively. These values indicate no significant changes in the peak

acceleration calculated for the four-segment model of case 6. The results

illustrate the considerable attenuation of peak acceleration that is pro­

vided by these relatively soft diaphragms. The shear force transmitted to

the ends of these diaphragms is reduced from 7.5 kips for the plywood

diaphragm (case 10) to 0.54 kips for the straight-sheathing diaphragm

(case 12).

5-23

, -",

__

_CA

SE7

(HA

ST

IC)

_+

_CA

SE9

(HY

STER

ETI

C)

r0 I

\I

I

\I

,I..

I

,\;

VV

812

0 ..... x4

NU W V

I.....

... :z - a

:z0

0 - ~ W .....I W

VI

UI

UN

<t:

-4~

VI

a:l <t:

-8

FIG

UR

E5

-15

.C

OM

PAR

ISO

NO

FA

CC

ELE

RA

TIO

NT

IME

-HIS

TO

RY

RES

PON

SES

ATM

IDP

OIN

TO

FPL

YWO

OD

01AP

HR

AGM

MO

DE

LS"

CAS

ES'

7AN

D9

'

-12o

24

68

TIM

E,

SEC

1012

14

I'.. "o CT\ ~

16

;;0 I

"'-J 00 ..... \.n I~ 0

'..... o

12.

ii

ii

ii

II

8

_._

CASE

9

--e-

CASE

11

INPU

TEL

CENT

RO19

40N

-S(S

CALE

DTO

0.40

G)

"-- - - ""

z4 1

[\i

.\"

re

/e["

~\

~l

A!\1

\i

•u

I~.

« ...J

\Jl

:lW·l~Y

/I N

""-4

\Y

.,}\J

l

-.~ \:

+I 4

" ,.....

-12'

0

II

I

0'1

02

4,

I«

68

II

1«

1012

1416

TI

ME,

SEC

Rela

tiv

ep

eak

dis

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en

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ng

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ab

solu

tein

pu

t·d

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en

tfr

om

the

ab

solu

tep

eak

mid

po

int

dis

pla

cem

en

t.

FIGU

RE5-

16.

COM

PARI

SON

OFAB

SOLU

TEDI

SPLA

CEM

ENTS

ATM

IDPO

INT

OFPL

YWOO

DAN

DST

RAIG

HT-

SHEA

THED

DIAP

HRAG

MM

ODEL

S,CA

SES

9AN

D11

;a i'-

J(X

)..... \J

l I 4:­

0' ..... o

R-7815-4610

A comparison of the response of the plywood and strai~ht-sheathed

diaphragms indicate that the periods of the latter are much longer, whereas

the peak accelerations are much lower. The peak displacements vary between

8 and 11 in. for both diaphragms (Figs. 5-16 and 5-17).

The above results indicate that the eight-segment model provided

a better representation of the response of the diaphragms. Addition of the

second-mode contribution resulted in a more intense response with longer

periods and larger displacements.

The results also indicate that the El Centro record, when compared

to the Castaic record, has a wider and stronger long-period content. There­

fore, this input was found to be more critical for studying the response of

the above diaphragms. However, the El Centro record has strong long-period

peaks and valleys. Therefore, its use must be substantiated by other records

with strong long-period content. The results also indicate that the viscous

damping effect of roofing materials reduced both the acceleration and the

displacement of the diaphragm

It is of interest to note that the results of this study indicated

diaphragm periods ranging from 1.73 sec for case 1 to 11.5 sec for the softest

diaphragm of case 12. These results are in contrast to those obtained by

Blume, et al. (Refs. 12, 13) and Rea, et al. (Ref. 14), where relatively

shorter periods ranging between 0.17 and 0.75 sec were obtained from low

amplitude testing of full-scale school buildings. This discrepancy is prob­

ably a result of the highly nonl inear character of these diaphragms, which

results in lengthening the periods of these diaphragms when they are subjected

to the input level of the 0.40 g scaled El Centro used in this study. There­

fore, the preliminary analysis conducted in this study would indicate that

stiffening the softer wood diaphragms may not improve the performance of

these diaphragms in highly seismic areas.

5-26

-8

Ln "o 0'\ «

-12

II

II

II

II

1«

o4

812

1620

2428

32TI

ME,

SEC

Rel

ativ

epe

akd

isp

lace

men

tsw

ere

calc

ula

ted

bysu

btr

acti

ng

the

abso

lute

inp

ut

dis

pla

cem

ent

from

the

abso

lute

peak

mid

po

int

dis

pIa

cem

ent.

FIGU

RE5-

17.

COM

PARI

SON

OFAB

SOLU

TEDI

SPLA

CEM

ENTS

ATM

IDPO

INT

OFPL

YWOO

DAN

DST

RAIG

HT-

SHEA

THED

DIAP

HRAG

MM

ODEL

S,CA

SES

10AN

D12

::0 , -.....I co -..

VI I

..J:;- ""-.. o

R-7815-4610

5.2 ANALYSIS OF IN-PLANE MASONRY-WALL ROCKING

5.2.1 SYSTEM DESCRIPTION

The wall considered in the following calculations is shown in

Figure 5-18. The wall is modeled as a rigid rectangular shear panel of

height H and width D (Fig. 5-19). The following assumptions are made in the

analysis.

a. Horizontal earthquake motion is applied to degree-of-freedom 1.

b. Wall is driven horizontally through the horizontal inter­

actor spring 11. This spring is tuned to a high frequency

so that it will transmit the ground motion to the base of

the wa 11.

c. Wall responds at degrees-of-freedom 2, 3, and 4.

d. Soil is represented as 10 one-way, bilinear, hysteretic

springs (i.e., compression only).

e. Output consists of wall motions at degrees-of-freedom 2, 3,

and 4, in addition to forces and deformation in the soil

springs, Nos. 1 through 10, and wall motions at the top and

bottom of the wall centerline.

Parameters used in the analyses are

H = 40 ft = 480 in.

t = 9 in.w

t f = 18 in.

p = 0.10 kips/ft2 = 100 lb/ft 2

HID = 0.25, 1.0, and 1.5

5-23

R-7815-4610

I' D -I --i r- t wI

~

r:t

H WALL

ks

-1.__ h~~~~~~~~1~~1~~1!~~~~~~~1~:~1~~~1~~~~!~~~~!~11~1~11~1~!~~!!11~~!1!I~~1~~~~~~~I~±l~~~:~~~!~~11~~1~!~1~~!1~!~1~1!~111~~1I~~1~~1~~I~}~:~~11~;~:~~~~~~m~1:1~1m~!~1~irlffiA ;.;~ ~tf

H = HALL HEIGHTD = WALL WI DTH

t = WALL THICKNESSw

tf

= FOUNDATION WIDTH

k = SOIL STIFFNESSs

H/D = 0.25 + 1.5

t /t f = 0.5 (t = 9 IN.)w wp = WEIGHT OF WALL = 100 LB/FT2

k =.100 to 800 PSI/IN.sn = DUCTILITY COEFFICIENT

FOR sal LS

FIGURE 5-18. MASONRY WALL AND SUPPORTING FOUNDATION

5-29

R-7815-4610

INPUTMOTION

DOF"

(0.-.-.

HORI ZONTALINTERACTORSP RI NG

50/20-----1Jo--~-7D/20----t

1------90/20-----1

3D/20----+-----l

WALL~

~--4~-D/10 (TYPICAL)

I

r---.. ---iDI-------I~DISpLACEMENT

~ v GAGE12.....-~

H

FIGURE 5-19. LUMPED-PARAMETER WALL MODEL CONSIDERED IN WALL-ROCKING ANALYSIS

5-30

R-781S-4610

Soi Is data for

k = 100 psi/in.s

and for

k = 800 psi/in.s

n = O.S

n = 0.0 (Fig. 5-20)

Inelasticity occurs at e = 1.0 in. and

The mass of the wall is calculated from the relation

The polar moment of inertia, J, of the wall is given by the equation

The soil-spring stiffness is calculated as follows:

k = 100 psi/in. n = 0.5s

k

H(*)100

K s 18 x 480 (O/H)= 10 t f • = '"'10 xs

4 (O/H) lb/in.K = 8.64 x 10s

5-31

R-7815-4610

F(+, CaMP.)

F /Iy

I III) n = 0.5, k = 100

I II 5

I ~~n = 0.0, k = 800s

I If.II e = 1.0 IN.

¥1y

ee

(+, COMP. )Y

BILINEAR HYSTERETIC SPRING (COMPRESSION ONLY)

K = INITIAL ELASTIC STIFFNESS, LB/IN.s

ks

• tf

• D/10

k = 100 TO 800 PSI/IN.s

F = YIELD LOAD (i.e., soil yield strength)y

n = DUCTILE COEFFICIENT FOR SOILS

FIGURE 5-20. SOIL SPRING CHARACTERISTICS

5-32

and for

ks = 800 psi/in. n = 0.0

R-7815-4610

K = 6.912.x 105 (D/H) lb/in.s

Table 5-3 provides properties of the lumped mass wall model for

three H/D rat ios.

The intensity of ground shaking used in the study of wall rocking

is the same as the intensity used earlier in this section for diaphragm

analysis. The N-S component of the 1940 El Centro record is scaled to 0.40 g

and used as input to the model. The first three seconds of the record were

used in the analyses. Damping was provided as viscous or hysteretic effects.

A 1% critical damping was considered for the vertical springs while a high

damping of 10% was specified for the sway spring.

5.2.2 DISCUSSION OF RESULTS OF WALL-ROCKING ANALYSES

A number of parametric cases were run as summarized in Table 5-4.

The case of a wall of H/D = 0.25 and k = 100 psi/in. did not result insany modification of the input motions. Therefore, this case was not pursued.

The results of case 1 indicate that for soft soils (k = 100 psi/in.) andsHID = 1.0, there is approximately 15% amplification of the motion at the top

of the wall (Displacement Gage 12). The motion of three points at the middle

line of the wall are plotted in Figure 5-21, which illustrates the change in

motion from the bottom of the wall (point 13) to the top of the wall (point 12).

This amplification is caused by the rocking and lifting of the two bottom

corners of the wall, as illustrated by the vertical displacements of springs

and 10 in Figure 5-22.

5-33

\.T1 I

W .r:-

TABL

E5

-3.

LUM

PED

MAS

SHO

DEL

PRO

PER

TIES

FOR

SELE

CTED

H/D

RATI

OS

H/D

0.2

51

1.5

0

D/H

41

0.6

6

D19

20in

.48

0in

.32

0in

.

M,

1b-s

ec2 /

in.

1658

414.

527

6.3

J,

lb-s

ec2 /i

n.

81.

592

x10

76

5.41

3x

107.

665

x10

K(o

fk

=10

0p

si/

in.)

,lb

/in

.5

44

3.45

6x

108

.64

x10

5.7

6x

10s

s

F(o

fk

=10

0p

si/

in.)

,lb

3.45

6x

105

44

8.6

4x

105

.76

x10

ys

K(o

fk

=80

0p

si/

in.)

,lb

/in

.6

6.9

12

x10

54.

608

x10

52.

765

x10

ss

F(o

fk

=80

0p

si/

in.)

,lb

66

.91

2x

105

4.60

8x

105

2.76

5x

10y

5

, -~ ;;0 I

-.....J c:>~ \.T

1 I .r:­

0'~ o

TABL

E5-

4.SU

MMAR

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WAL

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........ .. - -'"

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W V1

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all

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(3)

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(13)

(12

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Pea

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Pea

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if.

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atio

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atio

11

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00.

34-3

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0.44

1.10

0.24

0.3

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2.85

0.8

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3.75

1.15

21

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00.

05-3

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0.47

1.17

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50.

290.

0003

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51

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ampl

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31

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6.10

1.36

AA

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gpe

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ound

acce

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tio

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ngin

vert

ical

spri

ng

s--l

%

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ampi

ngin

sway

spri

ng

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%

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ed

isp

lace

men

tssh

own

inth

ista

ble

are

peak

ab

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CASE

1

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RE5-

22.

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ING

OFTW

OBO

TTOM

CORN

ERS

OFW

ALL,

CASE

1

R-7815-4610

The continuous rocking of the wall and lifting of the corners

resulted in a gradual buildup of response in the vertical direction, where

peak absolute displacement reached 0.24 in. while peak acceleration was

0.32 g (Table 5-4). However, the rocking displacements and accelerations

were very sma II due to the 1arge rotary inert ia that was associ ated wi th the

assumption of a 40 ft x 40 ft rigid wall.

The results of case 2 for HID = and k of 800 psi/in. indicates

that increasing the stiffness of the soil from 100 to 800 psi/in. created

very stiff supporting springs. No rocking, lifting, or amplifying of the

motion was observed. This indicates that, for such a model, input motions

are transmitted through the structure with virtually no change.

The results of case 3, where H/D was increased to 1.5 and ks

was held at 100 psi/in., indicate a larger lifting and higher amplification

than those reported for case 1. The response at the top of the wall (point 12)

indicate approximately 36% ampl ification, as illustrated by Figure 5-23. A

peak lifting of 1.70 in. is shown in Figure 5-24. The peak vertical dis­

placement was 0.47 in. while the peak vertical acceleration was 0.60 g.

Fi gure 5-25 ill us tra tes the effect that i ncreas i ng HID and k hass

on the response at the top of the wall (point 12). This comparison indicates

that large ampl ifications would be expected for higher H/D values associated

wi th soft soi 1 springs. I t should be emphasized that the rotational dis­

placements in the above three cases were very small and would indicate that

the rigid body mathematical model must be modified to include both internal

deformations and soil deformations. However, these prel iminary studies

indicate that the response of the vertical element of the selected representa­

tive building is strongly affected by the stiffness of the supporting soil

and the height to width ratio of the element. Further research with a model

that includes wall deformations is needed to determine bounds of the response

and to study other effects such as variations of input motion.

5-38

6,,

I~

II

,I

7''''\

II

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.*

12TO

PI

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RY

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CASE

3

;;0 I -.....t co ~ Vl I .l:""

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~

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=48

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=1.

5

k=

100

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1.0

IIIii

tiii

I

0.5

:za

-'-

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.ft

If-

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21.

62

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'

FIGU

RE5-

24.

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ING

OFTW

OBO

TTOM

CORN

ERS

OFW

ALL,

CASE

3..... a

'-.

.- ,

co "",.... 0"'1 ~

.dI

\j

~,

CASE

1H

/D=

1.a

k=

100

PS

I/IN

.s

CASE

3H

/D=

1.5

k=

100

s

CASE

2H

/D=

1.a

k s=

800

PS

I/IN

.

-212TO

P

tI/

'"M

ASO

NRY

WAL

L

3~

/I

.~ ~~.

ISWAY

SP

RIN

G

I,,,

,,.,-

.,I

.L...l·

~IN~~

~**

7///

/.-7/

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...7.

&/7

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6Iiiiiii

......

'<I

i

4 2 -4

z VI

(D 0::(

-2

a

t­ Z w 4 w ua

I......

0::(

-=~

I\

"I

I

a

\J"l I -lO

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;;;0 I

"-J co ~ \J"l I -!=""

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3·2

2.8

2.4

2.0

1.2

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PARI

SON

OFAB

SOLU

TED

ISPL

ACE

MEN

TSOF

TOP

OF

WAL

LFO

RCA

SES

1,

2,

AND

3

0.8

0.4

FIG

URE

5-25

.

-6I

II

I'

Ir

II

a

R-7815-4610

SECTION 6

CONCLUSiONS OF PHASE I STUDY AND RECOMMENDATIONSFOR PHASE I I STUDY

6.1 CONCLUSIONS OF PHASE I STUDY

1. Most masonry research programs have been directed towards

studying masonry for new construction. Research programs for

mitigation of earthquake hazards in existing unreinforced

masonry buildings are meager and still in the early stages.

2. ATC-3 is the state-of-the-art tool for describing the

ground shaking at various sites across the United States.

However, the smooth elastic response spectrum recommended in

ATC-3 is not the ideal means for describing the design ground

shaking input needed in the present study for evaluating the

response of various components of existing unreinforced masonry

buildings.

3. The response of wood diaphragms is highly nonl inear when sub­

jected to the level of shaking expected in highly seismic zones.

Therefore, low-amplitude tests are not adequate to predicting

the response of these diaphragms in highly seismic zones.

4. The wood diaphragms studied in Phase I have periods that range

between 1.73 and 11.5 sec and are strongly influenced by

earthquake ground motions that have a strong long-period

content.

5. Overturning effects of in-plane forces on masonry walls are

important, and are strongly dependent on the height-to-width

ratio (HID) of these walls and the stiffness of the support­

ing soil. Walls with HID: 1 on soft soild would ampl ify

the input earthquake motions.

6-1

R-7815-4610

6.2 RECOMMENDATIONS FOR PHASE I I STUDY

In order to further evaluate and extend the findings of Phase I,

the following recommendations are given.

1. ATC-3 should be used to describe the intensity of earthquake

shaking at various sites to be studied in Phase I I.

2. An ensemble of time-history ground motions would be selected

at each site based on the above criteria. These records

should have response spectra that relate to the standard

spectra proposed by ATC-3.

3. Additional analyses

ses would include a

of earthquake input

retrofit methods on

be studied.

of diaphragms are needed. These analy­

larger number of segments and a variety

motions. In addition, the effects of,the response of these diaphragms should

4~ An experimental program of diaphragms that includes a pseudo­

static and -dynamic series of tests is needed. Pseudo­

static tests would account for loading and unloading under

load reversal. Dynamic tests would be performed for low­

amplitude and large-amplitude earthquake forces. These tests

would provide data for correlation with the results of the

analyses conducted in the Phase II study and for confirmation

of the trends described in the Phase I study.

5. Further investigation is needed for the overturning effects

of in-plane forces on masonry walls. This would include a

model that accounts for wall deformations and supporting soil

stiffness. In addition, various earthquake input ground

motions would be used. Bounds on the response of walls with

different HID ratios and various supporting soil stiffnesses

would be prOVided.

6-2

6.

7.

R-7815-4610

Analyses of the one-story building studied in Section 5

should be extended to include both wall and diagphragm

response in the model.

A model of a multistory building should be analyzed for

various time histories. Response of critical elements should

be evaluated.

8. Torsional capabil ities of diaphragms and existing

unreinforced masonry buildings need to be studied.

9. The effect of out-of-plane earthquake forces on the response

of unreinforced masonry walls of different height-to-thickness

ratios needs to be investigated, both analytically and

expe r imen ta 11 y.

10. The effect of coupling probable vertical motions with

horizontal time histories on the response of the above

models needs further investigation.

11. A simple method of determining upper and lower bound proper­

ties of existing unreinforced masonry walls is needed. Results

of pin tests, bed joint tests, and 4 ft x 4 ft prism tests

should be correlated with masonry wall strength.

12. Effect of various retrofit methods on the response of existing

URM buildings should be studied both analytically and

experimentally.

13. Experimental data on joints, panels, piers, and walls, from

previous studies by others, should be analyzed and evaluated.

This step would extend the data base provided by the present

program to include all available pertinent data.

6-3

R-7815-4610

SECTION 7

REFERENCES

1. Hegemier, G.A. "Mechanics of Reinforced Concrete Masonry: A LiteratureSurvey,'1 At1ES-NSF-TR-75-5. San Diego, CA: Univ. of Calif.,1975.

2. Mayes, R.L. and Clough, R.W. "A Literature Survey-Compressive, Tensile,Bond and Shear Strength of t1asonry," EERC 75-15. Berkeley, CA:Univ. of Calif., 1975.

3. Agbabian Assoc. The Response of an Eleven-Story Reinforced-ConcreteMasonry Building to Earthquake Ground Motion~ R-3200-2211.El Segundo, CA: AA, 1972.

4. Young, G.A.; Adha.m, S.A.; and Ts'ao, H.S. Response of Two MultistoryReinforced-Concrete Masonry Buildings to Earthquake GroundMotion~ P72-131-2410. El Segundo, CA: Agbabian Assoc., 1972.

5. Hegemier, G.A. Earthquake Response and Damage Prediction of Reinforced­Concrete Masonry Multistory Buildings: A Consortium Proposalfor Continued Research to be Conducted under the Sponsorshipof the National Science Foundation. UCSD-3237. San Diego, CA:Univ. of Calif., Oct 1975.

6. Barclay, B.; Clark, J.M.; and Ewing, R.D. Earthquake Response and DamagePrediction of Reinforced Concrete Masonry Multisto~J Buildings:Experimental Studies~ Numerical Studies~ and Computer ProgramModifications~ R-7512-1-3908. El Segundo, CA: Agbabian Assoc.,Jul 1975.

7. Hegemier, G.A.; Krishnamoorthy, G.; and r~unn, R.O. "An Experimental Studyof Concrete t1asonry under Seismic Type Loading,I' rJBS BuildingSci. Series 106. Earthquake Resistant Masonry Construction:National Workshop. Wash i ngton, DC: tJat 11 Bureau of Standards,Sep 1977.

8. Mayes, R.L. and Clough, R.I,1. "Cyclic Tests on Concrete Masonry Piers,"Proc. 44th Annual Convention~ Struct. Eng. Assn of Calif.San Francisco: SEAC, 1975, p 26.

9. Esteva, L. "Behavior under Alternating Loads of Masonry Diaphragms Framedby Reinforced Concrete Members," presented at the Int. Symp.on the Effects of Repeated Loading of Naterials and Struc.Elements~ R.I.L.E.M.~ Mexico City~ Mexico~ Sep 15-17~ 1966.

7-1

R-7815-4610

REFERENCES (CONTINUED)

10. Fattal, S.G. and Cattaneo, L.E. Structural Performance of Masonry WallsUnder Compression and Flexure. Washington, DC: Nat'l Bureauof Standards, Jun 1976.

11. Mayes, R.L. and Galambos, T~V. "Large-Scale Dynamic Shaking of Eleven­Story Concrete Buildings," in Proc. 46th Annual Conventionof the Struct. Eng. Assoc. of Calif.~ Coronado, Calif., 1977.

12. Blume, J.A.; Sharpe, R.L.; and Elsesser, E. A Structural-Dynamic Investi­gation of Fifteen School Buildings Subjected to SimulatedEarthquake Motion. Sacramento, CA: State of Calif. Dept. ofPublic Works, 1961.

13. Blume, J. A. The Earthquake Resistance of California Schoo l Bui ldings­Additional Analyses and Design Implications. Sacramento, CA:State of Calif. Dept. of Public Works, 1962.

14. Rea, D.; Bouwkamp, J.G.; and Clough, R.W. Dynamic Properties of McKinleySchool Buildings~ EERC 68-4. Berkeley, CA: Univ. of Calif.,Nov 1968. (pa 187 902)

15. Forest Products Lab (FPL). Diaphragm Action of Full-Scale DiagonallySheathed Wood Roof or FZoor Panels. Madison, WI: FPL, Apr 1955.

16. Atherton, G.H. and Johnson, J.W. Diagonally Sheathed Wood Diaphragm~.

Corvallis, OR: Oregon Forest Research Lab, Oct 1951.

17. Stillinger, J.R.; Johnson, J.W.; and Overholser, J.L. Lateral Testson Full-Scale Lumber-Sheathed Diaphragms. Corvallis, OR:Oregon Forest Products Lab., Oct 1952.

18. Stillinger, J.R. Lateral Tests on Full-Scale Lumber-Sheathed RoofDiaphragms. Corvall is, OR: Oregon Forest Research Lab.,Oct 1953.

19. Johnson, J.W. Lateral Tests on Full-Scale Lumber-Sheathed Roof Diaphragmsof Various Length-Width Ratios. Corvallis, OR: Oregon ForestResearch Lab., Oct 1954.

20. Johnson, J.W. Lateral Tests on 12-by-60 ft and 20-by-80 ft Lumber­Sheathed Roof Diaphragms. Corvallis, OR: Oregon Forest ResearchLab., Oct 1955.

21. Burrows, C.H. and Johnson, J.W. Lateral Test on Full-Scale Roof Diaphragmwith Diamond-Pattern Sheathing. Corvallis, OR: Oregon ForestResearch Lab., Oct 1956.

7-2

R-7815-4610

REFERENCES (CONTINUED)

22. Stillinger, J.R. IILateral Tests on Full-Scale Lumber and Plywood-SheathedRoof 0iaph ragms,.1 in Symp. on Methods of Testing Building Con­struction~ ASTM-STP-166. New York: Amer. Soc. of Mech. Eng., 1955.

23. Oregon Forest Labs. (OFL). Lateral Tests on Full-Scale Lumber and Plywood­Sheathed Roof Diaphragms. Corva11 is, OR: OFL, t1ar 1956.

24. Countryman, D. Lateral Tests on Plywood Sheathed Diaphragms. Tacoma, HA:Douglas Fir Plywood Assoc. Lab., Mar 1952.

25. Oregon Forest Research Lab. (OFRL). Lateral Tests on Full-Scale Plywood­Sheathed Roof Diaphragms. Corvall is, OR: OFRL, Oct 1953.

26. Countryman, D. and Colbenson, P. 1954 Horizontal Plywood DiaphragmTests. Tacoma, ~JA: Douglas Fir Plywood Assoc. Lab., Oct 1954.

27. Douglas Fir Plywood Assoc. (DFPA). 1954 Horizontal Plywood DiaphragmTests. Tacoma, WA: DFPA, Jan 1955.

28. Johnson, J.W. Lateral Test on a 12-by-60 ft Plywood Sheathed RoofDiaphragm. Corvall is, OR: Oregon Forest Research Lab.,Jan 1955.

29. Clark, W.B. and Hange, C.J. II\Jhen ... the Earth Quakes ... You Can Reducethe Danger," California Geology~ 2[1: 11, 1971, p 203.

30. Lew, H.S.; Leyendecker, E.V.; and Dikkers, R.D. Engineering Aspects ofthe 19?1 San Fernando Earthquake~ Bldg. Sci. Series 40.Washington, DC: Nat'l Bureau of Standards, Dec 1971.

31. Hudson, D.E. "Strong Motion Seismology,11 in Proc. Int. Conf. on Micro­zonation for Safer Construction Res. and Appl. Seattle~

Nov. 19?2~ Vol. 1, pp 29-60.

32. Schnabel, P.B. and Seed, H.B. Acceleration in Rock for Earthquakes inthe Western United States~ EERC-72-2. Berkeley: Univ. ofCalif. Earthquake Eng. Res. Center, 1972. (PB 213 100)

33. Schnabel, P.B. et al. SHAKE~ A Computer Program for Earthquake ResponseAnalysis of Horizontally Layered Sites~ EERC-72-12. Berkeley:Univ. of Calif. Earthquake Eng. Res. Center, Dec 1972.(PB 220-207)

7-3

R-7815-4610

REFERENCES (CONCLUDED)

34. Shannon & Wilson (SW) & Agbabian Assoc. (AA). Procedures for Evaluationof Vibratory Ground Motions of Soil Deposits at Nuclear PowerPlant Sites. Seattle, WA: SW & El Segundo, CA: AA, Jun 1975.(NUREG-75/072)

35. Seed, H.B., et al. Site-dependent Spectra for Earthquake Resistant Design3

EERC-72-12. Berkeley: Univ. of Calif. Earthquake Eng. Res.Center, Nov. 1974. (PB 240-953)

36. Applied Technology Council (ATC). Recommended Comprehensive SeismicDesign Provisions for Buildings~ FinaZ Review Draft~ ATC-3-0S.Palo Alto, CA: ATC. Jan 1977.

37. Newmark, N.M. and Hall, W.J. IISeismic Design Criteria for NuclearReactor Faci I ities,11 Proc. 4th World Conf. on Earthquake Eng.,Santiago~ Chile~ 1969.

38. Tissel, J.R. Horizontal Plywood Diaphragm Tests, Tacoma, WA: PlywoodAssoc, 1966.

7-4