REFERENCE

NBSIR 86-3494

NATL INST OF STANDARDS & TECH R.I.C.

A1 11 026311 08

Cheok, Geraldine S/Behavior of 1 /6-scale QC100 .U56 NO.86-3494 1986 V19 C.1 NBS-P Behavior of 1 /6-Scale Model Bridge

Columns Subjected to Cyclic

inelastic Loading

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Gaithersburg, MD 20899

November 1986

li

--QC100

.U56

86-3494

1986

EPARTMENT OF COMMERCE

XL BUREAU OF STANDARDS

ms

RESEARCH

INFORMATION CENTER

NBSIR 86-3494

BEHAVIOR OF 1 /6-SCALE MODEL BRIDGE

COLUMNS SUBJECTED TO CYCLIC INELASTIC

LOADING

Geraldine S. Check

William C. Stone

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Gaithersburg, MD 20899

November 1986

U.S. DEPARTMENT OF COMMERCE. Malcolm Baldrige. Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. DirBctor
» w

1 V- . I

3D<»Ca J300M 3iA02-e\f %0 Wt. VAHi

o»T2Aj3w tvjoyo OT osToataus 8».muj<

{)ikiAi

1} . '* i«mriO B

,0 eni

30J13M*-»00 10 tWaWTAA'B®:

ctn•^<^2j6 k) ucniiB Ml

\T«t(r>oc^J t!rthe«nig(rT3 l»nc

^90101 »imT gnlWft.l6j if

(KaSQS OM

.•IT aiit iatiwM .SVH *V. DO =*0 TM3Mt RA33Ct

*r ,**Q ,10¥Hlk^K^t»'•>3 ,<,OftAOi-'5/-V® 10 U*t*’W*- JASO

, ^M..y 3
ABSmACT

Circular, spirally reinforced concrete bridge columns were subjected to

cyclic inelastic loading in the laboratory. The bridge col\mns were onesixth scale models of prototype columns designed in accordance with

current California Department of Transportation (CALTE^ANS) specifications.

A total of six models were tested. Three of the models were constructed

with microconcrete, and three were constructed with ready-mix concrete

using pea gravel. Variables included the aspect ratio (height/width),

magnitude of axial load and the use of microconcrete vs. the use of a

ready-mix pea gravel concrete. Ihe models were subjected to slow reversed

cyclic loading with the axial load held constant.

Results from the tests are presented in the form of energy absorption,

load-displacement hysteresis curves, longitudinal steel strains along the

bar, and displacement profiles. Comparisons of the ultimate moment

capacities, measured displacement ductilities, plastic hinge lengths, and

the failure modes for the six models are discussed. Comparisons with

previous studies are presented along with a discussion of design codes in

the U.S., Zealand, and Japan.

A series of graj^cs-based computer programs were developed to speed the

analysis and interpretation of e^qserimental data. Source code is presented

for subroutines which integrate the area bounded by the load-deflection

hysteresis curves; animate test specimen motion synchronized to position on

load-deflection curve; plot individual cyclic strain energy and total

strain energy for a given specimen; and vhich permit comparison of energy

absorption performance between 2-6 specimens.

Keywords: Axial Load; Behavior; Bridges; Columns; Conputer Graphics;

Concrete; Confinement; Ductility; Energy Absorption; Failure; Lateral Load;

Microconcrete; Modelling; Plastic Hinge; Scale Effects.

1
H^EEACE

The majority of highway and mass transit bridges in the United States with

reinforced concrete columns have been in place for many years and either

were not specifically designed for earthquake loading or were designed with

minimum criteria. The adequacy of these columns to withstand heavy seismic

excitation is suspect, as many have failed in previous earthquakes.

Dynamic anaylses of structures responding elastically to ground motions

recorded during severe earthquakes have shown that the theoretical response

inertia loads are generally significantly greater than the static design

lateral loads recommended by previous codes. However, these structures can

survive severe earthquakes provided they are able to absorb and dissipate

seismic energy by ductile behavior in the inelastic regime. This point was

graphically demonstrated in the September 1985 Mexico Earthquake where

proper detailing often meant the difference between survival and collapse

of building structures.

Energy dissipation provided by the develcpment of ductile plastic hinges in

columns is essential to the satisfactory response under seismic loading of

many structures. In particular, a large portion of modem bridge

structures constructed in zones of high seismic activity ar^ supported by

piers consisting of one or more columns. Inelastic reponse of these bridge

structures under seismic attack will invariably involve plastic hinging of

the columns, unless mechanical energy dissipators are incorporated in the

design. Bridge column behavior is consequently fundamentally different

from that of building frames, vhere a capacity design approach is adopted

to ensure beam hinging by specifying column flexural and shear strengths to

be hi(^er than the maxiinum column loads associated with beam hinges forming

at maximum feasible beam strength.

This basic difference in philosophy between building frames and bridge

frames has meant that much of the research on building frames is not

directly applicable to bridge seismic design. Only two countries to this

date, Zealand and Japan, have specifically pursued extensive testing of

bridge columns to augment hi^way construction codes. There is still a

paucity of such research in the U.S., despite the obvious evidence of

problems in bridge design philosophy. These problems are typified by the

response of lifeline structures to the 1971 San Fernando earthquake, \\here

42 highway bridges recieved significant damage, and five structures

collapsed (see figure I). Much of the damage was a consequence of

inadequate detailing of the bridge columns resulting in:

a) insufficient ductility capacity to withstand the

inelastic displacements imposed.

b) shear failure in shorter columns

c) anchorage failure of longitudinal reinforcement in

plastic hinges forming at the column bases.

Damage to bridge piers in the San Fernando earthquake highlighted the need

for reassessment of existing seismic design practice for bridges in the

U.S. Since 1971, column design requirements have been changed and now

require additional confinement steel to avoid "birdcaging*' (compression

11
Collapsed

bridge

in

the

San

Fernando

earthquake
IV

Longitudinal

bar

buckling

-

"Bird

caging

effect

Fig.

II
at the footings and pier cap to avoid the pull-out problem (see figure

III). Until the initiation of the testing program described in this

report, these new designs had not been verified throu^ ej^jeriment.

It is now widely accepted that adequate ductility of column plastic hinges

can only be obtained if sufficient transverse confining reinforcement is

provided to confine the concrete core of the column, to prevent lateral

buckling of the longitudinal flexural reinforcement, and to provide

adequate shear reinforcement. IXiring the San Fernando earthquake, failure

of columns of several bridges and buildings could be directly attributed to

inadequate confinement of the plastic hinge regions. Nevertheless, the

amount and distribution of confining reinforcement necessary to insure

adequate ductility without significant strength degradation is still a

matter of controversy.

It is important to note that nearly all present design codes for bridge

column seismic details (with the previously noted exceptions of New Zealand

and Japan) have had their basis in the extensive research done on building

columns. Building columns are generally much smaller in cross section (12-

15 in) than the typical bridge column vdiich can easily run 48-60 inches and

larger. The reinforcement ratios differ greatly as well. These

differences and others, vhich are elaborated in greater detail in Chapter

1, may lead to substantially different performance of the column in a

seismic event.

In a worlcshop on earthquake resistance of highway bridges in 1979, the

Applied Technology Council stated that, "There is a pressing need for

experimental studies to determine the reserve capacities of various bridge

cortponents. Much of the considerable research work on column behavior has

been done on relatively small specimens and has been extrapolated for

bridges from tests of colimms typically used in buildings. Bridge columns

are larger and (lasually) lower stressed axially than building colimins and

this does not permit easy extrapolation from the present wealth of building

colimin data. Therefore work is (urgently) needed to determine whether the

behavior of small sections can be extrapolated to larger cross sections."

Furthermore, the ASCE-TCLEE Task Committee on research needs stated in

March of 1979 that, "experimental testing of selected reinforced concrete

(bridge) columns should be performed to determine the lateral resistance

and adequacy of reinforcement. Particular emphasis should be placed on

those columns designed using pre-1971 California criteria."

Based on these recommendations the National Bureau of Standards proposed,

in the fall of 1980, a test program to be known as the '*Large Scale Bridge

Column Project." EXie to the large costs associated with the conduct of

such full scale tests, sufficient funding did not became available until

mid-1983 at vhich time design work began on the specimens — full scale,

60-inch diameter columns — as well as the necessary laboratory test

fixtures. Sponsors for the project included the National Science Foundation

(NSF) , the National Bureau of Standards (NBS) , the Federal Highway

Administration (FHWA) and the California Department of Transportation

(CALTRANS). The objectives of the project were to address the following

topics:

V
VI

Pullout

of

the

longitudinal

bars

from

the

foundation

Fig.

Ill
a) The effect of scale factor on bridge column design (i.e. could

models be effectively used to predict full-scale behavior)

b) The effectiveness of current design details (i.e. would they

achieve the desired ductility).

c) Identification of symptomatic problems in present detailing

practices.

The project was initially divided into three phases. The first phase

consisted of the construction and testing of two highly instrumented full

scale 60-inch (1.52 m) diameter, spirally confined bridge columns, designed

to recent CALIRANS specifications to serve as benchmark data for subsequent

model tests and to verify at full scale the performance of the post-1971

design requirements. The prototype specimens were to replicate to the

maximum extent possible, actual bridge piers and the boundary conditions

and loading conditions that would be experienced in the field. A miiniinum

of two benchmark prototype tests will be performed to investigate two

general classes of bridge columns currently in use in seismically active

regions of the U.S. These included a short column measuring 15 feet (4.6

m) hi^ (susceptible to shear type failuires) and a tall colimnn measuring 30

feet (9.2 m) high vdiich would be used to investigate the performance of a

predominately flexure-type column with continuous longitudinal

reinforcement through the plastic hinge region. A special computer

controlled testing laboratory, known as the NBS Large Scale Structural

Research Facility, was designed and constructed to handle column axial

loads of 12,000 kips (53.4 MN) to simulate the dead weight of the bridge

superstructure, and lateral loads of up to 1,200 kips (5.34 MN) with

associated column moments of to 54,000 kip-feet ( 73.3 MN-m). Spiimens

weighing up to 4800 kips (21.36 MN) with heights of up to 60 feet (18.5 m)

and column diameters of up to 8 feet (2.44 m) could be accomodated in the

facility with access from a casting yard by means of a rail transport

system (see Figure IV).

Phase II, which was conducted in parallel with Phase I, involved the

construction and testing of precise 1/6-scale structural model r^licas of

the full scale prototypes under identical load histories and boiandry

conditions. Data gathering and sensor layout for the model specimens were

designed to be identical to those of the prototype so that direct

behavioral corrparisons could be made between the two. A further variable

studied in this phase was the effect of using microconcrete — the current

recommended structural modelling practice — versus the use of a small

nominal maximum size aggegate ready-mix concrete. The chief advantage of

the latter was one of cost effectiveness.

The third and final phase of the project will involve the conduct of

detailed comparisons between the model and prototype specimens. Such

comparisons will be based on ductility factor, energy absorption capacity,

ultimate moment capacity, plastic hinge length, and extent of yield

penetration in the longitudinal reinforcement.

Vll
This report is the first in a series detailing the results of the NBS Large

Scale Bridge Column Project and deals with the design, fabrication,

testing, and evaluation of the model column specimens. An extensive

literature review of previous bridge column research is presented in

Chapter two. Chapters three and four detail the design requirements for

similitude and the construction of the model specimens. Test results are

presented in Chapter five and a detailed discussion and evaluation of the

data is contained in Chapter six. Chapter seven provides a summary and the

conclusions.

Vlll
TARTK OF a^^TEOTS

PAGE

Abstract i

Preface ii

Table of Contents ix

List of Tables xiii

List of Figures xiv

1.0 Introduction 1

1.1 General 1

1.2 C^Dject and Scope of Ejqjeriment 2

1.3 Test Outline 3

2.0 Literature Reviev/ 8

2.1 General 8

2.2 Previous Research 8

2.2.1 Studies done in New Zealand 8

2.2.2 Studies done in Japan 18

2.2.3 Tests Perfom^ in Yugoslavia 29

2.3 Confining Reinforcement in the Plastic Hinge Region 37

2.3.1 ACI 318-77 38

2.3.2 CALTRANS 38

2.3.3 New Zealand Code 46

3 . 0 Similitude 48

3 . 1 General 48

3 . 2 Material 50

3.2.1 Reinforcement 50

3.2.2 Concrete 51

3 . 2 . 2 .Microconcrete 51

IX
3. 2. 2.

Pea Gravel 54

4.0 Specimen Design and Construction 57

4 . 1 Design 57

4.2 Construction Process 60

4.3 Model Casting 62

4 . 4 Instrumentation 62

5.0 Test Results and Observations 76

5.1 Introduction 76

5.2 Model N1 79

5.2.1 Model Properties 79

5.2.2 DUCniTTY FACTOR = 1, Cycle 1 79

5.2.3 DUCTILITY FACTOR = 2 , Cycles 2 & 3 79

5.2.4 DUCnLITY FACTOR = 4, Cycles 4 & 5 79

5.2.5 DUCniTTY FACTOR = 6, Cycles 6 & 7 79

5.2.6 DUCTILITY FACTOR = 8, Cycles 8, 9 & 10 ...... 85

5.2.7 DUCnilTY FACTOR = 10, Cycle 11 85

5.3 Model N2 85

5.3.1 Model Properties 85

5.3.2 DUCTILITY FACTOR = 1, Cycle 1 85

5.3.3 DUCTILITY FACTOR = 2, Cycles 2 & 3 89

5.3.4 DUCnilTY FACTOR = 4, Cycles 4 & 5 89

5.3.5 DUCnilTY FACTOR = 6, Cycles 6 & 7 89

5.3.6 DUCnUTY FACTOR = 8, Cycles 8 & 9 89

5.3.7 DUCnilTY FACTOR = 10, Cycles 10, 11, & 12 . . 89

5.3.8 DUCnilTY FACTOR = 12, Cycle 13 94

5.4 Model N3 94

5.4.1 Model Properties 94

X
5.4.2 DQCnLnY FACTOR = 1, Cycle 1 94

5.4.3 DUCTILITY FACTOR = 2, Cycles 2 & 3 94

5.4.4 DUCTILITY FACTOR = 3, Cycles 4 & 5 94

5.4.5 DUCTILITY FACTOR = 4, Cycles 6-15 100

5.4.6 DUCTTLITY FACTOR = 5, Cycle 16 100

5.5 Model N4 100

5.5.1 Model Properties 100

5.5.2 DUCTILITY FACTOR = 1, Cycle 1 100

5.5.3 DUCTILITY FACTOR = 2, Cycles 2 & 3 100

5.5.4 DUCTILITY FACTOR = 4, Cycles 4 & 5 108

5.5.5 DUCTILITY FACTOR = 6, Cycles 6 & 7 108

5.5.6 DUCTILITY FACTOR = 8, Cycles 8, 9, & 10 108

5.5.7 DUCTILITY FACTOR = 10, Cycles 11, 12, & 13 .. 108

5.5.8 DUCTTLITY FACTOR = 12, Cycles 14 & 15 108

5.6 Model N5 112

5.6.1 Model Properties 112

5.6.2 DUCTILITY FACTOR = 1, Cycle 1 112

5.6.3 DUCTILITY FACTOR = 2, Cycles 2 & 3 112

5.6.4 DUCTILITY FACTOR = 4, Cycles 4 & 5 112

5.6.5 DUCTILITY FACTOR = 6, Cycles 6 & 7 112

5.6.6 DUCTILITY FACTOR = 8, Cycles 8 & 9 112

5.6.7 DUCTILITY FACTOR = 10, Cycles 10, 11 & 12 ... 116

5.6.8 DUCTILITY FACTOR = 12, Cycles 13 & 14 116

5.7 Model N6 116

5.7.1 Model Properties 116

5.7.2 DUCTILITY FACTOR = 1, Cycle 1 121

5.7.3 DUCTILITY FACTOR = 2, Cycles 2 & 3 121

5.7.4 DUCTILITY FACTOR = 3, Cycles 4 & 5 121

XI
5.7.5 DUCTILITY FACTOR = 4, Cycles 6-15 121

5.7.6 DUCTILITY FACTOR = 5, Cycles 16-18 125

5.7.7 DUCTILITY FACTOR = 6 , Cycles 19 & 20 125

5.7.8 DUCTILITY FACTOR = 7, Cycles 21 & 22 125

5.7.9 DUCTILITY FACTOR = 8, Cycle 23 125

6.0 Discussion of Test Results 131

6.1 Column Deflection 131

6.2 Energy Absorption 145

6.3 Plastic Hinge Lengths 161

6.4 Confining Steel Strains 165

6.5 Ultimate Moments 166

6.6 Adequacy of Transverse Confinement 174

6.7 Failure Modes 175

6.8 Comparisons of Results With Previous Studies 176

7.0 Conclusions and Future Research Needs 178

7.1 Conclusions 178

7.2 Pratical implications 179

7.3 Areas of Future Research 180

References 181

A 185

impendix B 196

Appendix C 270

Xll
LIST OF TABIES

PAGE

1.1 Column Dimensions 7

2.1 Kuribayashi ' s Test Conditions 25

2.2 Corrparison of AASHTO and CALTRANS Current Specifications

Versus Those Prior to 1971 39

3.1 Similitude Requirements for Reinforced Concrete

Models 49

3.2 Microconcrete Mix Design 53

3.3 cylinder Test Data (conpressive strength in psi) for

Model Specimens 54

3.4 Pea Gravel Mix Design 56

4.1 Model Prcperties 61

6.1 Eiperimental Yield Displacements 138

6.2 load and Moments for Model N1 153

6.3 Load and Mcaments for Model N2 154

6.4 Load and Moments for Model N3 155

6.5 Load and Moments for Model N4 156

6.6 Load and Moments for Model N5 157

6.7 Load and Moments for Model N6 158

6.8 Ultimate Moment Capacities 162

6.9 Plastic Hinge Lengths 163

xiii
MST OF FIGURES

PAGE

I Collapsed Bridge in the San Fernando Earthquake iii

II longitudinal Bar Buckling - "Birdcaging Effect" iv

II longitudinal Bar Pullout from the Foundation vi

1.1 Prototype and Model Diinensions 4

1.2 Column Cross Section 5

2.1 Munro's Model 10

2.2 Gill's Model Dimensions 12

2.3 Gill's Tie Arrangement 13

2.4 Ang's Model Dimensions 15

2.5 Confinement Steel Comparision 17

2.6 Ohta's Model Dimensions and Test Set-Up 19

2.7 Kuribayashi 1/4 Scale Model Dimensions 21

2.8 KuribayasM l/4i/2 Scale Model Dimensions 22

2.9 Kuribayashi ' s Column Nos. 1 & 3 23

2.10 Kuribayashi ' s Column No. 2 23

2.11 Kuribayashi ' s Column No. 4 23

2.12 Kuribayashi ' s Column No. 5 & 6 24

2.13 Kuribayashi ' s Column No. 7 24

2.14 Ohno's Model Dimension and Test Set-Cp 27

2.15 Ohno's Loading Sequence 28

2.16 Petrovski's Flexure Model Dimensions and Steel

Arrangement 31

2.17 Petrovski's Shear Model Dimensions and Steel

Arrangement 32

2.18 Load History for Flexure Model Under Low Axial Load 33

XIV
2.19 Load History for Flexure Model Under High Axial Load 34

2.20 Load History for Shear Model Under Low Axial Load 35

2.21 Load History for Shear Model Under Hi^ Axial Load 36

2.22 Lap Splices in Vertical Column Reinforcement 45

3.1 Microconcrete Vs. Prototype Gradation ' 52

3.2 Pea Gravel Gradation 55

4.1 Prototype Steel Arrangement-Side View 58

4.2 Prototype Steel Arrangement-End View and Plan 59

4.3 Tying of Spiral Cage 63

4.4 Instrumented Cage 64

4 . 5 Tying Column Cage to Base Cage 65

4.6 column Dimension and Steel Layout 66

4.7 Casting of Microconcrete Bases 67

4.8 Flexure Colimm Axial Strain Gage Location and

Reinforcement Schedule 68

4.9 Shear Column Axial Strain Gage Location and

Reinforcement Schedule 69

4.10 Flexure and Shear Spiral Gage Location 70

4.11 Strain Gage Locations (Top View) 71

4.12 Embedment Gage 72

4.13 LVDT Locations for Shear Columns 74

4.14 LVDT Locations for Flexure Columns 75

5.1 Ejq)erimental Definition of Yield Displacement 77

5.2 TTF Test Set-Up 78

5.3 Loading History for Model N1 80

5.4 Model Nl, DF = 1, Cycle 1 81

5.5 Model Nl, DF = 4, Cycle 4 82

5.6 Model Nl, DF = 4, Cycle 5 83

XV
5.7 Model Nl, DF = 6, Cycle 6 84

5.8 Model Nl, DF = 10, Cycle 11 86

5.9 Model Nl, DF = 10, Cycle 11 87

5.10 Loading History for Model N2 88

5.11 Model N2, DF = 1, Cycle 1 90

5.12 Model N2, DF = 2, Cycle 2 91

5.13 Model N2, DF = 6, Cycle 6 92

5.14 Model N2, DF = 8, Cycle 9 93

5.15 Model N2, DF = 12, Cycle 13 95

5.16 Model N2, DF = 12, Cycle 13 96

5.17 Loading History for Model N3 97

5.18 Model N3, DF = 1, Cycle 1 98

5.19 Model N3, DF = 3, Cycle 3 99

5.20 Model N3, DF = 4, Cycle 6 101

5.21 Model N3, DF = 4, Cycle 7 102

5.22 Model N3, DF = 4, Cycle 10 103

5.23 Model N3, DF = 5, Cycle 16 104

5.24 Loading History for Model N4 105

5.25 Model N4, DF = 1, Cycle 1 106

5.26 Model N4, DF = 2, Cycle 2 107

5.27 Model N4, DF = 4, Cycle 4 109

5.28 Model N4, DF = 10, Cycle 12 110

5.29 Model N4, DF = 12, Cycle 15 Ill

5.30 Loading History for Model N5 113

5.31 Model N5, DF = 1, Cycle 1 114

5.32 Model N5, DF = 4, Cycle 4 115

5.33 Model N5, DF = 10, Cycle 11 117

XVI
5.34 Model N5, DF = 10, Cycle 12 118

5.35 Model N5, DF = 12, Cycle 13 119

5.36 Loading Histoiry for Model N6 120

5.37 Model N6, DF = 1, Cycle 1 122

5.38 Model N6, DF = 2, Cycle 2 123

5.39 Model N6, DF = 4, Cycle 6 124

5.40 Model N6, DF = 4, Cycle 14 126

5.41 Model N6, DF = 5, Cycle 18 127

5.42 Model N6, DF = 6, Cycle 20 128

5.43 Model N6, DF = 8, Cycle 23 129

5.44 Model N6, DF = 8, Cycle 23 130

6.1 Load cycles for Model N1 132

6.2 Load cycles for Model N2 133

6.3 Load Cycles for Model N3 134

6.4 Load Cycles for Model N4 135

6.5 Load Cycles for Model N5 136

6.6 Load Cycles for Model N6 137

6.7 Column Displacements for Model N1 139

6 . 8 Column Displacements for Model N2 140

6.9 Column Displacements for Model N3 141

6.10 Column Displacements for Model N4 142

6.11 column Displacements for Model N5 143

6.12 Column Displacements for Model N6 144

6.13 Individual Cycle Energy for Model N1 146

6.14 Individual Cycle Energy for Model N2 147

6.15 Individual Cycle Energy for Model N3 148

6.16 Individual Cycle Energy for Model N4 149

6.17 Individual Cycle Energy for Model N5 150

XVI
a

I

s

I

a

a

6.18 Individual Cycle Energy for Model N6 151

6.19 Energy Absorbed up to Ultimate State as Defined by

Zahn 152

Strain Along Longitudinal Bar (Model Nl) 166

Strain Along Longitudinal Bar (Model N2) 167

Strain Along Longitudinal Bar (Model N3) 168

Strain Along Longitudinal Bar (Model N4) 169

Strain Along Longitudinal Bar (Model N5) 170

Strain Along Longitudinal Bar (Model N6) 171

6.26 Diagram for the Flexure Models 172

6.27 Diagram for the Shear Models 173

Cl Schematic of TTF 269

C2 Flexure Model in the TTF 270
1.0 INTRDDUCnCN

1.1 GeJiftr^l

Many modem bridge structures in zones of high seismic activity are

supported by bents consisting of one or more columns. In the United

States, seismic design of bridge columns has often been based on data

obtained from research performed on building* columns. The basis for doing

so may not be valid due to several important differences which exist

between bridge and building columns. These differences are as follows:

1. Building columns typically have significantly smaller cross

sections than bridge columns: 12-15 in. (304.8-381 mm) are

common dimensions for buildings vMle 48-60 in. (1219.2-1524

mm) are common dimensions for highway bridges.

2. Because building columns have smaller dimensions and require

more complex detailing at beam-column joints than bridge

columns, the use of reinforcing bars greater than a # 11

(1.41-in, 3.6 cm) is not common practice. By contrast, #14

and #18 [1.69-in and 2.26-in (4.3 cm and 5.7 cm) respectively]

reinforcing bars are commonly used in bridge columns.

Differences in bond characteristics between small and large

bars may also contribute to performance differences.

3. Building columns, in general, carry higher axial stresses than

do bridge columns.

4. The design approach to building frames has been based on

plastic hinges occurring in beams prior to columns. However,

the development of plastic hinges in bridge columns is

necessary for energy dissipation under seismic loading.

5. Bridge columns have smaller reinforcement ratios than building

columns, typically less than 2%.

The San Fernando earthquake of Feb. 9, 1971 provided a focal point for the

reassessment of seismic design practice in the united States. During that

seismic event, five highway bridges collapsed and 42 others sustained

significant damage [12]. The principal causes of damage were identified

as:

1. Insufficient ductility capacity of columns to withstand the

inelastic displacements experienced.

2. Shear failure in shorter columns.

3. Anchorage failure of longitudinal reinforcement in plastic hinges

forming at the column bases.

Since the San Fernando earthquake, modifications to the seismic design code

for the state of California and the AASHTO seismic design guidelines have

been irrplemented. Some of these modifications in CAUTE^S specifications

include:

1
o Increased irdniinum requirement for the volumetric reinforcement

ratio.

o Decreased spiral spacing.

o Lapped splices in longitudinal bars not permitted in plastic

hinge region.

o Extension of spiral into the footing.

o Inclusion of the axial load in the calculation of the required

volumetric reinforcement ratio.

In 1979, the implied Technology Council Workshop on Earthquake Resistance

of Highway Bridges [24] identified the need for verification of these

changes by means of full scale tests as being of national importance.

Specifically, the recommendations from the workshop called for

investigations to determine the ductile capacity of concrete bridge columns

and to determine the validity of extrapolating the bdiavior of structures

with large cross sections from the behavior of structures with small cross

sections.

To meet these research needs, the National Bureau of Standards began an

experimental program to investigate the performance of bridge columns

subjected to inelastic reverse cyclic loading. Sponsorship of this project

was jointly provided for by the National Science Foundation (NSF), the

California Department of Transportion (CALTRANS), the Federal Highway

Administration (FHWA), and the National Bureau of Standards (NBS). The

physical test program was conducted at NBS. This report details the

results of the model test program.

1.2 Object and Socpe of Experiment

The overall e:q)eriinental test program involves the construction and testing

of full and 1/6 scale model specimens. The objectives of the research

program were as follows ;

1. To determine the ductile capacity of bridge columns designed

to CAITRANS standards.

2. To determine the effects of scale on column behavior.

3. To study the effects of different aspect ratios on the

behavior of the column.

4. To study the effect of axial load on the behavior of the

column.

5. To determine the differences between the use of microconcrete

and ready-mix pea gravel.

2
The iirportance of the first two objectives has alreac3y been discussed. The

third and fourth objectives will help designers better understand column

behavior with respect to important design variables, thereby leading to

better design practices. The irrportance of the fifth objective is in the

amount of time and research funds that could be saved if the use of readymix pea gravel could be substituted for the use of microconcrete.

Two types of cantilevered bridge columns were designed and constructed in

accordance with recent CALTRANS specifications; both full scale and 1/6

scale columns were constructed. These specifications meet or exceed the

"Seismic Design Guidelines for Hi^way Bridges" [26]. One colimn design had

a relatively high moment to shear ratio, approximately 40 ft. (12.19 m)

thus the failure mode was expected to be dominated by flexural effects.

The second column type was designed to investigate performance in the

regime dominated by shear effects. These columns had a moment to shear

ratio of approximately 20 ft. (6.10 m). A total of two full scale

specimens are to be tested. As of this writing the first test (a column

with hi(^ moment to shear ratio) has been completed. Construction of the

other test specimen is underway. Two sets of three 1/6 scale specimens

were also built. One column in each set was designed to have a hi^ moment

to shear ration; the other models were designed to investigate shear

effects. Microconcrete was used for one set and ready-mix concrete with

pea gravel was used for the other.

The columns were evaluated based on the following criteria:

1. Energy absorption

2. IXictility capacity

3. Ultimate moment capacity

4. Effectiveness of the column confinement

1.3 Test Oitline

As mentioned above two types of full scale and model bridge columns were

designed for testing in the laboratory. The designs were r^resentative of

recent design practice in the state of California and are shown in Figs.

1.1 and 1.2. The tall (flexure) type specimen measured 30 ft. (9.14 m) in

height while the shorter (shear) type specimen was 15 ft. (4.57 m) in

height from the column base to the point of application of lateral load.

These heights were chosen so that both flexure and shear failure modes

could be examined. Both types of full scale specimens were circular in

cross section and measured 5 ft. (1.52 m) in diameter. Axial reinforcement

consisted of 25 grade 60 - #14 bars (1.69-in, 4.3cm) spaced evenly about

the perimeter of the colimru Transverse reinforcement consisted of grade

60 - # 5 (.625-in, 1.6cm) spirals at 3.5 in. (88.9 mm) on centers for the

30 ft. (9.14 m) column and grade 60 - #6 (.75-in, 1.9cm) spirals at 2.125

in. (53.97 mm) spacing for the 15 ft. (4.57 m) column.

3
PROTOTYPE

AND

MODEL

DIMENSIONS 4

NOTE:

Base

width

is

96

(28.375)
All

dimensions

in

inches

5

Section
Based on available modelling materials and testing apparatus, a scale of

1/6.1 was chosen for the model specimens. Three specimens, Nl, N2, and N3,

were constructed using microconcrete and three specimens N4, N5 and N6 were

constructed using ready-mix concrete with pea gravel. N3 and N6 were

ej^)ected to esdiibit a failure mode dominated by flexure vhile the remaining

models were designed to investigate the effectiveness of spiral

reinforcement in short columns to resist shear failure. The dimensions of

the models and prototype are also given in Table 1.1.

The models were subjected to reverse cyclic lateral loads and a constant

axial load. The applied axial load was to simulate the weight of the

bridge SL^jerstructure. Lateral load was then applied to achieve the yield

displacement (vhich will be referred to throu^out this report as 1-deltay) ; thereafter the models were loaded under displacement control to

achieve multiples of delta-y (e.g. 2-delta-y, 4-delta-y, 6-delta-y etc.)

imtil failure of the specimen. Lateral load histories are described in

detail in Chapter 5. To study the effect of axial load, one of the two

shear models in each set had an applied axial load of 0.1 f*c\r [26.87 kips

(119.52 kN) ] while the other had an axial load of 0.2f'^J^ [53.75 kips

(239.09 kN)]. The flexure models both had axial loads of 26.87 kips (119.52

kN). The axial load of 26.87 kips (119.52 kN) and 53.75 kips (239.09 kN)

correspond to 1000 kips (4,448.22 kN) and 2000 kips (8,896.4 kN) in the

prototype columns, respectively.

The tests were conducted using the NBS Tri-Directional Testing Facility

(TTF) [29] operating under displacement control. The columns were initially

loaded to the specified axial force prior to commencement of the lateral

loading. This axial load was held constant for the duration of the test.

The boundary conditions of the tests were a hinged condition at the top of

the column and a fixed condition at the column base (foundation).

Instrumentation included strain gages at selected points along the

longitudinal reinforcing bars, and on the confining spiral bar, and

external displacement transducers used to monitor column rotation and

lateral displacements.

6
TABLE 1.1 COLUMN DIMENSIONS

SPECIMEN TYPE

OF

CONCRETE

HEIGHT DIAMETER

(INCHES)

AXIAL

LOAD

(KIPS)

MODEL

N1 Microconcrete 2' - 5.5" 9.8 26.87

N2 Microconcrete 2' - 5.5" 9.8 53.75

N3 Microconcrete 4' - 11" 9.8 26.87

. N4 Pea Gravel 2* - 5.5" 9.8 26.87

N5 Pea Gravel 2' - 5.5" 9.8 53.75

N6 Pea Gravel 4* - 11" 9.8 26.87

PROTOTYPE

Flexure 3/4" Gravel 30' - 0" 60 1000

Shear 3/4" Gravel 15' - 0" 60 2000

7
2.0

mEE^TDRE REVIEW

2.1 General

Although many papers have been written concerning seismic design of

building columns, few papers have considered the design of bridge columns

for seismic loading. Research that has dealt with seismic performance of

bridge piers has been carried out principally in Zealand and in Japan.

These projects involved the testing of small to medium size columns. A

discussion of the projects relevant to this study is presented in the

following sections.

2.2 Previous Research

2.2.1 Tests Performed in Zealand

The tests conducted in New Zealand were si:5)ervised by Park and Priestley at

the University of Canterbury. These tests have been on-going over the last

decade. Test variables included the level of axial load (Pq), volumetric

reinforcement ratio (Pg), aspect ratio (I/D) vhere L = column height and

D = column diameter, and the effects of (differences in cross section shape.

The loading sequence for these specimens was as follows:

1) i^ly increasing lateral load until 75% of the (calculated ACI

ultimate moment has been induced at the (column base.

2) Measure (e5^)erimentally) the column deflection at this load

Remove the lateral load (return to starting position) then

apply lateral load in the direction 180 degrees opposite the

direction of the first lc»d application. Measure the column

deflection vhen 75% of the calculated Ad ultimate moment has

been inducod at the column base.

3) Take the average of the displacements obtained in steps 1 & 2

and divide by 0.75. Call the result of this calculation "onedelta-y*' (lAy), the reference yield deflection.

4) Continue to apply (cyclic lateral loading to the column with

two cycles each at multiples of one-delta-y ( +2, +4, +6, ... etc:.) until ultimate failure of the column.

Chapter 5.1 provides a detailed desccription of the irrplementation of this

testing procceciure. The ciisplaccement ciuctility, u, is defined as the ratio

of the maximum column displacement at the point of application of the

lateral load (in any cycle) to the yield displacement (measured at the

same loccation). The discussion presented below begins with Munro's work

in 1976.

One of the objectives of Munro's study [13] was to test a 1/3 scale model

of a 59 in. (1500 mm) ncminal diameter bridge pier. The model specimen had

an octagonal cross section with spiral reinforcement having a 19.68 in.

(500 mm) diameter. The column had a clear height of 78.74 in. (2000 mm).

The aspect ratio of this model was therefore 4. The longitudinal

reinforcement consisted of twenty pairs of 0.51 in. (13 mm) diameter

8
deformed bars. The spiral reinforcement consisted of a 0.31 in. (8 mm)

diameter round bar with a spacing of 1.34 in. (34 mm) on center. The steel

layout is shown in Fig. 2.1. The specimen was subjected to cyclic loading

and a low axial load (12 % of balanced ultimate load). The axial load was

sL^jplied by a concrete block, ^fthich r^resented the superstructure wei^t

of the bridge, cast monolithically on top of the column. This was done to

provide an inertial mass for shake-table tests v^ch were planned following

the static load tests. During the static tests the lateral load was

applied at the center of the block. The column was designed in accordance

with the Ministry of Works and Development (MWD) " Highway Bridge Design

Brief" [9].

The measured yield displacement of the column was 0.75 in. (19 mm). The

yield displacement was obtained by loading to an approximate displacement

ductility of 0.6 and by extrapolation of the moment-displacement plot to

the theoretical ultimate moment. Data from the test showed that the

strain in the spiral reinforcement reached only 70% of its yield

capacity at m = 6, indicating a significant reserve ductility. The

calculated plastic hinge length was 0.66 H where H was defined as the

overall column diameter. When compared with data from a previous study

\diich tested columns built to ACT 318-71 [1] requirements, it was found

that the MWD specifications provided adequate confii^ment whereas the ACI

318-71 [1] requirements were not adequate to prevent the longitudinal bars

from buckling for displacement ductilities greater than 5 [21]. The

lateral load vs maximum column lateral diaplacement hysteresis curves for

the model showed little decrease in the energy al^orbed per cycle (the area

within a single loop) nor a marked decrease in ultimate moment up to a

displacement ductility factor of 8. Hi^er ductility for the column was

felt possible as no spiral yielding or longitudinal bar buckling was

dDserved. However, verification was r»t possible due to the limited stroke

of the hyraulic actuator. An average drop of 9 % in moment capacity from

the first cycle at each ductility level was noted in the repeat cycle.

Munro also constructed a 1/6 scale model to be tested dynamically. However,

the test was halted ^^le the column was still in the elastic range due to

failure of the bearing sijpjport system of the shaking table.

Ng [16] tested Munro's 1/6 scale column specimen under cyclic static

loading. The axial stress due to the concrete block cast monolithically on

top of the column equalled 58 psi (0.4 MPa). The specimen was 9.8 in. (250

mm) in diameter and had a height of 39 in. (1000 mm). The aspect ratio of

the model was 4. Ten deformed bars of 0.51 in. (13 mm) diameter

constituted the longitudinal reinforcement. The lateral confinement was

provied by smooth, round bars of 0.17 in. (4.4 mm) diameter at 0.55 in. (14

mm) spacing on center. The transverse steel reinforcement ratio was

Pq = 0.015. The longitudinal steel reinforcement ratio was 0.02568.

A displacement ductility of 14 was reached without any visible sign of

longitudinal bar buckling or spiral yielding even thou^ the column had

been previously subjected to vigorous dynamic testing. The yield

displacement measured was 0.5 in. (11.86 mm). It was also noted that the

plastic hinge length did not increase as the ductility factor increased. A

drop in maximum lateral load of approximately 8 % was observed to exist

between the first and second cycles at a given displacement ductility.

9
(a) cage in mould

(b) pier base and strain gauges

Munro's Model [13]

FIGURE 2.1

10
The xnarnent-displacernent curve frcm the dynamic test [13] cornpared very well

with that obtained from this static test vhich indicated the acceptability

of using statically obtained hysteresis loops for predicting seismic

response [21].

All previous tests had been conducted with the specimens subjected to low

axial loads, 0.08 f'c\r less. In an effort to gain more information on

the behavior of columis with hi^ axial loads, Ng built and tested another

1/6 scale model. An axial stress of 0.5 f was chosen for the model. A

1.38 in. (35 mm) diameter prestressing bar located in the center of the

column was used to apply the axial load. Final load in this rod was

adjusted to account for loss due to creep prior to testing the column.

Longitudinal reinforcement was provided for with 10 - 0.47 in. (12 mm)

diameter deformed bars. Spiral reinforcement consisted of 0.17 in. (12 mm)

diameter smooth, round bars spaced at 0.39 in. (10 ram) on center. Design

provisions of the draft New Zealand concrete code [15] were followed with

the exception that the volumetric reinforcement ratio vhich was twice that

required by the code. The provided volumetric reinforcement was 0.0244.

The yield displacement obtained experimentally equalled 0.2 in. (5 mm). Ng

determined yield displacement in a manner similar to that used by Munro,

except that the model was initially loaded to a displacement ductility of

0.75 instead of 0.6. Stable load-displacement and moment-rotation loops

were obtained ip to a displacement ductility of 8, at vhich point the test

was stopped. No buckling of the longitudinal bars was observed, but

extensive yielding of the spiral reinforcement rp to 5.1 in. (130 mm) above

the base was noted at the end of the test. It was evident that a

displacement ductility of greater than 8 could have been achieved even

though the spiral had yielded as no longitudinal bar buckling was noted.

At 1.38 in. (35 mm) from the base, a maximum hoop strain of 6120

microstrain was recorded. This strain equalled 6 times the yield strain.

It was concluded that if the the amount of transverse steel used had been

that recommended by the code, bucikling of the longitudinal bars would have

occurred. The plastic hinge length calculated experimentally was about 5.3

in. (135 mm) or about 0.5 H vhere H was the overall column diameter. Again

no increase in plastic hinge length with increase in ductility factor was

noted.

A series of four full size columns were tested by Gill [10] for different

levels of axd.al load. These columns were designed in accordance with the

New Zealand's code of practice , DZ 3101, first draft [7]. The cross

sections of the columns were square with the sides equal to 21.7 in. (550

mm). The column is shown in Fig. 2.2. Twelve DH24, 0.94 in. (24 mm)

diameter deformed bars made up the longitudinal reinforcement. Round bars

were used for the transverse reinforcement. The transverse steel

requirement was modified to reflect the level of axdal load as required by

the code. Spiral steel reinforcement, Pg, for the columns ranged from

0.015 to 0.0349. The arrangement of the ties is shown in Fig. 2.3. The

specimens were held pinned at both ends. Axcial stress ranged from 0.21 f'^

to 0.60 f'^. Axd.al load was provided by a DAE^C Universal Testing Machine

(UTM) with a 2,248 kip (10 MN) capacity. The lateral load was applied at

mid-height of the column through a heavily reinforced stub. This heavy

reinforcement forced hinging to occur above and below the stub.

11
i

\

t

i

!

i

9‘^0

Gill's Model Dimensions [10]

FIGURE 2.2

12

.100
H

Z5

O

a

D/•H

- -I

D

a

•i—i o

0

a

CO

13

Gill's

Tie

Arrangement

[10]

FIGURE

2.3
The data from the tests showed good stability of the load-displacement

loops a displacement ductility of 6. For higher axial loads, a' greater

increase of the measured lateral load and moment was noted from the values

predicted based on ACI methods. Yield displacements ranged from 0.1 - 0.22

in. (2.5 - 5.7 mm) with lowest displacement corresponding to the specimen

with the highest axial load. No buckling of the vertical bars was

observed. Maximum hoop strain achieved was 8600 microstrain for the

specimen with the highest axial load. The length of the plastic hinge

region increased for hi(^er axial loads.

Potangaroa [23] tested columns similar to those of Gill [10]. This series

consisted of a total of five octagonal columns with spiral reinforcement.

The columns were a 2/5 scale of typical bridge columns with a diameter of

59 in. (1500 mm). Columns were 10.8 ft. (3.3 m) high with a diameter of

23.6 in. (600 mm). The longitudinal reinforcement consisted of 16 - 0.94

in. (24 mm) diameter deformed bars with a yield stress of 40 ksi (275 MPa).

The spiral reinforcement consisted of round bars with sizes ranging from

0.39 - 0.63 in. (10 -16 mm) diameters at spacings ranging from 2.16 - 2.95

in. (55 -75 mm). Units 1 to 4 complied with the first draft code of

practice, DZ 3101 [7]. Unit 5 corrplied with the MWD requirements [9] vhich

were more stringent than those specified in DZ 3101 [8]. The variables in

the test were the magnitude of axial load and the corresponding amount of

transverse reinforcement. The range of axial stress was from 0.15 f to

0.70 f*^ and the range of spiral reinforcement ratio was 0.0075 to 0.0261.

The specimens were loaded in the same manner as Gill [10] and the same

boundary conditions existed. The columns ejdiibited good stability of the

load-displacement loops i:p to a ductility factor of 8. Althou^ the spiral

reinforcement yielded early in the test (m= 2), it still provided

sufficient confinement to achieve m = 8. The extent of spiral yielding

increased with increased axial load. Unit 5 sustained minimal damage for

P^ = 0.35 f*^ Aq, while attaining a ductility of 8 and was further tested

with the axial ^oad increased to P^ = 0.70f A^. The latter test began and

ended at a ductility factor of 8.

Under high axial loads (Unit 5, second stage), it was found that the

plastic hinge extended into the secondary confined region (vhere the spiral

spacing was greater than in the primary confined region near the base of

the column). The use of different confinement steel ratios for different

sections of a column is allowed by the code [7]. However, in this test,

the extension of the plastic hinge into the less-confined region permitted

buckling of the longitudinal bars. This in turn led to the eventual

fracture of the bairs and column failure outside the primary confined area. Also, the P - A effects were significant for high axial loads. From the

data obtained for unit 5, a conclusion drawn was that the SEAOC/ACI

requirements for confininement steel quantities appeared to be excessive

for low axial loads and unconservative for high axial loads.

To study the effects of different aspect ratios (L/D), Ang [5] tested two

octagonal and two square coliamns. The details of reinforcement in the

columns satisfied the requirements of the second draft of DZ 3101 [7].

These columns were similar to Potangaroa's [23] and Gill's [10] except that

the diameter of the columns was reduced from 21.7 in. (550 mm) to 15.7 in

(400 mm) and the height was increased to increase the aspect ratio from 2

to 4. Fig. 2.4 shows the dimensions of these columns. The longitudinal

reinforcement used for the octagonal columns was 16 deformed 0.63 in. (16

14
DIMENSIONS OF SPECIMENS

Ang's Model Dimensions [5]

FIGURE 2.4

15

300
inm) diameter bars and for the square columns, 12 of the same size deformed

bars were used. The spacing of the spiral reinforcement ranged from 1.57 ~ 3.94 in. (40 - 100 mm). The volumetric ratios for the octagonal columns

were 0.00851 and 0.01522 and 0.0151 for the square columns. Axial stress

ranged from 0.12 f'^ to 0.53 f'^. The columns were loaded statically to a

displacement ductility of 8. In addition to this, the columns were further

tested dynamically.

Data from these tests indicated that, where adequate confinement in the

potential plastic hinge region was provided, the load-deflection hysteresis

loops exhibited excellent stability (no pronounced drop in peak lateral

load ) \jp to ductility factors of 8 for the octagonal columns and 6 for the

square colimms. These results held true over a wide range of aspect ratios.

The onset of ultimate failure under static loading was evidenced in all

these tests by buckling of the longitudinal bars. Unit 2, the specimen

with the highest axial load, had sustained severe damage and was not

subjected to further testing. The units which underwent dynamic testing

failed as a result of fracture of the longitudinal bars and/or spiral. The

ductility was, therefore, affected by the increase in aspect ratio as the

columns tested by Potangaroa [23] and Gill [10] had displacement

ductilities of at least 8 without any visible sign of longitudinal bar

buckling. Equivalent plastic hinge length was also found to be independent

of the displacement ductility factor. Under hi^ axial loads, the plastic

hinge length was observed to increase. The transverse steel provided for

confinement in the plastic hinge region was found to be sufficient to carry

the shear. The transverse steel strength was determined from design

equations in the code [8] and the shear strength carried by the column was

obtained experimentally. The performance of these specimens showed that

reinforcement detailed in accordance with the second draft was sufficient

for ductile behavior for low and high axial loads. Due to the lower

volumetric ratio of confining steel required by the first draft of DZ 3101

[7] and ACI 318-77 [2] for high axial loads, it was felt that the same

ductile behavior mi^t not be achieved. Fig. 2.5 shows a conparison of the

voliametric ratios as required by the first draft of DZ 3101 [7], the

second draft of DZ 3101 [8] and ACI 318-77 [2]. A significant increase in

strain in the spiral reinforcement was noted in specimens with high axial

load. This was initially evidenced by extensive yielding of the spiral

steel at low ductility levels and strain hardening during later stages of

testing.

Some common findings from these studies were that the moment capacities

predicted by ACI column charts were conservative when compared to the

values found experimentally. This was reasoned to have been the result of

adopting a conservative value of 0.003 for the ultimate concrete strain and

a result of strain hardening of the reinforcing steel. The ultimate

concrete strain was found to be much greater than 0.003. The confined

concrete stress was calculated using the following equations:

f'cc = f'c + 4.1 fi (2.1)

vAiere f-i is defined assuming spiral has yielded as

fl = ^ ^

^p (2.2)

16
Confinement Steel Comparison [5]

FIGURE 2.5

17
Agp = area of spiral reinforcement = yield strength of spiral reinforcement

dg = diameter of column to outside of spiral

Sj^ = spiral pitch

Combining equations (1) and (2) will result in

f fV. (1 + 2.05 Pg ^h)

» = ft

cc c

(2.3)

It was foiand that these equations would result in a better estimate of the

ultimate strength than that determined by means of the ACT column charts.

The plastic hinge length ranged from 0.4 H to 0.64 H, vhere H was equal to

the column diameter, and could reasonably be taken as 0.5 H [22].

Althou<^ the spirals or ties yielded early in the tests at M = 2 or m = 4,

they still provided adequate confinement of the column. It was the opinion

of the authors that it was not justifiable to provide additional spiral

reinforcement to maintain spiral stresses within the elastic range.

2.2.2 Studies Performed in Japan

Seismic testing of bridge models in Japan has principally been conducted at

the Public Works Research Institute (PWRI). The following paragraphs

describe some of the work performed on models under static loading. The

yield displacement in the tests was defined as that displacement at vhich

the longitudinal bars reached yield strain. A specimen was considered to

have failed vhen the lateral load fell below the initial yield load after

ultimate load had been achieved.

Ohta [18] tested six specimens of rectangular cross sections as shown in

Fig. 2.6. The dimensions of the specimens were 15.75-in by 31.5-in. (400-

mm by 800-mm) and had a height of 5-ft-5-in (1650-mm). The shear-span

ratios for these models were 4. The shear-span ratio was defined as the

column height to column diameter ratio (L/d) and is equivalent to the

aspect ratio as used in the New Zealand studies. Configurations of the

hoops were singular, double, and combined single hoop with cross-ties.

These hoop configurations are also shown in Fig. 2.6. The volumetric

reinforcement ratio for the confining steel ranged from 0.04 to 0.16. The

longitudinal steel ratio for all the models was 0.0082. The maximum

spacing of the ties was the minimum dimension of the column as specified

in the Japan Society of Civil Engineers standards 1974. The spacing of the

hoops ranged from 3.93 in. to 15.75 in. (100 to 400 mm). Deformed bars with

a diameter of 0.75 in. (19 mm) were used for the longitudinal reinforcement

and round bars with a diameter of 0.35 in. (9 mm) were used for the hoops.

One of the units (specimen A) was tested under uni-directional (monotonic)

loading and the others were tested cyclically. The axial load applied was

71.94 kip (320 kN). Based on a concrete compressive strength of 4234 psi

(29.2 MPa), P /(f^ ) = 0.03425.

18
400

0 6 c SHAPES OP PECTAH6ULAP HOOP

SPKH

HEN SHf«

SPAN

RATIO

nOO« IhOOR

snc.<jRArioj CP

(Cffil |P.(%1|H0CR

'C#e.rjxiNL BAR ratio

Pt (A)

Itf tort Om-H/Ac

A 20 OOS 0 ‘I 9 4.U

20 [0 08 0 c

10 0 18 0 0 82 10

0 20 0 16 t I

E 20 0 16 c F 40 10 04 0 * LOAOINC I ONEDIRECTION; ^OCYCLESArS,.^S,.3S,.••

LQA0lHG I REVERSAL-. DCYLES AT 3,. 2S,.3S,.

SPECIM0<

Ohta's Model Dimensions and Test Set-Up [18]

Fig . 2.6

19
The colunins were cyclically loaded to yield displacement, 2 Ay, 3 Ay etc.

with the number of cycles equal to 10 for each displacement^ductrlity.

Stable loops were obtained for specimens loaded cyclically up to a

displacement ductility of 3, except for Specimen F vMch had the largest

hoop spacing [15.75 in. (400 mm)] and the smallest confining steel ratio

(0.04). Specimen F had stable load-deflection hysteresis loops (no

significant drop in maximum lateral load) up to a displacement ductility of

2. Specimen A reached a displacement ductility of 12, however, the axial

load was removed at 8 A due to the difficulty in maintaining the axial

load. At displacement ductilities of 3 or less, only flexural cracks formed

for specimen A. These cracks became inclined with greater displacement

ductilities. The other specimens had horizontal cracks forming corrpletely

throu^ the column core upon loading to A^ Diagonal crac3<s formed at 2-3

times A . The specimen with single hoops at a spacing of 3.94 in. (100

mm) and tne specimen with the double hoops absorbed more energy than did

the others and were therefore considered to be superior to single hoops

with cross ties. It was also concluded that a maximum spacing of 1/2 the

minimum column dimension would be adequate for hoops in the plastic hinge

region.

Models of a Ban-no-su Bridge pier of the Honshu-Shikoku Bridge were tested

by Kuribayashi et. al. [11] at the Public Works Research Institute. The

scales of these models were 1/4 scale for one and l/(4»/^) for six others.

The dimensions of the models are shown in Figs. 2.7 and 2.8. Arrangement

of the steel is shown in Figs. 2.9 to 2.13. Table 2.1 shows the test

conditions of the models. Ihe objectives of the study were to observe the

effects of loading conditions [uni-directional (monotonic) vs. cyclic], the

effects of a haunch ( see Fig. 2.9) at the column base, the effects of the

size of the longitudinal reinforcement without transverse reinforcement,

the dynamic behavior of a concrete column reinforced with steel frame

elements (SRC) as cortpared with a standard reinforced concrete column, and

the effects of studs attached to the base of the steel frame. Specimen No.

1 was cycled 3 times for each displacement ductility while the other

specimens were cycled 10 times for each displacement ductility. The aspect

ratios for all the models were ^proximately 4.

In general, yielding of the confining spiral had no significant irrpact on

the performance of the column. Only after fracture of a spiral bar in the

plastic hinge region did maximum lateral load begin to decrease noticeably.

Specimens No. 1 (monotonic loading) and No. 4 (large diameter longitudinal

reinforcement with no transverse reinforcement), failed in shear viiile the

other specimens failed in flexure. The strength and ductility of Specimen

No. 4 were also lower than that of the other specimens. The stiffness at

yield was found to be 1/3 - 1/4 of the initial stiffness. The yield and

ultimate load of specimen No. 1 and specimen No. 3 (basic model - with

haunch, no axial load, reversed loading) was about equal. However, the

ultimate displacement of No. 3 was 40% that of No.l. Dae to this observed

reduction, the displacement ductility of specimens loaded cyclically was

1/3 - 1/2 that of specimens loaded monotonically. The yield and ultimate

capacities of Specimen No. 3 was 20 - 30 % larger than Specimen No. 2

(without haunch). Specimen No. 7 (with axial load corresponding to the

superstructure weight) had a 20 % larger yield load, a 10 % larger ultimate

load and a 10 - 20 % smaller displacement ductility than did specimen No.

3. The maximum lateral load was observed to decrease significantly during

the second cycle at a particular displacement ductility. This was followed

20
500

1000

500

1500

1000

750

3250

Unit: mm

Kuribayashi's 1/4 Scale Model Dimensions [11]

FIGURE 2.7

21

1500

4000

1000
)

shows

dimensions

of

one-directional

loading

model

CQ

Cu H cScD

<D ' O'® I cQi

O'

CO'

(n

oj: S*k_. o:

22
Upper section Hunched section

Kuribayashi's Column Nos. 1 & 3 [11]

FIGURE 2.9

Stirrup D6

Kuribayashi's Column No. 2 [11] Kuribayashi’s Column No. 4 [11]

FIGURE 2.10 FIGURE 2.11

23

7(111
Kuribayashi's Column Nos. 5 & 6 [11]

FIGURE 2.12

1175

15 @ 37. 5 50 15 @37. 5 J

= 562.5 = 562.5 1

1

1

'

cvi CM '

r

'

D 6

1250

»•••

» • • •

> • !•• •«

i«

• • • • • #

• *1

,

• • •

• • « • • • • • • • 4 • •

• 4 • 4

» ••

f •

1 #

• 4 • i D 6

i

, i

1000

> •

» f »•

1 •

!•• ••

1 ••• «

1 • « • • • • •

• • • Lid

• • « • • • • • •

• • •

1 • • • «

• 4 •

•••

9•

• • • • • •

. 1 1

Kuribayashi's Coiumn No. 7 [11]

FIGURE 2.13

24
25

TABLE

2.1
by a more gradual decrease in maximum lateral load for the succeeding

cycles. The aseismic behaviors of RC and SRC columns were found to be

similar. The shear studs were determined to be ineffective in preventing

the pull-out of the steel frames in SRC columns.

Ohno and Nishioka [17] studied the effect of the number of loading cycles

at a ductility level on the energy absorption capacity of the column. Five

specimens with square cross sections, Fig. 2.14, were constructed. The

sides of the columns were 15.75 in. (400 mm) and the height was 74.8-in

(1900 mm). The aspect ratios for all the models were 4. Deformed bars of

0.75 in. (19 mm) in diameter and round bars of 0.35 in. (9 mm) in diameter

spaced at 3.94 in. (100 mm) were used for longitudinal and transverse

reinforcement respectively. The confining reinforcement ratio was 0.0032.

The longitudinal reinforx^ement ratio was 0.0082. The applied axial stress

for all specimens was 142 psi (0.98 MPa) except for Specimen No. 4 which

had an applied axial stress of 284 psi (1.96 MPa). This corresponded to

Pg/(f'^ Ag) = 0.079 for Specimen No.4 and Pg/(f' Ag) = 0.032 for all the

other sp&imens. The compressive strength of tSie Concrete was 3596 psi

(24.8 MPa).

The loading sequence for Specimen No. 1, L-1, was one cycle each at 1, 5,

and 8 times A The loading sequence for specimen No. 2, L-2, was one

cycle each at 1, 2, 3, ... , 8 Ay. The loading sequence for specimens

Nos. 3 and 4, was 1 cycle to A followed by 5 cycles each at 2, 3, 4, ... A y. L-4, loading sequence for Specimen No. 5 was 1 cycle to A

y

followed

by^lO cycles each at 2, 3, 4, etc. Ay. These loading sequences are shown

schematically in Fig. 2.15.

The length of the plastic hinge was found to be about 15.75 in. (400 mm)

vAiich was equal to the width of the column. This distance was measured from

the base. The center of rotation was at about 7.9 in. (200 mm) from the

base. The ultimate displacement was the displacement corresponding to the

failure load as described previously. For all specimens, the maximum

strength was obtained in the first cycle at 2 times delta y. The

cumulative absorbed energy, the sum of the energy absorbed by the column up

to ultimate failure, was about equal for Specimens Nos. 3 to 5. The

average of the three values is 128.5 ft-kip (95 kN-m). The cumulative

energy absorbed for Specimen No. 3 was 126.4 ft-kip (93.2 kN-m) as conpared

with Specimen No. 4 vbich had a cumulative absorbed energy of 123.8 ft-kip

(91.3 kN-m) and an axial stress double that of Specimen No. 3. Two major

findings from this study were :

. The axial stress was felt to have had no effect on the energy

absorption capacity of the column in this study.

- Total energy absorbed by the specimens was not influenced by

the number of loading cycles although the ultimate ductility

was influenced by the the number of cycles.

Studies [20] have also been carried out on the seismic resistance of

concrete bridge piers through the use of the Dynamic Structural Testing

Facility at IVJRI. Some of the conclusions from these tests are presented

in brief.

26
UOO 1*00 uoo _ 5 op. 3 0

0. '.5

ri-H

: ^ 3 ,iL tS

300

Ohno's Model Dimensions and Test Set-up [17]

FIGURE 2.14

27
«y

6

6

4

2

0

-2

-4

-6

-8

«y

4

2

0

-2

-4

«y

4

2

0

-2

-A.

1 23456789 10

1 23456789 10

1 23456789 10

Ohno's Loading sequence [17]

FIGURE 2.15

28
In a study [20] done in 1982 on the effect of dynamic loading and

longitudinal reinforcement ratio, both static and dynamic testing of model

piers were conducted.

. Yield and maximum strengths and yield displacements increased

with increasing longitudinal reinforcement ratio.

. Althou^ no significant differences in behavior were observed

between dynamic loading and static loading, the maximum

strength, ultimate displacement, and ductility factor for

specimens subjected to dynamic loading were slightly larger

than those subjected to static loading.

. Plastic hinge length increased proportional to the amount of

longitudinal reinforcement.

A study in 1983 [20] investigated the effect of column aspect ratio

(height/column diameter). Test results for a column with an aspect ratio

of 2.2 indicated that failure was dcminated by shear. Models with aspect

ratios of 3.8 and 5.4 had failure modes dominated by flexural effects.

These models were tested dynamically. Ductility factor (maximum lateral

displacement at failure/ yield displacement) was fourd to decrease as the

aspect ratio decreased.

A study [20] performed in 1984 showed that for high aspect-ratio columns

(dominated by flexural effects) under dynamic loading the effect of cross

sectional shape was insignificant if cross sectional area, height,

longitudinal and tie reinforcements were equal. Tests on small aspect

ratio columns (dcominated by shear effects) indicated that circular columns

performed better than square columns.

Reference 20 also discusses a series of tests which investigated the

effectiveness of continuous spiral reinforcement vs individual ties in

bridge columns. The test specimens were model columns with a diameter of

22-in (0.56) meters and aspect ratios of 4.7 and 3.3. The spiral pitch was

1 in. (25 mm) and was continuous from the column base to a height of 19.7

in. (500 ram). These showed significantly greater ductility factors than

similar models reinforced with individual ties at the same spacing. The

effect of spiral hoop on the maximum strength of the model was minor.

These findings were reported in a study done on the effect of spiral hoops

for columns piers with circular cross sections [20] in 1984.

2.2.3 Tests Performed in Yugoslavia

A series of four circular model columns were subjected to cyclic lateral

loads with constant axial load. Variables included the effect of

magnitude of axial load and the effect of column aspect ratio (L/D:

hei^t/diameter) . Two column heights were chosen: one to achieve a failure

mode predominated by flexural effects and a second to achieve failure in

shear.

The column heights (from footing to point of lateral load application) were

6' - 6.74" (200 cm) and 3' - 3.37" (100 cm) for the column heights of the

flexure and shear models respectively. The column diameter was 12.09 in.

(30.7 cm), the same for all specimens. The column aspect ratio (L/D) for

29
the flexure models was 6.51 and 3.26 for the shear models. The dimensions

of the footing were 47.2 x 15.75 x 19.7 in. (1.20 x .40 x. 50 m). Fig.

2.16 and 2.17 show the dimensions, steel layout and test set-up for the

model tests.

The longitudinal reinforcement for all models consisted of 12 - 0.472 in.

(12 mm) diameter bars. This resulted in a = 0.0183. The transverse

reinforcement consisted of individual circular hoops (not spirals) made

from 0.236 in. (6 mm) in diameter wire. The spacing of the hoops for the

flexure models was 2.95 in. (7.5 cm) near the fixed (cantilevered) end and

was 5.91 in. (15 cm) for the remainder of the column height. [No

specifications were given in the report as to the extent of the more

heavily confined region]. A uniform hoop spacing of 2.95 in. (7.5 cm) was

used for the shear models. The confining steel volumetric ratio, Pg, .was

0.00628.

The aggregate used in the construction of the models was a river gravel

with a nominal maximum size of 0.630 in. (16 mm). The average concrete

compressive strength obtained from 7.87 x 7.87 x 7.87 in. (20 x 20 x 20 cm)

cubes was 3260 psi (463 lq)/cm^).

In each test set, flexure and shear, one of the models was subjected to an

axial load of 16.1 kips (14,805 J^) v^le the other was loaded to 28.2 kips

(25,908 kp). This resulted in a P^/f* ratio of 0.043 for the lower

axial load and 0.075 for the hi(^er axial load.

The models were cycled three times while in the elastic range

(displacements less than yield displacement) and 5 times while in the

inelastic range (displacements greater than yield displacement). The load

histories for the flexure and shear models are shown in Figs. 2.18 through

2.21. The displacement increments while in the elastic range were very

small [0.04 in. (1 mm) for the shear models and 0.08 in. (2 mm) for the

flexure models] so that the yield displacements could be determined more

accurately. The yield displacement was defined as the displacement at

which no increase in lateral load was observed for an increase in

displacement

The experimentally measured yield displacement for the flexure model

subjected to the lower axial load (BS-Ml-El) was 0.59 in. (15 mm) and that

of the flexure model subjected to the higher axial load (BS-M1-E2) was 0.63

in. (16 mm). The ultimate ductility for BS-Ml-El was 4.58 and 3.31 for BSM1-E2. The criteria for determining ultimate failure not defined in the

paper.

The experimentally measured yield displacement for the shear model test

series was the same for both low axial load (BS-M2-E1) and high axial

load (BS-M2-E2) : 0.22 in. (5.5 mm). The ultimate displacement ductility

for BS-M2-E1 was 5.96 and 5.73 for BS-M2-E2. The damage for the flexure

models was due to nearly pure bending effects vhile failure of the shear

models was due to combined bending and shear effects.

The experimental maximum moment obtained for BS-Ml-El was 40.75 kip-ft

(5.63 t-m) and 45.24 kip-ft (6.25 t-m) for BS-M1-E2. The experimental

maximum moment values for the shear model BS-M2-E1 was 52.33 kip-ft (7.23

t-m) and for BS-M2-E2 was 55.80 kip-ft (7.71 t-m).

30
T«| CDrv3 • f

El Ho HttI ‘ ideAtif

1 ! 14 8 aS-M1-E1

2 I 25 9

' BS-M1-E2

Crea action 3—3

SO Crou Mctnn 2—2

Cfom acton 1—1

Petrovski's Flexure Model Dimensions and Steei Arrangement [35]

FIGURE 2,16

31
3939

gin

Aauator for pplyrng

axial foroa (Nl

Actuator for applyinf ro»om Wwar fore* (P)

d>-

Column

body

Stirrtipa ' —

(5>

footinfl of

iho column & *iePl

irvjiy'-L'ir ©“inMnLI ill! :^uuuui:-'%

oJU1

n

'! I ' l | Nl II ril

_JFi

liinrii fiii -illll ll II III :=:b

r

Iron platoa

Iron ritif

vrrr

—i-l— — nm

>=zd y[

1

)

1

1

1 1

i

*

1 ii 1 0-Hi! li; rn

i '

! 1

> 1

1

1

. I i|

. r ii r—

1

1 ^r 0"

;8 19 I ’ T

' r - ’

1 1 u«s

f

130 i •0

T«t eonOitoni

El No 1 NItl Identification

1 i 14.8 BS-Mr-EI

2 1 25.B BS-M2 -E2

J4-

so

Croaa aocimn 2-2

Croaa mctwn 1-1

Petrovskies Shear Model Dimensions and Steel Arrangement [35]

FIGURE 2.17

32
;rr

uy

cot

sef

33

Petrovski's

Load

History

for

Flexure

Model

Under

Low

Axial

Load

[35l

FIGURE

2.18
34
35

Petrovski's

Load

History

For

Shear

Model

Under

Low

Axial

Load

[351

FIGURE

2.20
36

Perovski’s

Load

History

For

Shear

Model

Under

High

Axial

Load

[35]

FIGURE

2.21
Conclusions from the tests were;

1. P - A relationship for the models could be categorized into 4

ranges: Range I, 0 <A< A^^; Range II A^< A < A y;

Range III A < Ay < A^; and Range IV A < A^ < A^.

2. Range I is the elastic range of the structure and is

characterized by a constant slope.

3. Range II is characterized by the slightly nonlinear

relationship between P and A with the intial point at Aj^and

the end point at A y. The P - A relationship may be

approximated by a line with a slope less than the slope of

the line in the elastic range,

4. Range III is characterized by plastic deformation in vhich

Py =

^roax

^considered constant Die initial point of ms

range is at Ay and the end point is at A A ^

is defined

as the point at which the lateral force begins to decrease

significantly. - '

5. Range IV is the regime characterized by significant decreases

in the lateral load with increased displacement. The initial

point of this regime is at A^ and the end point is at A

6. Based on ranges of displacements, two general ranges could be

defined. The first one up to yield point (conditionally

linear behavior) with a small range of deformations and the

second one to failure (nonlinear behavior).

7. Only fine craclcs were observed in the linear range at the

most critical cross-sections and the element would still be

considered functional without any structural repair.

8. Lateral load decreases in the nonlinear range with increased

displacements thereby increasing the damage to the element

leading to the eventual failure of the element.

9. The number of cycles at a constant ductility also affects the

stiffness deterioration.

10. Assesment of damage due to an earthquake should include:

2.3 Ocnfining Reinforoement in the Plastic Hinge Region

This section hi^li(^ts current code requirements for transverse steel in

the plastic hinge zone of bridge columns. The requirements are those

specified by ACI 318-77 [2], CALTRANS [28], and the New Zealand code [8].

The requirements of ACI 318-77 [2] are discussed because these

a. , A o-F +*>10 o1 omon+- b.

C.

37
specifications were part of the latest version of the ACI building code

^en the design of the prototype columns began. The Japanese practice is

not discussed as no translated version of the design code was available to

the authors. However, in a paper by Kuribayashi, et.al. [36] which

outlines the Japanese Road Association's 1980 specification for earthquakeresistant design of highway bridges, a displacement ductility of 2 was

recommended for design of reinforced concrete (RC) bridge piers. This

factor of 2 is based on an analytically determined value of approximately 6

for RC bridge piers. The analytical method was also based on monotonic

loading. As noted in reference 11, the displacemednt ductility is smaller

for specimens loaded cyclically than for specimens loaded monontonical ly.

Therefore, using a factor of safety of 3, the value of 2 was recommended

for design purposes. Also, it is not common practice in Japan to use

spirals in circular bridge columns [38], but rather to use circular hoops.

This is due to the difficulty of constructing large diameter spirals.

The focus of the discussions vhich follow will be on the requirements for

circular concrete columns.

2.3.1 ACI 318-77 [2]

Confining reinforcement is required for moment resisting connections for a

distance from the face of the connection that is equal to or greater than:

1.

The diameter of the column or the larger dimension of a

rectangular column.

2, One-sixth the clear hei^t of the column.

3. 18 in. (457.2 mm)

The spiral reinforcement ratio is the greater of = 0.45 - 1) ^ (2.4)

= 0.12 (f / fy) (2.5)

^ere is the yield strength of the spiral not to exceed 60,000 psi (414

MPa) . These equations remain unaltered in the ACI 318-83 code [3]. The

size of the spiral should be greater than or equal to a #3 bar (0.375

in [9.5-ram] diameter). The clear spacing between spirals should not exceed

3 in. (76.2 mm) nor be less than 1 in. (25.4 mm).

2.3.2 CAIflRANS [28]

CALTRANS provisions for bridge column reinforcement [28,34] can be regarded

as a superset of current AASHTO provisions [32,33]. Since they are

generally more conservative and specific than AASHTO specifications (see

Table 2.2 for a summary comparison) the 1983 CACIRANS requirements will be

discussed in this section.

38
TABLE

2,2

COMPARISON

OF

AASHTO

AND

CALTRANS

1983

SPECIFICATIONS

VERSUS

THOSE

PRIOR

TO

1971 1 •H • ca *H

m

-C3 (U c • • 3 00 u • *H CQ «U CO g o

44 \ (0 44 rH O 04 04 IS CO

m CM •H ir> c 00 CO 43 CO •H CO 00 CP CO U U 04 H U 4J U CQ <0 * A

00 o C CQ W4 CO O g CO •H 04 cO •H O

CM • O -H (0 r4 44 0) 04 -H (3444 CQ O • • o •H .Q 3 CP 43 CQ CO 04 C4 iH rH g

v(

44 O ’>0' C 44 CQ 04 g CO o m CO CO 44 C VO u CO U 44 U •H 04 U CJ * *H

CO o <v •H fC

U 44 CO O OV44 43 •H OV 'O

CTl O' e 44

U C u O 44 (34

U IS iH < )4 0) o CO CO CP 04 CO CQ O * \ (U u u 0^ iH C 43\44 44 CQ rH w CO 44 U • O 44 U C CO •H 4J rH O 44 CO z < (U O C 44 C (0 •H c CJ 1 * O — CO O < S 44 -H 04 r4 O -H CO 44 rH 04 04 • 1 K v| CO C E -O g 3 CO 'O a, O N 44 04 C * u 1 E-* •H *H 04 04 CP Oc 3 CQ U -H cO N-H c O

iH •U CD |<

U CP C CQ 44 * O CQ CP •H •H 44 1 < o u •H C cO •H U C * 04 CQ rH 1 u 1 • • 3 CO 44 * CP CO -H C * u CO O o C r4 • cr 14 C4 X c 04 g •H X CP C * CO * • 1 •H (0 C 04 U 04 CO O rH cO CP •HO C c 1 S C -H U cO u S rH U <0 rH g CO S Vl-H •H 11 1 04 1 3 1 43 CP CQ U • 1 44 1 44 04 44 c rH V O 00 O rH 1 •H CO 44 C • •H CO CQ •H CO 44 U 44 \CO O

00 (P*H C CO CQ CP 04 04

U fH C4 CSU (34 04 CN O CO CJ o C VO 04 C C U,C CO iH C0\ •H no * 44 \ • Vl • O -U g *0 g O CP44 O CO OcrH U (Jj-O C * CO rH 04 04 CQ U

CO o r4 C 44 04 04 3 iH

U 43 CO 1 CO CQ -H C 04 1 N 44 •H * O

Wift vl

<U O *0 O O iH 04 CO CQ C4 43

U •HU rH •H CP g 44 44 g 04 u CO O 44 43 04 04 U 44 o in S CP CQ 04 fH (0 a\ O 0) • U O 04 U O 44 g 43 U 04 C * O 44 U U CO -H * VO CP U G •H 44 CQ •H 44 O 44 CO on 44 04 O * CP u TJ C *

cr> < 14 >4 >H 3 C "O a> CQ 44 Z C 43 c CP * O *43 X CP •H -H C

iH (U o g cr-H >1 0) C •H 44 04 44 O C C (3 44 * <0 CO O4 * •H

(0 44 44 04 04 IH -H •H CM O O rH •H -H fQ -H eg IQ iH CO

03 < cu c < U

U C 44 O CQ\ • 1 14 O C CQ •H 0) o\o Z £ -H 04 CO U rH 04 04 O 04 04 • CO CO CO « •H 04 CQ 04 0 rH CO < VI CO 0) 04 >1 > U C4 CO 1 M 44 44 44 43 u 04 \ c» 43 U N •HU* U r4 04 O CQ rH •H CO 1 (0 44 04 CQ 44 * in CP\ 44 CO •H U 'O A

r* "O c CO iH 44 (0 OV

U 04 44 O C . C CO o CQ 0 C o fH -H CO * U rH 44 04 04 U CQ 04 U •H /v|^H 1 CQ o 44 CO • 3 o • cO CQ U CQ CQ <0 CO O • U 44 CP 04 g CO * CJ rH 04 • g o • C C 00 U •H iH U 04 C X CP C g CO 04 X 00 CUO g 04 C • * CO o H *H Vw CO Oj O CO r4 •H U CO av 04 04 •H •H iH CO \ CQCU44 •H 43 •H c C-H S 13 ID i3 CO U J3 CJ <C3 04 g cO O 43 4J -O CJ g in >o CO o 44 44 E •H •H >0

CQ •H * U 1 CO C O 04 3 U • CQ -H N * 44 CO 44 rH g *-H 04 •H CQ ^ c 10 C CQ 44 (Q CP*H U U 04 U CO •H CO •H

CO 00 C VO CO O g •H •O'

CO o O 44 iH 44 <11 Oc>a rH X 04 • r4 C 44 3 CP CQ c CO u CO o <u o O C cb 44 g CP U

CO VI

vw g U CO 44 O CP •H

00 o <u • •H fO

U O * 04 CO (34

lj> u c U C U CQ c u je (Q iH O' U U >H CO CO c OV*H 04 44 04 < 0) O g u o e -p CQ 44 o \ 44 44 O 44 U •H •H CO cO CQ u 0

CO CU C C 44 C CO CQ CJ 04 04 CO s < g -H 0) iH •H CO 44 U g o 0) 03 VI

CO (U T3 g 3 > (3< O CP-H o N •HU* 04 04 CP o CQ 44 •H • < TJ C U CP C U * 04 04 CQ C iH fH *H •H C CO o* U X 43 CO 43 •H o * cO 3 CO 44 CO CO 4J\44 • • C C 00 cr u o o 04 g rH C 00 o •H *H 04 U 04 z rH 44 1 44 S -O ift U cO U CJ CO O iH o E CO 13

04

CQ CQ CO

N

00 44 •H rH rH * o H CQ * CO *0 44 CQ 04 • CP^H CQ U U C O 44 o c iH 04 •H CO * CO VI O 44 CO 44 (3| U X OV

ro rH C U 04 CQ * 04 CO 04 CN

0) •H g c 44 g U

O)

VW g (34 CO 44 -H CO CP

CP O 0) CQ -H o 04 04 CO VO < O CO 'O CO u 43 CQ Ok \ U U c 44 cn CP44 04 C iH iH o> o o O 04 c 44 CQ 0 CO 44 44 •H U •H o 04 CO U •H o l< (U C CO 43 O U 43 04 CO CQ B

V| £ -H •H O CJ CO • 44 g O CO CO 04 > 44 (34 X -H CJ > < - •HU* o •H 04 CQ CO 44 44 0 < iH rO C u (3443 go 04 M o »H *H dc 44 U C4 43 (34 • * CO * CO CO * \ 44 o C C 00 o X VO 04 C rH 0

•H -H \ z <0 \rH CQ -H 1 44 Z S 'O m S rH CJ •H g rH O

CP

CO 44 44 c 44 H c rH C •H 44 C

r4 4J CO 04 CO 04 CJ 0 04

<u c C g 44 C g CO g o; (u •H 04 O -H 04 (34 04 04 4J S rO CJ 'O o CO N CJ 03 (U 44 3 U CP 3 U •H H

(JM • u O 44 O C 44 o iH CQ iH 0 -H •H 44 •H -H 44 cO CO VM

CU CP 3 0) o> c C4 CP C u o c cr N c -H CO C -H •H C *H •H O 0) •H o 04 Oj O 04 (34 •H (34 04 B B 03 B B 03 B B CO S CQ B

4Jc

0)e

<uooc

•H

(Uu

0)

(U

4-) CQ 44O

<uU<

II co

•H (H

4J (0 O U

<U >H

CO CO

(U x: <u 4J xi

4J 44O 44O

(Q

(V

U

U <U

(0

<U

CO e

CO (0 O -H

>4 Q O

II II C4 J O' CQ < T3

cs

m

39

CONTINUED
TABLE

2.2

COMPARISON

OF

AASHTO

AND

CALTRANS

1983

SPECIFICATIONS

VERSUS

THOSE

PRIOR

TO

1971

(Continued)

03 3 • 03 1 1 g 1 C 4J - 0 iH <0 O4 CP Q4 3 I •P g • p 0 m jG . 44 -H 0 03 n} 3 03 >1 -H 1 1—1 (0 0 3 • 03 4J 03 -H \ 01 44 0 CP U U 0 •H 43 44 03 03 1 CO iH T3 C -H 03 4J 4-1 Qj OkCM -H 03 44 3 03 as P 01 Eh P 43 1 C4 (0 <U C 0 03 xi 03 03 3 P 03 03 03 -H 01 03 44 3 1— o<o 0) u 03 CP^ 03 P 0 .3 • g ^ 03 43 03 43 CP -H 43 TJ 03 •H

•H ,H cac P rH •H fO P 4-3 03 3 n p <13 44 43 44 Ok 01 • 44 rH 43 'O 03 I CO O4 <U 'O 4-» (0 P 03 (0 03 3 3 iH <0 43 44 nj 03 iO O4 03 44 3 p

00 03 ^ 0 0 p .3 C -3 CP g g 0 3 44 03 44 0 03 <0 3 *H (0

<yi 00 03 03 4-1 0 as 3 4J 4.3 3 3 C3 (Q 3 > 3 0 CQ -H t-i rH 0 >i44 03 iH C 03 03 C Xi 03 44 rH rH 43 03 3 0 •H rH rH «H 0 ^ 43 • •H £i TD (U 0 -u • g -p 0 3 0 0 'O 44 0 *H 4:3 03 Oi 3 44 44 - 44 44 1 CQ <U r-l •H 03 -p 3 •H -H 03 U 0 03 •H <a 'O 43 •WCrOGiH433 c Z 03 0 iH -P 4-4 rH ^ pH X P iH T3 3 44 03 03 03 44 03 44 3 1 < <13 4-> Qu 0 • 04 4-> 0 <13 O4'0 4-3 <13 »0 *H 03 CI4 03 • <0 • •H03p43'00)0'g 0 a 0 (0 C c 03 -H 0 4-3 03 03 03 44 44 u :» 44 44 44 43 44 3 44 3 03 03 1 E-t •H 0» rH •H g CO <0 4J g 4J CP <0 0 44 • 44 44440CP030103C4 03 u 1 1-:) iH > -p a P P 03 04-P 0 3 P 03 04iH CP 44 3 3 O4 P P N U C Qj <0 P 3 C4 (0 03 4-1 0 P (0 -H Ui 44 -H 0 P 3 iH 0 44 0 044rH 03 034444 O •H 0 W 0 ^ «H 1-:] O4 0 Oi CPiH g 4-i 0 4:: El4 O' iH <0 rH 44 rH mo<0iH'oou44 3 44 1 p T3 3 44 r—

3 0 3 p 3 3 03 • rH •CJ 44 O4 3 0 p 3 X 3 44 44 CO as 3 P 04 * O443 44 3 04 44 <0 0 3 p 00 33 3 44 0^ 3 04 3 3 3

•H rH 3 'O P rH 44 3 3 p rH 3 44 -X g

o» Cu 3 'O 3 0 3 CP 0 43 3 3 3 O4 0 44 44 3

VO 3 0 u CM 43 44 3 3 44 CP 43 43 3 3 3 CP 0

CP 00 3 rH 0 0 3 44 4= TJ 3 3 3 p

rH 3 3 43 43 rH 3 • 3 rH 0 N g 3 0

iH 43 'O <v 44 3 3 p 03 •H 43 3 44 3 •H 3 P 44

CQ 3 T3 3 0 3 3 3 •H •H 3 0 44 3 z Oi 0 O4 3 O4 0 0 3 •H 3 o 03 • P 3 •H < 3 44 o< g 04 g •H 3 p 44 3 •H 3 3 -o X 3 0 3 0 3 P 3 3 44 0 3 •iH 0 44 0 g 3 44 X 44 U

Eh •H 3 rH 0 rH 3 iH 43 0 •H 3 •H 3 44 CP 44 3 rH

1-3 rH > 44 p 0 rH g 3 rH 3 CP 3 44 3 •H 3 3 < 04 3 p 3 p 0 0 O4 3 Q4 CUrH 3 3 -H 3 3 3 *H X

CJ CQ 43 0 'C3 0 44 1-3 3 g 3 3 04 P 3 g rH 0 P >1 44 3 3 3 • > 1 • •H 43 CP 44 3 TJ

as 3 g 3 3 O4 0 iH 1 43 O4 3 3 3 0 •H mH 3 3 3 O4 'O g •H 0 44 p 73 rH 44 •H *H 3 3 3 3 44 3 •H 3 3 3 >1 3 44 pH rH 3 O4 3 •H 43 CpiO CP • 3 3 3 P 3

CQ as O443 0 44 3 3 CP 3 X TJ 3 p

CQ p p 03 3 44 3 P g 3 fH Eh 3 3 3 0

•H 0 3 • rH 04 3 3 44 g 3 44 3 X 3

04 04 3 CP 3 •H 3 3 CQ O4 3 •H 44 0

CQ 3 'D O4 •H 44 3 CP 3 3 • 3 rH 3

00 3 3 0 0 44 3 3 3 03 TJ 44 0^44

ov 3 TJ rH CM rH 0 3 •fH • 3 3 0 3 0 •> rH •H rH rH 3 3 3 0 43 3 •D 3 u 3 44 3 p 3 -H p 3 0 •H H 3 44 X 3 0 3 » 0 44 0 3 3 rH 0 0 44 •H 3 a 0 44 3

Eh 3 0 •H 3 p CU*H 44 44 rH crx >1 CP g Z U 3 O4 44 u 3 3 44 3 •H a 3 44 44 3 3 3

CQ •H 43 3 • 3 •H 3 p g 3 p CP 3 3 3 < rH -o 3 0 rH p O4 3 3 p 3 3 (0 P P < O4 0 GO •rH 0 O4 3 3 rH 43 3 44 3 3 X iH 44 0

CQ 44 g 1-3 3 -Q 1-3 O444 a 0 -H rH 44

U 3 44 £ OJ03 CP u C 0) 0) >

>- 03 4J C

03 (0 O JJ >

•H

03 O

03

0> 4J U C

04 3 e o o g U (0 C 4-1 as O

0) 0)N 4J -H

03 C C

(V 0) g g

0) o; o u

k-l u o o

4-1 4-i c c

•H -H

<u a;

-C • U J-) CP c c a; o g

rH Oku c o

0) 4-1 g c

C4*H O 0) H U > tt> a; x:

’O -P 1 3 - P •H 3 3 3 44 X 0 • •3 3 CP3 X443 >3133 344 3 3 3 33GPI443P iHP-H3 443)

r4 T3 3 043043-HOPCP344 3344g 3344

(0 3 P O^X 33X4433'33P'H333 P33 CM P T5 3 344 *H 3CU33 0>i -H3 3P3 m •H ,H 44 rH 44rH3P rH344 «PPP344g

O4 3 CP 0 04*H 33 0403 «i44300033 3 2 CM 44G3344XX33 rH^G4444 3 3

CP \ OO 344 X33-H333G3 3p VO 3 3 r4 I-H3043 OEh 043>g3-H-H •.>0

9t H X3 1 33P3rH344 3>i3-H3P33r^*H44

rH •H 3 3 »-] 04*h •H443333PrH'333 3 0 03 >3* 443PX 0433*H 0 3 44 *3 •H3P 333'3043 3033 g33 B 3 3 4433 »XOg33X *P44 X *PPP • CQ t4 3 O4 3*H^<344-fHS44rH4430433443004 3 < iH > O4 3rHg3 3^344 •g*H3 •44g'3N < Ou 3 <0 0 043*H C 3 3-H44 3*H 0 3 344*H 3 O 3-H

CQ X rH J3g44-HP3gO0'^3P440'-''O333 3 3 1 •H •H 3 1 3 3 3 3 3 P U 3 rH 3 ^ 0 M 3 3 0 -H rH 44

C4 •H p •H CP 3 3 -P 0 rH *H iH 3 3 -H 3

Eh a 04 O4 0 *H 3 3

CQ CQ CQ kJ 'O QO g

40

CONTINUED
TABLE

2.2

COMPARISON

OF

AASHTO

AND

CALTRANS

1983

SPECIFICATIONS

VERSUS

THOSE

PRIOR

TO

1971

(Continued)

M 4J (U <U c o G X3 IH iH (0 VW (U 4J O (U

(0 VM • i-i • g (0 ox:

00 IH >1 »o o • c o c 0) O 4J cs •H XI cfl c C7> c -H m -H O O44J *0

Ctt ‘iH 3 c x; -H IH G 0) 44 • OJ >0 0*H»4J 0 0 iH G 0 4J cn 0^ 4J >-i 4-> >H cjkvo CO C ro 44 (0 *H *H

00 M-i 4JtanjO(OC •*H» GOG 44 IH 44

9) o (Ox: <uj3a>cao o •H jj O’ G <U 44

iH C 4J 'O

W iH *H ,o 0) G 0 0 44 0

0) -H a> u • V iH /\

M 'H 44 0 0) (0 CO C7k go a: (u cjk • ^ 0) 0 g z n> uinOxiCCO CBO Ok iH CO 0 CM n) O4 < IH wcnocO'HO COG to «0 *0 C H \-H nj K O •EHiHX5-HrHSJ3'Of3'a IH G <0 0 r4 >0 0

EH X CO a> 0 44 CQ

i-q O >0 44 4J (Q Cfl < c c • G X -H 0) • V C <U rH CM h4 <U TJ r4 iH g

I—

0

IH r4 tn 44 44 <0 44 'O 0 44 0 <u

CO CQ G 44 c •O r4 0 44 IH VO o G 0> N G 0

a\ •H 0) > >H 0) Oi

iH CO 44 0 IH g O4 • •H X r4 0 (U 3 G

CO > 0 x: 0 u] g z o 0 H 3 < IH r4 44 44 0 IH r4 K Ok (0 ta 44 0) 0

Eh

U • <U G X3 0 o •H O' ? 'H g < z O444 0 0> 0) >1

C-) CO 44 iH IH g xt

44 1 CQ 44 0 1 IH x> » o> 0

4J -H g 0 0 Ok

(0 c 0 iH IH 0|

1—

3 CM IH 0 3

CO o \ 44 44 44 CQ tn 0) V f-i 0 G

IH X3 1 (0 °H IH O 4J iH •O iH 0 0> • cn x: G 0 IH x: G

00 c; 44 (0 <U > g g

o> C O 44 (U rH 0) G

iH <0 *i X iH to g iH

>o X <U 44 0 o CO c <u 0 G 44 0

Eh 1-H 0) • rH 44 0 0 S (0 G CO <0 N >i

CO >H 4= 0) G IH • <H 44 X < •HO U •H cn iH G < 04 <Q >1 3 Oi44 0 0) 'O

CO O ^ 4J CO 44 x: g 0) e >1 0 X ^ iH

ff**l 44 44 (0 44 *0

CSJ 0 44 0 <u fO CO CQ G 44 G 73 iH 0 44 IH O G 0 N C 0

Ok •H 0 > -H 0) Ok

VO (0 44 0 U g Ok

Ok H X rH 0 0 3

iH > 0) X3 0 CQ o oU r4 44OH* 44 0 IH G s 04 to CQ 44 0> g

CO

U . tt» G X3 3 < o •H C7> ^ -H g rH < z Ok44 0000 CO 44 r4 IH g 0

0) IH C iH

CTk <0 0 ICS Ok

<0 u •H

U «s u IH -H CQ *H CJ M O 04 C Ok

Ok x: CO to <U CO 0 o O fO 44 44

Eh G 44 G X 44 G < O 03 W 0 *H

41
biOZowM<

cuzou

1—

u Hj* w cn 0s CO Eh CTl c

VO 0

CO ov •H 0 fH (0 CO •H

(Xi CO > a z 0 > < p « Cu

CO Eh z iX 0 0 < z M CJ

Eh<

CJMbM

CJb3 O4 fO

CO

m

(Q n c

00m 0

CTl CO •H

iH ov CQ iH •H

CO > z 0 0 < Eh p

03 04

EH CO

P) < 0 < < z u Eo

4Jo\ • O' c c o U 4J o o o a; 'O (p CO <U (p 4J <0 3 P C c CO 0 c ^ 14^ p 0) 0) p C X3 1 C 0 1 0) 3 1 dJ (U p 0 (0 x: x: Oi •H Dv Q> 0 •H C E 0 X p E G 4J XI -p

4J GO •H 0 P •H 4J -H p (U 3 (U c <u p 0 4-( rH c CN (0 P 0 CO P 0) 0 c; c <u 0 4-> c • d> -P (p u 0 »—

P 0 IP CO 0 p (p c p •H IP E p p C -H ,H Xi (0 • • 0 (0 u 4J (P <u 04 0 0 4J <u 0 (0 •H 0 0 ov

04

Oi CO (Q C CO p -o p •H (p c E 0 (p O4 U >1 CQ X) -P CO •H p 04 m 4-i 0 c CO • c 0 0 p c 'O DV (0 3 (p c 0 c

iH ov p o> (0 E CO x:

M (U CO CO •H t) p 0 •p c C <U (p E 0 <u XI (0 iH 0 p 0 p DV 0 E 0) p <u CO 4J ip <u (V •H x; 0 3 <u g

a\ (p c; <u •H 0 0) p <u p •H 0 c • p 4JU 4J -PC G <u Oi c

iH CO £3 p (0 -G 0 Q4X) 'O •'NO X (0 >1 3 -H XI 0 G •H z ^ -H c p E p p E E iH <U O4 iH v O4 0 0 jO -P p XI 0 < '0(0 (U 0 a; 4-> (p 0 0 (U (0 0 (U p (0 (0 CO 4J S C (p 0 'O

Eh K rH g E (p E CO 0 ip 0 E p G X3 0 p rH 0> (0 0 0 (p XI <u Eh <u 4-> iH (U rH <U • CT»JG 0 c (0 CO CC PI 4J >1 (0 0) 4J (0 E cr C 0 (0 OrH CQ 0 < • • (0 (0 -P P G (0 G (0 4J (0 0 -H 0 0) c 3

IH

U CN <0 G £ (0 3 4J PI CO (0 (p 4J x: 'o XI p •p 0

(0 CQ D'-H

«0 'O C OQ •H (0 CP

a> T3

0)u

>1 o

(0 JS e oc

TJ nj c

(0 >1

iH C Wi E <U S O4

r-l O O t-i O O4

0) 0^ A u

*i (0

(4-1 I-H O (0u E "H O Oi P CO O 0) X) x:p

0) p JC (4-1 <0 4J O

4-> (Q

0) R) X3 C

XI *0 dl

dl IP XI JS 0 (0 XI

r-o c 0

CN x: *p xa CO CQ XI E c OV P CQ 0 C dl (0 ov •p dl XI VO (0 rH

CTl •p dl c

rH > XI X3 0 0 C rH 0 p dl >, K 04 E <0 CQ CO< 0 O4 E (0 0 < z Ip fp 04

dl (0 (0 > p 0

dl <p

'O Q O4 dl C rH 0) C Ip CQ x: 0 (0 O4 3 0 (0 II XI •P P (0 c •P P CJ> dl CJ CQ *P C«i *P CQ -P C 'OC IP M C Ol X4 C 04 -p P £h 0

C(4 dl CO 0 c dl CO 0 XI 0 XI XI 0 XI XI 0

Eh X (p C CJ X IP c 0 p* lf> M 0 -P U 0 -p b4 ouzou

42
TABLE

2.2

COMPARISON

OF

AAStiTO

ANC

CALTRANS

1983

SPECIFICATIONS

VERSUS

THOSE

PRIOR

TO

1971

(Continued)

>1 *1

25*1 r1

ns 1 n1

CQ >r^ • <U O (0 c c

<4-1 C0>— CO iH 4J *H 43 o o \ >•<4-1 aV3 (0 4J 4J •H *H -o C\< <U + 0) <0 CP CQ VM O -OOH U 3 CQ <u c

•H <4-1 <4-1 in O' O’ ca 14 0> •H CP-^\ CO • 0) 0)

0) iH OM O CQ r-4 a0) *H 1 u 0) • " a> u CP T3 43

00 1 >^4-> 4-1 4J 4) <U C 44 CN c; <U in<Ui4-l>i(U 4343 H iH CP c CP cxv) a CQ a 4J 43 (0 C \ C< •(0CO<4-l--..<0 -H4J 44 (U CO CP •H \iH *H \ 0^ 0) O O C rH

00 < 43 0> -o O -ex C •H O

<T> < + 4J <44 -o a 44

N C

iH LD C3 43 <W 43 O C CQ •• g

•Hinin+JrHCM\4-> 14»0 • 4J^ ••HflJr-4 OM <4-10—*

to CQ l-l 3

CO • 1—( (0 O iH z< O CQ*0^3*|34^ iH

nj o — O’©

—' »co^^ CU 43 O •

*C3 C4 C

aI iH • . • 4-» O M rH 0) • *H OlAl CO aI CQ <+4 3 C <0 C X VO a (0 iH H rH fH O •H “H ^ < Q. (Uco oocQ omn}i-)>H 44 <4H S rH CS O 43'»- O « O >04J

4J C C (0 C <U0) -a • • ijflj* un]V^3 4J • • • 1 9

[341 11

iH

>1

oa >M-o

>4-1 1—

CCS OJ3cn 04343CSCP M <4-l4.» V|-l4.»E-l'-'a) O CQ rH CS cn

Pa -H

VO9V i iH o CQ 3

CQ < c C z \ o o < O' •H •H z < CQ CQ

E-i •H H

in > > < o o U • u u o Cu |3«

cn 11 11 oz Oz

CO 1 cn (3 CQ CQ 00 < c c

OV \ o o

iH CP •H •H < CQ CQ o •H •H

in > > X O o

03 • u l-l ;5 o Qa 04 Al

la a oz oz m

>1

VO CQ

<4-1 \-o

<4-1

1—

cn 1 VO o CQ CQ

CTl < c c

iH \ o o

CP M-l •H o < CQ CQ X •H •H

CO in > > o o • U H o Oa Oi A|

ca a OZ

CJ C -H ozc o

CP CP *H 44 O -H c C CQ •H 44 •H 4J •H 44 <0 44 CQ CJ c c C C iH •H (0 C M •H r-4 0) •H rH (U 04 <U C rH <U O

<4-1 <U 4-1 <4-1 (U 44 CP •H Ol CP*H o C 0) C C (U C 0) C <4H C (P O O O 44 O 43 -H <U <4H -H 0> CJ (Q O CJ W CJ 44 X Q O X X

II II

II O >1 O CQ < >4-1 ^-l

VO

43

Area

of

the

concrete

core >

Concrete

compressive

strength •

Yield

strength

of

the

spiral

reinforcement
The potential plastic hinge zone is defined as the greater of the

following:

1. The maximum horizontal dimension of the column.

2. One-sixth the column length.

3. 24 in. (609.6 mm)

For the flared end of a flared column, the plastic hinge length is equal to

the flare length plus the greater of 1, 2, or 3 above.

For columns with diameters less than or equal to 3 ft. (914mm), the

required confining reinforcement ratio is given by:

Pg = 0.45[A^A^ - 1] 0.5 + 1.25

'c Ag

( 2 . 6)

For columns with diameters greater than 3 ft. (914 mm)

,

p

s

F'

0.12 ^ c 0.5 + 1.25 (2.7)

However, pg from either Eqs. (2.6) or (2.7) can not be less than

ps

0.45 -

Ac

( 2 . 8 )

The minimum spiral is a steel wire of size W3.5 (0.221 in. [5.6 mm]

diameter) for columns with a minimum dimension less than or equal to 20 in.

(508 mm). For columns greater than 20 in. (508 mm) in diameter, the

minimum spiral is a wire of size W9.5 (0.348 in. [8.8 mm] diameter). The

maximum clear spacing of spirals is limited to 3 in. (76.2 mm) and the

minimum clear spacing is the greater of 1 in. (25.4 mm) or 1-1/3 times the

maximum size of the aggregate.

Table 2.2 summarizes AASHTO and CAITRANS provisions vhich are pertinent to

the design of bridge columns. These are presented for two cases:

specifications which were in effect prior to the 1971 San Fernando

Earthquake, and those \\^ch are currently in effect. The most inportant

changes occur in the specification of allowable conditions for lap splices

in longitudinal reinforcement and in the recognition of the irrportance of

confining reinforcement within potential plastic hinge regions.

Prior to 1971 the permitted locations of lapped splices in longitudinal

reinforcement along the height of a bridge column were not specified by

either AASHTO or CACTE^ANS. The 1983 CAITRANS code recognizes the problem

of potential column failure within plastic hinge regions by stating that

"Lap splices are not permitted [at all] for columns of 34 feet (10 m) or

less" (see Fig. 2.22). For column heights greater than 34 feet (10 m) lap

44
a

LUXo

UJoz K

Ld

UJ

U.

ro<X

h-X

LUK<

LUX

CDHXo

lUz3

-Jo

CJ HXo

UJo

CJ

cn

cn

UJXOH

UJ

UJ

u.

ro

45

Lap

Splices

in

Vertical

Column

Reinforcement

FIGURE

2.22
splices are permitted in the region from the footing to 2/3 of the column

height for columns whose base has been designed as a hinge. For fixed

columns (cantilevered) greater than 34 feet (10 m) in height, lap splices

are not allowed in the region 10 feet (3 m) above the column footing and in

the area within 10 feet (3 m) of the column cap soffit. Since plastic

hinge length generally falls within one column diameter for cantilevered

systems, the 10 foot (3 m) no-splice region seems adequate to prevent

longitudinal bar pullout within a potential plastic hinge for common

diameter bridge columns. It is furthermore iirportant to note that no lap

splices at any location along the column hei(^t are permitted v^en #14 and

#18 ( 1.7 and 2.25 in. — 43 and 57 mm) bars are used.

A new requirement for the content of confining (spiral) reinforcement in

potential plastic hinge regions has been added which reflects need, for

additional confining reinforcement at hi<^er axial loads to prevent lateral

buckling of longitudinal reinforcement. The new confining content

requirements are equivalent to those presently recommended in the New

Zealand code.

Another new provision deals with the end anchorage of spiral reinforcement.

In order to prevent loss of confinement during an earthquake, vhen spiral

reinforcement cover is likely to have spalled away, specific

recommendations have been made to assure positive end anchorage vhich does

not depend on bond for development of bar strength. This has taken the

form of a mechanical anchorage in which all spiral reinforcement is

terminated by a minimum 135° bend that is hooked around an intersecting

longitudinal reinforcing bar. Recent specifications have limited the

use of 135° bends for construction reasons. Welded splices, vhich require

a backing bar, are also permitted.

Finally, the 1983 CALTRANS specification defines the potential plastic

hinge region as the greater of: the maximum horizontal column dimension

(equal to the diameter for circular columns); 1/6 the column hei^t; or 24

in. (0.6m).

2.3.3 New Zealand Oode [8]

The potential plastic hinge for a column bearing an axial stress, P^, of

less than or equal to 4> 0.3 f

Ag

is the greater of:

1. The column diameter or the larger dimension of a rectangular

column

2. Where the moment exceeds 0.8 times the maximum moment at that

end.

For Pq > ^0.3 f Ag (where <t> is the strength reduction factor =0.9 for

confined members), •Qie plastic hinge length is 1.5 times the above value.

This requirement reflects the finding that the plastic hinge length

generally increases in proportion to column axial load.

46
The volumetric ratio for columns using spirals or hoops is the greater of:

Pg = 0.45 \ - 1

^

0.5 + 1.25 ^e

Ac fyh 'c Ag

(2.9)

or

Pg = 0.12 0.5 + 1.25 ?e ( 2 . 10 )

The maximum column load, Pg, allowed is 0.7 <t> unless it is shown that

Pg is less than 0.7 <t> Pg, where Pg is the axial load of the column

corresponding to zero eccentricity. A displacement ductility capacity of 8

can be expected if this required amount of transverse reinforcement were to

be provided.

The center-to-center spacing of the spiral or hoops is the lesser of:

1. One-fifth the least lateral dimension.

2. 6 times the longitudinal bar diameters.

3. 7.9 in. (200 mm).

Longitudinal bars are spaced a maximum of 7.9 in. (200 mm) on centers in

the plastic hinge zone. Lap splices in the longitudianl reinforcement in

the potential plastic hinge region is not permitted by the code. The

center of the splices is to be located in the middle quarter of the column

hei^t unless it can be shown that plastic hinging cannot develop at the

column end. Anchorage of the transverse reinforcement in the potential

plastic hinge zone is specified by full strength lap welds or by at least a

135° hook around a longitudinal bar with an extension of 8 times the

transverse bar diameter into the concrete core.

47
3.0 siMmrnjDE

3.1 General

Many design ccxies are based on tests conducted using structural models to

predict the behavior of the prototype structure. This is the result of the

impractical ity of construction, the difficulty of testing, and costs

involved in the lose of large or full scale specimens. As stated earlier,

one of the objectives of this study was to determine the effects of changes

in scale, if any.

A true model is one which exhibits complete similitude to the prototype

[25]. Obtaining a true model of a reinforced concrete structure is

difficult due to the inelastic nature of concrete and to it being a

composite material. Sabnis et. al [25] proposed that a "practical true

model" could be used for modelling reinforced concrete structures. The

similitude requirements for this modelling and for the true model are

listed in Table 3.1. Ihe scale factors in Table 3.1 relate a model quantity

to a prototype quantity. The scale factors for stress and strain, s<j and

s ^ , respectively are both equal to unity for the practical true model.

is equal to one if the material of the prototype and model is the same.

For true modelling, the following conditions apply

and

vhere the primed variables are the scale factors for the reinforcing steel.

Steel was used for the model reinforcement for this test and this,

therefore, results in sj = 1.

The requirement for geometrical similitude is such that linear dimensions

of model and prototype are related by a constant, s^. Prototype loads

and model loads are related in the following manner for s^ = s^ = 1 :

Concentrated load, Q; (3.3)

Line load, w: II (3.4)

Pressure, q; (3.5)

Moment, M: = Mp (3.6)

(3.1)

(3.2)

vhere the subscripts "m" and "p" represent model and prototype quantities

respectively

48
TABLE 3.1 SIMILITUDE REQUIREMENTS FOR REINFORCED CONCRETE

MODELS [25]

1

1 PRACTICAL

1 TRUE TRUE

1 QUANTITY

1 DIMENSION MODEL MODEL

1

1

1 Concrete stress fl“2 1

1

1 Concrete strain - 1 1

1

1 Modulus of concrete

1 FL"2 S,r 1

Q

H

1

1 Poisson's ratio 1 1

E-t <

i-:i W >H

1

1 Mass density FL"^ S,/Si 1/Si

ff: Eh 1

i-q 0^W 1 Reinforcing stress fl“2 S<r 1

< Oj H 1 W

EH

O

pc; p^

1 Reinforcing strain - 1 1

1

1 Modulus of FL“2 S, 1

1

1 reinforcing

1

1

1 Bond stress

1

1

1

FL“2 Scr 1

1

1

1 Linear dimension L Si Si

>H 1 pc:

1 Displacement Eh L Si Si

H 1 S

O 1 Angular displacement - 1 1

H - O 1

1 Area of reinforcemnt

1

1

1

L^ (Si)2 (Si)2

49
3.2 Material

3.2.1 Peinforcement

Similitude requirements for model reinforcement are [6]:

1. The stress-strain curve for the model reinforcement must be

similar to that for the reinforcement used in the prototype

2. Equal yield strength for both model and prototype

reinforcement

3. Similar bond characteristics for both model and prototype

reinforcement

The use of deformed wire for model reinforcement is recommended to simulate

proper bond characteristics. The only available deformed wire that was

suitable for the longitudinal reinforcement was D6 deformed wire [27]. The

deformations of the D6 wire were in the form of indentations rather than

raised ribs as in the prototype reinforcement. It was, however, not

possible to obtain deformed wire for the other required wire sizes. As a

result of lasing the D6 wire for the model longitudinal reinforcement, the

scale factor, was:

= 6.1

vhere Dp = Diameter of a #14 bar = 1.693 in. (43 mm) = Diameter of a D6 wire = 0.276 in. (7 mm)

All other reinforx:::ement and dimensions were then scaled using s^^ = 6.1.

The yield stress of the pirototype steel was approximately 70,000 psi (483

MPa). When tested, the yield stress of the D6 wire was found to be around

88,000 psi (607 MPa). It was also noted that the stress-strain cuorve for

the model steel had a rounded shape with no well-defined yield point. The

prototype steel had a well defined yield point. As a result the model bars

had to be heat-treated to lower their yield stress and to change the

characteristic stress-strain curve of the model steel to match that of the

full-scale reinforoing steel.

A heat treatment of 1162° F for 1 hour was determined to produce the

desired changes in model steel propeorties during tests at the bureau of

standards using a precision furnace. The bulk of the model steel was

then processed at a commercial facility. This resulted in a well defined

yield stress of 57,000 psi (393.1 MPa), somewhat lower than the desired

value.

A similar procedure was used to treat the model spiral reinforx::ement, vhich

had an initial yield point of 113,600 psi (783 MPa). Heat treating this

steel for 1 hour at 1013° F produced a yield stress of 80,000 psi (552

MPa). An additional 20 minutes at 1036° F further reduced the yield stress

to 69,000 psi (476 MPa). This was considered sufficiently close to that

50
for the prototype [64,000 psi (441 MPa)] to satisfy similitude

requirements. These differences in steel yield were accounted for when

corrparing the behavior of model and prototype specimens.

3.2.2 Concrete

3. 2. 2.1 MICROOONCRETE

Classical structural modelling theory calls for scaling of all conponents

of a structure, including materials characteristics. In the case of a

conposite material such as concrete, similitude considerations generally

result in scaling of aggregates such that the aggregate gradation curve for

the model specimen is related to the prototype aggregate gradation curve by

the scale factor s^^. Concrete designed by means of such scaling

procedures is referred to as microconcrete. It was used in this test

series for for the construction of specimens Nl, N2 and N3.

Large aggregate used for the full-scale specimen was a 3/4 in. (19 mm)

nominal maximum size river gravel. Fig. 3.1 shows the gradation of the

prototype aggregate and the acceptable limits, shown by the lighter dashed

lines, as specified by CALTE^S. Fig. 3.1 also shows the gradation of sand

(labelled "White Marsh Concrete Sand") vhich was used as aggregate for the

microconcrete. This gradation, represented by the heavy solid line in Fig.

3.1, generally fell within the scaled down acceptable limits, represented

by the lighter solid lines in the Fig. 3.1, except for the high number

(finer) sieve sizes. The difficulty of achieving high volumetric

percentages of very fine particle sizes is typical in microconcrete design

and variance from the gradation limits in the high number sieve sizes is

generally considered acceptable.

A mix design was developed to produce a 4000 psi (27.6 MPa) 2 7-day

compressive strength concrete. Due to the fineness of the aggregate, it

was difficult to achieve good workability without greatly increasing the

water/cement (W/C) ratio. Rather than increase water content, however, a

superplasticizer (conforming to requirements of ASTM C494-F) was used to

increase workability. The concrete for the model columns was mixed at NBS

following casting of the base beams using a similar strength ready-mix

concrete. Amounts of materials produced in the laboratory for casting

the columns are given in Table 3.2.

51
100

90

80

70

60

50

40

30

20

10

0

Microconcrete Vs. Prototype Gradation

No. No.

100 50

No. No.'flow

' 8 4 --

Fig. 3.1

52

3/4
TABLE 3.2 Micrcx:oncrete Mix Design

Material/Property LB/CY

Cement (Type I, PortlandCement) 699.3 (2016.2)

Sand (dry) 2724.3 (7854.6)

Water 461.0 (1329.2)

w/c 0.61

Slurtp without siperplasticizer 1/2 in.

(12.7 mm)

(Flexure)

1 - 3/16 in.

(30.2 mm)

(Shear)

Slump with superplasticizer 2 - 1/2 in.

(63.5 mm)

(Flexure)

5 - 1/4 in.

(133.3 mm)

(Shear)

Due to the small volume of concrete produced during laboratory casting

operations, 3 by 6 in. (76.2 by 152.4 mm) cylinders were used instead of

standard 6 by 12 in. (152.4 by 304.8 mm) cylinders. The use of the smaller

cylinders has been shown [14] to produce the same ccaipressive strengths as

the standard size cylinders. Fifteen of the 3 by 6 in. (76.2 by 152.4 mm)

were cast for each colxmn specimen so that a minimum of three cylinders

would be available for strength testing at 3,7, 14, and 28 days age. The

three remaining cylinders were tested on the day of the column test. Table

3.3 presents the compressive strengths and their standard deviations for

column specimens Nl, N2, and N3.

53
Table 3.3 Cylinder Test Data (coirpressive strength in psi) for Model

Test Specimens

Model No. N1 N2 N3 N4 N5 N6

1 Age (days) |

1

1 3 1 2242 2242 2042 2653 3013 2653

S.D. 1 28 28 22 111 7 111

1 7 1 2858 2858 3082 3169 3534 3169 ‘ S.D. 1 90 90 78 107 71 107

1 14 1 3209 3209 3431 3492 3839 3492

S.D. 1 137 137 39 46 157 46

1 28 1 3393 3393 3537 3643 3822 3643

S.D. 1 119 119 130 46 66 46

1 Test 1 3490 3490 3681 3545 3534 3367

S.D. 1

1 99 77 75 108 170 79

Each test represents the average of three 3x6 in. (76.2 by 152.4 inm)

cylinder breaks. 1 psi = 6.9 KPa ; S.D. = standard deviation of three

cylinder tests; "Test” = corrpressive strength on day of column test.

3. 2. 2. 2 PEA GRAVEL OONCRETE

As an alternative to microconcrete a ready-mix concrete was used for three

of the column specimens. These specimens were cast using a nominal 3/8 in.

(9.5 mm) maximum size washed river gravel aggregate (known as "pea

gravel") with a specified 28 day strength of 4000 psi (27.6 Mpa). The

gradation for this aggregate is shown in Fig. 3.2. The amounts of the

materials used for the pea gravel mix are shown in Table 3.4. Conpressive

strengths and standard deviations for each column specimen are presented in

Table 3.3 (specimens N4, N5, and N6).

54
ONISSVd

%

Pea Gravel Gradation

Fig. 3.2

55

3/4
TABLE 3.4 Pea Gravel Mix Design

Material/Property LB/CY (kg/m3)

Cement (Type I, Portland Cement) 605.7 (1746.4)

Water 370.4 (1067.9)

Sand (dry) 1460.0 (4209.5)

Pea gravel (dry) 1575.0 (4541.1)

w/c

Slump without superplasticizer

0.61

4 in. (101.6 mm)

56
4.0 SPECIMEN EESIC2I AND OONSIKJCriCN

4.1 Design

The prototype columns (see Fig. 1.1) were designed based on CALTRANS

specifications effective in 1983. The longitudinal reinforcement for both

prototype columns (flexure and shear) consisted of 25 # 14 [1.7 in.; 43mm]

grade 60 deformed bars. These bars were spaced at 6.82 in. (173.2 mm)

center-to-center around the column. The longitudinal reinforcement ratio

was 0.0199. The transverse reinforcement for the flexure prototype column

consisted of spirals made from # 5 [0.625 in.; 16mm] grade 60 deformed bar

spaced at 3.5 in. (88.9 mm) on center. The transverse reinforcement for

the prototype shear column consisted of spirals made from # 6 [0.75 in.;

19mm] grade 60 deformed bar spaced at 2.125 in.' (53.97 mm) on center.

The spirals extended into the base (footing) to the point of tangency of

the longitudinal bar hooks. The steel arrangement for the prototype is

shown in Figs. 4.1 and 4.2. This was one of the modifications in the

CALTRANS provisions [28] since the San Fernando earthquake. Prior to this

earthquake, the spiral was not required to extend into the footing of the

column. The volumetric spiral reinforcement ratio was 0.00633 for the

prototype flexure column and 0.01479 for the prototype shear column.

Due to the availability of the D6 model deformed wire for the longitudinal

reinforcement (the closest match to an integer scale factor of the

prototype longitudinal reinforcement) a 1/6.1 scale was dDtained. Refer to

ASTM A-496 [27] for the wire properties. The axial loads for the models

were:

Nl, N2, N4, N5: Pg/f'j, Ag = 0.09

N3, N6; Vf'c *g = 0-18

based on a design f'^^ = 4000 psi (27.6 MPa). Actual concrete strengths

obtained in the lab frcm ccatpression tests of 3 by 6 in. cylinders for the

models were approximately 3500 psi (24.1 MPa) on the average. These tests

were conducted v^en the models were tested. The longitudinal reinforcement

ratio for all the models was ~ 0.0199. This was provided by 25 - D6

bars.

The transverse steel requirement was governed by Eqs. (2.7) and (2.8). The

volumetric ratio required by Eq. (2.7) resulted in

Pg = 0.12 ^ c

3.5

0.5 + 1.25 "^e

Ag = 0.12 [ 0.5 + 1.25 (0.09) ] 57 = 0.0045 for Nl, N3, N4 and N6

57
Prototype

Steel

Arrangement

-

Side

View

LU

CC

58

Bottom

tension

steel

2

layers

15

#14
Prototype

Steel

Arrangement -

End

and

Plan

Views o

ora.z

ui

Uj

Qii-'

CMC

0>E

(0Q.

CO

!iv T!i CO

b)

in

C4

LU

C£3g

Li.

59

Top

long,

reinf.:

15

#11

bars

at

even

spacing

Bottom

long,

reinf.: 2

layers

15

#14

bars

even

spacing
Pg = 0.12 2:1 [ 0.5 + 1.25 (0.18) ] 57 = 0.0053 for N2 and N5

The volumetric ratio required by Eq. (2.8) resulted in

= 0.45

= 0.45 (

- 1

75.43 3.5 - 1 ) 65.61 57 = 0.0041 for all models

The final volumetric ratio was therefore governed by Eq. (2.7) for the

models with lower axial load and by Eq. (2.8) for the models with the

higher axial load. The actual Pg provided was 0.00694 for the flexure

models and 0.01452 for the shear models. These values are a result of

following standard design practices used by CAIUMNS. Table 4.1 summarizes

the details of the models.

The footing (base) of the column was heavily reinforced to prevent any

failure occurring to it. The dimensions of the base were not scaled down

by a factor of one-sixth as required for geometrical similitude. This was

because the base had to be conpatible with an existing structural testing

facility (see Appendix C) to prevent any uplift during the test and to

simulate a fixed boundary condition. The d^th of the base was chosen so

that the models would fit into the testing facility with a minimum amount

of relocation required of the servo-hydraulic rams. These changes in base

dimensions were considered to have no detrimental effects on the results

of the tests since the prototype base was designed to operate in the

elastic range under actual test conditions. The amount of base

reinforcement was scaled down at (1/6.1)^ of that used in the prototype.

4.2 Oonstmction Process

The formwork for the base was constructed using high-density, plasticcoated plywood. This type of plywood was selected because of its strength,

durability, non-stick qualities, and for the smooth finish imparted to the

concrete which aided in detection of cracking. The joints in the formwork

were sealed by a water-proof tape and the forms were oiled prior to

casting.

The column was formed using Sonotubes, a commercially available cylindrical

form made of spun paper. A 10-inch (25.4 cm) inside diameter Sonotube was

selected as an initial best-estimate of the required model column diameter.

This was then split down its length, and the circumference reduced by the

amount needed to result in a 9.8 in. (24.89 cm) diameter. Metal strapping

was used to seal the split tube. Water-proof was used to seal the seam

prior to casting.

60
TABLE

4.1

MODEL

PROPERTIES

I

I <3 o o o o o o

(U CJ iH <N 1—1 rH CM rH

PM • • • • • • M-l o o o o O O

CQ in in PM 00 r>- 00 00 00 Q^H • • • • • • PM ^ VO CO VO VO CO VO

cs in <N C«4 in CM

C>H o o> 1—1 in 'St - CQ <T> 00 CO VO

M-l PM CO VO in in CO

CO CO CO CO CO CO

CN cs cs CM

in in a\ in m <Tl CQ VO VO

1—

o 1—

1—

o

o o o o o o • • • • • •

. o o o o o o

ELD

RESS p

(ksi)

cn <T\ M EH CQ VO VO VO VO VO VO

CO JH W 4-1

U

i-q S

(< M

« U

H <

PM PM CO CO CO

IT) COIT) CO in

inCO

inCO in

o Q, o o o o

<

M

PMCO m

'TD

z

o

CQ

>1

>H M-l

r- c^ c^ m in m m m m

cs J -H

I o w

I s w

I O E-t w

I i-:i CO <

o

in

u

QO

iH CS CO S Z Z ^ in VO z z z

61
The base reinforcement, consisting of stirrups, shrinkage, tension and

corrpression steel, was tied first. The D6 deformed wires used to model the

longitudinal column reinforcement were mounted in a separate jig. Preformed spiral coils were then tied to the longitudinal reinforcement (see

Fig. 4.3) to form the finished column. The longitudinal bars were

instrumented with electrical strain gages prior to tying the spiral. The

gages on the spiral were placed after the column cage was corrpletely tied.

Fig. 4.4 shows a close up of an instrumented Column cage. The locations of

the various strain gages are shown on Figures 4.8 and 4.9. The

instrumented column cage was then tied to the base cage as shown in Fig.

4.5. Fig. 4.6 shows the sizes of the steel wires used ini the model and the

arrangement of the steel.

4.3 Model Casting

The casting of the models was done in two phases. The bases in each set

were cast first and then the columns were cast a few days later creating a

cold joint at the column-base joint, as is common practice in industry. The

microconcrete for the bases of models N1 - N3 was mixed without the use of

superplastizers and as a result substantial vibrating was necessary to

ensure that the concrete flowed between the ti<^tly spaced reinforcement.

The casting of one of the microconrete bases is shown in Fig. 4.7.

The pea gravel mix was easier to place and no problems were encountered

with premature set. Si:53erplastizer was not included in the pea gravel mix.

Slump tests were used as a guide to determine the workability of the

concrete. The air content was also measured.

4.4 Instrumentaticai

A total of 49 strain gages were used for each model. The majority of the

gages were placed in the potential plastic hinge region. Figs. 4.8 - 4.10 show the location of these strain gages. The gages in the base and

outside the potential plastic hinge region were used to monitor the

progression of yielding in both longitudinal and confining spiral

reinforcement. Figure 4.11 shows typical strain gage placements in the

model columns. Type 2 gages were redundant backups for the "Type 1" gages

applied to the longitudinal reinforcement in the anticipated plastic hinge

region. Both Type 1 and 2 gages were aligned parallel to the

reinforcement to measure axial strain. Type 3 gages were placed at 45° off

the axis of loading (see Fig. 4.11) to monitor any eccentric bending during

the test.

Five embedment strain gages, oriented vertical, and parallel to the axis of

loading, were placed across the width of the column-base joint, along the

column centerline, and were used to monitor the axial strain variation

through the column. Fig. 4.12 shows a sketch of a typical flexurecoirpensating embedment gage used in the models.

Two LVDTs were used to measure the rotation at the base of the column.

These were attached to the column by means of a piece of all-thread bar.

The all-threads were inserted into a hole drilled into the column and then

held in place by an epoxy for the microconcrete models. The all-threads

were screwed into anchors placed in the column forrrwork prior to casting of

62
Tying of spiral cage

Fig. 4.3

63
li'T

64

Instrumented

column

cage
Tying column cage to base cage

Fig. 4.5

65
COLUMN DIMENSIONS AND STEEL LAYOUT

9.8

0.33

S'luare

cross-section

25-D6 (0.276 dia.)

1. GA 1 2 at 0.57

N3 & N6

2. GA 11 at 0.35

N1,N2,N4,N5

All dimensions

in inches

0.33

24.25

NOTE: Width of the base is 28.375

FIGURE 4.6

66

I

o
Casting of microconcrete bases

Fig. 4.7

67
FLEXURE COLUMN AXIAL STRAIN GAGE LOCATION AND REINFORCEMENT SCHEDULE

All dimensions

in inches

1-in. = 25.4mm

145 psi = 1 MPa

Smooth spiral bars

0.106 ^ at 0.57*pitch

models N3 & N6

25-D6 deformed

reinforcing bars

Fy = As = Ps =

FIGURE 4.8

60 ksi 1.50 in2 0.00694

68
SHEAR COLUMN AXIAL STRAIN GAGE LOCATION AND REINFORCEMENT SCHEDULE

9.8

All dimensions

in inches

1-in. = 25.4mm

145 psi = IMPa

29.5

Smooth spiral bar

0.120*0 at 0.35* pitch

Models N2,N1,N4,N5

25-D6 deformed

reinforcing bars

As

= 60 ksi = 1.50m2

= 0.01452

FIGURE 4.9

69
FLEXURE AND SHEAR SPIRAL GAGE LOCATION

9.8

Spiral pitch

Flexure (F):

Shear (S):

Bar ^ 0.57 0.106

0.35 0.120

All dimensions in inches

1-in. = 25.4mm

145 psi = 1 MPa

F: 11

S: 5

F: 9

S: 4

F: 9

S: 4

F & S: 6

fy (ksi)

69

64

FIGURE 4.10

70
STRAIN GAGE LOCATIONS

(Top View)

Loading Direction

Type 1 bars have 9 gages

Type 2 bars have 4 gages in positions A-D

Type 3 bars have 1 gage in position A*

* Refer to Figs. 4.8 and 4.9

Fig. 4.11

71
EMBEDMENT GAGE

Inner sealant, acrylic

water proofing

Butyl rubber sealant

Shrink fit waterproof

armor

Two 0.031*, 120 ohm

strain gages in series

4/40 threaded end

anchor

0.135' diameter

aiuminum ailoy rod,

threaded 4/40 for

0.125' at each end

Strain gage iead

wires (26 gage wire)

9

Fig. 4.12
Two LVDTs were used to measure the rotation at the base of the column.

These were attached to the column by means of a piece of all-thread bar.

The all-threads were inserted into a hole drilled into the column and then

held in place by an epoxy for the microconcrete models. The 3II-threads

were screwed into anchors placed in the column formwork prior to casting of

the concrete for the pea gravel models. Two or four additional LVDTs were

used along the height of the column for the shear and flexure models

respectively. One of the LVDTs for each of the models was placed at the

same height as the point of lateral load appplication to measure the

maximum displacement e5q)erienced by the column. The other LVDTs were used

to measure the displacement of the column at various heights along the

column. Figs. 4.13 - 4.14 show the location of the LVDTs.

73
LVDT LOCATIONS FOR SHEAR COLUMNS

All dimensions

in inches

1“in = 25.4mm

Fig. 4.13

7 4

frame
LVDT LOCATIONS FOR FLEXURE COLUMNS

-^ 9. 8

—*

Ail dimensions

in inches

(1-in. = 25.4mm)

19.5

Rigid

frame

19.5

Fig. 4.14

75
5.0 TEST RESUEES AND OBSERVATIC»JS

5.1 Irit^xxiucticai

The determination of the yield load and the loading sequence are the same

as the method and procedure used by Priestley et. al. [37] . The ultimate

moment of the column was calculated using the ACI column charts [4]. The

yield load was assumed equal to 75 % of the lateral load vhich would induce

ultimate ACI moment in the column. The column was loaded to the yield load

in both the forward (south) and reverse (north) directions and the two

displacements measured. The "yield” displacement in each direction was

then obtained by dividing the experimentally determined deflection (as

described above) by 0.75. The average of the two deflection values was

then used as the yield displacement, A y. The calculation of the

experimental yield displacement is shown in Pig. 5.1.

In general, the loading sequence for the shear model tests was one cycle at

Ay, two cycles each at u = + 2, + 4, + 6 , ... . If a significant drop in

the moment capacity of the column in the second cycle as corrpared with the

fiorst cycle at the same ductility level was noted, the-column was subjected

to a third cycle at that ductility level. The loading history for the

flexure models was one cycle at A y, two cycles each at m = + 2 and + 3.

Instead of two cycles at m = + 4 as with the shear models, the flexure

models were subjected to 10 cycles at m = + 4. The reason for this

deviation was that the maximum achievable m as governed by the maximum

stroke of the hydraulic ram for model N3 was 5. It was decided then to

consider the effects of the number of loading cycles on the column

behavior. The tests were stopped vhen most of the bars had fractured.

The model columns were tested in the TTF (Tri-Directional Test Facility), a

general purpose three axis structucal testing system at the National Bureau

of Standards (See Appendix C). The columns were first loaded axially to a

pre-determined force which simulated the gravity loading of the bridge

superstructure. Lateral force was then increased to yield load. The

direction of loading was north-south (see Fig. 5.2 for specimen test setup) with the first excursion to the south. The first cycle was conducted

under load control (loadcell feedback to the closed loop servo-hydraulic

actuator system) while the remainder of the test was conducted under

displacement control (displacement transducer feedback to the closed loop

servo-hydraulic actuator system). Cracks were hi^lighted as they formed

so that they could be seen more clearly in photographs. Hiotographs were

taken at the end of most of the excursions.

The remainder of this chapter presents a detailed discussion of test

specimen properties and observations of behavior made during each test.

The observations are presented in the form of a cycle-by-cycle log keyed to

figures showing significant changes in column appearance (e.g. crack

extension, failure of reinforcement etc.). The reader should bear in mind

that the test specimen was mounted in a loading system in which lateral

load was applied in a direction parallel to the north-south magnetic axis.

The fiirst excursion in any load cycle was always southward, followed by a

return to the initial position, a subsequent northward excursion, and a

return to initial position vhich completed the cycle.

76
EXPERIMENTAL DEFINITION OF

YIELD DISPLACEMENT

Fig. 5.1

77
TTF TEST SET-UP

Upper (loading) Computer controlled

78
5.2

Mociel N1

5.2.1 MODEL PROPERTIES

= 3490 psi (24.08 MPa)

Pq = 26.87 kips (119.6 KN)

M^ (experimentally) = 38.35 ft-kip (52.0 kN-m)

Pj^ = 10.8 kips (48.06 KN)

Ay (experimentally) = 0.38 in. (9.65 mm)

where Pj^ is the lateral "yi©l<^" load. The load history is shown in Fig.

5.3.

5.2.2 DQCriLriY FACTOR = 1, CYCLE 1 ’ - Hairline flexure and shear cracks appeared v^en the lateral load was equal

to 7.5 kips (33.37 KN) or approximately 69 % of the calculated yield load.

Cracks were observed up to a height of 1* - 8” (50.8 cm) above the base.

See Fig. 5.4.

5.2.3 DUCTILITY FACTOR = 2 , Cycles 2 & 3

Existing cracks prc^gated and new. cracks formed - both flexure and shear.

On the excursion south, second cycle,^very minor crushing appeared to be

occurring at the base of the south side of the column.

5.2.4 DUCTILITY FACTOR = 4, CYCLES 4 & 5

Cycle 4: Crushing of the column base on the south side was evident during

the southward excursion with flaking occurring on the excursion north. See

Fig. 5.5.

Cycle 5: Pieces of concrete, one about 1 in. X 2 in. (2.54 X 5.08 cm ) fell off the south side on the excursion south. All spall dimensions are

width X hei^t. This is shown in Fig. 5.6. Additional shear cracks formed.

Some flexure crack widths were approximately 0.375 in. (9.5 mm). An area

in the base foundation beam adjacent to the south side of the column

began to spall, as if the colimm was pulling out.

5.2.5 DUCTILITY FACTOR = 6, CYCLES 6 & 7

Cycle 6: On the excursion south, some crack widths on the north side of

the column were about 1/4 in. (6.35 mm). The base around the column on the

north side showed signs of uplifting also. A radial crack. Fig. 5.7, at

about a distance of 2.5 - 3 in. (64 - 77 mm) out from column, appeared in

the base on the south side. On the subsequent excursion nori±i, the column

base on the north began to spall. A few additional cracks formed.

79
loading

history

for

model

N1

80
Model Nl, DF = 1, Cycle 1

Fig . 5.4

i

81
Model Nl, DF = 4, Cycle 4

Fig . 5.5

82
83

Model

Nl,

DF

=

4,

Cycle

Fig

.

5.6
84

Model

Nl,

DF

=

6,

Cycle

Fig

.

5.7
Cycle 7: On the excursion south, the column base on the north spalled off.

The spall areas on both the north and south sides of the column were

approximately 6 X 2 in. (15.24 X 5.08 cm). A few additional cracks formed.

5.2.6 DUCTILITY mCTOR = 8 , CYCLES 8 , 9 & 10

Cycle 8 : Three pops were heard during the first southward excursion. No

visible sign of fracture could be seen as the concrete obscured the

longitudinal bars frcm view. These sounds could have been the breaking of

ties used to tie the longitudinal bars to the spiral cage, as was observed

in another test. Severe crushing of the column base on the south side was

noted. Buckled longitudinal bars were visible on both the north and south

sides of the column. The lateral load on the excursion south was about 66%

of the yield load.

Cycle 9: Again, the sound of fracturing "bars" was heard twice. The

longitudinal bars had buckled out by approximately an inch (25.4 mm). The

spiral was still intact but had yielded. This was most likely due to it

sliding 1:5) along the buckled longitudinal bars, allowing it to reduce its

stress.

Cycle 10; Ten longitudinal bars had buckled and one was completely

fractured on the south side of the column.

5.2.7 DUCTILITY FACTOR = 10, CYCLE 11

Six longitudinal bars on the north side and seven on the south side had

fractured. Fig. 5.8 shows the entire column and a close-up showing the

fractured bars is shown in Fig. 5.9.

5.3 Model N2

5.3.1 PROPERTIES

f'^^ = 3349 psi (23.11 MPa)

P^ = 53.75 kips (239.2 kN)

(experimental) = 46.52 ft-kip (63.07 kN-m)

Pj^ = 11.15 kips (49.6 kN)

Ay (experimental) = 0.22 in. (5.59 mm)

The loading history is shown in Fig. 5.10.

5.3.2 DUCmiTY FACTOR = 1, CYCLE 1

Only flexure cracks were noted upon loading the column to the yield load.

These appeared as horizontal cracks initiating at the north and south

centerlines of the column and propagating to the east and west centerlines.

85
MODEL N1

A KIP

S|3.9 IN

Model Nl, DF = 10, Cycle 11

Fig. 5.8

86
I

Fig.

5.9
LOADING

HISTORY

FOR

MODEL

N2

CO

88

Fig.

5.10
These reached a height of 1' - 2" (35.6 cm). The load at first cracking

was to 7.8 kips (34.69 kN) or approximately 70 % of the calculated yield

load. The crack initial pattern is shown in Fig. 5.11.

5.3.3 DUCITLITY FACTOR = 2, CYCLES 2 & 3

"

Shear cracks evidenced by propagation of previously horizontal flexure

cracks at a pronounced inclination (approximately 45^. This is shown in

Fig. 5.12. Flexure cracks had formed to a height of 1' - 10" (55.9 cm)

above the base of the column.

5.3.4 mCITLITY FACTOR = 4, CYCLES 4 & 5

Crushing of the concrete and formation of vertical cracks about 1 - 2 in.

(25.4 - 50.8 mm) in length were noted. The column could be seen to be

separating from the base by about 0.1 in. (2.5 mm) and the width of cracks

was about 0.1 in. (2.5 mm).

5.3.5 roCITLiTIY FACTOR = 6, CYCLES 6 & 7

Cycle 6: More crack propagation was observed with, new cracks forming.

Additional crushing of the column base on the north and south sides with

spalling on the south side occurred. Some of the flexure cracks near the

base of the column were about 3/16 in. (4.8 mm) wide. The crack pattern

is shown in Fig. 5.13.

cycle 7: Spalling on both the north and south sides occurred. A piece of

concrete about 5X3 in. (12.7 X 7.6 cm) fell off on the south side.

Unfortunately, the LVDT measuring the rotation came off along with it. The

spiral did not a{^)ear to have yielded.

5.3.6 mCTTLETY FACTOR = 8, CYCLES 8 & 9

CYCLE 8: New flexure and shear cracks formed. The widths of some cracks

ranged from 3/16 in. - 1/4 in. (4.8 - 6.3 mm). Some uplifting of the base

on the northeast side was noted. A spiral about 2 in. (5.08 cm) up from

the base on the south could be seen to have yielded. Fig. 5.14 shows the

spall area and the yielded spiral.

CYCLE 9: A longitudinal bar on the south side buckled. Spirals above and

below the previously yielded spiral on the south also appeared to have

yielded.

5.3.7 DUCTILITY FACTOR = 10, CYCLES 10, 11, & 12

CYCLE 10: A total of six bars on the south side and a total of five bars

on the north side were c±)served to have buckled at this point. Spalling on

the north side was noted in this cycle. A spiral 2 in. (5.08 cm) from the

base on the north side appeared to have yielded. The spiral 2 in. (5.08

cm) from the base on the south side fractured.

CYCLES 11 & 12: Ei^t longitudinal bars were observed to have buckled on

the south side. The spall area on the south side measured approximately

about 9X4 in. (22.9 X 10.2 cm) and 10 X 4 in. (25.4 X 10.2 cm ) on the

89
Model N2, DF = 1 , Cycle 1

Fig. 5.11

90
Model N2, DF = 2, Cycle 2

Fig. 5.12

91
Model N2, DF = 6, Cycle 6

Fig. 5.13

92
!

i

Model N2, DF = 8, Cycle 9

Fig. 5.14

f

93 *
north side. Three longitudinal bars on the soul^ fractured in cycle 12.

The lateral load was reduced to 0.78 Py in the 12^ cycle.

5.3.8 DUCITKETY FACTOR = 12, CYCLE 13

Three longitudinal bars on the north broke and two additional bars broke on

the south in this cycle. Fig. 5.15 shows the fractured bars on the south

and Fig. 5.16 shows the spall area on the south side.

5.4 Model N3

5.4.1 MODEL PROPERTIES

f*^ = 3681 psi (25.4 MPa)

Pq = 26.87 kips (119.6 kN)

M^ (experimental) = 43.79 ft-kip (59.37 kN-m)

Pj^ = 5.4 kips (24 kN) - ' - Ay (experimental) = 1.01 in. (25.6 mm)

The loading history is shown in Fig. 5.17.

5.4.2 DUCITLITY FACTOR = 1, CYCLE 1

Flexure cracking began at 2.7 kips (12.0 kN) or approximately 50 % of the

calculated yield load. No shear cracking was observed. Fig. 5.18 shows

the crack pattern. - ^

5.4.3 DUCITLETY FACTOR = 2, CYCLES 2 & 3

Few additional cracks formed at this ductility level. The crack widths

ranged from 0.08 - 0.1 in. The severity and number of cracks were similar

on both the north and south sides. Very minor crushing of the south side

occurred.

5.4.4 DUCnUTY FACTOR = 3, CYCLES 4 & 5

Some spalling on the south side occurred. The LVDT used to measure the

south rotation came off along with the concrete cover. Some spalling also

occurred on the north side. The crack widths were approximately 0.16 in.

(4 ram). A few vertical cracks about one inch (25.4 mm) in length formed. A

spiral about 3 in. (7.6 cm) above the was noted to have fractured vhen the

cover spalled off. The fracturing of the spiral was unexpected. However,

upon inspection of the spiral, the south bar was observed to been damaged

during the drilling of the column to install the LVDTs used to measure the

rotation. The influence vhich this had on the energy absorption performance

is discussed in section 6.2. Fig. 5.19 shows the spalling of the south

side.

94
lybdel N2, DF = 12, Cycle 13

Fig. 5.15

95
96

Model

N2,

DF

=

12,

Cycle

13
LOADING

HISTORY

FOR

MODEL

N3

97

Fig.

5.17
Model N3, DF = 1, Cycle 1

Fig. 5.18

98
Model

N3
5.4.5 DUCnLITY FACTOR = 4, CYCLES 6-15

CYCLE 6: Formation of additional vertical cracks occurred. The crack

pattern is shown in Fig. 5.20 for the south side following the excursion to

the south. The spiral about 3 in. (7.62 cm) above the base Tractured on

the north side. Upon inspection, the spiral had also sustained minor

damage during the drilling process. Additional spalling was also observed.

CYCLES 7 - 10; Vertical bars on both the north and south sides were

c±>served to have buckled. Spalling to a hei^t of 5 in. (12.7 cm) from

the base was noted. Figs. 5.21 and 5.22 show the fractured spiral and the

buckled bars respectively.

CYCLES 11 - 15; The column had spalled almost entirely around its

cicumference. Three longitudinal bars on the north and three on the' south

fractured with the first fracture occurring on the eleventh cycle on the

north side.

5.4.6 DUCITUirY FACTOR = 5, CYCLE 16

A 4

^

longitudinal bar on the south fractured in this cycle. The lateral

load had decreased to approximately 0.30 Py. The extent of damage is shown

in Fig. 5.23. ^

5.5 Model N4

5.5.1 MODEL PROPERTIES

f*^ = 3545 psi (24.46 MPa)

P^ = 26.86 kips (119.53 kN)

M^ (experimental) = 37.48 ft-kip (50.82 kN-m)

Pj^ = 10.87 kips (48.37 kN)

A

y

(experimental) = 0.21 in. (5.33 ram)

The loading history is shown in Fig. 5.24.

5.5.2 DUCTILITY FACTOR = 1, CYCLE 1

Lateral load at first cracking was 9 kips (40.0 kN) or approximately 83 %

of the calculated yield load. The cracks were hairline flexure cracks

which reached a height of about 1' - 2” (35.56 cm) on both the north and

south sides. Fig. 5.25 shows the cracked column.

5.5.3 DUCTILITY FACTOR = 2, CYCLES 2 & 3

The flexure cracks propagated to the east and west sides of the column and

additional cracks appeared up to a height of 1' - 8.5" (52.1 cm). Crack

propagation and formation occurred mainly during the second cycle. The new

crack pattern is shown in Fig. 5.26.

100
Model N3, DF = 4, Cycle 6

Fig. 5.20

101
Model N3, DF = 4, Cycle 7

Fig. 5.21

102
I

103

Model

N3,

DF

=

4,

Cycle

10

Fig.

5.22
104

lyfcdel

N3,

DF

=

5,

Cycle

16

Fig.

5.23
LOADING

HISTORY

FOR

MODEL

N4

CO

105

Fig.

5.24
Model N4, DF = 1, Cycle 1

Fig. 5.25

106
Model N4, DF = 2, Cycle 2

Fig. 5.26

107
5.5.4 DUCrinCTY FACTOR = 4, CYCLES 4 & 5

Minor crushing of the base on the south side occurred. Additional flexure

cracks appeared near the base of the column. Some of the cracks began to

proceed downwards at an angle of about 20° - 30^ as they propagated

towards the east and west sides of the column as shown in Fig. 5.27. Most

of the cracking occurred during the fourth cycle.

5.5.5 mCTTLITY FACTOR = 6, CYCLES 6 & 7

Spalling on the south side of the column occurred with a piece about 1-1/2

X 1-1/2 in. (3.8 X 3.8 cm) falling off. The spalling did not expose the

spiral at this stage. Separation of the column from the base was about

0.04 - 0.08 in (1 -2 ram). Few additional cracks formed at this load stage.

5.5.6 DUCTILITY lACTOR = 8, CYCLES 8, 9, & 10

Spalling on the north began during the 8^ cycle. The spall area on the

south was about 9 X 2.5 in. (22.9 x 6.3 cm). The spall area on the north

was about 7-1/2 X 1-1/2 in. (19.1 X 3.8 cm) at the end of the 10^ cycle.

No add^ional cracks were observed. No lateral load drop was noted after

the 9

^

cycle. However, a third cycle at DF = 8 was carried out since the

counterpart of this model, Nl, was cycled three times at DF = 8. The

objective in doing this was to precisely replicate loading history in an

effort to isolate possible differences in energy absorption performance

between the two columns.

5.5.7 DUCTILITY FACTOR = 10, CYCIES 11, 12 & 13

CYCLE 11: Yielding of spirals at the column-base joint was observed during

this cycle. Four buckled bars on the South side were also notedCYCIE 12: A spiral on the north side approximately 0.5 in. (12.7 mm) above

the base fractured. A total of 8 longitudinal bars and 7 longitudinal bars

on the north and south sides, respectively, had buckled at this load stage

as shown in Fig. 5.28.

CYCLE 13: A longitudinal bar on the north side fractured vhile two on the

south side fractured. The peak lateral load was reduced to 0.56 Py in this

cycle. ^

5.5.8 DUCnilTY FACTOR = 12, CYCLES 14 & 15

IXiring the 14^ cycle, three additional longitudinal bars fractured on the

north which increased the total number of fractured bars on the north to

fo^. An additional longitudinal bar on the south fractured during the

15^ cycle. These fractured bars are shown in Fig. 5.29.

108
^todel N4, DF = 4, Cycle 4

Fig. 5.27

t

109
110I

Model

N4,

DF

=

10,

Cycle

12

Fig.

5.28
Model N4, DF = 12, Cycle 15

Fig. 5.29

111
5.6 Mcx3el N5

5.6.1 MODEL EROPERITES = 3534 psi (24.38 MPa)

P^ = 53.75 kips (239.19 kN)

M^ (experimental) = 46.61 ft-kip (63.23 kN-m)

Pj^ = 11.15 kips (49.61 kN)

(experimental) = 0.19 in. (4.83 mm)

The loading history is shown in Fig. 5.30.

5.6.2 DUCTILITY FACTOR = 1, CYCLE 1

Hairline flexure cracks, six on the north side and five on the south side,

appeared at this load stage. Two shear cracks were also observed on the

south side of the column. The cracks reached a hei^t of 1* - 4 1/2" (41.9

cm) on the south side and 1' - 2" (35.6 cm) on the north side of the

column. The crack pattern on the south is shown in Fig. 5.31.

5.6.3 DUCTILTTY FACTOR = 2, CYCLES 2 & 3

The flexure cracks began to proceed downwards at angles of about 20° - 30°

as they propagated to the east and west sides of the columns. Additional

flexure cracks appeared up to a height of 1* - 8" (50.8 cm) on the south

side of the column. ^

5.6.4 DUCITLETY FACTOR = 4, CYa.ES 4 & 5

Minor crushing occurred at the base of the column on both the north and

south sides. Some additional shear cracks formed on the east and west

sides of the column. The crack pattern for this load stage is shown in

Fig. 5.32.

5.6.5 DUCTTLETY FACTOR = 6, CYCLES 6 & 7

More crushing was observed at the base of the column on both the north and

south sides. Additional shear and flexure crack formation were also noted.

Some of the crack yddths were about 0.08 in. (2 mm). The south side

spalled off on the 7^ cycle with the spall area approximately equal to 5 X

1-1/2 in. (12.7 X 3.8 cm).

5.6.6 DUCnLTTY FACTOR = 8, CYCLES 8 & 9

Some additional flexure cracks were noted on the north side of the column.

Some new shear cracks were also observed on the east and west sides of the

column. The north side of the column began to spall off with the area of

spall measured approximately 6X2 in. (15.2 X 5.1 cm).

U2
LOADING

HISTORY

FOR

MODEL

N5

I

CO

113

Fig.

5.30
Mcxiel N5, DF = 1, Cycle 1

Fig. 5.31

114
!

Model N5, DF = 4, Cycle 4

Fig. 5.32

115
5.6.7 DUCnUTY FACTOR = 10, CYCLES 10, 11 & 12

CYCLE 10: A succession of cracking sounds was heard like that viiich would

be produced by three bars fracturing although no visual verification was

possible. The spall areas on the north and south sides of the column were

8X2 in. (20.3 x 5.1 cm) and 6 X 2 in. (15.2 X 5.1 cm) respectively. Two

longitudinal bars were observed to have buckled on the south side of the

column. The spiral at the column-base joint on the south side and the

three spirals immediately above appeared to have yielded.

CYCLE 11: A spiral on the south side of the column at about 2 in. (5.1 cm)

above the base fractured as indicated in Fig. 5.33. One bar on the

northeast side of the column was noted to have fractured, probably in the

previous cycle. Four and six longitudinal bars on the south and north

sides of the column, respectively, had buckled. Four spirals on the north

side of the column appeared to have yielded. The spall area on the south

was about 9X2 in. (22.9 X 5.1 cm) with the spall area on the north

unchanged.

CYCLE 12: The spall area on the south increased to about 9 X 3 in. (22.9 X

7.6 cm). A spiral on the northwest side of the column about 3/8 in. (9.5

mm) above the base fractured. The fractured spiral is shown in Fig. 5.34.

5.6.8 DUCITLrTY FACTOR = 12, CYCLES 13 & 14

Four longitudinal bars fractured in succession on the north side of the

column making a total of five fractured bars on the north side. Three

longitudinal bars broke in succession on the south and two more a little

later on, A longitudinal bar on the south was observed to have fractured,

probably one of the snaps heard earlier. A total of 6 fractured bars were

observed on the south side. The spali area and the fractured bars on the

south side are shown in Fig, 5.35. The peak lateral load in the 13^ cycle

was reduced to approximately 0.60 Py

5.7 Model N6

5.7.1 MODEL PROPERTIES

f'^. = 3367 psi (23.22 MPa)

Pg = 26.87 kips (119.53 kN)

M^ (experimental) = 36.87 ft-kip (49.99 kN-m)

Pj^ = 5.4 kips (24.0 kN)

(experimental) = 0.66 in. (16.8 mm)

The loading history is shown in Fig. 5.36.

116
11-7

Model

N5,

DF

=

10,

Cycle

11

Fiq.

5.33
Model N5, DF = 10, Cycle 12

Fig. 5.34

118
Model N5, DF = 12, Cycle 13

Fig . 5.35

119
LOADING

HISTORY

FOR

MODEL

N6

120

Fig.

5.36
5.7.2 mCITIITY FACTOR = 1, CYCLE 1

Hairline flexure cracks were observed at a lateral load of 2.25 kips (10

kN) on the first excursion south and at a load of 2.64 kips (11.7 kN) on

the first excursion north. These loads are 41.7 % and 487 9 % of the

calculated yield load for the lateral load to the south and north

respectively. Cracks formed to a hei<^t of 2'- 0" (61 cm) on the north

side and up to 2'- 2" (66 cm) on the south side. The south side of the

column is shown in Fig. 5.37.

5.7.3 mCITLrTY FACTOR = 2, CiCLES 2 & 3

More flexure cracks appeared on both the north and south- sides of the

column. The existing cracks prcpagated to the east and west sides of the

column as shown in Fig. 5.38. A crack was noted at the column-base joint.

Very minor crushing of the column at the base on the south side was also

noted.

5.7.4 mCITLrTY FACTOR = 3, CYCLES 4 & 5

Minor flaking of the south side began at a lateral Load of 5.8 kips (25.8

kN) and at a lateral load of 6.6 kips (29.4 kN) on the north side. Both

occurrences were in the 4^ cycle. Two additional flexure cracks were

dDserved on the north side of the column. The width of cracks ranged from

0.08 in to 0.12 in. (2-3 mm). The column appeared to be hinging at

approximately 3 in. (7.6 cm) above the base on the north side.

5.7.5 mCTTLCTY FACTOR = 4, CYCLES 6-15

CYCLES 6-9: Formation of some shear cracks was observed on the east side

of the column. IrKZxeased 'flaking on both the north and south sides of the

column occurred. This is shown in Fig. 5.39. A piece of concrete cover

about 2X2 in, (5.1 X 5.1 cm) spalled off on the south side of the column

during the 6

^

cycle. Maximum crack width measured was approximately 0.25

in. (6.3 mm).

CYCLES 10 -12

Spalling on both the north and south sides continued. Spall areas were

about 8X2 in. (20.3 X 5.1 cm) on the south and 5X2 in. (12.7 X 5.1 cm)

on the north. The spalling exposed the spiral on the north side of the

column. The LVDT measuring the rotation on the ^yth came off along with

the cover concrete when it spalled during the 12^ cycle. The spiral on

the south was esqxDsed vhen this occurred and two of the spirals, one about

2 in. (5.1 cm) above the base and the one above that, showed signs of

straightening out between the longitudinal bars.

CYCLE 13: One longitudinal bar on the south was noted to have buckled. A

third spiral on the south began to straighten out between the vertical

bars. Additional cover concrete on the north side appeared to be ready to

spall off. The concrete core seemed to be intact (i.e. no cavities in the

core were noted).

CYCLE 14: Two longitudinal bars on the south side were noted to have

buckled. The spiral 2 in. (5.1 cm) above the base on the south fractured

121
Model N6, DF = 1, Cycle 1

Fig. 5.37

122
Model N6, DF = 2 , Cycle 2

Fig. 5.38

123
Model N6, DF = 4, Cycle 6

Fig. 5.39

124
on the excursion south. The spiral 2.75 in. (7.0 cm) above the base on the

north fractured on the excursion north. Three longitudinal bars on the

north side could be seen to have buckled. In general, the buckling of bars

proceeded in accordance with their distances from the column E-W

centerline. That is to say, the southern most longitudinal b^ v^ch lies

on the N-S centerline typically buckled first following a sufficiently

large excursion to the south. Subsequently, the two adjacent bars to

either side would buckle next. Fig. 5.40 shows the fractured and the

buckled bars. The spall areas on the south was 8 X 4.5 in. (20.3 X 11.4

cm) and 7 X 4.5 in. (17.8 X 11.4 cm) on the north.

CYCLE 15: Three additional longitudinal bars on the south buckled. The

spiral below the previously fractured spiral on the south fractured. The

location of the second fracture was directly below that of the first

fracture. Five longitudinal bars on the north had buckled by this load

stage. Spall areas were 9 X 4.75 for the south side in. (22.9 X 12.1 cm)

and 8 X 4.5 in. (20.3 X 12.1 cm) on the north side. A cavity on the south

side was beginning to form in the concrete core.

5.7.6 mCTimY FACTOR = 5, CYCLES 16 - 18

More spalling occurred with the spall areas increasing to 12 X 4.5 in.

(30.5 X 11.4 cm) on the south side and 11 X 5 in. (27.9 X 12.7 cm) on the

north side. Ei(^t longitudinal bars each on the south and the norih sides

had buckled. The extent of the spall area and the buckling of the bars is

shown in Fig. 5.41. In the 17^ cycle, the peak lateral load dropped to

approximately 0.50 Py. This indicated, for all practical purposes, the

useful end of the test.

5.7.7 mCTTLITY FACTOR = 6, CYCLES 19 & 20

Two longitudinal bars fractured during the 19^ cycle on the south side as

depicted in Fig. 5.42. A longitudinal bar on the north side fractured

during the 20^^ cycle, and two other bars on the north appeared to be

necking down. The cover concrete around the base of the column had

essentially spalled off entirely i:p to a height of about 5 in. (12.7 cm)

5.7.8 DUdTLTTY FACTOR = 7, CYCLES 21 & 22

• • • Three additional bars on the north fractured during the 21®^ cycle.

Hinging appeared to have occurred at about 2 in. ( 5.1 cm) above the base.

With the exception of two bars, one on the east and the other on the west

sides, all the longitudinal bars had either fractured or buckled at this

load stage.

5.7.9 DUCTILITY FACTOR = 8, CYCLE 23

Only one excursion (half a cycle) was made at this ductility level before

the test was stopped. An additional longitudinal bar on the north

fractured maJcing a total of 5 fractured bars on the north side. Fig. 5.43

shows the north side of the column and Fig. 5.44 shows the south side of

the column at the end of the test.

125
126

Model

N6,

DF

=

4,

Cycle

14

Fig.

5.40
Model

N6,

DF

=

5,

Cycle

18

Fig.

5.41
128

Model

N6,

DF

=

6,

Cycle

20

Fig.

5.42
Model N6, DF = 8, Cycle 23

Fig. 5.43
130

Model

N6,

DF

=

8,

Cycle

23

Fig.

5.44
6.0 DISCCJSSICN OF RESUIIES

6.1 Oolimin Deflection

The best measure of column performance in cyclic load tests is a plot of

the lateral load as a function of maximum lateral deflection. For the

cantilevered bridge column tests conducted in this e5^)erimental program the

lateral load was applied at the top of the column, as would be the case

vtien inertial loads from the hi^way superstructure are irrposed in a real

earthquake. Column lateral displacements were measured at several

locations along the height of the column (see Figs 4.13-4.14), and thus

many load-deflection histories are available for study. To expedite

conparison of performance between different column tests, we will use only

the maximum lateral deflection record, corresponding to the displacement at

the point of application of the lateral load. Hereafter, the phrase "loaddeflection curve" or "load-deflection history** will refer to experimentally

obtained plots of these loads and displacements during the conduct of

cyclic load tests.

The load deflection curves for all the models tested in this study

exhibited stable behavior until fracture of either the spiral or

longitudinal bars occurred as indicated in Figs. 6.1 to 6.6. In these

figures, the overall performance of the column was measured by plotting the

lateral displacement at the top of the column as a function of the lateral

load. The spiral fractured in all the models except for model Nl. The

spiral in Nl slid ipward along the longitudinal bars thereby relieving the

stress in the spiral and leaving it intact. Fracture of a longitudinal bar

was marked by a significant drop in lateral load. This type of behavior

is visible in Figs. 6.1 - 6.6 as a vertical drop on the load-deflection

plots near the point of maximum lateral^load for a given cycle.

The displacement ductilities at ultimate column failure are given in Table

6.1. The column was consider^ to have **failed" (reached ultimate) when

the moment, including the P - a effect, resisted by the model was smaller

than the greater of 80 % of the maximum (north or south) moment measured

during the first cycle to m = + 2. This definition of the ultimate

failure was the same as that used in a study by Zahn et. al. [30].

Ultimate failure as defined by the Japanese researchers in section 2.2.2,

results in the same displacement ductilities as those obtained using Zahn's

definition. Displacement ductilities obtained for the shear models (I/d =

3) were 10 and 12 for models N4 and N5 respectively as cxmpared with 8 and

10 for the shear models constructed from microconcrete, Nl and N2

respectively. Displacement ductility for the flexure model (L/D = 6)

constructed from ready-mix concrete was 5 as compared with 4 for the

microconcrete model.

The measured yield displacements for the microconcrete models with the

lower axial load were much greater than those for the models constructed

from ready-mix concrete with the lower axial load. Yield displacements of

models with the higher axial load, N2 and N5, were, however, the same. The

displacement profiles of the models are shown in which 6.7 - 6.12.

131
1

delta

y,

cycle

1

7-6

delta

y,

cycle

2

delta

y,

cycle

1

8-8

delta

y,

cycle

2

delta

y,

cycle

2

9-8

delta

y,

cycle

COo

CMC CM c c E o> < CO

CMc

0)

0) o CD E

. o (S. T— T- CM

CO id lO o o CM id d N. d d d d CM d (N II II II II II II II

II II (D 0.

a> <

(fl < a(A a

CO

k.

C/3 cc c

Q. CD CO

CM T- CM CO Tcnu

X

u

X

u

X

LlI u

X

_lp.

(/)

X

Z)o

a

a

o

X

x

o

COu

u

>

C_) Q

X

o

CO

LU

cc3

CD

(ScLi>o auon ibiwoziaoH

132
J

I

j

1

'i

I

(0 C\J o> c OVJ c c £

< CM 05 in **" £ 00 _c 0) o CO

. O

if3 T— CM N. oj —

in in O o *“ CM in

'•'i 00 T— d d d d CM o m

II II

II II. II II II II II

(D C3) (0 V) CO CO c Q. < < a a

k_CO 'a m CO

Q.

GO ro ro

I o

I

00

I

cnLUI

a

z

u

c

Ulu

<r

-JA.

CO

z:c3

-IO

u

(Mr

LU

(=) O

c

O

U.

COU

-JCJ>

u

CO

<ro

CNJ CO

LU

GC3

g

LU

csdi><) auon nuiwoziaoH

133
1

delta

y,

cycle

1

9-4

delta

y,

cycle 4

2

delta

y,

cycle

1

10-4

delta

y,

cycle 5

2

delta

y,

cycle

2

11-4

delta

y,

cycle 6

3

delta

y,

cycle

1

12-4

delta

y,

cycle 7

O) . 9- < JC c

CO c

a>0) 0) CD c

CD c

CD E

E

N. Tt — T— O O N- oq lO o O (N in r CD r- c> d CD CD CM O C\J

II II II II II II II

II II 0) O) CO CO (0 c

0. A A a a c5 'a CD CO

o (» Oi o <D CD (D 6 O u u > > >« >* o u o o

>* >» >* >*

(0 CO CO CO

0) <0 (U (D •o •o T3 O

rf in

CO in (0

I I I CM C*5

cvj CJ CO

(0 CD 0 0

o- O U u

>» >. > >. u u o o

>» >• 9s

CO ca 0 0

CD 0 0 0

a T3 a •O

COm (0 CO

LO LO

0" rs

CO

LlI X

u

X

X

LiJ X

UJu

X

_lpcoX

_lo

u

ro

UJQ

o

X

QCo

u.

inUJ

_Ju

>

o

Q

X

o

CO

cd

LU

C£

D

o

<s<ii>o auoi nyiKioziyoH

134
JI I w

oi .9- < ^ ^ 00 r CD O (N

II II (D CL

CL

CV4c CVJ c c E

CJ 0) in E 00 c 0) rf o CO

T— CM N.

ir> in o o CM in

s. d d d d CM

II II II II II II II

O) <

<n < a

CO a

15 CO

CO c

'a OQ CO

00

too

tooI

00

touIu

z:

z:LUC

LUU

CE

-JP-

(Oc

Z)oo

LUaono

Ll.

(/) LUu>oQ

(TO

135

FIGURE

6.4
1

delta

y,

cycle

1

8-8

delta

y,

cycle

O) <

(0Q.

04O

CO

Oic

0)

a

(N

in

Tj- co

c

CD E

E

^ o in T" CVJ 1^

N- in in O o <N in

C\J CO d c> d d C\J d in

II II II II II II II

II II (0

u.CO ®

CL

O) < < a»a

~ca c

Q. CQ CO

>. 2

®

T3

00

I 0)

® ® ® ® ®

a •a -D -o "a O O O CVi 04

I I I 04 CO ^

04 CM CM ® ® ® ® ® ®

o o o O o O

>« >. > >* > >

o o o o o o

>* >% >< >« >.

ca ® ® ® ® ® ®

•a O a o a o

04 04 (O (0

04 CO in cc

= ® ® k_ c 3

04 ^ 04 CO ^ 04 ® (D ® ® ® _® 0*00000 >»>»>»>>*>>

o o o o o o

GO ro ro

I 00

I

C/J UJX

u

X

X

UJX

UJu

<r_i

Q-U)

X3

o

(J

LO

UlQO

X

q:o

cn

Ul

_iu

>

u

COX

o

CD

LU

GC3

O

Li.

(s<ii>o ayon lyiwoziaoH

136
O)

COQ.

CMc c c E

< jx: CO

CMc

0) 0) o

CD CD CD E

, o N- y— o O h- T” 00 d LO o o OJ d

CD N- d d d d CM d

II

(]}

CN

II

II II II II II II II

Oi CA c/) CO c

Q. < < a a k. 'a

CO

ca CQ

r" oo o)

ffl 0) 0) o o

r- CVJ CO CVJ ^ CM O 0} <D 0} 0> O 0) ~ o "o o o o o _ 52 o o o OOOOOOOOOOO

>. >.

ca CO > >»

(0 cd > > >.

cd CO cd

>. >»

Cd CO

'O’

I CM CO

CD d) O T3 m m to (o CO

I I Tt to CO NI I <» O)

I O -r- CM t“i“i-t-t-i-t-t-CMCMCM

T“ CM CM ® d> « 0 ffl o o o o o >>.>.>, >1 o o o o cj

^ CM

_d} _o> o o > >. o o

CO «t

0) 0) o o > >*

CJ CJ >> >,

cd CO

CM CM CO CO

I I I CM CO

>. >»

CO CO

oj 0) a -o

I I 00 OJ

to CO

03 ®

CJ CJ > >«

CJ o

>. >

Cd CO

03 0) T3 -a

(Sdl^) CMn rnflMDZIHOH

LDu

Q

o

21

Ck: o

toa

>

u

Q

tro

_J

CO

cd

UJ

OC3

O

137
TABLE

6.1

YIELD

DISPLACEMENTS

>1

<3 o o CM

00 1—

rH rH in D

<3

• 00 CM iH tH (T» VO 2 CO CM o CM rH VO >1 M • • • • • • < o O iH o o o

Q CO CO VO CO CO VO \P

VO VO iH m CO m <y» CO CO CM

rH •H o^ 00 o CO u U] p CM CM CO CO CO CO

CNJ CO

CN

CO

csCO

in in m

CO a

I

I C7> (Ul <

Oi I O

I -

I M-l

I

i-:i w

P

o

s

CM CM CM CM 1 1—1 in m m in a\ 1 CO

VO VO *—

rH iH o iH iH o

o o o o o o 1 o

o o o o o o 1 “

o o o o o o

iH CS iH iH CS I—I

j in

O O O O O O IH

I ^

I II

I o

I ^

fH (N CO in VO S S S S S 2

138

(33)
COLUMN

DISPLACEMENTS

FOR

MODEL

N1

139

LATERAL

DISPLACEMENT

(in.)
COLUMN

DISPLACEMENTS

FOR

MODEL

N2

COLUMN

HEIGHT

(In.)

140

LATERAL

DISPLACEMENT

(In.)
J

z

CO

CVJ

CM

CO

CO

141

LATERAL

DISPLACEMENT

(In.)

COLUMN

DISPLACEMENTS

FOR

MODEL

N5

^

COLUMN

HEIGHT

(In.)

143

LATERAL

DISPLACEMENT

(in.)
COLUMN

DISPLACEMENTS

FOR

MODEL

N6

z

CO

144

LATERAL

DISPLACEMENT

(In.)
6.2 Energy Absorption

One means of measuring the ability of a structure to withstand an

earthquake is to calculate its energy,absorption capacity. ^ The energy

absorbed by a column during a particular load cycle can be determined by

integrating the area within the lateral load vs. displacement curve. This

was done in this study by the use of a special computer graphic

integration procedure, as described in J^pendix A.

The energy absorbed per cycle for each model up to conpletion of testing is

shown in Figs. 6.13 - 6.18. A comparison of the total energy absorbed by

the models up to ultimate failure is shown in Fig. 6.19. The total energy

for a given test was determined by summing individual cycle energies up to

the cycle which met the ultimate failure criteria previously described.

The energy absorbed by the models can be seen to decrease markedly upon

fracture of the spiral. This is shown graphically in Figs. 6.14 - 6.19.

Also, as indicated in the figures, ultimate failure of the columns occurred

soon after fracture of the confining spiral.

As shown in Fig. 6.13, the absorption capacity of the models constructed

with ready-mix concrete is greater than that of the microconcrete models.

The energy absorbed by specimen N4 is approximately 12% greater than that

absorbed by specimen Nl, and the energy absorbed by N5 is 8% greater than

that absorbed by N2. This increase may result frcm aggregate interlock in

the pea gravel models, a phenomenon not found in microconrete models

because of the small aggregate size. The energy absorbed by the

microconcrete flexure model, N3, is much less than that absorbed by the

flexure model, constructed with ready-mix concrete N6, as was ej^ected due

to the premature failure of the spiral. The energy absorbed up to the

point of spiral fracture,^ m = 4 fir^ cycle, for model N3 was 151.5 kipin. (2.46 N-m) compared with 86.9 kip-in. (1.41 N-m) for model N6 up to the

same ductility and cycle as model N3. This difference was a result of the

measured yield displacement, 0.66 in. (16.8 mm), for model N6 as compared

with a measured yield displacement of 1.01 in. (25.6 mm) for model N3. If

the energy absorbed by model N6 was multiplied by the ratio of these yield

displacements (1.01/0.66 = 1.53) this would result in 133.0 kip-in. (2.16

N-m) which would indicate that the behavior of model N3 would have been

CQiriparable to that of N6 if the spiral in N3 had not prematurely fractured.

The models with higher axial load, N2 and N5, showed a greater energy

absorption capacity than the models with lower axial load, Nl and N4. This

increase in energy absorption was not found by Ohno and Nishioka [17] for

higher axial loads. It is, however, reflected in their proposed

equations, Eqs. (6.1) & (6.3), to predict energy absorption of columns. In

particular Eq. (6.1) predicts that the ultimate moment is proportional to

the axial load.

This difference in energy absorbed due to the different axial loads would

have been greater if the P - a effect had been included in the energy

absorption calculation. This is due to the greater influence of the

P - A effect on the flexural strength of a column for higher axial load as

shown in Tables 6.2 to 6.7 and as observed by Potangaroa [23]. The

variables in these tables were defined as:

145
INDIVIDUAL CYCLE ENERGY FOR MODEL N1

Fig. 6.13

146
70

60

50

40

30

20

10

0

INDIVIDUAL CYCLE ENERGY FOR MODEL N2

10

1 = 1 Ay, cycle 1 2 = 2 Ay, cycle 1 3 = 2 Ay, cycle 2

4=4 Ay, cycle 1 5=4 Ay, cycle 2

6=6 Ay, cycle 1 7=6 Ay, cycle 2

8=8 Ay, cycle 1 9 = 6

- Ay, cycle 2

10^ =10 Ay, cycle 1

1 1^=10 Ay, cycle 2

12*^ = 10 Ay, cycle 3

13^=12 Ay, cycle 1

a = -ultimate state

as defined by

Zahn et al [30]

b = spiral fracture

c = longitudinal bar

fracture

Fig. 6.14

147
ENERGY

ABSORBED

(kip-ln)

INDIVIDUAL CYCLE ENERGY FOR MODEL N3

1=1 Ay, cycle 1 2 = 2 Ay, cycle 1 3 = 2 Ay, cycle 2

4=3 Ay, cycle 1 5^=3 Ay, cycle 2

6*^ = 4 Ay, cycle 1 7 = 4 Ay, cycle 2

8 = 4 Ay, cycle 3

9® = 4 Ay, cycle 4

10 = 4 Ay, cycle 5

11^=4 Ay, cycle 6

12^=4 Ay, cycle 7

13^ =4 Ay, cycle 8

14 =4 Ay, cycle 9

15 =4 Ay, cycle 10

16^ =5 Ay, cycle 1 a = ultimate state

as defined by

Zahn et al. [30]

b = spiral fracture

c = longitudinal bar

fracture

Fig. 6.15

148
60

60

40

30

20

10

0

INDIVIDUAL CYCLE ENERGY FOR MODEL N4

4

5

6

7

11

1=1 cycle 1 2 = 2 Ay, cycle 1 3=2 Ay, cycle 2

4=4 Ay, cycle 1 6 =4 Ay, cycle 2

6=6 Ay, cycle 1 7 = 6 Ay, cycle 2

8 = 8 Ay, cycle 1 9=8 ^\y, cycle 2

10 = 8 Ay, cycle 3

11 =10 Ay, cycle 1 12^ = 10 Ay, cycle 2

13^*^ = 10 Ay, cycle 3

14 = 12 Ay, cycle 1 16^ = 13 Ay, cycle 2

a = ultimate state

as defined by

Zahn et al. [30]

b = spiral fracture

c = longitudinal bar

fracture

Fig. 6.16

149
INDIVIDUAL CYCLE ENERGY FOR MODEL N5

1=1 Ay, cycle i 2=2 Ay, cycle 1 3=2 Ay, cycle 2

4=4 Ay, cycle 1 6 =4 Ay, cycle 2

6=6 Ay, cycle 1 7=6 Ay, cycle 2

8=8 Ay, cycle 1 9=8 Ay» cycle 2

10^ = 10 Ay, cycle 1 11^ = 10 aV, cycle 2

12*^ = 10 Ay, cycle 3

cycle 1 14 =12 Ay, cycle 2

a = ultimate state as

defined by Zahn

et al. [30]

b = spiral fracture

c = longitudinal bar

fracture

150
ENERGY

ABSORBED

(kip-in)

INDIVIDUAL CYCLE ENERGY FOR MODEL N6

1 = 1 Ay, cycle 1 2 = 2 Ay, cycle 1 3=2 Ay, cycle 2

4 = 3 Ay, cycle 1 5 = 3 Ay, cycle 2

6=4 Ay, cycle 1 7 = 4 Ay, cycle 2

8=4 Ay, cycle 3

9=4 Ay, cylce 4

10 = 4 Ay, cycle 5

11 = 4 Ay, cycle 6

12 = 4 Ay, cycle 7

13 = 4 Ay, cycle 8

14 b = 4 cycle 9

15^ = 4 Ay, cycle 10

16 = 6 Ay, cycle 1 17^ =5 Ay, cycle 2

18 = 5 Ay, cycle 3

19^ = 6 Ay^ cycle 2

20^=6 Ay. cycle 2

21^= 7 Ay. cycle 1 22 = 7 Ay, cycle 2

a = ultimate as defined by Zahn et al. [30]

Fig. 6.18

151
350

300

250

200

150

100

50

0

ENERGY ABSORBED UP TO ULTIMATE STATE

AS DEFINED BY Zahn et aL[30]

Fig. 6.19

152
TABLE b.2 Loads and Moments for Model N1 H A

P

e P - A M Total

Cycle (Kip) (In.) (Kip) (Kip-Ft) (Kip-Ft) (Kip-Ft)

11,

10.966 0.237 26.37 26.96 0.52 27.48

n.N 11.299 0.223 26.70 27.78 0.50 28.28

21,

12.548 0.711 26.10 30.85 1.55 32.40

21,

14.594 0.716 25.68 35.88 1.53 37.41

22,

11.980 0.722 25.50 29.45 1.53 30.98

22,N 14.299 0.689 25.48 35.15*’^ “ 1.46 36.61

41,

13.258 1.596 24.37 32.59 3.24 35.83

41.

14.408 1.453 24.22 35.42 2.93 38.35

42.

12.059 1.560 23.31 29.65 3.03 32.68

42.N 13.740 1.455 24.32 33.78 2.95 36.73

61,

12.627 2.423 23.22 31.04 4.69 35.73

61.

13.471 2‘.211 ^3.96 33.12 ^ 4.42 37.54

62,

11.292 2.442 23.10 27.76 4.70 32.46

62,N 12.731 2.238 23.75 31.30 4.43 35.73

81.

7.151 3.248 23.72 17.58 6.42 24.00

81,N 10.850 3.029 24.45 26.67 6.17 32.84

82,

1.745 2.768 25.42 4.29 6.86 10.15

82,7.681 3.049 28.31 18.88 7.19 26.07

83.

2.239 3.271 27.59 5.50 7.52 13.02

83.N 5.499 3.038 28.99 13.52 7.34 20.86

101, S 0.484 4.100 29.41 1.19 10.05 11.24

101,

3.249 3.79 29.94 8.43 10.68 19.11

153
TABLE 6.3 Loads and Moments for Model N2

Cycle

H

(Kip)

A

(In.)

P

e(Kip)

“h

(Kip-rt)

P -A"

(Kip-Ft)

M Total

(Kip-Ft)

11,

11.976 0.169 54.72 29.44 0.77 30.21

11,10.958 0.166 53.93 26.94 0.75 27.69

21,

15.970 0.407 52.88 39.26 1.79 41.05

21,

15.149 0.405 52.82 37.24 1.78 39.02

22,

15.405 0.410 52.52 37.87 1.79 39.66

22,14.913 0.405 53.38 36.66 1.80 38.46

41,

16.267 0.868 51.94 39.99 3.76 43.75

41,14.801 0.870 51.94 36.39 3.76 40.16

42, S . 15.954 0.871 53.07 39.22 3.85 43.07

42,

14.596 0.871 52.56 35.88 ' 3.81 39.69

61,5 16.270 1.353 52.63 40.00 5.93 45.93

61.

14.534 1.356 52.85 35.73 5.97 41.70

62,

15.808 1.351 52.22 38.86 5.88 44.74

62 ,N 14.222 1.358 57.38 34.96 5.93 40.89

81,

15.643 1.830 52.85 38.46 8.06 46.52

81,13.875 ' 1.835 -^2.78 34.11 8.07 42.18

82,

15.007 1.832 52.91 36.89 8.08 44.97

82,13.242 1.792 53.09 32.55 7.93 40.48

101, S 14.151 2.373 52.92 34.78 10.46 45.25

101,11.302 2.265 53.66 27.78 10.13 37.91

102, S 11.497 2.379 53.85 28.26 10.60 38.94

102,

8.699 2.272 53.59 21.39 10.15 31.54

103. S 9.060 2.389 53.37 22.27 10.63 32.90

103, N 5.611 2.284 53.73 13.79 10.23 24.02

121,4.700 2.897 53.48 11.55 12.91 24.47

121,3.323 2.729 54.00 8.17 12.28 20.45

154
TABLE 6.4 Loads and Moments for Model N3

Cycle

H

(Kip)

A

(In.)

P

e(Kip) (Kip-Ft)P - A

(Kip-Ft)

M Total

(Kip-Ft)

11,

5.861 0.635 27.59 28.82 1.46 30.28

11,

5.535 0.729 26.44 27.21 1.61 28.82

21,

-7.157 2.157 25.42 35.19 4.57 39.76

21,

6.573 1.906 24.59 32.32 3.91 36.23

22,

6.875 2.163 25.00 33.80 4.50 38.30

22,

6.360 1.908 24.83 31.27 3.95 35.22

31,

6.464 3.126 26.13 31.78 6.81 38.59

31,6.175 2.785 26.25 30,36 6.09 36/45

32,

6.167 3.200 25.17 30.32 6.71 37.03

32,

5.953 2,795 25.31 29.27 5.90 35.17

41,

6.802 4.354 28.53 33.44-- 10.35 43.79

41,

5.915 3.933 29.06 29.08 9.52 38.60

42,

6.152 4.173 29.96 30.25 10.42 40.67

42.

5.259 3.013 29.78 25.86 7.48 33.34

43,

4.602 4.146 30.93 22.63 10.69 33.32

43,N 4.414 3.981 30.60 21.70 10.15 31.85

44,

3.817 ^ 4.154 .^29.90 18.77 10.35 29.12

44,

3.522 3.865 31.69 17.32 10.21 27.53

45,

3.130 4.161 29.46 15.43 10.22 25.65

45.

2.976 4.025 29.92 14.63 10.04 24.67

46,

2.598 4.168 31.64 12.77 10.99 23.76

46.N 2.699 3.883 30.68 13.27 9.93 23.20

47.

2.042 3.760 33.83 10.04 10.60 20.64

47.

2.71 4.031 33.80 13.32 11.35 24.67

48,

1.631 4.161 32.53 8.02 11.28 19.30

48,

2.784 4.013 33.73 13.69 11.28 24.97

49,

1.515 4.434 27.56 7.45 10.18 17.63

49,

2.723 3.622 25.16 13.39 7.59 20.98

410, S 1.372 3.648 27.64 6.75 8.40 15.15

410,N 2.701 3.70 28.35 13.28 8.74 22.02

51,

5.500 5.073 26.82 27.04 11.34 38.38

51.

5.016 4.328 30.05 24.66 10.84 35.50

155
TABLE 6.5 Loads and Koments for Model N4

Cycle

H

(Kip)

A

(In.)

P

e(Kip) (Klp-Ft)

P - A

(Kip-Ft)

M Total

(Kip-Ft)

11,

10.713 0.143 26.77 26.34 0.32 26.66

11, N 11.11 0.158 25.93 27.31 0.34 27.65

21,

13.571 0.367 25.33 33.36 0.77 34.13

21, N 13.541 0.371 24.86 33.29 0.77 . 34.06

22,5 12.830 ^ 0.370 25.52 31.54 0.79 32.33

22,13.237 0.370 25.54 32.54 0.79 33.33

41.5 14.047 0.791 25.120 34.53 1.66 36.19

41,13.669 0.790 25.46 33.60 1.68 35.28

42,

13.268 0.797 25.66 32.62 1.70 34.32

42, N 13.241 0.791 25.16 32.55 1.66 34.21

61.5 13,990 1.229 25.48 34.39 2.61 37.00

61, N 13.431 1.227 25.28 33.02 2.58 35.60

62,

13.114 1.234 25.58 32.24 2.63 34.87

62,13.091 1.227 25.67 32.18 2.62 34.80

81,

13.788 1.677 25.60 33.90 3.58 37.48

81, N 12.915 1.699 25.19 31.75 3.57 35.32

82,5 12.818 1.691 25.49 31.51 3.59 35.10

82,

12.356 1.672 25.25 30.38 3.52 33.90

83,

12.418 1.691 25.40 30.53 3.58 34.11

83,

11.960 1.672 25.31 29.40 3.53 32.93

101, S 12.700 2.150 24.77 31.22 4.44 35.66

101,

11.559 2.111 25.68 28.42 4.52 32.94

102,11.113 2.153 25.30 27.32 4.54 31.86

102,9.818 2.118 26.53 24.14 4.68 28.82

103,

8.594 2.186 25.84 21.13 4.71 25.84

103,

6.264 2.131 26.32 15.40 4.67 20.07

121,

4.441 2.651 26.52 10.92 5.86 16.78

121,

5.304 2.549 25.84 13.04 5.49 18.53

122,2.909 2.658 26.57 7.15 5.89 13.04

122,

2.838 2.564 26.70 6.98 5.70 12.68

156
TABLE 6.6 Loads and Moments for Model N5 - -

Cycle

H

(Kip)

A

(In.)

P

e(Kip) (Kip-Ft) P - A

(Kip-Ft)

M Total

(Kip-Ft)

11,

n:38i 0.148 49.78 27.98 0.61 28.59

11,

8.480 0.109 49.37 20.85 0.45 21.30

21,

16.099 0.392 49.037 39.58 1.60 41.18

21,

15.718 0.335 47.00 38.64 1.31 39.95

22,

15.249 0.392 48.50 37.49 1.58 39.07

22,

15.440 0.344 47.94 37.96 1.37 39.33

41,

16.870 0.082 48.82 41.47 3.26 44.73

41,

16.674 0.768 47.91 40.99 3.07 44.06

42,

16.411 0.799 48.13 40.34 **

3.20 43.54

42,N 16.309 0.777 48.39 40.09 3.13 43.22

61,

16.068 1.207 48.01 39.50 4.83 44.33

61,16.295 1.204 46.68 40.06 4.68 44.74

62,

15.834 1.217 46.83 38.93 4.75 43.67

62,15.977 1.199 47.43 39.28 4.74 44.02

81,

16.324 ^ 1.629 A7.72 40.13 6.48 46.61

81,

15.700 1.606 47.51 38.60 6.36 44.96

82,

15.747 1.633 47.32 38.71 6.44 45.15

82,

15.312 1.614 47.39 37.64 6.37 44.01

101, S 14.688 2.056 46.44 36.11 7.96 44.07

101,

13.691 2.014 47.25 33.66 7.93 41.59

102, S 13.099 2.064 47.51 32.20 8.17 40.37

102,N 12.490 2.016 47.09 30.70 7.91 38.61

103, S 12.002 2.071 49.49 29.50 8.54 38.04

103.N 10.996 2.028 49.44 27.03 8.36 35.39

121,

6.952 2.523 48.22 17.09 10.14 27.23

121,N 6.617 2.416 49.38 16.27 9.94 26.21

122, S 5.957 2.532 47.91 14.64 10.11 24.75

122,N 5.661 2.430 50.17 13.92 10.16 24.08

157
TABLE 6.7 Loads and Moments for Model N6

H A ^e ^ P-AM Total

Cycle (Kip) (In.) (Kip) (Kip-Ft) (Kip-Ft) (Kip-Ft)

11,

5.836 0.500 29.13 28.69 1.21 . 29.90

11,

5.400 0.484 27.06 26.55 1.09 27.64

21,5.605 1.329 23.54 32.47 2.61 35.08

21,

6.665 1.444 21.65 32.77 2.60 35.37

22,

6.169 1.333 20.63 30.33 2.29 32.62

22,

6.488 1.447 21.21 31.90 2.56 34.46

31,

6.437 2.050 21.11 31.65 3.61 35.26

31,

6.556 2.168 20.94 32.23 3.78 36.01

32,

6.152 2.048 21.38 20.25 3.65 33.90

32,6.442 2.164 21.45 31.67 3.87 35.54

A1,S 6.515 2.751 21.10 32.03 4.84 36.87

41,6.486 2.805 20.72 31.89 4.84 36.73

42.5 6.297 ' 2.758 2T.26 30.96 4.89 35.85

42,

6.347 2.809 21.12 31.21 4.94 36.15

43,6.061 2.759 21.33 29.80 4.90 34.70

43,

6.286 2.809 21.28 30.91 4.98 35.89

44,

6.026 2.759 20.22 29.63 4.65 34.28

44,

6.153 2.814 19.59 30.25 4.59 34.84

45,5.938 2.763 19.70 29.20 4.54 33.74

45,6.046 2.800 22.96 29.73 5.36 35.09

46,

5.797 2.766 20.14 28.50 4.64 33.14

46,

6.000 2.800 19.17 29.500 4.47 33.97

47,5.744 2.760 19.51 28.24 4.50 32.74

158
Continue TABLE 6.7

Cycle

H

(Kip)

A

(In.)

P

e(Kip) (Kip-Ft)

P - A

(Kip-Ft)

M Total

(Kip-Ft)

47,

5.971 2.803 19.86 29.36 4.64 34.00

48,

5.641 2.763 19.76 27.73 4.55 32.28

48,5.819 2.767 19.70 28.61 4.54 33.15

49,

5.433 2.802 19.39 26.71 4.53 31.24

49,N 5.579 2.778 19.06 27.43 4.41 31.84

410,

5.000 2.811 18.82 24.58 4.41 28.99

410,N 5.086 2.726 18.16 25.01 4.13 29.14

51,

4.889 3.543 20.01 24.04 5.91 29.95

51,

4.610 3.196 23.08 22.67 6.15 28.82

52,

4.100 3.570 23.04 20.16 6.85 27.01

52,

3.852 3.190 23.50 18.94 6.25 25.19

53,

2.588 ^3.593 iT.Ul 12.72 7.01 19.73

53,N 3.300 3.191 24.06 16.23 6.40 22.63

61,

4.503 4.322 23.79 22.14 8.57 30.71

61,

2.695 3.677 24.31 13.25 7.45 20.70

62,

2.331 3.628 25.10 11.46 7.59 19.05

62,N 3.047 4.123 25.98 14.98 8.93 23.91

71,

5.191 4.845 26.92 25.52 10.87 36.39

71,N 2.800 4.598 26.79 13.77 10.27 24.04

72, S 4.489 4.922 25.24 22.04 10.35 32.42

72,

2.225 4.491 24.21 10.94 9.06 20.00

159
H = Lateral lead (kips)

Pq = Axial load (3d.ps) = Moment at the base of the column due to H (kip-ft)

P - A = Moment due to P^ (kip-ft)

“Total = % + P - A (kip-ft)

The energy absorbed by models N4 and N6 was essentially equal. These

models V\hich were constructed using ready-mix "pea gravel" concrete, were

loaded to the same magnitude of axial load, but had different aspect

(moment/shear) ratios and loading sequence. This would agree with the

conclusion drawn by Ohno and Nishioka [17] that the total energy absorbed

by a column is independent of the loading sequence.

Ohno and Nishioka [17] proposed that the energy absorption capacity of a

column could be predicted if the cross section, and the concrete and

reinforcing steel properties of the column were known.- The proposed method

is as follows:

vhere

^ = plastic moment (kN-m)

a^ = cross sectional area of tensile reinforcement

fy = yield stress of tensile reinforcement (MPa)

N = axial load (kN)

b — width of cross section (cm)

D = depth of cross section (cm)

f*^ = corrpressive strength of concrete (MPa)

0p = ultimate column rotation (rad)

Ip = plastic hinge length (cm)

]y^ = 0.8 a^. fy D + 0.5ND [1 - N/(bDf'^)] ( 6 . 1) for

N < 0.4 bDf'^

0 p

= 2|cos”^ (lp/2x) - cos“^[(lp + Al)/2x]} V180

Wc = MpBp

( 6 . 2 )

(6.3)

160
X = yj Ip^ + / 2 (cm)

s = distance between tension and compression

reinforcement (cm) .

- Al = length of elongation in the tensile steel = (% elongation) (Ip) (cm) = energy absorption capacity (kN-m)

The percent elongation of the steel at fracture for the NBS prototype

longitudinal bars was 15.5 % based on mill test reports. Since this

information was not available for the D6 wire used in the models, the

prototype value was used in the calculation of 0p. The ultimate moments

and the moments predicted using Eq. (6.1) are given in Table 6.8. The two

values corrpare very well. Calculation of 0p yielded very low values and

as a result Eq. (6.3 ) gave low energy absorption predictions yien compared

with the values obtained from the integration of the hysteresis curves.

This difference between the values obtained from Eq. (6.3) and the

e5^)erimental values could also be because the energy obtained throu^ the

use of Eq. (6.3) is calculated as the area under the load displacement

curve (monotonic curve) \^ch was constructed from the peak lateral loads

obtained from a reversed cyclic test while the NBS experimental values

r^resented the summation of the energy dissipated in each cycle up to the

ultimate failure of the column. The low values of 0 p

from the analytical

calculation could be due to the manner in vhich the plastic hinge length

was measured (see section 6.3) or to the assumed value for the elongation

percentage of the D6 wire.'

6.3 Plastic Hinge Lengths

An attempt was made to obtain the experimental plastic hinge length for

each of the models. The plastic hinge length was taken as that length over

which the majority of the longitudinal bars in the column had yielded.

This length was determined experimentally as the hei(^t at vhich the strain

gages indicated yielding of the longitudinal bars had occurred. The

strains were those measured for the two cycles at m = 4 for the shear

models and the two cycles at m = 3 for the flexure models. The plastic

hinge was assiamed to have fully developed at these respective stages.

These values are given in Table 6.9. In addition, the extent of observed

concrete spalling is also given in Table 6.9.

Ertpirical equations have been developed for the prediction of plastic hinge

lengths. Two such equations are by Baker and Corley [31] and are as

follows:

Baker's equation [31]:

Ip = 0.8 k-j^ k3 (z/d)c (6.4)

161
TABLE

6.8

ULTIMATE

MOMENT

CAPACITIES

CN

a,

CD

P4X

d) a

CVJ VO

o«aMU< M

ISa

s,ozu

EH<ZM

Eh

I-:; <3

EhSuzM

cr; u

04X

&a o

VO

o^o o

CV) CN

r-- cs

<y» CM

CO

m

CO o

VO

VOo

COCN

IDCO• 00CO

<Ti CNo • CO CO o CO in

VO <T» tH o o CO

N. . . . . . • EH • VO 00 00 VO

EL41 04 OCO CO CO CO CO

CN VO 00 1—

in VO 00 • . • . • VO <J^ VO VO

CO CO CO 1 D 11 M 1 U 1

CN 1 ^

.55 .32 .32 .55 .32 1 < I1 in VO m m VO in 1 !1 CO CO CO CO CO CO < 1 Eh - 1 Z 1 Ci] 00 m VO r>* O 1 Z z . • . • • • 1 M M <y\ iH CO 00 o^ rH 1 1 0^ o in in

fU u CO CO CN CO CO CO M 04X —

a

>H 1 04 CO 1 U CO iH CN VO m VO 1 z • 00 CO in o\ O 1 a • iH . • iH . 00 r-' 1 • CN VO 00 04 1 o rH rH iH uQOZ

CNs

COS s

inZ

VOZ

CN CO

162

Including P- A

effect.

Summation

of

energy

absorbed

up

to

ultimate

state

as

defined

by

Zahn

[30].

Based

ona

plastic

hinge

length

equal

to

the

spalled

height.
TABLE

6.9

PLASTIC

HINGE

LENGTHS 1 00 00 00 00 1 VO - vo | « • ••••• 1 o VO VO 00 ^ 00 1 o !

PHu 1 CM

m o CM

m I 00 CO 00 CO r- < 1 • • • • • • PQ 1 m VO iH m VO iH 1 iH iH « EH

CD ffl W J U < < M U U S CO CC zM I o• o• o moo

CO ^ • • • m cs CO

m Qa

OhD U CO u < z u M S s z U o CO M z

Eh Q M

CO u <; < CO C« J < Eh zM Q\ CO CO

m CO CO 'X) O iI w CO H H

CT» C7> C S5 •H •iH T3

1—

1—

Q) H •H

>1

4H 44 O O

4-) 4-5 45

CJi CJ^ •H •H

(U 45 45

0) 0) x; 45

Eh EH • •

>41

w

a. a. o o o o o o

rm

0) Q) TD • ro . (U -P <U 44

0) 45 0) 45 O O CJ5 X -H X -H

0) (U 0 0

45 45

4J 44 ^ CQ 45 0

O'-H cn-H

•H ^ •H 45

<D 4J 0 44 45 45 C S5 CQ (0 W (CJ H 45 •H 45 45 4J 45 44

4-> 44

44 4J O 44 0

<0 4J 03 44

<0 (C3 CO (U 0 0

£5 5-1 C 5-4 •H CT> •H 01

(0 (C3 U (U U 0

4J 42 44 42

CO 0 O o

fO 4-5 ro 44

(U 0

S-l >1U >1 D M D i-H CO (D 0 0

CCJ ^ Cd 4aC <U -H 0 -H Z .-H Z rH

UQoZ

iH OJ CO '?!* z z z z m VO z z

iH CN

163
^ere

kQ_ = 0.7 for mild steel or 0.9 for cold-worked steel

k3 = 0.6 v^en f = 5100 psi (35.2 N/ram^) or 0.9 for

f'^ = 1700 psi (11.7 n/mm^) , assuming

f = 0.85 X cube strength of concrete

z = distance of critical section to the point of contraflexure

d = effective depth of member

c = neutral axis depth at ultimate moment

Corley ' s equation [31]:

Ip = 0.5d + (z/d) (6.5)

The values obtained for these equations are also given in Table 6.9.

An alternative experimental method for determining plastic hinge length

which has been used in New Zealand is to instrument the potential hinge

region with a large number of displacement transducers (LVDTs) such that a

sufficient number of data points are available to determine local

curvature. Because of data channel limitations at the time of conduct of

the NBS model tests, a traTie-off was made between external LVDTs and strain

gages placed on longitudinal reinforcement. It was felt that the extent of

longitudinal bar yielding could be more precisely determined using the

internal gages.

The calculated plastic hinge lengths based on measured strains were greater

than those predicted by Baker and Corley [31] as shown in Table 6.9. These

lengths did not appear to increase with increasing displacement ductility

as indicated by the strain readings along the longitudinal bar at higher

displacement ductilities. This finding was also noted in references [5],

[16], and [23].

Table 6.9 shows that the extent of spalling in the plastic hinge region

was greater for models subjected to higher axial load. It was also greater

for models constructed using microconrete than for those constructed with

ready-mix concrete. Increased plastic hinge lengths for greater axial

loads were also noted in references [5], [10], and [23].

The extent of the spalled region was also dependent on column aspect ratio.

Those models dominated by flexural behavior (I/D = 6) exhibited spalling in

the plastic hinge region to a greater height than for those models whose

behavior was dominated by shear (I/D = 3). This phenomenon was observed

irrespective of the material used for construction of the columns.

164
The extent of yield penetration along longitudinal bar's averaged 0.3 D or 3

in. (7.6 cm) into the base. This was determined by strain gage measurements

along the longitudinal bars. Yielding of one of the longitudinal bar^ for

model N5 was noted to extend to about 0.51 D [5 in. (12.7 c^) ] into the

base. This yielding occurred at m = 6 with a strain of 8300 m e recorded.

Plots of peak cycle strains (averaged for north and south excursions) are

shown in Figs. 6.20 - 6.25. Only four cycles were plotted since the strain

gages debonded during large plastic elongations of the longitudinal bars.

6.4 Ocjnfining Steel Strains

The results from model N3 will not be included in this discussion because

of premature damage to the spiral. Some gages used to monitor strain in

the confining spiral steel, especially those at the base of the column,

were damaged during the casting of the models. The determination of the

extent of yielding of spiral reinforcement was therefore based on the

remaining gages and by visual inspection. A spiral was considered to have

yielded if significant straightening of the spiral between longitudinal

bars was observed.

Yielding of spiral reinforcement for all models was,,concentrated in the

region beginning 0.05D [0.5 in. (12.7 mm)] into the base and extending

approximately 0.2D [2 in. (5.08 cm)] above the base. Fracture of the spiral

reinforcement generally occurred during the next ductility level fol lowing

first yielding of the spiral. The exception to this was specimen N5, ^ich

ejdiibited yielding of the spiral at M = 6, with subsequent fracturing at a

ductility level of m = 10.

Measured strains in spiral reinforcenoit averaging approximately 420 jue were

noted at a height of 0.51 D [5 in. (12.7 cm)] above the base and 400

approximately 0.1 D [1 in.t2.35 cm)] into the base for the shear specimens.

Yielding of one spiral at approximately 0.71 D [7 in. (17.8 cm)] into the

base was noted for model N5 at m = 6. The recorded strain was 2700 at

that load stage and remained piractically unchanged for the remainder of the

test. This would agree with the yield penetration into the base of one of

the longitudinal bars in model N5 as noted earlier. Yielding of this

particular spiral could have been caused by localized buckling of the the

longitudinal bar due to a large piece of aggregate pressing against it.

The measured strain in the spiral reinforcement for model, N6 (I/D = 6) was

approximately 200 m€ at 0.2 D [2 in. (5.08 cm) ] into the base and 150 at

1.02 D [10 in. (25.4 cm)] above the base. Based on the results of this

test, it would appear that the CALTRANS requirement to extent the spiral

into the footing to the point of tangency of the longitudinal bar hook is

very conservative.

6.5 Ultimate Mcment

The P-M curves for the flexure and shear models are shown in Figs. 6.26 and

6.27 respectively. The ultimate moments, including P - a effect, for the

models with low axial load exceeded the predicted values using the ACI

design charts for <i> = 1 by an average of 11 %. This increase from the ACI

value in moment capacity was slightly greater for the microconcrete models

than for those specimens constructed with ready-mix concrete. The ultimate

moments for the two models (N2 and N5) with higher axial load showed an

increase of 27% over those calculated using ACI procedures. This increase

165
9000

1—1 CSl T—

0) QJ o;

1—1 1—

1^ a U a o CJ o

#1 <1 <3 <

<3 CN <T

iH CN ro "T

o o o o

CVJ Tf ID 00

IN LO M ^

CKlIUyiSOaGIU) KJiyaiS >IU3<i "Bnu

(f) u

X

u

o

Ld

COX

OQ\

X

-I

o

(J

X

o

q:

Ll

UJ

u

XX

CO

LUQ

O

X

CX) X

1-^ Q

3

LDX

o

UDX

o

_lX

X1—4 X

h“

CO

X

UJ

p.

166
9000

rH CNI I—I

0) 0) 0) r—

rH u u o

CJ o u

r« <3 < <

1 CN

CN fO '3’

o

CVJ r\

o

o

LO

o

o

IDM

o

o

00

CKiiuaisodDiu) wiyais >iy3dL •3ny

CDU

I

u

o

UJ

CD

CE

pqX

Z

z:3

o

a

21O

u.LUU

z:CE

CD

t—

n

/-s

CVJ u

Q

O

n

Oil CE

PQ

-1

CE

21

ID

O

UD

z:o

CN

Cr> H

(E

CZ

h—

CD

CE

LlI

(1.

167
9000

rH CNI I—t

(V 0) OJ

1-H i—H rH O U u

pH o o u

0S 0K 0K >><] <I <] 1 CM cn

CM

m <T ro

7L

COuXuXou

COX

cq\XX

-JouXoX

L.

UJUX

CO

LUQOXX

CQXXQX

CDXoXo

-IXXX

COXu

p-

(N(N

vx) H

fa o

CVJ r\ o

LO o

CD

ro o

CD

CKiiuaisoaGiu) KJiuais >iU3ci ’Bny

168
0008

rH CN

(1) 0) (U rH rH rH o O O

Sh u CJ o

>, <1 <1 <3

1 CN -<r

CN 00 <r

<r

hJ

tdCO

CO

111 X

u

X

o

LU

COX

mX

-J

o

u

UJX

o

Q::

UJ

u

X

h”

CO

•—I

X

cq

-JX

IDX

o

IDX

o

X

H—

CO

X

UJ

p00

CM

<.0

•iH

O

U)

o

CD

5T

O

CMro o

CD

cwiuaisoaoiu) KJiuais >iu3d 39ua3nu

169
9000

r—t CN rH

0) 0) 0) 1^ r—

rH o a a o u o

0>k >^<l <J <

<3 CN CN <T

rH CN cn

\S) z:

COuIuo•-> u

cn(r

OQ\

z:ouo

LlUUz

cr

C/) Q

LJQOC

(E

CQ

-J

crzQZ

hLD ^ ZO tj) -I -H

fa o

(T

(T

(i: cn

(LU

P- o

CM

f\ o

M"

LO O

ID

ro o

CD

(Kiiyaisoaoiu) wiyais »y3d ‘any
9000

171
359^^

DIAGRAM

FOR

FLEXURE

MODELS

(sd!>i) avon

172

MOMENT

(kip-ft)
P-M

DIAGRAM

FOR

SHEAR

MODELS

173

MOMENT

(kip-ft)
in ultimate moment from the predicted values for higher axial loads was

also noted by Gill [10] and Kuribayashi [11]. The experimentally observed

ultimate moments were found to be nearly identical between companion

specimens cast from microconcrete and ready-mix concrete. It also appears

that the ACT design charts produce lower estimates of ultimate moment for

hi^er axial loads. The ultimate moments obtained ejq^erimental ly and those

from the ACI design charts are given in Table 6.8.

As in previous studies [11], [13], and [16], a drop in lateral load was

noted during the second cycle at a given ductility level. This was because

the majority of the cracks formed during the first cycle. The successive

decrease in lateral load was more pronounced vhen spiral yielding was also

involved. On the average, for all six models, the maximum- lateral load

during any second cycle at a given ductility level decreased by 3.9 % with

respect to that observed during the first cycle. This decrease was

smaller for two models with higher axial load — an average of 2.72 % as

compared with an average drop of 4.47 % for the four models with the lower

axial load. This could be due to the closure of cracks under higher axial

loads vhich would permit an increase in the lateral load.

6.6 Adequacy of Transverse Oonfinonent

The spiral reinforcement used in the model studies appears adequate to

obtain displacement ductilities 10 for shear models (L/D = 3) and

displacement ductilities of 4 for flexure models (I/D = 6). Beyond these

ductilities fracture of spiral reinforcement and buckling of longitudinal

reinforcement generally occurred. The spacing of the spirals was adequate

to prevent longitudinal bar buckling as long as the spiral remained intact.

It would therefore appear that in order to increase the ductility capacity

for these columns, the amount of spiral reinforcement would have to be

increased, or, contrarily,' the size and number of longitudinal bai:s would

have to be increased in an effort to forestall buckling. Studies

performed in New Zealand [16] have shown that larger diameter bars i:ised for

spiral reinforcement, placed at a greater spacing but achieving the same

reinforcement ratio as that used in this study, have resulted in higher

achievable ductility factors for a given column. Further research is

warranted to investigate the optimum spiral reinforcement ratio as well as

the effect of bar size and pitch.

Neither ACI [2] nor CALTIMNS [28] currently have a ductility requirement

for bridge columns corresponding to that implemented in the New Zealand

code [8]. Such a quantification can be highly subjective and will depend

on, among other things, seismic history at a potential construction site,

distance from active faults, local sub-surface soil conditions, and

anticipated dynamic response including soil -structure interaction.

CALTRANS defines the potential plastic hinge length over v^ich transverse

reinforcement (as defined by CALTRANS; see section 2.3.2 of this paper) is

required as the greater of:

1. Diameter of column = 9.8 in.

174
2 . Required Length of Confining Spiral = Height of column / 6.0

a. 59 in./ 6 = 9.8 in.(25cm) for models N3 and N6

b. 29.5 in./ 6 = 4.9 in. (12.5cm) for models Nl, N2, N4/ and N5

3. But not less than 24 in. (full scale). For the models this

requirement becomes 24 in./ 6.1 = 3.9 in., which is less than

either of the above requirements.

The length over vhich the extra transverse confinement was required was,

therefore, equal to 1.0 D [9.8 in. (25 cm)] for the flexure specimens.

This value is greater than the observed maximum extent of surface spalling — 0.51D [5 in. (13 cm)] — but less than the calculated plastic hinge

length based on measured strains. A similar situation exists for the shear

specimens: the required length of spiral was 0.5D [4.9 in. (12.5 cm)].

This can be compared with an average observed spall length of 0.31D [3 in

(7.6 cm) and a calculated longitudinal bar yield length of between 0.8-l.lD

[8-11 in. (20-28 cm)] for the model shear columns. Given these

conflicting data it is hot possible to draw any definitive conclusions

regarding the sufficiency of current CAITRANS recommendations as to the

required length of spiral in the plastic hinge region. It should be noted,

however, that the data presented in Table 6.9 indicate that the CALTRANS

confinement lengths calculated above would be less than the plastic hinge

lengths calculated using the procedures suggested by Corley and Baker in

all but one case, that being for the flexure column (L/D = 6) using the

Corley procedure. This would indicate a possible unconservative

situation if we assume that it is desirable to have transverse confinement

extending beyond the potential plastic hinge region.

6.7 EATIDRE ' —

The failure mode for models N3 and N6 was dominated by flexural effects.

This failure mode consisted of the formation of horizontal flexural cracks

in the vicinity of the plastic hinge region, followed by gradual extension

of the cracks around the circumference of the column. Increased lateral

displacerr^t resulted in spalling of concrete at the base of the column to

a height of approximately one column diameter, followed by yielding of

spiral reinforcement, fracture of the spiral, and, ultimately, buckling and

fracture of longitudinal reinforcement in the plastic hinge region. The

aspect ratio (I/D) for the flexural models was 6.

The failure mode for models Nl, N2, N4 and N5 was similar to that for the

flexure specimens, with the exception that extensive diagonal cracks formed

on the sides of the column in the plastic hinge region prior to spalling.

Despite the presence of diagonal cracking, the column aspect ratio (I/D =

3) was not sufficiently low to permit a pure shear failure. Japanese

studies [20] have shown that columns with aspect ratios of 2.2 do exhibit

failure in pure shear, \\hile columns with aspect ratios of 3.8 and 5.4 are

dominated by flexural effects. It would appear from this study that

columns with aspect ratios of greater than 3 will result in a flexural

failure mode.

175
6.8 (XMPARISOT OF RESDIIES WHH PREVIOUS STUDIES

The column test par'ameters used in the New Zealand and the Japanese studies

were somewhat different from those used in the NBS study. For example,

higher axial loads and greater amounts of transverse*' steel were

investigated in the studies performed in New Zealand. Different loading

histories and transverse steel ratios were also a deterrent to possible

coirparisons of results from this study with those performed in Japan.

However, some direct coirparisons between previous studies and the current

NBS work can be made. For example, most researchers have obseirved that

yielding of the transverse steel had no significant effect on the lateral

load. Fracturing of the spiral did cause a significant drop in the lateral

load as noted both by NBS and a Japanese study [11].

Also, a drop in the lateral load for repitions following the first cycle at

a particular ductility level was noted in the NBS study and the New Zealand

and Japanese studies. In a study done by Gill [10], the yield displacement

was found to decrease for higher axial loads. The yield displacement for

the NBS microconcrete shear models was smaller for the model subjected to

the higher axial load (0.38 in. for the lower axial - load and 0.22 in. for

the higher axial load). This effect was less pronounced for the models

constructed using ready-mix concrete in the NBS study (0.21 for the lower

axial load and 0.19 in. for the hi(^er axial load). Finally, the failure

mode for columns with an aspect ratio of 3 or greater was predominated by

flexural effects.

One difference between the results of the NBS work and of a study done by

Ng [6] is that for similar transverse reinforcement ratios, the model in

Ng's study achieved a hi^er displacement ductility than the NBS models.

Although the transverse reinforcemeiTt ratios were similar, the bar size

used in Ng’s models was larger and the spiral pitch was greater than those

used in the NBS study. The longitudinal reinforcement ratio for Ng's

model was also greater by approximately 25 %.

Petrovski and Ristic's [35] tests, performed in Yugoslavia, used similar

transverse and longitudinal reinforcement ratios to the flexure models in

the NBS study. Their loading history, however, was significantly

different. Some useful comparisons between the Yugoslav and NBS tests

are as follows:

1. Columns subjected to a higher axial load had a higher experimental

maximum moment.

2. The experimental yield displacements were approximately equal

between Petrovski's tests and those for the NBS ready-mix models.

These values, specifically, were 0.61 in. and 0.22 in. ( 15.4mm

and 5.6mm) for Petrovski's flexure and shear models, respectively

and 0.66 in. and 0.20 in. (16.7mm and 5mm) for the flexure and

shear models cast using ready-mix concrete at NBS. No difference

in the yield displacement was noted for different axial loads in

the Yugoslav tests.

176
3 . The ultimate displacement ductilities for the Petrovski's flexure

models were 4.58 and 3.31 for the models subjected to the lower

and hi^er axial loads, respectively. These values are sli<^tly

lower than those obtained for the MBS flexure models.

4. The ultimate displacement ductilities for Petrovski's shear models

were 5.96 and 5.73, for the models siabjected to the lower and

hi^er axial load, respectively. These values are much lower than

those obtained for the NBS shear models and could be a result of

the lower transverse steel ratio used in Petrovski's study.

5. The loading history, transverse steel ratio, and the aspect ratio

for the flexure models are sufficiently similar for the Yugoslav

and NBS tests to bear direct cortparison. The slight difference in

the ultimate displacement ductilities as noted in observation 4

would seem to indicate that the cycling of an element 5 or 10

times at a particular displacement ductility does not

significantly effect the ultimate displacement ductility.

177
7.0 CmCEDSimS AND lUTORE RESEARCH NEEDS

7 . 1 o»raxisic»«s

Current CALURANS specifications [28] were sufficient to prevent pullout of

the longitudinal bars from the footing for all specimens tested, and to

prevent shear failure in columns with L/D = 3 for axial loads of 0.10

and 0.20 Ultimate displacement ductilities of 10 were achieved for

shear speciirfens with L/D = 3 and displacement ductilities of five for

specimens with L/D = 6. CALTRANS does not presently specify a minimum

ductility level required for column design. However, experimentally

observed ductilities for NBS model specimens compared favorably with

similar columns tested in New Zealand. Specific results from the model

tests are as follows:

1. Material Dependent Behavior: Microconcrete vs. Ready-Mix Concrete

o Slightly higher ultimate displacement ductilities were

obtained for models cast with ready-mix concrete. This

behavior is believed to result from aggregate, interlock in the

ready-mix concrete, where significantly larger nominal mean

sized aggregates were used.

o Models constructed from ready-mix concrete exhibited an

average of 10.25 % (the difference between models N3 and N6

was omitted in this calculation due to the premature fracture

of the spiral in model N3) higher total energy absorption

capacity than their microconcrete counterparts. This appears

to be a consequence of the extended ductility ac±iieved throu^

aggregate interlock in the inelastic regime; since energy

dissipated per cycle was corrparable prior to ultimate failure.

o No difference in the experimental ultimate moments between the

two types of concrete was observed.

2. Effect of Magnitude of Axial Load.

Tests were conducted to determine the effect of axial load on specimens

with L/D = 3. Two axial load levels were investigated: P = O.lOf’^g

and 0.20 f'^Ag* These tests indicated:

o Hi^er energy absorption capacity for models subjected to

higher axial load: a 13.5 % rise was noted for microconcrete

models and an 8.8 % rise for models constructed from ready-mix

concrete at axial loads of O.lOf'^A- and 0.20f'^A^

respectively. ^

o Higher displacement ductilities were achieved for models

subjected to higher axial load.

o Ultimate moments for models with higher axial load were

greater than for those with the lower axial load. This is a

natural consequence of moving towards the balance point on the

P-M curve from an initially low axial state of stress.

178
o Experimentally measured ultimate moments were greater than

those predicted using ACI methods; this was particularly

pronouced at hi^er axial loads. The percent increase from the

ACI predicted values were 10.8 for the models subjected to the

lower axial load and 27.4 for the models subjected* to the

higher axial load. It would, therefore, appear that the ACI

method results in conservative ultimate moment predictions for

columns under high axial loads (greater than 0.2 f'^ Ag).

3. Plastic hinge length increases with increasing aspect ratio (I/D)« It

does not, however, appear to increase for increased displacement

ductility.

Testing of the fii^ full-scale prototype flexure colimin was coirpleted at

the end of July, 1986. Detailed results from that test were not available

in time for inclusion in this report. However, the ultimate displacement

ductility from the prototype specimen was approximately six. This

cortpares favorably with the displacement ductility factor of five obtained

for the flexure model constructed with ready-mix concrete.

7.2 H?ACTICAL AITIJCATI(^

The findings from this study point towards some practical applications for

the design engineer. It was found that, in general, the spiral strains in

the "foundation" base at a depth of 0.1 D [1 in. (25 mm)] were 400

microstrain or less, well below yield strain. This would irdicate that the

requirement to extend the spiral into the footing to the point of tangency

of the longitudinal bar hook may be overly conservative.

The probable plastic moment as defined by CALTRANS [^8] is 1.3 times the

nominal ultimate moment. This represents the maximum anticipated moment

that a supporting foundation would need to resist. This design factor

increase of 30 % from the roninal ACI moment agrees well with the 27.4

% obtained for models subjected to higher axial load (0.2 f'^ A„).

However, it would seem to be conservative for models subjected to lower

axial load (less than 0.1 f’^ Ag). A reduction of this multiplier for

structures subjected to lower axial loads would seem warranted and would

result in smaller, less costly footings.

The maximum extent of yielding of the longitudinal bar^ into the footing

was 0.51 D [5 in. (127 mm)]. The corresponding value for yield penetration

into the footing for the prototype column would then be 30 in. (760 mm) for

a 60 in. (1,52 m) column. The basic development length for a #14 bar (the

longitudinal reinforcement used in the NBS prototye column) is 86 in. (2.18

m) based on a concrete strength of 3500 psi (24 MPa) as was the case for

the models. This development length would therefore appear to be adequate

for anchorage of longitudinal reinforcement.

179
7.3 FtrrURE RESEARCH NEEI^

Coitparisons between NBS iiKxiel test results and similar tests cxDnducted in

New Zealand and Japan have indicated that use of larger size spiral

reinforcing bars at larger spacing may prove more effective *'in achieving

greater displacement ductility than the use of smaller diameter spiral

reinforcing bar at closer spacing. Furthermore, the use of larger

longitudinal bars, and/or greater numbers of longitudinal reinforcing bars,

than presently required by CAIIERANS specifications may stay the onset of

longitudinal bar buckling, and therefore also increase ultimate ductility.

Both techniques merit further detailed investigations to establish

statistically useful trend information. Along these lines, use has been

made in Japan of independent hoops for transverse confining reinforcement

in lieu of a continuous spiral for large diameter columns. The

effectiveness of this approach, as compared to the use of a continuous

spiral, should be investigated.

Higher displacement ductilities and energy absorption capacities were

achieved in models subjected to higher axial loads. This suggests that

increasing triaxial confining forces within the plastic hinge region might

lead to higher displacement ductilities, and hencQ greater ability to

dissipate energy. One possible , approach would be to use active

reinforcement in the form of lateral prestress. The level of prestressing

and the method used to achieve the prestress, particularly vhere stressing

lengths are short, should be among the parameters for future

investigation

Another method to help increase the ductility of bridge columns may be to

use a perforated metal casing either in addition to or instead of the

spiral in the potential plastic hinge region. This is suggested as a

result of observed column failure oceurring soon after the fracturing of

the spiral. The thickness of the casing, the toughness and type of

material from which it is fabricated, and the length of of the casing

should be some of the parameters considered.

Finally, the testing of the first full scale prototype specimen has proven

the feasiblity of conducting such tests within the laboratory. Following

the results of similitude studies relating the behavior of the model to

prototype specimens, it may be desirable to conduct further benchmark (full

scale) tests vhich address the important questions of the performance of

existing bridge columns designed using pre-1971 specifications, and the

effectiveness of (as-yet-untested) retro-fit techniques vhich are now being

used to bring these columns up to current standards.

180
REFERENCES 1.

ACI Committee 318, 'Gilding Code Requirements for Reinforced

Concrete", ACI 318-71, American Concrete Institute, 1971.

2.

ACI Committee^ 318, "Building Code Requirements for Reinforced

Concrete", ACI 318-77, American Concrete Institute, 1977.

3.

ACI Committee 318, "Building Code Requirements for Reinforced

Concrete", ACI 318-83, American Concrete Institute, 1983.

4.

Ad Committee 340, "Design Handbook", in accordaiK^e with the Strength

Design Method of ACI 318-77, Vol. 2, SP-17A(78), American Concrete

Institute, 1978.

5.

Ang, Beng Ghee, Park, R., and Priestley, M. J. N., "Ductility of

Reinforced Concrete Brieve Piers Under Seismic Loading*', Department of

Civil Engineering, IMiversity of Canterbury, New Zealand, Feb. 1981.

6.

Carpenter, James E., Roll, Frederic, and Zelman, Maier I.,

"Techniques and materials for structural models" in Models For

Concrete Structures, Ad Publication SP-24, 1970.

7. "Code of Practice for the Design of Coixirete Structures", First Draft

DZ 3101, Standards Association of N^ Zealand, 1978

8. "NZS 3101: 1982 'Code of Practice for the Design of Concrete

Structures'" (Two volumes: code and ccramentary). Standards Association

of New Zealand, 1982.

9.

"Highway Bridge Design Brief", Ministry of Works and Development, New

Zealand, Issue C, July 1973.

10. Gill, Wayne D., "Ductility of Rectangular Reinforced Concrete Columns

with Axial Load", D^)artment of Civil Engineering, University of

Canterbury, New Zealand, Feb. 1979.

11. Ruribayashi, Eiichi, et. al., "Reversed Cyclic loading Test of Bridge

Pier Models", Technical Memorandum of FWRI No. 1801, Earthquake

Engineering Division, Earthquake Disaster Prevention Department,

Public Works Research Institute, Ministry of Construction, October,

1981.

181
12.

Lew, H. S., Leyendecker, E. V., and Dikkers, R. D., Engineering

Aspects of the 1971 San Fernando Earthquake, NBS Building Science

Series #40, Dec. 1971.

13.

Munro, I. R. M., Park, R., and Priestley, M. J. N., "Seismic Behaviour

of Reinforced Concrete Bridge Piers", Department of Civil Engineering,

University of Canterbury, Zealand, Feb. 1976.

14.

Nasser, K. W., Kenyon, J. C., '*Why Not 3X6 Inch Cylinders for

Testing Concrete Compressive Strength ?" in the Journal of the

American Concrete Institute, Proceedings V. 81, January-February 1984

/ No. 1.

15.

"New Zealand Draft Concrete Code", New Zealand National Society for

Earthquake Engineering.

16.

Ng, Kit Heng, Park, R., and Priestley, M. J. N., MSeismic Behaviour of

Circular Reinforced Concrete Bridge Piers", Department of Civil

Engineering, University of Canterbury, New Zealand, Feb. 1978.

17.

Ohno, Tomonori and Nishioka, Ta3cashi, "An Ej^jerimental Study on Energy

Absorption Capacity of Columns in Reinforced Concrete Structures", in

Structural Engineering/Earthquake Engineering, Proceedings of the

Japan Society of Civil Engineers, Vol. 1, No. 2, Oct. 1984.

18.

Ohta, Minoru, "Experimental Study on the Behavior of Reinforced

Concrete Bridge Piers Under Horizontal Load Reversals", Public Works

Research Institute, Ministry of Construction.

19.

Park, R., and Priestley, M. J. N., "Code Provisions For Confining

Steel in Potential Plastic Hinge Regions of Columns in Seismic

Design", University of Canterbury, New Zealand.

20.

"Performance and Strengthening of Bridge Structure and Research

Needs", Proceedings - Second Joint U. S. - Japan Workshop, September,

1985.

21.

Priestley, M. J. N., and Park, R., "Seismic Resistance of Reinforced

Concrete Bridge Columns", University of Canterbury, New Zealand.

22.

Priestley, M. J. N., and Park, R., Strength and Ductility of Bridge

Substructures, RRU Bulletin 71, University of Canterbury, Dept, of

Civil Engineering, Dec. 1984.

182
23.

Priestley, M. J. N., Park, R., and Potangaroa R. T., "Ductility of

Spirally Confined Concrete Columns", Journal of Structural Division,

Proceedings of the ASCE, Vol. 107, Jan. 1981. 24.

"Recommendations for Future Research", Applied Technology Council

Workshop on Earthquake Resistance of Highway Bridges, Jan. 1979.

25.

Sabnis, Gajahan M., Harris, Harry C., White, Richard N., Mirza,

M. Saeed, Structural Modeling and E>q)erimental Techinques, Prentice

Hall, 1983.

26.

"Seismic Design Guidelines for Highway Bridges", Applied Technology

Council, FHWA RD 81/081.

27.

"Standard Specifications for Deformed Steel Wire for Concrete

Reinforcement", ASTM A-496, Vol. 01.04, 1984.

28.

"Standard Specifications for Highway Bridges" as amended by AASHTO

interims thrcaj^ 1984 with revisions by CAITRANS, AASHTO, 1983.

29.

Woodward, Kyle and Rankin, Frank, ”Ihe NBS Tri-Directional Facility",

NBSIR 84-2879, U. S. Department of Commerce, National Bureau of

Standards, May 1984.

30.

Zahn, F. A., Park, R., and Priestley M. J. N., "Design of Reinforced

Concrete Bridge Columns For Strength and Ductility", Department of

Civil Engineering, University of Canterbury, New Zealand, March, 1986.

31.

Park, R., and Paulay, T., Reinforced CoiKrete Structures, John Wiley &

Sons, New York, 1975.

32.

Standa3:d Specifications for Hic^way Bridges, adopted by the American

Association of State Hi^way Officials, 10 th. ed., Nov. 1969.

33.

Standard Specifications for Highway Bridges, adopted by the American

Association of State Highway and Transportation Officials, 13 th. ed.,

1983.

34.

"Bridge Planning and Design Manual", Vol. 1 - Design Specifications,

California Department of Transportation, Jan. 1971.

183
35 .

36.

37.

38.

Petrovski, Jakim and Ristic, Danilo, "Reversed Cyclic Loading Test of

Bridge Column Models", Report IZII 84 — 164, Institute of Earthquake

Engineering and Engineering Seismology, University of "Kiril and

Metodij", Skoje, Yugoslavia, Sept. 1984.

Kuribayashi, Eiichi, et. al., "New Specifications for EarthquakeResistant Design of Japanese Highway Bridges" in the Proceedings of

the 12th Joint Meeting of the US-Japan Panel on Wind and Seismic

Effects, NBS SP 665, Washington, D.C., 1980.

Personal communication with Dr. M.J.N Priestley, Universtiy of

Canterbury, 1985.

Personal communication with Mr. Kbichi Minosaku, Public Works Researxdi

Institute, 1986.

184
APPENDIX A: PROGRAM **TCJRBO-IOOP**

Measurement of the amount of energy absorbed by a bridge column subjected

to reversed cyclic loading is a difficult process, involving the evaluation

of the summation of the areas enclosed by the lateral load vs lateral

deflection curves generated for each cycle. Because typical ej^jerimentally

derived load-deflection curves e>diibit noise and other irregularities (due

to such physical phenomena as the fracture of reinforcing bar^ and sudden

crTOshing of concrete), evaluation of the area bounded by such curves is not

easily tractable through numerical integration procedures.

An alternative, rapid method for the evaluation of cyclic strain energy was

developed for this project. Each hysteresis curve for a particular model

test was plotted individually on a high resolution (1280 x 1024 pixel)

color raster device. The area enclosed by that curve was then filled with

a specified color. The number of pixels of that color was then tabulated.

A conversion factor was then used to convert the tabulated number to units

of energy in kip-in (kN-mm). This value represented the energy absorbed by

the model for that cycle. The process of integrating each load cycle for

one model test can then be corrpleted in a matter of minutes by automating

the entry of data from each cycle. A window size of 800 by 800 pixels was

used to determine the energy absorption capacities. This resulted in less

than 1 % error over that for a window size of 1280 by 1024 pixels while

greatly increasing computational speed.

A FORTRAN program listing of "Turbo_Loop” is presented in the following

pages. This was implemented on a VAX 11/750 computer system with a DMA

driven Raster Technologic Qne/80 cxDXbr raster display device. A second

FORTRAN program, "Graph" , is presented in i^pendix B. This is a graphics

post-processor written specifically for the interactive analysis of cyclic

column test data. It uses as input the data produced from Turbo-Loop.

185
Q •kicic'k'k'k'k'k'kicie-ifk'kicicic’k'k'k'k'k'k'k-k-kick'kik-k-k'k-k-k-k'k-k-k-k-k'k-k-k'k'k-k-k-k-k-k-k-k-k^-k c

C PROGRAM TURBO_LOOP

C

C PURPOSE:

C

C CALCULATE THE ENERGY ABSORBED BY A STRUCTURE SUBJECTED

C TO CYCLIC LOADING BY INTEGRATING THE AREA WITHIN THE

C EXPERIMENTALLY OBTAINED HYSTERESIS CURVES.

C

C METHOD:

C

C THE INTEGRATION IS DONE BY "COUNTING THE DOTS" WITHIN

C A HYSTERESIS CURVE. THE HYSTERESIS CURVE IS PLOTTED ON

C A HIGH RESOLUTION COLOR GRAPHICS DEVICE. THE HYSTERESIS

C CURVE IS THEN FLOODED WITH A PARTICULAR COLOR WHICH HAS

C A COLOR INDEX, A, ASSOCIATED WITH IT AND THE BACKGROUND

C WITH A DIFFERENT COLOR WHICH HAS COLOR INDEX, B,

C ASSOCIATED WITH IT. THE PROGRAM THEN COUNTS THE NUMBER

C OF PIXELS WITH COLOR INDEX A. THIS NUMBER REPRESENTS

C THE AREA WITHIN THE HYSTERESIS CURVE IN PIXELS WHICH IS

C THEN CONVERTED TO UNITS OF ENERGY (KIP-IN)

C

C IMPLEMENTATION:

C

C

C GRAPHICS:

C

C THE PROGRAM MAKES USE OF A RASTER TECH MODEL ONE/8

0

C COLOR GRAPHICS DEVICE WHICH HAS A RESOLUTION OF 1280 BY

C 1025 PIXELS FOR OUTPUT DISPLAY . CONSULT THE RASTER

C TECHNOLOGIES HANDBOOK FOR EXPLANATION OF CALLS TO THE

C "ONELIB" LIBRARY.

C

C DATA FORMAT

C

C DATA FOR TURBO_LOOP IS GENERATED THROUGH THE FOLLOWING

C PROCEDURE

C

C 1) NBS SPECIFIC:

C GENERATE PLOT FILES CONSISTING OF ONE COLUMN EACH

C OF THE Y-COORDINATES ( TYPICALLY LOAD ) AND THE XC COORDINATES (TYPICALLY DISPLACEMENT ) . THESE PLOT

C FILES ARE AUTOMATICALLY GENERATED USING PROGRAM

C UT:$DDP FROM ANY SET OF TEST DATA OBTAINED EITHER

C BY THE TTF FACILITY OR BY THE LARGE SCALE TEST

C FACILITY IN BUILDING 202. EACH PLOT FILE SHOULD

C ONLY REPRESENT ONE CYCLE.

C

C 2) NBS SPECIFIC:

C STRIP KEY DATA FROM THE PLOT FILES NEEDED BY TURBO_

C LOOP. THIS CAN BE DONE AUTOMATICALLY BY RUNNING THE

C CONVERSION PROGRAM "POLYCONV" OR "JLG" AND ENTERING

C THE NAMES OF THE TWO PLOT FILES, THE FILENAME OF THE

C CONVERTED DATA ( MUST HAVE AN " . INP" EXTENSION ) AND

186
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

C 3)

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

THE IDENTIFYING TITLE TO BE PLOTTED ON THE RASTER

TECH ONE/8 0. THE CONVERTED FORMAT AFTER RUNNING

"POLYCONV" OR "JLG” IS AS FOLLLOWS

A) TITLE (A80 FORMAT)

B) XMIN, XMAX, YMIN, YMAX, NPTS

WHERE:

XMIN - MINIMUM VALUE OF THE X-COORDINATE IN

(E12.5 FORMAT)

XMAX - MAXIMUM VALUE OF THE X-COORDINATE IN

(E12.5 FORMAT)

YMIN - MINIMUM VALUE OF THE Y-COORDINATE IN

(E12.5 FORMAT)

YMAX - MAXIMUM VALUE OF THE Y-COORDINATE IN

(E12.5 FORMAT)

NPTS - NUMBER OF DATA (X,Y) PAIRS IN

(15 FORMAT)

C) EXAMPLE: THE (X,Y) PAIRS IN 2*(E12.5) FORMAT

0.1567E+00 0.0020E+00

0.2389E+00 0. 0789E+00

ETC.

NOTE THERE MUST BE 'NPTS' NUMBER OF SUCH PAIRS

[GENERAL USERS NOTE] PROGRAM WILL ACCEPT ANY

EXTERNALLY GENERATED TEST DATA FILES PROVIDED

THEY HAVE THE ABOVE FORMAT.

NBS SPECIFIC:

LOAD A TAPE ON DRIVE MMO : ( THE ONLY ONE ON THE PDP

11/34)

THE TAPE HAS TO BE INITIALIZED AS A

FILES-11 TAPE. THIS HAS TO BE DONE ONLY ONCE.

A) LOGIN ON THE PDP 11/34

B) ALLOCATE MMO:

GO TO STEP D IF TAPE HAS BEEN INITIALIZED.

NOTE: INITIALIZATION OF THE TAPE CAN ONLY BE

DONE FROM A PRTVILEDGED ACCOUNT.

C) INS

FILE? DLO: [1,54] INI

INITIALIZE/DENSITY=1600 MMO : YOURLABLE_NAME (

CHARACTERS

)

D) MOUNT MMO : YOURLABLE_NAME

E) COPY CONVERTED_FILENAME . INP MMO

(WHERE THE CONVERTED_FILENAME . INP IS THE OUTPUT

FROM "POLYCONV" OR "JLG")

187
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

F) DISMOUNT MMO:

G) DEALLOCATE MMO:

H) LOGOUT (AND TRANSFER TAPE TO VAX TAPE DRIVE)

4) NBS SPECIFIC

ON THE VAX 11/750

A) LOAD TAPE

B) LOGIN

C) ALLOCATE MSAO:

D) MOUNT/OVERRIDE= (ACCESSIBILITY, IDENTIFICATION,

OWNER_IDENT) MSAO

OR

IF THE PROGRAM IS AVAILABLE TYPE:

0PDP_TO_VAX

E) COPY MSAO :CONVERTED_FILENAME. EXT

TO? YOUR WORK DIRECTORY FOR RUNNING TURBO_LOOP

F) DEALLOCATE MSAO:

G) DISMOUNT MSAO:

[GENERAL USERS]

5) IT IS POSSIBLE (AND DESIRABLE) TO PROCESS AN ENTIRE

CYCLIC LOAD TEST IN ONE BATCH OPERATION; TO DO THIS,

CREATE A FILE CALLED "LIST. LIS” WHICH CONTAINS THE

CONVERTED FILENAMES WITHOUT THEIR EXTENSIONS. EACH

FILENAME SHOULD^ BE ON A DIFFERENT LINE

EXAMPLE

IF A TEST HAS 5 LOAD CYCLES AND THE CONVERTED FILE

NAMES WERE CYCLEl.INP, CYCLE2.INP, ... , CYCLE5.INP,

THE FILE "LIST. LIS” SHOULD CONTAIN THE FOLLOWING:

CYCLEl

CYCLE2

CYCLES

CYCLE

CYCLES

6)

YOU ARE NOW READY TO CALCULATE THE ENERGY WITHIN A

HYSTERESIS CURVE USING TURBO_LOOP. TO START THE

PROGRAM TYPE:

RUN [ CHEOK . INTEG ] TURBO_LOOP OR

FOR GENERAL USERS, SIMPLY RUN THE EXECUTABLE

(COMPILED AND LINKED) VERSION OF TURBO_LOOP . FOR

188
C 7) THE RESULTS WILL BE STORED IN THE FILE OR SERIES

C OF FILES CALLED "CONVERTED_FILENAME . OUT" IN THE

C FOLLOWING FORMAT:

C

C LINE 1: TITLE AS GIVEN IN THE CONVERSION PROCESS IN

C STEP 2

C LINE 2: ICOUNT (110 FORMAT) , AREA (F10.5 FORMAT)

C

C ONE OUTPUT FILE WILL BE CREATED FOR EACH INPUT FILE

C IN "LIST. LIS".

C

C OTHER SUBROUTINES CALLED: NONE OTHER THAN THE RASTER

C TECH "ONELIB" CALLS.

C

C LAST EDIT SESSION: 8-12-86

189
c *********************************************************

c

C PARAMETER DEFINITIONS

C

C TITLE

C FILENAME

C INFILE

C

C

C OUTFILE

C

C YSIZE

C XSIZE

C VERTS (1,N)

C VERTS ( 2, N)

C NVERTS(I)

C I COUNT

C

C AREA

C XFACTOR

C

C

C YFACTOR

C

C

C XRANGE

C YRANGE

C

C

C SUBROUTINES CALLED: NONE OTHER THAN RASTER TECH ONE/ 80

C ONELIB CALLS . SEE APPENDIX B'^FOR DEFINITION OF CALLS

C

C

Q ********************************************************

c

c

CHARACTER* 80 TITLE

CHARACTER FILENAME*10 , INFILE*14 , OUTFILE*14

C

DIMENSION X(IOOO) ,Y(1000)

INTEGER*2 VERTS (2 , 1000) ,NVERTS (1)

INTEGER*2 IX, lY , XSIZE , YSIZE

INTEGER*4 TOTAL

BYTE IVAL( 13 10720)

C

C SET PROGRAM VARIABLES

C

C PROMPT USER FOR WINDOW SIZE

C

TYPE *,' ENTER SIZE OF WINDOW ' TYPE *,' A 500 X 500 WINDOW RESULTS IN +1% ERROR'

TYPE *, ' X SIZE = ' READ *, XSIZE

TYPE *, • Y SIZE = ' READ *, YSIZE

TITLE OF A PARTICULAR CYCLE IN A TEST

FILENAMES WHICH ARE LISTED IN FILE LIST. LIS

FILE WHICH CONTAINS THE TITLE, MAXIMA AND MINIMA,

NUMBER OF DATA POINTS AND DATA FOR A PARTICULAR

CYCLE

FILE WHICH WILL STORE THE TITLE OF THE CYCLE AND THE

ENERGY DISSIPATED FOR THAT PARTICULAR CYCLE

WINDOW SIZE IN Y DIRECTION

WINDOW SIZE IN X DIRECTION

X-COORDINATE OF POINT N IN INTEGER* 2 FORMAT

Y-COORDINATE OF POINT N IN INTEGER*2 FORMAT

NUMBER OF VERTICES IN POLYGON I

THE NUMBER OF PIXELS WITHIN THE HYSTERESIS

CURVE

THE AREA WITHIN THE HYSTERESIS CURVE

(UNITS: PIXELS/UNIT OF LENGTH) THE

CONVERSION FACTOR TO CHANGE THE UNITS

OF LENGTH INTO NUMBER OF PIXELS

(UNITS: PIXELS/UNIT OF FORCE)

THE CONVERSION FACTOR TO CHANGE THE UNITS

OF FORCE TO THE NUMBER OF PIXELS

THE MAXIMUM DISPLACEMENT FOR THAT CYCLE

THE MAXIMUM FORCE FOR THAT CYCLE

190
oooo

ooo

ooo

oooo

ooo

oooo

ooo

oooo

ooo MAXIMUM WINDOW SIZE IS 1278 BY 1022

IF(XSIZE.GT.1278) XSIZE =_1278

IF(YSIZE.GT.1022) YSIZE = 1022

XSIZE4 = XSIZE

YSIZE4 = YSIZE

INITIALIZE THE RASTER TECH MODEL ONE/8 0 GRAPHICS DEVICE

TYPE *, 'INITIALIZE THE GRAPHICS DEVICE'

CALL RTSET (1,180)

CALL RTINIT (' GDAO :

' , 5

)

CALL ENTGRA

CALL READF(l)

LOAD THE COLOR MAP

CALL LUT8 (0,255, 135,0) ! CALL LUT8 (1,0, 0,255) I CALL LUT8 (2,0,255,0) ! CALL LUT8 (3, 0,0,255) ! CALL LUT8(4,0,0,0) 1 CALL LUT8 (6,255,255,255) I CALL LUT8(5,IRED,IGRN,IBLU)

ORANGE

BLUE

GREEN

BLUE

BLACK

WHITE

OPEN FILE WHICH CONTAINS THE LIST OF CYCLES TO BE

PLOTTED

OPEN ( 1 , FILE= ' LIST . LIS ' , STATUS= ' OLD ' , ACCESS=

1 ' SEQUENTIAL '', FORM= ' FORMATTED ' ) READ THE FILENAME

500 CONTINUE

LOOP ON THIS READ STATEMENT UNTIL ALL THE LOAD CYCLES

HAVE BEEN PROCESSED

READ ( 1 , FMT=1 , END=1000 ) FILENAME

1 FORMAT (A20)

VARIABLE FILENAME IS UPDATED WITH EACH CYCLE

TYPE *, 'WORKING ON FILE' , FILENAME

ATTACH THE " . INP" AND ".OUT" EXTENSION TO THE FILENAME

INFILE=FILENAME// ' . INP

OUTFILE=FILENAME// ' . OUT

OPEN INDIVIDUAL CYCLE PLOT FILE

OPEN (UNIT=2 , FILE=infile , ACCESS= ' SEQUENTIAL ' , FORM=

191
ooo

oooooo

o

ooo

o

H

ooo

non

ooo

ooo

ooo

1

' FORMATTED

REWIND 2

/ STATUS= ' OLD ' )

OPEN CONVERTED_FILENAME.OUT FILE FOR STORING RESUJjTS

OPEN (UNIT=3 , FILE=OUTFILE , ACCESS= ' SEQUENTIAL ' , FORM=

1 ' FORMATTED ' , STATUS= ' NEW '

)

REWIND 3

GET DATA FROM CYCLE PLOT FILE "TITLE"

READ (2, 2) TITLE

2 FORMAT (A80)

WRITE THE TITLE IN THE ' CONVERTED_FILENAME . OUT

WRITE (3, 6) TITLE

6 FORMAT(X,A80)

GET MAX AND MIN VALUES AND THE NUMBER OF POINTS

READ (2, 3) XMIN,XMAX, YMIN,YMAX,NPTS

3 FORMAT(4(E12.5,3X) ,15)

GET THE DATA POINTS

DO 100 I=1,NPTS

READ(2,4) X(I) , Y(I)

00 CONTINUE

4 FORMAT (2 (E12.5,3X)

)

CLOSE (UNIT=2)

SCALE THE DATA

XRANGE=MAX(ABS (XMAX) ,ABS (XMIN)

)

YRANGE=MAX (ABS ( YMAX) , ABS ( YMIN)

)

XFACTOR=XSIZE/ (2 . *XRANGE)

YFACTOR=YSIZE/ (2 . *YRANGE)

LOAD DATA PAIRS INTO THE INTEGER*2 VECTORS: VERTS ( I, J)

[NOTE: THIS IS A RASTER TECH ONE/80 SPECIFIC DIRECTIVE

USED IN A HARDWARE POLYGON PLOT COMMAND] AND SCALE

THESE TO SCREEN COORDINATES

DO 200 I=1,NPTS

VERTS (1,1) =IFIX (X ( I

) *XFACTOR)

VERTS (2,1) =IFIX ( Y ( I

) * YFACTOR)

200 CONTINUE

FLOOD THE BACKGROUND

CALL VAL8(0) I ORANGE

CALL FLOOD

192
oooo

oooo

ooo

noon

oooooo

o

ooo DRAW AXES • CALL VAL8(6) ! WHITE

CALL MOVABS(-XSIZE/2,0)

CALL DRWABS(XSIZE/2,0)

CALL MOVABS(0,-YSIZE/2)

CALL DRWABS(0,YSIZE/2)

DRAW THE CURVE

THE PRMFIL SUBROUTINE FILLS THE ENCLOSED CURVE WITH

COLOR VALUE 1

CALL PRMFIL (1)

ASSIGN THE COLOR VALUE 1 TO THE PIXELS INSIDE THE

POLYGON ALL OTHERS ARE ORANGE

CALL VAL8(1) ! BLUE — - CALL MOVABS(0,0)

PLOT THE POLYGON (LOAD CYCLE) ON THE SCREEN

NVERTS(1)=NPTS

CALL POLYGN(l,NVERTS, VERTS)

INTEGRATE BY 'COUNTING THE DOTS'

TYPE *,'HERE WE GOl ' IX=(-XSIZE/2)

IY=(YSIZE/2)

TYPE *

,

' YSIZE= ' , YSIZE ,

' XSIZE= ' , XSIZE

TYPE *, 'MOVING TO: IX=',IX,', IY=',IY

MOVE TO UPPER LEFT CORNER OF THE WINDOW. WINDOW ORIGIN

AT SCREEN CENTER

CALL MOVABS(IX,IY)

TYPE *, 'READING WINDOW'

C

C BLANK THE DISPLAY SCREEN TO SPEED UP CALCULATIION

C PROCESS (REFRESH OF SCREEN IMAGE REQUIRES CPU TIME.

C BY TURNING THIS OFF, THE TIME TO CONDUCT PIXEL READ

C OPERATIONS ARE CONSIDERABLY REDUCED)

C

CALL BLANK (1)

TYPE *, 'WINDOW SIZE: ',XSIZE+1,' BY ',YSIZE+1

C

C READ THE VALUE OF THE PIXELS (RED, GREEN, BLUE) IN

C THE WINDOW BY SCANNING FROM LEFT TO RIGHT AND TOP

C TO BOTTOM

C

193
non

^

oooo

oooo

w

oooooooo

ooo

CALL READW(YSIZE+1,XSIZE+1,IVAL)

CALL BLANK (0)

C

TYPE *

,

' INTEGRATING

C

C NOTE THAT XSIZE4 = XSIZE AND YSIZE4 = YSIZE

C TOTAL IS EQUAL TO THE TOTAL NUMBER OF PIXELS IN THE

C THE WINDOW. IT IS USED AS A COUNTER IN THE DO LOOP

C TO EXTRACT FROM THE TOTAL NUMBER OF PIXELS ONLY THOSE

C WHICH HAVE THE COLOR VALUE OF 1.

C

TOTAL=(XSIZE4+l) * (YSIZE4+1)

INITILIZE THE COUNTER

ICOUNT=0

BYTE VECTOR *IVAL* CONTAINS THE COLOR LOOK-UP DEFINITION

FOR EACH PIXEL IN THE WINDOW. COMPARE THE COLOR OF EACH

PIXEL TO SEE IF IT MATCHES THAT ASSIGNED TO THE

HYSTERSIS LOOP (COLOR VALUE = 1) . IF IT DOES, ADD ONE

TO THE COUNTER, ICOUNT, WHICH REPRESENTS THE SUM OF ALL

PIXELS OF THAT COLOR

DO 300 1=1, TOTAL

IF(IVAL(I) .EQ.l) ICOUNT=ICOUNT+l

00 CONTINUE

TYPE *

,

' INTEGRATION COMPLETE

TYPE *

,

' ICOUNT= ' , ICOUNT

CONVERT THE NUMBER "OF PIXELS TO ENERGY UNITS AND STORE

THE VALUE IN "AREA"

AREA=FLOAT (ICOUNT) / (XFACTOR*YFACTOR)

TYPE *, *AREA=' ,AREA

WRITE THE VALUES OF ICOUNT AND AREA INTO FILE CALLED

' CONVERTED_FILENAME . OUT * WRITE ( 3 , FMT=7 ) ICOUNT , AREA

FORMAT (X, *ICOUNT=' ,110, ' AREA= ' ,F10.5)

CLOSE (3)

LOOP BACK TO THE READ STATEMENT AND GET ANOTHER FILENAME

GOTO 500

C

1000 CONTINUE

CLOSE (1)

C

CALL QUIT

CALL EXIT

C

STOP

END

194
APPENDIX B: FROGRftM "GRAEW*

A FORTRAN program listing of "Graph"^ is presented in the toileting section.

This was implemented on a VAX 11/750 computer system with a DMA driven

Raster Technologies One/80 color raster display device.

Graph is an interactive program which permits the user to graphically

display the results from a cyclic load test on a raster device. The user

is presented with a menu from TAhich the following may be chosen:

1. A plot of the lateral load vs. column displacement history

simultaneoiasly with an animation showing the deflected position of the

coliimn. The user has the choice of plotting either the total energy

dissipated by the column during the test or plotting the energydissipated per cycle. Each plot occi:5)ies one screen quadrant.

2. A coirparison of the energy dissipated per cycle for a maximum of three

tests. This subroutine also allows interactive scaling of individual

test data so that a scale factor between tests can^ be determined.

3. A plot of the total energy dissipated during a test. Up to six tests

may be displayed simultaneously.

4. A plot of the lateral load vs. column displacement using the entire

screen. This enlarged display allows the user to determine if anything

unusual occurred during a certain portion of the test; for example, a

drop in load due to the fracturing of spiral or longitudinal

reinforcement

195
Q ********************************************************

C

C PROGRAM GRAPH

C

C PURPOSE

C

C TO PRESENT THE DATA FROM CYCLIC TESTS ON A

C GRAPHICS DEVICE.

C

C GRAPHICS ; . - C

C THE PROGRAM MAKES USE OF A RASTER MODEL ONE/ 80

C COLOR GRAPHICS DEVICE FOR OUTPUT DISPLAY. CONSULT

C THE RASTER TECHNOLOGIES HANDBOOK FOR EXPLANATIONS

C OF CALLS TO THE "ONELIB" LIBRARY.

C

C

C

C FILE STRUCTURE:

C

C PROGRAM GRAPH IS ACTUALLY A COLLECTION OF GRAPHICS

C ORIENTED PROGRAMS WHICH SERVE AS AIDS FOR THE INTERPRETATION

C OF CYCLIC LOAD DATA FROM DYNAMIC OR PSUEDO-DYNAMIC TESTS.

C SPECIFICALLY, A MENU OPTION PERMITS ACCESS TO THE FOLLOWING

C SUBPROGRAMS

C

C O ANIMATED PLOTTING OF THE LOAD DISPLACEMENT CURVE WITH

C A VISUAL QUEUE IN THE FORM OF A DEFLECTING COLUMN SPECIMEN.

C THIS PROGRAM ALSO PLOTS (ON THE SAME SCREEN) EITHER THE

C TOTAL ENERGY DISSIPATED DURING THE COURSE OF A SPECIFIC TEST

C OR THE ENERGY D'ISSIPATED TOURING EACH CYCLE (AS A BAR TYPE

C HISTOGRAM)

C

C Subroutines involved: [MAIN, CYCLE, COLPLOT, ENERGY,

C INDIVENE]

C

C o COMPARISON OF ENERGY ABSORBED PER CYCLE FOR UP TO THREE

C COMPLETE TESTS. PLOTTED AS A BAR TYPE HISTOGRAM.

C INTERACTIVE SCALING OF THE VALUES ALLOWS FOR EASY

C DETERMINATION OF THE SCALE BETWEEN TESTS.

C

C Subroutines involved: [COMPARE, REDRAW]

C

C O COMPARISON OF TOTAL ENERGY ABSORBED DURING A COMPLETE

C TEST WITH UP TO SIX DIFFERENT TESTS BEING COMPARED.

C CURRENT OPTIONS PERMIT NON-DIMES lONALIZATION OF ENERGY WITH

C RESPECT TO DIFFERING VALUES OF F ' C AND DELTA-y. THE PROGRAM

C SUMS ENERGY DISSIPATED UP TO THE ULTIMATE STATE OF THE

C STRUCTURE. THE ULTIMATE STATE BEING DEFINED AS 0.8 TIMES

C THE MOMENT AT U = 2 (AS DISCUSSED IN THE MAIN PAPER)

C

C Subroutines involved: [COMTOTAL]

C

C o LOAD-DISPLACEMENT LINE PLOT ONLY. USES FULL SCREEN

C DIMENSIONS FOR GREATER DETAIL IN ANALYSIS OF BEHAVIOR.

196
C TO BE CONTRASTED WITH THE FIRST, OPTION IN WHICH THE LOAD

C DISPLACEMENT PLOT APPEARS IN THE LOWER LEFT HAND QUADRANT

C OF THE SCREEN.

C

C Subroutines involved: [LINEPLOT]

C

C EACH OF THESE PROGRAMS REQUIRES DATA ENTRY IN A SPECIFIC FORMAT.

C THE AVAILABLE DATA WILL BE IN ONE OF TWO POSSIBLE FORMS:

C

C a) A FILE CONTAINING (X,Y) COORDINATE PAIRS WHICH CAN BE USED

C TO GENERATE, FOR EXAMPLE, LOAD-DISPLACEMENT HYSTERSIS PLOTS

C FOR A SPECIFIC TEST. AS DESCRIBED BELOW, THIS DATA MUST

C BE IN A SPECIFIC FORM WHICH INCLUDES A TITLE FOR THE DATA,

C THE DATA MAXIMA AND MINIMA, THE NUMBER OF (X,Y) PAIRS, AND

C (X,Y) DATA.

C

C b) AS FILE CONTAINING A DATA TITLE, AND THE INTEGRATED AREA

C INSIDE ONE HYSTERESIS LOOP FOR A SPECIFIED TEST. THESE CAN

C BE GENERATED AUTOMATICALLY USING THE PROGRAM TURBO_LOOP

C DESCRIBED IN APPENDIX A.

C

C

C

C Example:

C

C

C A TEST CONTAINS FIVE COMPLETE LOAD CYCLES. THE FOLLOWING FILES

C MUST BE GENERATED:

C

C LOAD-DISPLACEMENT FILES (GENERATED AT NBS USING POLYCONV. THESE

C CAN BE GENERATED EXTERNALLY D^ING ANY PROGRAM WHICH PRODUCES

C A FILE HAVING OUTPUT IN THE FORMAT SPECIFIED BELOW:

C

C 1) CYCLEl.INP

C 2) CYCLE2.INP

C 3) CYCLES. INP

C 4) CYCLE4.INP

C 5) CYCLES. INP

C

C Total Energy per Cycle Files (Output from TURBO-LOOP)

C

C 6) CYCLEl.OUT

C 7) CYCLE2.0UT

C 8) CYCLE3. OUT

C 9) CYCLE4.0UT

C 10) CYCLES. OUT

C

C TO AID IN AUTOMATING THE PROGRAM, A NUMBER OF ADDITIONAL FILES

C ARE NECESSARY. THESE ARE AS FOLLOWS:

C

C a) LIST. LIS: ONLY USED IN TURBO_LOOP. CONTAINS THE LOAD

C DISPLACEMENT FILES TO BE ANALYZED (INTEGRATED) . IN THE

C ABOVE EXAMPLE, FILES 1-S WOULD BE IN LIST. LIS. WITH ONE

C FILENAME PER LINE, WITHOUT THE EXTENSION " . INP" — THE

C PROGRAM AUTOMATICALLY ADDS THOSE DURING EXECUTION. UPON

197
C EXECUTION WITH INPUT AS LIST. LIS, THE OUTPUT FROM TURBO_

C LOOP WILL BE FILES 6-11 AS LISTED ABOVE, WITH THE

C EXTENSION ".OUT" APPENDED.

C

C b) FILENAME. LIS: ANY' FILENAME SUPPLIED BY THE USER CONTAINING

C A LIST OF ".INP" FILES AS DESCRIBED ABOVE (A LIST OF

C SPECIFIED LOAD CYCLE FILES FOR A GIVEN TEST) WITH THE

C FILE EXTENSION ".LIS". USED IN PROGRAM GRAPH FOR PROCESSING

C OF ONE SPECIFIC SET OF TEST DATA. IN THE ABOVE EXAMPLE,

C FILENAME. LIS WOULD INCLUDE FILES 1-5 AND FOR THIS EXAMPLE

C IS THE SAME AS LIST. LIS. NOTE THAT FILENAME . LIS , LIKE

C LIST. LIS, CONTAINS THE FILE TTILES, ONE PER LINE, WITH NO

C EXTENSION ".INP".

C

C C) SEEFILE.LIS: A FILE CONTAINING A DATABASE CONSISTING OF ALL

C FILENAME. LIS FILES IN THE USER'S DIRECTORY. USED FOR DATA

C MANAGEMENT (AND TO JOG THE USER'S MEMORY OF JUST WHAT

C HE/SHE HAS AVAILABLE)

C

C d) REFTITLE.LIS: USED ONLY IN SUBROUTINE COMPARE, WHICH

C DISPLAYS INDIVIDUAL CYCLE ENERGIES FOR ONE TO THREE

C DIFFERENT TESTS. THE FILE REFTITLE.LIS CONTAINS A LIST

C (ONE PER LINE) OF ALL POSSIBLE DESCRIPTORS FOR EXISTING

C LOAD CYCLES. THE TITLES IN THE FILES WITH THE ".OUT"

C EXTENSION MUST HAVE THE **EXACT** SAME FORMAT. FOR THIS

C SET OF TESTS, THE TITLES MUST BE IN FORMAT:

C

C DISPLACEMENT-DUCTILITY "DEL" , CYCLE-NUMBER-AT-GIVEN-DUCTILITY

C

C WHERE

C

^ ^ . C DISPLACEMEMT DUCTILITY IS AN INTEGER BEGINNING IN COLUMN 2

C CYCLE-NUMBER-AT-GIVEN-DUCTILITY IS AN INTEGER VALUE EQUAL

C TO THE CYCLE NUMBER AT A GIVEN DUCTILITY LEVEL.

C

C NOTE: THE FORMAT MAY BE CHANGED BUT IF SO, IT MUST BE

C CHANGED IN BOTH THE REFTITLE.LIS AND IN EACH OF THE FILES

C WITH THE ".OUT" EXTENSIONS.

C

C FOR EXAMPLE, SUPPOSE TESTl HAS THE FOLLOWING CYCLE DESCRITORS

C

C 1 DEL, 1

C 2 DEL, 1

C 2 DEL, 2

C 4 DEL, 1

C 4 DEL, 2

C

C

C and TEST2 has

C

C 1 DEL, 1

C 2 DEL, 1

C 2 DEL, 2

C 3 DEL, 1

C 3 DEL, 2

198
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

3 DEL, 3

THE FILE REFTITLE.LIS TO BE USED WHEN COMPARING THESE TWO TESTS

SHOULD APPEAR AS FOLLOWS:

REFTITLE.LIS

1 DEL, 1

2 DEL, 1

2 DEL, 2

3 DEL, 1

3 DEL, 2

3 DEL, 3

4 DEL, 1

4 DEL, 2

IF ADDITIONAL TESTS ARE TO BE COMPARED, THEN REFTITLE.LIS SHOULD

INCLUDE ALL UNIQUE CYCLE DESCRIPTORS FOR THE SET OF TESTS IN

ASCENDING ORDER (DUCTILITY FIRST, CYCLE NUMBER AT A PARTICULAR

DUCTITLITY SECOND) - -

DATA FORMAT:

THE FOLLOWING PROCEDURE IS USED TO GENERATE THE DATA

1) GENERATE PLOT FILES CONSISTING OF ONE COLUMN

EACH OF THE .Y-COORDINATES ( TYPICALLY LOAD) AND

THE X-COORDINATES ('TTYPICALLY DISPLACEMENT)

THESE PLOT FILES ARE AUTOMATICALLY GENERATED

USING PROGRAM UT:$DDP FROM ANY SET OF TEST

DATA OBTAINED EITHER BY THE TTF FACILITY OR BY

THE LARGE SCALE TEST FACILITY IN BUILDING 202.

EACH PLOT FILE SHOULD ONLY REPRESENT ONE CYCLE.

2) STRIP KEY DATA FROM THE PLOT FILES NEEDED BY

GRAPH. THIS CAN BE DONE AUTOMATICALLY BY

RUNNING THE CONVERSION PROGRAM "POLYCONV" OR

"JLG" AND ENTERING THE NAMES OF THE TWO PLOT

FILES, THE FILENAME OF THE CONVERTED DATA

( MUST INCLUDE ".INP" EXTENSION) AND THE

IDENTIFYING TITLE TO BE PLOTTED ON THE RASTER

TECH MODEL ONE/8 0. THE CONVERTED FORMAT AFTER

RUNNING "POLYCONV" OR "JLG" IS AS FOLLOWS:

A) TITLE (A80 FORMAT)

B) XMIN, XMAX, YMIN, YMAX, NPTS

WHERE

XMIN - MINIMUM VALUE OF THE X-COORDINATE IN

E12.5 FORMAT

XMAX - MAXIMUM VALUE OF THE X-COORDINATE IN

199
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

E12.5 FORMAT

YMIN - MINIMUM VALUE OF THE Y-COORDINATE IN

E12.5 FORMAT

YMAX - MAXIMUM VALUE OF THE Y-COORDINATE IN

E12.5 FORMAT

NPTS - NUMBER OF DATA POINTS (X,Y) IN

15 FORMAT

C) EXAMPLE OF THE (X,Y) PAIRS IN E12 . 5 FORMAT

0.2845E+00 0.1798E+00

0. 1008E+01 0.7333E+00

ETC.

NOTE THERE MUST BE ‘NPTS’ NUMBER OF SUCH

PAIRS

NOTE THAT EXTERNALLY GENERATED FILES CAN BE

DIRECTLY ENTERED USING THE VAX 11/750 SYSTEM

PROVIDED THEY HAVE THE ABOVE FORMAT.

3) LOAD A TAPE ON DRIVE MMO : ( THE ONLY ONE ON

THE PDP 11/34) . THE TAPE HAS TO BE INITIALIZED

AS A FILES-11 TAPE. THIS INITIALIZATION IS

DONE ONLY ONCE.

A) LOGIN ON THE PDP 11/34

B) ALLOCATE MMO:

. GO TO STEP D IF THE TAPE HAS ALREADY BEEN

INITIALIZED.

NOTE: INITIALIZATION CAN ONLY BE DONE

FROM A PRIVILEDGED ACCOUNT.

C) INS

FILE? DLO: [1,54] INI

INITIALIZE/DENSITY=1600 MMO : YOURLABLE_NAME

(6 CHARACTERS)

D) MOUNT MMO : YOURLABLE_NAME

E) COPY CONVERTED_FILENAME.INP MMO:

(WHERE THE CONVERTED_FILENAME . INP IS THE

OUTPUT FROM “POLYCONV” OR "JLG")

F) DISMOUNT MMO:

G) DEALLOCATE MMO:

H) LOGOUT ( AND TRANSFER TAPE TO VAX TAPE

DRIVE)

4) ON THE VAX 11/750

A) LOAD TAPE

B) LOGIN

C) MOUNT/OVERRIDE= (ACCESSIBILITY

,

IDENTIFICATION, OWNER_IDENT) MSAO

200
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

OR

IF THE PROGRAM IS AVAILABLE TYPE:

0PDP_TO_VAX

D) COPY MSAO:CONVERTED_FILENAME.INP

TO? YOUR WORK DIRECTORY FOR RUNNING GRAPH

E) DEALLOCATE MSAO

F) DISMOUNT MSAO:

5) CREATE A FILE WITH AN ".LIS” EXTENSION WHICH

CONTAINS THE CONVERTED_FILENAMES WITHOUT THEIR

EXTENSIONS. EACH FILENAME SHOULD BE ON A

SEPARATE LINE.

6) RUN THE PROGRAM "TURBO_LOOP" TO OBTAIN THE

ENERGY ABSORPTIONS.

7) CREATE A FILE CALLED "REFTITLE . LIS" WHICH

CONTAINS A LIST OF TITLES IN A CERTAIN FORMAT.

SEE DOCUMENTATION FOR SUBROUTINE COMPARE FOR

MORE DETAILS.

8) YOU ARE NOW READY TO DISPLAY YOUR RESULTS FROM

YOUR TESTS. TO START THE PROGRAM TYPE:

RUN [CHEOK.INTEG] GRAPH

OR

USER HAVING PROGRAM IN HIS/HER DIRECTORY WILL

TYPE "RUN GRAPH"

LAST EDIT SESSION 12-16-86

201
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

•k-Jck'k-k-k-k-k-k-k'kifickic'k'Jeifk'k-k-k-k-k-k-k-krk-k-k-k-k-k-k-k'k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k^k-k GRAPHICS SUBROUTINES FOR THE RASTER TECH MODEL ONE/ 80

NOTE THAT THE PARAMETERS IN THE CALL STATEMENTS MUST

BE IN INTEGER*2 FORMAT

RTSET(1, 180)

RTINIT( 'GDAO:

ENTGRA

LUT8 (I,R,G,B)

VAL8 (I)

FLOOD

PRMFIL(I)

TEXTN(X, Y,K,L)

TEXT1(I, J)

TEXTC(I, J)

MOVREL(IX,IY)

MOVABS(IX,IY)

POLYGN(I, J,K)

RECTAN(IX,IY)

DRWABS(IX,IY)

EMPTYB

QUIT

IDENTIFIES THE GRAPHICS MODEL

5) INITIALIZES THE SYSTEM; ACTIVATES DMA

I/O PORT

ENTER GRAPHICS MODE

CHANGES THE COLOR ENTRIES IN "I" OF

COLOR LOOK-UP TABLE TO THE SPECIFIED

R, G, B VALUES

SETS THE CURRENT PIXEL COLOR VALUE TO

THE VALUE "I"

CHANGES ALL DISPLAYED PIXELS TO THE

CURRENT PIXEL COLOR VALUE

SETS FLAG TO INDICATE WHETHER THE

GRAPHIC PRIMITIVES ARE DRAWN FILLED

OR UNFILLED WITH THE CURRENT PIXEL

VALUE

1=1 FILLED 1=0 UNFILLED

SETS TEXT SIZE TO X & Y VALUES AND THE

ANGLE OF THE TEXT TO THE K & L VALUES

DRAWS HORIZONTAL TEXT STRING, J, WHICH

CONSISTS OF I CHARACTERS

SETS TEXT SIZE TO I AND THE ANGLE, J,

AT WHICH THE TEXT IS TO BE DRAWN

MOVES CURRENT POINT BY RELATIVE AMOUNT

SPECIFIED BY IX & lY

CHANGES CURRENT POINT TO POINT SPECIFIED BY IX & lY

DRAWS "I" NUMBER OF POLYGON WHICH HAS

"J” NUMBER OF VERTICES WHICH HAVE "K"

COORDINATES

DRAWS RECTANGLE WITH ONE CORNER AT THE

CURRENT POINT AND THE OPPOSITE CORNER

SPECIFIED BY (IX, lY)

DRAWS A LINE FROM CURRENT POINT TO

POINT SPECIFIED BY (IX, lY)

EMPTIES THE BUFFER CONTENTS TO THE

GRAPHICS DEVICE

EXITS GRAPHICS MODE AND RETURNS TO

ALPHA MODE

•k-k-k-k-k-k-k-kieicicic-k-k-k-kidcifk-k-k-k’k-kic-k-k-k-k-k-kicic-kifk-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-kic

CHARACTER* 80 TITLE

CHARACTER FILENAME *10, INFILE *14, OUTFI LE *14, NAME *10,

1 XNAME*14, XNOMBRE*14, YLIST*9,ZLIST*14,ANAME*80

DIMENSION X(400) , Y(400)

202
oo

oooooo

oonoo

ooo

ooo

INTEGER*2 TITLE (40) ,IDX(16) ,IDY(16)

,

1 OVERTIT (15)

INTEGER* 2 IX , lY , NCOUNT , DISPMT , ENERABS

INPUT IDX AND IDY VALUES TO USED FOR BOLD TEXT

DATA IDX/0,1, 0,-1, 0,1, 1,0, 0,1, 0,0, 0,-1, -1,-1/,

1 IDY/0, 0,1, 0,1, 0,0, -1,-1, 0,1, 1,1, 0,0,0/

REAL MAXX,MINX,MAXY,MINY

ASK USER FOR TYPE OF PLOTS

1104

311

TYPE

TYPE

TYPE

TYPE

TYPE

TYPE

TYPE

TYPE

DO

11

2

3

4

5

6

YOU WANT'

= LOAD-DISPLACEMENT AND ENERGY PLOT' = COMPARISON OF ENERGY ABSORBED/CYCLE

= COMPARISON OF TOTAL ENERGY ABSORBED

= SEE AVAILABLE LIST OF TESTS FOR' = LOAD-DISPLACEMENT LINE PLOT ONLY'

= EXIT'

READ (5, 311) lANSl

FORMAT (12)

IF(IANSl.EQ.l) GOTO 1002

IF(IANS1.EQ.2) GOTO 1102

IF(IANS1.EQ.3) GOTO 1101

IF(IANS1.EQ.4) GOTO 1108

IF(IANS1.EQ.5) GOTO 1109

IF(IANS1.EQ.6) GOTO 1003

I

I

IF OPTION #4 IS CHOSEN, SHOW AVAILABLE TESTS FOR PLOTTING

1108

1007

1004

1005

TYPE *,

TYPE *,

TYPE *,

OPEN (10

1 FORM=

TYPE *,

READ (10

FORMAT (A80)

TYPE 1004,ANAME

GOTO 1007

CONTINUE

GOTO 1104

AVAILABLE LIST OF TEST FILE NAMES FOR PLOTTING'

I FILE= ' SEEFILE .LIS', ACCESS= ' SEQUENTIAL '

,

FORMATTED ' , STATUS= ' OLD '

)

I FMT=1004, END=1005) ANAME

IF OPTION # 2 IS CHOSEN, CALL SUBROUTINE TO COMPARE THE

ENERGY ABSORBED/CYCLE

1102 CALL COMPARE (IDX, IDY)

GOTO 1104

203
o

o

o

o IF OPTION # 3 IS CHOSEN, CALL SUBROUTINE TO COMPARE THE

TOTAL ENERGY ABSORBED

C

C

C

C

C

C

C

C

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

1101 CALL COMTOTAL(IDX,IDY)

GOTO 1104

IF OPTION # 5 IS CHOSEN, CALL SUBROUTINE TO FOR LOADDISPLACEMENT LINE PLOT

1109 CALL LINEPLOT(IDX,IDY)

GOTO 1104

*******************************************

IF OPTION # 1 IS CHOSEN, BEGIN ROUTINE

A) TO PLOT THE LOAD-DISPLACEMENT CYCLES

B) TO PLOT THE INDIVIDUAL OR CUMULATIVE ENERGY PLOT

C) TO SHOW THE ANIMATED COLUMN MOVEMENT

ALL ON THE SAME SCREEN

VARIABLE DEFINITIONS;

MAXX

MINX

MAXY

MINY

YLIST

ZLIST

XNAME . INP

XNOMBRE . OUT

DISPMT

ENERABS

TOTDISP

TOTENERGY

IDX, IDY

MAXIMUM X-COORDINATE (DISPLACEMENT) VALUE

AMONG ALL THE CYCLES IN A TEST

MINIMUM X-COORDINATE (DISPLACEMENT) VALUE

AMONG ALL THE CYCLES IN A TEST

MAXIMUM Y-COORDINATE (FORCE) VALUE

MINIMUM Y-COORDINATE (FORCE) VALUE

FILE WHICH CONTAINS THE LISTING OF FILES

(XNAME) IN WHICH THE PAIRS OF DATA POINTS ARE

STORED.

EQUIVALENT TP YLIST WITH '.LIS' EXTENSION

FILE WHICH CONTAINS THE PAIRS OF DATA POINTS

FOR ONE CYCLE TO BE PLOTTED. SEE DOCUMENTATION IN TURBO_LOOP FOR CONVERTING THE TEST

DATA FROM THE PDP 11/34 TO THE VAX 11/750.

FILE WHICH CONTAINS THE TITLE OF THE CYCLE

AND THE ENERGY ABSORBED FOR THAT CYCLE

INDEX TO LOCATE THE X-COORDINATE OF THE

POLYGON WHICH SHOWS THE CUMULATIVE ENERGY PLOT

IN SUBROUTINE ENERGY

INDEX TO LOCATE THE Y-COORDINATE OF THE

POLYGON WHICH SHOWS THE CUMULATIVE. ENERGY PLOT

IN SUBROUTINE ENERGY

MAXIMUM TOTAL DISPLACEMENT THAT THE STRUCTURE

TRAVELS

MAXIMUM TOTAL ENERGY THAT THE STRUCTURE

ABSORBED

VARIABLES USED IN A DO-LOOP WHICH RESULTS IN

204
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

BOLD TYPE PRINT ON THE GRAPHICS DEVICE.

BASICALLY, THE PIXELS ARE REDRAWN ONE PIXEL

UP OR DOWN OR "SMEARED" TO PRODUCE THIS

BOLD EFFECT

X(I) VECTOR WHICH CONTAINS THE X-COORDINATES OF THE

HYSTERESIS CURVE ( TYPICALLY DISPLACEMENT)

Y(I) VECTOR WHICH CONTAINS THE Y-COORDINATE OF THE

HYSTERESIS CURVE (TYPICALLY LOAD)

NCOUNT INDEX USED TO CHANGE THE PLOT COLORS

INFILE. INP SAME AS XNAME.INP

OUTFILE . INP SAME AS XNOMBRE . OUT

OVERTIT OVERALL TITLE OF THE PLOT

SUBROUTINES CALLED:

1) CYCLE

2 ) COLPLOT

3) ENERGY OR INDIVENE

********************************************************

DETERMINE THE MAXIMUM AND MINIMUM VALUES FOR THE TEST.

THESE VALUES WILL BE USED TO SCALE THE PLOTS

Initialize variables into which the max. and min. values

will be stored.

1002 MAXX =0.0

MINX =0.0

MAXY =0.0

MINY =0.0

TOTDISP =0.0

TOTENERGY =0.0

DISPMT = 0

ENERABS = 0

AREAMAX =0.0

C

CLOSE (10)

TYPE *

, ' ' TYPE *

,

' BEGIN LOAD-DISPLACEMENT PLOT

TYPE *, 'ENTER NAME OF LIST FILE (9 CHARACTERS)

READ (5,518) YLIST

518 FORMAT (A9)

ZLIST = YLIST//' .LIS'

C

C Open the file where all the test names have been stored

C

OPEN ( 1 , FILE=ZLIST , STATUS= ' OLD ' , ACCESS= ' SEQUENTIAL '

,

1 FORM= ' FORMATTED '

)

1130 CONTINUE

C

C LOOP ON THIS READ STATEMENT UNTIL ALL THE FILES HAVE

205
oooo

oooo

ooo

oooo

ooooo

oooo

ooo

ooooo

on BEEN READ

READ ( 1 , FMT=1 , END=1100 ) NAME

PUT EXTENSION ON THE FILENAME.

All files to be used have to have the extension ".INP"

or ".OUT"

XNAME=NAME// ' . INP

XNOMBRE = NAME// ' . OUT

OPEN FILE CONTAINING THE DATA POINTS

OPEN ( 4 , FILE=XNAME , ACCESS= ' SEQUENTIAL ' , FORM= ' FORMATTED '

,

1 STATUS= ' OLD '

)

REWIND 4

OPEN FILE CONTAINING THE RESULTS OF THE ENERGY

CALCULATION FROM TURBO_LOOP

OPEN ( 11, FILE=XNOMBRE,ACCESS=' SEQUENTIAL' , FORM= ' FORMATTED '

,

1 STATUS= ' OLD '

)

REWIND 11

TITLE HAS TO BE READ BECAUSE THE FILE IS SEQUENTIAL I.E.

ITEMS LOCATED BEFORE THE DESIRED ITEM HAVE TO BE READ

BEFORE THE DESIRED ITEM CAN BE READ

READ (11, 46) TITLE

6 FORMAT ( 4 0A2)

READ THE VALUE OF THE ENERGY ABSORBED PER CYCLE FROM THE

'.OUT' FILE

READ (11,50) I COUNT , AREA

50 FORMAT (8X, 110, 7X,F10. 5)

CLOSE (UNIT=11)

READ THE TITLE FROM THE FILE CONTAINING THE DATA POINTS

READ (4, 45) TITLE

45 FORMAT(40A2)

Open the test file and extract from it the max. and min.

values

READ (4,40) XMIN , XMAX , YMIN , YMAX

40 FORMAT(4(E12.5,3X)

)

CLOSE (UNIT=4)

DETERMINE THE MAX AND MIN VALUES OF X AND Y FROM ALL THE

TESTS TO BE INTEGRATED.

TOTDISP = TOTDISP + ABS(XMAX) + ABS(XMIN)

TOTENERGY = TOTENERGY + AREA

206
ooo

oooooooo

IF(XMAX.GT.MAXX) MAXX = XMAX

IF(XMIN.LT.MINX) MINX = XMIN

IF(YMAX.GT.MAXY) MAXY = YMAX

IF(YMIN.LT.MINY) MINY = YMIN

IF(AREA.GT.AREAMAX) AREAMAX = AREA

GO TO 1130

1100 CONTINUE

REWIND 1

NCOUNT=0

INITIALIZE THE GRAPHICS DEVICE

CALL RTSET( 1,180)

CALL RTINIT (

' GDAO :\ 5 ) CALL ENTGRA

LOAD THE COLOR MAP

CALL LUTS (0,255,200,255)

CALL LUTS U/ 255, 150, 255)

CALL LUT8(2, 255, 0,255)

CALL LUTS (3, 188, 150,234)

CALL LUTS (4, 0,0, 190)

CALL LUTS (5,75,75,255)

CALL LUTS (6, 0,255, 255)

CALL LUT8(7,175,255,255)

CALL LUTS (8, 0,200, 200)

CALL LUTS (9, 0,175,0)

CALL LUT8(10,130,230,130)

CALL LUTS (11,0,255,0)

CALL LUT8(12,165,255,165)

CALL LUTS (13,255,255,175)

CALL LUT8(14,255,255,100)

CALL LUT8(15,255,175,50)

CALL LUTS (16,255, 120,0)

CALL LUTS (17, 255, 0,0)

CALL LUTSES, 255, 130, 130)

CALL LUT8(19,255,175,175)

CALL LUTS (20,255,200,200)

CALL LUTS (21,200,200,200)

CALL LUT8(22,150,150,150)

CALL LUTS (23,75,75,75)

CALL LUTS (24, 30, 30, 30)

CALL LUTS (30,255,255,255)

CALL LUTS (31, 0, 0, 0)

CALL LUT8(32, 255, 246,0)

VERY LIGHT PURPLE

LIGHT PURPLE

RED PURPLE

PURPLE

BLUE PURPLE

BRIGHT BLUE

BRIGHT LIGHT BLUE

LIGHT BLUE

BLUE GREEN

OLIVE GREEN

LIGHT OLIVE GREEN

BRIGHT GREEN

LIGHT GREEN

LIGHT YELLOW

LIGHT YELLOW

YELLOW-ORANGE

ORANGE

RED

DUSKY PINK

LIGHT PINK

PALE PINK

LIGHT GRAY

GRAY

DARK GRAY

GRAY-BLACK

WHITE

BLACK

CHROMIUM YELLOW

ENTER THE OVERALL TEST TITLE

TYPE *

, ' ' TYPE ENTER TEST TITLE (15 CHARACTERS)'

207
ooo

oo

on

ooo

oooo

ooo

READ (5,461) OVERTIT

461 FORMAT (15A2)

TYPE *

, ' • TYPE *, 'PROCESSING MODE'

TYPE *

,

'

= AUTO

TYPE *

,

'

0

= MANUAL

READ (5,5001) NAUTO

5001 FORMAT(I2)

FLOOD THE BACKGROUND

CALL VAL8(31) ! BLACK

CALL FLOOD

PLACE THE OVERALL TITLE IN THE UPPER LEFT CORNER OF THE*

SCREEN

CALL VAL8(32)

CALL TEXTN(90,90,0,0)

CALL MOVABS(-580,450)

DO 470 1=1,16

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXT1( 15, OVERTIT)

0 CONTINUE

ASK USER FOR TYPE OF ENERGY PLOT

TYPE * TYPE * TYPE * TYPE * READ *

I I

' CUMULATIVE ENERGY OR INDIVIDUAL ENERGY'

' 1 = CUMULATIVE ENERGY PLOT'

' 2 = INDIVIDUAL ENERGY PLOT'

ANW

open(l, f ile=ZLIST, status= ' old ' , access= ' sequential '

,

1 form= ' formatted '

)

500 CONTINUE

read(l, fmt=l,end=1000) filename

1 format (a20)

type *, 'working on file ', filename

PUT EXTENSION ON FILENAME

inf ile=filename// ' . inp

outfile=f ilename// ' . out

C

C

C OPEN 'FILENAME. INP' TO READ THE DATA POINTS NECESSARY TO

C PLOT THE HYSTERESIS LOOPS

C

OPEN (UNIT=2 , FILE=infile , ACCESS= ' SEQUENTIAL ' , FORM= ' FORMATTED ' , 1 STATUS= ' OLD '

)

REWIND 2

208
o

o

o

c

C OPEN 'FILENAME. OUT' TO OBTAIN THE ENERGY CALCULATED BY

C PROGRAM 'TURBO_LOOP'

C

OPEN (UNIT=3 , FILE=OUTFILE , ACCESS= ' SEQUENTIAL ' , FORM= ' FORMATTED '

,

1 STATUS= ' OLD '

)

REWIND 3

C

READ (2, 2) TITLE

2 FORMAT ( 4 0A2)

READ (3, 60) TITLE

60 FORMAT(40A2)

READ (3, 55) ICOUNT, AREA

55 FORMAT (8X, 110, 7X,F10. 5)

C

READ (2,3) XMIN , XMAX , YMIN , YMAX , NPTS

3 FORMAT(4(E12.5,3X) ,15)

READ DATA POINTS AND STORE IN X(I) AND Y(I) VECTORS

DO 100 1=1, NPTS

READ(2,4) X(I) ,Y(I)

100 CONTINUE

4 FORMAT (2 (E12.5,3X)

)

C

CLOSE (UNIT=2)

C

CLOSE (3)

C

C COLPLOT PLOTS THE ANIMATED MOVEMENT OF THE COLUMN IN THE UPPER

C LEFT QUADRANT OF THE SCREEN AS DATA POINTS ON THE HYSTERESIS

C CURVE ARE PLOTTED IN THE LOWER LEFT QUADRANT OF THE SCREEN

C

CALL COLPLOT ( NPTS , X , Y , IDX , IDY , NCOUNT , MAXX , MAXY

,

1 MINX,MINY, XMAX, XMIN)

C

C CYCLE REPLOTS THE HYSTERESIS CURVE SHOWN IN COLPLOT

C EXCEPT THIS ROUTINE FILLS THE AREA WITHIN THE CURVE WITH

C A COLOR DETERMINED BY 'NCOUNT'

C

CALL CYCLE (NPTS , NCOUNT , IDX , IDY , TITLE , MAXX , MAXY , MINX

,

1 MINY,X,Y)

C

C USER HAS THE OPTION TO CHOOSE EITHER 'ENERGY' OR

C 'INDIVENE' SUBROUTINE

C

C ENERGY PLOTS THE TOTAL ENERGY ABSORBED BY THE STRUCTURE

C IN THE UPPER RIGHT QUADRANT OF THE SCREEN

C

IF(ANW.EQ. 1) CALL ENERGY (XMAX, XMIN, NCOUNT, TOTDISP,

1 TOTENERGY , AREA , DI S PMT , ENERABS , I DX , I DY

)

C

C INDIVENE PLOTS THE INDIVIDUAL CYCLE ENERGY BAR GRAPH

C HISTOGRAM IN THE UPPER RIGHT CORNER OF THE SCREEN

C

209
o

o

o

o

o

o

IF ( ANW . EQ . 2 ) CALL INDIVENE (AREA , NCOUNT , XMAX , XMIN

,

1 AREAMAX,TOTDISP,IDX,IDY)

C

NCOUNT=NCOUNT+

IF (NAUTO .EQ. 1) GOTO 500

TYPE *

, ' ' TYPE *, 'ANOTHER CYCLE ? 1=YES,0=NO'

READ *,ANS

IF (ANS.EQ.O) GOTO 1000

GOTO 500

C

1000 CONTINUE

CLOSE (1)

GOTO 1104

1003 TYPE *,'************* BYE ************** CALL QUIT

CALL EXIT • STOP

END

210
Q *********************************************************

c

C SUBROUTINE CYCLE

C

C PURPOSE: TO PLOT THE HYSTERESIS CURVES OBTAINED FOR A

C STRUCTURE FROM A CYCLIC TEST

C

C CALLED FROM: MAIN

C

C USAGE : CALL CYCLE (NPTS , NCOUNT , IDX , IDY , TITLE , MAXX , MAXY

,

C MINX, MINY,X,Y)

C

C PARAMETERS

C

C NPTS NUMBER OF POINTS USED TO PLOT THE HYSTERESIS

c CURVE

c NCOUNT' INDEX USED TO CHANGE THE COLOR OF THE PLOT

c IDX SEE MAIN PROGRAM

c IDY II II II c TITLE TITLE OF THE PARTICULAR CYCLE TO BE PLOTTED

c E.G . 2 DEL, 2

c MAXX SEE MAIN PROGRAM

c MAXY II II II c MINX II II II c

c

MINY II II II

c

c OTHER SUBROUTINES CALLED: NONE (OTHER THAN THE RASTER

c

c

TECH ' ONELIB' ROUTINES: SEE PROGRAM 'MAIN' ) c

c

c

SUBROUTINE SPECIFIC PARAMETERS:

c

c XSIZE LENGTH OF X-AXIS

c YSIZE LENGTH OF Y-AXIS

c OFFSETX USED TO OFFSET THE X-COORDINATE OF THE AXES

C ORIGIN BY A SPECIFIED AMOUNT

C OFFSETY USED TO OFFSET THE Y-COORDINATE OF THE AXES

C ORIGIN BY A SPECIFIED AMOUNT

C XRANGE MAX DISTANCE IN THE FORWARD DIRECTION OR THE

C MAX DISTANCE IN THE REVERSE DIRECTION THAT THE

C COLUMN WAS DISPLACED. USED TO SCALE THE X-AXIS

C YRANGE MAX LATERAL LOAD REQUIRED TO DISPLACE THE

C STRUCTURE IN THE FORWARD DIRECTION OR THE MAX

C LATERAL LOAD TO DISPLACE THE STRUCTURE IN THE

C REVERSE DIRECTION. USED TO SCALE THE Y-AXIS

C XFACTOR UNIT: PIXELS/UNIT LENGTH. USED TO CONVERT

C UNITS OF LENGTH TO NUMBER OF PIXELS

C YFACTOR UNIT: PIXELS/UNIT FORCE. USED TO CONVERT UNITS

C OF FORCE TO NUMBER OF PIXELS

C LEY DEFINES THE Y-COORDINATE OF THE UPPER LEFT

C CORNER OF THE RECTANGLES USED IN THE LEGEND

C REY DEFINES THE Y-COORDINATE OF THE LOWER RIGHT

C CORNER OF THE RECTANGLES USED IN THE LEGEND

211
ooo

ooo

oooooo

oooo

oooo

c

c

OFFXl X-COORDINATE

X-AXIS

OF THE : c

c

OFFX2 X-COORDINATE

X-AXIS

OF THE : c

c

OFFYl Y-COORDINATE

Y-AXIS

OF THE : c

c

OFFY2 Y-COORDINATE

Y-AXIS

OF THE '

c

c

TITLE NAME OF THE ' CYCLES

CYCLE IN

c

c

c ************************************************'***'****

c

c

c

c

c

c

SUBROUTINE CYCLE (NPTS , NCOUNT , IDX , IDY , TITLE , MAXX

,

1 MAXY,MINX,MINY,X, Y)

DIMENSION X(400) , Y(400)

INTEGER* 2 NCOUNT , LEY , REY , OFFSETY , OFFSETX , OFFXl

,

1 OFFX2,OFFYl,OFFY2,XSIZE,YSIZE

INTEGER*2 IDX(16) ,IDY(16) ,NVERT(1) , VERTS ( 2 , 4 00 )

,

1 TITLE (40)

REAL MAXX, MINX, MAXY,MINY

SET PROGRAM VARIABLES

XSIZE = 640

YSIZE = 512

SET OFFSET VALUES SO THAT THE PLOT IS DRAWN IN

THE THIRD QUADRANT

OFFSETX = -300

OFFSETY = -250

NCOUNT = ZERO FOR THE FIRST CYCLE PLOT. THE RANGE

ONLY NEEDS TO BE SET ONCE AND THEREFORE THE PROGRAM

WILL SKIP THE NEXT STATEMENTS FOR CYCLES GREATER THAN

ONE

IF (NCOUNT. GT.O) GOTO 3010

DETERMINE THE XRANGE AND YRANGE

XRANGE=MAX(ABS (MAXX) ,ABS (MINX)

)

YRANGE=MAX(ABS (MAXY) , ABS (MINY)

)

DETERMINE THE XFACTOR AND YFACTOR

XFACTOR=XSIZE/ (2 . *XRANGE)

212
oooo

ooo

ooo

ooo

ooo

ooo

ooo

oooo

YFACTOR=YSIZE/ (2 . *YRANGE)

C

C

C DRAW THE CURVE

C

C

C The outer DO loop is used so that when J=l, the polygon

C is filled and when J=2, the polygon is outlined

C

C

3010 DO 210 J=l,2

CONVERT THE DATA POINTS INTO INTEGER* 2 FORMAT AND ALSO

TO NUMBER OF PIXELS

DO 200 I=1,NPTS

VERTS (1,1) =IFIX (X ( I

) *XFACTOR)

VERTS (2,1) =IFIX ( Y ( I

) * YFACTOR)

200 CONTINUE

DRAW AXES

CALL VAL8(30) I WHITE

DEFINE THE ENDS OF THE X & Y AXES

OFFXl = ( -XSIZE/2 + OFFSETX)

OFFYl = ( -YSIZE/2 + OFFSETY)

OFFX2 = ( XSIZE/2 + OFFSETX)

OFFY2 = (YSIZE/2 + OFFSETY)

MOVE CURRENT POINT TO THE LEFT END OF THE X-AXIS

CALL MOVABS (OFFXl, OFFSETY)

DRAW LINE TO THE RIGHT END OF THE X-AXIS

CALL DRWABS(OFFX2, OFFSETY)

MOVE CURRENT POINT TO THE BOTTOM OF THE Y-AXIS

CALL MOVABS ( OFFSETX , OFFYl

)

DRAW A LINE TO THE TOP END OF THE Y-AXIS

CALL DRWABS (OFFSETX, OFFY2)

DETERMINE WHETHER TO FILL THE POLYGON OR NOT USING THE

DO LOOP INDEX

IF(J.EQ.l) CALL PRMFIL(l)

IF(J.EQ.2) CALL PRMFIL(O)

C

C DETERMINE THE CURRENT PIXEL COLOR USING THE DO LOOP

C INDEX, NCOUNT

213
non

o

ooo

oooo

ooo

ooo

ooo

ooo

ooooo

ooo

IF(J.EQ.l) CALL VAL8 (NCOUNT) ! VARIED COLORS

IF(J.EQ.2) CALL VAL8(30) ! WHITE

CALL MOVABS ( OFFSETX , OFFSETY

)

DRAW POLYGON

NVERT(1)=NPTS

CALL P0LYGN(1,NVERT, VERTS)

DRAW LEGEND TO ASSOCIATE THE COLOR OF THE LOOPS WITH A

CYCLE NUMBER. THE LEGEND IS A SERIES OF RECTANGLES

FILLED WITH THE APPROPRIATE COLORS

LEY = -50 - 20*NCOUNT

REY = LEY - 25

MOVE TO THE UPPER LEFT CORNER OF THE RECTANGLE

CALL MOVABS (275, LEY)

CALL RECTAN(300,REY)

PLACE THE TEXT 20 PIXELS TO THE RIGHT OF THE RECTANGLE

CALL MOVABS (320, REY)

CALL RASTER TECH ROUTINE TO SET SIZE OF TEXT

CALL TEXTN(30,30,0,0)

SET CURRENT PIXEL VALUE TO WHITE

CALL VAL8(30)

IN BOLD TYPE, PLACE THE TITLE OF THE CYCLE NEXT TO THE

COLORED RECTANGLE

DO 400 I = 1,4

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXT1( 40, TITLE)

400 CONTINUE

EMPTY CONTENTS OF BUFFER ONTO THE SCREEN

CALL EMPTYB

210 CONTINUE

RETURN

END

214
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

•k'k-k-k-k'k'kifkic'kicifk-k-kifk-k-kic-k-k-k-k-k-k-k-k-k-k-kifk-Jck-kii’k-k-k-k-k'k-k-k-k-k-k-k-k^-k-k-k-k SUBROUTINE ENERGY

PURPOSE: PLOTS THE CUMULATIVE ENERGY ABSORBED BY THE

STRUCTURE SUBJECTED TO CYCLIC LOADING

CALLED FROM: MAIN PROGRAM

USAGE

CALL ENERGY

(

XMAX , XMIN , NCOUNT , TOTDISP , TOTENERGY , AREA

,

DI S PMT , ENERABS , I DX , I DY

)

PARAMETERS

XMAX

XMIN

MAXIMUM VALUE OF THE X-COORDINATE (TYPICALLY

DISPLACEMENT)

MINIMUM VALUE OF THE Y-COORDINATE (TYPICALLY

FORCE)

c NCOUNT SEE MAIN PROGRAM

c TOTDISP II II It c TOTENERGY II II II c AREA ENERGY ABSORBED : c DISPMT SEE MAIN PROGRAM

c ENERABS II II II c IDX II It II c IDY II II II

OTHER SUBROUTINES CALLED: NONE ( OTHER THAN THAN THE

RASTER TECH 'ONELIB' ROUTINES. SEE PROGRAM 'MAIN'.)

SUBROUTINE SPECIFIC PARAMETERS:

XTIC DISPLACEMENT EQUAL TO 100 PIXELS IN UNITS OF

LENGTH

YTIC LOAD EQUAL TO 100 PIXELS IN UNITS OF FORCE

XDIV EQUIVALENT TO XTIC IN CHARACTER FORMAT

YDIV EQUIVALENT TO YTIC IN CHARACTER FORMAT

INTXDIV EQUIVALENT TO XTIC IN INTEGER*2 FORMAT

INTYDIV EQUIVALENT TO YTIC IN INTEGER*2 FORMAT

XSCALE UNITS: PIXELS/UNIT LENGTH. USED TO CONVERT

LENGTH TO NUMBER OF PIXELS

YSCALE UNITS: PIXELS/UNIT FORCE. USED TO CONVERT

FORCE TO NUMBER OF PIXELS

TOTX TOTAL DISTANCE THAT A STRUCTURE WAS

DISPLACED IN A GIVEN CYCLE

XO DEFINES THE X-COORDINATE OF THE LOWER LEFT

CORNER OF THE POLYGON USED IN THE HISTOGRAM

YO DEFINES THE Y-COORDINATE OF THE LOWER LEFT

CORNER OF THE POLYGON USED IN THE HISTOGRAM

XI DEFINES THE X-COORDINATE OF THE UPPER RIGHT

215
ooo

ooo

ooo

ooo

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

CORNER OF THE POLYGON. EQUAL TO THE TOTX

Y1 DEFINES THE Y-COORDINATE OF THE UPPER RIGHT

CORNER OF THE POLYGON. EQUAL TO THE TOTAL

ENERGY ABSORBED IN A GIVEN CYCLE

X2 SUMMATION OF THE TOTAL DISPLACEMENT OF THE

STRUCTURE IN A GIVEN CYCLE FOR ALL THE CYCLES

Y2 SUMMATION OF THE ENERGY ABSORBED PER CYCLE FOR

ALL THE CYCLES

SUBROUTINE ENERGY ( XMAX , XMIN , NCOUNT , TOTDISP

,

1 TOTENERGY , AREA , DISPMT , ENERABS , IDX , IDY

)

INTEGER*2 NCOUNT , XO , YO , DISPMT , ENERABS , JX

,

1 X1,Y1,X2,Y2, JL

INTEGER*2 NVERT(l) ,VERT(2,5) ,IDX(16) ,IDY(16)

CHARACTER* 2 XDIV ( 3 )

, YDIV ( 3

)

INTEGER*2 INTXDIV ( 3 ), INTYDIV ( 3

)

EQUIVALENCE (XDIV, INTXDIV)

EQUIVALENCE (YDIV, INTYDIV)

IF NCOUNT IS GREATER THAN ZERO, THE TITLES AND THE AXES

WILL ALREADY HAVE BEEN DRAWN AND DO NOT NEED TO BE

REDRAWN

IF (NCOUNT. GT.O) GOTO 300

DRAW THE AXES WITH THE ORIGIN AT (50,50)

MOVE TO ORIGIN

CALL MOVABS(50,50)

DRAW THE X-AXIS, 550 PIXELS IN LENGTH

CALL DRWABS(600,50)

MOVE TO THE ORIGIN

CALL MOVABS(50,50)

DRAW THE Y-AXIS, 450 PIXELS IN LENGTH

CALL DRWABS(50,500)

INSERT TITLE FOR THE HISTOGRAM

CALL TEXTN(40,40,0,0)

CALL MOVABS (200,-30)

216
ooo

ooo

ooo USE DO LOOP FOR BOLD TEXT

DO 420 1=1,9

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXT1(23, 'TOTAL ENERGY ABSORPTION')

420 CONTINUE

LABEL X-AXIS

CALL MOVABS (350,5)

CALL TEXTN(35,35,0,0)

DO 450 1=1,9

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXT1(14, 'DISP. (INCHES) ')

450 CONTINUE

LABEL Y-AXIS

CALL MOVABS (0,150)

CALL TEXTC(30,90)

DO 460 1=1,9

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXT1(15, 'ENERGY (KIP-IN) ')

460 CONTINUE

C

C

C FIND THE SCALE OF THE AXES: X-AXIS = 500 PIX,

C Y-AXIS = 400 PIX

C

XSCALE = 500.0/TOTDISP

YSCALE = 400. O/TOTENERGY

C

C DRAW THE TIC MARKS ON THE AXES

C

C X-AXIS, DIVIDED INTO 5 SEGMENTS WITH EACH SEGMENT EQUAL

C TO 100 PIXELS

C

CALL TEXTN(17,17,0,0)

DO 350 L=l,5

JX = (50 + L*100)

CALL MOVABS (JX, 46)

CALL DRWABS(JX,54)

XL = L

C

C ASSIGN SCALE VALUES TO THE AXIS

C

C TRANSLATE DATA, XTIC, FROM INTERNAL STORAGE TO CHARACTER

C FORMAT USING "ENCODE" STATEMENT

C

C USE EQUIVALENCE STATEMENT TO PUT THAT DATA (WHICH IS NOW

C IN CHARACTER FORMAT) TO INTEGER* 2 FORMAT

C

XTIC = (1. 0/XSCALE*100. 0) *XL

217
ooooooooooo

ooo

ooo

ooooo

ooo

ENCODE (6,351, XDIV) XTIC

351 FORMAT (F6. 2)

JL = 35 + L*100

CALL MOVABS (JL, 35)

USE DO LOOP TO OBTAIN BOLD NUMBERS

DO 353 N=l,4

CALL MOVREL(IDX(N) ,IDY(N)

)

CALL TEXT1(6,INTXDIV)

353 CONTINUE

350 CONTINUE

Y-AXIS, DIVIDED INTO 4 SEGMENTS WITH EACH SEGMENT EQUAL . TO 100 PIXELS

CALL TEXTC(15,90)

DO 360 L=l,4

JX = (50 + L*100)

CALL MOVABS (46, JX)

CALL DRWABS (54, JX)

ASSIGN SCALE VALUES TO THE AXIS

XL = L

YTIC = (1.0/YSCALE*100.0) *XL

ENCODE (6,352, YDIV) YTIC

352 FORMAT (F6. 2)

JL = 35 + L*100

CALL MOVABS (40, JL)

USE DO LOOP TO OBTAIN BOLD NUMBERS

DO 354 N=l,4

CALL MOVREL(IDX(N) ,IDY(N)

)

CALL TEXT1(6,INTYDIV)

354 CONTINUE

360 CONTINUE

THE PLOT IS PRESENTED AS A SIDEWAYS BAR GRAPH WITH THE

WIDTH OF EACH BAR EQUAL TO THE ENERGY ABSORBED FOR A

GIVEN CYCLE

SET NO. OF VERTICES IN POLYGON

NVERT(l) = 4

DEFINE THE POSITION OF THE VERTICES

300 XO = DISPMT + 50

YO = ENERABS + 50

CALL MOVABS (X0,Y0)

218
oooo

on

non

ono

non

non

ooo

non

on DEFINE LOWER LEFT CORITER OF THE POLYGON

VERT (1,1) = 0

VERT (2,1) = 0

DEFINE THE LOWER RIGHT CORNER OF THE POLYGON

VERT(1,2) = 600-X0

VERT (2,2) = 0

SUM TOTAL DISPLACEMENT AND ENERGY

TOTX = ABS(XMAX) + ABS (XMIN)

X2 = DISPMT

Y2 = ENERABS

DISPMT = DISPMT + IFIX (TOTX*XSCALE)

ENERABS =IFIX(AREA) *YSCALE + ENERABS

XI = DISPMT - X2

Y1 = ENERABS - Y2

DEFINE THE UPPER LEFT CORNER OF THE POLYGON . VERT (1,4) = XI

VERT (2, 4) = Y1

DEFINE THE UPPER RIGHT CORNER OF THE POLYGON

VERT (1,3) = 600 - XO

VERT(2,3) = Y1

DRAW FILLED POLYGON

CALL VAL8(NCOUNT)

CALL PRMFIL(l)

CALL P0LYGNU/NVERT,VERT)

OUTLINE THE POLYGON IN WHITE

CALL VAL8(30)

CALL PRMFIL(O)

CALL POLYGN(1,NVERT, VERT)

CALL EMPTYB

RETURN

END

219
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

•k-kifk-k-k^kic-k'kic-k-k-k-k-k-k-k'k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k'k-k-k-k-k-ifk-k-kTfk-k-k-k-k-k-k-k-k-k-fck SUBROUTINE INDIVENE

PURPOSE: TO PLOT THE ENERGY ABSORBED IN EACH CYCLE BY

A STRUCTURE AS A BAR CHART TYPE HISTOGRAM.

THE WIDTH OF EACH BAR REPRESENTS THE DISPLACEMENT

DUCTILITY AT THAT CYCLE WHILE THE HEIGHT

REPRESENTS THE ENERGY DISSIPATED DURING THAT

CYCLE ( THE AREA INSIDE THE HYSTERESIS CURVE)

CALLED FROM: PROGRAM MAIN

USAGE : CALL INDIVENE (AREA , NCOUNT , XMAX , XMIN , AREAMAX

,

TOTDISP,IDX,IDY)

PARAMETERS

AREA

NCOUNT

XMAX

XMIN

AREAMAX

TOTDISP

IDX

IDY

ENERGY ABSORBED BY STRUCTURE IN A PARTICULAR

CYCLE

INDEX USED CHANGE THE COLOR OF THE PLOT

MAXIMUM X-COORDINATE

MINIMUM Y-COORDINATE

TOTAL ENERGY ABSORBED BY THE STRUCTURE, USED TO

SET THE ON THE Y-AXIS

SEE MAIN PROGRAM

II II II

II II II

OTHER SUBROUTINES CALLED: NONE (OTHER THAN THE RASTER

TECH 'ONELIB' SUBROUTINES. SEE PROGRAM MAIN)

SUBROUTINE SPECIFIC PARAMETERS:

SCALEX

SCALEY

TICY

DIVY

INTDIVY

DELY2

XTOT

XO

XDISP

YENER

UNITS: PIXESL/UNIT LENGTH. CONVERTS UNITS

OF LENGTH TO NUMBER OF PIXELS

UNITS: PIXELS/UNIT ENERGY. CONVERTS UNITS OF

ENERGY TO NUMBER OF PIXELS

AMOUNT OF ENERGY EQUAL TO 100 PIXELS IN UNITS

OF ENERGY

EQUIVALENT TO TICY IN CHARACTER FORMAT

EQUIVALENT TO TICY IN INTEGER*2 FORMAT

LENGTH EQUIVALENT TO 2 TIMES DELTA Y IN NUMBER

OF PIXELS. USED TO SHOW THE SCALE FOR THE BAR

WIDTHS

TOTAL DISTANCE THAT A STRUCTURE WAS DISPLACED

IS A GIVEN CYCLE

VARIABLE USED IN LOCATING THE UPPER RIGHT

CORNER OF THE BAR IN THE HISTOGRAM

SUMMATION OF THE TOTAL DISPLACEMENT OF A

STRUCTURE IN A GIVEN CYCLE OVER ALL THE CYCLES

ENERGY ABSORBED IN A GIVEN CYCLE IN NUMBER OF

PIXELS

220
ooo

oooo

oooo

ooo

ooooooo

ooo

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

k-k-kifk-kifk-k-k-k-k-k-k-kifk-k-k-k-k-k-k-k-k-k-k-kifk-k-k-k-k-k-k-k-k-kifk-kifkifkii-k-k-k-k-k-k-k-k-k

SUBROUTINE INDIVENE (AREA , NCOUNT , XMAX , XMIN , AREAMAX

,

1 TOTDISP,IDX,IDY)

INTEGER* 2 NCOUNT , JX , XO , XTOT , YENER, XDISP , JL, DELY2 , lY

INTEGER*2 IDX(16) ,IDY(16) ,NVERT(1) ,VERT(2,5)

CHARACTER* 2 DIVY(3)

INTEGER* 2 INTDIVY(3)

EQUIVALENCE ( DIVY , INTDIVY

)

IF NCOUNT = 0, THEN THE SUBROUTINE PLOTS THE AXES AND

TITLE. FOR NCOUNT GREATER THAN 0, THIS REDRAWING IS

UNNECESSARY AND THE PROGRAM SKIPS THIS PART OF THE ROUTINE

IF (NCOUNT. GT.O) GOTO 600

SET THE COLOR VALUE FOR THE AXES

CALL VAL8(30) i WHITE

BEGIN DRAWING AXES IN THE UPPER CORNER OF THE SCREEN

WITH THE ORIGIN AT (50,50)

X-AXIS, LENGTH = 550 PIXELS

CALL MOVABS (50,50)

CALL DRWABS(600,50)

Y-AXIS, LENGTH = 450 PIXELS

CALL MOVABS (50, 50)

CALL DRWABS (50,500)

FIND THE SCALE FOR THE X & Y AXES. USE ONLY A LENGTH OF

X-AXIS = 500 PIXELS, Y-AXIS = 400 PIXELS

SCALEX = 500. O/TOTDISP

SCALEY = 400.0/AREAMAX

SET THE TEXT AT 90 DEG. FOR VERTICAL TEXT ALONG THE

Y-AXIS

CALL TEXTC(25,90)

DRAW TICK MARKS ON Y-AXIS

221
oooo

ooo

non

oooo

DO 620 1=1,4

JX = 50 + 1*100

CALL MOVABS (46, JX)

CALL DRWABS(54, JX)

XL = I

TICY = (1.0/SCALEY*100.0) *XL

CONVERT TICY TO CHARACTER FORMAT AND THEN TO INTEGER*2

FORMAT USING THE ENCODE STATEMENT

ENCODE (6, 621, DIVY) TICY

621 FORMAT (F6.0)

MOVE TO LOCATION TO PLACE THE VALUE OF THE TICK MARKS

JL = 25 + 1*100

CALL MOVABS (40, JL)

USE DO LOOP TO OBTAIN BOLD NUMBERS

DO 622 N=l,4

CALL MOVREL(IDX(N) ,IDY(N)

)

CALL TEXT1(6,INTDIVY)

622 CONTINUE

620 CONTINUE

PLACE THE TITLE, 'SCALE', IN THE UPPER RIGHT CORNER OF

THE SCREEN

CALL VAL8(30) ! WHITE

CALL MOVABS (380, 450)

CALL TEXTN(30,30,0,0)

DO 610 I = 1,4

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXTl ( 5

,

' SCALE '

)

610 CONTINUE

C

C PLOT A SCALE FOR DUCTILITY FACTOR USING 2 TIMES DELTA Y

C

C FIND THE LENGTH OF 2 DELTA Y. DELTA Y IS DEFINED AS THE

C AVERAGE OF THE DISPLACEMENT TO YIELD LOAD IN THE FIRST

C CYCLE IN THE FORWARD DIRECTION PLUS THE DISPLACEMENT IN THE

C REVERSE DIRECTION DIVIDED BY 0.75.

C

C THE FACTOR OF 2 IS APPLIED BECAUSE THE STRUCTURE

C WAS DISPLACED 2 DELTA Y IN ONE DIRECTION AND 2 DELTA Y

C IN THE REVERSE DIRECTION RESULTING IN A TOTAL DISPLACEMENT

C OF 4 TIMES DELTA Y. THEREFORE, DEL2 IS NOT ACTUALLY 2 TIMES

C DELTA Y BUT IS HOWEVER, REPRESENTATIVE OF THE TOTAL

C DISPLACEMENT AT 2 TIMES DELTA Y.

C

C THE CONSTANT 375 IS ADDED TO MOVE THE LOCATION

C OF THE SCALE TO 375 PIXELS RIGHT OF THE SCREEN ORIGIN

C

DELY2 = IFIX( (ABS (XMAX) +ABS (XMIN) *4 . 0/3 . 0) *2 . 0*

222
ooo

ooo

ooo

oooo

1 SCALEX)+375

C

C DRAW THE SCALE WHICH IS A LINE REPRESENTING THE WIDTH OF

C THE BAR FOR 2 DELTA Y

C

CALL MOVABS(375,415)

CALL DRWABS(375,425)

CALL MOVABS(DELY2,415)

CALL DRWABS(DELY2,425)

DO 660 1=1,4

lY = 418 + I

CALL MOVABS (375,IY)

CALL DRWABS(DELY2,IY)

660 CONTINUE

LABEL SCALE REPRESENTING DISPLACEMENT DUCTILITY. PLACE THE

LABEL 25 PIXELS TO RIGHT OF THE SCALE

DELY2 = DELY2 +25

CALL MOVABS (DELY2, 415)

CALL TEXTN(25,25,0,0)

DO 670 1=1,4

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXTl ( 9

,

' 2 DELTA Y '

)

0 CONTINUE

INSERT TITLE OF THE HISTOGRAM

CALL TEXTN(40,40,0,0)

CALL MOVABS (175,-30)

DO 630 1=1,9

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXTl (2 3, 'ENERGY ABSORPTION/CYCLE '

)

630 CONTINUE

LABEL X-AXIS

CALL MOVABS (125,5)

CALL TEXTN(35,35,0,0)

DO 640 1=1,9

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXTl (3 3, 'WIDTH OF BARS = TOTAL CYCLE DISP.')

640 CONTINUE

LABEL Y-AXIS

CALL MOVABS (0,150)

CALL TEXTC(30,90)

DO 650 1=1,9

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXTl (15, 'ENERGY (KIP-IN) ')

650 CONTINUE

C

C SET NO. OF VERTICES IN POLYGON USED TO REPRESENT A BAR

C ON THE HISTOGRAM

223
ooo

oooo

ooo

ooooo

oooooo

oono

ooooo

oooo

c

NVERT(l) = 4

c

C DEFINE VERTICES

C

C INITIALIZE VALUES

C

XDISP = 0

XTOT = 0

THIS PART OF THE SUBROUTINE PLOTS THE INDIVIDUAL CYCLE

ENERGY AS A BAR ON THE HISTOGRAM

600 XO = XDISP + 50

MOVE TO THE LOWER RIGHT CORNER OF THE LAST BAR DRAWN OR

IN THE CASE OF THE FIRST BAR, MOVE TO THE ORIGIN OF THE

AXES

CALL MOVABS(X0,50)

FIND THE TOTAL DISPLACEMENT OF THE COLUMN FOR THE CYCLE,

XTOT

XTOT = IFIX( (ABS(XMAX) + ABS (XMIN) )

1 SCALEX)

XDISP = XDISP + XTOT

NOTE: THE POINTS DEFINED BY VERT(I,J) ARE RELATIVE TO THE

CURRENT POINT AS DEFINED BY THE MOVABS CALL

DEFINE THE LOWER LEFT CORNER OF THE BAR

VERT (1,1) = 0

VERT (2,1) = 0

DEFINE THE LOWER RIGHT CORNER OF THE BAR BY MOVING OVER

TO THE RIGHT BY AN AMOUNT EQUAL TO THE DISPLACEMENT TRANSVERSED

IN A GIVEN CYCLE

VERT(1,2) = XTOT

VERT (2, 2) = 0

SCALE THE HEIGHT OF THE BAR

YENER = IFIX(AREA*SCALEY)

DEFINE THE UPPER RIGHT CORNER OF THE BAR BY MOVING UP AN

AMOUNT EQUAL TO THE ENERGY DISSIPATED IN A GIVEN CYCLE

VERT (1,3) = XTOT

VERT (2, 3) = YENER

DEFINE THE UPPER LEFT CORNER OF THE BAR

224
nooo

o

ooo

ooo

VERT (1,4) = 0

VERT (2,4) = YENER

DRAW BAR FILLED WITH COLOR VALUE

CALL VALS(NCOUNT)

CALL PRMFIL(l)

CALL POLYGN(l,NVERT,VERT)

OUTLINE THE BAR IN WHITE

CALL VAL8(30)

CALL PRMFIL(O)

CALL POLYGN ( 1 , NVERT , VERT

)

CALL EMPTYB

RETURN

END

NCOUNT

225
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

-k-k-k-kifk-k-kic-k-k-k-k-kifk-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-ifk-kifk-k'k-kifk-k-k-kic-kifk-k-k-k-k-k-k

SUBROUTINE COLPLOT

PURPOSE: TO ANIMATE THE COLUMN MOVEMENT AS THE THE

HYSTERESIS CURVE IS BEING PLOTTED

CALLED FROM: PROGRAM MAIN

USAGE : CALL COLPLOT (NPTS , X , Y , IDX , IDY , NCOUNT , MAXX , MAXY

,

MINX , MINY , XMAX , XMIN

)

PARAMETERS

NPTS NUMBER OF DATA POINTS IN A GIVEN CYCLE

X(I) X-COORDINATE OF THE DATA POINT TYPICALLY THE

DISPLACEMENT

Y(I) Y-COORDINATE OF THE DATA POINT

IDX SEE MAIN PROGRAM

IDY " " ” NCOUNT " ” " MAXX " " " MAXY " " " MINX ’• " " MINY " ” " XMAX MAXIMUM X VALUE FOR A PARTICULAR CYCLE

XMIN MINIMUM X VALUE FOR A PARTICULAR CYCLE

OTHER SUBROUTINES CALLED: NONE (OTHER THAN THE RASTER

TECH 'ONELIB' SUBROUTINE CALLS. SEE PROGRAM MAIN)

SUBROUTINE SPECIFIC PARAMETERS:

SCALE

COLX

OFFSETX

OFFSETY

XSIZE

YSIZE

XRANGE

YRANGE

XFACTOR

YFACTOR

IA,IB

UNITS: PIXELS/UNIT LENGTH. ARBITRARY VALUE

CHOSEN TO MAGNIFY THE ANIMATED COLUMN DISPLACEMENT

DISPLACEMENT OF COLUMN IN NUMBER OF PIXELS

USED TO RELOCATE THE X-COORDINATE OF THE

ORIGIN OF THE AXES FROM THE SCREEN ZERO

USED TO RELOCATE THE Y-COORDINATE OF THE

ORIGIN OF THE AXES FROM THE SCREEN ZERO

LENGTH OF X-AXIS IN PIXELS

LENGTH OF Y-AXIS IN PIXELS

MAXIMUM DISTANCE THAT THE STRUCTURE WAS

DISPLACED IN EITHER THE FORWARD OR REVERSE • DIRECTION FROM ALL THE CYCLES IN A TEST

MAXIMUM LOAD REQUIRED TO DISPLACE THE STRUCTURE

IN EITHER THE FORWARD OR REVERSE DIRECTION

FROM ALL THE CYCLES IN A TEST

UNITS: PIXELS/UNIT OF LENGTH. USED TO CONVERT

COLUMN DISPLACEMENT TO NUMBER OF PIXELS

UNITS: PIXEL/UNIT OF FORCE. USED TO CONVERT

THE LATERAL LOAD TO NUMBER OF PIXELS

VARIABLES USED TO DETERMINE THE LOCATION OF

226
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

ARROW

ENDARR

lEND

XO

XI

X2

Y1

Y2

OFFXl

OFFX2

OFFYl

OFFY2

XC * YC

XCl & YCl

XC2 & YC2

THE ARROW HEAD

LEFT END OF THE ARROW WHICH SHOWS THE

DIRECTION OF THE LATERAL LOAD. THIS POINT IS

LOCATED 70 PIXELS TO THE RIGHT OF THE COLUMN.

LOCATES WHICH END, LEFT OR RIGHT, OF THE

ARROW SHAFT THE ARROW HEAD SHOULD GO

LOCATES THE END OF THE ARROW HEAD

USED TO IDENTIFY THE DATA POINT PLOTTED PRIOR

TO THE CURRENT DATA POINT

X-COORDINATE OF THE DATA POINT PLOTTED PRIOR

TO THE CURRENT DATA POINT

X-COORDINATE OF THE CURRENT DATA POINT TO BE

PLOTTED

Y-COORDINATE OF THE DATA POINT PLOTTED PRIOR

TO THE CURRENT DATA POINT

Y-COORDINATE OF THE CURRENT DATA POINT

X-COORDINATE OF THE LEFT (NEGATIVE) END OF

THE X-AXIS

X-COORDINATE OF THE RIGHT (POSITIVE) END OF

THE X-AXIS

Y-COORDINATE OF THE BOTTOM (NEGATIVE) END OF THE

Y-AXIS

Y-COORDINATE OF THE TOP (POSITIVE) END OF THE

Y-AXIS

DEFINES A POINT ALONG THE DEFLECTED LENGTH OF

THE COLUMN IN REAL NUMBER FORMAT

DEFINES THE LAST POINT ALONG THE DEFLECTED

COLUMN LENGTH TO BE PLOTTED IN INTEGER*

FORMAT

DEFINES THE CURRENT POINT ALONG THE DEFLECTED

COLUMN LENGHT TO BE PLOTTED IN INTEGER*

FORMAT

********************-************************************

SUBROUTINE COLPLOT ( NPTS , X , Y , IDX , IDY , NCOUNT , MAXX

,

1 MAXY, MINX,MINY,XMAX,XMIN)

DIMENSION X(400)‘, Y(400) ,XC(20) ,YC(20)

INTEGER*2 COLX , NEWX , NEWY , OFFSETX , OFFSETY , XO , XI , Y1

,

1 X2 , Y2 , OFFXl , OFFX2 , OFFYl , OFFY2 , XSIZE , YSIZE , ARROW,

2 ENDARR, lEND

INTEGER*2 IDX (16) , IDY (16) , VERTS ( 2 , 400) ,NVERTS(1)

,

1 YCl, YC2,XC1,XC2,XC10,YC10

REAL MAXX, MINX, MINY, MAXY

CALL PRMFIL(O)

CALL VAL8 (30)

227
ooo

ooo

oooo

ooo

ooo

oooo

ooooo

oooo

oooo

C SET SCALE EQUAL TO 20 PIX/INCH SO THAT THE MOVEMENT OF

C THE COLUMN IS MAGNIFIED

C

IF(MAXX.GT.5) SCALE = 4.0

IF(MAXX.LE.5) SCALE = 20.0

SET PROGRAM VARIABLES

XSIZE = 640

YSIZE = 512

XC(1) = 0.0

YC(1) = 0.0

SET OFFSET VALUES SO THAT THE PLOT IS DRAWN IN

THE THIRD QUADRANT

OFFSETX = -300

OFFSETY = -250

IF NCOUNT > 0, THE AXES AND TITLES HAVE ALREADY BEEN

PLOTTED AND DO NOT NEED TO BE REPLOTTED AND THE NEXT

PART OF THE ROUTINE IS OMITTED

IF (NCOUNT. GT.O) GOTO 3001

DETERMINE THE XRANGE AND YRANGE WHICH ARE USED TO SCALE

THE X & Y AXES RESPECTIVELY

XRANGE=MAX (ABS (MAXX) , ABS (MINX)

)

YRANGE=MAX(ABS (MAXY) , ABS (MINY)

)

DETERMINE THE SCALE FOR THE X-AXIS, XFACTOR

XFACTOR=XSIZE/ (2 . *XRANGE)

DETERMINE THE SCALE FOR THE Y-AXIS, YFACTOR

YFACTOR=YSIZE/ (2 . *YRANGE)

DRAW AXES USED FOR THE HYSTERESIS CURVE PLOTS

CALL VAL8(30) ! WHITE

DETERMINE THE ENDS OF THE X AND Y AXES

OFFXl = ( -XSIZE/2 + OFFSETX)

OFFYl = ( -YSIZE/2 + OFFSETY)

OFFX2 = ( XSIZE/2 + OFFSETX)

OFFY2 = (YSIZE/2 + OFFSETY)

DRAW THE X-AXIS

CALL MOVABS (OFFXl, OFFSETY)

228
non

ooo

ooo

oooo

oooo

ooo

CALL DRWABS (0FFX2 , OFFSETY)

DRAW THE Y-AXIS

CALL MOVABS (0FFSETX,0FFY1)

CALL DRWABS ( OFFSETX , 0FFY2

)

INSERT TITLES

CALL VAL8(30) i WHITE

CALL MOVABS(-315,20)

CALL RASTER TECH ROUTINE TO SET TEXT SIZE AND FOR

HORIZONTAL TEXT

CALL TEXTN(35,35,0,0)

LABEL Y-AXIS

DO 410 1=1,9

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXTl ( 4

,

' LOAD '

)

410 CONTINUE

LABEL THE X-AXIS

CALL MOVABS (-10,-280)

DO 430 1=1,9

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXTl ( 12 ,

' DISPLACEMENT '

)

430 CONTINUE

DISPLAY OVERALL TITLE OF PLOT

CALL MOVABS (-250,-450)

CALL TEXTN(40,40,0,0)

DO 440 1=1,9

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXTl ( 24 ,' LOAD-DISPLACEMENT CYCLES '

)

440 CONTINUE

3001 CONTINUE

C

C THE ANIMATED COLUMN WILL BE SHOWN IN THE UPPER LEFT

C CORNER OF THE SCREEN

C

C DRAW BASE OF THE COLUMN

C

CALL MOVABS (-500,225)

CALL RECTAN(-100, 100)

C

C READ IN THE DATA POINTS AND CONVERT TO INTEGER* 2 FORMAT AND

C TO NUMBER OF PIXELS

C

DO 220 I=1,NPTS

229
oooo

ooo

non

oooo

nooo

ooo

ooo

VERTS (1,1) = IFIX(X(I) *XFACTOR)

VERTS (2, I) = IFIX(Y(I) *YFACTOR)

DETERMINE lA AND IB

IF(X(I) .EQ.XMAX) lA = I

IF(X(I) .EQ.XMIN) IB = I

220 CONTINUE

DRAW THE MOVEMENT OF THE COLUMN

DO 240 I=1,NPTS

THIS LOOP IS USED TO ERASE THE COLUMN IN ITS PREVIOUS

POSITION

DO 230 J=l,2

IF(J.EQ.l) CALL VAL8(30) I WHITE

IF(J.EQ.2) CALL VAL8(31) I BACKGROUND COLOR, BLACK

IF I > 1, THE COLUMN AT ZERO POSITION SHOULD NOT BE

DRAWN

IF(I.GT.l) GOTO 245

DRAW COLUMN AT ZERO POSITION

CALL MOVABS(-330,225)

CALL RECTAN(-270,425)

CALCULATE COLX

245 COLX = IFIX(X(I) *SCALE-330.0)

DEFINE LOAD ARROW DEFLECTION. ARROW IS USED TO INDICATE THE

DIRECTION OF THE LATERAL LOAD

ARROW = COLX + 70

C

C IF I < lA, THE COLUMN IS DEFLECTING TO THE RIGHT AND THE

C ARROW HEAD IS LOCATED AT THE RIGHT END OF THE ARROW

C SHAFT

C

IF(I.LE.IA) ENDARR = ARROW + 75

C

C IF I > lA, THE COLUMN IS DEFLECTING TO THE LEFT AND THE

C ARROW HEAD IS LOCATED AT THE LEFT END OF THE ARROW

C SHAFT

C

IF(I.GT.IA.AND.IB.LE.IB) ENDARR = ARROW

C

C IF lA < I < IB, THE COLUMN IS DEFLECTING TO THE RIGHT AND THE

C ARROW HEAD IS LOCATED AT THE RIGHT END OF THE ARROW

C SHAFT

C

230
ooo

ooo

ooo

IF(I.GT.IB) ENDARR = ARROW + 75

DRAW ARROW USING DO LOOP TO CREATE BOLD EFFECT

DO 235 N=l,5

DRAW THE ARROW SHAFT, LENGTH =75 PIXELS

CALL MOVABS (ARROW, 417+N)

CALL DRWABS ( ARROW+7 5 , 4 1 7 +N

)

DRAW ARROW HEAD

CALL MOVABS (ENDARR, 417+N)

IF(I.LE.IA) LEND = -20

IF(I.GT.IA.AND.I.LE.IB) LEND = 20

IF(I.GT.IB) lEND = -20

CALL DRWABS (ENDARR+IEND,437+N)

CALL MOVABS (ENDARR, 417+N)

CALL DRWABS (ENDARR+IEND,398+N)

235 CONTINUE

C

C DRAW COLUMN MOVING

C

C THE COLUMN HEIGHT IS DIVIDED INTO 10 DISCRETE SEGMENTS

C OR 10 POINTS WITH EACH POINT EQUAL TO 20 PIXELS ABOVE

C THE PREVIOUS POINT

C

DO 231 M = 1,10

IM = M+1

XN =M

C

C DEFINE THE COORDINATES OF THE (N+1) DATA POINT. RECALL

C THAT XC(1) AND YC(1) HAVE ALREADY BEEN DEFINED

C PREVIOUSLY

C

XC(IM) = 20.0*XN

C

C GIVEN A VALUE OF X, THE VALUE OF Y IS FOUND BY THE EQUATION

C FROM McGUIRE AND GALLAGHER, "MATRIX STRUCTURAL

C ANALYSIS", 1979, PG. 87

C

C Y = [X**2 (3*L - X)]/6*EI

C

C

YC(IM) = (X(I) *SCALE) * (XC(IM) **2) * ( 600 . 0-XC (IM) )

/

1 16000000.0

C

C CHANGE THESE VALUES TO INTEGER* 2 FORMAT

C

C XCl & YCl DEFINE THE LAST POINT (N-1) TO BE PLOTTED

C

C XC2 AND YC2 DEFINE THE CURRENT POINT (N) TO BE PLOTTED

C

YCl = IFIX(YC(M)

)

231
oo

ooooooooo

ooooooooo

oooo

ooo

oooo

YC2 = IFIX(YC(IM)

)

XCl = IFIX(XC(M))

XC2 = IFIX(XC(IM))

C

C DRAW THE DEFLECTED LEFT LINE OF THE COLUMN

C

C MOVE THE LAST POINT TO BE PLOTTED

C

CALL MOVABS(-330+YC1,225+XC1)

DRAW A LINE FROM THE LAST POINT (N-1) TO THE CURRENT

POINT (N)

CALL DRWABS(-330+YC2,225+XC2)

DRAW THE DEFLECTED RIGHT LINE OF THE COLUMN

CALL MOVABS(-270+YC1,225+XC1)

CALL DRWABS(-270+YC2,225+XC2)

231 CONTINUE

DRAW A LINE AT THE TOP OF THE COLUMN CONNECTING THE LEFT

AND RIGHT VERTICAL COLUMN LINES

YClO = IFIX(YC(11)

)

XCIO = IFIX(XC(11))

CALL MOVABS(-330+YC10,225+XC10)

CALL DRWABS(-270+YC10,225+XC10)

SHOW THE LOAD-DISPLACEMENT CORRRESPONDING TO THE COLUMN

MOVEMENT

WHEN J = 2, THE COLUMN IN ITS PREVIOUS POSITION IS

'ERASED' OR STATED MORE ACCURATELY, REDRAWN IN

BACKGROUND COLOR. THE HYSTERESIS PLOT IS

HOWEVER, NOT ERASED. THE GOTO 230 WILL ENSURE THIS.

IF(J.EQ.2) GOTO 230

IF I = 1, THIS IS THE FIRST DATA POINT TO BE PLOTTED.

MOVE TO THE ORIGIN OF THE AXES AND THE 'GOTO 260'

STATEMENT DIRECTS THE PROGRAM TO DRAW A LINE FROM THE

AXES ORIGIN TO THE FIRST DATA POINT

IF I > N FOR N > 1, DEFINE THE (N-1) POINT AS (XI, Yl)

AND THE CURRENT POINT AS (X2,Y2).

IF(I.GT.l) GOTO 250

CALL MOVABS (OFFSETX,OFFSETY)

GOTO 260

250 XO = I-l

XI = OFFSETX + VERTS (1,X0)

Yl = OFFSETY + VERTS(2,X0)

MOVE TO THE (N-1) POINT PLOTTED

232
ooo

oooooooo

ooo

ooo

CALL M0VABS(X1,Y1)

260 X2 = OFFSETX + VERTS (1,1)

Y2 = OFFSETY + VERTS (2,1)

DRAW A LINE FROM THE (N-1) POINT TO THE N th POINT

CALL DRWABS(X2,Y2)

CALL EMPTYB

230 CONTINUE

240 CONTINUE

DRAW COLUMN AT ZERO POSITION

CALL VAL8(30)

CALL MOVABS (-330,225)

CALL RECTAN(-270,425)

ERASE THE CYCLE

CALL VAL8(18)

NVERTS(l) = NPTS

CALL MOVABS (OFFSETX , OFFSETY)

CALL POLYGN(l,NVERTS, VERTS)

CALL EMPTYB

RETURN

END

233
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

***************'***************************************•***

SUBROUTINE COMPARE

PURPOSE: TO COMPARE ENERGY ABSORBED PER CYCLE BETWEEN A

MAXIMUM OF 3 TESTS. THIS COMPARISON IS

PRESENTED IN A BAR GRAPH TYPE HISTOGRAM. SCALING

OF VALUES PERMITS THE EASY DETERMINATION OF THE

SCALE BETWEEN TESTS.

THESE ENERGIES HAVE BEEN NORMALIZED BY THE

YIELD DISPLACEMENT AND THE CONCRETE

COMPRESSIVE STRENGTH. THE USER MAY CHOOSE

NOT TO DO SO BY ENTERING ONES FOR THE YIELD

DISPLACEMENTS AND CONCRETE COMPRESSIVE STRENGTHS.

CALLED FROM: PROGRAM MAIN

USAGE : CALL COMPARE ( I DX , I DY

)

PARAMETERS

IDY SEE MAIN PROGRAM

IDX SEE MAIN PROGRAM

OTHER SUBROUTINES CALLED: REDRAW AND RASTER TECH 'ONELIB'

ROUTINES. SEE PROGRAM MAIN.

SUBROUTINE SPECIFIC PARAMETERS:

ISIZE

LENX

LENY

ORIGINX

ORIGINY

ALIST(I)

ATITLE

BLIST

BTITLE

CTICK

TICK

INTTICK

NUMCYCLE(I)

SETS THE SIZE OF THE CYCLE TITLES TO BE

PLOTTED

LENGTH OF X-AXIS

LENGTH OF Y-AXIS

X-COORDINATE OF THE ORIGIN OF THE AXES

Y-COORDINATE OF THE ORIGIN OF THE AXES

I th FILENAME OF TEST TO BE COMPARED. THIS

FILE CONTAINS THE NAMES OF ALL THE CYCLES,

ONE PER LINE, IN A GIVEN TEST. THESE NAMES

ARE THE CONVERTED FILENAMES. SEE

DOCUMENTATION IN PROGRAM MAIN FOR MORE

INFORMATION

NAME OF A CYCLE CONTAINED IN ALIST

EQUIVALENT OF ALIST BUT WITH '.LIS' EXTENSION

ATTACHED

EQUIVALENT OF ATITLE BUT WITH '.OUT' EXTENSION

ATTACHED

THE AMOUNT OF ENERGY EQUAL TO 100*1 PIXELS

WHERE I = 1, 2, ... TO THE NUMBER OF DIVISIONS

OF THE Y-AXIS IN UNITS OF ENERGY

EQUIVALENT TO CTICK IN CHARACTER FORMAT

EQUIVALENT TO CTICK IN INTEGER*2 FORMAT

THE TOTAL NUMBER OF CYCLES IN THE I th TEST

234
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

INUMCYC TOTAL NUMBER OF CYCLES FOR ALL THE TESTS

USED TO SCALE THE X-AXIS

EQUIVALENT OF INUMCYC IN REAL NUMBER FORMAT

MAXIMUM ENERGY ABSORBED PER CYCLE FORM ALL

THE TESTS TO BE COMPARED. USED TO SCALE THE

Y-AXIS

YIELD DISPLACEMENT OF THE I th TEST

CONC_COMP(I) CONCRETE COMPRESSIVE STRESS OF THE I th TEST

ATIT(I,J) J th TITLE OF CYCLE IN THE I th TEST

INTITLE EQUIVALENT TO ATIT IN INTEGER* 2 FORMAT

ENERGY ( I, J) ENERGY ABSORBED IN CYCLE J OF THE I th TEST

XCYC

ENERGYMAX

YIELD(I)

ZTIT(I)

NUMTEST

CSCALEY

NTEST

NDONE(I)

XO

YO

XI

Y1

X2

Y2

LYl

LY2

PRE SCALE

I th TITLE CONTAINED IN FILE ' REFTITLE . LIS

NUMBER OF TESTS TO BE COMPARED

UNITS: PIXEL/UNIT OF ENERGY. CONVERTS THE

ENERGY ABSORBED TO NUMBER OF PIXELS

VARIALBLE USED TO TRANSFER OUT OF THE LOOP TO

PLOT THE BAR GRAPH WHEN ALL THE CYCLES HAVE

BEEN PLOTTED

VARIABLE USED TO ENSURE THAT NTEST IS

INCREMENTED ONLY ONCE BY THE I th TEST TO BE

COMPARED

X-COORDINATE OF THE LOWER LEFT OF THE BAR

Y-COORDINATE OF THE LOWER LEFT OF THE BAR

X-COORDINATE OF THE UPPER RIGHT OF THE BAR

Y-COORDINATE OF THE UPPER RIGHT OF THE BAR

X-COORDINATE USED TO POSITION THE TITLE OF

THE CYCLE ABOVE THE BAR

Y-COORDINATE USED TO POSITION THE TITLE OF

THE CYCLE ABOVE THE BAR

Y-COORDINATE OF THE LOWER LEFT OF THE RECTANGLES

USED IN THE LEGEND

Y-COORDINATE OF THE UPPER RIGHT OF THE

RECTANGLES USED IN LEGEND

VARIABLE PASSED BACK FROM SUBROUTINE REDRAW. IT IS AN

ARRAY WHICH STORES THE SCALE FACTOR FOR EACH TEST. THE

SCALING IS CUMULATIVE. I.E. IF A TEST HAS BEEN SCALED

BY A FACTOR OF "a" AND SCALING OF THE SAME TEST IS

ASKED FOR AGAIN, THIS TIME BY A FACTOR OF "b", THE

RESULTING ENERGY THAT IS PLOTTED IS SCALED BY ab

•kifk-k-k'krk’kie-k-kic'kicieickifk'ifkititrk'k-k'kieifkickic'k-kifk'k-k-k-k-k-kic-k'k-k'kit'k'k'k’k-k-k-k-k

SUBROUTINE COMPARE (IDX, IDY)

INTEGER*2 IDX (16) , IDY (16) ,INTTICK(4) , INTITLE ( 7 , 50 , 50 )

,

1 LTITLE(7,50) , TEST (3, 100) , REPEAT (3)

INTEGER*2 XO , YO , XI , Y1 , X2 , Y2 , LYl , LY2 , LY3 , ISIZE

,

1 ORIGINX , ORIGINY , LENX , LENY , TESTNO

C

CHARACTER*14 ALIST(50) ,ATIT(50,50) ,ZTIT(50)

CHARACTER*9 ATITLE

CHARACTER* 18 BLIST,BTITLE
onooooo

oooo

ooo

o

oooo

c

c

c

CHARACTER*2 TICK (4)

DIMENSION ENERGY(50,50) , NUMCYCLE ( 100 ) ,TOTAREA(10)

,

1 NDONE(IO) , YIELD (5) , CONC_COMP ( 5 )

, PRE_SCALE ( 3

)

EQUIVALENCE (TICK, INTTICK)

EQUIVALENCE ( ALIST , LTITLE)

EQUIVALENCE (ATIT , INTITLE)

INITIALIZE GRAPHICS DEVICE

CALL RTSET (1,180)

CALL RTINIT (' GDAO :

' , 5

)

CALL ENTGRA

TYPE *

, » ' TYPE BEGIN COMPARISON OF ENERGY ABSORBED/CYCLE'

TYPE *

, ' ' TYPE HOW MANY TESTS WOULD YOU LIKE TO COMPARE?

1 (3 MAX)

READ(5,700) NUMTEST

00 FORMAT (12)

IF (NUMTEST . GT . 3 ) NUMTEST=3

ENERGYMAX =0.0

TYPE *

, ' ' READ TEST NAMES TO BE COMPARED

DO 701 1=1, NUMTEST

TYPE 795,1

795 FORMAT (' ENTER LIST FILE NAME ' , 12 ,' TO BE COMPARED’)

READ (5, 703) ALIST (I)

703 FORMAT (A14)

TYPE 748, ALIST (I)

NOTE FOR PROPER COMPARISON, FC AND DELTA Y SHOULD BE

FACTORED INTO THE RESPONSE

748 FORMATC YIELD DISPLACEMENT FOR ',A14,'= ?')

READ(5,*) YIELD(I)

TYPE 749, ALIST (I)

749 FORMATC CONCRETE COMPRESSIVE STRENGTH IN KSI

1 FOR ' ,A14, '= ? '

)

READ ( 5

, *

)

CONC_COMP ( I

)

BLIST = ALIST (I)//' .LIS'

J IS USED TO DETERMINE THE NUMBER OF CYCLES IN A GIVEN

TEST. IT IS INITIALIZED AT THIS POINT.

J = 1

INITIALIZE TOTAREA(I)

236
TOTAREA (I) = 0.0

C

C OPEN FILE CONTAINING THE LIST OF CYCLES

C

OPEN ( 12 , FILE=BLIST , ACCESS= ' SEQUENTIAL ' , FOPM= ’ FORMATTED ’

,

1 STATUS='OLD'

)

REWIND 12

C

C READ THE NAME OF THE FIRST FILE TO BE PLOTTED

C LOOP ON THIS READ STATEMENT UNITE ALL THE FILES HAVE

C BEEN READ

C

798 READ(12,FMT=703,END=799) ATITLE

C

C ATTACH '.OUT' EXTENSION TO THE NAME JUST READ

C

BTITLE = ATITLE// '

OUT ' C

C OPEN THE ' . OUT ' FILE

C

OPEN ( 7 , FILE=BTITLE , ACCESS= ' SEQUENTIAL ',FORM= ' FORMATTED '

,

1 STATUS= ' OLD '

)

REWIND 7

C

C READ THE TITLE OF THE CYCLE AND STORE IT IN ATIT (I,J)

C

READ(7,704) ATIT(I,J)

704 FORMAT (A14)

C

C READ THE ENERGY ABSORBED IN THAT CYCLE AND STORE IT IN

C ENERGY (I,J)

C

READ (7,705) I COUNT , ENERGY ( I , J

)

705 FORMAT (8X, 110 , 7X, FIO . 5 ) C

C NORMALIZE THE ENERGY ABSORBED BY THE YIELD DISPLACEMENT

C AND THE CONCRETE COMPRESSIVE STRENGTH

C

ENERGY(I,J) = ENERGY(I,J)/(YIELD(I)*CONC_COMP(I)

)

C

C DETERMINE THE MAXIMUM ENERGY ABSORBED PER CYCLE FROM ALL

C THE TESTS TO BE COMPARED

C

I F ( ENERGY ( I , J ) . GT . ENERGYMAX) ENERGYMAX = ENERGY ( I , J

)

C

C FIND THE NUMBER OF CYCLES IN TEST (I) AND STORE IT

C IN NLrMCYCLE(I)

C

730 NUMCYCLE(I) = J

J = J + 1

GOTO 798

799 CONTINUE

C

C FIND THE MAX. ENERGY ABSORBED FROM AMONG THE MODELS

C

237
ooo

non

ooo

ooo

ooooo

ooo

non

ooo

c IF(TOTAREA(I) . GT . TOTENERGY) TOTENERGY = TOTAREA(I)

CLOSE (12)

CLOSE (7)

701 CONTINUE

LOAD COLOR MAP

CALL LUTS (48, 150, 150, 150) I GRAY

! RED

! BLACK

! BLUE

CALL LUTS (50, 255, 0,0)

CALL LUTS (51, 0,0,0)

CALL LUTS (52,0,0,255)

CALL LUTS (53,255,255,200)

CALL LUT8(54, 0,255,0)

! YELLOW

! GREEN

FLOOD BACKGROUND

CALL VAL8(48) ! GRAY

CALL FLOOD

DEFINE THE ORIGIN AT (-450,-460)

ORIGINX = -450

ORIGINY = -460

SET THE LENGTH OF THE AXES

X-AXIS = 900 PIXELS

Y-AXIS = 900 PIXELS

LENX = 900

LENY = 900

CALL VAL8(51) ! BLACK

DRAW THE AXES USING DO LOOP TO THICKEN THE LINES

DO 706 1=1,5

DRAW THE X-AXIS

CALL MOVABS (ORIGINX, ORIGINY-3+I)

CALL DRWABS (ORIGINX+LENX, ORIGINY-3+I)

DRAW THE Y-AXIS

CALL MOVABS (ORIGINX-3+I , ORIGINY)

CALL DRWABS (ORIGINX-3+I , ORIGINY+LENY)

706 CONTINUE

SET SCALE FOR Y-AXIS

C DRAW TICK MARKS AND THE VALUES FOR EACH TICK MARK

CSCALEY = 800. 0/ENERGYMAX

C

C

C CALL SUBROUTINE FOR VERTICAL TEXT

C

238
ooo

oono

ooo

oooo

oooooooooo

oooo

ooo

CALL TEXTC(35,90)

DIVIDE THE Y-AXIS INTO 8 SEGMENTS

DO 707 I = 1,8

IX = ORIGINY-2 + 1*100

DO 708 J = 1,3

CALL M0VABS(0RIGINX-5,IX+J)

CALL DRWABS (ORIGINX+5 , IX+J)

708 CONTINUE

CALCULATE CTICK WHICH IS THE AMOUNT OF ENERGY EQUAL TO

1*100 PIXELS IN UNITS OF ENERGY

XI = I

CTICK = (1. 0/CSCALEY*100. 0) *XI

CONVERT CTICK INTO CHARACTER FORMAT AND STORE IT IN TICK

USING THE ENCODE STATEMENT

ENCODE (I,J,K)

I = NUMBER OF CHARACTERS IN TO BE TRANSLATED TO

CHARACTER FORMAT

J = REFERS TO THE FORMAT STATEMENT

K = ARRAY NAME REFERENCE

ENCODE ( 8 , 7 0 9 , TICK) CTICK

709 FORMAT (F8. 2)

II IS USED IN POSITIONING THE VALUES NEXT TO THE TICK

MARKS

II = ORIGINY-55 + 1*100

CALL MOVABS(ORIGINX-20,II)

DO 710 J =1,4

CALL MOVREL(IDX(J) ,IDY(J)

)

CALL TEXT1(8,INTTICK)

710 CONTINUE

707 CONTINUE

LABEL Y-AXIS

CALLVAL8(51) 1 BLACK

CALL RASTER TECH ROUTINE TO SET SIZE OF TEXT AND FOR

VERTICAL TEXT

CALL TEXTC(70,90)

CALL MOVABS ( ORIGINX- 100, ORIGINY+200)

DISPLAY TITLE OF Y-AXIS

DO 712 1=1,9

CALL MOVREL ( IDX ( I ), IDY ( I )

)

CALL TEXTl (29, 'ENERGY/ (DELTA Y * FC) (IN**2)')

239
ooo

ooo

non

ooo

oooo

oooo

ooo

oooo

oooo

ooo

712 CONTINUE

DISPLAY TITLE FOR PLOT

CALL VAL8(51)

CALL RASTER TECH SUBROUTINE TO SET SIZE OF TEXT AND FOR

HORIZONTAL TEXT

CALL TEXTN(60,60,0,0)

BEGIN WRITING THE TITLE IN THE LOWER LEFT CORNER OF THE

SCREEN

CALL MOVABS (-375,-500)

DISPLAY TEXT ON SCREEN

DO 750 IK=1,16

CALL MOVREL(IDX(IK) ,IDY(IK)

)

CALL TEXTl (26, 'COMPARISON OF CYCLE ENERGY')

750 CONTINUE

FIND THE TOTAL NUMBER OF CYCLES FROM ALL THE TESTS TO

DETERMINE THE WIDTH OF BAR IN THE BAR GRAPHS

INUMCYC = 0

DO 711 I=1,NUMTEST

INUMCYC = NUMCYCLE(I) + INUMCYC

711 CONTINUE

XCYC = INUMCYC

FIND THE MAXIMUM WIDTH OF THE BAR SO THAT ALL THE BARS

WILL FIT ON THE X-AXIS

CSCALEX = 900.0/XCYC

INITIALIZE NTEST

NTEST = 0

ISCALEX IS THE INTEGER FORM OF CSCALEX

ISCALEX = CSCALEX

K IS USED AS AN INDEX TO LOCATE XO

K = 0

OPEN FILE 'REFTITLE.LIS'

OPEN ( 9 , FILE= ' REFTITLE . LIS ' , ACCESS= ' SEQUENTIAL '

,

1 FORM= ' FORMATTED ' , STATUS= ' OLD '

)

REWIND 9

240
ooo

oooo

oooo

C READ THE TITLES OF THE CYCLES CONTAINED IN REFTITLE.LIS

C AND STORE THE TITLE IN ZTIT(I). NOTE THAT THE COUNTER

C IS SET AT 39 BECAUSE THERE ARE 39 TITLES IN REFTTLE.LIS.

C IF THE NUMBER OF TITLES IN REFTITLE.LIS IS CHANGED THE

C COUNTER MUST BE CHANGED TO EQUAL THIS NEW NUMBER.

C

DO 726 IP = 1,39

READ (9, 727) ZTIT(IP)

726 CONTINUE

727 FORMAT (A14)

CLOSE (9)

INITIALIZE NDONE WHICH CAN BE SET EQUAL TO ANY NUMBER

OTHER THAN ZERO

DO 745 I = 1,NUMTEST

NDONE (I) = I

745 CONTINUE

INITIALIZE THE VARIABLES USED TO STORE THE LOCATION OF THE

BARS

II = 0

' 12 = 0

13 = 0

CALL SUBROUTINE TO FILL IN BAR GRAPH

CALL PRMFIL(l)

C

C BEGIN LOOP TO COMPARE THE TITLE OF A CYCLE FROM A TEST

C TO A TITLE IN THE REFERENCE LIST OF TITLES, ZTIT.

C REFTITLE.LIS CONTAINS 39 TITLES AND AS A RESULT THE OUTER

C LOOP, DO 713, IS LOOPED 39 TIMES.

C

DO 713 J = 1,39

DO 714 I = 1,NUMTEST

C

C IF J IS GREATER THAN THE NO. OF CYCLES IN TEST (I), THEN

C ALL CYCLES IN THAT TEST HAS BEEN PLOTTED. CONTROL IS

C THEN TRANSFERRED TO STATEMENT 715 WHERE NTEST IS

C INCREASED BY ONE. WHEN NTEST EQUALS THE NUMBER OF

C TESTS, NUMTEST,THEN ALL THE TESTS HAVE BEEN PLOTTED AND

C CONTROL IS TRANSFERRED OUT OF THE LOOP AND THE PROGRAM

C CONTINUES

C

IF(J.GT.NUMCYCLE(I) ) GOTO 715

C

C IF THE J th TITLE IN THE I th TEST, ATIT(I,J), MATCHES

C THE J th TITLE, ZTIT(J), IN REFTITLE.LIS THEN THAT CYCLE

C ENERGY IS PLOTTED

C

C IF NOT, TRANSFER TO STATEMENT 716 WHERE ATIT(I,J+1) IS

C SET EQUAL TO ATIT(I,J) SO THAT IT MAY BE COMPARED TO

C ZTIT(J+1) UNTIL A MATCH IS FOUND

241
ooooo

non

oooo

oooo

oooo

oooo

c

IF(ATIT(I, J) .NE.ZTIT(J) ) GOTO 716

C

C M IS USED AS AN INDEX SO THAT BAR GRAPHS FROM THE SAME

C TEST ARE PLOTTED IN THE SAME COLOR

C

M = 49 + I

CALL VAL8 (M)

K = K + 1

STORE THE "PLACEMENT" OF THE BAR IN TEST(I,J)

I.E. THE N th BAR TO BE PLOTTED

IF(I.EQ.l) THEN

II = II + 1

11 = II

ENDIF

IF(I.EQ.2) THEN

12 = 12 + 1

II = 12

ENDIF

IF(I.EQ.3) THEN

13 = 13 + 1

II = 13

ENDIF

TEST(I,II) = K

XO AND YO ARE THE X & Y COORDINATES OF THE LOWER LEFT

CORNER OF THE BAR GRAPH

XO = ORIGINX+3+(K-l) *ISCALEX

YO = ORIGINY+3

XI AND Y1 ARE THE X & Y COORDINATES OF THE UPPER RIGHT

CORNER OF THE BAR GRAPH

XI = ISCALEX + XO

Y1 = IFIX(ENERGY(I, J) *CSCALEY)+ORIGINY

DRAW THE BAR TO REPRESENT THE ENERGY ABSORBED IN THAT

CYCLE

CALL MOVABS(XO,YO)

CALL RECTAN(X1, Yl)

X2 & Y2 LOCATE THE POSITION TO WRITE THE TITLES

X2 = XI - 7

Y2 = Yl + 5

ISIZE IS THE SIZE OF THE TEXT

ISIZE = ISCALEX + 7

LABEL BARS WITH THEIR APPROPRIATE TITLES

242
c

CALLVAL8(51) I BLACK

CALL TEXTC(ISIZE,90)

CALL MOVABS(X2,Y2)

DO 717 IJ = 1,4

CALL MOVREL(IDX(IJ) ,IDY(IJ)

)

CALL TEXTl (14, INTITLE (1, I, J)

)

717 CONTINUE

C

C AFTER THE BAR HAS BEEN PLOTTED AND LABELED, CONTINUE WITH

C THE NEXT CYCLE

C

GOTO 714

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

INCREMENT J IN ATIT(I,J) TO ATIT(I,J+1) AND

ENERGY(I,J) TO ENERGY (I , J+1)

EXAMPLE:

GIVEN: ATIT(I,1)

ATIT(I,2)

AND

ZTIT(l) =

ZTIT(2) =

ZTIT(3) = ZTIT(4) =

= B, ENERGY (1,1) = D, ENERGY (I, 2)

A

B

C

D

5

3

FOR J = 1

ATIT(I,1) = B DOES NOT MATCH ZTIT(l) = A AND

THE PROGRAM TRANSFERS TO STATEMENT 716 WHERE

ATIT(I,3) IS "CREATED” AND SET EQUAL TO ATIT(I,2) = D

AND ATIT(I,2) IS SET EQUAL TO ATIT(I,1) = B AND

ENERGY (I, 3) IS ALSO "CREATED" AND SET EQUAL TO

ENERGY (I, 2) = 3 AND ENERGY (I, 2) IS SET EQUAL TO

ENERGY (1,1) = 5. THE NUMBER OF CYCLES IS INCREASED

BY ONE TO ACCOUNT FOR THIS "NEW" ADDITION.

FOR J = 2,

ATIT(I,2), NOW EQUAL TO B, IS COMPARED WITH ZTIT(2) = B.

SINCE THESE TWO TITLES MATCH, THE CYCLE ENERGY IS PLOTTED

IF NOT, TRANSFER TO STATEMENT 716 WILL OCCUR AGAIN.

FOR J = 3,

ATIT(I,3) = D IS COMPARED WITH ZTIT(3) = C. THESE

TITLES DO NOT MATCH AND THE PROGRAM TRANSFERS TO

STATEMENT 716 WHERE

ATIT(I,4) IS "CREATED" AND SET EQUAL TO ATIT(I,3) = D

ENERGY (1,4) IS "CREATED" AND SET EQUAL TO ENERGY (I, 3)

EQUAL TO 3 AND NUMCYCLE IS INCREASED BY ONE TO ACCOUNT FOR

THIS 'NEW' ADDITION.

243
oooo

ooo

ooo

oooo

o

oooo

c

C FOR J=4

,

C

C ATIT(I,4) NOW EQUAL TO D IS COMPARED WITH ZTIT(4) = D

C AND A MATCH IS FOUND. THE CYCLE IS THEN PLOTTED.

C

C

716 DO 718 II=NUMCYCLE(I) , J,-l

ATIT(I,II+1) = ATIT(I,II)

ENERGY (1,11+1) = ENERGY (I, II)

718 CONTINUE

NUMCYCLE(I) = NUMCYCLE(I) + 1

GOTO 714

C

C NDONE(I) IS EQUAL TO ZERO ONLY WHEN ALL THE CYCLES IN

C TEST (I) HAVE BEEN PLOTTED. NDONE(I) IS SET EQUAL TO

C ZERO WHEN THIS COMPLETION IS FIRST NOTED. THE 'IF'

C STATEMENT ENSURES THAT NTEST IS ONLY INCREMENTED ONCE

C FOR EACH TEST.

C

715 IF(NDONE(I) .EQ. 0) GOTO 714

NDONE(I) = 0

INCREMENT NTEST BY ONE ONLY WHEN ALL THE CYCLES IN A

GIVEN TEST HAS BEEN PLOTTED.

NTEST = NTEST + 1

IF (NTEST. EQ.NUMTEST) GOTO 719

714 CONTINUE

713 CONTINUE

DRAW THE LEGEND IN THE UPPER RIGHT CORNER OF THE SCREEN

TO SHOW COLORS AND CORRESPONDING TESTS NAMES

719 DO 720 IM = 1,NUMTEST

DO 721 IN = 1,2

M = 49 + IM

FOR IN = 1, COLOR THE RECTANGLE WITH COLOR VALUE M

IF(IN.EQ.1)CALL PRMFIL(l)

IF(IN.EQ.2)CALL PRMFIL(O)

FOR IN = 2, OUTLINE THE RECTANGLE WITH BLACK

IF(IN.EQ.1)CALL VAL8 (M)

IF(IN.EQ.2)CALL VAL8(51)

DEFINE THE Y-COORDINATE OF THE UPPER LEFT CORNER OF THE

RECTANGLE

LYl = 375-30* (IM-1)

C

244
ooo

ooo

o

ooo

oooo

oooo

ooo

ooo

C DEFINE THE Y-COORDINATE OF THE LOWER RIGHT CORNER OF THE

C RECTANGLE

C

LY2 = 375-30*IM

c

C MOVE

c

TO THE UPPER LEFT CORNER OF THE RECTANGLE

CALL MOVABS(450,LY1)

C DRAW THE RECTANGLE

CALL RECTAN(490,LY2)

INSERT THE TITLES 5 PIXELS TO THE RIGHT OF THE RECTANGLES TO

ASSOCIATE A COLOR WITH A TEST

LY3 = LY2 + 5

CALL RASTER TECH SUBROUTINE TO SET THE SIZE OF THE TEXT AND

FOR HORIZONTAL TEXT

CALL TEXTN(37,37,0,0)

CALL MOVABS(505,LY3)

DISPLAY TITLES ON THE SCREEN

722

721

720

C

DO 722 10=1,9

CALL MOVREL(IDX(IO) ,IDY(I0)

)

CALL TEXT1(14,LTITLE(1,IM)

)

CONTINUE

CONTINUE

CONTINUE

CALL EMPTYB

INITIALIZE REPEAT

780

DO 780 I = 1,NUMTEST

REPEAT (I) = 0

CONTINUE

PROMPT USER FOR SCALING OF ENERGIES BETWEEN MODEL AND PROTOTYPE

725 TYPE DO YOU WANT TO SCALE THE ENERGY? 1 = YES, 0 = NO

READ (5, 770) IANS2

770 FORMAT (12)

TYPE *

, ’ ' IF(IANS2.EQ.O) GOTO 900

C

C WARN USER TO SCALE THE TEST(S) WITH THE SMALLER VALUES

C AS THE SCALE FOR THE Y-AXIS WHICH IS SET FOR THE LARGER

C VALUES WILL NOT BE CHANGED

C

TYPE ' *** NOTE ***' TYPE CHANGE SCALE (S) FOR THE TEST(S) WITH SMALLER VALUES

245
1 ONLY'

TYPE ' ' C

C INITIALIZE SCALE FOR THE TESTS

C

DO 790 II = 1,NUMTEST

PRE_SCALE(II) =1.0

790 CONTINUE

C

C SHOW USER THE LIST OF TESTS AND PROMPT FOR THE NUMBER OF THE

C TEST TO BE SCALED

C

901 DO 735 I = 1,NUMTEST

TYPE 740,I,ALIST(I)

735 CONTINUE

740 F0RMAT(4X,I1, ' = ',A14)

TYPE ' ' TYPE ENTER THE NUMBER OF THE TEST TO BE SCALED'

READ (5,770) TESTNO

BLIST = ALIST (TESTNO)//' .LIS'

.TYPE * ,

' ' TYPE ENTER SCALE FOR ', ALIST (TESTNO)

READ (5,*) SCALE

CALL REDRAW_BARS ( BLIST , TESTNO , SCALE , TEST , ORIGINX , ORIGINY

,

1 CSCALEY, ISIZE, ISCALEX, YIELD, CONC_COMP, REPEAT, PRE_SCALE)

C

C SHOW THE CURRENT SCALES FOR THE TESTS

C

TYPE *

, ' ' DO 800 II = 1,NUMTEST

TYPE SCALE FOR ', ALIST ( II ),'

' , PRE_SCALE ( II

)

800 CONTINUE

C

C PROMPT USER FOR SCALING ANOTHER TEST

C

TYPE *

, ' ' TYPE SCALE ANOTHER TEST? 1 = YES, 0 = NO '

READ(5,770) IANS3

IF(IANS3.EQ.l) GOTO 901

C

900 RETURN

END

C

C

C

246
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

k-k-k-k‘k-k-k-k-k‘k-k'k-k-k-k-kick-k-k'kifk-k-k-k-k-k-k-k‘k‘k-kifk‘k-k‘k-k‘k-k-k-k-k-k:k‘k'k-k-k-kick-k-k-k-k SUBROUTINE COMTOTAL

PURPOSE: TO SHOW THE COMPARISON OF THE ENERGY UP TO

ABSORBED BY A STRUCTURE SUBJECTED TO CYCLIC

LOAD. THE COMPARISON IS SHOWN IN A BAR TYPE

HISTOGRAM. A MAXIMUM OF 6 COMPARISONS CAN BE

MADE

CALLED FROM: PROGRAM MAIN

USAGE : CALL COMTOTAL (I DX, IDY)

PARAMETERS

IDX SEE MAIN PROGRAM

IDY " " " OTHER SUBROUTINES CALLED: NONE ( OTHER THAN RASTER

TECH 'ONELIB' ROUTINES. SEE PROGRAM MAIN)

SUBROUTINE SPECIFIC PARAMETERS:

NUMTEST

ALIST

BLIST

ATITLE

BTITLE

ATIT(I, J)

TOTAREA(I)

TOTENERGY

ORIGINX

ORIGINY

LENX

LENY

CSCALEY

CSCALEX

CTICK

TICK

INTTICK

XO

YO

XI

NUMBER OF TESTS TO BE COMPARED

TEST FILE NAME WHICH CONTAINS ALL CYCLE NAMES

EQUIVALENT TO ALIST BUT WITH '.LIS' EXTENSION

CYCLE NAME CONTAINED IN BLIST

EQUIVALENT TO ATITLE BUT WITH ' . OUT

EXTENSION

J th TITLE IN THE I th TEST CONTAINED IN BTITLE

TOTAL ENERGY ABSORBED IN THE I th TEST

MAXIMUM TOTAL ENERGY ABSORBED BY THE STRUCTURE FROM

AMONG ALL THE TESTS TO BE COMPARED

X-COORDINATE OF THE ORIGIN OF THE AXES

Y-COORDINATE OF THE ORIGIN OF THE AXES

LENGTH OF THE X-AXIS

LENGHT OF THE Y-AXIS

UNITS: PIXELS/UNIT OF ENERGY. USED TO

CONVERT UNITS OF ENERGY TO NUMBER OF PIXELS

UNITS: PIXELS/NO. OF TESTS COMPARED. USED TO

FIT THE TOTAL NUMBER OF TESTS TO BE COMPARED ON THE

X-AXIS

AMOUNT OF ENERGY EQUAL TO 1*100 PIXELS IN

UNITS OF ENERGY WHERE 1=1, 2

,

... TO THE NUMBER

OF DIVISIONS OF THE Y AXIS

EQUIVALENT TO CTICK IN CHARACTER FORMAT

EQUIVALENT TO CTICK IN INTEGER*2 FORMAT

X-COORDINATE OF THE LOWER LEFT CORNER OF A

BAR IN THE HISTORGRAM

Y-COORDINATE OF THE LOWER LEFT CORNER OF A

BAR IN THE HISTORGRAM

X-COORDINATE OF THE UPPER RIGHT CORNER OF A

BAR IN THE HISTOGRAM

247
o

o

o

o

o

o

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

Y1 Y-COORDINATE OF THE UPPER RIGHT CORNER OF A

BAR IN THE HISTOGRAM

LYl Y-COORDINATE OF THE UPPER LEFT CORNER OF THE

RECTANGLE USED IN THE LEGEND

LY2 Y-COORDINATE OF THE LOWER RIGHT CORNER OF THE

RECTANGLE USED IN THE LEGEND

LY3 Y-COORDINATE USED TO PLACE THE TITLE ASSOCIATING

A COLOR WITH A CYCLE NEXT TO THE RECTANGLE IN

THE LEGEND

SUBROUTINE COMTOTAL ( IDX , IDY)

INTEGER*2 IDX (16) , IDY (16) ,INTTICK(4) , LTITLE ( 7 , 50

)

INTEGER*2 XO , YO , XI , Y1 , LYl , LY2 , LY3

,

1 ORIGINX,ORIGINY,LENY,LENX

CHARACTER* 9 ATITLE

CHARACTER*14 ALIST ( 50 )

, ATIT ( 50 , 50

)

CHARACTER* 18 BLIST , BTITLE , CTITLE

C

C

C

C

700

CHARACTER*80 TITLE

CHARACTER* 2 TICK (4)

DIMENSION TOTAREA(IO) , ENERGY ( 50 , 50

)

EQUIVALENCE (TICK, INTTICK)

EQUIVALENCE ( ALIST , LTITLE)

TYPE *

, ’ ' TYPE *,' BEGIN COMPARISON OF TOTAL ENERGY ABSORBED'

TYPE *

, ' ' TYPE *,'HOW MANY TESTS WOULD YOU LIKE TO COMPARE?

1 (6 MAX)

READ (5,700) NUMTEST

FORMAT (12)

IF (NUMTEST. GT. 6) NUMTEST=6

INITIALIZE TOTENERGY

TOTENERGY =0.0

READ TEST NAMES

TYPE *, ' ' DO 701 1=1, NUMTEST

TYPE 795,1

795 FORMAT (' ENTER LIST FILE NAME ',12,' TO BE COMPARED')

248
oo

oooooo

ooo

oooo

ooo

ooo

oooo

ooo

ooo

READ(5,703) ALIST(I)

703 FORMAT (A14)

BLIST = ALIST(I)//' .LIS'

C

C J IS USED TO DIFFERENTIATE THE ENERGY FOR A CYCLE IN A

C GIVEN TEST AND IS INITIALIZED AT THIS POINT

C

J = 1

OPEN LIST FILE CONTAINING THE NAMES OF ALL THE CYCLES

OPEN ( 6 , FILE=BLIST , ACCESS= ' SEQUENTIAL ' , FORM= ' FORMATTED '

,

1 STATUS= ' OLD '

)

REWIND 6

TOTAREA = TOTAL ENERGY ABSORBED IN THE TEST

TOTAREA(I) =0.0

READ THE CYCLE NAME IN THE LIST. LOOPING ON THE READ

STATEMENT UNTIL ALL THE NAMES HAVE BEEN READ

8 READ(6,FMT=703,END=799) ATITLE

BTITLE = ATITLE//' .OUT'

OPEN THE CYCLE FILE

OPEN ( 7 , FILE=BTITLE , ACCESS= * SEQUENTIAL ' , FORM= ' FORMATTED '

,

1 STATUS= ' OLD '

)

REWIND 7

READ THE TITLE OF THE CYCLE

READ(7,704) ATIT(I,J)

14 FORMAT (A14)

READ THE PIXEL COUNT FROM THE NUMERICAL INTEGRATION AND THE

ENERGY FOR THAT CYCLE

READ (7,705) I COUNT , ENERGY ( I , J

)

705 FORMAT (8X, 110, 7X,F10. 5)

SUM ENERGY FOR TEST (I) AND STORE IN TOTAREA (I)

TOTAREA (I) = TOTAREA (I) + ENERGY(I,J)

SUM THE ENERGY ONLY UP TO THE ULTIMATE STATE. ULTIMATE STATE

15 DEFINED AS WHEN THE HORIZONTAL LOAD IS LESS THAN 0.8 TIMES

THE HORIZONTAL LATERAL LOAD OBTAINED DURING THE FIRST CYCLE

AT 2 TIMES DELTA Y. (SEE ZAHN, F. A., REFERENCE [30])

IF(J.LT.2) GOTO 730

CTITLE = ATITLE// ' . INP

OPEN THE FILE WHICH CONTAINS THE DATA POINTS AND THE MAX.

249
OOO

OOO

OOOOO

0*t^000000

OOOOW

OOOH

ooo

oo AND MIN. VALUES

OPEN (20, FILE=CTITLE , ACCESS= ' SEQUENTIAL ' , F0RI4= ' FORMATTED '

,

1 STATUS= ' OLD '

)

REWIND 20

READ THE TITLE

READ (2 0,10) TITLE

0 FORMAT ( 4 0A2)

READ THE MAX AND MIN DISPLACEMENTS AND LOADS

READ (20,30) XMIN , XMAX , YMIN , YMAX , NPTS

0 FORMAT(4 (E12.5,3X) ,15)

CALCULATE THE ULTIMATE LOAD AS 0.8 TIMES THE PEAK LATERAL

LOAD AT 2 TIMES THE YIELD DISPLACEMENT

IF(J.GT.2) GOTO 40

ULTLOAD = 0.80 * YMAX

GOTO 730

COMPARE THE PEAK LATERAL LOAD FOR EACH CYCLE TO THE ULTIMATE

LOAD. IF THE LOAD FOR THAT CYCLE IS LESS THAN THE ULTIMATE

LOAD, THE TOTAL ENERGY WILL ONLY BE SUMMED UP TO AND INCLUDING

THIS CYCLE

0 IF (YMAX. LT. ULTLOAD) GOTO 799

730 J = J + 1

GOTO 798

799 CONTINUE

FIND THE MAXIMUM ENERGY ABSORBED FOR A GIVEN TEST FROM

AMONG ALL THE TESTS TO BE COMPARED AND STORE IT IN

TOTENERGY

IF(TOTAREA(I) .GT.TOTENERGY) TOTENERGY = TOTAREA (I)

CLOSE (6)

CLOSE (7)

CLOSE (20)

701 CONTINUE

INITIALIZE GRAPHICS DEVICE

CALL RTSET (1,180)

CALL RTINIT (

' GDAO :

' , 5

)

CALL ENTGRA

LOAD COLOR MAP

CALL LUT8 (48, 150, 150, 150)

CALL LUT8(50,255,0,0)

CALL LUT8(51,255,255,100)

! GRAY

! RED

! YELLOW

250
ooo

ooo

ooo

oooo

noo

onoooo

ooo

ooo

CALL LUTS (52 , 0, 0, 255)

CALL LUTS (53,0,0,0)

CALL LUTS (54, 0,255,0)

CALL LUTS(55, 255, 0,255)

BLUE

BLACK

GREEN

PURPLE

FLOOD BACKGROUND

CALL VALS(4S) GRAY

CALL FLOOD

DEFINE ORIGIN OF AXES AT (-450,-460)

ORIGINX = -400

ORIGINY = -450

SET LENGTHS OF X-AXIS AND Y-AXIS

X-AXIS = 900 PIXELS

Y-AXIS = 900 PIXELS

LENX = SOO

LENY = 800

DRAW AXES

CALL VAL8(53)

DO 706 1=1,5

CALL MOVABS (ORIGINX, ORIGINY-3+I)

CALL DRWABS (ORIGINX+LENX, ORIGINY-3+I)

CALL MOVABS (ORIGINX-3+I , ORIGINY)

CALL DRWABS (ORIGINX-3+I , ORIGINY+LENY)

706 CONTINUE

SET SCALE FOR THE Y-AXIS, YLENY IS EQUAL TO LENY IN REAL

NUMBER FORMAT

YLENY = LENY

CSCALEY = ( YLENY-100.0)/TOTENERGY

CALL RASTER TECH ONE/SO ROUTINE FOR VERTICAL TEXT

CALL TEXTC(30,90)

DIVIDE THE Y-AXIS INTO 7 SEGMENTS

DO 707 I = 1,7

IX = ORIGINY-2 + 1*100

DRAW TICK MARKS AND THE VALUES FOR EACH TICK MARK

DO 708 J = 1,3

CALL MOVABS (ORIGINX-5 , IX+J)

CALL DRWABS (ORIGINX+5, IX+J)

708 CONTINUE

C

251
ooo

ooo

oooo

ooo

oooo

oooooooooo

on CALCULATE CLICK

XI = I

CLICK = (1.0/CSCALEY*100.0) *XI

CONVERT CLICK INTO CHARACTER FORMAT AND STORE IT IN TICK

USING THE ENCODE STATEMENT

ENCODE (I,J,K)

I = NUMBER OF CHARACTERS TO BE TRANSLATED TO CHARACTER

FORMAT

J = REFERS TO THE FORMAT STATEMENT

K = ARRAY NAME REFERENCE

ENCODE ( 8 , 7 09 , TICK) CLICK

09 FORMAT (F8.0)

II IS USED IN POSITIONING THE VALUES NEXT TO THE TICK

MARKS

II = ORIGINY-55 + 1*100

CALL MOVABS(ORIGINX-20,II)

DO 710 J1 =1,4

CALL MOVREL(IDX(Jl) ,IDY(J1)

)

CALL TEXT1(8,INTTICK)

710 CONTINUE

707 CONTINUE

LABEL Y-AXIS

CALL VAL8(53)

CALL TEXTC(70,90)

CALL MOVABS (ORIGINX-100 , ORIGINY+2 00

)

DO 712 1=1,9

CALL MOVREL ( IDX ( I )

, IDY ( I )

)

CALL TEXT1( 15, 'ENERGY (KIP-IN)')

712 CONTINUE

FIND THE SCALE FOR THE X-AXIS. THIS IS ACTUALLY THE WIDTH OF

THE BARS

XLENX = LENX

CSCALEX = (XLENX-75.0)/NUMTEST

ISCALEX IS THE INTEGER FORM OF CSCALEX

ISCALEX = CSCALEX

K IS USED AS AN INDEX TO LOCATE XO

K = 0

C

C SET THE SIZE OF THE TITLE OF THE HISTOGRAM TO 70 X 70

C PIXELS

C

252
oo

oooo

o

ooo

oooo

oooo

ooo

ooo

ooo

ooo

ooo

CALL TEXTN (70,70,0,0)

CALLVAL8(53) ! BLACK

BEGIN THE TITLE IN THE UPPER LEFT CORNER OF THE SCREEN

CALL MOVABS (-400,425)

WRITE THE TITLE ON THE SCREEN

DO 740 IK = 1,16

CALL MOVREL(IDX(IK) ,IDY(IK)

)

CALL TEXT1(32, 'TOTAL ENERGY ABSORBED BY COLUMN')

0 CONTINUE

CALL SUBROUTINE TO FILL IN BAR GRAPH

CALL PRMFIL(l)

BEGIN LOOP TO PLOT BAR GRAPH

DO 714 I = 1,NUMTEST

M IS USED TO CHANGE THE COLOR OF THE BAR GRAPHS

M = 49 + I

CALL VAL8(M)

K = K + 1

XO & YO ARE THE X & Y COORDINATES OF THE LOWER CORNER OF

THE BAR GRAPH

XO = ORIGINX+3+(K-l) *ISCALEX

YO = ORIGINY+3

XI AND Y1 ARE THE X & Y COORDINATES OF THE UPPER RIGHT

CORNER OF THE BAR GRAPH

XI = ISCALEX + XO

Y1 = IFIX(TOTAREA(I) *CSCALEY)+ORIGINY

DRAW THE BAR (RECTANGLE)

CALL MOVABS (X0,Y0)

CALL RECTAN(X1, Yl)

714 CONTINUE

DRAW THE LEGEND IN THE UPPER RIGHT CORNER OF THE SCREEN

TO SHOW THE BAR COLORS AND CORRESPONDING TEST NAMES

DO 720 IM = 1,NUMTEST

DO 721 IN = 1,2

M = 49 + IM

FOR 1=2, THE RECTANGLE IS FILLED WITH THE APPROPRIATE

253
oo

o

o

non

oooo

oooo

ooo

non

ooo

oooo

ooo

no BAR COLOR

IF(IN.EQ. 1) CALL PRMFIL(l)

FOR IN = 2, THE RECTANGLE IS OUTLINED IN BLACK

IF (IN. EQ. 2) CALL PRMFIL(O)

SET THE CURRENT PIXEL COLOR VALUE. THIS IS A FUNCTION OF

THE VALUE OF 'IN'

IF(IN.EQ. 1) CALL VAL8 (M)

IF(IN.EQ.2)CALL VAL8(53)

DEFINE THE UPPER LEFT CORNER OF THE RECTANGLE

LYl = 325-30* (IM-1)

DEFINE THE LOWER RIGHT CORNER OF THE RECTANGLE

LY2 = 325-30*IM

DRAW THE RECTANGLE

CALL MOVABS(420,LY1)

CALL RECTAN(460,LY2)

INSERT TITLES NEXT TO THE RECTANGLES 5 PIXELS TO THE

RIGHT OF THE RECTANGLE

LY3 = LY2 + 5

CALL RASTER TECH SUBROUTINE FOR SIZE OF TEXT AND FOR

HORIZONTAL TEXT

CALL TEXTN(37,37,0,0)

CALL MOVABS (485,LY3)

DISPLAY TITLES ON THE SCREEN

DO 722 10=1,9

CALL MOVREL(IDX(IO) ,IDY(IO)

)

CALL TEXT1(14,LTITLE(1,IM)

)

722 CONTINUE

721 CONTINUE

720 CONTINUE

CALL EMPTYB

RETURN

END

254
Q ********************************************************

c

C SUBROUTINE LINEPLOT

C

C PURPOSE: STAND-ALONE PACKAGE TO PLOT THE HYSTERESIS

C CURVE OF A STRUCTURE SUBJECTED TO CYCLIC

C LOADS. USES FULL SCREEN (IN CONTRAST) TO

C SUBROUTINE CYCLE WHICH USED 1/4 OF THE SCREEN)

C

C CALLED FROM: PROGRAM MAIN

C

C USAGE: CALL LINEPLOT (IDX, IDY)

C

C PARAMETERS

C

C IDX SEE MAIN PROGRAM

C IDY " " " C

C OTHER SUBROUTINES CALLED: NONE ( OTHER THAN RASTER

C TECH 'ONELIB' ROUTINES. SEE PROGRAM MAIN)

C

C SUBROUTINE SPECIFIC PARAMETERS:

C

C NAUTO

C

C

C

C

C NCOUNT

C

C X(I)

C Y(I)

C YLIST

C

C ZLIST

C NAME

C

c

C XNAME

C TITLE

C XSIZE

C YSIZE

C XRANGE

C

C YRANGE

C

C XFACTOR

C

C YFACTOR

C

C OFFXl

C

C OFFX2

C

C OFFYl

VARIABLE USED TO DETERMINE 'AUTOMATIC (I.E.

NO INPUT REQUIRED BY USER) PLOTTING OF

HYSTERESIS CURVES OR MANUAL PLOTTING

NAUTO = 1 AUTOMATIC

NAUTO = 0 MANUAL

VARIABLE USED TO CHANGE THE COLOR OF THE

HYSTERESIS PLOT

X-COORDINATE OF THE I th DATA POINT

Y-COORDINATE OF THE I th DATA POINT

NAME OF THE TEST FILE WHICH CONTAINS ALL THE

NAMES OF THE CYCLES IN THAT TEST

EQUIVALENT TO YLIST BUT WITH '.LIS' EXTENSION

NAME OF FILE OF A GIVEN CYCLE. THIS FILE

CONTAINS THE DATA POINTS AND TITLE OF THE

CYCLE

EQUIVALENT TO NAME BUT WITH ' . INP

EXTENSION

TITLE OF THE CYCLE IN XNAME FILE

LENGTH OF X-AXIS IN PIXELS

LENGTH OF Y-AXIS IN PIXELS

THE MAXIMUM DISTANCE THE STRUCTURE WAS DISPLACED

IN EITHER THE FORWARD OR REVERSE DIRECTIONS

THE MAXIMUM FORCE TO DISPLACE THE STRUCTURE IN

EITHER THE FORWARD OR REVERSE DIRECTIONS

UNITS: PIXELS/UNIT LENGTH. USED TO CONVERT

LENGTH TO NUMBER OF PIXELS

UNITS: PIXELS/UNIT FORCE. USED TO CONVERT

FORCE TO NUMBER OF PIXELS

X-COORDINATE OF THE LEFT (NEGATIVE) END OF

THE X-AXIS

X-COORDINATE OF THE RIGHT (POSITIVE) END OF

THE X-AXIS

Y-COORDINATE OF THE BOTTOM (NEGATIVE) END OF

255
o

o

o

c

C 0FFY2

C

C OFFSETX

C

C OFFSETY

C

C IRED,

C JRED

C

C IGREEN,

C JGREEN

C

C I BLUE,

C JBLUE

C

c

c

c ********************************************************

c

c

SUBROUTINE LINEPLOT ( IDX , IDY)

CHARACTER f ilename*10 , inf ile*14 , outfile*14 , NAME*10

,

1 XNAME*14, XNOMBRE*14, YLIST*9,ZLIST*14,ANAME*80

c

DIMENSION X(400) , Y(400)

INTEGER*2 TITLE (40) , IDX (16) , IDY (16)

,

1 OVERTIT(20) ,X1(400) , Yl(400)

INTEGER* 2 IX , I Y , NCOUNT , LEY , REY , OFFSETX , OFFSETY

,

1 OFFXl , OFFX2 , OFFYl , OFFY2 , IRED , IGREEN , IBLUE

,

2 JRED, JGREEN, JBLUE

INPUT IDX AND IDY VALUES TO USED FOR BOLD TEXT

REAL MAXX,MINX,MAXY,MINY

C

C DETERMINE THE MAX AND MIN VALUES OF X AND Y FROM ALL

C THE TESTS TO BE INTEGRATED.

C

C Initialize variables into which the max. and min.

C values will be stored.

C

C

1002 MAXX =0.0

MINX =0.0

MAXY =0.0

MINY =0.0

TOTDISP =0.0

C

TYPE *

, ' ' TYPE *, 'BEGIN LOAD-DISPLACEMENT LINE PLOT'

TYPE *, 'ENTER NAME OF LIST FILE (9 CHARACTERS)'

READ (5,518) YLIST

518 FORMAT (A20)

THE Y-AXIS

Y-COORDINATE OF THE TOP (POSITIVE) END OF

THE Y-AXIS

AMOUNT BY WHICH THE X-COORDINATE OF THE AXES

ORIGIN IS MOVED FROM THE SCREEN ZERO

AMOUNT BY WHICH THE Y-COORDINATE OF THE AXIS

ORIGIN IS MOVED FROM THE SCREEN ZERO

DETERMINES THE AMOUNT OF RED TO BE USED

IN COLOR(X) WITH 0 = NO RED USED, AND 255 = MAXIMUM AMOUNT OF RED USED

DETERMINES THE AMOUNT OF GREEN TO BE USED

IN COLOR(X) WITH 0 = NO GREEN USED, AND 255 = MAXIMUM AMOUNT OF GREEN USED

DETERMINES THE AMOUNT OF BLUE TO BE USED

IN COLOR(X) WITH 0 = NO BLUE USED, AND 255 = MAXIMUM AMOUNT USED

256
ooo

o

oooo

ooo

nooooo

oooo

ooooo

ooo

ooo

ZLIST = YLIST// ' .LIS

Open the file where all the cycle names have been stored

OPEN ( 1 , FILE=ZLIST , STATUS= ' OLD ' , ACCESS= ' SEQUENTIAL '

,

1 FORM= ' FORMATTED '

)

1130 CONTINUE

READ THE CYCLE NAME

READ ( 1 , FMT=1 , END=1 1 0 0 ) NAME

PUT EXTENSION ON THE FILENAME.

All files to be used have to have the extension ".INP"

or ".OUT"

XNAME=NAME// ' . INP

Open the test file and extract from it the max. and min.

values

OPEN ( 4, FILE=XNAME,ACCESS=' SEQUENTIAL* ,FORM= ' FORMATTED ’

,

1 STATUS= ' OLD *

)

REWIND 4

TITLE HAS TO BE READ BECAUSE THE FILE IS SEQUENTIAL I.E.

ITEMS LOCATED BEFORE THE DESIRED ITEM HAVE TO BE READ

BEFORE THE DESIRED ITEM CAN BE READ

READ(4,45) TITLE

45 FORMAT (40A2)

READ THE MAX AND MIN VALUES FROM THE FILES

READ (4, 40) XMIN,XMAX, YMIN,YMAX

40 FORMAT(4(E12.5,3X)

)

CLOSE (UNIT=4)

DETERMINE THE SCREEN BOUNDS BASED ON MAX AND MIN X & Y

VALUES

TOTDISP = TOTDISP + ABS (XMAX) + ABS (XMIN)

IF(XMAX.GT.MAXX) MAXX = XMAX

IF (XMIN. LT. MINX) MINX = XMIN

IF(YMAX.GT.MAXY) MAXY = YMAX

IF(YMIN.LT.MINY) MINY = YMIN

GO TO 1130

1100 CONTINUE

REWIND 1

NCOUNT TO PLOT THE CURVES IN DIFFERENT COLORS

NCOUNT=0

257
o

o

o

o

o

o

INITIALIZE THE GRAPHICS DEVICE

CALL RTSET( 1,180)

CALL RTINIT (

' GDAO :

' , 5

)

CALL ENTGRA

LOAD THE COLOR MAP

CALL LUT8(0,255,200,255) ! CALL LUT8 (1,255, 150, 255) I CALL LUT8(2,255,0,255) ! CALL LUT8(3,188,150,234) ! CALL LUT8(4,0,0,190) ! CALL LUT8(5,75,75,255) ! CALL LUT8(6,0,255,255) ! CALL LUT8(7,175,255,255) ! CALL LUT8(8, 0,200, 200) ! CALL LUT8 (9, 0, 175, 0) ! CALL LUT8 (10, 130, 230, 130)

CALL LUT8(11, 0,255,0) I CALL LUT8(12,165,255,165)

CALL LUT8(13,255,255,175)

CALL LUT8(14,255,255,100)

CALL LUT8 (15,255, 175,50) ! CALL LUT8(16, 255, 120,0) ! CALL LUT8(17,255,0,0) ! CALL LUT8(18,255,130,130)

CALL LUT8(19,255,175,175)

CALL LUT8 (20,255,200,200)

CALL LUT8 (21,200,200,200)

CALL LUT8(22,150,150,150)

CALL LUT8 (23,75,75,75) ! CALL LUT8(24,30,30,30) I CALL LUT8(30,255,255,255)

CALL LUT8 (31, 0,0,0) ! CALL LUT8(32, 255, 246,0) ! C

TYPE ' ' TYPE *

,

' ENTER TEST TITLE

READ (5,461) OVERTIT

461 FORMAT(20A2)

TYPE *

, ' ' TYPE *, 'PROCESSING MODE'

TYPE *

,

'

= AUTO

TYPE *,'0 = MANUAL'

READ (5,5001) NAUTO

5001 FORMAT(I2)

C

C FLOOD THE BACKGROUND

C

CALL VAL8(31) ! CALL FLOOD

C

VERY LIGHT PURPLE

LIGHT PURPLE

RED PURPLE

PURPLE

BLUE PURPLE

BRIGHT BLUE

BRIGHT LIGHT BLUE

LIGHT BLUE

BLUE GREEN

OLIVE GREEN

LIGHT OLIVE GREEN

BRIGHT GREEN

LIGHT GREEN

LIGHT YELLOW

LIGHT YELLOW

YELLOW-ORANGE

ORANGE

RED

DUSKY PINK

LIGHT PINK

PALE PINK

LIGHT GRAY

GRAY

DARK GRAY

GRAY-BLACK

WHITE

BLACK

CHROMIUM YELLOW

(20 CHARACTERS)

BLACK

258
C PLACE OVERALL TITLE IN TOP CENTER OF SCREEN

C

CALL VAL8(32) I CHROMIUM YELLOW

C

C CALL RASTER TECH SUBROUTINE TO SET SIZE OF TEXT AND FOR

C HORIZONTAL TEXT

C

CALL TEXTN(90,90,0,0)

CALL MOVABS (-175,450)

C

C BEGIN 'WRITING' TITLE ON SCREEN

C

DO 470 1=1,16

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXT1( 15, OVERTIT)

470 CONTINUE

C

C OPEN THE TEST FILE CONTAINING THE CYCLE NAMES AGAIN IN

C PREPARATION FOR PLOTTING

C

open (1, f ile=ZLIST, status= ' old' , access=' sequential '

,

1

form= ' formatted '

)

c

500 continue

C

read (1, fmt=l, end=1000) filename

1 format (a20)

type *, 'working on file ', filename

c

C PUT EXTENSION ON FILENAME

C

infile=filename// ' . inp

c

C

C READ INDIVIDUAL CYCLE DATA

C

OPEN (UNIT=2,FILE=infile,ACCESS=* SEQUENTIAL' , FORM= ' FORMATTED '

,

1 STATUS= ' OLD '

)

REWIND 2

C

C

READ (2, 2) TITLE

2 FORMAT ( 4 0A2)

C

READ (2,3) XMIN , XMAX , YMIN , YMAX , NPTS

3 FORMAT(4(E12.5,3X) ,15)

C

C READ THE DATA POINTS

C

DO 100 1=1, NPTS

READ(2,4) X(I) , Y(I)

100 CONTINUE

4 FORMAT(2(E12.5,3X)

)

C

CLOSE (UNIT=2)

259
non

ooooNJ

non

ooonoon

ooo

oooo

oooo

ooo

oooo SET LENGTHS OF THE X & Y AXES

XSIZE = 1000

YSIZE = 850

SET OFFSET VALUES TO PLACE ORIGIN AT -20,0

OFFSETX = -20

OFFSETY = 0

IF NCOUNT > 1, THE X & Y SCALE FACTORS AND RANGES WILL

ALREADY HAVE BEEN DEFINED AND DO NOT NEED TO BE REDEFINED

IF (NCOUNT. GT.O) GOTO 3010

FIND THE MAXIMUM DISPLACEMENT AND LOAD FROM AMONG ALL THE

CYCLES

XRANGE=MAX ( ABS (MAXX) , ABS (MINX)

)

YRANGE=MAX(ABS (MAXY) ,ABS (MINY)

FIND THE SCALES FOR THE X AND Y AXES

XFACTOR=XSIZE/ (2 . *XRANGE)

YFACTOR=YSIZE/ (2 . *YRANGE)

DRAW THE CURVE

THE OUTER LOOP IS USED TO THICKEN THE LINES IN THE PLOT

3010 DO 210 J=l,4

SCALE THE DATA AND LOAD IT INTO INTEGER* 2 VECTORS

DO 200 I=1,NPTS

X1(I)=IFIX(X(I) *XFACTOR) + J - 2 + OFFSETX

Y1(I)=IFIX(Y(I) *YFACTOR) + J - 2 + OFFSETY

00 CONTINUE

AGAIN IF NCOUNT > 0, THE AXES WILL ALREADY HAVE BEEN

DRAWN AND DO NOT NEED TO BE REDRAWN

IF (NCOUNT. GT.O) GOTO 211

CALLVAL8(30) ! WHITE

DEFINE THE ENDS OF THE X & Y AXES

OFFXl = ( -XSIZE/2 + OFFSETX)

OFFYl = ( -YSIZE/2 + OFFSETY)

OFFX2 = ( XSIZE/2 + OFFSETX)

OFFY2 = (YSIZE/2 + OFFSETY)

260
ooo

ooo

non

ooo

oooo

ooo

oooooto

o

ooo

ooo

ooo DRAW THE X-AXIS

DO 213 IM = 1,3

CALL MOVABS (OFFXl , OFFSETY+IM-2

)

CALL DRWABS(0FFX2, OFFSETY+IM-2)

DRAW THE Y-AXIS

CALL MOVABS (OFFSETX+IM-2 , OFFYl)

CALL DRWABS (OFFSETX+IM-2 , 0FFY2

)

13 CONTINUE

DRAW POLYGON

11 CALL VAL8 (NCOUNT)

CALL PRMFIL(O)

CALL MOVABS (XI (1) ,Y1(1)

)

DO 215 II = 2,NPTS

CALL DRWABS (XI (II) ,Y1 (II)

)

5 CONTINUE

DRAW LEGEND

IF J = 1, FILL THE RECTANGLE WITH COLOR VALUE = NCOUNT

IF(J.EQ.l) CALL PRMFIL(l)

IF(J.EQ.l) CALL VAL8 (NCOUNT)

IF J = 2, OUTLINE THE RECTANGLE IN WHITE

IF(J.EQ.2) CALL PRMFIL(O)

IF(J.EQ.2) CALL VAL8(30)

IF J > 2, THE LEGEND DOES NOT NEED TO REDRAWN AND THE

PROGRAM SKIPS THE NEXT SECTION

IF(J.GT.2) GOTO 212

DEFINE THE UPPER LEFT CORNER OF THE RECTANGLE

LEY = -25 - 22*NCOUNT

DEFINE THE LOWER RIGHT CORNER OF THE RECTANGLE

REY = LEY - 25

DRAW THE RECTANGLE

CALL MOVABS (385, LEY)

CALL RECTAN(410,REY)

LABLE LEGEND

261
CALL MOVABS (430,REY)

CALL TEXTN(30, 30, 0, 0)

CALL VAL8(30)

C

C USE DO LOOP TO CREATE BOLD EFFECT

C

DO 400 I = 1,4

CALL MOVREL(IDX(I) ,IDY(I)

)

CALL TEXTl (40, TITLE)

4 00 CONTIInTUE

212 CONTINUE

CALL EMPTYB

210 CONTINUE

C

NCOUNT=NCOUNT+

IF (NAUTO .EQ. 1) GOTO 500

TYPE *

, ' ' TYPE *, 'ANOTHER CYCLE ? 1 = YES, 0 = NO

READ *,ANS

IF (ANS.EQ.O) GOTO 1000

goto 500

c

1000 CLOSE (1)

C

C PROMPT USER FOR COLOR CHANGE

C

10005 TYPE CHANGE COLORS ? 1 = YES, 0 = NO'

READ *,ICANS

C

C IF NO COLOR CHANGE IS NEEDED, GO TO THE END OF THE

C SUBROUTINE

C

IF(ICANS.EQ. 0) GOTO 10001

C

C DETERMINE IF THE BACKGROUND COLOR IS TO BE CHANGED

C

TYPE BACKGROUND COLOR, CHANGE ? 1 = YES, 0 = NO

READ *, IBACK

C

C IF NO CHANGE TO THE BACKGROUND COLOR IS NEEDED, ASK USER

C FOR THE NEXT COLOR CHANGE

C

IF(IBACK.EQ.O) GOTO 10002

C

C IF SO, PROMPT USER FOR COLOR VALUES

C

TYPE *,' ENTER VALUES FOR RED, GREEN BLUE'

READ *,IRED,IBLUE,IGREEN

C

C CHANGE THE COLOR VALUES FOR THE BACKGROUND IN THE

C LOOK-UP TABLE TO THE ONE ASKED FOR BY THE USER

C

CALL LUT8(31,IRED,IBLUE,IGREEN)

CALL EMPTYB

C

262
ooo

oooo

oooo

10002 TYPE *,'AXES AND TITLE COLORS, CHA.NGE ? 1

READ *,IAXIS

YES, 0 = NO I

IF NO COLOR CHANGE TO THE AXES OR TITLES IS NEEDED, LOOP

BACK AND PROMPT USER FOR COLOR CHANGE AGAIN

IF(IAXIS.EQ. 0) GOTO 10005

TYPE ENTER VALUES FOR RED, GREEN, BLUE’

READ *, JRED, JGREEN, JBLUE

CHANGE THE COLOR VALUES FOR THE AXES AND TITLES IN THE

COLOR LOOK-UP TABLE TO THE ONE ASKED FOR BY THE USER

CALL LUTS (30, JRED, JGREEN, JBLUE)

CALL EMPTYB

LOOP BACK AND PROMPT USER FOR COLOR CHANGE

GOTO 10005

10001 CONTINUE

C

RETURN

END

263
c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

k-k-k-k-k-k-k-kicie-kicifk-k-k-k-kic-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-kifkifk-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k SUBROUTINE REDRAW_BARS

PURPOSE: USED TO ERASE AND REDRAW THE BARS REPRESENTING THE

INDIVIDUAL ENERGY SO THAT THE USER MAY INTERACTIVELY

SCALE THE ENERGY VALUES

CALLED FROM SUBROUTINE COMPARE

USAGE : CALL REDRAW_BARS ( BLIST , TESTNO , SCALE , TEST , ORIGINX

,

ORIGINY , CSCALEY , ISIZE , ISCALEX , YIELD , CONC_COMP

,

REPEAT)

PARAMETERS

TRANSFERRED INTO THE SUBROUTINE:

BLIST

TESTNO

SCALE

ORIGINX

ORIGINY

ISIZE

CSCALEY

ISCALEX

YIELD

CONC COMP

THE NAME TO THE TEST TO BE REDRAWN

THE NUMBER OF THE TEST TO BE REDRAWN

SCALE USED TO MODIFY THE ENERGY,

X-COORDINATE OF THE ORIGIN OF THE AXES

Y-COORDINATE OF THE ORIGIN OF THE AXES

SIZE OF THE TEXT

SCALE FOR THE Y-AXIS, USED TO CONVERT FROM UNITS

OF ENERGY TO NUMBER OF PIXELS

SCALE FOR THE X-AXIX, USED TO DEFINE THE WIDTH OF

THE BARS

YIELD DISPLACEMENT OF A PARTICULAR TEST

CONCRETE COMPRESSIVE STRENGTH

TRANSFERRED OUT TO SUBROUTINE COMPARE:

PRE_SCALE ARRAY WHICH STORES THE SCALE FACTOR FOR EACH TEST.

SCALING IS CUMULATIVE. I.E. IF A TEST HAS BEEN

SCALED BY A FACTOR OF "a” AND SCALING OF THE SAME

TEST IS ASKED FOR AGAIN, THIS TIME BY A FACTOR OF

"b” THE RESULTING ENERGY THAT IS PLOTTED IS

SCALED BY ab.

SUBROUTINE SPECIFIC PARAMETERS:

ENERGY (I)

SCALED_ENER

ATITLE

BTITLE

ATIT

REPEAT

NOCYCLE

ENERGY FOR CYCLE I

(I) THE SCALED ENERGY I.E. ENERGY*SCALE

TITLE OF THE FILE FOR A CYCLE. THIS FILE CONTAINS

THE TITLE OF THE CYCLE, ATIT AND THE DATA POINTS

OF THAT CYCLE.

EQUAL TO ATITLE WITH ".OUT" EXTENSION

TITLE OF A CYCLE IN FILE ATITLE

VARIABLE USED TO DETERMINE IF A TEST HAS BEEN

SCALED PREVIOUSLY

ARRAY WHICH STORES THE NUMBER OF CYCLES FOR EACH

TEST ***************************************************************

264
ooo

ooo

toHOOo

ooo

non

ooooo

o

o

o

o

o

o

oo SUBROUTINE REDRAW_BARS ( BLIST , TESTNO , SCALE , TEST , ORIGINX

,

1 ORIGINY , CSCALEY , ISIZE , ISCALEX , YIELD , CONC_COMP , REPEAT

,

2 PRE_SCALE)

INTEGER*2 TESTNO , TEST ( 3 , 100 ) ,IDX(16) ,IDY(16)

,

1 INTITLE (7, 50, 50) , ORIGINX, ORIGINY , XO , YO , XI , Y1 , X2 , Y2

,

2 REPEAT (3) ,ISIZE

CHARACTER* 18 BLIST, BTITLE

CHARACTER* 14 ATIT(50,50) ,ATITLE

DIMENSION ENERGY(50,50) , SCALED_ENER ( 50 , 50 ) ,YIELD(3)

,

1 CONC_COMP ( 3 )

, NOCYCLE (50), PRE_SCALE ( 3

)

EQUIVALENCE (ATIT , INTITLE)

DATA IDX/0, 1,0, -1,0, 1,1, 0,0, 1,0,0, 0,-1, -1,-1/,

1 IDY/ 0 , 0 , 1 , 0 , 1 , 0 , 0

, -1 , -1 , 0 , 1 , 1 , 1 , 0 , 0 , 0/

CHECK IF THE TEST HAS BEEN SCALED BEFORE, IF IT HAS THE

ENERGY PER CYCLE WILL NOT BE INITIALIZED BUT REMAIN AS IT

PREVIOUSLY WAS

IF(REPEAT(TESTNO) .GT.O) GOTO 140

OPEN THE FILE WHICH CONTAINS THE LIST OF THE TITLE OF EACH CYCLE

OPEN ( 1 , FILE=BLIST , ACCESS= ' SEQUENTIAL ' , FORM= ' FORMATTED '

,

1 STATUS= ' OLD '

)

REWIND 1

INITIALIZE VARIABLE USED AS A COUNTER OF THE NUMBER OF CYCLES

JJ = 1

READ THE TITLE OF THE CYCLE

0 READ ( 1 , FMT=2 0 , END=100 ) ATITLE

0 FORMAT (A14)

BTITLE = ATITLE// ' . OUT

OPEN THE FILE WHICH CONTAINS THE ENERGY ABSORBED FOR A CYCLE

OPEN ( 2 , FILE=BTITLE , ACCESS= ' SEQUENTIAL ' , FORM= ' FORMATTED '

,

1 STATUS= ' OLD '

)

REWIND 2

READ THE TITLE OF THE CYCLE AND THE ENERGY

READ (2, 20) ATIT ( TESTNO, JJ)

READ (2 , 30) ICOUNT, ENERGY ( TESTNO, JJ)

30 FORMAT (8X, 110, 7X,F10. 5)

265
no

ooo

ooo

ooo

ooo

oooo

ooo

o

non

h

oooo NORMALIZE THE ENERGY BY THE YIELD DISPLACEMENT AND CONCRETE

COMPRESSIVE STRENGTH

ENERGY (TESTNO,JJ) = ENERGY (TESTNO , JJ) / (YIELD (TESTNO)

1 CONC_COMP(TESTNO)

)

JJ = JJ + 1

CLOSE (2)

GOTO 10

CONTINUE

CLOSE (1)

SCALE THE ENERGY

NOCYCLE (TESTNO) = JJ

140 DO 50 M = 1, NOCYCLE (TESTNO)

SCALED_ENER( TESTNO, M) = ENERGY (TESTNO , M) *SCALE

0 CONTINUE

CALL PRMFIL(l)

BEGIN LOOP TO ERASE THEN DRAW THE BARS

DO 110 I = 1, NOCYCLE (TESTNO)

FOR K = 1, ERASE THE OLD BAR

FOR K = 2, DRAW THE NEW BAR

DO 120 K = 1,2

IF(K.EQ.l) CALL VAL8(48) I BACKGROUND, GRAY

IF(K.EQ.2) CALL VAL8 ( 49+TESTNO)

DEFINE THE LOWER LEFT COORDINATES OF THE BAR

XO = ORIGINX + 3 + (TEST (TESTNO, I) -1) *ISCALEX

YO = ORIGINY + 3

DEFINE THE UPPER RIGHT CORNER OF THE BAR

XI = ISCALEX + XO

IF(K.EQ.l) Y = ENERGY (TESTNO, I)

IF(K.EQ.2) Y = SCALED_ENER (TESTNO, I)

Y1 = IFIX(Y*CSCALEY) + ORIGINY

ERASE/ DRAW THE BAR

CALL MOVABS(X0,Y0)

CALL RECTAN(X1, Yl)

DEFINE THE COORDINATES TO PLACE/ERASE THE TITLE OF THE CYCLE

X2 = XI - 7

Y2 = Yl + 5

SET COLOR VALUE TO GRAY TO ERASE AND BLACK TO REDRAW

266
c

IF(K.EQ.l) CALLVAL8(48) i GRAY

IF(K.EQ.2) CALLVAL8(51) 1 BLACK

C

C SET THE TEXT SIZE AND ORIENTATION

C

CALL TEXTC(ISIZE,90)

C

C MOVE TO THE COORDINATES TO PLACE THE TITLE

C

CALL MOVABS(X2,Y2)

DO 130 L = 1,4

CALL MOVREL(IDX(L) ,IDY(L)

)

CALL TEXTl ( 14 , INTITLE ( 1 , TESTNO , I )

)

130 CONTINUE

120 CONTINUE

110 CONTINUE

C

C SET REPEAT = TESTNO

C

REPEAT (TESTNO) = TESTNO

C

C SET ENERGY TO SCALED ENERGY

C

DO 150 I = 1, NOCYCLE (TESTNO)

ENERGY (TESTNO,!) = SCALED_ENER (TESTNO , I)

150 CONTINUE

C

C MULTIPLE THE PREVIOUS SCALE BY THE NEW SCALE AND STORE IT IN

C PRE_SCALE TO KEEP TRACK OF THE SCALE FOR EACH TEST

C

PRE_SCALE (TESTNO) = SCALE*PRE_SCALE (TESTNO)

C

CALL EMPTYB

RETURN

END

267
APPENDIX C: TEIE-DIE^ECncmL TESIII^G EACHJTY (TTF)

The installation of the TTF at NBS began in 1981 and was conpleted in 1984.

Its capabilities include application of controlled displacements and/or

forces in three orthogonal directions simultaneously as well as moments

about each axis. One of the uses of the TTF is for "quasi-static"

testing. Specimens approximately 10 ft. (3.05 m) in length, 10 ft.

(3.05 m) wide and 12 ft. (3.66 m) high or smaller could be tested in the

TTF.

The loading surface of the TTF consists of two crossheads. The lower

crosshead is attached to a structural tie-down floor. The upper crosshead

is attached to the lower one by means of three double-ended hydraulic

actuators which are part of a general closed-loop, servo-controlled

hydraulic system. Each of the vertical hydraulic actuators has a total

stroke of 12 in. (300 mm) and a load capacity of 150 kips (670 kN) in

tension and coirpression. The horizontal actuators, parallel to the northsouth axis of the TTF, have a stroke of 12 in. (300 mm) and a load capacity

of 85 kips (380 kN) in tension and compression each. The horizontal

actuator parallel to the east-west axis of the TTF has a stroke of 6 in.

(150 mm) and a load capacity of 220 kips (975 kN) in tension and

compression. The horizontal actuators are attached by swivel end fittings

to the crossheads and vertical post-tensioned concrete buttresses which

serve as relatively stiff reaction walls. The vertical actuators also have

swivel end fittings which are used to attach the bottom crosshead to the

upper crosshead. These swivel fittings allow the actuators to have an

unrestrained rotation of 270° in the plane of the swivel and about 10° in

the other planes. The hydraulic actuators, data acquisition and data

manipulation are controlled by a DEC PDF 11/34 computer. A schematic of

the TTF is shown in Fig. C.1 with a model column installed and a photograph

of a model being tested in the TTF is shown in Fig. C.2.

268
E

Schematic of TTF

FIGURE C1

269
270

jyiodel

in
irS-iUA

w.S. 3“PT. 0.- COMM.

BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Puolication Date

SHEET (See instructions} MBSIR 86-3494 J-AUU.VRY 1987

4. Tl : Lc: AN C 5U 3TITLE

BEHAVIOR. OF 1/6-SCALE MODEL BRlDGh COLUMNS SUBJECTED TO CYCLIC INELASTIC LOADI^JC

5. AUTHOR(S)

Ceraldine S. Cheok and William C. Stone

6. PERFORMING ORGANIZATION (If joint or other than N BS, see in struction s) NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

1. National Science Foundation (NSF)

2. National Bureau of Standards (NBS)

3. Federal Highway Administration (FH^vA)

4. California Department of Transportation (CALTRANS)

10.

SUPPLEMENTARY NOTES

I

i Document describes a computer program; SF-135, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-^ord or less factual summary of most significant information , If document includes a si gn i fi cant

bi bliography or literature survey, mention it here)

Circular, spirally reinforced concrete bridge columns were subjected to cyclic

inelastic loading in the laboratory. The bridge columns were one-sixth scale models

of prototype columns designed in accordance with current California Department of

Transportation specifications. A total of six models were tested. Three of the models

were constructed with microconcrete, and three were constructed with ready-mix concrete

using pea gravel. Variables included the aspect ratio, magnitude of axial load, and

the use of microconcrete versus ready-mix. The models were subjected to slow reversed

cyclic loading with the axial load held constant. Results from the tests are presented

in the form of energy absorption, load—displacement curves, longitudinal steel strains,

and displacement profiles. Comparisons of the ultimate moment capacities, measured

displacement ductilities, plastic hinge lengths, and the failure mode for the six models

are discussed. Comparisons with previous studies are presented along with a discussion

of design codes in the U.S., New Zealand, and Japan. A series of graphics-based

computer programs, developed to speed the analysis and interpretation of the experimental data, are discussed. Source code is provided.

12.

KEY WORDS (Six to twelve entries; alphabet! cal order; capitalize only proper names; and separate key words by semicolon sj Behavior; Bridge Columns; computer graphics; concrete; ductility; energy

absorption capacity; failure; lateral load; microconcrete; modelling; plastic hinge

13. availability

y; Uni imited

: For Official Distribution. Do Not Release to NTIS

, i Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

291

15. Price

$24.95

USCOMM-OC 6043-P30
.?v \

1.

"j r,.-

. '*' b«* j*o»<T ^

r ./ • n rtV dW

I

' ii > o • •» y ^‘•

..'v: , "1 '

’ j. /*

;0)li|aM*tr 10 UA3A01 Jt^

JOH Jur*** 10 T0yf5

I t.o

•‘‘Tf

• ^ %Mr

r.'^v »>n*t68 im

K . ^.y| -? Jjj^* y,, iH

.c

‘‘ - • 'f: f

i

»fr-f .^i'- . •••• ’•i^ ^ - • •' •• ’ V 7

.cO

o-v IJOl

Vj ', v^,-*» * ;. ^r‘ I

' '

^!...

' •':?^./ ;-. ^ '"

' ’ ; '«ndLr' < 4*'-^ '

' ..'

f-t. -Ijsfj

«•• -;» • •'*

r : ‘j’' J «' > < '*^ - ‘

•• ^ ,.' . ’.in / j

- ' *^i' ’l^' • ^ r It

lO-l

i.' '':, sr '-/ .

'*'*7'

< il T L f I •' - w y* > . n" f. ' f . '^ -'''•^ i, -w

.j

. .. .„

• ( •.; vii--

• • ^ •< »r

I

.' “

-» f."-«

' - ^

Titir

;’ **7

. " vC ; (

. ‘

-'u. ' .yil’C^bor, ;a.ioT->ir«V7:'l« ^0

,1 *_'

. ' »

' " t

f

I • dv-‘- '.- r

' -

'' a

'1

I ^ ^l•^^

ii tgi -- —

Q0M^«»kV ; V ^ ^ g; V

Aw W

rta nl \ ^

mubblia'

a«3oLi^3iljt90^ ^

.10 4»lw

*V .

:! 10X9000.1

iXfi ortJ fioJtv

iro»^ )MJ^A

^nmJ>^,.>OIi5otq jj

..hr* ::l3&Blq ,8»lottX9d^^

vf^iq rtstv «A08il0<|00C3*

orfi OLt

br^I

...^

i

I,