Strengthening of Existing Continuous Composite...

K. F. Dunker F. W. Klaiber F. K. Daoud W. E. Wiley W. W. Sanders, Jr. July 1987

Strengthening of Existing Continuous Composite Bridges

Sponsored by the Highway Division, Iowa Department of Transportation, and the Iowa Highway Research Board

.,:' .1 ·,,~ I.~··\~·{" • •

c ..:_~ eng1neer111:g research institute

iowa state university

f;t.. Iowa Department ~l of Transportation

The procedures and recommendations expressed in this report are those of the authors and not necessarily those ot the Highway Division ot the Iowa Department of Transportation.

Final Report K. F. Dunker F. W. Klaiber F. K. Daoud W. E. Wiley W.W. Sanders, Jr.

July 1987

Strengthening of Existing Continuous Composite Bridges

Sponsored by the Highway Division, Iowa Department of Transportation and the Iowa Highway Research Board Iowa DOT Project HR-287 ER! Project 1846 ISU-ER!-Ames-88007

Engineering Research Institute Iowa State University

Iowa Department of Transportation

v

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

ABSTRACT

1. INTRODUCTION

1.1. Background

1.2. Objectives and Scope

1.3. Research Program

1.4. Literature Review

1.5. Selection and Rating of Prototype Bridge

2. DESCRIPTION OF TEST SPECIMENS

2.1. Model Bridge

2.1.1. Description

2.1.2. Physical Properties

2.1.2.1. Concrete

2.1.2.2. Steel

2.2. Full-scale Negative Moment Region Mockup

2.2.1. Description


2.2.2.1. Concrete

2.2.2.2. Steel

3. TESTS AND TEST PROCEDURES

3.1. Model Bridge Instrumentation and Tests

3.1.1. Instrumentation

3.1.2. Post-tensioning Tests--Positive Moment Regions

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1

3

3

4

5

7

32

39

39

39

50

50

53

53

54

60

60

60

63

63

63

66

vi

3.1.3. Post-tensioning Tests--Negative Moment Regions

3.1.4. Post-tensioning Tests--Positive and Negative Moment Regions

3.1.5. Vertical Load Tests

3.1.6. Combination Tests--Vertical Load Plus Post-tensioning

3.2. Instrumentation and Tests for the Full-scale Negative Moment Region Mockup

72

73

74

77

77

3.2.1. Instrumentation and Vertical Load Mechanism 77

3.2.2. Preliminary Vertical Load Tests 86

3.2.3. Post-tensioning Tests--Straight Tendons 88

3.2.4. Post-tensioning Tests~-Harped Tendons 91

4. ANALYSIS AND TEST RESULTS 97

4.1. Model Bridge Analysis and Test Results 97

4.1.1. Preliminary Analysis 97

4.1.2. Finite Element Analysis 101

4.1.3. Strain and Deflection Data Interpretation 109

4.1.3.1. Time Effects 109

4.1.3.2. Symmetry 111

4.1.3.3. Superposition 114

4.1.4. Effects of Post-tensioning 119

4.1.4.1. Single Beam Schemes 119

4.1.4.2. Multiple Beam Schemes 131

4.1.4.3. Distribution 144

4.1.4.4. Tendon Force Changes 145

4.1.5. Effects of Vertical Loads 152

vii

4.2. Analysis and Test Results for the Full-scale Negative Moment Region Mockup

4.2. 1. Analysis

4.2.2. Preliminary Vertical Load Tests

4.2.3. Effects of Post-tensioning

4.2.4. Effects of Vertical Loads

4.2.5. Tendon Force Changes

5. SUMMARY AND CONCLUSIONS

5. 1. Summary

5.2. Conclusions

6. RECOMMENDED FURTHER RESEARCH

7. ACKNOWLEDGEMENTS

8. REFERENCES

APPENDIX .A: Framing Plans and Details for the Model Bridge

APPENDIX B: Plans and Details for the Fullscale Negative Moment Region Mockup

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207

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LIST OF FIGURES

Fig. 1.1. Two-span, prestressed steel truss for an aircraft hangar in Melsbroeck, Belgium, circa 1953. 10

Fig. 1.2. Experimental two-span, prestressed composite beam, circa 1964. 10

Fig. 1.3. Three-span, prestressed composite girder for an Oakland, California apartment building, circa 1967. 12

Fig. 1.4. Concept for strengthening of a two-span steel beam by post-tensioning, circa 1968. 12

Fig. 1.5. Concept for a two-span, prestressed steel beam, circa 1968. 14

Fig. 1.6., Six-span Welland Canal Bridge, Canada, strengthened by post-tensioning, 1968. 14

Fig. 1.7. Two-span, wrought iron truss bridge in Aarwangen, Switzerland, strengthened by post-tensioning, 1969. 16

Fig. 1.8. Concept for a four-span, prestressed steel beam, circa 1969. 16

Fig. 1.9. Concept for a two-span, prestressed steel beam, circa 1975. 18

Fig. 1.10. Six-span bridge over the Rhone River, France, strengthened by post-tensioning, 1975-76. 18

Fig. 1.11. Multiple-span, Erskine Bridge over Clyde River, Scotland, strengthened by post-tensioning, 1976. 20

Fig. 1.12. Steel stringers in Pit River Bridge, California, strengthened by post-tensioning, 1979., 20

Fig. 1.13. Concept for reduction of deflection in simple span bridges, West Germany, circa 1980. 22

Fig. 1.14. Three-span bridge over the Netekanaal, Belgium, strengthened by post-tensioning, 1981. 22

Fig. 1.15. Five-span bridge over Rhone River, France, strengthened by post-tensioning, 1981. 24

x

Fig. 1.16. Experimental, two-span, prestressed composite bridge model, circa 1982. 24

Fig. 1. 17.

Fig. 1.18.

Fig. 1.19.

Fig. 1.20.

Fig. 1. 21.

Fig. 1.22.

Fig. 1.23.

Fig. 2.1.

Fig. 2.2.

Fig. 2.3.

Fig. 2.4.

Fig. 2.5.

Fig. 2.6.

Fig. 2. 7.

Fig. 2.8.

Fig. 2.9.

Fig. 3.1.

Fig. 3.2.

Fig. 3. 3.

Nine-span bridge over Highway L284, West Germany, strengthened by post-tensioning, circa 1983. 26

Multiple-span Autobahn bridge, West Germany, strengthened by post-tensioning, 1984. 26

Three-span Waiwaka Terrace Bridge, New Zealand, strengthened by post-tensioning, 1985. 28

Ten-span prestressed composite girder, Bonners Ferry Bridge, Idaho, circa 1985. 28

Experimental, two-span bridge model, circa 1986. 30

Prototype V12(1957) series bridge, 125-ft length. 33

Critical stress locations and beam stiffness assumptions, prototype Vl2(1957) series bridge. 36

Model bridge. 40

Photographs of model bridge. 41

Model bridge coordinates. 44

Pouring of concrete deck for model bridge. 47

Support tie-down system. 48

Concrete dead weight. 51

Correlation between full-scale mockup and prototype. 55

Full-scale mockup. 56

Photographs of mockup. 58

Locations of strain-gage sections. 64

Location of post-tensioning system in positive and negative moment regions. 67

Post-tensioning schemes (PTS) employed on bridge model. 70

xi

Fig. 3.4. Locations of vertical load points. 76

Fig. 3.5. Vertical loading mechanism for full-scale mockup. 80

Fig. 3.6. Photographs of end conditions for the full-scale mockup. 81

Fig. 3.7. Strain gage locations for full-scale mockup. 82

Fig. 3.8. Vertical displacement measurement (DCDT) locations, on full-scale mockup. 84

Fig. 3.9. Threadbar tendon arrangement. 89

Fig. 3.10. Harped cable arrangement. 92

Fig. 4.1. Moment diagrams for three-span beam, negative moments applied to spans. 99

Fig. 4.2. Moment diagrams for three-span beam, positive moments applied near interior support. 100

Fig. 4.3. SAP IV finite element model. 103

Fig. 4.4. Quarter symmetry finite element model. 106

Fig. 4.5. Load cases analyzed with SAP IV finite element model. 107

Fig. 4.6. Bottom flange strains for PTS-9. 112

Fig. 4.7. Bottom flange strains for PTS-9 and super-position of PTS-1 through PTS-6. 116



Fig. 4.10. Bottom flange strains for PTS-1 + PTS-3 + PTS-5. 124


Fig. 4.12. Bottom flange strains for PTS-10 + PTS-16. 127


Fig. 4.14. Bottom flange strains for PTS-12 + PTS-17. 130

Fig. 4.15. Top and bottom flange strains for LC2 and PTS-9. 132

xii

Fig. 4.16. Bottom flange strains for LC 9. 135


Fig. 4.18. Bottom flange strains for LC 6 and PTS-20. 138

Fig. 4.19. Bottom flange strains for LC 18 and PTS-21, Stage 2. 139

Fig. 4.20. Bottom flange strains for LC 5 and PTS-21. 141


Fig. 4.22. Percent of increase or decrease in the tendon force for PTS-21. 150

Fig. 4.23. Percent of increase or decrease in the tendon force for PTS-9. 151

Fig. 4.24. Bottom flange strains for 6-kip vertical load at LP 1 and LP 3. 154



Fig. 4.27. Load-deflection curves for initial vertical loading, Test 1. 160

Fig. 4.28. Final crack pattern in full-scale mockup deck. 162

Fig. 4.29. Strains at Section 4 for full-scale mockup with post-tensioning.


Fig. 4.31. Load-deflection curves for straight tendon post-tensioning and vertical load.

Fig. 4.32. Load-deflection curves for harped tendon post-tensioning and vertical load.

Fig. 4. 33. Strains at Section 4 for full-scale mockup with vertical load and post-tensioning.

164

165

167

169

170

xiii

Fig. 4.34. Strains at Section 5 for full-scale mockup with vertical load and post-tensioning.

Fig. 4.35. Change in tendon force.

Fig. A.1. Framing plan.

Fig. A.2. Exterior beam: EB-1, EB-2.

Fig, A.3. Interior beam: IB-1, IB-2.

Fig. A.4. Shear lug plan.

Fig. A.5. Shear lug details.

Fig. A.6. Weld and stiffener layout.

Fig. A.7. Stiffener details.

Fig. A.8. Splice details.

Fig. A.9. Tab layout.

Fig. A.10. Tab details.

Fig. A.11. Diaphragms.

Fig. A.12. Bearing details.

Fig. A. 13. Bracket details.

Fig. B.l. Steel beam layout elevations.

Fig. B.2. Coverplates.

Fig. B.3. Bearing stiffeners, Section A-A.

Fig. B.4. Shear lugs.

Fig. B.5. Composite beam, Section B-B.

Fig. B.6. Deck-reinforcing plan.

Fig. B.7. Deck blockout and insert plan.

Fig. B.8. Bracket for threadbar tendon.

Fig. B.9. Bottom flange strengthening angles.

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216

xiv

Fig. B.10. Bracket for cable tendons.

Fig. B.11. Saddle for cable tendons.

Page

217

219

xv

LIST OF TABLES

Table 1.1. Overstress with respect to allowable inventory stress, prototype V12(1957) series bridge. 36

Table 2.1. Physical properties of concrete. 52

Table 3.1. Vertical load tests. 75

Table 3.2. Mockup tests. 78

Table 4.1. Comparisons of bottom flange strains between symmetrical sections for PTS-9. 113

Table 4.2. Comparisons of bottom flange strains between vertical load tests with and without superposition. 117

Table 4.3. Variation in tendon force because of applying additional post-tensioning. 147

ABSTRACT

The need for upgrading a large number of understrength and obsolete

bridges in the United States is well known, and Iowa has many of the

bridges that require upgrading. Iowa began designing and constructing

continuous span, composite bridges earlier than other states, and con

sequently, there are many such bridges in Iowa. Because of changes in

bridge design standards and increases in truck loads, a considerable

number of the continuous, composite bridges in Iowa require posting for

reduced loads.

The posted bridges, if in otherwise good condition, often can be

strengthened at a cost considerably less than replacement cost. Because

strengthening should be based on adequate testing and design information,

the research described in this report was conducted to investigate the

potential of strengthening continuous bridges by post-tensioning.

The research program conducted and described in this report

included the following: a literature review, selection and rating of

a prototype continuous composite bridge, tests of a one-third-scale

continuous composite bridge model, finite element analysis of the bridge

model, and tests of a full-scale composite beam mockup for a negative

moment region.

The research program indicated that the strengthening of continu

ous, composite bridges is feasible. The primary objective in applying

the post-tensioning should be to provide moments opposite to those pro

duced by live and dead loads. Longitudinal distribution of that post

tensioning always must be considered if only exterior or only interior

beams are post-tensioned. Testing and finite element analysis showed

that post-tensioning of positive moment regions with straight tendons

was more effective than post-tensioning negative moment regions with

straight tendons. Changes in tension in tendons may be either benefi

cial or detrimental when live loads are applied to a strengthened bridge

and thus must be carefully considered in design.

3

1. INTRODUCTION

1.1. Background

Nearly half of the approximately 600,000 highway bridges in the

United States were built before 1940. The majority of those bridges

were designed for lower traffic volumes, smaller vehicles, slower speeds,

and lighter loads than they experience today. To compound the problem

further, maintenance has not been adequate for many of these older

bridges. Almost 40% of the nation's bridges are classified as deficient

and thus in need of rehabilitation or replacement according to the

Federal Highway Administration. The deficiency in some of these bridges

is their inability to carry current legal live loads. Rather than

posting these bridges for reduced loads or replacing them, strengthening

has been found to be a cost-effective alternative in many cases.

Many different methods exist for increasing the live load carrying

capacity of the various types of bridges. Through Iowa Department of

Transportation (Iowa DOT) Projects HR-214 [19] and HR-238 [9,10,18], the

concept of strengthening simple span, composite steel beam and concrete

deck bridges by post-tensioning was developed. These projects took

the concept from the feasibility phase through the implementation and

design methodology phase. Two simple span bridges (one 2.2 miles north

of Terril on N 14 and the other just south of the Greene-Webster County

line on I-144) were strengthened by post-tensioning during the summer

of 1982 and retested during the summer of 1984. Results of these tests

verified that strengthening of the simple span bridges by post-tensioning

is a viable, economical strengthening technique. The design methodology

4

developed by Dunker et al. [10] provided a procedure by which the

required post-tensioning force could be determined relatively easily.

This design methodology has since been used successfully by the Iowa

DOT and other agencies for strengthening of simple span composite

bridges.

As a result of the previous success, that is strengthening of simple

span bridges by post-tensioning, this study was undertaken to extend

the method to continuous span bridges. Because Iowa began designing

and constructing continuous, composite steel beam and concrete deck

bridges earlier than most states, Iowa has a considerable inventory of

those bridges in need of rehabilitation or replacement. This study

parallels the feasibility study completed for simple span bridges, and

it is anticipated that this study will be extended to an implementation

phase, in order to field test concepts developed in this report.

1.2. Objectives and Scope

Iowa has a considerable inventory ·of continuous span, composite

bridges that are structurally inadequate according to current AASJ!TO

Standards and Iowa legal loads. On the basis of experience from pre-

vious Iowa DOT simple span strengthening projects (HR-214 and HR-238),

it appeared that post-tensioning also could be implemented to strengthen

continuous bridges. The primary objective of this study, then, was to

determine the feasibility of strengthening continuous composite bridges

by posl-tensioi1ing. More specific objectives were

• to determine the best tendon configurations: intermittent straight, continuous straight, intermittent harped, o·r con-

5

tinuous harped tendons for post-tensioning positive or negative moment regions or both.

• to determine the best method for attaching tendons in negative moment regions.

• to determine the distribution of post-tensioning forces and moments longitudinally and transversely within the bridge for various post-tensioning schemes.

• to determine whether the deck contributes to and/or could be made to contribute to the composite section in negative moment regions.

These objectives were pursued by the research team through under-

taking a comprehensive literature review, testing a one-third scale

bridge model in the Iowa State University (ISU) Structural Engineering

Research Laboratory, testing of a full-scale mockup of a composite

bridge beam in the laboratory, and conducting a finite element analysis

of the laboratory bridge model for various combinations of post-tensioning

forces and vertical loads.

1.3. Research Program

The research program consisted of the distinct parts outlined

above but with an emphasis on laboratory testing. Initially a compre-

hensive literature review was performed, which extended beyond the

earlier literature reviews for simple span structures (9,18,19]. The

review made use of the many international references obtained in the

National Cooperative Highway Research Program (NCHRP) Project "Methods

of Strengthening Existing Highways Bridges" (20].

In order to begin the laboratory testing program, the researchers

consulted with the Iowa DOT Office of Bridge Design and obtained plans

6

for standard continuous, composite bridges. From the various sets of

plans the V12(1957) series of composite, three-span bridges was selected,

and from that series, a 125-ft-long prototype bridge was chosen. The

prototype bridge was rated for bending stress in order to determine

amounts and locations of overstress.

From the prototype bridge plans, a one-third scale model was

designed and constructed in the ISU Structural Engineering Research

Laboratory. The steel beams for the model were built up from steel

strip and plate because no wide flange sections were available that

would accurately model the prototype bridge beams at one-third scale.

The beams were fitted with steel tabs which served as attachments for

brackets for straight tendons in all negative moment regions and in

positive moment regions for the exterior beams. The steel frame for

the model was instrumented with strain gages, and the concrete deck

was poured on top of the frame. The model was subjected to a variety

of post-tensioning, vertical load, and combined load schemes. During

all load tests, strains and deflections were monitored.

Also from the plans for the Vl2(1957) series of bridges, a full·

size mockup was constructed for a typical bridge beam above an interior

support. The mockup consisted of a salvaged wide flange bridge beam

on which a concrete deck was poured. Two tendon configurations were

tested on the mockup: straight, threadbar tendons and harped, cable

tendons. Along with the tendons, strengthening angles were added to

the lower region of the mockup for some of the tests. The various

load schemes in the testing program included post-tensioning and verti

cal loads. During all tests, strains and deflections were monitored.

7

Several of the preprocessing and postprocessing computer programs

from earlier research projects [9,10] were adapted for use with con

tinuous bridges such as the three-span prototype bridge. Those programs

were utilized with SAP IV [3], a well-known finite element program in

order to analyze the laboratory model bridge. For the finite element

analysis, a series of post-tensioning schemes were analyzed, which

included some of the schemes tested in the laboratory.

The results from the various parts of the research program are

summarized in this report. The literature review and rating of the

prototype are given in Sections 1.4 and 1.5, respectively. Chapters 2

and 3 describe the bridge model and mockup tested in the laboratory as

well as the test procedures employed. The results from the laboratory

testing program and the finite element analysis schemes are summarized

in Chapter 4. Following the results are the summary and conclusions in

Chapter 5.

1.4. Literature Review

Since the 1950s there have been numerous examples of prestressing

of continuous span, composite structures. The examples include both

new structures and existing structures that required strengthening.

There also has been a certain amount of laboratory testing of prestressed

continuous structures, development of analysis methods, and development

of catalogs of tendon configurations. In addition to the summary of

literature which is given below, there are literature reviews in Refer

ence [19] for simple span structures and in Klaiber et al. [20] for

simple and continuous span structures.

8

The literature review which follows is a summary of the examples

of actual structures, laboratory testing, and catalogs of tendon con

figurations available on the subject of prestressing continuous struc

tures. The examples have been arranged in chronological order and

have been selected to show the variety of concepts, the application of

the concepts, and the successes and problems when some of the concepts

were applied. Although the emphasis is on composite bridges, reinforced

concrete and prestressed concrete bridge structures and steel and com

posite building structures are included when necessary to illustrate a

full range of concepts. Many of the concepts have been explored during

the testing and analysis portions of this project, as described in

Chapters 2 through 4.

One of the first modern examples of a con.tinuous, pres tressed

steel structure was the aircraft hangar designed in the early 1950s by

G. Magnel and constructed in Melsbroeck, Belgium [12]. The two-span

truss which supports the roof near the open wall of the hangar is

illustrated in Fig. 1.1. Each span of the truss is prestressed with

two cables in a harped configuration. The tendon configuration provides

a negative moment in the positive moment regions of each span and also

a positive moment in the negative moment regions near the central sup

port. Because the negative moment near the central support is larger

than the positive moment on each span, the tendons were overlapped so

that there were four tendons above the central support. The ends of

the tendons were then anchored at truss panels with double diagonals.

The tendon configuration chosen by Magnel was optimal for the two-span

steel truss.

9

In 1964, Tachibana et al. [25] published a paper on experimental

work with two-span composite beams that simulate a two-girder bridge.

Two beams were constructed with the tendon configuration as shown in

Fig. 1.2. One beam was prestressed before the deck was poured, and

one beam was prestressed after the deck had cured. The latter is equi-

valent to a strengthening condition. During the prestressing, it was

evident that there was a certain amount of prestress loss even with

lubricated saddles and jacking from each end of the cable. Each beam

was loaded to failure with concentrated loads placed at four-tenths of

the span length from the beam ends. The beam which had been prestressed

before the deck was poured had a relatively low deck-cracking load

above the central support but had essentially the same ultimate load

as the beam prestressed after the deck had cured.

A surprising result of the tests was that the plastic hinges at

the concentrated loads and the central support formed at essentially

the same load. This would indicate that the concrete deck had the

same effect in both compression and tension. The authors attributed

this behavior to several causes:

o Even though the deck had cracked, the reinforcing continued to carry the deck tension and thus delayed the increase in tension strain in the steel beams

o The reduction in moment of inertia for the cracked section at the interior support caused moment to be shifted to the beam spans.

In the 1960s, Hoadley developed analysis methods for prestressed

composite beams. Hoadley made the suggestion that for a typical three-

span bridge beam, only the center, longest span need be prestressed

[13]. This concept was applied in the design of a three-span floor

2 CABLES tl 2 CABLE~~ STEEL TRUSSj;ip

~ 4!1tS rs rs 1 ZJ 21 ?J, 4 v e ~SJ SJ "'11 1s iS rs rs 1 2121 f'\;l> ~

I I I j,. 250.92 FEET ,.j,. 250.92 FEET ,.i

Fig. 1.1. Two-span, prestressed steel truss for an aircraft hangar in Melsbroeck, Belgium, circa 1953.

DOUBLE WEB APPLIED LOAO SAOOLE t t CONCRETE OECK STEEL BEAM ~ /

CONNECTORS WITH SHEAR "Fl ! !~ f / 1 WIRE ROPE

' I I 13.12 FEET •!• 13.12.FEET _1 1 ..

Fig. 1.2. Experimental two-span, prestressed composite beam, circa 1964.

,_ 0

11

structure for an aparLn1ent buildir1g, as sl1own in Fig. 1. 3. The straight

tendons over the central region of the center beam span were tensioned

so as to reduce the tension in the composite concrete deck over the

supports and thus to minimize cracking. Because of longitudinal distri

bution, the moments generated by the eccentric tendons also reduced

the stresses in the bottom flange of the beam over the center span and

over the interior supports.

In 1968 Kandall [16] pointed out the differences between the pur

pose for prestressing concrete and the purpose for prestressing steel

beams. For concrete the purpose is to overcome the tension weakness

of concrete; whereas for steel the purpose is to reverse the effect of

the applied loads. The prestressing method which Kandall suggested

for strengthening a two-span steel beam, which is illustrated in

Fig. 1.4, actually involves attaching supplementary load-carrying

mechanisms to the beam. The existing steel beam provides lateral sup

port for new, free-to-slide compression members and attachment for

tendon brackets for the harped tendons. By adding the compression

members, the undesirable effect of the axial force caused by the post

tensioning does not affect the beam. By placing the compression member

near the top of the steel beam and anchoring tendons near the bottom

of the steel beam, a larger eccentricity is utilized to reduce the

required tendon force. If a tendon is simply applied near the

flange of a steel beam, the eccentricity will be only half as large as

that achieved by Randall's mechanism.

Several Polish authors prepared an analysis reference for pre

stressed steel structures, which was then translated and published in

22-INCH DEEP STEEL PLATE GIRDER

16 1/4-INCH DIA. WIRES EACH SIDE .( 7-INCH PRESTRESSED CONCRETE SLAB !·· • ..-.... T ·.·~ •D-. "!: :,.·,. ~ • f .•,:"'$: ·: .-•• -;. ··'<'"''': ;,:; •• ·._ ·!!'. ••• ·.: ...

p I I I 1- 15. 33 FEET .. L 27 .33 FEET _i_ 15.33 FEET _i .....

CONTINUOUS

~---·---------·- --1

Fig. 1.3. Three-span, prestressed composite girder for an Oakland, California apartment building, circa 1967.

FREE COMPRESSION MEMBER

BRACKET TO REDUCE BUCKLING LENGTH OF COMPRESSION MEMBER TENDON BRACKET

l(Qz! : 2f'¢/' : ?!JI ~:~::~ :::~oN

Fig. 1.4. Concept for strengthening of a two-span steel beam by post-tensioning, circa 1968.

-"'

13

German in 1968 [5]. The reference includes a variety of straight and

harped tendon configurations for simple and continuous span structures.

The configuration illustrated for a two-span steel beam in Fig. 1.5 is

one of the configurations. The tendon configuration is similar to that

utilized earlier by Magnel and bears a strong resemblance to a bent-bar

pattern for a two-span reinforced concrete beam.

One of the alternatives for strengthening an existing simple span

structure is to post-tension the structure in such a way so as to make

it a continuous structure. This alternative was utilized by Vernigora

et al. [28] in strengthening a six-span, reinforced concrete tee beam

bridge over the Welland Canal in Ontario, Canada. The harped cable con

figuration, shown for a typical span in Fig. 1.6, was employed over the

entire length of the bridge in order to provide the continuity. The

harped cable minimized the tendon force by providing maximum eccentricity

at critical moment locations and minimized the axial force component

which would cause axial shortening. Even with the reduced axial short

ening, it was necessary to replace most of the bridge bearings with new,

relatively friction-free bearings. In order to eliminate the expansion

joints between the spans and provide better lateral load transfer, ends

of beams were cut away, and new diaphragms were cast and post-tensioned.

Because the lateral distribution of the post-tensioning was unknown,

all tendons were jacked in two stages, and thus approximately equal

tendon forces were obtained.

The strengthening mechanism shown in Fig. 1.4, which Kandall pub

lished in 1968 [16], was applied to a bridge in Aarwangen, Switzerland

in 1969 [23]. The mechanism was used in order to strengthen the bridge

/STEEL TENDON /NEUTRAL AXIS

f ttt·f Ia:fb! :Lt I ' 1- STEEL BEAM

Fig. 1.5. Concept for a two-span, prestressed steel beam, circa 1968.

', ·:;.<>.'

POST-TENSIONED, REINFORCED CONCRETE DIAPHRAGM

REINFORCED CONCRETE TEE SADDLE 2 CABLES, NINE 0.5-INCH STRANDS

·p· .. -.» •.. ......-~-:;·;-p..:.··9"• i ... .-~·,"'·?• -·.; D' .•: 1t.-ll~ •_: ""-'° ... 16.'f--D ....

S •i• 43.50 FEET TYPICAL SPAN 1

Fig. 1.6. Six-span Welland Canal Bridge, Canada, strengthened by post tensioning, 1968.

,... ~

15

for heavier loads and to prevent excessive deflections. The two-span

wrought iron truss bridge with compression member and tendons is illus

trated in Fig. 1.7. The compression member was attached to the top

chord of each bridge truss with connections that permitted the member

to slide longitudinally, except at the central pylon. Cables were

harped at the quarter points of each truss span and tensioned against

the compression member. Even with carefully designed saddles and rein

forcing at the quarter points, friction forces were high, and there

was need for repairs during post-tensioning. The truss was monitored

with strain gages before and after post-tensioning. Measured strains

generally were 3% to 20% less than computed strains, and after nine

months, only 5% to 7% of the initial tendon forces had been lost.

Brodka and Klobukowski described a variety of concepts and appli

cations for prestressed steel structures in their reference work which

was translated from Polish and published in German in 1969 [6]. One

of the concepts for a four-span, prestressed steel beam is shown in

Fig. 1.8. The alternating bottom and top tendons in positive and nega

tive bending moment regions is similar to the straight bar pattern

commonly used for reinforcing concrete beams.

Another concept for prestressing steel beams is shown in Fig. 1.9.

The harped tendon is placed only at the central support of a two-span

beam in such a way so as to provide prestressing for the negative moment

region where bending moment is maximum. The concept is one of many

included in the work by Ferjencik and Tochacek [12). The work is written

in German but from a Czechoslovakian viewpoint.

ONE STEEL CABLE EACH SIDE OF TRUSS

ADDITIONAL, STEEL SLIDING COMPRESSION MEMBER

' I I I j,. 157 .44 FEET .,j. 157 .44 FEET .,j

Fig. 1. 7. Two-span, wrought iron truss bridge in Aarwangen, Switzerland, strengthened by post-tensioning, circa 1969.

STEEL BEAM"'- /TENDON

~ I I xr I I 1 i ... ~ '4' 1 4'' 4' :

Fig. 1.8. Concept for a four-span, prestressed steel beam, circa 1969.

();

17

The early prestressed concrete bridges constructed in France by

means of successive cantilevering often developed problems caused by

insufficient prestress. The initial prestressing forces did not ade

quately account for losses caused by concrete creep, temperature move

ments, and cable friction. Virlogeux (29] briefly described the

strengthening of a six-span, double-tee bridge over the Rhone River,

which is illustrated in Fig. I.IO. Twelve cables, extremely long,

were tensioned and anchored at the ends of the bridge in order to pro

vide the prestress required to replace the unexpected losses. The

tendons were placed a small distance below the deck and supported at

regular intervals to prevent excessive sag.

In the mid I970s, design standards for box girder bridges were

revised in the United Kingdom and thus made it necessary to strengthen

many long span bridges. The Erskine Bridge over the Clyde River near

Glasgow, Scotland was one of the bridges that required strengthening

to satisfy the then new Merrison requirements (24]. The harped tendon

arrangement illustrated in Fig. I.II was utilized at the approach span

piers to provide a part of the required strengthening. A11choring the

threadbar tendons at diaphragms within the steel box section required

·that the diaphragms be strengthened.

During the last decade California has strengthened many steel and

composite bridges by means of post-tensioning (22]. One of the earliest

strengthening projects was the Pit River Bridge, which was framed with

trusses, floor beams, and multiple-span stringers. When the bridge

was widened and brought up to then-current standards in I979, it was

necessary to strengthen the wide-flange stringers in negative moment

STEEL BEAM TENDON

Fig. 1.9. Concept for a two-span, prestressed steel beam, circa 1975.

PRESTRESSED CONCRETE ~6 CABLES FOR /TEE EACH OF TWO TEES

- --------- - 9µ Ti lT lT II I I I I I l i il64. O~j • 262 .40,.j,. 262 .40 ..,j ,.262 .40 .,i,.262 .40,. i l64 .O~j

~ 1~ ~·

NOTE: ALL DIMENSIONS ARE IN FEET

Fig. 1.10. Six-span bridge over the. Rhone River, France, strengthened by post-tensioning, 1975-76.

~

"'

19

regions, as shown in Fig. 1.12. Because the post-tensioning cables

would add compression stress to the already overstressed bottom flanges,

steel bars were bolted to the bottom flanges of each stringer in the

negative moment region. The steel bars lowered the neutral axis of

the stringer and thus provided additional eccentricity and moment from

the tendons. The bars therefore served a dual purpose: to increase

the post-tensioning moment and to carry a portion of the post-tensioning

axial force in the compression region of the stringer.

The earlier Welland Canal Bridge example made use of post-tensioning

to create a continuous span bridge from a series of simple spans.

Jungwirth and Kern (15] present a similar example for a series of simple

spans for a composite steel beam and concrete deck bridge. Figure 1.13

illustrates the two basic components: new reinforced concrete diaphragms

over the support and straight tendons in the negative moment region.

The purpose of the post-tensioning was simply to reduce deflections on

the spans and eliminate problems with expansion joints at the supports.

No compression bars were required for the bottom flanges because in a

series of simple spans before the post-tensioning is applied, the bottom

flanges have very minimal tension stresses.

A series of prestressed concrete bridges constructed over the

Netekanaal in Belgium in 1955 developed problems because of inadequate

initial prestress and apparent loss of prestress. DeBuck et al. [8]

outlined the problems as water damage, incomplete grouting and subse

quent corrosion of prestressing cables, and inadequate prestress due

to underestimates of the effects of creep and overestimates of the

Fig. 1.11. Multiple-span, Erskine Bridge over Clyde River, Scotland, strengthened by post-tensioning, 1976.

CONCRETE DECK-..__ 1STEEL TENDON /TENDON BRACKET • l · .·~:; ~-:;;·--:· 1 .. : :, ~- • .,0. · :1··~· • .. · •· . ·,. 0 •• o ·, ~ ?·· (...,; · . . 0 .- • :~: • •• o·~

STEEL STRINGER -'l;~~==='=ir====,.....===~====J ADDITIONAL COMPRESS ION BAR FLOOR BEAM

Fig. 1.12. Steel stringers in Pit River Bridge, California, strengthened by post-tensioning, 1979.

N 0

21

modulus of elasticity of the concrete. The tee beam bridge was strength

ened with additional harped cable prestressing shown in Fig. 1.14.

The cables were harped in the vertical direction as shown in the figure

and also in the horizontal direction in order to pass the cables through

openings in cross frames. Cables were anchored at new steel cross

beams attached in the end spans. In the regions where the steel beams

were attached to the existing prestressed concrete webs, steel plates

were epoxy-bonded to the concrete webs in order to carry the additional

local stress of the post-tensioning. Along the bottom surface of the

beams in the center span, steel plates were epoxy-bonded in order to

prevent potential tension overstress if a certain amount of the original

prestress had been lost.

The Pont du Givors over the Rhone River in France was strengthened

by post-tensioning in 1981 [21]. The bridge was a five-span, pre

stressed concrete, double box girder, as shown in Fig. 1.15. The bridge

had water leakage into the boxes and cracks caused by inadequate initial

prestress and loss of prestress. The harped cable pattern chosen for

strengthening essentially reversed a part of the moment caused by

applied loads. In order to provide the change in direction for the

tendons near the centers of the long spans, new reinforced concrete

diaphragms were cast in the box sections. Before the post-tensioning

was applied, all cracks were injected with epoxy.

One of the lingering questions regarding composite action in con

tinuous span bridges has been the effect of the deck and shear connectors

in the negative moment regions. Without evidence of dependable composite

action, most bridge engineers when computing section properties for

REINFORCED CONCRETE DIAPHRAGM

STEEL BEAM~ I u,;;1 I '\, j TENDON BRACKET

Fig. 1.13 Concept for reduction of deflection in simple span bridges. West Germany, circa 1980.

ADDITIONAL STEEL CROSS BEAMS

CABLE TENDONS PRESTRESSED CONCRETE TEE BRIDGE

I<

I I I I · . I I j,. 78. 72 FEET ..j.. 131. 20 FEET ,.j,. 78. 72 FEEl....j

Fig.· 1.14. Three-span bridge over the Netekanaal, Belgium, strengthened by post-tensioning, 1981.

N

"'

23

bridge beams, neglect the concrete deck in negative moment regions.

Lack of composite action causes early cracking of the concrete deck

and loss of stiffness, as indicated by the tests conducted by Tachibana

et al. [25].

One potential method for obtaining dependable composite action in

negative moment regions is to prestress the deck above supports so

that it remains in compression under all service loading conditions.

That method was analyzed and tested by Kennedy and Grace [17] for a

two-span bridge model. Two five-beam bridge models were constructed

at one-eighth horizontal scale and one-third vertical scale: one model

without prestressing and one model with longitudinal deck prestressing

above the interior support. A longitudinal section through the pre

stressed model is given in Fig. 1.16. The deck in the model without

prestressing cracked above the central support at a relatively low

load; however the deck in the model with prestressing did not crack

until a much larger load was applied. The model without prestressing

had deflections and strains approximately 15% larger than the model

with prestressing. The distribution pattern of those deflections,

from beam to beam across the bridge model, did not vary significantly

between models, however. Thus the deck prestressing eliminated cracking,

maintained composite action, and maintained the stiffness of the bridge

model under what could be considered to be service loading conditions.

Many of the prestressed concrete bridges constructed by canti-

lever construction in West Germany in the 1960s and early 1970s developed

severe cracking near the construction joints a few years after construc

tion. The nine-span bridge described by Holzapfel et al. in Refer-

ence 14 is one of the bridges with construction joint problems. For

ANCHORAGES

ADDITIONAL DIAPHRAGM

CABLE TENDONS PRESTRESSED CONCRETE BOX GIRDER

I I NOTE: ALL DIMENSIONS

I I I ARE IN FEET L ....i_ 360.80 .. J .... J.. 360.80 .. i • .. I I - -1~ -.~ ~,-_

98.40 65.60 98.40

Fig. 1.15. Five-span bridge over Rhone River, France, strengthened by post-tensioning, 1981.

CONCRETE DECK :.,,,..· .. ·· .............. _,._ ....... · ... . I I

STEEL DIAPHRAGM

TENDONS

I I

I I I 1.,. 5.00 FEET •I• 5.00 FEET •I

Fig. 1.16. Experimental, two-span, prestressed composite bridge model, .circa 1982.

N ....

25

the bridge it was determined that the causes of the cracking were:

minimal prestressing near the construction joints, inadequate provisions

for temperature and shrinkage, and minimal reinforcement for tension

stresses near the construction joints. The bridge was strengthened

with harped cables, and the harped configuration was achieved by adding

a steel diaphragm between the prestressed concrete beam webs at each

construction joint as shown in Fig. 1.17. The harped configuration

was chosen because it minimized the required cable force and thus mini

mized the elastic shortening of the relatively long bridge. In order

to further adjust stress conditions in the bridge, the bridge was jacked

to slightly higher elevations at three of the supports after post

tensioning.

Another West German bridge with a different problem was strengthened

with a harped tendon arrangement similar to the arrangement described

in the previous example. The Autobahn bridge reported by Engelbach

[11] had corrosion and loss of prestress in the tendons for one of the

four prestressed beams within the bridge. 'In order to avoid the unknown

distribution effects if only the deficient beam were post-tensioned

for strengthening, all of the beams were post-tensioned equally by

using the harped tendon scheme illustrated in Fig. 1.18.

In order to provide a haul road for several relatively large and

heavy preassembled industrial equipment parts, a series of bridges was

strengthened in New Zealand. The Waiwaka Terrace Bridge described by

Blakeley et al. [4] was strengthened by partial length cable tendons

as illustrated in Fig. 1.19. The tendons were placed on both sides of

each of the six beam webs and tensioned by depressing them at the saddles

PRESTRESSED CONCRETE TEE BRIO.GE

CABLE TENDONS .ADDITIONAL STEEL. DIAPHRAGM

I ,.j,. 95.12 FEET TY·PICAL SPAN ,.j,. ~

Fig •. 1.17. Nine-span bridge over Highway L284,. West Germany, Strengthened by· post-tensioningc,. circa I983'.

PRESTRESSED' CONCRETE

r~ > i':JC.B~lllGC • ~' . • •• lA~t181'" ~· ITT .

I 116· FEET TYPICAL SPAN; '

s •I'" •I•· '

Fig. 1. 18. Mu1tiple-span Autobahn bridge, West Germany, strengthened by post-tensioning, 1984.

N m·.

27

rather than by longitudinal jacking. The tendons, by means of the

harped configuration and longitudinal distribution of the forces and

moments applied by the tendons, strengthened the bridge the required

amount without running the entire length of the bridge. The axial

force applied by the tendons apparently would have overstressed the

compression zones at the bottoms of the haunches, and thus it was neces

sary to bolt and epoxy-bond steel plates to those haunches for compres

sion strengthening. In concept, this compression strengthening is

similar to that used for the Pit River Bridge [22].

On the ten-span Bonners Ferry Bridge, constructed recently in

Boundary County, Idaho, both the steel girders and the concrete deck

were prestressed in negative moment regions above the piers [27]. The

prestressing was applied in two stages by straight tendons located as

shown in Fig. 1.20. In the first stage, tendons attached to the girders

reduced the dead load tension stresses in the top flanges to an allow

able level. In the second stage the tendons, placed in the deck and

tensioned after the deck had cured, eliminated the tension in the deck

under full .service live load. Thus, the second stage of prestressing

made use of the concept analyzed and tested by Kennedy and Grace [17]

and assured full composite action throughout the bridge, even in the

negative moment regions. The full composite action reduced deflections

and improved the fatigue strength of the bridge. Use of the prestress

ing also provided enhanced redundancy through the multiple load path

network.

A recent experimental research program at Concordia University in

Montreal, Canada explored prestressing of continuous steel bridges

REINFORCED CONCRETE

"§ L''.' ~o:E f I ' I TET:~oo; ' !fl' I SADDLE ; I I .

. I I I L 45.00 FEET _,_ 60.00 FEET _,_ 44.06 FEET -1--·--

CROSS FRAME

Fig. 1.19. Three-span Waiwaka Terrace Bridge, New Zealand, strengthened by post-tensioning, 1985.

CABLE TENDONS CONCRETE DECK

I I I I l

H ~ 155.00 FEET TYPICAL SPAN •le ________,

STEEL PLATE GIRDER

Fig. 1.20. Ten-span, prestressed composite girder, Bonners ferry Bridge, Idaho, circa 1985.

N

""

29

[26]. A scale model of a two-span, two-web plate girder bridge with

an orthotropic steel deck was constructed of plexiglass. The model

was tested and analyzed with six different tendon configurations, one

of which is shown in Fig. 1.21. The authors were unable to reach any

strong conclusions regarding the different tendon configurations.

They did point out, however, that the tendon configuration shown in

Fig. 1.21 would be reasonably optimal if the design of the two-span

bridge were governed by negative dead load moment.

The prestressing examples reviewed above either specifically state

or imply that prestressing steel structures or post-tensioning existing

structures for strengthening purposes is different from prestressing

new concrete structures. Post-tensioning for strengthening continuous

bridges generally must be conceived in such a way as to reverse the

moments caused by dead and live loads rather than to overcome a tension

weakness in the structure. One exception is the case of continuous

composite structures. In this case, if the post-tensioning can be applied

in such a way as to eliminate tension in the deck above supports, full

composite action can be achieved throughout the structure rather than

only in positive moment regions.

The examples illustrate a variety of tendon configurations:

straight, harped, and harped with an additional compression member.

Straight tendons are the simplest to use; however straight tendons

require larger forces because of minimal eccentricity. In negative

moment regions of composite structures, it may be difficult to achieve

any eccentricity, and in that case, straight tendons apply only an

axial force. In many cases straight tendons applied to negative moment

31

regions require additional compression reinforcing for the applied

compression forces. Harped tendons can more nearly reverse the applied

dead and live load moments and, therefore, require smaller tendon forces

to strengthen a given bridge. The reduced force becomes especially

important when relatively long bridges are post-tensioned and there is

concern for axial shortening. When harped tendons are used with sep

arate compression members, the mechanism created is more efficient

than a simple harped tendon. With the additional compression member,

the eccentricity of the tendon is increased; the increased eccentricity

can be used to provide more strengthening capacity or to reduce the

required tendon force.

The behavior of the entire continuous bridge must be considered

when the bridge is strengthened by post-tensioning. Post-tensioning

is distributed longitudinally within a continuous structure; there are

several examples where the engineer has made use of post-tensioning at

one or more locations and not only strengthened these regions but also

strengthened all critical stress regions. None of the examples cited

above, however, deal with transverse distribution of post-tensioning.

In fact there are several examples where the engineer post-tensioned

all beams or applied the post-tensioning in stages in order to avoid

the unknown effects of lateral distribution.

The literature review shows that continuous composite bridges can

be strengthened by post-tensioning. For existing continuous bridges,

post-tensioning can be used to reverse the moments caused by applied

dead and live loads and may be able to overcome the tension weakness

in the concrete deck over supports and achieve full composite action

throughout a bridge.

32

1.5. Selection and Rating of Prototype Bridge

Iowa began designing and constructing continuous span steel stringer

bridges relatively early in comparison with other states, and for that

reason, Iowa has a considerable inventory of those bridges. The Office

of Bridge Design at the Iowa DOT provided the researchers with plans

for six standard series of continuous span bridges from the period

1939 to 1960, which might be candidates for a prototype bridge.

In selecting a standard series for a prototype bridge, the

researchers considered the following factors. The bridge series must

have a roadway wide enough for two standard 12-ft traffic lanes. A

considerable number of bridges should have been constructed in Iowa

from the standard plans so that if strengthening is applied to a bridge

as part of another phase of this research, a suitable bridge will be

available in central Iowa. The shortest bridge in the standard series,

at a scale no less than one-third full size, must fit space available

in the ISU Structural Engineering Research Laboratory.

Considering these factors and the advice of the Office of Bridge

Design, the Vl2(1957) series of bridges was selected for the prototype.

This series was in effect for approximately eight years, and a search

of the Iowa DOT records indicated that 100 to 150 bridges were con

structed from the standard plans for that series. In order to minimize

the size of the laboratory model, the shortest Vl2(1957) bridge, 125 ft,

was selected. A transverse section of that bridge is given in Fig. l.22a,

and a longitudinal section is given in Fig. l.22b.

NEUTRAL); THICKENED -~ORA-PED TENDON I PLEXIGLASS GIRDER BRIDGE AXIS BOTTOM FLANGE"' MODEL - . ----~-,_ - - """' · =t

4 I : I j,. 12.75 FEET ,.j,. 12.75 FEET ,,

1

Fig. 1.21. Experimental, two-span bridge model, circa 1986. '-" 0

r-cco z·-o 1:·-0

., .. "

z:-o

'" ·--r

Z'-0

·-7

,,...~o

Z'-0

~"

Cl..oCtdV'IO'.J'-

NottL,: 13.otton'"I. ot ~lab f'6 to be. o e.+l"a·19 ht Hr.c. bc.+w~«..f"'\ houf"\ch&&

1~0

~---:-i

-l.i-i r '

r br96. on") ! ~ o~re- r~ ! ~~· 0

9'- -Conti"-· ""' ' I 11 I ' =--1! ' , I '°' C....,_,.., , ' 'i:> ' ~ '" • I • '$· =··

I\ '~1~.)' .. ~"" '1 -:0,"-----~I;; 11 -" I !l " ... ' '\ ' -- I . ..,., , . . , . ?~-· I..:.

~C~3.-~ ~ 5\d V:OA(J-<.:.)~ eJ..to>lf> ! f.. 4> r I t~

, I

J i,.!_--(,, 7·-.~

~lric:<jt oboul ~ UJ.' '·¥Pl• =c.=""'1 ~""' ~- _!)eab<::><..A :·-1~1·-o

"1'-S ! ---- ·----r-a -----~

MAl..F INTERMEDIATE SECTION MAl.F ~ECTION NEA.Q. AaUTMENT

a. TRANSVERSE SECTION

-'°- .~o RDil SecliOn !:_r/,_"'-0 • 12 5'·0

1.1~ Spt:7ce~ ~ gJ f.O.:vs o lop)

Nole All open holes m roil to be l'rtled wdl> bolts

tl. JOga formod s1a4 mn11d!>hown)cr tOLJ/'5_3•ro;J. .jptu:.ioi 6-<Jbolfs

-,~ f ....., (::;;,-, ~,.-.! VIOA-·zt-----.z.....,,-,.,:.,.,,~:;r-----,----:y"

l:l:C:: : i ~ . .. : ::;;:: :· (

Spec.iol Wt7hr Ji_.,,~ f- @ f~~-,. f "t;crs i>, lL ·-Lap ;n dircdi'ifl oF +raffic

"'°"""'.!"':'-· -,= -i- .. re ~=-4 :::r:;n T--,-

- 10.,

!.~

Jee , .. V!OA-7 ~t, ~.,~.>'&~1~~~~~~~~a~>rS~d~--~~~ ~ . ~ ; ~ fli f ~ : l jr ' ; ~ii !f L-.W..J -; •• I "t _ *

f-""\ M G , - ~.. . . . '/nc/ude.s § for ;a1h/ tc conv,:;s -- -----'= .5ok L SP4F £AR VA(J Sole ,f SP4£

Mos./ZMP4E Alas.It MP4F Sok; SP/ Sole£ SP/ NEAR t l?bwY R«kr RI Rocker Rt

_ 10 _____________ 3{J"(} ____ ·-----. ~~-!."'!!'~------ __________ 49'-o. ___ ___________ Mus~MP! ____ _ .J9_to_. ------· -- _10...;

b. LONGITUDINAL SECTION

Fig. 1.22. Prototype VIZ (1957) series bridge, 125-ft length.

w w

34

Figure 1. 22a shows the ·bridge to have a 24-ft wide roadway with

low, integral curbs and four steel beams made composite with the con

crete deck. Because the bridge was designed before the change in AASHO

bridge design specifications that required a large increase in wheel .

load fraction for exterior beams, the exterior beams are smaller than

the interior beams.

Figure 1.22b shows the bridge to have three spans. The two end

spans are 38 ft long, and the center span is 49 ft long. The longi

tudinal section shows.the steel beams to be coverplated on both top

and bottom near the piers. The section also shows that there were two

beam splices within the center span and that those splices consisted

of both flange and web splice plates in order to achieve shear and

moment continuity.

According to the Office of Bridge Design, there are two typical

problems with continuous, composite steel beam-concrete deck bridges:

the bridges often have coverplates over the piers that are not long

enough, and the compression flange of the steel beams at the piers often

is overstressed. The bending stress checks given later in this section

indicate that the prototype bridge has both problems described above

and additional overstresses at other locations.

On the basis of Iowa DOT records, and with the assistance of nine

county engineers' offices, the researchers located two of the V12 (195 7)

bridges in central Iowa. Two of the researchers briefly inspected one

of the bridges on old US 30 in Greene County.

Under current AASHTO specifications [1,2), Iowa DOT policies,

and Iowa legal truck loads, a V12(1957), 125-ft long bridge requires a

35

minor load restriction because bending stresses in stee1 beams exceed

the allowable operating stress of 24.75 ksi for A7 steel. With the

assistance of the Office of Bridge Design, the researchers performed a

partial rating for bending stress for the prototype bridge in order to

determine the magnitudes and locations of overstress. The bending

stress checks were conducted with the current AASHTO Bridge Design

Specifications [2] and supplemented with usual Iowa DOT practice and

Iowa legal truck loads as noted below:

• Truck loads were taken to be Iowa legal loads: Type 3 and Type 4 straight trucks, Type 3S2(A), Type 3S2(B), and Type 383 trucks and semi-trailers, and Type 3-3 truck and trailer.

• Only one truck per lane was placed on the bridge.

• Curbs and steel bridge rails were considered to be long-term dead load.

• A future wearing surface of 19 psf was included in the longterm dead load.

• Moments along the bridge were based on moments of inertia which changed as follows. For positive moment regions, composite beam moments of inertia were computed with integral curbs for exterior beams and concrete decks with deducted wearing surfaces for both interior and exterior beams. For negative moment regions over the piers, beams and coverplated beams were considered to be noncomposite; the deck and reinforcing were neglected.

On the basis of standard Vl2(1957) plans and Iowa DOT specifica-

tions, the steel for the prototype bridge was taken to be A7 with a

yield stress of 33 ksi, and the concrete deck and curb were assumed to

have a 28-day strength of 3000 psi.

Results of the bending stress checks are given in Table 1.1.

Figure 1. 2.3 supplements the table in showing the assumptions for live

load moments of inertia and the sections at which stresses were checked.

• I

38'

1

., .. i

• •• II III IV

36

125' 49'

• • • IV Ill II

38'

• I

I = SECTION FOR MAXIMUM POSITIVE MOMENT AT 0.4L FROM ABUTMENT, END SPAN

II= SECTION AT THEORETICAL COVERPLATE CUTOFF, END SPAN

III = SECTION FOR MAXIMUM NEGATIVE MOMENT, PIER

IV= SECTION AT THEORETICAL COVERPLATE CUTOFF, CENTER SPAN

V = SECTION FOR MAXIMUM POSITIVE MOMENT AT 0.5L FROM PIER, CENTER SPAN

Fig. 1.23. Critical stress locations and beam stiffness assumptions, prototype Vl2 (1957) series bridge.

Table 1.1. Overstress with respect to allowable inventory stress, prototype Vl2 (1957) series bridge.

OVERSTRESS, ksi

SECTION I II II I IV

EXTERIOR TOP FLANGE +4.41 +6.13 +0.84 BEAM

v

BOTTOM FLANGE +5.16 -6.02 -6.13 -2.45 +7.65

INTERIOR TOP FLANGE +1.42 +2.45 BEAM

BOTTOM FLANGE +6.27 -2.76 -2.45 -0.46 +7. 71

NOTE: - INDICATES COMPRESSION OVERSTRESS

+ INDICATES TENSION OVERSTRESS

37

The table shows the largest overstresses that would require load

restriction (posting) at Section V on the center span for both exterior

and interior beams. There are also relatively large overstresses at

Section I on the end spans for both exterior and interior beams and at

Sections II and III on the exterior beams. The majority of the critical

stress locations show overstresses with respect to the allowable inven

tory stress of 18 ksi.

On the basis of the bending stress checks, it is apparent that

all critical positive and negative moment sections in both exterior

and interior beams are overstressed. Strengthening of the prototype

bridge by post"tensioning, therefore, would require stress relief in

all of those regions, in order to keep bending stresses within the

allowable inventory stresses.

39

CHAPTER 2. DESCRIPTION OF TEST SPECIMENS

This chapter outlines the details of the model and mockup used in

this investigation. The instrumentation employed, procedures followed,

and the actual tests performed are presented in Chapter 3. Discussion

and analysis of results as well as behavior characteristics noted during

testing are presented in Chapter 4. This chapter, as well as the next

two chapters of this report, has been subdivided into two sections;

the first section pertains to the bridge model, while the second sec

tion pertains to the full-scale negative moment region mockup.

2.1. Model Bridge

2.1.1. Description

The model bridge (Figs. 2.1 and 2.2) was constructed to be, as

nearly as possible, a one-third-scale replica of the three span V12(1957)

bridge (illustrated in Fig. 1.22). The scale was selected to make the

model as large as possible, yet to fit within the confines of the Struc

tural Engineering Laboratory.

As shown in Fig. 2.1, the steel frame is composed of four longi

tudinal beams connected transversely by 24 diaphragms; for additional

information on the framing and structural steel details, see Appendix A.

Note that the exterior stringers are 1 in. shallower than the interior

stringers which correctly models the 3 in. difference in stringer height

found in the prototype. Plan view dimensions shown in Figs. 2.1 and

A.l are one third of the values given on the original Vl2(1957) plans.

Thus the bridge model follows the principles of similitude and will

respond to loadings essentially the same as the prototype.

1" c ROWN

L r

6" --"-"'"

BM 1 I BM 2 I BM 3 I BM 4

40

8 1 -8"

..... ' --=- r- ....

I #3@ 10 1/2"' TRANSVERSE

/#3, -..- - - - --

··~ LONGI~DI~~~ ._ -13.33" ,2.25"

-

2'-6.67" 2'-6.67" 2'-6.67" 6" i.o-"-

it_BMl If. BM2 lj:_BM3 it_BM4

a. CROSS SECTION AT MID-SPAN (SEC A-A)

- -1' -4"1 ~ I 3'-4" sL... .

6'-5.5" ''-5.31" f;L5.34" 6 '·5.5"

12'-9.5" 16'-4" 12'-9.5"

41 '-11"

b. PLAN VIEW 2 1/2 11

M 3" r ·1

----1/8"

L1::a!illl~ 3/ 16" 3/16"

c. SECTION B-B d. SECTION C-C

Fig. 2.1. Model bridge.

a. STEEL FRAME b. FORMWORK AND REINFORCING

c. DECK WITH CURBS d. TWO VERTICAL LOADS Fig. 2.2. Photographs of model bridge.

.,, ,_.

42

Each steel stringer consists of three lengths that are bolted

together to make the 41-ft 11-in. continuous stringer. As illustrated

in Fig. A.8, each connection consists of six flexural plates and two

shear plates; twenty-two 1/2-in.-diameter, high-strength bolts (8 per

flange and 6 per web) were used in each connection. For composite

action between the concrete deck and the steel stringers, angle-plus-bar

shear connectors were welded to the top flanges of the stringers.

Figure A.5 illustrates the size of the connectors while the spacing

utilized is given in Fig. A.4.

Because of the size limitations of the steel stringers, the post

tensioning brackets had to be placed on top of the slab in the negative

moment regions and under the lower stringer flanges in the positive

moment regions. Also, because of the eccentricities resulting from

the brackets in these locations, the resulting ratio of post-tensioning

moment to force was significantly larger than the ratio that would

result in the field when post-tensioning brackets are positioned below

the upper flange and above the lower flange in the negative and positive

regions, respectively.

Tabs for attaching post-tensioning brackets were welded to the

top flanges in all eight negative moment regions and to the bottom

flanges in all the positive moment regions of the exterior beams (see

Figs. A.9 and A.10). Preliminary analysis of a three-span continuous

beam indicated that the moment produced by post-tensioning is a function

of the distance between the brackets. Two tabs are required to connect

one bracket; however, three tabs were welded on each side of the eight

negative moment regions so that two different lengths of post-tensioning

43

tendons could be tested (Q1

= 123 in. and Q2 = 99 in. in Fig. 2.3).

The locations of the negative tabs, the interior positive tabs (see

Fig. A.9), and the beam splices are approximately where the inflection

points would occur if a uniformly distributed load were applied to the

three-span bridge model. The distance between the brackets (post

tensioning lengths of Q3

= 95 in. for end spans and Q4 = 111 in. for

middle spans as illustrated in Fig. 2.3) in the positive moment regions

and negative moment regions are also shown in Fig. A.9. Also shown in

Fig. 2.3 are the coordinates of the supports, coverplates, splices,

diaphragms, and anchorages.

Figure A.11 shows that there are two types of diaphragms: inter

mediate diaphragms and pier or abutment diaphragms. The intermediate

diaphragms are channels with steel plates welded on the ends. These

channels are connected to the webs of the longitudinal girders by bolts

through the end plates as shown in Fig. A.11. The abutment diaphragms

are also channels; however, they are attached by bolting through their

webs to stiffeners that were welded to the webs of the longitudinal

stringers as shown in Fig. A.6.

The model bridge is supported on four reinforced concrete walls,

10 in. wide, 3 ft high and 12 ft 6 in. long. At each abutment or pier,

each longitudinal girder is supported on a roller that is placed on a

1/2-in. steel plate that was grouted on the abutment or pier as shown

.in Fig. A.12. A transit was utilized for leveling the abutments and

piers to make sure that they were at the same elevation.

After the steel stringers and diaphragms were assembled (see

Fig. 2.2a), formwork was constructed (see Fig. 2.2b) and the concrete

z

l • 0.

• o.

y ..

;,:_, • o.

44

a. COORDINATE AXES

~ ~ • • 152. 348. inches

b. y-COORDINATES FOR SUPPORTS

x = :'. 46 INCHES

47'. 0 . .. 122. 182.192.

inches

0 :;;; .. . 308. 318. 378.

c. y-COORDINATES FOR EXTERIOR BEAM

• 120.

x = + 15.33 INCHES

40 .. 184. 192.

inches

0 ;fa; .. 308.316. •

380.

d. y-COORD!NATES FOR INTERIOR BEAM

Fig. 2.3. Model bridge coordinates.

~ • 500.

~ • 500.

~ • 500.

45

z

Ly J J J [ [ [ [

• • • • • • • • o. 76. 152. 217.33 282.67 348. 424.0 500.0 inches

e . y-COORDINATES FOR DIAPHRAGMS

. t-z.· .• Y90.50102.50 201.50 213.50 298.50 397.50 409.50 ~ • •• •• 286.50•• ••

• • ~. • A • .for 14.50 109.50 194.50 305.50 390.50 485. 50

inches f. y-COORDINATES FOR ANCHORAGES

95'~~ g. TENDON LENGTHS

Fig. 2.3. Continued.

46

deck was placed as shown in Fig. 2.2c. Note that Fig. 2.2c also shows

the curbs that were cast in place two weeks after the deck. The posi

tive moment regions of the concrete slabs were placed before the nega

tive moment regions. Figure 2.4 shows the casting sequence of the

concrete deck. The model deck thickness of 2.25 in. (l/3 that of the

prototype) precluded the placement of reinforcement in two layers as

would be the case in the prototype bridge. Reinforcement (#3 at 10.5 in.

transverse and #3 at 14 in. longitudinal) was placed at mid-depth in

the deck; additional #3 reinforcement was placed longitudinally in the

negative moment regions.

The concrete deck has a crown (see Fig. 2. la) caused by the change

in depth between the exterior and interior beams. The average deck

thickness is 2.65 in., which is slightly larger tha.n one-third of the

deck thickness of the prototype bridge (2.25 in.). This deck thickness

is the average of 48 measurements taken at different locations on the

bridge. The curb was placed two weeks after the concrete deck. As

shown in Fig. 2.la, the desired width and total depth (deck+ curb

height) are 4 in. and 5.58 in., respectively. The average measured

curb width was 3.88 in., while the average curb height was 5.50 in.

The curb dimensions were obtained by averaging 16 measurements taken

at different locations along the curb.

In order to prevent uplift of the model bridge caused by various

post-tensioning and vertical loading conditions, tie downs were fabri

cated and placed at e~ch stringer support (see Fig. 2.5). These tie

downs were designed to prevent vertical uplift, but to permit horizontal

movements.

47

12'-9 1/2" ·1· 16'-4" 12 '-9 1/2"

'

1 2 3

8'-11 1/4'' 7'-6 1/4'' 8'-11" 7'-6 1/4" 8'-11 1/4"

a. POUR SEQUENCE

b. PHOTOGRAPH OF POURING BRIDGE DECK

Fig. 2.4. Pouring of concrete deck for model bridge.

48

8"

13" BAR: 3/4" x 1 1/2" x 16"

a) PLAN VIEW

7 /8" DIA. HOLE CORED THROUGH DECK ..-- BAR: 1/8" x l" x 12"

DIA. x 12"

REINFORCED CONCRETE DECK

.--\~~=~b~ri

3'-0" BRIDGE BEAM

1/4" DIA. THREADED ROD

CONCRETE ANCHORS ANGLE: 2" x 2" x 3/16" x 12"

ABUTMENT

b) SECTION

Fig. 2.5. Support tie-down system.

49

::E UJ I-Vl >-Vl

z 3 0 Cl

I UJ ..... I-::i:: I-..... 3

UJ

"' Cl ..... 0::

"' --' UJ 'O Cl OJ 0 g ::E

•rl .µ . <:

"O 0 u

"' . N . bO

•rl ~

50

The dead load stresses in the model were approximately 1/9 the

dead load stresses in the prototype. As the purpose of the model was

to determine its response to live loads and post-tensioning, no attempt

was made to add dead load to the model to simulate the actual dead

load in the prototype.

To produce live load stresses in the prototype bridge, two 6-kip

concrete weights were constructed in the laboratory. Live load stresses

in the model resulting from one of the 6-kip weights, as a result of

the principles of similitude, duplicate the stresses in the prototypes

resulting from a 54-kip weight. Each 6-kip vertical load is a 3-ft

x 3-ft x 4-ft 8-in. concrete block that has a 1-ft x 1-ft x 4-in.

concrete block integral with its base to approximate a concentrated

load and which simplifies placing the weight on the bridge (see Fig. 2.6).

Although the actual weights of the blocks were 6020 lbs and 6010 lbs,

they will be referred to as 6-kip loads in the remainder of this report.


2.1.2.1. Concrete

Twelve standard cylinders (6 in. diameter x 12 in. long) and two

beams (6 in. x 6 in. x 30 in.) were made during the placing of both the

concrete deck and curbs. The maximum aggregate size used in both con

crete mixes was 3/8 in. These cylinders and beams were subjected to

the same curing conditions as the slab and the curb. Table 2.1 presents

the slump, unit weight, compressive strength, and modulus of rupture of

the concrete slab and curb. Each modulus of rupture value given is the

average of four tests, while each compressive strength value given is

the average of three tests for either the slab or the curb. The

51

1· 3'

~, 12" 12"

r-!)6"

Lt A

4"

t

,--1 I I L_J

3' 12"

Lt b. SECT ION A-A

a. ELEVATION VIEW

F.ig. 2. 6. Concrete dead weight.

52

Table 2. 1. Physical properties of concrete.

Slump Unit Weight

(lb/ft3) ' ' (in.) f (psi) f (psi) c r

Deck 2.75 140 3450 447

Curb 4.25 142 3355 445

53

compressive strength of the concrete in the bridge model was slightly

higher than the specified concrete compressive strength in the proto

type bridge. However, the concrete compressive strength in the proto

type bridge is most likely higher than that specified; thus the concrete

compressive strength in the model and prototype are probably very close.

2.1.2.2. Steel

Because the steel strength was not one of the variables being

studied in the investigation and because the bridge was tested within

the steel elastic stress range, no tension tests were conducted on any

of the steels utilized in this testing program. In the analysis pre

sented in Chapter 4, nominal values of the modulus of elasticity of

the steel beams and Dywidag tendons were assumed to be 29,000 ksi and

24,000 ksi, respectively. These assumed values were based on steel

tension tests made in other research projects.

2.2. Full-scale Negative Moment Region Mockup

As previously noted, the size of the stringers in the bridge model

forced placement of the post-tensioning tendons above the deck in the

negative moment region and below the bottom flange in the positive

moment region. In order to investigate the effect of post-tensioning

below the deck and also to investigate other post-tensioning schemes

in the negative moment region, a full-scale model of a negative moment

region within a continuous bridge was constructed. This full-scale

model of the negative moment region in a continuous bridge will hence

forth simply be referred to as the mockup.

54

2.2.1. Description

Figure 2.7 illustrates how the mockup simulates the negative moment

region in a continuous bridge. (Compare the bridge moment diagram shown

in Fig. 2.7b to the mockup moment diagram shown in Fig. 2.7d.)

The mockup was constructed to replicate the negative moment region

of the Vl2(1957) bridge series. General dimensions of the mockup are

given in Fig. 2.8, whereas photographs of the mockup are given in Fig. 2.9.

Detailed drawings and structural steel details are presented in Appen-

dix B. Review of plans for the Vl2(1957) bridge series indicated that

the beam and coverplate for an interior stringer of a given length bridge

are approximately the same size as those of an exterior stringer of

the next longer length bridge. Interior stringers can be idealized as

symmetrical tee beams; an exterior stringer can be thought of as an

unsymmetrical tee beam because of the unequal flange widths on each

side of the beam and the presence of the integral curb. As a result

of the shape of the composite exterior beam, post-tensioning stress

distribution may differ somewhat between an interior and an exterior

stringer. In the present investigation, it was intended to only test

a mockup of an interior stringer. However, the mockup was constructed

with stirrups in the concrete slab (see Fig. 2.8b) so that curbs could

be added and portions of the slab removed if desired in the future.

Such changes could transform the mockup of an interior stringer into

the configuration of an exterior stringer.

For the Vl2(1957) series, inflection points are located at approx

imately 11, 13. 25, and 16 ft on each side of an interior pier support

for bridges of 125, 150, and 175 ft, respectively. Space limitations

55

UNIFORM LOAD

h i I 4 t *

t J7. t + l I:

0.3 L1 .1. 0.4 L1 .1 .. 0.3 Ll

:I Ll

a. SPANS FOR V12 (1957) BRIDGE SERIES

0.43 M1 0.43 M1 0.43 M1 ~ r--= + ~ r--= + ==>.

[E w 0.09 L1 0.09 L1 0.09 L1 0.09 L1

b. MOMENT DIAGRAM FOR Vl2 (1957) BRIDGES WITH UNIFORM LOAD

CONCENTRATED

.--~~~~~----,...-~~~~~---'·LOAD rf7 79?1/

L3 '

c. MOCKUP SPANS

~<1 --~.:2 I 0.5 L2 0.5 L2

*ASSUMING L3 = 1_ 4

d. MOMENT DIAGRAM FOR MOCKUP

Flg. 2.7. Correlation between full-scale mockup and prototype.

HOLES FOR VERTICAL HOLE FOR HOLD DOWN COVERPLATES LOAD MECHANISM

/ Ar 1sTIFFENER CONCRETE DECK"' ~ .•.,·.~r :·.~\ :··-·';~::.·.·:•,o"'·~··-:-1_·, .... ·o· •. • -·~ "···.··I~'·.-:-•-: ... -:,·: .. :-: \<1-.:':''-'__'.Q':. ::. ·.~·,,.~·.'"·· • ;<>.-:'.'. ·: •. •.• ·,

I I

W24x76

1 Cf_ SUPPORT AL Cf_ SUPPORT I I

6'-6" 6'-6" .1 12'-8" 12'-5"

15'-5"

13'-2" 16'-10"

30'-0"

a. ELEVATION

Fig. 2.8. Full-scale mockup.

"' ""

CONCRETE DECK

STIFFENERS WITH CUT OUTS FOR TENDONS

COVER PLATE

57

6'-3"

3'-1 1/2"

STIRRUPS

COVERPLATE

l:v 1135.::lf314"

b. CROSS--SECTION A-A


58

w _, ca

"' u Cl z:

"' (/)

I-::::>

~ u 0 _, (/)

caw > >.:o

uo w ex'. Cl'"' u

"" z: ~ 3 <J 0 0 Cl 13 Cl "' _, 0 0 :::t: "' .<:: u.. ~ 0 ... z: bl) 0 0 ...... .µ I- 0

"' .<:: _, p.; _, "' I-(/)

z: °' ...... N

.Cl bl) ·..<

"'

""' ex'. 0 3 ::;;:: ex'. 0 u.. Cl w I-w _, c.. ::;;:: 0 u

"'

59

within the Structural Engineering Laboratory limited the overall length

of the mockup to 30 ft and also required that the abutments already in

place for the bridge model be used in testing the mockup. Thus dimen

sion L3

in Fig. 2.7c was required to be 12.67 ft.

In reviewing the Iowa DOT list of surplus beams, the authors deter

mined that a W24 x 76 x 34-ft long beam, was available. As this is

the size of an interior stringer in a 150-ft V12(1957) series bridge,

this beam was obtained and cut to the 30 ft length required for the

mockup.

Although coverplates on a 150-ft Vl2(1957) bridge extend 9.5 ft

on each side of a pier support center line, the mockup's coverplates

were limited to a shorter length. Jacking clearances for the harped

cable post-tensioning scheme allowed the coverplates to extend only

6.5 ft on each side of the support (see Figs. 2.8a and B.la). Cover

plate thickness and width were chosen to match the depth and moment of

inertia of the prototype.

The bearing stiffeners, sole plate, roller, and bearing plate

were chosen to reflect typical components on the prototype. Shear

connectors were the angle-plus-bar type. Their size and spacing were

duplicated from those on the prototype (see Fig. B.4).

Applying the AASHTO effective width requirements for an interior

stringer of the prototype, it was determined that the mockup required

a concrete slab 6 ft 3 in. wide (see Figs. 2.8b and Fig. B.5). Also

shown in these figures is the slab thickness of 6.5 in., which duplicates

the thickness of Vl2(1957) bridge decks. Figure B.7 illustrates the

location of the blackouts and holes that were formed in the slab. The

60

holes (formed with 3-in. diameter PVC pipe) were for the hold downs and

loading hardware to pass through. The two larger blockouts shown i.n

Fig. B.7 were provided to allow use of through deck post-tensioning

cables at a later date if desired. Transverse deck reinforcing, both

bar size and spacing, was duplicated from the prototype (see Figs. B.S

and B.6). Longitudinal reinforcing (see Figs. B.5 and B.6) was the

same bar size as in the prototype and was spaced as for an interior

beam with slight modification so that it would also work for an exterior

beam if the curb were added later.


2.2.2.1. Concrete

Fifteen standard cylinders (6 in. diameter x 12 in. long) and two

modnlus of rupture beams (6 in. x 6 in. x 30 in.) were made during the

pouring of the concrete deck. All cylinders and rupture beams were

subject to the same curing conditions as the deck. Cylinders were

broken at seven days to determine if formwork could be removed. Cylin-

ders were also broken at 14 and 28 days. The 28-day compressive strength,

f ' was 6700 psi and modulus of rupture, f ', was 477 psi. Unit weight c ' r

was 144.S pcf. This compressive strength is considerably higher than

that found in the prototype bridge. However since the testing program

employed (see Secs. 3.2.2 through 3.2.4) involved elastic tests rather

than ultimate strength tests, this greater concrete strength was of no

great concern.

2.2.2.2. Steel

As was the case in the model bridge, no tension tests were con-

ducted on the steels utilized in this portion of the testing program.

61

The steel beam (W24x76) was assumed to be A7 structural steel because

of its age. All new steel used (coverplates, sole plates, bearing

stiffeners, and strengthening angles) was A36 steel. Since all testing

was performed in the elastic range, variations in yield strengths and/or

ultimate strengths of the various structural steel elements has essen

tially no effect on the results. A modulus of elasticity of 29,000 ksi

was assumed for all structural steel.

Straight tendons were 1 1/4-in. diameter Grade 150 Dywidag thread

bars. Cable tendons were 7/16-in. diameter Grade 270 seven wire stress

relieved, Qo/Qax prestressing strand. Since all testing was done in

the elastic range and both the Dywidag threadbars and prestressing

strand were instrumented and calibrated, it was not necessary to deter

mine the actual moduli of elasticity, yield strengths, or other material

properties.

63

3. TESTS AND TEST PROCEDURES

This chapter outlines the details of the specific tests and events

that occurred in conducting of the laboratory tests. Each test program

(for example, bridge model tests and mockup tests) consisted of several

individual tests. In the following sections, only test setups, instru

mentation and procedures will be outlined; discussion and analysis of

results obtained as well as the behavior will be presented in Chapter 4.

The instrumentation for all tests consisted of electrical-resistance

strain gages (strain gages) and direct current displacement transducers

(DCDTs). The strain gages were temperature compensated and were attached

to the specimens with recommended surface preparation and adhesive. Three

wire leads were used to minimize the effect of the long lead wires and

any temperature changes. All strain gages were water-proofed with a

minimum of two layers of protective coatings. Strain gages and DCDTs

on the bridge model and mockup were read and recorded with a computer-

ized data acquisition system (DAS). A switch and balance unit and

strain indicator were used to read the strain gages on the threadbars

and strands; these data were recorded by hand in all tests.

3.1. Model Bridge Instrumentation and Tests

3.1.1. Instrumentation

A total of 64 strain gages were mounted on the four beams in the

bridge model. Figure 3.1 indicates the location of the strain gages;

at each of the 16 sections instrumented, four strain gages were oriented

with their axes parallel to the axis of the beam. Two of the four

~ f cp BRIDGE I SECTIONS

BEAM 4

BEAM 3

I ~ i I t I I g i BEAM 2

~ \ 5 I <p I 3

I ~ BEAM 1

-lj..-2" l OIAPH.

' ~~4"

~SUPPORT it_ SPAN

PLAN VIEW

-1~4" it_ SUPPORT ~~2"

it_ OIAPH.

Fig. 3.1. Locations of strain-gage sections.

CJ'> .,.

65

gages were on the top flange of the beam and two were on the bottom

flange. All strain gages were placed at a distance equal to one-sixth

the flange width in from the flange edge. This distance was approxi

mately 1/2 in. and ranged from a minimum of 0.41 in. for the exterior

beams to a maximum of 0.58 in. for the coverplated regions of the inter

ior beams. As may be seen in Fig. 3.1, the majority of the instrumen

tation was on Beams 1 and 2; however, sufficient instrumentation was

placed on Beams 3 and 4 (Sections 3, 4, 7, 8, 11 and 12) so that symmetry

could be verified.

Two strain gages were also mounted on each threadbar with their

axes parallel with the longitudinal axis of the bar. Two compensating

strain gages mounted on a steel plate were connected to the active

strain gages on the threadbars in a full bridge arrangement. In this

arrangement, the strain gages on the threadbars read the actual value

of the axial force in threadbar as bending strains were cancelled.

Twelve DCDTs were utilized to measure the vertical displacements

of the beams. These DCDTs were placed at the center of each beam in

each span.

When a uniform load is applied to a three-span beam, it generates

regions of positive and negative moments. Regions in the vicinity of

Sections A, C, and E shown in Fig. 3.1 are referred to as positive

moment regions; regions in the vicinity of Sections Band D are referred

to as the negative moment regions.

The longitudinal beams of this bridge were identified as 1 through

4 (see Fig. 3.1). A particular region of a given beam can thus be

identified by beam number and section. For instance, the positive

66

moment regions of Beam 4 shown in Fig. 3.1 are identified as 4-A, 4-C,

and 4-E, while the negative moment regions are identified as 4-B and

4-D.

For clarity, the bridge testing program will be described in five

phases: post-tensioning the positive moment regions, post-tensioning

the negative moment regions, post-tensioning both the positive and

negative moment regions, vertical loading, and combination of vertical

loading and post-tensioning.

The followi11g procedures were us·ed i11 each of the testing programs:

• Record "zero" strain readings and "zero" deflection readings with the data acquisition system.

• Apply predetermined increment of force at desired location.

• Take strain gage and DCDT readings as in Step 1. Record any behavioral changes.

• Remove force from tendon(s) and take second "zero" strain and deflection readings as in Step 1.

• Repeat Steps 1 and 2 if post-tensioning scheme requires posttensioning to be applied to several locations on the bridge.

3.1.2. Post-tensioning Tests--Positive Moment Regions

Post-tensioning a positive moment region refers to the case when

a tendon was placed in a positive moment region and a specified force

was applied to it. As can be seen in parts a and c of Fig. 3.2, tendons

were placed well below the neutral axis of the composite beam to gener-

ate a negative moment and a compressive force in this particular region.

Preliminary analysis indicated that the overstresses in the exterior

beams of the prototype bridge could be eliminated by post-tensioning

all the exterior positive moment regions with a force of 60 kips.

Thus, a force of 60/9 (6.67 kips) would be required in all the tendons

.· ':.·

• • . -:·.·;.·-:.. -

ANCHOR TABS BRIDGE BEAM BRIDGE DECK

HOLLOW CORE HYDRAULIC. CYCLINDER

~.;.-.o:.,· ... ~· .. 5·X-:i.:;;~ ... :.;:•:.. ~.·• .. : .,o·•.".'.; ... <-; "·~ ·~·:·~·· ~?;. 0•• ;~~·-·-·j-l:.~;~-~:-;;:o~.-:;;.,

POST -TENSIONING BRACKET

POST -TENSIONING BRACKET

•

• • POST-TENSIONING

TENDON

a. POSITIVE MOMENT REGION

JACKING CHAIR

BRIDGE DECK

POST-TENSIONING TENDON

JACKING CHAIR

• • • •

0 "co'•·:· '··,.·-· '· ... ':. ~; .,,; •:,: .•·~: t •. • •· •. ~ • .:._,:, ·: •': ;:·.O;; ·• :.,··. " ... -,"';··:·· .• · ...

7

BRIDGE BEAM

b. NEGATIVE MOMENT REGION

Fig. 3.2. Location of post-tensioning system in positive and negative moment regions ..

HOLLOW CORE HYDRAULIC CYCLINDER

NUT #1

"' -.J

68

c. TENDONS IN POSITIVE MOMENT REGION

d. TENDONS IN NEGATIVE MOMENT REGIONS

Fig. 3.2. continued

69

in the exterior positive moment regions of the model to produce the

desired stress reduction. However to obtain strains of a magnitude

that could be measured accurately, this force was increased to 20 kips.

Tests involving post-tensioning the exterior positive moment

regions are shown in Fig. 3.3. Nine different arrangements were inves

tigated and represented by post-tensioning schemes 1 through 9, hence

forth referred to as PTS-1, PTS-2, etc. The number assigned to the

various post-tensioning schemes was also used as the test number; for

example, Test No. 1 was PTS-1.

The following loading procedures were used in PTS-1 through PTS-9.

In PTS-1 through PTS-6, a 20-kip force was applied to the tendons in

increments of 5 kips; see Fig. 3.3 a through f for the location of

post-tensioning in each scheme. In PTS-7, a 10-kip force was applied

to the tendons in regions 4-A, 4-E, 1-A and 1-E simultaneously (see

Fig. 3.3g). This test was repeated with a 20-kip force applied to the

same regions.

In PTS-8, a 10-kip force was applied to the tendons in regions

4-C and 1-C simultaneously (see Fig. 3.3h). This test was repeated

with a 20-kip force applied to the same regions.

In PTS-9, a force of 10 kips was first locked in the tendons in

regions 4-C and 1-C simultaneously. Next a force of 10 kips was applied

to the tendons in regions 4-A, 4-E, 1-A and 1-E simultaneously (see

Fig. 3.3i). This test was repeated with a force of 20 kips applied to

the same regions and following the same steps. The numbers beside the

post-tensioning regions in parts i, u and v of Fig. 3.3 indicate the

order in which the post-tensioning was applied.

70

I a. PTS-1 h. PTS-8

2 1 2

I I 2 1 2 b. PTS-2 i . PTS-9

c. PTS-3 j. PTS-10

d. PTS-4 k. PTS-11

e. PTS-5 1. PTS-12

f. PTS-6 m. PTS-13

g. PTS-7 n. PTS-14

Fig. 3.3. Post-tensioning schemes (PTS) employed on bridge model.

71

~· I I I o. PTS-15 s. PTS-19

I I I I p. PTS-16 t. PTS-20

1 1

I I I f I ti q. PTS-17 u. PTS-21

1

I I I 21 1 12 r. PTS-18 v. PTS-22


72

3.1.3. Post-tensioning Tests--Negative Moment Regions

Post-tensioning a negative moment region refers to the case when

a tendon was placed in a negative moment region and a specified force

was applied to it. Tendons were placed above the neutral axis of the

composite beam (see parts b and d of Fig. 3.2) in order to produce a

positive moment and a compression force at this particular region.

As previously noted, tabs were positioned so that all eight nega

tive moment regions could be post-tensioned. Tests involving post

tcnsioning the negative moment regions, PTS-10 through PTS-21, are

shown in parts j through u of Fig. 3.3.

The following loading procedures were used in each of these post

tensioning schemes. In PTS-10 through PTS-13 a 20-kip force was applied

to the tendons in increments of 5 kips; see parts j through m of Fig. 3.3

for the location of post-tensioning in each scheme. As may be seen in

parts j and k of Fig. 3. 3, the only difference between PTS-10 and PTS- li

is the bracket location. In PTS-10, the interior tabs were used for

mounting the brackets; thus 99 in. of the beam was subjected to post

tensioning (see Fig. 2.3). The exterior tabs were used in PTS-11;

thus 123 in. of the beam was subjected to post-tensioning. There is a

similar difference between PTS-12 and PTS-13.

In PTS-14 through PTS-19, a 20-kip force was applied to the tendons;

see parts n through s of Fig. 3.3 for the location of post-tensioning

in each scheme.

In PTS-20, a 20-kip force was applied in increments of 5 kips to

the tendons in regions of 4-B, 1-B, 4-D and 1-D simultaneously (see

Fig. 3.3t).

73

In PTS-21 (see Fig. 3.3u), a 10-kip force was first locked in the

tendons in regions 4-B, 1-B, 4-D and 1-D simultaneously. Next, a force

of 10 kips was applied to the tendons in regions 3-B, 2-B, 3-D and 2-D

simultaneously. This test was repeated with a 20-kip force applied in

the same regions.

3.1.4. Post-tensioning Tests--Positive and Negative Moment Regions

PTS-22 was the only scheme that involved post-tensioning both the

negative and positive regions together as shown in Fig. 3.3v. The

following loading procedure was used. A 20-kip force was first locked

in the tendons in regions 3-B, 2-B, 3-D and 2-D simultaneously. Next

a 20-kip force was applied to the tendons in regions 4-C and 1-C simul

taneously. As previously noted, the number beside the post-tensioned

regions in Fig. 3.3v indicates the order of post-tensioning.

Four 60-kip capacity, hollow core, hydraulic cylinders were used

to apply the required force to the 5/8-in. diameter tendons in all the

previously described tests. Figure 3.2d illustrates one of the jacks

in position. When it was desired to post-tension beams and collect

data at various post-tensioning load levels, such as in PTS-1 through

PTS-6, and PTS-10 through PTS-13, the procedure was to apply the desired

force with the hydraulic cylinders, collect the desired data and release

the force. However, for some load cases, such as PTS-9, PTS-21, and

PTS-22, the force had to be locked on some of the beams before post

tensioning the remaining beams.

Locking the force in a given beam was accomplished as follows.

First the desired force was applied to the tendons by the hydraulic

cylinder acting against the jacking chair (see parts a and b of Fig. 3.2).

74

Nut 2, identified in this figure, was then tightened so that a force

slightly higher than desired was in the tendon to offset seating losses.

The hydraulic cylinders were then released, and the force was locked

in the tendon (and thus the beam) by Nut 2 seated against the post

tensioning bracket. All post-tensioning tendon forces were determined

by measuring the axial strain in the tendon.

3.1.5. Vertical Load Tests

Tests involving vertical loading are represented in Table 3.1 as

Tests 23 through 26. In Table 3.1, the numbers from 1 to 21 listed

under the vertical loading heading represent 21 different positions at

which concentrated loading could be applied; location of the 21 points

are given in Fig. 3.4. Depending upon the test, one or both of the

previously described concrete dead weights were positioned on the bridge.

The concrete weights were placed on 9-in. x 9-in. x 1-in. neoprene

pads to approximate a concentrated load. Figure 2.2d is a photograph

of the two 6-kip loads being applied to the bridge simultaneously.

Test 23 involved placing one 6-kip load at the various loading

points. As indicated in Table 3.1, the load was not applied at load

points 7, 14, and 21, all on Beam 1 since the crane was unable to

reach these points because of their close proximity to the laboratory

wall. Test 24 involved placing two 6-kip loads simultaneously at

various loading points on the bridge; the various combinations tested

are given in Table 3.1.

The test procedure outlined in Section 3.1.1 was again used with

the only difference being the type and location of the loading applied.

75

Table 3.l. Vertical load tests.

Test Vertical Loadin11 Points'°' Nu1nber PTS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

23 None • • • • • • • • • .. .. .. • .. .. • • .. • •

• • • •

• .. • •

• • • •

• • 24 None • •

0 • • •

• • • •

• • • •

• • • •

• • •

• •

• 25 21 •

• • • •

• •

• •

• 26 9 •

I • I • , .. •

• • - loaded. * See Fig. 3.4 for location.

1. I I 81 T : 115 • ,_ ___ _)r ____ J----i-1·~~ L ___ , ____ 1~rr__ 1 ':3.33"

44 I I 11 I I 18 I +. ,______ ----i---~-4-+---+-----Fg___ 1';3.33"

6 I I 13 I I 20 + 7 I 14 1 -1 ~21 1'-3.33"

Cf_ BRIDGE I Cf_ DIAPHRAGM f Cf_ DIAPHRAGM

Fig. 3.4. Locations of vertical load points.

···~

2'

i 2'

l 2' t

CL BEAM 4

-6.67" Cf_ BEAM 3 -6.67" Cf_ BEAM 2 -6.67" Cf_ BEAM 1

.... °'

77

3.1.6. Combination Tests--Vertical Load Plus Post-tensioning

Tests involving a combination of a vertical load and post-tensioning

are designated in Table 3.1 as Tests 25 and 26. These tests involved

both post-tensioning forces and vertical loading. As Table 3.1 indicates,

only two post-tensioning schemes were used--namely, PTS-9, where a 20-kip

force was locked in all exterior positive moment regions, and PTS-21,

where a 20-kip force was locked in all negative moment regions.

Loading procedures, data collection procedures, and so forth were

the same as those previously presented. In each of the tests (25 and

26) the post-tensioning forces were applied and locked in prior to the

addition of vertical loading. Previously described instrumentation of

the tendons permitted measurement of force changes in the tendons as

the position of the vertical force(s) was changed.

3.2. Instrumentation and Tests for the Full-Scale Negative Moment Region Mockup

This section outlines the details of the specific tests and pro-

cedures used in testing the mockup. Some of the tests performed on

the mockup consisted of several steps. The various tests performed on

the mockup are summarized in Table 3.2. Note that test number does

not indicate order of completion.

3.2.1. Instrumentation and Vertical Load Mechanism

Instrumentation for all tests conducted on the mockup consisted

of strain gages, DCDTs and one load cell. At the beginning of all

tests, an initial reading was obtained for all instrumentation with

78

Table 3.2. Mockup tests.

Partial Load Test Tendon Strengthening Applied Before

fl Arrangement Angles Used? Post-Tensioning?

1 no 2 no 3 yes 4 straight no no 5 straight no yes 6 straight yes no 7 straight yes yes 8 harped no no 9 harped yes no

79

the DAS. After waiting a few moments, a zero reading was taken. This

procedure allowed identification of any instrumentation problems before

actual testing began.

The vertical loading mechanism is shown in Fig. 3.5. This figure

indicates that the left and right "inflection points" were located 12 ft

8 in. and 12 ft 5 in. respectively, from the "interior support." The

left inflection point hold down was preloaded with a 75-kip clamping

force to hold the beam on the support when loading was applied to the

free end of the beam.

The load cell shown in Fig. 3.5 measured the force exerted by one

of the two hollow core hydraulic jacks used. Since the jacks were in

parallel, the load cell read one-half the total vertical load. This

loading mechanism produced the desired negative moment (see Fig. 2.7d)

between the two "inflection points." Photographs in Fig. 3. 6 show the

hydraulic cylinder in position to apply vertical load and the arrange

ment of threadbars and structural tubes which were used to vertically

restrain the pinned support.

The strengthening angles shown in Fig. 3.7 were present during

all tests performed on the mockup. For tests where the angles were to

be ineffective (i.e., not carrying an axial force) the angles were

supported at two points on the bottom flange of the beam and were held

in place by one bolt partially tightened. This arrangement kept the

dead load constant for all tests conducted and eliminated the possibil

ity of damaging the instrumentation when the angles in the various

tests were intended to be effective or ineffective.

30'-0"

13' -0" 12'-8"

PRELOADED HOLD DOWN

. ·~ · ... ." •, ...... o" • :.. • • ., • • ' ' . • •• • ·" • • • • "" . • •.

"

\

~ ... \

\

PINNED SUPPORT = END SPAN INFLECTION POINT

INTERIOR SUPPORT = PIER

17'-0"

12'-5" '

I HYDRAULIC CYLINDER-........,

LOAD CELL----.. . ..... .-· .:. ·- .. ~ . -.··~:~ • •• <> - • , • • • :,. ••

/TIE-DOWN FLOOR ,

• 111~ SLACK SPACE 7

VERTICAL LOAD POINT = CENTRAL SPAN INFLECTION POINT

j

Fig. 3.5. Vertical loading mechanism for full-scale mockup.

00 0

a. FREE END WITH HYDRAULIC CYLINDERS b. HOLD DOWN END WITH TENSIONED THREAD BARS FOR APPLICATION OF VERTICAL LOAD AND STRUCTURAL TUBE-BEARING FRAME

Fig. 3.6. Photographs of end conditions for the full-scale mockup.

co ,_.

<D

23 7 /8"

® ®®

Ar i I '

® © ©

@* ® ®

Br ....-COVERPLATE I I

'

AL COVERPLATE-"' B~

l' -0" l' -0"

6'-0" 5'-6"

7'-0" 7'-6"

10'-6" 11 '-6"

SUPPORT 'i_

a. LAYOUT

24 3/8"

(jj

--..

/W24x76 ,

['-...STRENGTHENING ANGLES

*NUMBERED SECT! ONS REFER TO GAGE~ LOCATED ON THE BEAM AN D COVERPLATE

**LETTERED SECT! ONS REFER TO GAGES LOCAT ED ON THE STRENGTHENING ANGLES

2 1/2" 2 1/2"

~-j§§§§t\s§§§j ; 1 11/16" LT 5/16" TYPICAL

Li-i i-i --..,2 7/16"

[ ~r-5/16" TYPICAL

b. SECTION A-A c. SECTION B-B

Fig. 3.7. Strain gage locations for full-scale mockup.

00 N

83

Strain gages were mounted at selected locations on the steel beam,

coverplates and strengthening angles as well as on the various tendons.

Each strain gage was bonded with its axis parallel to the axis of the

beam or the tendon.

Strain gage locations on the beam, coverplates and strengthening

angles are shown in Fig. 3.7. Strain gages were offset from the support

center line because of the sole plate. They w~re also offset from the

coverplate cutoff points to avoid the high stress gradients at these

locations. A total of 28 strain gages were placed on the beam and

coverplates, and eight more were placed on the angles. At each of the

numbered sections in Fig. 3.7, there were four strain gages on the

beam, two on the top beam flange, and two on the bottom beam flange.

At each of the lettered sections in Fig. 3.7, there were two strain

gages (one on each angle) on the lower surface of the angle. As illus

trated in Fig. 3.7 at three locations, the strain gages on the angles

are at the same section as strain gages on the beam. Figure 3.8 shows

the positions of the DCDTs used for measuring vertical displacements.

Positions A and B were used for all tests. Position C was used for

the tests without post-tensioning applied and for tests with straight

tendons. Position D was used for the tests with the harped cable

tendons. When the DCDT was located at position C for the harped tendon

tests, it was bumped repeatedly while the jacks and chairs were moved

from one tendon to another during the tensioning operation. The DCDT

was therefore moved from position C to position D. A total of three

DCDTs were used to measure deflections for each test. Although not

shown in Fig. 3.8a, a dial gage was positioned to detect any lateral

movement of the mockup.

x

SUPPORT

© <[_

~ I 6'-0'' 5'-611 .

12'-8''

@

I

12'-5''

- -

© VERTICAL LOAD APPLICATION POINT

+

16'-9 1/2"

Fig. 3.8. Vertical displacement measurement (DCDT) locations on full-scale mockup.

@

I

CXl

"""

85

Both of the 1 1/4-in. $ Grade 150 Dywidag threadbar tendons were

instrumented with strain gages. One strain gage was placed on each of

the "flat" sides of a bar to cancel bending effects. As was done with

the tendon used on the bridge model, each threadbar was calibrated by

placing it in a universal tension-compression machine and recording

strains for various applied tensions. Least squares linear regression

was used to provide a calibration factor relating indicated strains to

tension loads. Correlation of indicated strain to applied load was

excellent with R2 > 0.9995 for each gage.

Grade 270 prestressing strand was used for the harped tendon tests.

Each of the six cable tendons was instrumented with strain gages.

Because a cable is made up of six strands wrapped around a seventh,

placing strain gages on them was somewhat more difficult than placing

strain gages on the threadbars. In order to cancel bending effects,

strain gages were placed on opposite outer strands at each location.

One pair of gages was placed near the middle, and another pair near one

of the quarter points on each cable tendon. Therefore a total of four

gages were placed on each cable (see Section 3.2.4).

Because of the length and the number of gages on each cable, it

was necessary to use a different method for calibration. Two cables

were simultaneously tensioned between widely spaced rigid frames. By

using identical hollow core jacks attached to the pump in parallel,

tension in the cables could be measured with one load cell. Each cable

pair was then calibrated by recording strains and tension loads with

the DAS. For each strain gage, least squares linear regression was

used to provide a calibration factor that related indicated strain to

86

the tension in the cable. Correlation of indicated strains to applied

loads was excellent with R2 > 0.998 for each gage.


Three tests (Tests 1, 2 and 3 in Table 3.2) were performed on the

mockup without post-tensioning applied. These tests were: an initial

cracking test, a post-cracking test, and a strengthened beam test.

During these tests, the straight tendon and associated brackets were

in place on the mockup but were not allowed to take load. This was

done for convenience and to minimize potential damage to the instrumen

tation and its wiring.

The initial cracking test (Test 1 in Table 3.2) was performed to

determine initial behavior of the beam because of cracking of the con

crete and to approximate field conditions on an actual bridge. Since

post-tensioning techniques investigated here are intended as rehabili

tation measures, they would be applied to a bridge that has been in

service for many years. As a result of this service and weathering,

the concrete deck would be cracked in the regions of negative moment.

Setup for the initial cracking test was relatively straightfor

ward. No post-tensioning was applied, and the strengthening angles

were not effectively attached to the beam. After taking a zero reading

with the DAS, vertical load was applied in three cycles with increasing

peak loads. For this particular test, smaller increments were used

than in the standard vertical load cycles used for all other tests.

When a crack occurred, the load after cracking was maintained while

data was recorded. Load was then returned to the level obtained just

prior to occurrence of the crack whereupon data was again recorded.

87

Loading was then resumed until another crack occurred. This technique

simplified the observation of crack effects.

For the first loading cycle, the top load obtained was about 20

kips or approximately one half the peak load of a standard load cycle.

For the second cycle, the top load was about 30 kips or approximately

three-fourths of the peak load. For the third cycle, the load was

increased to the peak load of 43 kips. After the final load cycle,

the mockup was allowed to rest for several minutes before data was

taken to determine the final deflections.

After the initial cracking test, Test 2 (see Table 3.2) was per

formed to determine the basic strength and behavior of the beam.

Behavior of other tests will be compared to the results of this test.

Although the straight tendons and their brackets were in place, no post

tensioning was applied; as in Test 1, the strengthening angles were

also present but were not effectively attached to the beam.

In Test 3, the angles were securely attached to the beam's web to

determine their effectiveness as a strengthening measure. For this

test, as for the previous two) the threadbar tendon and brackets were

in place but no tension was applied.

Vertical loading conformed to a standard load cycle. Three load

cycles were applied to the beam in an effort to "seat" the angles on

the beam. Even though the bolts securing the angles were tightened by

the turn of the net method, some slip between the beam web and the

angles occurred. This method of seating the angles was intended to

give a better indication of their final effectiveness.

88

3.2.3. Post-tensioning Tests--Straight Tendons

Four tests (Tests 4 through 7 in Table 3.2) were performed to

evaluate the effectiveness of post-tensioning with straight tendons.

These tests explored how the mockup responded with and without the

addition of the strengthening angles. In addition, post-tensioning

was done while a partial vertical load was present. This partial load

was removed and reapplied to simulate replacement of a portion of the

bridge deck and its effect on tendon tension.

The arrangement of the 1 1/4-in. <I> Dywidag threadbars used on the

mockup is illustrated in Fig. 3.9. One threadbar was mounted on each

side of the beam web. Anchorage brackets were positioned with a one

inch clearance between the bracket and the top flange. Details on the

brackets are given in Fig. B.8 of Appendix B. The brackets were bolted

to the beam web using 7/8-in.-diameter A325 high strength bolts. As

shown in Fig. 3.9b, the threadbars were located 19.41 in. above the

bottom of the lower coverplate. This position is 6.71 in. above the

centroid of the W24x76 plus coverplates but 3.51 in. below the centroid

of the completely composite section over the support. Because of the

compactness of the brackets, the bearing stiffeners over the support

center line had to be notched as was shown in Fig. 2.8b. Threadbar

strain gages were located near the midpoint between the anchor brackets.

Two 120-kip hollow core jacks connected in parallel were used to ten

sion the threadbars.

The strengthening angles used were 5 in. x 5 in. x 3/8 in.; they

extended 9 ft 6 in. on each side of the support center line and were

not in contact with the bearing stiffener. Details of their placement

I

-- -30 1 -0 11

13'-2 11 16 1 -10 11

l 1·

9'-9 3/4" 10'-9 314" PLACE OF ANCHORAGE

6 1 -6 11 ·~ PLATE =

1· • 1· 6 1 -6 11

... COVERPLATE ·1 BRACKET-....._ !:'. ....-TOP OF BEAM

;:=; -THREADBAR TENDON '"" -fl TENDON

WITH SPLICE I: 7/8" DIA. BOLTS

I

mm•rn I· .. j~ I ......_ - ··--· -

I 19 SPACES@ 6" = 9'-6" A .. !!! 19 SPACES@ 6" = 9'-6" I • • ! I l • • ·3.11 311

t SUPPORT

a. THREADBAR TENDON

/\:~:'.1;;~:u~~~/'.:/if~~~;:~.{:::r:~::;:;;:::;;:::,:~~:.::::;:;;t::r~~\~i Ii

19.41" THREADBAR TENDON

4 1111 STRENGTHENING ANGLES, 5x5x3/8

·~ W24x76 WITH COVERPLATES

b. SECTION A-A c. PHOTOGRAPH OF STRAIGHT TENDON AND ANCHORAGE

BRACKET

Fig. 3.9. Threadbar tendon arrangement.

co <D

90

are shown in Fig. B.9. As shown in this figure, a spacing of 6 in.

was used for the 7/8-in.-diameter A325 high-strength bolts. A 1-in.

space was maintained between the angle flange and the bottom flange of

the beam.

Test 4, the first test, was the most basic of the straight tendon

tests since the angles were not effectively attached to the beam web.

After zero readings were obtained, the threadbars were tensioned until

their total tension was approximately 100 kips, at which time they

were locked off and the hydraulic pressure released. Seating losses

at lockoff were small, less than 5% of the maximum tension before lock

off. A standard vertical load cycle was then applied after which the

threadbar tension was released.

Test 5 was similar to Test 4 except that the threadbars were ten

sioned while a partial vertical load was present. For this test, as

for Test 4, the strengthening angles were not attached to the beam

web. After the zero readings were taken, a vertical load of 20 kips,

approximately one-half of the peak load, was applied. The threadbars

were then tensioned to a total of approximately 100 kips and locked

off while the vertical 20-kip load was held constant. Seating losses

were again less than 5% of the maximum tension before lockoff. Vertical

loading was then resumed until the peak load of 42 kips was obtained.

Next the vertical load was completely removed and reapplied as in a

standard load cycle. The vertical load was then reduced until approxi

mately 20 kips, or one-half the peak load remained. The threadbar

tension was released and the remaining vertical load removed.

91

For Test 6 the strengthening angles were bolted securely and were

thus effective in carrying axial stress. Tensioning of the threadbars

and application of vertical load followed the same procedure as for

Test 4. However, two vertical load cycles were performed.

For Test 7 as for Test 6, the strengthening angles were bolted

securely. The loading and tensioning procedure for this test, however,

was identical to that used in Test 5.

3.2.4. Post-tensioning Tests--Harped Tendons

Two tests (Tests 8 and 9 in Table 3.2) were performed to evaluate

the effectiveness of post-tensioning with harped cable tendons. These

two tests explored how the mockup responded to the cable tendons with

and without the addition of the strengthening angles. Because of the

difficulty involved in tensioning the cables, tests with a partial

vertical load were not performed.

The arrangement of the cable tendons on the mockup is shown in

Fig. 3.10. Three cable tendons were placed on each side of the beam

web. The harp saddle brackets (see details in Fig. B.11) were mounted

as high on the beam web as possible while avoiding the web-flange fillet.

The anchorage brackets (see details in Fig. B.lO)'were mounted as close

to the bottom flange as possible but also avoiding the web-flange fillet.

The anchorage brackets were positioned so that the axis of the center

cable was perpendicular to the tendon-bearing faces of the bracket. As

may be seen by comparing the dimensions given in Fig. 3.9a and Fig. 3.lOa,

the anchorage brackets were located almost directly below where the

straight tendon anchorages had been.

N '-. -..,. ' --

~::~~~~~··r1·~~-::-:--::-:-~-__jlQO~·-~s~"~~~~~---I.. 4 '-10 1/4" ' r. ~

9'-11'/4"

I ' ·I· 5'-10" '!.

! I A~ · 'I Ii. TENDON+=----- 4-+--' L I _..-COVERPLATE i I

s CABLE TENDON '-:r+-f

SADDLE

FACE OF ANCHORAGE PLATE

'.::'. /TOP OF BEAM -<!'

::.... l ANCHORAGE PLATE

' A~ COVERPLATE STRENGTHENING ANGLES 1. 16 SPACES@ 6" = 8'-0" .,i j j. 17 SPACES@ 6" = 8'-6"

3n 311 Ii. SUPPORT

a. CABLE TENDONS

:~:::_:·:·::·:~~: .:7J;:}X~?.}:fY'·'.T:~~-;:_;:::::.'.~·:: ~ t:.~: ;:;;}~: ": ~u. I ~-1 Ji*'!' IR . t B

~CABLE TENDONS r-

22.75"

4 1111 STRENGTHENING ANGLES, 5x5x3/8

' ~ W24x76 WITH COVERPLATES

b. SECTION A-A

Fig. 3.10. Harped cable arrangement.

~ N

STRAIN GAGE PAIR

!_ <[_

4'-10 1/4" 5 1 -10 11

9. -11 1/4" 10 1 -8 11

SUPPORT <[_

c. SECTION B-B

ANCHORAGE BRACKET

BEAMWEB Hf BEAM WEB

8 1/4" <[_

TOP CABLE-----~B 31

4' 9 1/4"

BOTTOM CABLE_,........-- _,,--

MIDDLE CABLE

d. PHOTOGRAPH OF HARPED CABLES AND ANCHORAGE SYSTEM Fig. 3.10. Continued.

<.O w

94

Shear loads in both types of brackets were carried by 7/8-in.

diameter A325 high-strength bolts. Loads causing the brackets to "peel"

away from the beam web were carried by high-strength threaded bars

that passed completely through the brackets to clamp the brackets to

the beam web. Gusset plates incorporated into the brackets transferred

loads exerted by the cable tendons to the beam web.

As shown in Fig. 3.lOb, the cable tendons were located 22.75 in.

above the bottom of the lower coverplate. This position is 10 in.

above the centroid of the W24x76 plus coverplates and only 0.23 in.

below the centroid of the completely composite section over the support.

When compared to the threadbar tendons, the cable tendons are 3.34 in.

higher on the beam at this cross section. In order to provide clearance

past the lower flange for the hydraulic cylinders and jacking chairs

used to tension the cables, the cable tendons were placed further from

the beam web than the threadbar tendons.

Two 60-kip hollow core hydraulic cylinders were used to tension

each pair of cables. Only one pair of tendons was tensioned at a time

to reflect probable tensioning operations in the field. When the cables

were tensioned (each was tensioned to the same peak load before lockoff),

the top pair was done first, then the middle pair, and finally the

bottom pair (see Fig. 3.10c). When tension in the cables was released,

this order was reversed. Seating losses were quite high, approximately

14% to 18% of the maximum tension before seating. This was primarily

due to the type of anchoring chucks employed and the relatively short

tendon lengths used.

95

Cable tendon strain gage placement, shown in Fig. 3.lOc, was

designed to verify symmetry of tendon tension and to determine friction

losses over the harp saddles. To reduce friction losses, the harp

saddles were smoothed as much as possible and lubricated with grease.

Measured friction losses were 3% or less over the saddles, and there

fore the precautions were successful. As previously noted, the DCDT

at position C was moved to position D to avoid bumping it during the

cable tensioning process.

The first test involving the harped cable tension, Test 8 in

Table 3.2, was done without the strengthening angles securely attached

to the beam web. After obtaining a zero reading with the DAS, the top

cable pair was tensioned and seated, followed by the middle pair and

then the bottom cable pair. Two standard vertical load cycles were

then applied. Cable tension was then released in the reverse order of

application.

In Test 9 the strengthening angles were securely attached to the

beam web. Because of the interference with the cable anchorage bracket,

the angles had to be shortened as shown in Fig. 3.lOa. The same cable

tensioning and vertical-loading procedure was used for this test as in

the previous test.

97

4. ANALYSIS AND TEST RESULTS

As in Chapters 2 and 3, Chapter 4 is divided into two main sections,

the first section for the model bridge and the second section for the

mockup. Wherever possible in the section for the model bridge, finite

element analysis results are plotted with experimental results, in

order to provide a complete picture of the behavior of the model bridge

and to show the degree of correspondence between theory and experiment.

In the section for the mockup, theoretical results based on classical

analysis are often presented with the experimental results in order to

bracket the experimental data between the theoretical conditions for

the mockup with and without composite action.

4.1. Model Bridge Analysis and Test Results

4.1.1. Preliminary Analysis

To determine the desired location of the post-tensioning brackets

on the bridge model, the authors conducted a parameter study for moments

applied to a three-span beam. The span lengths of the beam used in

the study correspond to those of the beams in the model bridge. The

beam analyzed had a constant moment of inertia, as opposed to the vary

ing moments of inertia along the actual model bridge beams. As will

be noted later, the general trends exhibited in the analyzed beam also

occur in the model bridge beams.

Two examples of the parameter study are given here. Both examples

are designed to reverse the effects of ordinary service loads applied

to the beam. In both examples, moments are applied to the beam which

98

could be applied in practice by means of straight tendons. For the

three-span beam illustrated in Figs. 4.1 and 4.2, there are five

regions in which critical service design moments occur. The two

regions over the interior supports will be referred to as negative

moment regions, and the three remaining regions will be referred to as

positive moment regions.

The first example, for applying negative moments to the positive

moment regions is given in Fig. 4.1. Figure 4.la shows the moment

diagram for moments applied two feet from the supports, and Fig. 4. lb

shows a similar moment diagram for moments applied three feet from the

supports. From the two moment diagrams, it is apparent that the appli

cation of the moments to the beam spans affects both the service load

positive moment regions on the spans and the service load negative

moment regions above the interior supports. The amount of moment

distributed to the critical design moment locations varies with the

position of the applied moments. Applied moments located closer to

the interior supports distribute more moment to the support region

than applied moments located farther from the interior supports. The

moment at the interior supports is 7.05 foot-kips (in Fig. 4.la),

whereas in Fig. 4.lb the moment is 5.71 foot-kips. Conversely, applied

moments located farther from the interior supports distribute more

moment to the beam spans. In Fig. 4.la the moment on the center span

is -1.27 foot-kips, whereas in Fig. 4.lb the corresponding moment is

-2.61 foot-kips.

The second example for applying positive moments to the negative

moment regions is given in Fig. 4.2. Figure 4.2 is arranged in the

-"' +' 4--

7.0

i-'.' 0. 0 z w.J ::<: ~

-7.0

-'£

+' 4--

7.0

i 0.0 w.J ::<: ~

-7.0

iB 8.33tn 8.33'~ 3.33n-k 8.33r~~ 8.33wk

8 . 33'~

(a) MOMENT APPLIED TWO FEET FROM SUPPORTS

t5 8 .33

n k '·"t,'. ~ 3

:, 8.33

n · k s.33f~3 .f 3 s '·'''' ., s.33()

(b) MOMENT· APPLIED THREE FEET FROM SUPPORT

Fig. -4.1. Moment diagrams for three-span beam, negative moments applied to spans.

<.O <.O

+-' 4--

1

""

7.0

i-'.' 0. 0 z LU ::E:

~ -7.0

+' 4-

1

""

7.0

i-'.' 0 .0 z LU ::E: 0 ::E:

-7.0

8.33?. k ~.33 ft "k 8 .33~· k \33 ft "k

m "1 ]J_ ,; "1 ff: 17 . ~ /, I 2•1 2ol I 2:2ol 77,"

1 .... 1 .. 111 111 •I• url J

(a) MOMENT APPLIED TWO FEET FROM SUPPORT

8.33ft"k 8.33ft"k 8.33ft•k 8.33ft•k

~ ' ~ ' ii --\, 3·~;-17- ---- . \.;···3,~3, ,J ~

/ ~ ~ 7/

ssss\S&~ ~ ~wssssss

(b) MOMENT APPLIED THREE FEET FROM SUPPORT

Fig. 4.2. Moment diagrams for three-span beam, positive moments applied near interior support.

..... 0 Cl

101

same manner as Fig. 4.1, with the moment diagram for applied moments

two feet from the supports in Fig. 4.2a and three feet from the supports

in Fig. 4.2b. The comments regarding moment distribution made with

respect to Fig. 4.1 also apply to Fig. 4.2.

In general, the parameter study showed that design of post-tensioning

for strengthening purposes will be more complex for continuous beam

bridges than for simple span bridges. Application of post-tensioning

moments to one or more regions of a continuous bridge will affect all

regions. The continuous bridge will distribute applied moments both

longitudinally as demonstrated above and transversely as demonstrated

for simple span bridges in References [9,10,18,19].

Because of the longitudinal distribution effects and the changes

in the magnitudes of moments depending on the locations at which moments

are applied, the tendon bracket locations for the model bridge were

set to make provisions for tensioning both positive and negative moment

regions and for changing the length of tendons in negative moment regions.

Budget limitations prevented placing bracket tabs in all regions and

providing tendon length adjustment for all regions on the model bridge.

Any significant gaps in the test program for the model bridge were

covered by the finite element analysis study.

4.1.2. Finite Element Analysis

The continuous, composite bridge model constructed in the ISU

Structural Engineering Laboratory is a variably stiffened orthotropic

plate and, therefore, is structurally quite complex. In previous

research and development of a design manual for simple span, composite

bridges, the authors found finite element theory to be best suited of

102

several theories for analysis of such bridges [9]. Finite element

theory can take into account the complexities of the bridge and also

give information on distribution of moments and axial forces.

The finite element model for the laboratory bridge model was

developed for use with SAP IV [3], a well-known finite element pro

gram available to the authors through the ISU Computation Center.

Because of the complexity of the finite element model, a preprocessing

program was written to generate the model by using quarter symmetry.

Two programs written previously for simple span bridges, which draw a

finite element model before and after deformation, were used to verify

the model and to draw deflected shapes. A new program was written to

plot the strains along top and bottom flanges of each of the beams in

the laboratory model bridge.

The basic finite element assembly for the laboratory bridge model

is given in Fig. 4.3. Previous experime11ls with mesh sil'.:e [9] i11di-

cated that reasonable accuracy could be achieved by dividing a full

size concrete bridge deck into approximately 30-inch-square shell ele

ments. The fact that the bridge model is at one-third scale suggested

that the shell elements be approximately 10 in. square. With consider

ation of the di.mensions of the laboratory bridge model and locations of

the steel beams, the elements were made 7.67 in. wide and 8.33 in. long.

Between the exterior beam and curb, a row of shell elements, which are

narrow and long, were placed to complete the deck.

Deck shell elements were given elastic properties for concrete

with the 28-day strength of 3450 psi determined by testing. Deck prop

erties and the finite element model assume that the deck behaves

BEAM ELEMENT WITH END RELEASES (NO SHEAR CONNECTOR)

FORCE AT

103

BEAM ELEMENT (CURB)

SLAVE NODE LINKED TO DECK NODE

SHELL ELEMENT (DECK)

BOUNDARY ELEMENT WITH NOMINAL STIFFNESS

...... ~---BEAM ELEMENT (STEEL BEAM OR STEEL BEAM AND COVER PLATE)

r---BEAM ELEMENT WITH ARBITRARILY LARGE STIFFNESS TO APPLIED FORCE

TENDON ANCHORAGE ----BEAM ELEMENT (DIAPHRAGM)

a. ISOMETRIC VIEW

BEAM ELEMENT (CURB)

,.----, SHELL ELEMENTS (DECK)

.. ::··:·:~'.::::·.:-.-::~ ~~~~~~-BEAM ELEMENTS ~ (SHEAR CONNECTOR)

"""""=~c;;;;~~BEAM ELEMENT (STEEL BEAM)

BEAM ELEMENT (DIAPHRAGM)

~------BEAM ELEMENT (TO BRACKET)

b. SECTION THROUGH EXTERIOR BEAM

Fig. 4.3. SAP IV finite element model.

104

elastically in both compression and tension and that composite action

is achieved in accordance with the input stiffness for the shear con

nectors. Past research has shown that the treatment of the deck as

an elastic material gives accurate results for composite bridge struc

tures loaded within the service load range. In order to avoid numerical

problems with the crowned deck, boundary elements with a small and

arbitrary rotational stiffness were placed at deck nodes as required.

Curbs integral with the model bridge deck were modeled as beam

elements, approximately 8.33 in. long, with elastic properties based

on a 28-day concrete strength of 3355 psi. Since there is no signifi

cant slip between integral curbs and the bridge deck, curb beam nodes

were linked as slave nodes to deck nodes directly below.

Each steel beam was modeled by beam elements having elastic prop

erties as computed for noncomposite beams. Where section properties

changed because of change in width and thickness of flanges (to simu~

late presence or absence of coverplates), beam elements shorter than

the 8.33 in. deck node spacing were linked together.

Rather than link the steel beam elements directly to the concrete

deck shell elements by means of slave nodes, flexible beam elements

were inserted for the connection in order to model shear connector slip

and to obtain information regarding the forces on shear connectors.

The flexible beam elements were given stiffnesses to approximate the

load-slip characteristics of the shear connectors in the laboratory

bridge model. When the shear connector location did not match the

8.33 in. mesh, the flexible beam link was placed at the nearest set of

beam-deck nodes. Moving the link previously has been shown to have

105

little effect on the overall finite element model behavior [9]. If no

flexible beam link occurred at a set of beam-deck nodes, a spacer link

without load-slip characteristics was inserted. Torsional and trans

verse stiffnesses of the beam web were given to the flexible and spacer

beam links in order to correctly model the web behavior [9].

The beam elements used to model diaphragms were attached directly

to the main bridge beam elements. For the post-tensioning brackets or

arbitrary elevations of applied forces, vertical beam elements with an

arbitrarily large stiffness were attached to the bridge beam elements

and extended as far above or below the bridge beam elements as necessary.

Post-tensioning tendons were not included in the finite element model

because inclusion of the tendons adversely affects bandwidth, solution

time, and the overall finite element analysis cost.

Right-angle bridges with structural symmetry, which are symmetri

cally post-tensioned and loaded such as the laboratory bridge model,

can be modeled with the quarter symmetry finite element model shown in

Fig. 4.4. In order to reduce analysis cost, the finite element analysis

was limited to the symmetrical post-tensioning and vertical loading

cases shown in Fig. 4.5. Since most of the strengthening requirements

in practice are symmetrical, the authors decided that the additional

cost and time required for unsymmetrical analyses were not justified.

For some unsymmetrical cases, experimental results are given in Sec

tion 4.1.4.1; those results give the behavior of the laboratory bridge

model under unsymmetrical post-tensioning conditions.

_.........-MIDSPAN OF """-· CENTER SPAN

·-...........

. .---· <CENTER

OF BRIDGE

INTERIOR---' BEAM ELEMENT

.DECK SHELL ELEMENT

EXTERIOR BEAM ELEMENT

z

x~ I ·----- y ~ •

----ANCHORAGE NODE WITH BEAM ELEMENT TO EXTERIOR BEAM

PIER SUPPORT NODE

NOTE: BOUNDARY ELEMENTS ARE NOT SHOWN

Fig. 4.4 Quarter syrrunetry finite element model.

CURB BEAM ELEMENT

ABUTMENT SUPPORT NODE

..... a

"'

107

I a. LC 1 (SAME AS PTS-7)* h. LC 8

I b. LC 2 (SAME AS PTS-9)* i. LC 9

c. LC 3 j. LC 10

~ * d· LC 4 k. LC 11 (SAME AS PTS-22)

I * e. LC 5 (SAME AS PTS-21) l. LC 12

I I I I * Ill

f. LC 6 (SAME AS PTS-20) m. LC 13 (SAME AS PTS-8)

g. LC 7 n. LC 14

Fig. 4.5. Load cases analyzed with SAP IV finite element model.

108

o. LC 15 s. LC 19

LP 11

• P· LC 16 t. LC 20

I LP 4

I I LP. 18 • q. LC 17 u. LC 21

r. LC 18


109

4.1.3. Strain and Deflection Data Interpretation

Considerable quantities of data were gathered during testing of

the bridge model. Some of the data, even though redundant, were

gathered to provide a check of the bridge model as well as the instru

mentation. Because most of the strains measured on the top flanges of

the steel beams were very small and thus more subject to instrumentation

errors than the larger bottom flange strains, only the bottom flange

strains will be reported for most tests. Among the remaining data,

only the most significant will be reported.

In order to gain some concept of the magnitude of uncertainties

regarding the model construction and instrumentation, the data were

systematically compared over the first few months of testing to deter

mine what effect curing and cracking of the concrete deck would have

on reliability of the results. Symmetry and superposition also were

used as devices to check the reliability of the results. The checks

of time effects; symmetry, and superposition are summarized in the

following sections.

4.1.3.1. Time Effects

Because the concrete deck was constructed monolithically, the

entire length of the bridge was subjected to the effects of shrinkage.

The shrinkage was evidenced by bridge beams lifting off of the end

supports by amounts ranging from 1/8 to 3/16 in. during the deck-curing

period. Before any tests were conducted on the model bridge, all beams

were pulled down to their supports. The tie downs (see Fig. 2.5) did

not cause any immediate cracking of the deck.

110

After the deck had cured and the bridge was tied down at the sup

ports, a series of post-tensioning and vertical load tests were con

ducted. Those tests, including PTS-1, PTS-3, PTS-10, PTS-12, and

PTS-20, were then repeated two months later. During the initial two

month testing period, the deck cracked many times and thereby relieved

most of the shrinkage stresses. The final crack pattern included cracks

at approximately the two-thirds sections on the end spans, the interior

support sections, and the quarter sections of the center span.

The second series of tests gave larger strains and deflections.

Strains increased by 10%, on the average, and deflections increased by

16%, on the average. The increases are similar to those which occurred

(but were not systematically documented) during testing of the simple

span, composite bridge model in the ISU Structural Engineering Labora

tory [19].

The increases also are very close to the 15% increases in strains

and deflections noted by Kennedy and Grace during testing of an unpre

stressed, two-span, composite bridge model [17]. Kennedy and Grace

attributed the increase in strains and deflections to cracks in the

deck at the interior support and to subsequent loss of composite action

in the negative moment region. They were able to show that with deck

prestressing, composite action was maintained; the increase in strains

and deflections did not occur.

The increase in strains and deflections noted for the continuous

bridge model are probably the result of both deck shrinkage and loss

of composite action in the negative moment regions. The simple span

model tested earlier at ISU had no negative moment regions, and yet it

111

exhibited a gain in strains and deflections when deck shrinkage

stresses were relieved by cracking. Because no comparable data is

available on the actual increase in strains and deflections, the amount

of increase caused by shrinkage and the amount of increase caused by

loss of composite action in negative moment regions cannot be determined.

4.1.3.2. Symmetry

If loading is symmetrical with respect to an axis of structural

symmetry, all displacements, forces, and moments will be symmetrical

with respect to the same axis. Because the model bridge has two axes

of structural symmetry, symmetrical post-tensioning and vertical loads

were applied to the model in order to check the symmetry of the model

construction. Data presented in this section are for PTS-9, which is

one of the symmetrical post-tensioning schemes.

PTS-9 consists of applying post-tensioning to all of the positive

moment regions, A, C, and E, of the exterior beams 1 and 4, as shown

in Fig. 4.6. Since only four hydraulic jacking cylinders were avail

able, the tendons were tensioned sequentially, which partially accounts

for the 1.5% difference among the final tendon forces. Because the

tendons were applied to the positive moment regions of the exterior

beams, much of the post-tensioning effect is due to moment rather than

axial force; and therefore the strains are larger and more reliable

than for other post-tensioning schemes.

Figure 4.6 illustrates the longitudinal symmetry for bottom flange

strains for Beam 1, Fig. 4.6a, and for Beam 2, Fig. 4.6b. Transverse

symmetry for Sections A, B, and C is shown in Fig. 4.6c, d, and e

respectively. Similar numerical comparisons are available in Table 4.1.

112

700

~ . c:

..... 350 ... ---... . • • c: ..... ;:1

0 ~

z: • ...... <l'.

"' - -f--350 • (/)

• • • • -700

I I I I I I I I I

A B c D E BMl BM2 BM3 BM4

a. BEAM 1 c. SECTION A

700 ~

c: ::. 350 - '-. • c: • .....

• • • ;:1 0 ... --~

Z'. • • • ...... <l'.

"' f--350 -(/)

-700 I I I I I I I I I

A B c D E BMl BM2 BM3 BM4

b. BEAM 2 d. SECTION B

4 I 20 .16 K 19.88K 19 .86K I

700

ii 1350 '-1

20.06K 19.90K 20K _......! . c:

A B c D E ..... 0 --...

KEY c: • • ..... ;:1

~-350 '-z: • ...... <l'.

"' I I I I tn-700

BMl BM2 BM3 BM4

e. SECTION c

Fig. 4. 6. Bottom flange strains for l'TS-9.

Table 4.1. Comparisons of bottom flange strains between symmetrical sections for PTS-9.

a. Longitudinal Comparison

Beam 1

Sec. A Sec. E Sec. B Sec. D

Strain

Percentage Difference

-514 -521

1.4%

b. Transverse Comparison

Section A

BM 1 BM 4 BM 2

Strain -514 -533 -174

Percentage Difference 3.6%

220 242

9.5%

Section B

BM 3 BM 1 BM 4 BM 2

-168 221 226 83

3.5% 2.2%

Beam 2

Sec'. A Sec. E Sec. B Sec. D

-174 -160 83 98

8.4% 16.6%

Section C

BM 3 BM 1 BM 4 BM 2 BM 3

93 -381 -322 -137 -113

11.4% 16.8% 19.2%

..... ..... w

114

Overall, the magnitude of the differences between symmetrical sections

or beams do not vary a great deal; however, the percentage differences

vary from a low of 1.4% for a large strain to a high of 19.2% for a

moderately low strain. The percentage differences in the table average

9.3, which generally is acceptable for experimental work.

In general, it appears that the largest percentage differences

between symmetrical strains are for strains distributed by the bridge.

In Table 4.la, the percentage differences are smaller for the post

tensio11ed sectior1s A and E than for the unpos'L-Lensioned sections B

and D. In Table 4.lb, the post-tensioned beams 1 and 4 usually have

smaller percentage differences than the unpost-tensioned beams 2 and

3.

There is a certain amount of error on symmetrical strains, and

this error can be attributed to two primary causes: imperfections in

the steel beams, concrete deck, and concrete curbs, and imperfections

in application of the post-tensioning. Because the bridge model was

constructed at one-third scale, ordinary tolerances in beam depth,

deck thickness, and curb dimensions have a greater effect than the

same differences at full scale. Because the errors which can be attri

buted to symmetry of the construction are relatively small, no adjust

ments were made to data in subsequent use and interpretation of the

data.

4.1.3.3. Superposition

Another method for checking experimental results is to superpose

data taken from separate load tests and compare the superposition data

with data taken from a combined load test. In this section, superposi

tion is used with v~rtical load tests to make such a comparison.

115

Figure 4.7 shows bottom flange strains plotted for the sum of the

strains from individual load tests for 6-kip loads at LP4 and LP18 and

for the load test with two 6-kip loads on the model bridge. The solid

dots represent the superposition of the two separate tests, and the

open dots represent the single test. All of the parts of the figure

show little difference between the two conditions, and in some cases,

it was difficult to plot the small difference between the two conditions.

Table 4.2 gives the same comparisons as Figure 4.7 but in numeri

cal form. The largest percentage difference between the results from

superposition and the individual test is 13%, and the differences aver

age only 6.2%. Since this difference is quite small, it is reasonable

to use superposition in interpreting the experimental results.

Differences for superposition were shown to be somewhat larger

for post-tensioning schemes [7]. At least part of the increased differ

ence was shown to be caused by secondary effects in tendons. When

post-tensioning is applied in stages, the forces in tendons that are

locked in place change slightly, and the changes cannot be included in

superposition of individual tests. These changes were generally on

the order of 3% to 4%.

Table 4.2 also permits a check of symmetry, and on the average,

differences are 11.3%. This percentage is very close to the average

noted for PTS-9 in Section 4.1.3.2. This average is inflated by two

very large percentage differences for small strains in Table 4.2a. If

those large percentage differences are neglected, the average is only

4.7%. In general, vertical loading is likely to give more accurate

results because the application of the load is not affected by imper

fections in the bridge model construction.

c: ·~ 350 -...... . c: ·~

z ~

.a: 1=-350 V)

116

i

e -700 ....__...._____.. __ ...._ _ __, _ __.. _ _.

A B C D E a. BEAM 1

700.---~-~--~----~

<:: :::::. 350 -. <::

2 o 1-----'o,__ ____ e ___ -1

z ~

.a: "" t;;-350 -

_ 700 .___._1 _..._1 _ ___.1 __ .__1_...__ I__. A B C D E

b. BEAM 2

!------------·-··-------

I . I

BMl BM2 BM3 BM4

c. SECTION A

e e

I I I I BMl BM2 BM3 BM4

d. SECTION B

20.16K I 19.88K 19.86K }l·r-1--0---::,----+---....... , ?00.-------------,

. 350 t-

20 .06K I 19.90K 20K 'J A B C D E :::::.

KEY .

ePTS-9 .~ oSUPERPOSITION ;:i.

FOR PTS-1 ~-350 ..,_Q THROUGH PTS-6 ;:::;

~ t;:;_700'--1'--~~-'-1 ~~-~1'-----1'-'

BMl BM2 BM3 BM4

e. SECTION C

Fig. 4. 7. Bottom flange strains for PTS-9 and superposition of PTS-1 through PTS-6.

Table 4.2. Comparisons of bottom flange strains between vertical load load tests with and without superposition.

-

a. Longitudinal Comparisons

Beam l Beam 2

A B c D E A B c D E

Strain for superposition of 6 kips LP 4 + LP 18 acting separately 116 -14 -80 -7 117 264 -71 -86 -79 299

Strain for 6 kips at LP 4 and LP 8 acting .... .... simultaneously 125 -15 -76 -7 120 269 -74 -78 -90 296 ..._,

Percentage Difference 7.5% 6.8% 5.1% 0% 2.5% 1.8% 4.1% 9.7% 13.0% 1.0%

Table 4.2. (Continued)

b. Transverse Comparison Section A Section B Section C

1 2 3 4 1 2 3 4 1 2 3 4

Strain for superposi-tion of 6 kips at LP 4 + LP 18 acting separately 116 264 242 118 -14 -71 -71 -14 -80 -86 -92 -80

Strain for 6 kips at LP 4 and LP 8 acting simultaneously 125 269 269 126 -15 -74 -77 -15 -76 -76 -82 -75

Percentage ..... ..... difference 7 .5% 1.8% 10.5% 6.5% 6.8% 4.1% 8.1% 6.8% 5.1% 9.7% 11.5% 6.4% co

119

Checking the experimental data with respect to time and cracking

effects, symmetry, and superposition showed relatively small errors;

such errors are generally within accepted standards for experimental

work. Therefore, in subsequent analysis and presentation of experi

mental data, the validity of symmetry and superposition will be assumed

and used to give a more complete presentation of results.


The laboratory post-tensioning tests were conducted for tendon

forces of 10 and 20 kips. Because the larger forces produced larger

strains, which were less subject to zero shift and other instrument

variations, only data for the 20-kip forces will be presented in the

following sections. Because symmetry was validated in Section 4.1.3.2,

data from symmetrical tests were utilized to complete data sets for

single beam schemes. Data points from symmetrical tests are always

noted with separate symbols in the figures so that they may be readily

identified.

4.1.4.1. Single Beam Schemes

Post-tensioning of single beams was tested with the objective of

determining the feasibility for strengthening a deficient beam or

deficient beam region. In practice the deficiency could be caused by

damage from localized corrosion or from an overheight vehicle colliding

with the bridge. Within the limitations of the bracket tab locations,

various service load positive and negative bending moment regions were

post-tensioned. The graphs for bottom flange strains presented in this

section show the longitudinal and transverse distribution effects for

various localized post-tensioning schemes.

120

The first series of post-tensioning schemes presented involve

post-tensioning of positive moment regions. Figure 4.8 gives the bottom

flange strains for PTS-1, in which the positive moment region for the

end span of one exterior beam was post-tensioned. A force of 20.2 kips

was applied to Beam 4 in region A. In the figure, the data set is

completed by use of the four data points from PTS-5, which are given

with open square symbols.

As could be expected, the largest strains occur on the post

tensioned beam, Beam 4, and the strains gradually decrease for Beams 3,

2,. and 1 across the bridge. The far exterior beam, Beam 1, has very

small bottom flange strains, but some of which are in the reverse

direction from those applied to Beam 4. Those reverse strains would

be undesirable from a strengthening viewpoint.

Along Beam 4, the strains decrease gradually from left to right

for the sections at which strains were measured. The strains at Sec

tions A and B would be in the correct direction for strengthening, but

the strains at Sections C and D would be in the reverse direction for

strengthening. The strain at Section E is small but in the correct

direction for strengthening. In general for this post-tensioning scheme,

the strains decrease in both transverse and longitudinal directions

away from the post-tensioned region, and some of the strains are not

beneficial with respect to strengthening the bridge.

PTS-3, for which strains are given in Fig. 4.9, is the second in

the series of positive moment region post-tensioning schemes. Here

the positive moment region for the center span is post-tensioned with

a force of 19.71 kips. The maximum strain transmitted to the post-

~

c ·~ 500 ...__

c ·~

0 z ~

<(

"" t;-500

c ·~ 500 ...__ c ·~

z ~

<(

0

"" t; -500

c :::::_ 500 c ·~

z: ~

<( 0::

0

t; -500

~

c ·~ 500 ...__

c ·~

::L 0 ~

:z ~

<(

"" t; -500

~

- • -

• -

-...

'-

-

-~

20.2K

ll 1

A

Fig. 4.8.

121

• - •

- •

-

! I I ;

B c D

Bottom flange strains

-

•

-

E

for PTS-1.

BM4

e PTS-1 a PTS-5

BM3

BM2

BMl

.;: 500

....... . c:

0 z ...... ~ 1--500 Vl

.;: 500 ...... c::

z ...... <( IX

0

t;:;-500

<:: ·~ 500 ...... <::

z ...... <( IX

0

t;:;-500

c:: :::. 500 <:: ·~

z ...... <( IX

0

t;:;-500

-

-

-

~

-

...

-

-

122

• I I •

•

... -•

- -..

- ... -

lrl~~+-~--1~-+~~~+-~1--~-+~~ 19. 71 K

i I A B c D E

Fig. 4.9. Bottom flange strains for PTS-3.

BM4

e PTS-3 m PTS-3

FROM SYMMETRY

BM3

BM2

BMl

123

tensioned beam, Beam 4, is smaller in this scheme than for PTS~l. The

probable reason is that the post-tensioning effects are distributed in

two directions longitudinally, rather than in one direction. As in

PTS-1, the strains decrease in both longitudinal and transverse direc

tions away from the post-tensioned region. Again some of the strains

are beneficial and some are not.

For the last positive moment region scheme presented here, which

is constructed as the superposition of PTS-1, PTS-3, and PTS-5, all

positive moment regions along Beam 4 were post-tensioned. The bottom

flange strains shown in Fig. 4.10 indicate that less strain is trans

mitted to the positive moment region on the center span at Section C

than to the positive moment regions on the end spans at Sections A and

E. The smaller strain occurs even though the tendon forces are approxi

mately equal and all of the tendons were positioned at the same eleva

tion with respect to the beam and the neutral axis. The smaller strain

is due to the larger center span length and, to a lesser extent, to

the difference in end conditions between the center span and the end

spans.

Strains decrease for the first interior beam, Beam 3, and are es

sentially zero for the second interior beam, Beam 2. For the far

exterior beam, Beam 4, the strains are reversed and would not be bene

ficial with respect to strengthening the bridge.

Two sets of schemes for post-tensioning negative moment regions

are presented next. The first set is for an exterior beam, and the

second set is for an interior beam. For all of the negative moment

post-tensioning schemes, straight tendons were placed above the deck,

..-;-

.~ 500 .._ . c: .....

z ~

cl:

0

r=-500 (/)

~ . .;: 500

s:: ..... ;:1 0

:z: ~

cl:

l=-500 (/)

s:: ::::::. 500 <:: .....

0 z ~

cl:

"' t;:;-500

s:: ::::::. 500 s:: .....

0

-

- • -

• '-

--

~

-

-~

20.2Kips

I A

124

h

•

4

•

-

-

!

19.71Kips

I I B c

•

I

•

-

-

I

19.92Kips

D E

llM4

'. ePTS-1 + PTS-3

+ PTS-5 •PTS-1 + · PTS-3

+ PTS-5 FROM SYMMETRY

BM3

BM2

BMl

Fig. 4.10. Bottom flange strains for PTS-1 + PTS-3 + P'l'S-5.

125

a condition that was necessary because of the scale of the model but

which would not be possible in practice. For all of the schemes pre

sented here, the shorter tendon option permitted by location of the

bracket tabs was employed because the shorter tendon option gave larger

strains in the negative moment regions. Thus the behavior of the bridge

was consistent with the behavior described in Section 4.1.1 and illus

trated in Fig. 4.2.

PTS-10, for which strains are given in Fig. 4.11, consists of

post-tensioning one negative moment region for the exterior beam, Beam 4,

through Section B. The maximum strains illustrated in Fig. 4.11 are

much smaller than the strains for positive moment region post-tensioning

shown in Fig. 4.8 and 4.9. The reason for the smaller strains for the

negative moment post-tensioning is primarily the smaller eccentricity.

The tendons above the deck had an eccentricity that was only about

half that of the tendons below the beams, and therefore, the tendons

in positive moment regions applied much larger moments than the tendons

in negative moment regions.

Because the strains presented in Fig. 4.11 are small, it is diffi

cult to see the distribution effects. Those effects are similar to

those for PTS-1 and PTS-3, however. The strains decrease in both longi

tudinal and transverse directions away from the post-tensioned region,

and not all of the strains are beneficial with respect to strengthening.

In Fig. 4.12, the strains for the superposition of PTS-10 and PTS-16

are given. For this superposition scheme, both negative moment regions

along the exterior beam, 4, are post-tensioned. The strains shown for

the sections along Beam 4 are similar to, but smaller than, the strains

~ . -~ 500 ...,,_ . i::; ·~

0

c: •.-'- 500 ...,,_ .

0 z ~

·~ t;;-.500

-~ $00 ...,,_ . ;:i 0

z ..., ·"'!'. f:'.-500 Vl

c: ·~ 500 -,....,,,..

D

~

'-

-

-

-

.....

-

-

12'6

• -

• •

... •

-- - -

- --

! 1----+I l--+-1--+--I --+--1 --+--! +----II I A B C D E

Fig. 4.11. Bottom flange strains for PTS-10.

BM4

•PTS-10 aPTS-16

BM3

BM2

BMl

s:: ·~ 500 ---.. c ·~

z ~

<(

"" i/;-500

.~ 500

2 0

z ~

<(

~-500 Vl

-~ 500 ---.. s::

;:1. 0

z ~

<(

~-500 Vl

-~ 500

2 0 z <(

-

-

-

-

-

~

-

-

127

j I

• • •

- •

- -

- --

~-500

vi 119klPS il9.75k'1P' l t--1 -+-I -+-i -+-1--+----+· ---+:---t A B C D E

Fig. 4.12. Bottom flange strain distribution for PTS-10 + PTS-16.

BM4

e PTS-10 + PTS-16 • PTS-10 + PTS-16

FROM SYMMETRY

BM3

BM2 ·

BMl

128

for the corresponding positive moment post-tensioning scheme given in

Fig. 4.10. The bottom flange strains decrease for Beam 3 and are very

near zero for Beam 2. The strains then reverse slightly for the far

exterior beam, Beam 1. All of the strains would be beneficial with

respect to strengthening except those for Beam 1.

Strains for PTS-12, a negative mo.ment post-tensioning scheme for

an interior beam are given in Fig. 4.13. In PTS-12, Beam 3 was post

tensioned at Section B. This particular scheme had the effect of post

tensioning the entire bridge somewhat symmetrically in the transverse

direction. The strains for all of the beams are in the same direction

as those for the post-tensioned beam, and the strains for Beam 4, which

was not post-tensioned, are the largest. All of the strains except

those at Section E are beneficial for strengthening. Because of the

wide distribution of post-tensioning throughout the bridge, even the

maximum strains are very small.

Figure 4.14 shows the strains for the superposition of PTS-12 and

PTS-17. In this superposition scheme, both of the negative moment

regions along Beam 3 are post-tensioned. All of the strains are in

the correct direction for strengthening, and Beams 4, 3, and 2 have

approximately equal strains at each of the sections along the bridge,

Sections A through E. The strains are relatively small in comparison

with the strains caused by positive moment region post-tensioning.

For the single beam schemes, the following should be noted. Not

all of the effects of the post-tensioning will be desirable with

respect to strengthening. If an exterior beam is post-tensioned, the

far exterior beam will be subjected to strains in the same direction as

.;:'. 500 --.. c: ·~

2 0 . z ~

<( Clo'.

t;:;-500

,...., c: 500 --.. c:

2 0 . z ~

<(

f=-soo (/}

c: 500 --.. . c: ·~

3 0 . z ~

<( Clo'. t;:;-500

'C c:

:::::. 500 c:

. 0 z

~ t;:; -500

~

-

-

-

-

-

-

-

ii Fig.

•

-

-

-

A 4. 13.

129

-

-

-

..

i ,20.10 "''

i I I I B c D Bottom flange strains

-

-

--

-

E for PTS-12.

BM 4

e PTS-12 oPTS-17

BM 3

BM 2

BM 1

.;: 500 ---.. c: ·~

z ~

d'.

0

:=-500 (/)

.;: 500

;::>. 0

z ~

~ 1---500 (/)

c: ·~ 500 --... . c: ·~

z ~

d'.

0

:=-500 (/)

c: ::::::. 500 c: ·~

z ~

d'.

°'

0

t;:;-500

-

.....

-

-

-

-

-

.....

130

.. • • •

• ... • -

- • -

- - -

ll-1--+---+---l----+-+----1---l !' ''l""'' !' ,,,_T,,,

I A B c D E

BM4

ePTS-12 + PTS-17 •PTS-12 + PTS-17

FROM SYMMETRY

BM3

BM2

BMl

Fig. 4.14. Bottom flange strains for PTS-12 + PTS-17.

131

service load strains; and those post-tensioning strains are not bene

ficial. If only one positive or negative moment region along a beam

is post-tensioned, other regions of the beam may be subjected to strains

that are not beneficial, depending on the position of the post-tensioning

and the location of the section in question. Post-tensioning of an

interior beam may generate larger strains in the adjacent exterior

beam than in the post-tensioned interior beam. Post-tensioning of an

interior beam generally distributes post-tensioning throughout the

bridge much more uniformly than post-tensioning of an exterior beam.

4.1.4.2. Multiple Beam Schemes

The multiple beam post-tensioning schemes presented in this section

are much better suited to strengthening continuous, composite bridges

than single beam schemes. The multiple beam schemes are more difficult

to handle experimentally than single beam schemes because of the large

number of tendons and sequential use of jacking cylinders. The multiple

beam schemes, however, are much easier to handle analytically than

single beam schemes if the analysis makes use of symmetry. For these

reasons much of the presentation in this section is derived from the

quarter symmetry finite element model described in Section 4.1.2.

Three types of post-tensioning schemes for the model bridge are

presented in this section: a series of positive moment regions, a

series for negative moment regions, and a scheme for combined positive

and negative moment regions. Figure 4.15, gives beam strains for post

tensioning the three positive moment regions of both exterior beams.

For this first figure, both top and bottom flange strains are illus

trated in order to demonstrate that the top flange strains are generally

+1000 ~ . <= ·~ ...... TOP FLANGE, LC 2 TOP FLANGE, PTS-9 c: ·~

;:i. 0 ~

.... ;;-;i-.;;~;.-..--. ... ....................... ~ ........ . z ,... c:( er: BOTTOM FLANGE, LC 2 BOTTOM FLANGE, PTS-9 I-(/)

-1000

4 OHIO a. INTERIOR BEAM ~ :i,

+1000 --;-

"' ·~ ......

"' \ ·~ • • ;:i.

.. 0 '• ~.:· ..... r ...... J .. cy ...... ..

• .· /

............... !._ ......... ..

• ·. -................ u ...... - ......... .. .. ··~ .. ........ ~., ...... "': ........ :.,·i

• • • • ,• ~ .

z ,... c:( er: 1-(/)

-1000

., . • ·. • • : \1 .·

41 ) 2ok ( I 4 T ) 2ok ( 1 'iO I ) 2ok ( I 4 b. EXTERIOR BEAM

Fig. 4.15. Top and bottom flange strains for LC 2 and PTS-9.

...... (A)

"'

133

very small and will be of little benefit or harm for strengthening a

bridge.

Both the finite element analysis strains for LC2 and the experi

mental strains for PTS-9 are given in Fig. 4.15. There are some minor

differences between the finite element and experimental strains at the

various sections along the bridge. The differences are most apparent

for the larger strains on the post-tensioned exterior beam. There are

several reasons for the differences. The finite element model assumed

complete composite action throughout the bridge and also elastic behavior

of the concrete deck in both compression and tension, whereas the experi

mental model was subject to deck shrinkage and subsequent cracking

which does not meet the finite element model assumptions. The finite

element model also did not account for local variations in steel beam

properties, concrete deck thickness, and curb dimensions in the experi

mental model. There are also some differences between the 20-kip tendon

forces assumed for the finite element model and the tendon forces

actually applied.

The only noticeable patterns in the differences between the finite

element and experimental strains are in Fig. 4.15b. It is apparent

that the experimental top flange strains are slightly smaller and that

the experimental bottom flange strains are shifted slightly in the

direction of compression. The reason for the differences is not obvious,

and the differences do not occur for negative moment post-tensioning,

as will be noted later. The differences generally are small, however,

and the overall correlation between finite element and experimental

strains is very good.

134

For the bottom flange strains from the finite element analysis,

there are very large strains on either side of each of the points at

which post-tensioning is applied. In practice, such large strains

would not exist because a post-tensioning bracket applies moment over

a finite length rather than at a point, as is assumed in the finite

element analysis. There also are large changes in strain at the points

where coverplates begin or end, and those changes are likely to occur

in the actual bridge, but perhaps not quite so suddenly.

Figure 4.15 shows that the post-tensioning applied with equal

tendon forces transmits the largest bottom flange strains to the posi

tive moment regions of the end spans, less strain to the negative moment

regions above the supports, and the least strain to the positive moment

region of the center span. The strains could be adjusted by changing

the tendon forces, moving the points at which post-tensioning is applied,

or both. A comparison of Figures 4.15a and 4. lSb shows that the strains

distributed to the interior beams are one third to one half of the

strains applied to the exterior beams. This distribution is very similar

to that determined for the simple span bridge model ih previous research

[ l] .

LC9, the scheme illustrated in Fig. 4.16 is for post-tensioning

of all positive moment regions of the interior beams. The bottom flange

strain pattern is very similar to that $hown in Fig. 4.15, except that

the exterior and interior beam strains are reversed. When the interior

beams are post-tensioned, about one-third to one-half of the post

tensioning transmitted to the interior beams is distributed to the

ext.erior beams.

+1000 --;-c: ·~ -c: ·~

2;. 0 . z ~

;;ii t;; -1000

+1000 --;-c: •r -c: .•r

:1 0 ~ . z ~

<i:

"" I-V>

-1000

I ~\2 .. ok < I~ --"k-H I .®,. . 7 . ... -T Mi" 1 > 20 < ~I ) 2ok ( a. INTERIOR BEAM

4- - HH • b. EXTERIOR BEAM ~ ~

Fig. 4.16. Bottom flange strains for LC 9.

.... "' <.n

136

Figure 4.17 gives the bottom flange strains for LC3, in which all

positive moment regions in the model bridge are post-tensioned. Both

the exterior beam strains illustrated in Fig. 4.17b and the interior

beam strains illustrated in Fig. 4.17.a have the characteristic shape

of the stri1in diagrams for post-tensiimed beams in the two previous

figures. Eq.u<1l tendon forces for all beams cause slightly larger

str<ii11s .in the exterior be<i.ms, as can be noted by comparing Figs. 4.17a

11nd 4.17b. 'l'he larger strains are caused by the transverse distribu

tio.n. c;::haraCteristics of the b:ridge, which from previous :research depend

on a complex interaction of several factors.

Figure 4.18 begins the sedes of negative moment region post

tensiorting si;:hemes. In Fig. 4.18, the finite element strains are given

for LC6 and the experimental strains for PTS-20, both of which are

schemes in which the exterior beams were post-tensioned. The tendons

for the exterior beams are of the shorter length used in the testing

of the model bridge. The only signific<1nt strains appli.ed to the model

bridge are the finite element strains near the points of post-tensioning

application, and those strains would not be realized in practice because

of the finite length of the post-tensioning brackets. There is some

strain distributed from the post-tensioned exterior beams to the interior

beams, but 11H applied and distributed strains are small and thus dif

ficult to compare. Finite element and experimental strains correlate

well, with no obvious pattern of deviations.

Strains for LC18 and Stage 2 of PTS-21 are plotted in Fig. 4.19.

For these schemes, post-tensioning was applied to the negative moment

regions of the interior beams. Figures 4.19a and 4.19b are very nearly

+1000 ~

<= ·~ ........

<= ·~

.2:- 0 Tr----1----:---t--+-~------h. . :z: ~

< a< f-

"' -1000

+1000 ~

<= ........ <= ·~

;1 0 ~ . z: ~

< a< f-

"' -1000

4-r-H-->-2oi<( ___ T 4 1 --)- 20k ( 1 4 1 > 20k ( 14

a. INTERIOR BEAM

------_ -- -- k - I --~4~ -I > 2ok ( I ~ ____ k ----1 OiO _ I > 20 (

4~ - ) 20 ( b. EXTERIOR BEAM

Fig. 4.17. Bottom flange strains for LC 3.

.... (;.) _,

+1000 ---;-c: ·~ --,._

c: ·~

..2:. 0 .

PTS-20

z !;( I -1000 'LC 6 "' I-

(/)

+1000 --;c: ·~ ...... . c: ·~

4 40 4 a. INTERIOR BEAM ~

;:1. 0 1 1· •'I I"• ·1 ~ ~ ~ . ~ ~ z ~

<(

"' I-(/)

-1000 k k I ) 20 ( I I ) 20 ( l 4 4 -- •m-•••• m•

b. EXTERIOR BEAM Oi' - ~ Fig. 4.18. Bottom flange strains for LC 6 and PTS-20.

.... w co

+1000 .....,. c: ·~ --.. c: ·~

PTS-21

2 o I I .. • • _,_ I ' 1~ _,.. • .............. • r I ,,-• . z ~

ex: 0:: IV)

-1000

+1000 .....,. c: ·~ --.. c:

LC 18

k k I ) 20 ( l I ) 20 ( I

__,;..~--HU • Oi 4 Jl a. INTERIOR BEAM

·~

2 oJ--===~-"""~~---~:::=:e~-:::==--~=e.-.._--o=====--. z ~

ex: 0:: IV)

-1000

4 ~ b. EXTERIOR BEAM ~ ~ Fig. 4.19. Bottom flange strains for LC 18 and PTS-21, Stage 2.

.... w "'

140

the reverse of Figs. 4.lSa and 4.lSb. It appears that slightly more

post-tensioning was distributed from the post-tensioned interior beams

to the exterior beams, which is consistent with the data from the posi

tive moment p9st-tensioning schemes described above.

Figure 4.20 completes the series of negative moment region post

tensioning examples. Finite element bottom flange strains from LCS,

and experimental strains from PTS-21 show excellent correlation, as

they do for the two pi:evious schemes. The point application of post

tensioning to the finite element model creates larger strains near

these points for the exterior beams than for the interior beam, but as

noted previously, the larger strains ai:e not likely t9 have !lnY practi

cal meaning. This particular post-tensioning scheme transmits the

lai:gest strains to the center spans of the beams, in comparison with

the strains transmitted to the other critical stress sections.

In the last scheme presented in this section, all positive and

negative moment regions within the bridge were post-tensioned with

e~ual tendon forces. Figure 4.21 illustrates the bottom flange strains

for that scheme. As could be expected from the previous schemes, post

tensioning all regions creates the largest strains. The strains and

the strain patterns are very similar to those for post-tensioning all

the positive moment regions, which is illustrated in Fig. 4.17. There

is a slight increase in the bottom flange strains at the interior sup

ports and a more noticeable increase in strains for the center span as

a result of the superposition of the negative moment region post

tensioning.

+1000 ...... c: .....

....... c:

PTS-21

2; 0 I I , • ,_,I 1~1 ·~ ~· .

z ~

~ I-VI

-1000

+1000 ~ c:

LC 5

k k I ) 20 ( ULH I ) 20 ( I 4 H :Qi - ----------

a. INTERIOR BEAM --4~.;._,__L ~

.....

....... c: .....

c or~~f~~~11;:::::::::;~f'=4==~;ac=~ ....... • ,-1 1---- • r I ........ • :z:: ~

~ IV)

-1000 k k

I ) 20 ( I I ) 20 ( I 4- ~

"'" b. EXTERIOR BEAM OiO ~ Fig. 4.20. Bottom flange strains for LC 5 and PTS-21.

.... .... ....

+1000 ~ c: ·~ ..... . c: ·~

~ o-1-o~~~~~~~-+-~~~~~-+~~~~~~~----1-~~~~~--i1----~~~~~-.--1-"-

. z ...... ~ ·tn -1000

+1000

k . k I )20( I I )20( I

4 I > 20k < · I 4 I > 20k < 1 4. r > .zok < 1 ~ . .

a. INTERIOR BEAM

,...,. c: ·~

---. s::: ·~

2:; orr=-=iH~=L-j. . z ..... ~ IV'>

-1000

1 · > zok < · · 1 1 > zok < · 1

4 I > 20k < 1 · 4 I > 20k < I 4 · I > 20k < I 4 b. EXTERIOR BEAM

Fig. 4 •. 21. ]3ottom flange strains for LC 19.

.... "' N

143

The multiple beam schemes presented in this section demonstrate

that post-tensioning of the positive moment regions has the largest

effect in reversing the service load behavior of the bridge and appears

to have greater potential for strengthening than post-tensioning of

negative moment regions. Post-tensioning the positive moment regions

beneficially affects all critical design sections within the bridge.

When all of the positive moment regions were post-tensioned, the result

ing strains were approximately 300 to 600 µ inches per inch, which cor

respond to 9 to 18 ksi. Those stresses are in the range required to

strengthen the prototype bridge. The transverse distribution, when only

exterior or only interior beams are post-tensioned, appears to be similar

to that for simple span bridges; and that distribution will be explored

further in the next section.

Although the negative moment region post-tensioning did not appear

very promising for reversing the service load behavior of a bridge in

either single beam or multiple beam schemes, it may have value for

providing dependable composite action throughout the bridge. The possi

bility of providing composite action will be explored in the second

part of this chapter when interpreting the results of the full-size

mockup. The post-tensioning schemes applied to the mockup also may

provide better reversal of the service load behavior because the neutral

axis of the mockup was lowered by the addition of angles bolted to the

web near the bottom flanges. The harped tendon configuration also will

have a greater moment effect than the straight tendons used in the

bridge model tests.

144

4.1.4.3. Distribution

A continuous bridge will distribute post-tensioning both longi

tudinally and transversely, as demonstrated in the two sections for

single and multiple post-tensioning s.chemes. The distribution effects

can be obtained most accurately by finite element analysi<>. Al though

the distribution effects in the two directions may be interrelated, it

may be possible to separate the effects for design purposes, if extreme

accuracy is not req1lired.

Longitu<linal distribution of moments can be determined by treating

the post-tensioned beams as individual composite beams with variable

stiffnesses as required by coverplated regions and composite action or

lack thereof. Many relatively easy-to-use calculator and computer pro

grams are a.vaila.ble that can analyze beams with variable moment of

inerti'I. an<l applied moments. :Sy shifting application points for moments

longitudinally an<l experimenting with magnitudes of moments, it should

be possible to design a tendon arrangement that provi<les the required

stress relief for individual beams. If all beams are post-tensioned

in all positive moment regions, the proce<lure suggested above may be

sufficiently accurate for design.

Howevei;, if the strengthening requirements s.uggest that only

exterior or only interior beams be post-tensioned, the strengthening

design must consider the transverse distribution because some of the

post-tensioning will be distributed away from the post-tensioned beams.

Some preliminary study on transverse distribution was conducted by

dividing the model bridge into five regions on the basis of dead load

inflection point secti.ons. The equations developed for sill\Ple span

145

bridges in Reference 10 were applied to those regions as if they repre

sented simple span bridges and then distribution fractions were computed.

Those fractions were compared with force and moment fractions determined

from finite element analyses of the model bridge. The fractions deter

mined from the simple span equations were reasonably accurate, but not

accurate enough for design purposes.

On the basis of the experimental and finite element work conducted

in this study, it appears that longitudinal distribution may be con

sidered accurately through conventional, continuous-beam analysis if

all bridge beams are post-tensioned in the same manner. If beams are

not post-tensioned in the same manner or if there are significant dif

ferences between the stiffnesses of adjacent beams, then the transverse

distribution must be considered either through finite element analysis,

a similarly accurate analysis method, or a design procedure yet to be

developed. Preliminary study indicates that a method for computing

transverse distribution fractions, similar to the method for simple

span bridges, could be developed for continuous bridges.

4.1.4.4. Tendon Force Changes

Whenever there is a change in deflection of a post-tensioned beam,

the forces in eccentric or harped tendons will change. The change in

deflection may be caused by application of more post-tensioning or by

the applicat:Lon of vertical load. Both of these conditions were tested

in the bridge model.

Because only four hydraulic jacking cylinders were available in

the laboratory, the more complex post-tensioning schemes required

staged jacking. Two or four tendons were tensioned at the first stage,

146

and then two or four tendons were tensioned at the second stage in

order to complete the test.

Table 4.3 lists the gains and losses between the first and second

stages of post-tensioning for three schemes. In PTS-9 for post

tensioning the three positive moment regions of the exterior beams,

the two tendons on the center spans were tensioned (Stage 1) followed

by the tensioning the four tendons on the end spans (Stage 2). As

shown in Fig. 4. 3a between stages .one and two, there were force gains

of 3.4% and 4.3% in the center span tendons.

The post-tensioning of all negative moment regions in PTS-21 was

staged by tensioning the four tendons for the exterior beams and then

tensioning the tendons for the four interior beams. Shown in Table 4.3b

are the losses that occurred when the interior beams were tensioned;

there were losses of 3.1%, 3.1%, 3.0% and 2.9% in the exterior beam

tendons when the second stage post-tensioning was applied.

The third post-tensioning example, in which all interior beam

negative moment regions and exterior beam, center span positive moment

regions were post-tensioned (shown in Table 4.3c for PTS-22), was staged

to apply the negative moment region post-tensioning before the positive

moment region post-tensioning. Between the two stages, the tendons

above the interior beam supports lost 3.0%, 3.0%, 3.4% and 3.1% of the

force applied at the first stage.

All of these examples for staged post-tensioning show relatively

small gains or losses in post-tensioning force, in the range of 3% to

4%. The gains and losses are for post-tensioning forces in the range

required to relieve stresses in the bridge model approximately equi-

Table 4.3.

a. PTS-9

Post-tensioning Scheme

PTS-9

b. PTS-21

Post-tensioning Scheme

PTS-21

Variation in tendon force because of applying additional post-tensioning.

Stage

1 2

Stage

1 2

1-B

1-A

0 20.04

19.49 3.2% loss

Post-tensioning Force Applied to Region

1-C

19.3 3.4% gain

1-E

0 20

4-A

0 20.14

4-C

19.05 4.3% gain


1-D 2-B 2-D 3-B 3-D 4-B

19.47 0 0 0 0 18.63 3.0% loss 18.38 19.08 18.25 18. 72 3.1% loss

4-E

0 19.86

4-D

18.66 2.9% loss

..... -I'-

"'

Table 4.3. (Continued)

c. PTS-22

Post-tensioning Scheme Stage 1-C 4-C

PTS-22 1 0 0 2 19.47 19.55


2-B 3-B 2-D

19.27 19 .27 19 .11 3.0% loss 3.0% loss 3.4% loss

3-D

19.11 3.1% loss

.... .,.. co

149

valent to those required for the prototype bridge. Although these

gains or losses are small they should be included in the design of the

strengthening system.

As vertical live loads are applied to a bridge strengthened by

post-tensioning, forces will change in the tendons. For a simple span

bridge, the tendon forces will always increase when a vertical load is

applied unless the load is applied with extreme eccentricity with respect

to the center line of the bridge, a condition which is impractical.

Thus, in practice, the tendon force increases will provide additional

post-tensioning when most needed.

For continuous bridges, the changes in tendon forces will not

necessarily be beneficial. Figure 4.22 illustrates the exterior beam

and interior beam tendon force changes for PTS-21, a scheme in which

all negative moment regions were post-tensioned. In order to present

the changes in force changes more clearly, the experimental points

have been joined with lines; the lines do not represent a comparison

with theory, as in earlier figures. Percentage changes in tendon force

are given for nine different positions of a 6-kip vertical load. As

the figure shows, most of the force changes are positive; however, there

are a few load positions for which the changes are negative, which

indicates a decrease in tendon force.

Figure 4.23 for PTS-9, in which all positive moment regions along

exterior beams were post-tensioned, shows the tendon force changes for

an end span tendon and for a center span tendon. The force changes

are for the same 6-kip load and load points as used for constructing

7

6

5

4

""" " u.J

"' 2 < f-z u.J 1 '-' "' u.J 0.. 0

-1

-2

-3

-4 2 3 4

150

5 6

o EXTERIOR BEAM, TENDON LOCATION 4-B

A INTERIOR BEAM, TENDON LOCATION 3-B

11 13 18 20

LOAD POINT NUMBER

Fig. 4.22. Percent of increase or decrease in the tendon force for PTS-21.

6

5

4

~ 3 . w <.!) 2 <( f-:z w 1 u 0:: w 0..

0

-1

-2

-3

-4 2

Fig. 4.23.

__....,.IY'

3

151

..A--..ti °""-//

4 5 ' 6

o END SPAN TENDON, LOCATION 4-A

c. CENTER SPAN TENDON, LOCATION 4-C

A, I \ I \ I ' I ~

I \

11 13 18

LOAD POINT NUMBER

20

Percent of increase or decrease in the tendon force for PTS-9.

152

Fig. 4.22. For many of the load points, Fig. 4.23 shows negative tendon

force changes or losses in force.

For the continuous bridge model, the total tendon force change

from negative to positive is approximately 20% of the applied load.

For the simple span bridge model tested during previous research, the

maximum tendon gain for a comparable extreme load position was approxi

mately 10% of the applied load [19]. Thus there are larger changes in

tendon force for the continuous bridge model. Part of the increased

magnitude of the changes in tendon forces comes from locating the. posi

tive moment region tendons below the beams. Here they have more eccen

tricity than the tendons for the simple span bridge model. The

remainder of the tendon force change is due to the flexibility of the

bridge.

Because the tendon force changes are both positive and negative

and the magnitude of the changes may be larger than for a simple span

bridge, tendon force changes are an important factor to consider in

designing the strengthening of continuous bridges by post-tensioning.

Allowable stresses may have to be checked with maximum tendon force

gain and maximum tendon force loss in order to provide adequate checks

of the post-tensioning design.


In addition to the post-tensioning tests, the continuous bridge

model in the ISU Structural Engineering Research Laboratory was sub

jected to a series of vertical load tests. The vertical load tests

used one or two 6-kip vertical loads on the bridge deck at the load

points shown in Fig. 3.4. The vertical load tests used one or two 6-

153

kip vertical loads on the bridge deck at the load points shown in

Fig. 3,4. The vertical load tests were, for the most part, unsymmetri

cal. Only two were comparable to the symmetrical finite element

analyses.

Bottom flange strains at Sections A, B, and C for two separate

tests, with a single load at one load point in each test, are plotted

in each of Figs. 4.24, 4.25, and 4.26. The experimental points in the

figures are joined with lines in order to show the pattern of the strains

from beam. to beam across the bridge. In Fig. 4.24, the strains are

plotted for the two loading conditions: a 6-kip load at LPl and a

6-kip load at LP3. LPl is located at the center of the end span of

Beam 4, an exterior beam; and LP3 is located at the center of the end

span of Beam 3, and interior beam. The patterns for the two loading

conditions shown in Fig. 4.24a are very similar to those for a simple

span bridge (19]. In each loading case the loaded beam has the largest

strain, and the same general strain pattern is repeated in parts b and

c of Fig. 4.24 for the first interior support and center span sections.

Figure 4.25 presents the strains for 6-kip loads at LP8 and LPlO

at the center of the center span. Figure 4.25c for the strains at the

loaded section is similar to Fig. 4.25a for the end span loaded section.

Parts a and b of Fig. 4.25 are similar to the loaded section in Fig. 4.25c,

in that the loaded beam has the largest strain.

Figure 4.26 presents the strains for 6-kip loads at LP15 and LP17

at the center of the second end span. None of the graphs in Fig. 4.26

are for a loaded section. The loaded beam in each of the graphs has

the largest strain, as in Figs. 4.24 and 4.25, and Fig. 4.26c is the

154

~ 600

"' LP3~P •r ....... . 300 ----"' •r -"'-

__ ..o--~ 0

o--(/)

z ~

g-300 U')

-600 BMl BM2 BM3 BM4

a. SECTION A

---:- 600 "' •r

....... . 300 "' •r

"'-

(/) 0 ---z --"\LP 3 ~

cl: LP 1 :=-300

(/)


b. SECTION B

~ 600

"' •r ....... . 300 "' •r

"'-~

(/) 0 ---z

~

cl:

:=-300 (/)


c. SECTION c

Fig. 4.24. Bottom flange strains for 6-kip vertical load at LP 1 and LP 3.

155

600 ~

c: ·~ ; 300 '--s:: ·~ LP 8""' ;:1

0 ~

--,L~ 10 -z -v ..... c(

~-300 ... (/)

-600 I I I I

BMl BM2 BM3 BM4 · a. SECTION A

600 ~

c: ·~

; 300 s:: ·~ LP 8 ;:1

0 ~

z ----o- --o ..... --\LP c(

~-300 10 (/)


b. SECTION 8

600 . LP 10~~ c: ·~ / ; 300 / c: .-<:!"/ ·~ ----;:1

0 :z ..... c(

~-300 (/)


c. SECTION C


t: ..... ';- 300 t: .....

0 z: ~

~-300 f-V)

~ . c

600

::::. 300 <::: ..... ;::l. 0 ~

z: ~

~-300 f--V)

-600

600 ~

<:::

:.:; 300 <::: ..... ;::l. 0

z ~

~-300 f--V)

-600

156

LP 15

BMl a. SECTION A

LP 17

---LP 15

BMl BM2 BM3 BM4

b. SECTION B

~

.

/LP 15

-17/--

--<J ~ u

LP .....

I I I I

BMl BM2 BM3 BM4

c. SECTION C


157

same as Fig. 4.24c, except for instrumentation errors and differences

in distribution effects caused by construction imperfections in the

model bridge.

The vertical load tests are quite consistent with similar tests

for a simple span bridge model. The loaded beam generally has the

highest bottom flange strain. A certain amount of the load is carried

by all bridge beams.

4.2. Analysis and Test Results for the Full-scale Negative Moment Region Mockup

This section presents the data obtained from tests of the full-

scale composite beam mockup. Three types of data are presented: deflec-

tions of the vertical load point or free end of the beam, strain dis-

tributions at two mockup sections, and tendon forces. The deflections

for Tests 1 and 3 through 7 are taken at the application point of the

vertical load, whereas the deflections for Tests 8 and 9 are taken at

the free end of the beam. The deflections for Test 2 were taken both

at the vertical load and at the free end. Therefore, the deflections

for the two groups of tests cannot be compared directly. Strain dis-

tributions are shown for Section 4, which is at the support, and at Sec-

tion 5, which is away from the support but within the coverplated region.

The section locations are given in Fig. 3.7. Wherever possible, exper-

imental .results are compared with results from separate analyses in order

to determine the extent of the composite action. In these cases either

a coverplated steel section or a fully composite deck-beam section is

assumed.

158

The maximum applied vertical load for the testing program was

chosen to limit stresses in the steel beam and coverplates to 18 ksi

compression or tension under the various test conditions. The limita

tion was chosen to minimize the potential for lateral or torsional

buckling of the mockup beam because the beam was not laterally braced

at the free end or the central support.

4. 2. 1. Analysis

Except for some minor practical limitations, the mockup beam was

statically determinate until post-tensioning was applied and locked in

placed and until the beam was deformed because of application of verti

cal load or other loads. The mockup was considered to have a hinged

support at the hold-down end and a roller support at the central support

or pier. The hold-down end support in reality was not a perfect hinge,

and strain data indicated that there was a small amount of rotational

restraint caused by the hold down. The end near which the vertical load

was applied was a free end.

Because of the simplicity of the mockup, analysis was performed

with ordinary statics and classical methods, and there was no attempt to

analyze the mockup with finite element methods. For composite action,

the concrete deck was reduced to an equivalent area of steel by using a

modular ratio based on the relative moduli of elasticity of the concrete

and steel. Deflection computations took into account the variation of

moment of inertia along the beam.


Initially, after the concrete deck was cured, the mockup beam was

tested with cycles of vertical load during Test 1. Because the verti-

159

cal load applied a negative moment to the moskup and thus stressed the

concrete deck in tension, the deck cracked at various locations. The

effects of the deck cracking are indicated in Fig. 4.27, which contains

a load-deflection graph for the first three load cycles.

Figure 4.27a illustrates the theoretical conditions for the test.

As shown, the deflection was measured at the point at which the load was

applied. The load-deflection curves in Fig. 4.27b clearly distinguish

among the first three load cycles. During the first load cycle, the

deck cracked directly above the central support at the location of

maximum negative moment. Additional cracks occurred during the first

load cycle, and each crack caused an immediate increase in beam deflec

tion as well as an abrupt increase in strain in the top flange of the

steel beam. After the first load cycle when the vertical load was

totally removed, the mockup retained a permanent set. The permanent

set increased with each load cycle; the final displacement, after the

three cycles and the maximum vertical load had been applied and

~emoved, was 0.28 in.

With each crack there was a transfer of tension stress to the deck

reinforcing bars and a partial loss of composite action. The loss of

composite action increased deflections as shown in Fig. 4.27b and also

altered and increased strains measured in the steel beam. As will be

indicated in subsequent figures, the mockup beam tended to behave with

a certain amount of composite action that, from separate computations,

is slightly larger than the amount predicted by considering the rein

forcing bars in the deck to be acting with the steel beam.

160

----12 1 -8 11 12' -5"

a. TEST SCHEMATIC

p

----- fvERTICAL DEFLECTION

50 ----·------·---·--··-··-------····------·-1

40

. a.. 30 . Cl «: 0 ....]

....]

5 20 ,__. >--"' UJ >

10

0

SUBSEQUENT CRACKS

0.2 0.4 0.6 0.8

VERTICAL DEFLECTION, inches

b.. LOAD-DEFLECTION CURVES FOR THREE LOAD CYCLES

Fig. 4.27. Load-deflection curves for initial vertical loading, Test 1.

I I

161

The final deck crack pattern is given in Fig. 4.28. Figure 4.28a

gives the plan view of the deck with all of the significant cracks.

The transverse cracks across the deck in the central portion of the

mockup near maximum negative moment under vertical load are the most

closely spaced, as one would expect. A comparison of Fig. 4.28a and

4.28b shows that the cracks generally do not occur at a shear connector.

Cracks occur across the deck at the blockouts at which some of the

longitudinal deck reinforcing bars are terminated and near which the

coverplates are terminated.

There also are a few longitudinal cracks at the hold down and free

ends of the mockup beam. The hold-down forces apparently were suffi

cient to cause radial cracking of the deck and thus indicate that sub

stantial forces were applied with respect to deck strength.

Figure 4.28c (as well as Fig. 3. 7) gives the numbered sections at

which strain gages were located on the top and bottom flanges of the

steel beam. Strain data to be presented later is taken from the gages

at Section 4 near the support and at Section 5 which is within the

coverplated region but near the coverplate cutoff.


In this section, the effects of post-tensioning will be demon

strated through strain diagrams. In the series of figures in this sec

tion, experimental data is plotted along with theory for the coverplated

steel beam and. the fully composite beam. In the figures, experimental

data points are connected with lines to show the pattern of data and not

to indicate that theoretical results match experimental results. The

first test listed in the key below each graph is for the beam without

13' -2" 16' -10"

11'-7" i 12'-5"

1• C[_ HOLD DOWN • i • C[_ PIER •1

0

0

a. DECK CRACK PATTERN

C[_ VERTICAL LOAD

/

0

I

I>> >I > > I< < I< < < <<I b. SHEAR CONNECTOR LOCATIONS

<D <D® © I ® © 0 J. - - J,._ ____ __J._ J.. - ! J.. ..L. A. 'P"~~~~~----,oc~ ..... ~~~~~~~~~-..--,,..-~~~~~~~~~~ .... ~~~ .... ~~~~~~~ .....

c. STRAIN GAGE SECTIONS

Fig. 4.28. Final crack pattern in full-scale mockup deck.

(V') I -

<.O

..... "' N

163

strengthening angles, and the second test listed is for the beam with

strengthening angles.

Figure 4.29a gives the strains at Section 4 for the mockup with

the straight tendons, and Fig. 4.29b gives the strains for the mockup

with the harped tendons. Both graphs show that the experimental results

fall between theoretical results for the coverplated steel beam and the

fully composite beam. Both graphs also show that the strengthening

angles added near the bottom flange of the mockup had beneficial effects

in reducing compression strain on the bottom flange and in increasing

compression strain on the top flange. The angles reduce the bottom

flange compression strain by providing a larger cross-sectional area

and by lowering the neutral axis and thus providing a larger eccentricity

for the post-tensioning force. A detailed comparison of Figs. 4.29a for

the straight tendon and 4.29b for the harped tendon indicates that the

harped tendon provides more beneficial compression strain at the top

flange; and even though better than the straight tendon, the harped

tendon does add a small amount of compression strain to the bottom

flange that is not beneficial.

The strain diagrams in Fig. 4.30 are the same as the strain

diagrams in Fig. 4.29, except that those in Fig. 4.30 are for the

strains measured at Section 5. The strains are almost the same at both

sections, and all of the observations stated above for Fig. 4.29 apply

to Fig. 4.30. The largest variations in experimental strains between

the two sections are for the top flange strains, which are significantly

affected by the cracks in the deck, and therefore some variations should

be expected. In general, the experimental strains fall about midway

164

.--------1.~BJi:---------~ TOP FLANGE

\ \ \ \ \ \

COVERPLATE

STRENGTHEN ING ANGLES BOTTOM FLANGE

~--1--1----lL......-L-L-....J COVERPLATE -600

e--TEST 4 ._TEST 6

0

STRAIN, (µ in.fin.)

.or--STEEL BEAM, THEORY v--COMPOSITE BEAM, THEORY

a. STRAIGHT TENDON

600

.---------6-----00.----------. TOP FLANGE \ , j COVERPLATE

\ I \ I \ I \ I \ I ~I '

STRENGTHENING ANGLES BOTTOM FLANGE

1..-....1·1--_.___, _ _.____.~.___._-"---'---'---'-___J COVER PLATE -600

e--TEST 8 .__TEST 9

0

STRAIN,(µ in.fin.)

6--STEEL BEAM, THEORY '1;11--COMPOSITE BEAM, THEORY

b. HARPED TENDON

600


165

..--~-----<>-11~,..----------,TOP FLANGE \ f COVERPLATE

\ I \ I \ I \ \

\ STRENGTHENING ANGLES I BOTTOM FLANGE '---'--'-L'--'---..l.-...1'-<11e-...J''---''---~-'---'--'~ COVERPLATE

-600

e--TEST 4 ---TEST 6

0 STRAIN,(µ in.fin.)

t:i.--STEEL BEAM, THEORY 'V---COMPOSITE BEAM, THEORY

a. STRAIGHT TENDON

600

r------~e--vi:----------, TOP FLANGE \ I COVERPLATE

\ I \ I

\ I \ I \ I

STRENGTHENING ANGLES BOTTOM FLANGE

'--....J''---'--.__,__..___..._-11111 ~r-...1'--'---''----'--''---' COVER PLATE -600

e--TEST 8 II-- TEST 9

0


6--STEEL BEAM, THEORY 9-~COMPOSITE BEAM, THEORY

b; HARPED TENDON

600


166

between the theoretical extremes of coverplated steel beams and fully

composite beams. Thus there is only partial composite action in the

mockup for the post-tensioning schemes applied.


This section presents the effects of vertical loads both with and

without post-tensioning. A series of load-deflection curves are pre

sented first and then a series of strain diagrams. Each of the graphs

contains experimental data as well as theoretical results for the mockup

bean1 without and with composite actior1.

Figure 4.31a illustrates the test conditions for the load-deflection

curves given in Fig. 4.31b. For the tests with the straight tendon,

the deflection was measured at the point of the applied vertical load.

The lowest curve in Fig. 4. 31a gives the theoretical deflections'

for the steel beam with coverplates that is not post-tensioned, and

the uppermost curve gives the theoretical deflections for the fully

composite beam that is not post-tensioned. Both of the theoretical

curves are for the mockup without the strengthening angles. Because

the data for the mockup without strengthening angles and without straight

tendon post-tensioning falls between the two theoretical curves, the

mockup does have some composite action for vertical load, even with a

cracked deck. In the tests without and with post-tensioning, the angles

do stiffen the mock11p. This is evidenced by the steeper slopes for

the curves for the mockup with the angles in Tests 3 and 5, as opposed

to Tests 2 and 4, respectively. The post-tensioning does produce a

small amount of uplift indicated by the negative deflections. From

theoretical computations for the straight tendon, the uplift indicates

* 1-

50 T-

40 J ' I !

...

167

""" ~ =--12'-8" .1. 12'-5"

a. TEST SCHEMATIC

--ip

t

J--- fVERTICAL DEFLECTION

-------------·-1

oTEST 2 +TEST 3 <>TEST 4 c. TEST 5 xSTEEL BEAM, THEORY vCOMPOSITE BEAM, THEORY

o-t----,---tH"-*HL---,---.,,----.--.-----,---,--,.---1 -0.2 0 0.2 0.4 0.6

VERTICAL DEFLECTION, inches

b. LOAD-DEFLECTION CURVES

Fig. 4.31. Load-deflection curves for straight tendon post-tensioning and vertical load.

0.8

168

that the mockup was not behaving as if fully composite because in that

condition the mockup would deflect downward. The post-tensioning does

not stiffen the mockup, however, because the slopes of the curves for

post-tensioning are the same as the curves for the mockup without post

tensioning.

Figure 4.32 presents similar results to those in Fig. 4.31 but

for the mockup with the harped tendon. The test schematic irt Fig. 4.31a

shows that the deflection i.s measured near the free end of the mockup

rather than at the load point, and thus the deflections in Figs. 4.31

and 4.32 cannot be compared directly. The key given in Fig. 4.32b is

as follows: Test 2 is for the mockup without post-tensioning; Test 8

is for the mockup with post-tensioning; and Test 9 is for the mockup

with post-tensioning and strengthening angles.

The theoretical curves for the mockup (not post-tensioned) with

and without composite action are the uppermost and lowest curves,

respectively. The experimental curves show that post-tensioning causes

uplift but does not stiffen the mockup. The curve for post-tensioning

with angles, Test 9, and without angles, Test 8, indicate that the

addition of the stiffening angles makes the mockup slightly more flex

ible. The effect is very small, but the effect seems to have no reason

able explanation.

The next series of figures presents the strain data taken at Sec

tions 4 and 5 for the mockup with vertical load. In Figs. 4.33 and

4.34, the first graph in each figure is for the mockup without post

tensioning; the second graph in the figure is for the mockup with

straight tendon post-tensioning; and the third graph in the figure is

for the mockup with harped tendon post-tensioning.

U1 Cl. ·~

-"' . Cl.

Cl <l'. 0 _J

_J

<l'. u

1--

°' LLJ >

:f7 =

I. 12' -8"

169

== ------12'-5"

;; .I: ,,J ---1---iVERTICAL

16' -9 1/2" ,.. DEFLECTION

a. TEST SCHEMATIC

501

40 ~

30 I

I 20

10

-0.1 0.1 0.3

aTEST 2 +TEST 8 OTEST 9 XSTEEL BEAM, THEORY vCOMPOSITE BEAM, THEORY

0.5 0.7

VERTICAL DEFLECTION, INCHES

b. LOAD-DEFLECTION CURVES

Fig. 4.32. Load-deflection curves for harped tendon post-tensioning and vertical load.

0.9

-600

e--TEST 2 .__TEST 3

170

0

STRAIN,(µ in.fin.)

6--STEEL BEAM, THEORY 9-- COMPOSITE BEAM, THEORY

-600

e--TEST 4 .__TEST 6

a. VERTICAL LOAD

0

STRAIN,(µ in.fin.)

6--STEEL BEAM, THEORY ...,._-COMPOSITE BEAM, THEORY

b. VERTICAL LOAD AND STRAIGHT TENDONS

Fig. 4.33. Strains at Section 4 for full-scale mockup with vertical load and post-tensioning.

171

STRENGTHEN I NG l£.C.'-::::::::C::::i:=L--j__.l_--L.--1_...1--.l._j BOTTOM FLANGE ANGLES COVERPLATE -600 0 600

.,_TEST 8 ---TEST 9

STRAIN, (µ in./in.)

6-~STEEL BEAM, THEORY '17-~COMPOSITE BEAM, THEORY

c. VERTICAL LOAD AND HARPED TENDONS


172

STRENGTHENING BOTTOM FLANGE ANGLES L---1--.i.-.dl\IJ...11µ__.1._.L_-..J._-1----l_-1..._L-...J COVER PLATE

-600

e---TEST 2 11--TEST 3

0

STRAIN,(µ in./in.)

o--STEEL BEAM, THEORY 'll'--COMPOSITE BEAM, THEORY

a. VERTICAL LOAD

600

STRENGTHENING BOTTOM FLANGE ANGLES L--L..-~4Jl--8-'---1---l-...L---1c__..!___J._..L__j GOV ER PLATE

-600

e---TEST 4 11--TEST 6

0


o- -STEEL BEAM, THEORY Q--COMPOSITE BEAM, THEORY

b. VERTICAL LOAD AND STRAIGHT TENDONS

600

Fig. 4.34. Strains at Section 5 for full-scale rnockup with vertical load and post-tensioning.

173

STRENGTHENING BOTTOM FLANGE ANGLES ,____._--'~~--ll''---1---l-..J_--l_...1----1.._...1-.-J COV ERP LATE

-600

.,__TEST 8

.__TEST 9

0

STRAIN,(µ in./in.)

i:.--STEEL BEAM, THEORY 'li'-~COMPOSITE BEAM, THEORY

c. VERTICAL LOAD AND HARPED TENDONS


600

174

In Figs. 4.33a and 4.34a, the diagrams for the mockup with and

without the strengthening angles show that the strengthening angles

had some effect in reducing compression strain in the bottom flange

but little effect in changing the strain at the top flange of the beam.

The angles did shift the neutral axis downward on the steel beam.

A comparison of Figs. 4.33 and 4.34 shows that the strains measured

in the strengthening angles at Section 4 do not align with strains

measured in top and bottom flanges, but the strains measured in the

angles at Section 5 very closely align with top and bottom flange strains.

The fact that the strains do not align at Section 4 can be attributed

to shear lag. Section 4 is very near the ends of the angles, and the

stresses from the beam web have not been fully and uniformly distributed

to the angles. This indicates that if stresses are critical at the

support, it may be advisable to butt the angles to the stiffener and

to transfer stresses to the angles through direct bearing.

The straight tendon post-tensioning, for which strain diagrams

are given in Figs. 4.33b and 4.34b, increased the compression strains

in the bottom flange and decreased the tension strains in the top flange.

The same comment applies to the strain diagrams given for harped tendon

post-tensioning in Figs. 4.33c and 4.34c. Although the change in strain

for the top flange is beneficial, the change in strain for the bottom

flange is not. Since 100 µ inches per inch is equivalent to 2.90 ksi,

the post-tensioning applied to the mockup is not sufficient to overcome

the overstresses in the prototype bridge, and larger tendon forces

would be required even without considering longitudinal distribution

effects.

175

Figures 4.33 and 4.34 show the measured top flange strains to

fall about halfway between the theoretical conditions, as in Figs. 4.29

and 4.30. The bottom flange strains in Figs. 4.33 and 4.34 fall out

side of the theoretical extremes by 15% to 20%, however. There is

actually less compression strain for vertical load than computed.

This behavior might be explained by the mockup beam having one flange

that was heavily corroded or by changing composite action within. the

mockup as vertical load is increased; however, no definitive reason

for the behavior has been determined at this time. Further analysis

of the unexplained behavior will be included in Reference 30.

4.2.5. Tendon Force Changes

After post-tensioning has been applied to a beam such as the mock

up, any change in deformation of the beam will cause a change in tendon

force. The tendon force changes for the mockup under straight tendon

and harped tendon post-tensioning are given in Fig. 4.35. In Fig. 4.35a

the upper two curves give the change in tendon force for the straight

tendons, and the lower two .curves give the change in tendon force for

the harped tendons. The schematic given in Fig. 4.35b indicates that

the upper portion of each curve, showing increase in vertical load, was

plotted first; the lower portion, showing decrease in vertical load,

was plotted second. The gap between the two portions of each curve at

zero load is the seating loss at the anchorages of the tendons.

Tension in the straight tendons increases by about 5% with appli

cation of the .maximum vertical load; but tension in the harped tendons

increases by about 2%. The lower curve for the mockup with straight

tendons and strengthening angles rises more steeply than the curve for

Vl 0.

-"" . w u

"" 0

176

110 ~------------------------;-~-!

105 di----~ I

"- 100

aTEST 4 +TEST 6 OTEST 8 e:. TEST 9

_J

< u ~

fa:: w >

95

90 -+----,.--0 10 20 30

TENDON LOAD P, kips

a. TENDON FORCE VS. VERTICAL LOAD

INCREASE IN VERTICAL ~

L--~~-----sEATING ~DECREASE LOSS t LOAD

b. PLOT SCHEMATIC

IN VERTICAL

Fig. 4.35. Change in tendon forLe.

40

177

the mockup without the angles. The change in slope is caused by the

angles lowering the neutral axis of the mockup and thereby increasing

the eccentricity of the tendon and its sensitivity to bending deforma

tions in the mockup. There is a similar change in slope for the harped

tendon curves, but those curves are reversed in position with respect

to the straight tendon curves.

179

5. SUMMARY AND CONCLUSIONS

5.1. Summary

This report summarizes the research that has been completed in an

initial phase of investigation of strengthening of continuous, composite

bridges by post-tensioning. The research program included reviewing

the literature, selecting and rating a prototype bridge, constructing.

and testing a one-third scale model of the prototype, using finite

analysis on the scale model, and testing a full-scale mockup of the

negative moment region of a bridge beam.

The literature review involved a search of publications from both

the United States and foreign countries. Twenty-one examples of post

tensioned structures were reviewed in some detail as typical of the

many published concepts and applications of post-tensioning. Although

the examples emphasized the use of post-tensioning for strengthening

composite structures, examples for new construction and reinforced

concrete, prestressed concrete, and steel structures were given in

order to cover a wide range of concepts and applications that may be

of use for strengthening continuous, composite bridges.

The primary purpose of strengthening continuous bridges by post

tensioning must be to reverse the moments and resulting stresses from

service loads. This purpose may be accomplished with a variety of

tendon configurations, including straight and harped tendons of full

length or partial length with respect to the bridge. When negative

moment regions above supports are post-tensioned, it is often necessary

to add compression reinforcing to carry the axial force applied by the

180

post-tensioning. Longitudinal distribution of post-tensioning moments

is considered in the usual design process; however, previous to this

study, transverse distribution of post-tensioning has been avoided

through staged post-tensioning or post-tensioning all bridge beams

equally.

A secondary purpose for post-tensioning could be the assurance of

dependable composite action throughout a bridg~. Some testing of the

concept has been completed recently, and at least one bridge has been

designed and constructed on the basis of composite action throughout

the bridge, including the negative moment regions.

With the assistance of the Office of Bridge Design at the Iowa

DOT, a bridge from the Vl2(1957) series of standard, four-beam, composite

bridges was selected as the prototype for the laboratory model. The

selected 125-foot long V12(1957) bridge was rated for bending stress.

The rating determined that there were overstresses at all critical

positive and negative moment sections. Both exterior and interior

beams were overstressed, although the overstresses generally were larger

for the exterior beams.

On the basis of the 125-foot long prototype, a one-third scale

model was constructed and tested in the ISU Structural Engineering

Research Laboratory. Beams for the model were built up from plate and

strip, in order to achieve an accurate scale representation of the

actual bridge beams. The concrete deck was poured in accordance with

sequence instructions on the prototype plans. After the deck had cured,

the model was vertically restrained at supports to prevent beams from

lifting as a result of the low model weight and various cases of applied

181

loading. The model was fitted with tabs for tendon brackets below the

beams in positive moment regions of exterior beams and with tabs for

tendon brackets above the deck in all negative moment regions.

The bridge model was tested extensively over several months with

both unsymmetrical and symmetrical post-tensioning and vertical loads.

Unsymmetrical post-tensioning schemes generally gave desirable strains

in post-tensioned regions but undesirable strains in some of the other

regions. Most symmetrical post-tensioning schemes gave desirable

strains in all regions of the bridge model. Because the neutral axis

for the composite sections was very close to the bottom of the deck,

the strains generated by post-tensioning were largest at the bottom

flanges of the beams.

On the basis of earlier research at ISU for strengthening simple

span bridges, a finite element model was developed for symmetrical

post-tensioning and loading cases. With the finite element model, it

was possible to analyze some post-tensioning schemes that had to be

omitted from the model test program due to time and budget limitations.

In general, the finite element model gave strains and deflections that

closely matched those from the laboratory tests. Most of the symmetrical

cases, in which positive moment regions were post-tensioned and which

were summarized in this report, would be of use in practical situations

for strengthening exterior beams, interior beams, or all of the beams

in a given bridge.

For determining the potential for post-tensioning negative moment

regions above interior supports, a full-size composite beam mockup was

constructed and tested in the laboratory. Two different tendon con-

182

figurations were tested: a straight tendon placed near the underside

of the deck and a harped cable tendon. Both tendons were tested with

out and with strengthening angles bolted to the beam web near the lower

flanges of the beam.

In the research program, the post-tensioning schemes investigated

had limited strengthening value. Both the straight and harped tendon

schemes added beneficial and significant compression to the top flange

of the mockup. Neither scheme significantly reduced the compression

in the bottom flange, however. In fact, the post-tensioning actually

added a small amount of compression to the bottom flange in most cases.

The harped tendon configuration was slightly better than the straight

tendon configuration, and the strengthening angles were beneficial for

both tendon configurations.

Under both post-tensioning and vertical loading the mockup behaved

with partial composite action. The amount of the composite action was

approximately halfway between the extremes of no composite action and

full composite action. Substantially larger post-tensioning forces

than those applied to the beam during testing would be required in

order to assure full composite action in negative moment regions.

The brackets utilized with both straight tendons and harped tendons

performed well during the mockup testing program. Although the harped

tendon brackets performed well, after testing it appeared that some

modifications could be made in order to improve construction procedures

and to place the tendons closer to the beam web. Those modifications

would involve use of the original beam splices at the dead load inflec

tion points.

183

5.2. Conclusions

The following conclusions were developed as a result of this

study:

(1) The primary objective in applying post-tensioning to a composite bridge for strengthening should be to reverse the

·service load moment effects. In order to achieve this objective, straight tendons must be attached with a significant eccentricity. In practice, in most situations, this would mean placing tendons within positive moment regions on the spans of a continuous bridge.

(2) When post-tensioning is applied, both longitudinal and transverse distribution must be considered. Longitudinal distribution ordinarily will be considered during the analysis of the bridge as a series of individual continuous beams. Moment diagrams for the beams will show that the moments transmitted to the bridge are dependent on the location of post-tensioning brackets with respect to supports and that the moments will be distributed to both positive and negative moment regions. Transverse distribution must be considered only when some of the beams are post-tensioned or when all of the beams are not post-tensioned equally.

(3) Unsymmetrical post-tensioning of a continuous bridge, whether unsymmetrical longitudinally or transversely will cause some undesirable stresses. In many cases the undesirable stresses will be significant.

(4) Post-tensioning of negative moment regions with straight tendons will generally apply primarily an axial force. Although addition of compression strengthening angles or plates may give some eccentricity, the eccentricity will be much smaller than that which can be obtained in the positive moment regions; thus, post-tensioning of negative moment regions with straight tendons is unlikely to be effective.

(5) Post-tensioning of negative moment regions with harped tendons is more effective than post-tensioning with straight tendons, but the difference found in this study was small.

(6) Depending upon the position of the applied vertical loading, the change in the post-tensioning force in the tendons may be a gain or a loss. Thus, this change must be carefully taken into account when a post-tensioning strengthening scheme is designed for a given bridge.

185

6. RECOMMENDED FURTHER RESEARCH

On the basis of the literature review, model and mockup testing,

and finite element analysis, it would be logical to continue this

strengthening research as follows:

(1) Strengthening composite bridges of the type investigated in this study by post-tensioning is feasible; the next logical step would be to design and implement post-tensioning for an actual bridge. The strengthening for the bridge should be initially tested and then monitored for a period of several years to insure that no unforseen problems develop.

(2) If one assumes that the implementation phase of the strengthening is successful, there will be need for a design procedure for strengthening continuous composite bridges that is similar to the procedures presented in the manual [10] provided to the Iowa DOT for strengthening simple span composite bridges.

(3) It may be possible to strengthen a composite bridge by posttensioning all beams in the regions above the interior supports to achieve composite action throughout the bridge. Both analytical work and field testing of this concept would be needed before it could be implemented.

187

7. ACKNOWLEDGMENTS

The study presented in this report was conducted by the Bridge

Engineering Center under the auspices of the Engineering Research

Institute of Iowa State University. The research was sponsored by the

Highway Division, Iowa Department of Transportation, and the Iowa High

way Research Board under Research Project HR-287.

The authors wish to acknowledge the assistance and donations of

prestressing materials from the following persons and organizations:

• Jessie G. Barrido, PE, and Eugene Lamberson, PE, of Dywidag

Systems International USA, Inc., Lemont, Illinois

• Greg Gear, PE, of Prestressed Concrete Operations, Iowa Falls,

Iowa.

The authors extend sincere appreciation to the engineers of the

Iowa DOT for their support, cooperation, and counseling. A special

thanks is extended to the following individuals for their help in

various phases of the project:

• William A. Lundquist, Bridge Engineer

• John P. Harkin, Bridge Rating Engineer

• Vernon J. Marks, Research Engineer

• Thomas L. Ries, Assistant Resident Engineer

The county engineers' offices in the following counties assisted in

locating V12 and other composite, continuous bridges: Benton, Boone,

Carroll, Greene, Guthrie, Hamilton, Polk, Story, and Webster.

Special thanks are accorded the following students for their

assistance in various phases of the project: graduate student Douglas

188

L. Wood, and undergraduate students Joann Hansen, Mark Henderson, Darin

Johnson, Roger Khoury, and Pamela Pierce.

189

8. REFERENCES

1. American Association of State Highway and Transportation Officials. Manual of Maintenance Inspection of Bridges 1978. Washington: American Association of State Highway and Transportation Officials, 1979.

2. American Association of State Highway and Transportation Officials. Standard Specifications for Highway Bridges, 13th Edition. Washington: American Association of State Highway and Transportation Officials, 1983.

3. Bathe, K.~J., E. L. Wilson, Structural Analysis Program Linear Systems. Berkeley: of California, 1974.

and F. E. Peterson. SAP IV, A for Static and Dynamic Response of College of Engineering, University

4. Blakeley, R. W. G., R. S. Dowsing, R. J. Dunlop, R. J. Preston, and K. J. Thompson. "The Road to Motunui." The Institution of Professional Engineers New Zealand: Transportation, Vol. 12, No. 2/CE, July 1985, pp. 104-119.

5. Brodka, J., K. Jerka-Kulawinska, and M. Kwasniewski. Prestressed Steel Members--Static Computations. (Vorgespannte Stahltraeger-Statische Berechnung.) Koeln-Braunsfeld: Verlagsgesellschaft Rudolf Mueller, 1968 (German).

6.

7.

Brodka, J., and J. Klobukowski. Prestressed Steel Construction. ~~~~~~~~~~~~~~~~

(Vorgespannte Stahlkonstruktionen.) Berlin: Wilhelm Ernst & Sohn, 1969 (German).

Daoud, F. K. "Experimental Strengthening of Composite Model Bridge by Post-Tensioning." State University, Ames, Iowa, 1987.

a Three-Span M.S. Thesis, Iowa

8. DeBuck, J., T. Van Essche, D. Van Gernert, K. Gamski, R. Degeimbre, J. M. Rigo, and J. Wiertz. "Conception, Computation and Test Program for the Repair of Two Pres tressed Concrete Bridges." (Konceptie, Berekening en Proefprogramma voor de Herstelling van Twee Bruggen in Voorgespannen Beton.) Tijdschrift der Openbare Werken van Belgie, No. 2, 1981, pp. 1-35 (Flemish and French).

9. Dunker, K. F., F. W. Klaiber, B. L. Beck, and W. W. Sanders, Jr. "Strengthening of Existing Single-Span Steel-Beam and Concrete Deck Bridges. Final Report--Part II." ERI Project 1536, ISUERI-Ames-85231. Ames: Engineering Research Institute, Iowa State University, Ames, Iowa, 1985.

190

10. Dunker, K. F., F. W. Klaiber, and W. W. Sanders, Jr. "Design Manual for Strengthening Single-Span Composite Bridges by Posttensioning. Final Report--Part III." ERI Project 1536, ISUERI-Ames-85229. Ames,: Engineering Research Institute, Iowa State University, 1985.

11. Engelbach. "Report on the Strengthening of the Bridge over the Main River at Hochheim on the Federal Autobahn WiesbadenHochheim." (Erfahrungsbericht ueber die Verstaerkungsarbeiten an der Mainbruecke Hochheim (Vorlandbruecke) im Zuge der Bundesautobahn Wiesbaden-Hochheim (A 671). Wiesbaden:

12.

Hessisches Landesamt fuer Strassenbau, 1984 (German).

Ferjencik, P., and M. Tochacek. (Die Vorspannung im Stahlbau.) 1975, (German).

Prestressing in Steel Structures. Berlin: Wilhelm Ernst & Sohn,

13. Hoadley, P. G. "The Nature of Prestressed Steel Structures." Highway Research Report 200, Highway Research Board, 1967, pp. 11-26.

14. Holzapfel, M. W. Keim, J. Saettele, and A. Strobele. "Origin and Repair of Crack Damage in a Prestressed Concrete Bridge." (Entstehung und Beseitigung von Rissschaden an einer Spannbetonbruecke.) Beton- und Stahlbetonbau. Vol. 78, No. 6, June 1983, pp. 162-164 (German).

15. Jungwirth, D., and G. Kern. "Long-Term Maintenance of Pres tressed Concrete Structures--Prevention, Detection, and Elimination of Defects." (Langzeitverhalten von Spannbeton Konstruktionen-Verhueten, Erkennen und Beheben von Schaden.) Beton- und Stahlbetonbau, Vol. 75, No. 11, November 1980, pp. 262-269 (German).

16. Kandall, C. "Increasing the Load-Carrying Capacity of Existing Steel Structures." Civil Engineering, Vol. 38, No. 10, October 1968, pp. 48-51.

17. Kennedy, J. B., and Composite Bridges." Vol. 108, No. STll,

N. F. Grace. "Pre stressed Decks in Journal of the Structural Division

November 1982, pp. 2394-2410.

Continuous ASCE,

18. Klaiber, F. W., D. J. Dedic, K. F. Dunker, and W.W. Sanders, Jr. "Strengthening of Existing Single Span Steel Beam and Concrete Deck Bridges. Final Report--Part I." ERI Project 1536, ISU-ERI-Ames-83185. Ames: Engineering Research Institute, Iowa State University, 1983.

19. Klaiber, F'. W., K. F. Dunker, and W. W. Sanders, Jr. "Feasibility Study of Strengthening Existing Single Span Steel Beam Concrete Deck Bridges." ERI Project 1460, ISU-ERI-Ames-81251. Ames: Engineering Research Institute, Iowa State University, 1981.

191

20. Klaiber, F. W., K. F. Dunker, T. J. Wipf, and W. W. Sanders, Jr. "Methods of Strengthening Existing Highway Bridges. Preliminary Draft II, Final Report." ERI Project 1809. ISU-ERI-Ames-88040. Ames: Engineering Research Institute, Iowa State University, 1987.

21. Lecroq, P. "Additional Prestressing." (Precontrainte additionelle.) Annales de L'Institute Technique du Batiment et des Travaux Publics, No. 411, January 1983, pp. 96-103 (French).

22. Mancarti, G. D. "Strengthening California's Steel Bridges by Prestressing." Transportation Research Recoi;d 950, Transportation Research Board, 1984, pp. 183-187.

23. Mueller, T. "Alteration of the Highway Bridge over the Aare River in Aarwangen." (Umbau der Strassenbruecke ueber die Aare in Aarwangen.) Schweizerische Bauzeitung, Vol. 87, No. 11, March 13, 1969, pp. 199-203 (German).

24. "Sagging Erskine to Get a Rise." New Civil Engineer, No. 182, February 26, 1976, p. 9.

25. Tachibana, Y., K. Kondo, and K. Ito. "Experimental Study on Composite Beams Prestressed with Wire Cables." Final Report, International Association for Bridge and Structural Engineering, 7th Congress, Rio de Janeiro, August 10-16, 1964, pp. 677-683.

26. Troitsky, M. S., Z. A. Zielinski, and M. S. Pimprikar. "Experimental Evaluation of Prestressed Steel Plate Girder Bridges." Experimental Assessment of Performance of Bridges, Proceedings. Boston, Massachusetts, October 27, 1986, pp. 1-16.

27. United States Steel. "Bonners Ferry Bridge, Boundary County, Idaho, USS Bridge Report." Pittsburgh: United States Steel, 1985.

28. Vernigora, E., J. R. M. Marcil, W. M. Slater, and R. V. Aiken. "Bridge Rehabilitation and Strengthening by Continuous PostTensioning." Journal of the Prestressed Concrete Institute, Vol. 14, No. 2, April 1969, pp. 88-104.

29. Virlogeux, M. "External Pres tressing." (La precontrainte exterieure.) Annales de L'Institut Technique du Batiment et des Travaux, No. 420, December 1983, pp. 115-124 (French).

30. Wiley, William E. "Post-tensioning of Composite T-beams Subject to Negative Bending." M.S. Thesis in preparation, Iowa State University, Ames, Iowa, 1987.

193

APPENDIX A: FRAMING PLANS AND DETAILS FOR THE MODEL BRIDGE

3' -4" 3' -4" - ~~-~--i

2'-6" 2'-6" I ! 2'-6" 2'-6" I I

EB-1 --S-2 1 EB-2 1 ts-1 ---S-2

"'--s-1 I I -SP-1 I LsP-1 I s-v" < "'i' 2'-8" 2'-8" ";' "";' 2'-8" 2'-8" N

0 0 1 • <") ·l • 1 C> C> 6 C>

IB-1 0 l ~"l~B-~2~-------iF----::.--....,11-B--l .... ci~· ... ~-------iF-------.~--'-..s-1 I l's-2 Lse-2 I I Lse-2 '-s-2 I s-1/ -N <"} N N <"'> N

I < ! ! t ' ! Cl Cl 0 C> 0 Cl 0 Cl

IB-1 IB-2 18-1

'-s-1 NI Ml '-s-2 Lse-2 NI NI '-se-2 Ml's-2 I s-v" 6 6 6 0 6 6 ~ 6

EB-1 EB-2 EB-1

I s-1 I l"s-2 Lse-1 I I C~sP--•1 ..... "°f'l,~s--2----t!----s--1-:J;;fl\--

1 l I I I I

1.5" l 6'-4" I 6'-4" 5'-5.33" i S'-5.34" ! 5'-5.33" 6'-4" 6'-4" 1.5" ' '

12'-8" 16'-4" 12'-8"

41 '-11"

All STEEL SHALL HAVE A SPECIFIED NOTE: YIELD POINT, Fy "' 30 KS! TO 36 KSI THERE IS A PLANNED

0.16" GAP BETWEEN WELDING ELECTRODES SHALL BE BEAMS AT SP-1 & COMPATIBLE WITH PARTS TO BE CONNECTED. SP-2.

Fig. A.1. Framing plan.

~

~

~

~

~

~ I

N

~

"' ~ -"-'--

..... <O ~

0

195

1/8" CONTINUOUS WELD EXCEPT AS NOTED IN FIG. A.6.


FULL PENETRATION GROOVE WELDS

FRAMING PLAN SEE FIG. A.1.

3/16" PLATE

--1 r--3/8" PLATE :ri---· -;-5;,---.--i NOTE: 4 EB-1 REQUIRED, 2 EB-2 REQUIRED

Fig. A.2. Exterior beam: EB-1, EB-2.

. 0

196



NOTE: 4 !B-1 REQUIRED, 2 IB-2 REQUIRED

Fig. A.3. Interior beam: IB-1, IB-2.

FULL PENETRATION GROOVE WELDS

FRAM ING PLAN SEE FIG. A.1.

3/16" PLATE

PLATE

l. 50" l r_7_9,)__,_~8':...L.J2 • 50" 12 .50" ....1 ___ g;.~2° 12. 50" _,_il_~J_~_':.i_JI~. 25.~_,_?~~8''.._,_12 _ _,_~_Q~_-J ... J.2. 50" ....1--9. 58'.:..i __ l2_._5_Q'.'._,_.9. 38''.., lL 97"

< < < < < > > > > > > > > > > < < < -- '-.......3/16" FLANGE 16'-l.42" ~~<:::'.3C:/;:8,;-' -;:F;clA;-:Nc;GE;:--------~~

.45"6.25" 9.38" 9.38" 12 .50"

I I I I I < < < < <

--..3/16" FLANGE

4.79" 6.25" 6.25"

A. EB-1 PLAN

12. 50" 15.42" 12. 50"

I I < >

9'-7.84"

B. EB-2 AND rB-2 PLAN

9.38" I 9.38" .fl.25"6.4 "

I I I I > > > >

z " 115.84"

NOTE: SEVERAL SHEAR LUGS WERE OMITTED, ALTERED, OR MOVED TO CLEAR 1" BAR TABS, FLANGE SPLICES OR BEAM SPLICES.

l.5Q"11 •. 16,.25f , 16.25[' l6.2~j' 12 50" 15 .42" . ' 12, SQ" ! 9. 38'~ 1 _9 .38~.1.. 25\'6. 251' .9 .38': I .9 • 38_", . }2. 50". > • 12. 50" 1 . 9. 58"., .12. 5Q"_, .9 .JB~, s. 98"

< < < < < < < > > > > > > > > > > < < < ,,..___3/16~-FiANGE. 16'-1.42-.. ----- 3/8" FLANGE

C. IB-1 PLAN

Fig. A.4. Shear lug plan.

,_. "' ......

198

1/8 ..,.---r-'-C.1....-n

1/8

00 0

(V)

00

N

A. ELEVATION

L 1 3/4 x 1 3/4 x 1/8

NOTE: 196 SHEAR LUGS REQUIRED.

BAR 1/2 x 1/4

B. PLAN

Fig. A.S. Shear lug details.

4'-1.50" l'-10" 10'-1.92"

1· CONTINUOUS WELD ·r· 2" WELD "'I• CONTINUOUS WELD "\ 2" SPACE

I I

~lit_s-1 lit_D-2 l<f.s-2 I i 6'-4" i 6'-4" i 3'-3.92" . ... . .. .. ... a. EB-1 AND IB-1 LAYOUT

3' -0" - ~ 3'-7.84" . - - . 3'-0" -- -CONTINUOUS WELD 2" WELD, 2'' SPACE CONTINUOUS WELD

- - -I I I ! ' -I I l D-2 I t D-2 I

2'-1.25" i 5'-5.34" i 2'-1.25" .. JI ii _., II ..

b. EB-2 AND IB-2 LAYOUT

Fig. A.6. Weld and stiffener layout.

,__. <.O <.O

1/8

1/8

200

2" l/8"2"

• <:t N

N

1.lOJ Ji.10 11

a. STIFFENER S-1

NOTE: 8 S-1 ST! FFENERS REQUIRED

CLOSE FIT

-

b. STIFFENER S-2

NOTE: 8 S-2 STIFFENERS REQUIRED

= co CV)

r-<

N r-< . N

NOTE: ALL HOLES SHALL BE 0.56" DIA.

Fig. A.7. Stiffener details.

~-t

1. 31 11

~11.' ,.

C> U")

I

'

201

0.75;1 '1.5011

1 2.1711

11.5011

1 ,~.7511

.. • c .. • ..

I I I I ' ' .

. . ' i ¢ <P

0 0

0 0 I I I

' .. I f~~ll

411

a. SPLICE SP-1: EB-1 TO EB-2 NOTE: 4 SP-1 SPLICES REQUIRED

'.

3/16" PLATES

,.,,,..- 1/8 II STR Ip

' ' I

0 • 7 5 II 1 50 II 2 • 17 II 1. 50 II 14

. .. , . ·1· "I 0. 75 11

r -I !

. . ' I

¢

0

0 I

' .. I

b. SPLICE SP-1: IB-1 TO IB-2 NOTE: 4 SP-2 SPLICES REQUIRED

I I

.. . . ' "' I

¢ 3/16 11 PLATES

0 /1/8" STRIP

0 I I ... .. ' ' . .

II I

Fig. A.8. Splice details.

J

'

\

I

~ I I

I

~ rl ' 1 I I I •

7' - 11.50" 12" . 12" 2' - 10" 2' - 10" h2" .... .... ._

~

=

l"""1 ...., w 11 I

l"""1 l"""1

i l OMIT TABS & STIFFENERS FOR .U I I

2 1 ' - 7 • 50 ul 12" i BOTTOM FLANGE ON IB-l

~

f ' '

a. EB-1 AND IB-1 LAYOUT

5.92" II! !II I 1 !'!. !·! 12" 6' - 8" 12" . 5.92"

5r N 0 N

""' :1 ~OMIT TABS & STIFFENERS FOR ~ '

BOTTOM FLANGE ON IB-2~ l

b. EB-2 AND IB-2 LAYOUT

Fig. A.9. Tab layout.

3/16

1/8

203

. . ~ . H I 250" I 250" I 1" BAR I I ....._r---;---.-

0.69" DIA.

0.75"

1/4

C> LO

"J 3/8" BAR OR PLATE .AC--1-t:<:_:JI ___ _,_

BUILT-UP BEAM

a. SIDE ELEVATION b. END ELEVATION

NOTE: 24-1.75'' HEIGHT TABS, 48 STIFFENERS REQUIRED 48-4'' HEIGHT TABS, 96 STIFFENERES REQUIRED

NOTE: ALL WELDS SHOWN ON THIS SHEET SHALL BE MADE WITH E?OXX ELECTRODES.

Fig. A.10. Tab details.

1/8 TYP. EA. END

1/8 TYP. EA. STIFFENER

1.

c 5 x 6.7 2' - 6.29"

204

a. ABUTMENT DIAPHRAGM: D-1 NOTE: 6 D-1

1/8" STRIPL--ru TO GAGE

c 3 x 4.1

2' - 6.54"

b. INTERMEDIATE DIAPHRAGM: D-2 NOTE: 12 D-2 DIAPHRAGMS REQUIRED

c 4 x 5.4 2' - 6.29"

c. PIER DIAPHRAGM: D-3 NOTE: 6 D-2 DIAPHRAGMS REQUIRED

Fig. A.11. Diaphragms.

.1

M <D

0

"' N

"'

C 3 x 4.1 CENTERED ON END PLATE NOTE: ALL HOLES

SHALL BE 0.56" DIA.

STIFFENER " ~

BEAM -L.--- BUILT-UP

/i\ \ )

I

1.50" 1.50"

4"

a. SIDE ELEVATION

en N . 0

~t 0

en

" 0

NOTE: 16 BEARINGS REQUIRED

3"

4"

b. END ELEVATION

NOTE: WELD GROOVED PLATES TO BOTTOMS OF EB-1 & IB-1. CENTER EACH PLATE ON A STIFFENER AND USE MIN. 3'' OF 1/8" FILLET WELD.

Fig. A.12. Bearing details.

3/4" PLATE WITH MILLED GROVE

1'' DIA. LOOSE BAR

LOOSE PALTE 1/2" MIN. THICKNESS

N 0 (jl

6" -0.50" 0.50"

2. 50" . 2.50"

I I

:: °;:!· ... I ~

/ "" L 5 x 3 x 3/8, ''-" r-... D ~ !'- ........ ... "'

l/4V \ -/ l/4V I

I I

o.soJ 11.50"1 3" 11.50"1 II _. 11 • Ill •

a. END ELEVATION

_j_l N

M

I ..... 00

1~.50'~ 0.50" Lr

6.50" . 2.75" ' 2.75"

CHAMFER TO FIT TAB WELDS

0.69" DIA. HOLE- ;t::p

TYPICAL WELDS /T\-~, ~,.,..., 7 ..... EACH SIDE

~3/8" BAR OR PLATE I

- - 13.75" _I ,..,- --·-

18" ·~

b. SIDE ELEVATION NOTE: 16 BRACKETS REQUIRED

Fig. A.13. Bracket details.

STRIP REMOVED ON 4 BRACKETS TO CLEAR TABS

0.75" DIA. HOLE

0.75"

N 0

""

207

APPENDIX B: PLANS AND DETAILS FOR THE FULL-SCALE NEGATIVE MOMENT REG!ON MOCKUP

N ~ ~ .,. '

30'-0"

13' -2" 16 1 -10"

9'-9 3/4" i 10'-9 3/4" PLACE OF ANCHORAGE

I PLATE = : <t

1· 6'-6"

A- •1• 6'-6" ·1 1: .,.. TOP OF BEAM -COVERPLATE BRACKET'-

~ ~THREADBAR TENDON , ... -ft TENDON =

I

STIFFENER ' WITH SPLICE I. t 7/8" DIA. BOLTS

I rnvrRDI ATI="-- j ............... ~TRfNhTHfNTNh UNh! r' I 19SPACES@6"=9'-6" A'-::: )gSPACES@6"=9'-6" I

,. • ! I I 11 •

3" 3"

N M ~

°' N

~

9'-11'/4"

~-10

i

t SUPPORT

a. THREADBAR TENDON

10' -8"

1/4" .j.. 5'-10" "! A~ ; -COVERPLATE i

___ ..., '!_ FACE OF ANCHORAGE PLATE

N TOP OF BEAM

L. If_ TENDON~--

--~ ST! FFENER SADDLE t ANCHORAGE PLATE

COVERPLATE- AL.ITi l ' STRENGTHENING ANGLES

I 16 SPACES@ 6" = 8'-0" ,i j i.. .. 3" 3"

17 SPACES @ 6" = 8' -6"__J

'!_ SUPPORT

b. CABLE TENDONS

fig. B.l. Steel beam layout elevations.

N 0 00

A7, W24x76 FLANGE

JLT-UP

~END OF FILLET WELD

1/4 4"

1 A36 STEEL COVERPLATE

MULTIPASS ~ WELD '° ...... ..___

......

, ____ _ -----

a. END PLAN

b. END SECT! ON

Fig. B.2. Coverplates.

...... ......

NOTE: ELECTRODES ARE ER 70S-3 (WIRE)

N 0

'°

210

11 1/6" x 3/4" A36 COVERPLATE TOP AND BOTTOM

CLOSE FIT

...,_ ____ CUTOUT

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

NOTE: ELECTRODES ARE ER 70S-3 (WIRE)

W24x76, A7

1 3/4" 2" 1/4 1/4

FOR TENDON

1/2" THICK, A36 STIFFENER

.L~~~~~~'.'.:l1---3/4" THICK STEEL PLATE ..---2" DIA. STEEL ROLLER

STEEL-BEARING PLATE

Fig. B.3. Bearing stiffeners, Section A-A.

13'-2" 16'-10"

I'" "F==-it PIER SUPPORT ·1 I>> >I> > I< < I< < < <<I

9.87J 16" 37.50" 37.50" 37.50" 9.63! 37.50 37.50" 37.50" 37.50" 15" 6·

L5x5x3/8

1/4

/ / lj /~

?' 1' ·~ ~

b. SHEAR LUG PLAN

N '""' <Xi

9 .13"

a. LAYOUT PLAN

1/4

Fig. B.4. Shear lugs.

NOTE:

18.75"

ELECTRODES FOR ANGLE-BAR FILLETS ARE E 7014 ELECTRODES FOR LUG-BEAM FILLETS ARE ER 70S-3 (WIRE)

""

TOP OF COVERPLATE OR TOP FLANGE

c. SHEAR LUG ELEVATION

N .... ,_..

2 1/2"

6'-3°

9" 10" - 7" 9" 9" 7" 10" • 9" 2 1/2"

-·' .. -·· ·~. ·~ ... · ;.<>···... • ~. --· .•

: .~· ~~~ ·~~-~~~~~~: :~ ::.~-~;~ ~-i:~~·:·;-::::-~:.~ i=~.-~~·:'! =·:·~: /:.~· ~ ~::; ?0

• .~.· :·.':~· ~ ~ ·::;·~· .~°,;~Q· ~- ~ 0 :, ~,:_:.:; o. ·;. . •

ex: ~ LINE OF #5 BAR, FULL LENGTH

d BLOCKOUT #6 BAR AT l'-6 3/4" O.C., "'" ....- u TOP AND BOTTOM STAGGERED -..... ...... .....

H• I W 24x76 WITH COVERPLATES

.dtt¢£@iiii!s· I

Fig. B.5. Composite beam, Section B-B. (see Fig. B.6.)

N ..... N

30'-0"

13'-2" 16'-10"

I 7' -0il

B ,.j. 7' -0"

·1 l·-n·l-3" I

F i PIER

" \ _L.!5 BOTTOM BAR _Jll ·~ #5 TOP BARS

i-+- -J-_ ---- I ;; '. I I

I I II TYPICAL

V BENT #5 CURB BAR

1--4-l--I

I I

' I

.... 13

Fig. B.6. Deck-reinforcing plan.

I TYPICAL #6 BOTTOM~ #6 TOP-#6 BOTTOM II M

' BAR PATTERN . 1 -'"' I

-----+' II I

NOTE: 2-#4 BARS WERE SUBSTITUTED RANDOMLY FOR #6 TRANSVERSE BARS

N ,_.. w

13'-2"

l'-11", 2'-2" 7'-6"

3'' DIA. PVC INSERT

B

I I

30'-0"

PIER

3 1/2''x1Jl/4'' GROOVE

2'-2"x2'-0" DECK BLOCKOUT I I

B

Lr> M

16'-10"

8'-8" 21-211 .11_711 3'-0"

0

---rt_

0

Fig. B.7. Deck blackout and insert plan.

-N ..__ .--<

.--<

' N

0

' -

0 1--1 B;AMt~= ~

-1'> :J ~ N ..__ .--<

.--<

' -N

2"

5/16

NOTE: ALL ELECTRODES ARE E70XX.

l'-6"

2" 3" 3" 3" 3" 2"

0 >15/1? DIA H;:;S 1 1/4" DIA. HOLES

0 0

ALL BOLTS ARE A325, 7/8'' DIA.

= N

1 __ _15/16

I = (Y)

. ~

N

7 1/2"

1: , T 3 'I' :1

I I I

1/2" 5/16

L?DIA HOLE

N

---~ (Y)

l

T = N

---~ (Y)

7" 1/2" A36 STEEL PLATE LINE OF END PLATE


Fig. B.8. Bracket for threadbar tendon.

= "

N ,_, '-"

NOTE: ALL BOLTS ARE A325, 7/8" DIA. 1

A7, W24x 76 'I ~

::... ;>

'I; ,• ~ ~

~

A36, L5x5x3/8 615/16" DIA.

<") HOLES 'b 0 0 0 0

J

' I I

SPAC.ES@ 6"i I I I !SPACES I

6" I l I 6" I@ 6" • I I

DI MENSI - - --- . ' ' ' ' ' • '

THREADBAR TENDONS 91_911 1 l/2"!L 1/2" 9 I _911

' I DIMENSIONS FOR- l+*v 8'-3" I 8'-9" CABLE TENDONS • • ~

l PIER

a. ANGLES, SECTION A-A b. ANGLE-SOLT LAYOUT ELEVATION

Fig. B.9. Bottom flange strengthening angles.

•

3"

~

N ,_.. "'

q:_ 15/16" . fl 1 1/16" q:_ 15/16"

DIA. HOLES\ . I OJA. HOLES. Ir'"· HOLES 1 1/2" 3 1/2" 9 1/2" 1 1/2" 4 .. .. .. r

I i . i i ;,·, .

.J /

r --.. CV)

N 0 -- l

. ' 0 I

tj-

c --.. CV) 0 CV)

tj-.. I

• --.. ..... --0 0 l 0

CUT-AWAY CORNER AS REQUIRED FOR RIGHT OR LEH BRACKET

I_ .. I

0 0 0 0

~ • I ...._

...;:

I ' I 1 T .. .~ I 8' I 1 ·1 : .. . .. .. .. .. .. .. : l'-4"

a. SIDE ELEVATION

Fig. B.10. Bracket for cable tendons.

I -tj- ..... --.. CV)

cry

--= l co --... cry

NL i

N ,_, .._..

"'" --.....

1/2"

--.... ..--I .....

"'" ....... M

M

= N

'.'.:!:. :::;- ['· .......-t. = '

"'" 0 ....... I .-<

.--I : N

~ ..---I .....

"'" ....... M

M

N .......

"'" ....... .....

11 1/2" ----5u 411 Jul

•I• •l"4=taa·

1;4v "'- I 1___hl_ 1 1129 I ~ ,_

.....

l~aTAJ ,--.,,. --M

M' <j-

= ' ---1 I ~ 211 M

3/4" DIA. ----co ....... r-.....

\' .. I> ~l

..___

.....

..... .....

NOTE: ELECTRODES ARE E?OXX.

FACE OF PLATE TO BEAM WEB

2" 11" 4" 8"

1'-4"

b. ANCHORAGE END ELEVATION c. TOP ELEVATION

Fig. B.10. continued

"

N ....... ......

N

01 ....... ..... ..... ..... .....

I N ,_.

) I °'

1'-5 1/2" 11" 1 3/4" 1 1/4"

1 1/2" l/_4."_ _.1_ 3/4" 8 3/4" 1 1/ 4" 1/2" 1/2" <-'----

""" L1 1/2xl l/2xl/8

rl

= rl

""" --..._ 0 --. PIPE 5" OD -:::::::.--- ........

\_-..tX =-=-=,I !-~3/_:_16=-=====_J /It r I """ --..._ 1------l::==~------

'3!16V 2

(Y)

rl_ I ;;..r--- c; --..._

<(

(Y)

= rl

"'" --..._ rl

-'° __ ,....-!

--..._ ..,., rl

1' 11

1 1--:-t::==---~,, -1\i I 1'-- TS 3 1/2 ' 3 1/2 ' 1/40 I ---

3/16

L:_n_ 1 1/16" DIA. -1J I I ES '

- +- 'i 15/16" DIA. HOL 1/2"

<:T --..._ (Y)

00

0 0

i 15/16" DIA. HOLES

N --..._ rl

,.-;

~r-, 2 _, ... , r-if .. ~ 2 3/4". ., I

6"

(Y)

N = N --..._ rl

= T

""" --..._ (Y)

N

i (Y)

I -rl

°'

3/16

3/16 3/16

3 3

NOTE: ELECTRODES ARE E7014


Fig. B.11. Saddle for cable tendons.

3/16[> 3 3/16 3

N ,_. ""

N FACE OF PLATE TO BEAM WEB ,._,

1/4"~ f] ~

<DI

3 :1-:::1 I

~II ·- I

3Ll6~3 3/16 3

N N 0 '

--------- -

I ~ I L 6" 10" ,._, -

1' - 5 1/2" 1 1/2"

c. TOP ELEVATION

Fig. B.11. continued

Strengthening of Existing Continuous Composite...

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