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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. Physical Properties
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
ix
xv
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
157
158
158
161
166
175
179
179
183
185
187
189
193
207
ix
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. 4.8. Bottom flange strains for PTS-1. 121
Fig. 4.9. Bottom flange strains for PTS-3. 122
Fig. 4.10. Bottom flange strains for PTS-1 + PTS-3 + PTS-5. 124
Fig. 4.11. Bottom flange strains for PTS-10. 126
Fig. 4.12. Bottom flange strains for PTS-10 + PTS-16. 127
Fig. 4.13. Bottom flange strains for PTS-12. 129
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. 4.17. Bottom flange strains for LC 3. 137
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. 4.21. Bottom flange strains for LC 19. 142
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. 4.25. Bottom flange strains for 6-kip vertical load at LP 8 and LP 10. 155
Fig. 4.26. Bottom flange strains for 6-kip vertical load at LP 15 and LP 17. 156
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. 4.30. Strains at Section 5 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.
172
176
194
195
196
197
198
199
200
201
202
203
204
205
206
208
209
210
211
212
213
214
215
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. Physical Properties
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
Fig. 2.8. Continued.
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. Physical Properties
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
Fig. 3.3. Continued.
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.
3.2.2. Preliminary Vertical Load Tests
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
Fig. 4.5. Continued.
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.
4.1.4. Effects of Post-tensioning
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
Post-tensioning Force Applied to Region
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
Post-tensioning Force Applied to Region
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.
4.1.5. Effects of Vertical Loads
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
(/)
-600 BMl BM2 BM3 BM4
b. SECTION B
~ 600
"' •r ....... . 300 "' •r
"'-~
(/) 0 ---z
~
cl:
:=-300 (/)
-600 BMl BM2 BM3 BM4
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 (/)
-600 BMl BM2 BM3 BM4
b. SECTION 8
600 . LP 10~~ c: ·~ / ; 300 / c: .-<:!"/ ·~ ----;:1
0 :z ..... c(
~-300 (/)
-600 BMl BM2 BM3 BM4
c. SECTION C
Fig. 4.25. Bottom flange strains for 6-kip vertical load at LP 8 and LP 10.
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
Fig. 4.26. Bottom flange strains for 6-kip vertical load at LP 15 and LP 17.
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.
4.2.2. Preliminary Vertical Load Tests
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.
4.2.3. Effects of Post-tensioning
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
Fig. 4.29. Strains at Section 4 for full-scale mockup with post-tensioning.
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
STRAIN, (µ in.fin.)
6--STEEL BEAM, THEORY 9-~COMPOSITE BEAM, THEORY
b; HARPED TENDON
600
Fig. 4.30. Strains at Section 5 for full-scale mockup with post-tensioning.
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.
4.2.4. Effects of Vertical Loads
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
Fig. 4.33. Continued.
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
STRAIN, (µ in.fin.)
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
Fig. 4.34. Continued.
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.
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
1/8" CONTINUOUS WELD EXCEPT AS NOTED IN FIG. A.6.
1/8" CONTINUOUS WELD EXCEPT AS NOTED IN FIG. A.6.
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
a. SIDE ELEVATION b. END ELEVATION
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
a. SIDE ELEVATION b. END ELEVATION
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
Recommended