..##@,“,CM;G INSTITUTE

Glenview, Illinois 60025

PRECASTSEGMENTALBOX GIRDERBRIDGE MANUAL

.

PUBLISHED BY

PRESTRESSED CONCRETE INSTITUTE20 N. Wacker DriveChicago, Illinois 60606

ACKNOWLEDGEMENT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

FOREWORD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 1. DEVELOPMENT OF PRECAST SEGMENTAL BRIDGE CONSTRUCTION . . . . . . . . . . 1

1.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 TYPES OF PRECAST SEGMENTAL CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 ADVANTAGES OF PRECAST SEGMENTAL BRIDGE CONSTRUCTION . . . . . . . . . . . . . . . . 3

1.4 ALTERNATE DESIGN PROPOSALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.5 APPLICABILITY OF PRECAST SEGMENTAL CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . 5

1.6 APPLICATIONS OF PRECAST SEGMENTAL CONSTRUCTION IN NORTH AMERICA . . . . 61.6.1 Lievre River Bridge, Quebec . . . . . . . . . . . . . . . . . . . . . . . b . . . . . . . . . . . . . . . . . . . . 6

1.6.2 Bear River Bridge, Digby, Nova Scotia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.6.3 JFK Memorial Causeway, Corpus Christi, Texas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.6.4 Muscatatuck River Bridge, North Vernon, Indiana . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.6.5 Vail Pass Bridges, Colorado. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.6.6 Kishwaukee River Bridge, Winnebago County, Illinois . . . . . . . . . . . . . . . . . . . . . . . . 10

1.6.7 Sugar Creek Bridge, Parke County, Indiana. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.6.8 Turkey Run Bridge, Parke County, Indiana. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.6.9 Pennsylvania State University Test Track Bridge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.6.10 Other Precast Segmental Bridges in Planning, Design and Construction. . . . . . . . . . . . 1 1

s

CHAPTER 2. CONSIDERATIONS FOR SEGMENT DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1 GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 PRINCIPAL DIMENSIONS OF SEGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 DETAIL DIMENSIONS OF SEGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 PIER AND ABUTMENT SEGMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5 POST-TENSIONING TENDONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5.2 Permanent Post-Tensioning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5.3 Temporary Post-Tensioning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.4 Layout of Post-Tensioning Tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.6 MILD STEEL REINFORCEMENT CAGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.7 SHEAR KEYS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.8 EPOXYJOINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

CHAPTER 3. ANALYSIS OF PRECAST SEGMENTAL BOX GIRDER BRIDGES. . . . . . . . . . . . . . . . 27

3.1 GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 DEVELOPMENT OF PRELIMINARY BRIDGE DETAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.1 Selection of Span Arrangement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.2 Abutment Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.3 PierDetails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.4 Horizontal and Vertical Curvature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.5 BearingDetails.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 LONGITUDINAL ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.1 Erection Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.2 Creep Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.2.1 Creep Effects Resulting from Change of Statical System. . . . . . . . . . . . . 313.3.2.2 The Effect of Creep on Moments due to Support Settlements . . . . . . . . 33

3.4

3.5

3.6

3.7

3.3.2.3 The Effect of Creep in Reducing Restraint Forces due to Shrinkage. . . . 34

3.3.2.4 Determination of the Creep Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3.2.5 Example Creep Factor Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.2.6 Influence of Creep on Super-structure Moments. . . . . . . . . . . . . . . . . . . 37

3.3.3 Analysis for Superimposed Dead Load and Live Load. . . . . . . . . . . . . . . . . . . . . . . . . 41

3.3.4 Analysis for the Effects of Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.3.5 Shear Lag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.3.5.1 Computer Analysis of Shear Lag in Single-Cell Box Girder Bridges. . . . . 44

3.3.5.2 Consideration of Shear Lag in Bridge Designs. . . . . . . . . . . . . . . . . . . . . 49

3.3.6 Ultimate Strength Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

TRANSVERSE ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.4.2 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.4.3 Symmetrical Box Girder Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.4.4 Antisymmetrical Loading . . . . . . . . . . . . . . . . . . . . . . . . . ! . . . . . . . . . . . . . . . . . . . . 53

3.4.5 Evaluation of the Contributions of Transverse Bending, Longitudinal Bendingand Torsion to Resistance of Antisymmetrical Loading . . . . . . . . . . . . . . . . . . . . . . . 54

ANALYSIS AND TRANSVERSE POST-TENSIONING OF DECK SLABS . . . . . . . . . . . . . . . . 59

3.5.1 Live Load Plus Impact Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.5.2 Transverse Post-Tensioning of Deck Slabs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

ANALYSIS AND CORRECTION OF DEFORMATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.6.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.6.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.6.2.1 Phase A - Free Cantilever. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.6.2.2 Intermediate Phases B, B’ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.6.2.3 Phase C - Final Continuous System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.6.3 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.6.3.1 Correction of Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.6.3.2 Correction of Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.6.3.3 Correction of Superimposed Curvature. . . . . . . . . . . . . . . . . . . . . . . . . . 67 .

FABRICATIONXIF PRECAST SEGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1 .l General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1

4.1.2 Methods of Casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.1.2.1 The Long-Line Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1.2.2 The Short-Line Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1.3 Formwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.1.4 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.1.5 JointSurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.1.6 BearingAreas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2 HANDLING AND TRANSPORTATION OF PRECAST SEGMENTS. . . . . . . . . . . . . . . . . . . . . 76

4.3 METHODS OF ERECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.3.1 Cranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.3.2 WinchandBeam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.3.3 LaunchingGantry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.3.4 Progressive Placing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.3.5 Erection Tolerances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.3.6 Design of Piers and Stability During Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

$

3.6.3.4 Example Alignment Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.6.3.5 Notes on Alignment Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

COMPUTER PROGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.7.2 Sources of Computer Programs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

CHAPTER 4. FABRICATION, TRANSPORTATION AND ERECTION OF PRECAST SEGMENTS . . 71

4.1

4.3.6.1 Single Slender Piers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.3.6.2 Moment Resisting Piers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

CHAPTER 5. DESIGN EXAMPLE, NORTH VERNON BRIDGE, INDIANA. . . . . . . . . . . . . . . . . . . . . 85

5.1

5.2

5.3

5.4

5.5

5.6

GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

STRUCTURE DIMENSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

ORDER OF ERECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

POST-TENSIONING DETAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

DESIGN REQUIREMENTS AND LOADING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

DESIGN PROCEDURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.6.1 Step 1. Free Cantilever Plus Initial Cantilever Group 1 Post Tensioning . . . . . . . . . . . 89

5.6.2 Step 2. Completion of Tail Span Plus Continuity Group 2 Post-Tensioning . . . . . . . . 91

5.6.3 Step 3. Completion of Center Span. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.6.4 Step 4. Addition of Superimposed Dead Loads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.6.5 Step 5. Application of Live Load and Temperature Load . . . . . . . . . . . . . . . . . . . . . . 95

5.6.6 Step 6. Influence of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.6.6.1 Step 6a. Box Girder Dead Load Moment Redistribution Due to Creep. . 97

5.6.6.2 Step 6b. Post-Tensioning Moment Redistribution Due to Creep . . . . . . . 985.6.6.3 Step 6c. Effect of Prestress Losses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.6.7 Step 7. Final Stress Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.6.8 Step 8. Calculation of Transverse Moments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

, A P P E N D I X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 7

A.1 TENTATIVE DESIGN AND CONSTRUCTION SPECIFICATION FOR PRECASTSEGMENTAL BOX GIRDER BRIDGES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

A.2 SUMMARY OF PRECAST SEGMENTAL CONCRETE BRIDGES IN THE UNITED STATESAND CANADA WITH CROSS SECTIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

.A.3 NOTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

A.4 R E F E R E N C E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 8

Extreme care has been taken to have data andinformation in the Precast Segmental Box GirderBridge Manual as accurate as possible. However,as the Post-Tensioning Institute and PrestressedConcrete Institute do not actually make designsor prepare engineering plans, they cannot acceptresponsibility for any errors or oversights in theuse of Manual material in bridge project designsor in the preparation of engineering plans.

ACKNOWLEDGEMENTS

The majority of the technical material in this manual was developed under a contractwith the consulting firm of Bouvy, Van Der Vlugt & Van Der Niet/Segmental Technologyand Services (BVN/STS). H. H. Janssen prepared most of the BVN/STS material. The creepand shrinkage data in Chapter 3 reflects the procedures in Comite Europeen du Beton/Federation lnternationale de la Precontrainte bulletin d’information No. 111 published inOctober, 1975. Portions of Chapters 1, 2 .and 4 were adapted from the article by JeanMuller of Enterprises Campenon Bernard, “Ten Years Experience in Precast SegmentalConstruction” which was initially published in the January-February 1975 Journal of thePrestressed Concrete Institute. Some of the material in Chapter 4 was taken from “Recom-mended Practice for Segmental Construction in Prestressed Concrete” developed by the PCICommittee on Segmental Construction and first published in the March-April 1975 Journalof the Prestressed Concrete institute. The computer analysis for the effects of shear lagpresented in Chapter 3 was conducted by Professor Alex Scordelis of the University ofCalifornia at Berkeley. The prepublication drafts of the manual were reviewed by com-mittees of the Prestressed Concrete Institute and the Post-Tensioning Institute. Generaleditorial work in development of the manual was by Clifford L. Freyermuth, Post-Tension-ing Institute.

,

I

IF O R E W O R D

IIn the period since the conclusion of World War II, prestressed concrete in various forms

has emerged as a major factor in long span bridge construction. A number of prestressedconcrete box girder bridges with spans ranging to 700 ft. (210 m) have either beencompleted or are underway in the U.S. and Canada. A prestressed concrete deck has beenselected for the Dames Point Bridge in Jacksonville, Florida. This cable-stayed bridge willhave spans of 650 ft., 1300 ft., and 650 ft. (200-400-200 m) for a total length of 2600 ft.

I ’

(800 m). The Pasco-Kennewick cable-stayed bridge in the State of Washington utilizing pre-cast segmental construction will be completed in 1978 and has a main span of 981 ft. (299

ml.

In the late 1940’s, and in the 1950’s, many innovative construction methods were devel-oped in Europe for replacement of war damaged bridges. These construction methods pri-marily related to the use of prestressed concrete. In particular, the cast-in-place cantilever

amethod of segmental bridge construction developed by the firm of Dyckerhoff & Widmannin Germany opened the way to construction of concrete bridge spans in excess of 700 ft.(210 m).

Beginning in the mid 1960’s, the Freyssinet Organization developed technology in Francefor the use of precast segmental box girder bridges. This technology subsequently spread tocountries throughout the world, including, in recent years, Canada and the United States.As a contribution to the continuing evolution of prestressed concrete bridge construction,the Prestressed Concrete Institute and the Post-Tensioning Institute are pleased to presentthis joint publication on precast segmental box girder bridges.

!

CHAPTER 1

DEVELOPMENT OF PRECASTSEGMENTAL BRIDGE CONSTRUCTION

1.1 Introduction

The earliest known application of precast seg-mental bridge construction was a single spancounty bridge in New York State built in 1952.The bridge girders were divided longitudinally intothree precast segments which were cast end to end.After curing, the segments were transported to thejob site where they were reassembled and post-tensioned with cold joints.

The development of long span prestressed con-crete bridge construction techniques in Europe isoutlined in the Foreword. Of particular signifi-cance was the development of cast-in-place canti-lever segmental construction in Germany by thefirm of Dyckerhoff & Widmann, Inc. The technolo-gy of cast-in-place segmental construction wasadapted and extended for use with precast seg-ments in the Choisy-le-Roi Bridge over the SeineRiver south of Paris in 1962. The Choisy-le-RoiBridge, designed and built by EnterprisesCampenon Bernard, is shown in Fig. 1.1. Severalother structures of the same type were built in duecourse. At the same time, the techniques of pre-casting segments and placing them in the structurewere continually refined.

A major innovation for construction of precastsegmental bridges was the launching gantry whichwas used for the first time on the Oleron Viaduct,shown in Fig. 1.2, which was built between 1964and 1966. The Oleron Viaduct launching gantri/is shown in Fig. 1.3. The launching gantry makes itpossible to move segments over the completed partof the structure and place them in cantilever oversuccessive piers. Use of a launching gantry per-mitted completion of the Oleron Viaduct at anaverage of 900 linear feet (270 m) of finished deckper month. While the launahing gantry is a veryuseful means of erection in many cases, erectioncan also be accomplished by use of cranes andother means as described in Section 4.3.

Experience with major precast segmental bridgesin Europe allowed the refinement of the construc-tion process. Improvements were made in precast-ing methods and in the design of erection equip-ment to permit use of larger segments and longerspans, and which could accommodate horizontalcurvature in the roadway alignment.

The technique of precast segmental construc-tion not only gained rapid acceptance in Francebut spread to other countries. For example, theNetherlands, Switzerland and later Brazil and New

Zealand adopted the method. Many othercountries are today using the precast segmentaltechniques for various applications. The firstknown application of precast segmental box girderbridge construction in North America was a high-way bridge over the Lievre River in Quebec. TheLievre River Bridge was built in 1967 and has amain span of 260 ft. (79 m) with end spans of 130ft. (40 m). The Bear River bridge near Digby, NovaScotia, shown in Fig. 1.4 contains six interior spansof 265 ft. (81 m) and end spans of 203 ft. (62 m).The Bear River bridge was opened to traffic inDecember 1972.

The first U.S. precast segmental box girderbridge was built near Corpus Christi, Texas and wasopened to traffic in 1973. The Corpus Christibridge, shown in Fig. 1.5, has a central span of 200ft. (61 m) and end spans of 100 ft. (30.5 m). Sub-sequent to the Corpus Christi bridge, precastsegmental bridges have been completed in Indianaand Colorado, and a bridge of this type is nowunder construction in Illinois. A simple span pre-cast segmental bridge has been constructed at thePennsylvania State University test track as a re-search project sponsored by the Federal HighwayAdministration and the Pennsylvania Departmentof Transportation. Numerous precast segmentalbridges have been designed for other locations inthe U.S. and Canada, and it is expected that thistechnique will be widely used in the years ahead.

1.2 Types of Precast Segmental Construction

Two main types of precast segmental bridgeconstruction have developed which may be differ-entiated by the use of either cast-in-place concreteor epoxy joints.

A number of precast segmental bridges havebeen built using cast-in-place joints 3 to 4 in. (76to 102 mm) wide between segments. This procedureeliminates the need for match-casting and reducesthe dimensional precision required in casting thesegments, but it has major disadvantages includingthe requirement of falsework to support the seg-ments while the cast-in-place joint cures, and sub-stantial reduction in construction speed. Onbalance, the use of cast-in-place joints is not gen-erally attractive and for this reason this type ofjoint will not be considered further in this manual.

The prevailing system of precast segmentalbridge construction uses an epoxy resin jointingmaterial. The thickness of the epoxy joint is on theorder of l/32 in. (0.8 mm). The use of an epoxyjoint requires a perfect fit between the ends otadjacent segments. This is achieved by casting each

1

\

Fig. 1.1 - Choisy-le-Roi Bridge over the Seine River, Francet7)

Fig. 1.2 - Oleron Viaduct, Francef7)

segment against the end face of the preceding one(matchcasting) and then erecting the segmentsin the same order in which they were cast. Thismanual will consider only design and constructiontechniques for bridges using match-cast segmentsand an epoxy resin joint ing material .

1.3 Advantages of Precast SegmentalBridge Construction

The advantages of the use of precast segmentalconstruction techniques to the bridge engineer areas follows:

1. The economy of precast prestressed concreteconstruction is extended to a span range of 100 to400 ft. (30 to 120 m), and even longer spans maybe economical in circumstances where use of heavyerection equipment is feasible.

2. The precast segments may be fabricated whilethe substructure is being built, and rapid erectionof the superstructure can be achieved.

3. The method makes use of repetitive industria-lized manufacturing techniques with the’inherentpotential for achieving high quality and highstrength concrete.

4. The need for falsework is eliminated and allerection may be accomplished from the top of thecompleted portions of the bridge. These aspectsmay be particularly important for high-level cross-ings, in cases where it is necessary to minimizeinterference with the bridge environment, or whereheavy traffic must be maintained under the bridgeduring construction.

5. The structure geometry may be adapted to anyhorizontal or vertical curvature or any requiredroadway superelevation.

6. The effects of concrete shrinkage and creep maybe substantially reduced both during erection andin the completed structure because the segmentswill normally have matured to full design strengthbefore erection.

7. Except for temperature and weather limitationsrelated to mixing and placing epoxy, precast seg-mental construction is relatively insensitive to wea-ther conditions (see the weather restrictions on useof epoxy in Appendix Section A.l).

8. The esthetic potential of concrete construction.

9. Enhanced durability of bridge decks throughprecompression of the concrete and elimination ofcracking, and through use of high quality concreteproduced under conditions that permit a high levelof quality control.

The primary disadvantages of precast segmentalconstruction relate to the need for a somewhathigher level of technology in design, and the neces-sity for a high degree of dimensional control duringmanufacture and erection of the segments. At themoment, the temperature and other weatherrestrictions of epoxy jointing materials is also alimiting factor. The large number of successfulprojects in Europe and other parts of the world,and the growing number of completed projects inNorth America suggest that these obstacles will notinhibit rapid growth in the use of precast segmentalbridge construction.

1.4 Alternate Design Proposals

Up to the present time, precast segmental bridgeprojects in North America have been primarilyselected as the result of competit ive bidding againstother superstructure types. Given the economicconditions of the forseeable future, it is felt appro-priate that alternate proposals for any type ofsuperstructure should be permitted at either theowners or the contractors option on all majorbridge projects. Such a procedure would enhancecompetition, minimize construction costs, andencourage the innovation necessary to assureprogress in the development of bridge construc-tion techniques. To the fullest extent practicable,the contract documents should permit reasonableflexibility in span arrangements and other detailsnecessary to assure economical application of alter-native construction techniques. As one example ofthis point, the optimum ratios of end spans tointermediate span for three-span continuous rein-forced concrete or structural steel bridges areusually not economical for segmental construc-tion. For economy of a three-span precast segmen-tal bridge erected in cantilever, the end spansshould be approximately 50 percent of the lengthof interior spans. Of course, in long viaducts aportion of the end span can be built on falseworkwithout significantly affecting the overall structureeconomy. However, generally it is not equitable toselect strucJIural parameters to maximize economyof one type of construction, and then require thatany alternate design conform precisely to thoseparameters (presuming some flexibility is per-mitted by the factors controlling the structuregeometry).

It must also be recognized that use of alternatedesigns may entail some disadvantages. In particu-lar, additional engineering costs may be involved.Value engineering incentive clauses providing foralternative designs normally consider the addit ional

Fig. 1.3 - Oleron Gantryt7)

Fig. 1.4 - Bear River Bridge near Digby, Nova Scotia

engineering costs to both the contractor and theowner in establishing the net cost reduction result-ing from the alternative design proposal. Forvarious types of segmental concrete superstructures,these additional costs may be minimized byadvance recognition of the available constructionoptions in the contract documents. This may beaccomplished by using general rather than specificdetails in the contract plans in such a way that thespecific details on the fabrication drawings or con-struction plans for the options exercised by thecontractor can be checked against the contractdrawings. As examples of this procedure, contractdrawings may use Pe (force x eccentricity) diag-grams or envelopes for the post-tensioning require-ments rather than a specific number, size and loca-tion of tendons; and envelopes which indicate max-imum and minimum construction and service loadstresses along the structure.

1.5 Applicability of Precast SegmentalConstruction

The USR of precast segmental bridge construc-tion found initial acceptance for the span range of160 to 350 ft. (50 to 110 m). When thecantilevermethod of &on is used, this span range is stillconsidered to be the basic area of application.

a

0

0

0Fig. 1.6 - Rhone - Alpes Motorway Overpasses, Switzer-

land(‘)

Other factors contributing to selection of precastsegment4 construction are described in Section1.3.

In recent years, the advantages of precast seg-mental construction have been extended to shorterspan freeway overpasses in several Europeanprojects. The most notable application in thiscategory is the Rhone-Alpes Motorway which in-volved construction of 150 overpasses over a 5-year

Fig. 1.5 - Corpus Christi Bridge, Texas

Fig. 1.7 - Rhone - Alpes Motorway, Overpasses, Switzer-landf7)

Fig. 1.8 - Rhone - Alpes Motorway Overpasses, Switzer-landt7’

period. The bridges are three-span structures withmain spans ranging from 60 to 100 ft. (18 to 30m). The construction procedure for the Rhone-Alpes bridges is shown in Fig. 1.6. Significant fea-tures of these bridges include‘the complete elimina-tion of the normal closure joint, and the use ofconventional post-tensioning tendon profilesinstead of the cantilever type tendon arrangement.Stability during construction is provided by tem-porary supports close to the piers asshown in Fig.1.7, and by temporary post-tensioning bars

anchored along the deck surface as illustrated inFig. 1.8. The total construction time for a singleoverpass (foundations, piers, and superstructure)using this technique is less than 2 weeks.

A procedure for precast segmental constructiondeveloped primarily for the span range of 100 to160 ft. (30 to 50 m) is the concept of progressiveplacing discussed in Section 4.3.4. With this proce-dure, segments are placed continuously from oneend of the deck to the other in successive canti-levers on the same side of the various piers ratherthan in balanced cantilever at each pier.

1.6 Applicatiohs of Precast SegmentalConstruction in North America

1.6.1 Lievre River Bridge, Quebec

The Lievre River Bridge in Quebec,Fig. 1.9, was the first North American

shown inbridge of

precast segmental box girder construction. Thebridge, which was completed in 1967, utilizes atwo-cell box section and has spans of 130 ft. -260 ft. - 130 ft. (40-79-40 m). The 92 ton(84 t) pier segments of the Lievre River Bridgewere cast-in-place on the piers and the remainderof the superstructure was match-cast using a cast-ing bed set up on the river bank. Typical segmentsof the bridge were 9 ft. 6 in. (2.9 m) long andweighed from 38 to 52 tons (35 to 47 t). Thecasting of segments extended from Januarythrough June. During the winter months, the cast-ing operation was protected by an enclosure ofplastic sheeting supported on reusable steel trusses.The enclosure was assembled in sections 20 ft.(6.1 m) long and was lifted by crane to therequired location as work advanced. Under normalweather conditions, the erection pace for thebridge was two segments per day. Erection beganin August and the bridge was completed the sameautumn.

Fig. 1.9 - Lievre River Bridge, Quebec

1.6.2 Bear River Bridge, Digby, Nova Scotia

A precast segmental superstructure was selectedfor the Bear River Bridge near Digby, Nova Scotia,when alternate bids found precast segmentalconstruction at $3.36 million, compared to the lowbid for a steel structure of about $3.60 million.Another motivation for selection of the precastsuperstructure was the fact that Nova Scotia doesnot have steel fabricating facilities that would haveaccommodated the Bear River Bridge. This meantthat the money for superstructure labor andmaterials would largely have been spent outsidethe Province. On the other hand, selection of theprecast segmental superstructure resulted in use ofpredominantly local labor sources and localmaterials. The combination of direct cost savingsand use of local labor and materials led to theselection of the precast segmental superstructureeven though there had only been one prior use ofthis type of construction in Canada.

A construction view of the Bear River Bridgeis presented in Fig. 1 .lO. The bridge has six interiorspans at 265 ft. (80.8 m) each, and symmetricalend spans of 203 ft. 9 in. (62.1 m) for a totallength of 1997 ft. 6 in. (608.8 m). The precastsections are 37 ft. 6 in. (11.4 m) wide and 11 ft. 10in. (3.6 m) deep. Most sections were 14 ft. 2 in.(4.3 m) long and weighed about 90 tons (82 t).The top slab of the box is post-tensioned trans-versely to achieve a thickness of 10 in. (254 mm)at the centerline of the,section.

The geometry of the bridge included a varietyof circular, spiral, and parabolic curves as well astangent sections. In plan, the east end of the bridgehas two sharp horizontal curves connected to eachother and to the west end tangent by two spiralcurves. In elevation, the bridge is on a 2044 ft.(623 m) vertical curve with tangents of 5.5 and 6.0percent. There is approximately 28 ft. to 30 ft.(8.5 to 9.1 m) difference in elevation between theroadway surface at the abutments and at the centerof the bridge. Two sets of short line forms wereused to cast the segments to meet the exactinggeometry requirements. To attest to the accuracywith which the segments matched the plannedgeometry, two to four segments were erected eachworking day, and only nominal elevation adjust-ments were required in the abutting cantileverswhere the cast-in-place closures were completed atthe centers of the spans.

The bridge required 145 precast segments. Twosegments were constructed each working day, onein each short line form. The segments were castdirectly against the face of the matching segmentin the bridge which assured a perfect fit during

erection. Eight cast-in-place closure segments 4 ft.,(1.2 m) long were used at the center of the spansto join the abutting precast cantilever sections intoa fully continuous structure. Casting of the super-structure units began in mid March and was com-pleted by the end of August. Erection started thefirst of July and was completed at the end of Octo-ber, 1972. Grouting of tendons and placement ofcurbs, sidewalks and guardrails required about 1%months following erection of the last segment.

Fig. 1.10 - Bear River Bridge, Nova Scotia

1.6.3 J F K Memorial Causeway,Corpus Christi, Texas

The JFK Memorial Causeway is shown shortlyafter it was opened to traffic in the summer of1973 in Fig. 1.5. The precast segmental box girderportion of the bridge, the first of its kind in theUnited States, is shown in Fig. 1.11 as it appearedin late February, 1973. Erection of the 100 ft.(30.5 m) end span and 100 ft. cantilever are com-plete on one side and about one third complete onthe other side.

Precast segmental construction was selected forthe JFK Memorial Causeway following a compre-hensive model test program at the University ofTexas at Austin. Fig. 1.12 shows a general view ofthe model bridge during testing. Results and con-clusions from this test program indicated that thistype of construction is safe and dependable.” ) *Specific conclusions resulting from the tests are asfollows:

1. The segmental bridge model safely carriedthe ultimate design loads for all critical momentand shear loading configurations on which itsdesign had been based, as specified by the 1969Bureau of Public Roads Ultimate Strength DesignCriteria.

*Numbers in parenthesis refer to references listed in Appendix

Section A.4.

Fig. 1 .I 1 - Corpus Christi Bridge, Texas

Fig. 1.12 - Corpus Christi Bridge model test

2. The deflection under design live load in fourlanes (only three lanes required by live loadreduction factors) was approximately L/3200 inthe main span. This is much less than L/800 whichis generally considered as acceptable.

3. Positive tendons in the main span weredesigned as for an ideal three-span continuousbeam. Since the completed bridge was supportedon neoprene pads which have no vertical restraintagainst uplift, the outer ends were able to rise offtheir supports at loads greater than the design ulti-mate load, so that the structure did not act contin-uously at the ultimate conditions under main spanpositive moment loading. Even so, there was suffi-cient reserve strength in the main span to carrydesign ultimate load.

4. Under tests to failure with very highcombined moment and shear loading, flexuralcracks appeared near the epoxy joints in the topslab near the main pier. However, they joined thediagonal tension cracks and did not extend alongthe joints. There was no sign of any direct shearfailure at the joints. In tests of the full bridgemodel, approximately 75 percent of the theoreticalultimate shear load was applied in the maximumshear loading test prior to failure of the bridgeduring that test by flexure. No sign of shear dis-tress was evident. Subsequent tests of a three-segment model under severe shear loading as acantilever section indicated that full shear strengthof the unit was developed. Hence, the epoxy jointtechnique used did not reduce the design shearstrength.

5. During erection of the first few segments,tensile stresses occurred in the bottom slab as pre-dicted in the design. These stresses resulted fromthe large amount of prestress in the top slab at thisstage of erection. Temporary prestress devicessuccessfully controlled the effects of these stresses.

6. Theoretical calculation of the load factor forlive and impact loads required to form the firstplastic hinge agreed very well tiith the experimentalresults. These tests proved the accuracy and appli-cability of the ultimate load calculation procedure.

7. Near failure, major cracks concentrated nearthe epoxy joints which had no continuous conven-tional reinforcement. However, throughout theloading sequence, cracks were generally well dis-tributed because of the effective grouting and thestrength of the epoxy joints.

8. Transverse moment capacity of the bridgecross section was very adequate, as shown by thepunching shear load test results.

9. There was no adverse effect of the epoxyjoints on the slab punching shear strengths.

10. Bolts used for the temporary connection ofthe pier segments to the main piers yielded locallyunder the most critical unbalanced loading,although the calculated direct tensile stress was lessthan the actual yield strength. The bolts used inthe model were also below the yield strength laterspecified for the bolts in the prototype. Yieldingwas apparently caused by the large gap betweenthe pier segments and the pier, with consequentlocal bending, and was accentuated by the stressconcentrations in the threads.

11. The theoretical calculations were generally ingood agreement with the experimental results al-though there were some appreciable deviationsbetween the experimental and theoretical values ofstrain in the top slab in some stages of cantileverconstruction.

1.6.4 Muscatatuck River Bridge,North Vernon, Indiana

The second application of precast segmentalconstruction in the U.S. was the widening of a 45year old open-spandrel arch bridge on U.S. 50 overthe Vernon Fork of the Muscatatuck River inJennings County, Indiana. The 22 ft. (6.7 m)wide precast segmental box sections were erectedjust 1 ft. (0.3 m) away from the deck of theexisting arch bridge. The two decks are joinedby a longitudinal neoprene joint to provide a new44 ft. (13.4 m) wide driving surface. A view of theMuscatatuck River Bridge is presented in Fig. 1.13.Complete design calculations for the MuscatatuckRiver Bridge are presented in Chapter 5.

1.6.5 Vail Pass Bridges, Colorado

Construction was completed on a series of fourprecast segmental bridges on Interstate 70 west ofDenver over Vail Pass in 1976. The lengths of thebridges ranged from 390 to 830 ft. (119 to 253 m),and the main span lengths were either 200 ft.(61 m) or 210 ft (66 m). A single-cell box girdersection was used for the 42 ft. (12.8 m) wide seg-ments. A construction view of one of the Vail PassBridges is presented in Fig. 1.14. Alignment prob-lems were encountered at the closure of the firstVail Pass Bridge which required removal of aportion of the precast parapet, and use of anasphaltic wearing surface of varying thickness(maximum thickness of the asphaltic surfacing wasabout 11 in. (279 mm) at one point along onegutter line). The cause of the misalignment has notbeen specifically determined at this time.

Three later segments of l-70 over Vail Pass in-

eluded alternates for bridges with structural steel,precast segmental or cast-in-place segmental super-structures. In two of these cases, structural steelbridges were low, and in the third case, the low bidwas for cast-in-place segmental construction.

recreational purposes, the State of Illinois assumedspecial obligations for preservation of adjacentlandscape. A number of types of bridges wereevaluated by the State of Illinois Department ofTransportation. These included an orthotropicsteel box girder, a tied arch, and a segmental con-crete box girder. After an elaborate cost study, itwas determined that segmental concrete construc-tion offered not only an economical solution,but also it would most nearly fulfill environmentaland esthetic considerations.

Fig. 1.13 - Muscatatuck River Bridge, North Vernon,Indiana

Fig. 1.15 - Kishwaukee River Bridge, Illinois

1.6.7 Sugar Creek Bridge,Parke County, Indiana

The Sugar Creek Bridge in Parke County,Indiana, was completed in 1977. This three-spanbridge has end spans of 90 ft. (27 m), a centralspan of 180 ft. (55 m), and utilizes a single-cellbox section 30 ft. (9.1 m) wide.

Fig. 1.14 - Vail Pass Bridge, Colorado

1.6.6 Kishwaukee River Bridge,Winnebago County, Illinois

A model of the Kishwaukee River Bridge isshown in Fig. 1.15. The twin structures have endspans of 170 ft. (52 m) and three interior spans of250 ft. (76 m) each. The total length of each struc-ture will be about 1,170 ft. (360 m). The bridgewill span a wooded river gorge about 100 ft. (30m) above the normal water level in the river. Bidswere received by the Illinois Department of Trans-portation on the Kishwaukee River Bridge onSeptember 2, 1976. The construction special pro-visions permitted submission of alternate designproposals for the crossing, but the low bid wassubmitted for precast segmental construction.

The bridge is in an environmentally sensitivearea. Since the Kishwaukee River is used for

1.6.8 Turkey Run Bridge,Parke County, Indiana

Also completed in 1977, the Turkey Run Bridgein Parke County, Indiana, has two 180 ft. (55 m)spans, and utilizes two parallel boxes, each 22 ft.(6.7 m) wide. This bridge was constructed with theaid of temporary erection bents to reduce therequired depth of the box section.

1.6.9 Pennsylvania State University Test TrackBridge

A curved [radius of curvature 546 ft. (166 m)]precast segmental box girder bridge with a singlespan of 121 ft. (37 m) is now under test at thePennsylvania State University Pavement DurabilityTrack. The segments of this bridge were assembledon the ground adjacent to the bridge site, and the

entire superstructure was erected in one piece bycranes. Among the objectives of this researchproject, sponsored by the Pennsylvania Depart-ment of Transportation and the Federal Highway

Administration, was the evaluation of details forprecast segmental bridges, and investigation of theapplicability of precast segmental construction foruse as site-assembled grade separation bridges. Suchbridges might be used in situations where transportlength or haul weight restrictions do not permit theuse of precast l-girders.

1.6.10 Other Precast Segmental Bridges inPlanning, Design and Construction

The structures completed or under contractlisted above represent only the beginning of theapplications of precast segmental bridge construc-tion in North America. Additional structuresknown to be in various stages of planning, designand construction are listed in Table 1.1. Segmentcross sections for precast segmental bridges com-pleted to date, and for many of the bridges listedin Table 1.1 are presented in Appendix SectionA.2.

TABLE 1.1 PRECAST SEGMENTAL BRIDGES IN DESIGN AND CONSTRUCTION - 1978

Name Location Total

Fredericton Bridge

Kishwaukee River

Illinois River

lslington Ave. Extension

Fredericton,

New Brunswick

Highway 412Winnebago County,

Illinois

Highway 408between Pike & Scott

Counties, Illinois

Toronto, Ontario 600

St. Joseph River Benton Harbor, Michigan 4 0 8 98. 212,98

l-205 Columbia River Bridge Oregon - Washington 10,000 620 max.

Pike County

Cline Avenue

Kentucky

East Chicago,

Lake County, Indiana

Frankfort, Kentucky

Key West, Florida

372 93.5, 185, 93.5

6000 300 max.

Kentucky River

Long Key

780 323

12,144 118

1 ft. = 0.3048 m

-T

2540

1090

3300

394 max.

170,3@250,

170

390,550,3909@ 230

.ength, ft.Individual spans

TBox Girder Width

3 boxeseach box 27’ wide

2 boxes

each box 42’ wide2 - 2-lane roadways

2 boxes

each box 42’ wide2 - 2-lane roadways

2 boxes

each box 46’ wide

1 box 48’-6% wide

multiple boxes

143’total width

1 box 28’ wide

multiple boxes110’ total width

82’ total width

1 box 40’ wide

1 1

CHAPTER 2

CONSIDERATIONS FOR SEGMENT DESIGN

I’s”, and segmentlength “L”. These dimensions are shown for a typ-ical segment in Fig. 2.1.

In the most simple case, the segment width “W”is selected as equal to the width of the bridge.When the bridge width exceeds about 40 ft. (12m), or when it is necessary to minimize segmentweight or size, the structure width can be dividedinto a multiple of the segment width as shown inFig. 2.2. In this case, the transverse connection ofthe top slabs may be accomplished by transversepost-tensioning which extends through all theboxes and the cast-in-place joint(s).

As an alternative to use of multiple boxes forstructures wider than about 40 ft. (12 m), singleboxes with multiple webs have been used forwidths up to about 70 ft. (21, m). For intermediatewidths, single box sections may be used with inte-gral transverse floor beams under the roadwayslab (e.g., St-Andre de Cubzac Viaducts) or boxedcantilevers (e.g., Chillon Viaduct). These alterna-tives are illustrated in Fig. 2.3, which in addition,shows the evolution of segment size and weightfor a number of European bridges.

The construction depth “D” is determined bythe spans. Most European bridges have been builtwith span/depth ratios of 18 to 20. However, ratiosof 20 to 30 are considered feasible and structurallysatisfactory. Deflection tests on the model of theCorpus Christi Bridge with a span/depth ratio of25 resulted in a deflection of only L/3200 which is

Fig. 2.1 - Segment dimensions

w w1 I 1 Iio-i -.o-

/ CAST-IN-PLACE JOINT

Fig. 2.2 - Superstructure with parallel segments and

cast-in-place joint

only 25 percent of the deflection permitted insteel structures in the U.S. Span/depth ratios forend spans are usually somewhat lower than for in-terior spans. The shallower depth structures requiremore high strength post-tensioning materials. Var-iable depth structures become appropriate forspans in excess of 250 to 300 ft. (75 to 90 m). Inthis case, the span/depth ratios have normally beenselected as 18 to 20 at support and 40 to 50 atmidspan.

When webs are vertical, the bottom slab width“B” follows from the width “W” and the struc-turally acceptable length of the cantilever as dis-cussed below. Sloping webs present no problemwhen the box girder depth is constant, but dorequire significant form adjustments for produc-tion of variable depth segments due to the varia-tion in bottom slab width. A narrow bottom slabis desirable to reduce segment weight since thebottom slab area is usually a factor for structuralconsideration only in the negative moment areaadjacent to piers.

The segment length “L” has a pronounced effecton the economy of a bridge. The selection of thesegment length determines the total number ofsegments that must be produced and erected. Sincethe majority of the cost involved in production anderection is fixed per unit and only a small share ofthe cost is variable, economy is achieved by usingthe smallest number of segments consistent withtransportation requirements and the capacity of

.

2.1 General

Much of the economy of precast segmentalbridges results from the standardization and indus-trialization of the process of manufacturing thesegments. When design details permit repetition ofdaily actions, one segment per day can be manufac-tured from each form by a comparatively smallcrew. To achieve this rate of production, it is im-portant to avoid changes in the forms, to standard-ize the cage of mild steel reinforcement, and to usea repetitive layout of the post-tensioning tendons.It is always necessary to thicken the bottom slab ofthe segments near the pier. However, even thisminor variation in the details of the segments maydisturb somewhat the normal schedule of segmentproduction.

2.2 Principal Dimensions of Segments

The principal segment dimensions are top slabwidth “W”, construction depth “D”, width ofbottom slab “B”, web spacing

BRIDGE CROSS SECTIONAND MAX. SPAN (DIMENSIONS IN METERS)

CHOISY-LE-ROI

55M180 FT.

SEUDRE7 9 M

259 FT.

BLOIS91M

299 FT.

CHILLON104M

341 FT.

SAINT ANDREDE CUBZAC

9 5 M312 FT.

B3 SOUTH5 0 M

164 FT.

SEGMENTLENGTH

2.50M8.20 FT.

3.30M10.80 FT.

3.50M11.50 FT.

3.20M10.50 FT.

3.40M11.20 FT.

MAXIMUMSEGMENT WT.

(TONNES)

2 5

7 5

7 5

8 0

8 0

2.50M-3.40M 5 08.20 FT.-l 1.20 FT.

I

SAINT-CLOUD106M

348 FT. 1

41 0e 2.25M 130n’ 7.40 FT.

+ 1 t

Fig. 2.3 - Segment details of various European bridgest7)

1 4

erection equipment. Since the cost of handling anderection increases with “L”, it is necessary to makea study of the total in-place economy of varioussegment lengths to determine the most economicalvalue. When segments must be transported overhighways, the weight and size limitations usuallydetermine the value of “L”.

The spacing of webs “s” is normally determinedpurely on structural criteria. In principle, any webspacing can be utilized if all pertinent structuralaspects are thoroughly investigated using, if necess-

ary, m o r e sophisticated structural analysistechniques. The need for such analysis is greatlyreduced when the web spacing is selected in such away that the ordinary beam theory can be appliedfor longitudinal moments. The beam theory maybe used when the depth of the section is equal toor greater than l/30 of the span, and when thewidth “W” divided by the number of webs is notmore than 7% percent of the span length. For sec-tions such as shown in Figs. 2.1 and 2.2 the slabcantilever “C” is about one-fourth “WI’. For boxsections with more than two webs the slab canti-lever dimension should be selected to provide rea-sonable balance between cantilever and interiortransverse moments. Use of these criteria for deter-mining the number and spacing of webs also resultsin reasonable requirements for the depth of the topslab and the amount of transverse top slab rein-forcement.

Segment dimensions used on U.S. and Canadianprecast segmental bridges now completed or inadvanced stages of design are presented in Appen-dix Section A.2.

2.3 Detail Dimensions of Segments

The concrete dimensions of top slab, webs, bot-tom slab and haunches are determined by structur-al considerations and by numerous practical factorsrelated to production of the segments.

The top slab thickness (“a” in Fig. 2.1) usuallyranges from 7 to 10 in. (175 to 250 mm). It isnecessary to consider the following structuralfactors in selecting the top slab thickness:

1. Bending moments in the transverse directioncaused by slab dead load, permanent loadsand live load.

2. Compression zone requirements for longitu-dinal bending moments normally need be con-sidered in determining top slab thickness onlyin structures with spans of 350 ft. (110 m)or more.

3. Local bending stresses due to wheel loadsapplied directly over epoxy joints.

4. Local anchorage bearing and splitt ing stressesfor transverse post-tensioning (when used)require a minimum thickness of about 8% in.(216 mm) for tendon forces ranging from 100to 120 kips (445 to 534 kN).

In addition to the above structural considera-tions, the top slab thickness must be adequate toaccommodate four layers of transverse and longitu-dinal mild steel reinforcement, transverse andlongitudinal tendons, and minimum concrete coverof 2 in. (51 mm) on top and 1 in. (25 mm) on thebottom.

The dimensions of haunches “b”, “c” and “d”in Fig. 2.1 are determined by the transverse bend-ing moments and by the space required for theanchorages of the longitudinal post-tensioningtendons (see Figs. 2.10 and 2.12). It is normallynecessary to accommodate at least two layers oflongitudinal tendons. A concrete depth of 14 in.(356 mm) is required at anchorages of longitudi-nal strand tendons. A depth of 10 in. (254 mm)may suffice for bar tendons. Although it isessential to provide adequate space in the top slaband haunch thicknesses for the above considera-tions, it should also be kept in mind that the topslab is the heaviest part of the box girder, and fromthis standpoint it is desirable to keep those dimen-sions as small as practical.

The web thickness “e” is generally 14 in. (356mm) or more to provide room for the anchoragehardware of 12-strand tendons which are a fre-quently used tendon size. Minimum anchorage spacerequirements for bar tendons is about 10 in. (254mm). The 14 in. (356 mm) width may also be de-sirable or necessary to accommodate the burstingand splitting force from anchorages for 12.strandtendons. This thickness may be reduced when ten-dons are anchored in ribs or anchor blocks. Thick-nesses as small as 8 in. (203 mm) have been usedwith strand tendons when webs were vertically pre-stressed. When shear forces near supports are re-duced by upward shear from the post-tensioningtendons and segment depth is within the limitsdescribed in Section 2.2., the shear stress require-ments for highway bridges are generally met whenthe total width of webs amounts to 7 or 8 percentof the bridge width. The principal tensile stressesresulting from combination of vertical shear stressesand compressive stresses reach a maximum value atthe intersection of the top slab and the web. Effortsshould be made to keep these principal stresseswithin allowable limits [see AASHTO BridgeSpecifications,@’ @@ion 1.6.6. (B)] , and to avoid

the use of additional reinforcement for thispurpose. This requires the widening of the webs“f” as shown in Fig. 2.1.

The web is a stiff element in the box section andprovides substantial moment restraint to the topslab, and consequently transverse moments at thejunction of the web and top slab are high. In-creased concrete thickness, obtained by wideningto the web “f” as shown in Fig. 2.1, reduces theamount of reinforcement required. Particularattention should be given to lapping of reinforce-ment in this area to avoid discontinuity in areas ofhigh moment.

A different situation exists in positive and nega-tive moment areas relative to the required bottomslab thickness “g”. The structural significance ofthe bottom slab in the positive moment area re-lates only to the bottom slab contribution to thesection properties. As a result, the bottom slabthickness is usually reduced in positive momentareas to the minimum required to carry the slabdead load, and the space required for reinforce-ment and concrete cover. Space for one layer oftendons, mild steel reinforcement, and concretecover require a minimum bottom slab thickness ofabout 7 in. (178 mm). In the negative momentarea, the bottom slab thickness is controlled byhigh compressive stresses. Thickening of the bot-tom slab near piers is nearly always required tokeep the compressive stresses within the allowable

F = total compressiveforce in half ofbottom slab ofsingle box girder atSection 1.

F + AF = correspondingcompressive force atSection 2.

PLAN AF = shear force at theconnection of weband bottom slab.

BOTTOM SLAB

SECTION

Fig 2.4 - Longitudinal shear transfer by bottom slab to

web haunches

limits. The bottom slab thickening for this purposeshould be reduced to the minimum thickness re-quired in the shortest distance possible to facili-tate manufacturing of the segments.

The dimensions of the bottom slab haunches(“h” and “i” in Fig. 2.1) have a major structuraltask in the longitudinal negative moment area oftransferring the change of force in the bottom slabto the webs. This function is illustrated in Fig. 2.4.The force differential AF is transferred by longitu-dinal shear, and is the highest in the negativemoment area. The bottom slab haunches also assistin transmitting transverse bending momentsbetween the bottom slab and the webs, and reducethe amount of reinforcement required for thispurpose.

2.4 Pier and Abutment Segments

Pier and abutment superstructure segmentsdiffer from typical interior superstructure segmentsin that they normally require a diaphragm to assistthe webs in distributing the high shear forces tothe bearings. As illustrated in Fig. 2.5, vertical andtransverse post-tensioning can be used to transferthe shear from the webs through the diaphragm tothe bearings. The amount of post-tensioningutilized for this purpose is a function of the shearforces in the webs. In addition to the post-tension-ing tendons, the pier and abutment segment dia-phragms are normally heavily reinforced with non-prestressed reinforcement. The tendons extendingacross the diaphragm in Fig. 2.5 must be tied intothe diaphragm with bonded reinforcement to resisttendon splitting stresses at the corners of the open-ings. Precise analysis of diaphragm stresses requiresuse of finite element or other similar analyticaltechniques. However, an approximate analysisbased on force resolution is usually sufficient. Asshown in Fig. 2.5, it is essential that an opening bemaintained in both pier and abutment segmentdiaphragms sufficiently large to permit movementof men and equipment.

MILD STEEL RElNFORCEMENT OF & ~ TRANSVERSEDlAPHRAGM NOT SHOWN POST-TENSIONING

-DIAPHRAGM

SECTION AT PIER

Fig. 2.5 - Pier and abutment segments

16

Fig. 2.6 - Use of scaffold for stressing of tendons

erection. The anchorages for permanent longi-tudinal tendons to be stressed during erection maybe located either in the webs at the face of thesegment, or in special web stiffeners cast into thesegment for the purpose of providing a locationfor anchorage of permanent and temporary ten-dons that does not interfere with the erectionprocess. Fig. 2.6 shows stressing of tendons withanchorages located in the web faces. Fig. 2.7shows details of a segment with an interior stif-fening rib which provides a location for installa-tion, stressing and anchorage of longitudinal ten-

LONGITUDINAL SECTION A- A

(I) J O I N T

(2) WEB KEY

(3) SLAB KEY FOR ALIGNMENT

(4) POSSIBLE WEB STIFFENER FORTENDON ANCHORAGE

(5) HOLES OR INSERTS FOR HANDLINGAND PROVISIONAL ASSEMBLY

(6) LONGITUDINAL DUCTS FORPRESTRESSING TENDONS

dons with little interference with the erectionprocess. When tendons are anchored at the face ofa segment, a scaffold is normally used as shown inFig. 2.6 to facilitate installation and stressing oftendons. With interior ribs, or web stiffeners,these operations are accomplished from inside thebox. However, segments with interior ribs aremore difficult to manufacture, and selection ofsegment details in a particular case requires con-sideration of all aspects of manufacture, erec-tion, and installation, stressing and grouting ofthe tendons.

Continuity tendons are normally placed andstressed after the erection process and after theclosing of the castlin-place joints. Details for an-chorage of continuity tendons in the top slab overthe webs are presented in Fig. 2.8. This anchoragedetail has the disadvantage of allowing dirt, waterand extraneous material to enter the tendon ducts.This may cause blockages and other problems.Details for anchorage of continuity tendons inthe bottom slab are shown in Fig. 2.9. Continuitytendons may also be anchored in web stiffeners asillustrated in Fig. 2.7. The stressing pockets foranchors in the top slab should be kept as smallas possible to minimize conflicts with mild steelreinforcement or transverse post-tensioning ten-

TRANSVERSE SECTION B-B

Fig. 2.7 - Details of segment with web stiffener(‘) HORIZONTAL SECTION C-C

- A N C H O R A G E

-Spiral roinforcemont when required..~ . .by porr-r.n.,onrnB.

NOTE: Block-out dimensionsreinforcement dotoilswith the port-tanrionisystem used.

SECTION A-A

Fig. 2.8 - Top slab anchorage block-out

L- /SECTION B-B

NOTE: Specific reinforcement details and dimensionsof concrete bui ld-out vary with dif ferentpost-tensioning systems

a 4 - ##6 Hairpins ILength 2’-6” (0.8 m) - Typical for 12.strand tendon. Reinforcement requirement for other tendon sizes will vary.

SECTION#4 = 13 mm dia.#6 = 19 mm dia.

4'.4" (VARIES)

(1.3 m)

----a----

m-B-----a

----aB--e

PLAN- 2 - #4 Hairpins @ 5 in. (127 mm) ctrs.

(approx. HS show)

Fig. 2.9 - Bottom slab anchorage build-out

dons. For larger strand tendons, used for longitudi-nal post-tensioning, mild steel reinforcement isnormally required to assist in distribution of theprestressing force into the segment. Anchorage andtendon coupler blockout details to be used withbar tendons on the Kishwaukee River Bridge inIllinois are shown in Fig. 2.10.

Vertical post-tensioning is occasionally used toaccommodate high shear stresses, and for connec-tion of the superstructure to piers or abutmentsso that moments can be transmitted. Connectionsbetween the superstructure and the substructureare made by vertical tendons which pass throughthe pier segments and are anchored in the pier. Insome cases, coupling of the vertical tendons isnecessary, particularly when access to the anchor-ages at the surface of the piers is difficult. Mosttendons used to connect the superstructure to thesubstructure are relatively short, so it becomesimportant that allowance be made for the anchorseating loss. Vertical post-tensioning in webs, some-times called “prestressed stirrups”, may be used tohelp offset high principal stresses(3).

The stress in short vertical tendons may be sig-nificantly affected by anchorage seating losses.Lift-off tests are recommended to ensure that thecorrect stress has been applied to prestressed stir-rups. The maximum ultimate strength of theseindividual tendons has to be limited to about 200kips (890 kN) in order that they can be incorpor-ated within the normal web thickness. These ten-dons normally have an active stressing anchor and ablind or passive dead-end anchor which is em-bedded in the concrete. It is strongly recom-mended that web tendons be installed vertically toavoid passing through the joints.

Except for smaller segments, transverse post-tensioning of top slabs is recommended to mini-mize the top slab thickness and to provide assur-ance against the development of longitudinalcracking in the top slab. The transverse tendons inbridges only one segment wide can be stressed atany time after the segments have been removedfrom the forms.

Transverse post-tensioning may also be used toconnect the top slabs of superstructures containingmore than one segment in the transverse direction,as illustrated by Fig. 2.2. These tendons runthrough the longitudinal cast-in-place joint be-tween the segments. Placing, stressing and groutingof these tendons is done after erection and obvi-ously requires careful control of the deflectionsof adjacent catilevers. To facilitate placing the ten-dons, the width of the longitudinal joint must notbe less than 2 ft. (0.6 m). Narrower joints are

20

feasible provided adequate measures are taken toovercome non-alignment of ducts at the jointcaused by casting tolerances. Transverse tendonsmay be installed in flat bundles of three or fourstrands to maximize the tendon eccentricity.

In segments at and adjacent to piers, there are alarge number of longitudinal and transverse ten-dons, and careful detailing and placement are re-quired to assure that sufficient space is providedfor proper placement and vibration of the con-crete. For this reason, it is usually recommendedthat the transverse tendons be placed on top ofthe longitudinal tendons (also see discussion inSection 3.5.2 relative to bar tendon details usedfor Kishwaukee River Bridge).

2.5.3 Temporary Post-Tensioning

Most segmental structures with epoxy jointsare erected as cantilevers. Permanent cantileverpost-tensioning is applied after a segment has beenerected at each end of the cantilever. As a result,during the placing of the first segment at one end,the element has to be attached to the cantileverby means of temporary post-tensioning. The tem-porary post-tensioning also provides compressionof not less than 50 psi (0.35 MPa) in the joints tobe sure that the joints are properly closed and thatthe excess epoxy is squeezed out. It is recom-mended that uniformly distributed compressivestress be applied across the joints to avoid smalldifferences in the thickness of the epoxy jointwhich could affect the structure geometry. Thetemporary post-tensioning usually consists of barsbecause of the short length of the tendons (abouttwo times the length of the segments). In the bartendon details used for the Kishwaukee RiverBridge (Fig. 2.101, the permanent longitudinalpost-tensioning also serves to provide the tem-porary compression during erection. This facili-tated the construction process through elimina-tion of temporary stressing operations.

Temporary tendons, when required, may be lo-cated inside or outside the segments. It is oftensimplest to place the bars in the top and bottomslabs of the segments. The anchors may be placedin recesses at the joints. Alternatively, the connec-tion may be made by use of temporary steelattachments such as illustrated in Fig. 2.11. Be-cause the temporary bars are reused it is recom-mended that prestressing force be limited to about55 percent of the ultimate strength of the bars.The holes and the recesses for temporary tendonsand anchorages should be grouted after the perma-nent post-tensioning has been stressed.

PLAN Blockout to be filled Iwith mnrrrt+-_. . . . --. .-.-..

Bloc Lout ‘h”eopeng ;,;c,A’,” errin 9of

I rfor g r o u t i n g \-“-“” ,1 Cut Bar.raftar rtressing

__j /-as requared to fit blockout.

. :. .. -.

Sepment Jt. /

DEAD END DETAIL STRESSING END DETAIL

Segment Jt./

SECTION A-ABlockout in Blockout to be filled

with concrete l ftorstressing of tendon

Ie Tendon Lfo? Longit: duct

SECTION B-BSECTION B-B

Fig. 2.10 - Stressing and coupler blockout details - Kishwaukee River Bridge

Fig. 2.11 - Temporary steel fittings attached to deck foranchoring temporary prestressing bars

In place of permanent vertical post-tensioningbetween pier segments and piers, post-tensioningmay be employed temporarily to provide a mo-ment connection during cantilever erection only.After erection has been completed and the con-tinuity tendons have been placed and stressed,the temporary vertical post-tensioning at piers maybe removed. This permits use of sliding bearingsat piers in the finished structure to accommodatevolume changes due to temperature, shrinkage, andcreep.

2.5.4 Layout of Post-Tensioning Tendons

Unlike design of conventionally reinforced con-crete structural elements where a quantity of rein-forcement may be the final result of design calcu-lations, a practical tendon layout always requiresan iterative design process in which the designerand the detailer continuously exchange informa-tion. In the preliminary design stage, concretesections are assumed and bending moments andshear forces are calculated. Subsequently, an ini-tial number and eccentricity of tendons required tocounteract the bending stresses is determined alongwith the number and slope of tendons counter-acting shear forces. The preliminary design is com-pleted by determination of the required mildsteel reinforcement. The preliminary design re-sults must then be evaluated by the detailer on thedrawing board to see whether or not the prelimi-nary design assumptions can be achieved in prac-tice. This is usually not the case on the first try,and further iterations are then made. Detailing ofpost-tensioning tendons requires consideration ofminimum radius of curvature, spacing require-ments and avoidance of conflicts with mild steelreinforcement. Further, because of formworklimitations, tendons are always located and

anchored at the same location at the segmentjoints. In developing the tendon layout to complywith the above requirements, the number of ten-dons required is the design consideration of mostImportance.

Some practical suggestions relative to locationand detailing of tendon layouts aoae as follows:

1. Tendon spacing must be sufficient to permitplacement and vibration of concrete withoutdevelopment of voids or honeycomb. A cleardistance of 1% in. (38 mm) is required be-tween tendons during grouting to minimizethe possibility of grout transmission betweenadjacent ducts at the joints between seg-ments. A typical layout of ducts meetingthose requirements is presented in Fig. 2.12.

2. The bending radius of the tendons is deter-mined largely by the duct material. A semi-rigid duct of corrugated metal is preferable,and the minimum bending radius of such ductsis about 15 ft. (4.6 m). Pre-bending requiresan additional operation and complicatesplacement of the ducts. Sharp bends are un-desirable from the standpoint of installingtendons, friction losses, and the high concen-trated forces resulting on the concrete.

3. A free passage of 5 in. (127 mm) minimumwidth should be provided between tendonslocated over the segment webs for properplacement and vibration of concrete.

4. Crossing of longitudinal tendons in the nar-row part of the web should be avoided.

5. Tendon eccentricities should be made as largeas possible. Cantilever tendons can be spreadlaterally into the top slab and a second layerof tendons can be accommodated in the topslab haunches as shown in Fig. 2.12. Tendonsanchored in the first few segments remainwithin the web reinforcement because ofbending radius limitations. This results insome loss of eccentricity. Midspan conti-nuity tendons are placed in the bottom slab.

6. Cantilever strand tendons are anchored inthe webs and top slab haunches, or on webstiffeners. Cantilever bar tendons may beanchored in the slab as shown in Fig. 2.10.Shear tendons are anchored in webs. Con-tinuity tendons are anchored as described inSection 2.5.2. The anchorage of continuitytendons in the top slab combined with an-chorage of cantilever tendons in the websprovides a connection between the two

overlapping tendon systems through con-crete compression. In a layout where ten-dons are anchored in top and bottom slabs

Fig. 2.12 - Tendon spacing and 12-strand tendon anchor-

age details in top slab haunches

Fig. 2.13 - Tendon layout influence on the mode of sheartransfer between top and bottom slab tendons

only, the connection between tendon systemsis by shear in the webs. The shear transmis-sion was accommodated in the bar tendondetails used for the Kishwaukee River Bridgeby extending all longitudinal tendons one seg-ment length beyond the point required bydesign moments. The two means of providinga connection of the two tendon systems areillustrated in Fig. 2.13. Both systems havebeen used successfully, but the designershould keep in mind the difference by whichforces are transmitted between the two sys-tems of tendons.

7. The slope of continuity tendon anchorageswith respect to the top slab should be about25 degrees as shown in Fig. 2.8. This shortensthe block-out to acceptable limits (the block-outs interrupt the transverse reinforcement)and also reduces the tendency of the anchorto break out vertically. The 25 degree slope isalso appropriate for cantilever tendons an-chored in webs. The vertical component ofthe tendon is then about 40 percent of thetendon force. This provides a substantial re-duction in the shear forces in the webs above

the tendon anchors which may become animportant factor near the supports. Pre-stressed stirrups may also be used to accom-modate shear forces near supports.

8. Tendon lengths should be made as short aspossible. However, use of very short tendonsrequires careful consideration of diffusionof the prestress into the section and the pre-stress losses due to seating of the anchorage.From the structural viewpoint, the tendonlayout may be in accordance with the bend-ing moment diagram. However, the erectionprocedure and the available anchorage loca-tions usually require substantial adjustmentsto the tendon layout resulting solely fromstructural moment requirements.

2.6 Mild Reinforcement Cage

The amount of longitudinal and transverse rein-forcement required is determined by the designcalculations or from the nominal minimum amountsrequired to provide toughness during curing, hand-ling and erection of the segments.

During production of the segments, the rein-forcement is assembled and wire tied outside theform to make a solid cage that can be lifted intothe form without damage. Spot welding of crossingbars in forming the reinforcement cage requirescontrol of the carbon content of the bars to as-sure weldability without producing brittleness.Spot welding of reinforcement should be permittedonly when authorized by the Engineer. Tendonducts frequently pass through layers of reinforce-ment. Details should be developed to accommo-date the tendon trajectory without cutting thereinforcement. Fig. 2.14 shows a possible solu-tion to the case where tendons are located in thetop slab and anchored in the web. The top slaband web haunches permit use of two types ofhairpin bars, a and b, which permit the tendonsto pass easily.

Fig. 2.14 - Reinforcement details to permit anchorage oftop slab tendons in web

Shear Keys

Shear keys in the webs serve the dual purpose oftransferring shear during erection and providing aguide to assure the correct vertical position of thesegment. Horizontal alignment is obtained by useof a guide in the top slab. The erection shear re-sults from the weight of one or more segments(depending on the erection speed) or the upwardforce resulting from inclined post-tensioning ten-dons. Stability during erection is obtained throughthe combined action of the shear keys and the tem-porary (or permanent) post-tensioning in the topand bottom slab. As indicated in Section 2.5.3,the temporary post-tensioning is proportioned toprovide a uniform compression of not less than50 psi (0.35 MPa) across the entire joint. Theforces R, acting on the shear key and the jointdue to segment weight and temporary post-tension-ing are illustrated in Fig. 2.15(a), and due tosegment weight and final cantilever post-tension-ing in Fig. 2.15(b). The use of single web shearkeys such as shown in Fig. 2.15 requires carefulattention to reinforcement details in the shearkeys and in the web area adjacent to the keys.

w = Segment weightF1 = Temporary prestress

in top slabFz = Temporary prestress

in bottom slab

RI = Force on jointR2 = Shear key force

Fig. 2.15 (a) - Forces on shear key due to temporary post-tensioning and segment weight

F = Force in permanentt e n d o n

Fi2 = Shear key forceRI = Force in joint

Fig. 2.15 (b) - Forces on web shear keys

b

~Fig. 2.16 - Reinforcement requirements near web shear

keys

In conjunction with the loading cases in Figs.2.15(a) and 2.15(b), reinforcement should beprovided in webs to contain potential crack devel-opment in both the upward and downward direc-tions as shown in Fig. 2.16.

Recent European bridges have utilized multipleshear keys in the webs such as shown in Fig. 2.17.The multiple key eliminates the need to reinforcethe shear key and the adjacent web area, and it hasthe further significant advantage of relieving theepoxy of any shear transmission function. Thelarge number of interlocking keys [(l) in Fig.2.171 in the webs carry all the shear across thejoint without any assistance from the epoxy.Note also the keys across the top slab [(2) in Fig.2.171 which assist in obtaining segment alignmentduring erection and which may also provide sheartransfer due to concentrated loads on the deck.The use of the multiple key web design in Fig.2.17 is associated with a web stiffener (3) whichcontains tendon duct and anchorages for perma-nent (4) and temporary post-tensioning (6). Thetop slab has vertical holes (5) adjacent to the stif-fener which permit an attachment for handlingthe segment. The use of multiple web keys requiresa substantial web area free of anchorage pockets,tendon holes, and other interruptions which would

(1) Castellated web key.(2) Slab key for alignment.(3) Web stiffener.(4) Tendon duct and anchorage for final assembly(5) Insert for handling and temporary assembly(6) Tendon ducts for temporary assembly

Fig. 2.17 - Precast segment with multiple keys and webstiffener(‘)

reduce the available shear area of the keys. Thisleads to use of web stiffener details such as shownin Fig. 2.7, which involve additional effort duringproduction of the segments.

2.8 Epoxy Joints

As indicated in Section 2.7, the function of theepoxy joint is, to an extent, dependent on thedesign of the shear keys. However, in all cases, theepoxy will serve the following purposes:

1. During placement of segments, the epoxyacts as a lubricant which, in conjunction withthe keys in the web and top slab, assists inguiding the segment into proper alignment.

2. The epoxy layer acts as a stress distributionmaterial during erection and during post-tensioning. This is illustrated by the fact thatthe thin layer of epoxy cannot be pressed outof the joint entirely. In addition, any smallcavities and pores in the faces of the seg-ments are f i l led.

3. Epoxy can restore the tensile and shearstrength of the concrete across the joint.

4. Epoxy is required to serve as a joint sealantto prevent water from entering into tendonducts, and also to prevent grout leaks atjoints.

Concern is occasionally expressed about the lackof reinforcement extending through joints of pre-cast segmental bridges. Actually, there is a greatdeal of grouted high strength post-tensioning rein-forcement continuous through all joints. This rein-forcement exerts a very large compressive forceacross the joint which ensures that the joint willbe under compression (or perhaps very low tensilestresses at the bottom slab) under service loads.The safety of the structure in both shear and flex-ure at ultimate load is, of course, determined onthe basis of a cracked section, and there is, in this

Fig. 2.18 - Application of epoxy resin by “gloved hand”

case, little difference between a precast structurewith joints and a monolithic cast-in-place structure.

Application of epoxy to the joint surfaces isaccomplished by hand immediately prior to ap-plication of the temporary post-tensioning, asillustrated in Fig. 2.18. Prior to application of theepoxy, the joint surfaces are either sand blasted orwire brushed to remove any surface laitance. Thisis usually done while the segments are stockpiledawaiting erection.

Recommended specifications and tests forepoxies to be used in joints of segmental bridgesare presented in the “Tentative Design and Con-struction Specifications for Precast SegmentalBox Girder Bridges” developed by the PrestressedConcrete Institute’s Bridge Committee. Thesespecifications are presented in Appendix SectionA. l .

CHAPTER 3

ANALYSIS OF PRECASTSEGMENTAL BOX GIRDER BRIDGES

3.1 General

The material presented in this chapter dealsprimarily with those aspects of precast segmentalbridge design that differ from or require more de-tailed consideration than conventional types ofcontinuous prestressed concrete structures. Back-ground information on the fundamentals of analy-sis of continuous prestressed concrete structuresmay be obtained from References 2, 4, 5 and 18,Appendix Section A.4.

In general, analysis and design of precast seg-mental box girder bridges should conform to thelatest edition of the Specifications for HighwayBridges published by the American Association ofState Highway and Transportation Officials’6’, orto other applicable specifications for railway orrapid transit structures. Additional specificationsdeveloped by the Prestressed Concrete Institute forconsideration by the American Association ofState Highway and Transportation Officials toprovide specific coverage of precast segmentalbridges are presented in Appendix Section A.1.

In order to provide background on those aspectsof precast segmental bridge design that may re-quire special consideration, the discussions in thefollowing sections on the influence of creep,shear lag, temperature effects, and transverseanalysis are presented in much more detail thanmay be necessary for routine designs. As suggestedby the specifications in Appendix A.l., elasticanalysis using beam theory may be used in thedesign of precast segmental bridges of normalproportions. Consideration is given to shear lag inthe immediate vicinity of the supports when seg-ments are wider and/or shallower than normal(see Section 2.2).

Notation is generally explained as it is used inthe text. In addition, notation is presented inAppendix Section A.3.

3.2 Development of Preliminary Bridge Details

As in any bridge design, it is necessary to assumecross section dimensions and span lengths of aprecast segmental bridge before an analysis can bemade. The selection of the superstructure crosssection, normal span/depth ratios, and otherpertinent aspects of superstructure design arediscussed in Chapter 2. The method of erection,as discussed in Section 4.3, also has an affect on

the superstructure and substructure design, andshould be considered in selecting preliminarybridge details.

Selection of the span arrangement and otherconsiderations preliminary to the analysis phaseare considered in the following sections.

3.2.1 Selection of Span Arrangement”’

In selecting the span arrangement for a precastsegmental bridge, it is necessary to consider themethod of construction. When cantilever con-struction is used, the segments are erected in bal-anced cantilever starting from a pier and placingsegments on either side in a symmetrical opera-tion. This method of erection results in typicalsuperstructure components consisting of one-half of the main span length cantilevered from thepiers as shown in Fig. 3.1 (a). If the end span isselected as 65 to 70 percent of the interior span asin Fig. 3.1 (a), the small section of the superstruc-ture adjacent to the abutment will require use offalsework or some other erection procedure.

To provide a transition between span lengths Lland L2, for example at the transition betweenapproaches and main spans in a viaduct, an inter-mediate span of average length will optimize theuse of the cantilever concept, as illustrated inFig. 3.1 (b).

(4

0.66-07OL I L 1 065-070L

I0.4

Fig. 3.1 - Span arrangements for precast segmentalbridges(‘)

27

+SDmmI

i I

sp~~~&~~~. 11

Fig. 3 .2 - Effect of hinge location on deflection

Continuous bridges over 2000 ft. (610 m)long have been built without permanent hingesor expansion joints in the superstructure. It is de-sirable to keep the number of joints to a minimumto reduce maintenance costs and improve ridingquality. This may be accomplished by use of pierswhich permit longitudinal volume changes of thesuperstructure (for example the Chillon Viaductshown in Fig. 4.18), or by the use of bearingdetails that will accommodate substantial move-ment. In very long structures, intermediate expan-sion joints become necessary. Location of thesejoints near the dead load contraflexure point, asshown in Fig. 3.1 (c), will be helpful in reducingdeflection of the joint. Fig. 3.2 shows a compari-son of deflections and angle changes due to liveload in a 259 ft. (79 m) span with hinges located atmid-span and near the point of contraflexure.

3.2.2 Abutment Detaild7’

When geometric restraints will not permit opti-mum pier locations or span arrangements, abut-ment details may be developed to facilitate theconstruction procedure. Fig. 3.3 (a) shows a decksection cantilevered over a front abutment wall toachieve a longer than normal end span. A conven-tional bearing is provided at the front abutmentwall in Fig. 3.3 (a) and a rear prestressed tie isused to counteract uplift and to permit cantileverconstruction to proceed out to the first jointJl where a connection is made with the cantileverconstruction starting from the first intermediatepier.

With end span length on the order of 65 to 70percent of the interior spans, a special segmentmay be used at the abutment and one or two seg-ments may be temporarily cantilevered out toreach .the first balanced cantilever as shown in Fig.3.3. (b).

When end spans are only 50 percent of thelength of interior spans, as in Fig. 3.3 (c), an up-lift reaction has to be transferred to the abutmentduring construction and in the completed struc-ture. Abutment details that may be used to accom-plish this are shown in Fig. 3.3 (d). Here, the websof the main box girder deck are cantilevered underthe expansion joint into slots in the main abut-ment wall. Neoprene bearings are placed above

WEB- PRESTRESSING TENDONS

LONGITUDINAL SECTION

(dl UPLIFT ANCHOR DETAILS

SECTION C-C

Fig. 3.3 - Alternatives for construction of end spans(‘)

28

the webs to transmit the uplift force and, at thesame time, to allow the deck to expand freely.

3.2.3 Pier Details

Pier details should be developed with consider-ation given to the need to provide stability to thecantilevers during construction. Some details thathave been used to accomplish this are discussedand illustrated in Section 4.3.6.

3.2.4 Horizontal and Vertical Curvature

As noted in Chapter 1 and elsewhere, precastsegmental construction is readily adapted to nearlyany horizontal and vertical alignment by adjusting

the segment dimensions during casting. The BearRiver Bridge, shown in Figs. 1.4 and 1 .lO, and theSaint-Cloud Viaduct in France, shown in Fig. 3.4,are examples of bridges on curved alignment.

3.2.5 Bearing Details

Most European bridges have utilized laminatedneoprene bearings. However, the European specifi-cations for design of neoprene bearings are con-siderably less restrictive than U.S. specifications.

To accommodate large movements and heavyloads, the use of more expensive pot type bearingsusing neoprene to absorb rotation and a teflonlayer to permit volume changes may be appro-priate. Design information on these bearings isavailable from suppliers.

Heavy pier reactions during erection, or tem-porary prestressing of the pier segment to the pier,may require use of temporary bearing pads of steelor concrete. Details of this type are shown in Sec-tion 4.3.6 (see Figs. 4.20 and 4.21). The use offour bearings at piers as shown in Fig. 4.21 sub-stantially reduces the positive longitudinal liveload moments in the superstructure, as illustratedin Fig. 3.5.

3.3 Longitudinal Analysis

3.3.1 Erection Moments

During erection, the moments over the piersincrease with the addition of each pair of segments,as illustrated in Fig. 3.6. The additional momentcaused by adding segments No. 8 at each end ofthe cantilever is shown by the shaded area in Fig.3.6. These moments are resisted by post-tension-ing tendons in the top slab which may be anchoredat the face of the segments or in build-outs inside

Fig. 3.4 - Saint-Cloud Bridge, Paris, France(‘)

LIVE LOAD = 4K/ft (58.4 kN/m)

260’ 260’ 2 6 0I

MOMENTS IN FT KIPS x lo31 ft. kip = 1.356 kN-m

D O U B L E S U P P O R T S S I M P L E S U P P O R T S

Fig. 3.5 - Comparison of superstructure live load moments with simple and double pier supports(“)

the box section. The use of build-outs makes it cast segmental bridges during erection are modi-possible to place the segments and stress the ten- fied by thechange in statical system due to couplingdons in two separate operations, but tends to com- cantilevers and the post-tensioning used to connectplicate the process of manufacturing the segments. the cantilevers into a continuous structure. Subse-The amount of post-tensioning required to main- quent to casting the closure joint and stressingtain zero tensile stress in the top slab under the of the continuity tendons, the influence of con-erection moments (including weight of any erec- crete creep modifies both the cantilever and con-tion equipment) is readily calculated from the tinuity moments as will be illustrated in the fol-simple formula: lowing sections.

ME p We)-=-+-Zt A Zt

where M, = erection moment, in. lb.Z, = section modulus with respect to

top fibers, in.3P = post-tensioning force, lb.A = cross sectional area of pier seg-

ment, ins2e = eccentricity of post-tensioning

force, in.

The concrete area in the bottom slab at the piermust be sufficient to maintain compressive stressesto the value allowed by the specifications. Thestress f,, is calculated as:

f,, = !$+;-F’b

where z,-, = section modulus with respect to bot-tom fibers, in.3

3.2.2 Creep Analysis

The moments existing in the cantilevers of pre-

Creep deformation of concrete is that part ofthe inelastic deformation not caused by shrinkage.Creep deformations occur as a result of the inelas-tic response of concrete to long term loadings suchas dead load, post-tensioning forces, and perma-nent displacements. Restraint of creep deforma-tions causes redistribution of moments. This hap-pens, for example, when statical systems arechanged by connecting a cantilever structure intoa continuous structure. The effect of permanentdeformations by external causes is reduced bycreep. This occurs in the case of support settle-ments.

The relationship between creep deformationsand elastic deformations is linear. The ratio iscalled the creep factor 6. The following relation-ship can be expressed for $ :

where e,, = creep strain

Ee = elastic strainu = stressE = elastic modulus of concrete at age of

28 days

2(27 120

~-9~-7[+ [-"I 3~i-p -[--i-r-F[-q-Tp 1 6 j 7 j e j 9 j 1 0 1 n j

Fig. 3.6 - Dead load moment development during cantilever erectiont2’)

0 37I42?;a42% 3 1 5 6 5 40 ml----A

DAYS MONTHS YEARS

Duration of Loading

Fig . 3 .7 - Concrete stra ins vs. age and durat ion ofloading(7’

The relationship between total concrete strain andthe reference strain of a 28day old concrete sub-jected to short term load is illustrated in Fig. 3.7.The value of @I can be estimated from this figure

for various age concretes by simply subtracting 1from the ordinate. A more detailed procedure forevaluation of 8 is presented in Section 3.3.2.4

The following sections illustrate the effect ofconcrete creep on the magnitude of momentredistribution and reduction of the effects ofdeformations due to shrinkage and support settle-ments in precast segmental bridges.

3.3.2.1 Creep Effects Resulting From Change ofStatical System Due to Closure of CentralJoint

Fig. 3.8 (a) shows a double cantilever with anopen joint at B. The elastic deflection is 6 and theangle of rotation at the ends of the cantilevers isQ as shown in Fig. 3.8 (b). If the joint remainsopen, the deflection at time t will have increased toS(l + #,) and the angle of rotation to a(1 + #,),where #, is the creep factor at time t. For a uni-formly distributed load q applied when the con-crete is 28 days old, and a length of cantilever Q:

w3a=-6EI

where I = moment of inertia of the cantileversection

E = elastic modulus of concrete at 28 days

If the joint at B is closed after application of theload, the increase in angle of rotation a#, is re-strained. As a result, the moment M, develops as

31

( C l

Fig. 3.8 - Deformation of cantilevers before and after

closure

shown in Fig. 3.8 (cl. The moment M,, if actingin the cantilever, causes rotation at 6 defined aso.The magnitude of fl may be calculated as:

The restraint moment M, produces both elasticand creep deformations. During a time intervaldt, the creep factor increases by d$,. As a result,QI increases by (ud&, and p increases by pd@,(creep) and dp (elastic). From these relations andthe fact that there is no net increase in disconti-nuity after the joint is closed we may write thegeneral compatibility of angular deformationexpression :

(cu-PI

Integrating this expression:

-jr = In(cY-p)+C

Evaluating the constant of integration:

When $t = 0, p = 0 --f C = -lna

P- = (I-em@t)a

A graph of (l-e-@t) vs. values of 4 is presented inFig. 3.9.

Using the relationships for (II and p:

Substituting in the above, noting that 2!? = L

M, t qQ2(l-e+) = qLZ(l-e+t)

6 24

By evaluating the equation for M, for a largevalue of @t it is found that M, = qL2/24 which isthe same moment that would have been obtainedif the joint at B had been closed before the load qwas applied. This illustrates the fact that momentredistributions due to creep following a changein the statical system tend to approach themoment distribution that relates to the staticalsystem obtained after the change.

Fig. 3.9 - Variation in creep factors for both creep and

shrinkage

Referring to Fig. 3.10, the general relationship maybe stated:

M,, = (1-e-G) (M,,-M,)

where M,, = creep moment resulting fromchange of statical system

M , = moment due to loads before changeof statical system

M,, = moment due to same loads appliedon changed statical system

32

Fig. 3.10 - Moment curves for cantilever system (I), fixed-end system (II), and cantilever system with later construction toform fixed-end system (I I I)

3.3.2.2 The Effect of Creep on Moments due toSupport Settlements

Fig. 3.11 (a) illustrates a beam fixed at end Aand supported at end B. In Fig. 3.11 (b), the beamis assumed to settle suddenly at B a distance 6.The effect of this settlement is an additional mo-ment at A which can be calculated as:

M = -PR3El6

where P =-P3

In Fig. 3.11 (c), the support has been removed atB and the beam is loaded with a load equal to P.The deflection resulting from the load P in thetime interval dt increases by 6d@,. In Fig. 3.11(d), the support is again applied at B and the in-crease of the deflection 6d@, resulting from theload P is presumed to be eliminated by upwarddisplacement caused by an increase in the supportreaction in an amount of X,. The level of supportB does not change between Figs. 3.11 (b) and3.11 (d). The increase in the support reactionX, induces both elastic (by dX,) and creep (byX,d@,) deformations. Since there is no furtherdeflection after Fig. 3.11 (b), the elastic and creepdeformations due to the reaction X, may beequated to the creep deformation due to P. Thisgives the following expression:

(dX, + Xtd&) = Pd&

Solving this equation as in Section 3.3.2.1:

X, = P (l-e+t)

(4 1%

Fig. 3.11 - The effect of creep on moments due to support

settlements

33

The support reactions at B vary as follows: $J = 1.0, the value of e-d = 0.368, the final super-Immediately after settlement the support at B structure moments due to the 1 in. settlement atcarries: R - P support 2 are as shown in Fig. 3.12 (c).After the creep process, the support carries:R- P+ P (l-e”t) = R- Pe$tIn a similar manner, the moments at A due to thesettlement vary:Immediately after settlement: M = -PP

After the creep process:

M = -PQ + P (l-e-‘#‘t)Il

M = -pQe-@‘t

3.3.2.3 The Effect of Creep in Reducing Re-straint Forces due to Shrinkage

For this analysis, it is assumed that the shrink-age at infinity, +,, develops with time at the samerate as the creep factor. This assumption leads tothe equation:

The ultimate effect of creep on the reaction atB and moment at A resulting from a supportsettlement can be evaluated from the above form-ulas by considering the value of e-4 for variousvalues of 4 as follows:

6 1 23 4 5”

e-4 0.368 0.135 0.05 0.018 0.007 0It can be seen from the above that the effect of asupport settlement is reduced to zero by a largevalue of $J~. As in the case of change in the staticalsystem, the creep redistributions have the tendencyto approach the distribution belonging to the“system” obtained after the change.

where E,ht = shrinkage strain at time t

Esh = shrinkage strain at infinity

Development of the restraining force due toshrinkage will be illustrated for the beam ABshown in F/g. 3.13 (a) which is fixed against hori-zontal movement at both ends. Due to shrinkage,the beam shortens by:

To illustrate the application of the above, Fig.3.12 (a) shows a three-span superstructure sub-jected to a settlement of 1 in. at support 2. Fig.3.12 (b) shows the moment diagram resulting fromthe 1 in. settlement at support 2. For a value of

A sht = Esht Q

If the restraint to horizontal movement in the jointat B is temporarily released, the beam wouldshorten due to shrinkage. Applying an axial forceS, to the beam at B as shown in Fig. 3.13 (b),the beam elongates according to:

AS,=s,BEA

I

95,-O” I 190’-0” 95,-O”

\E, = 320 x lo6 K-W

t-F--Pi1 ft. = 0.3048 m (cl1 k-ft. = 1.356 kN-m1 k-ft.2 = 0.413 kN-mZ

Fig. 3.12 - Superstructure moments due to supportsettlement

For the same time interval, the force S, induceselastic (dS,QIEA) and creep (S,Qd#,IEA) elonga-tions which are equal to the shrinkage during the

f-I-#-(b)

Fig. 3.13 - Restraint force resulting from shrinkage

34

time interval. This leads to the following expres-sion:

E,,, ad@,/@ = S,Qd@,fEA+dS,Q/EA

-d@,=-dS,/EA

(Es,, /G3,/EA)

Integrating this expression as in Section 3.3.2.1gives:

s, = Esh EA(1-e-G)

@

The quantity E,~ EA is the force required if allthe shrinkage were taken elastically.

Setting this quantity equal to S, the above equa-tion becomes:

s = s (1-e‘“)f 0

4)

where 4 = 4..

A graph of the values of (l-e-@)/@ is presented inFig. 3.9. This graph illustrates the reduction ofshrinkage restraint forces by creep. The value of(l-e-@)/@ for 4 = 2.0 is about 0.43. This indicatesthat shrinkage restraint forces would be reduced 57percent for 4 = 2.0. In general, the creep reductionof the effects of a slow process, like shrinkage,can be evaluated by division of the results obtainedfrom a fast process like a sudden support settle-ment or a sudden change in statical system by thecreep factor 4.

3.3.2.4 Determination of the Creep Factor”‘)

The creep factor, $J, was defined in Section3.3.2 as the ratio of creep strain to elastic strain.For the precise determination of its value, @Imust be considered to be the sum of recoverablecreep, @d, and irrecoverable creep, I#J~:

4 = 4d + Gf

Recoverable creep and irrecoverable creep arereferred to below as “delayed plasticity” and“flow”, respectively.

Both C#I~ and @r are time dependent, but accord-ing to different relations. These relations are in-troduced into the expression for $ in the followingmanner:

4 = @d,Pd(t--to) + @Jr, p(t) - h,)]

where 4 ct ,t,) = magnitude of the creep factorat time t for a concrete specimenloaded at time t,.

Q dm = magnitude of “delayed elasticity”at infinity

bd(t--to) = factor variable from zero tounity indicating the variation of@d with time

@f- = magnitude of “flow” at infinity

Or(t) -Of&) = factor variable from zero tounity indicating the variation of& with time

to = theoretical age of concrete atloading (days)

t = theoretical time after casting

(days)The numerical value of delayed elasticity after aninfinite time has been determined as #d, = 0.4”“.The recoverable nature of this part of the creepfactor will have consequences only for temporaryloads acting on a structure, such as those appliedduring construction by launching girders or othertemporary erection equipment. For dead load,post-tensioning forces, and other permanentloads #d is added to the value of @f.

The variation of @d with time is shown in Fig.3.14, where the factor 0, is given as the ordinate,and the duration of the loading (t-t,) is the ab-scissa.

The fact that fld depends only on the durationof the loading explains the elastic tIatUre of @d.With time, the full deformation due to loading orunloading will develop. By comparison of Figs.3.14 and 3.16, fld develops somewhat faster thanpf: 30 percent of @d takes place in one day, 50percent after 30 days, and 90 percent within ayear.

The magnitude of the flow, @f,, at infinity de-pends on the relative humidity of the ambientmedium and the composition of the concrete.

10

fld

05

03

1 I I I I I1 5 1 0 5 0 1 0 0 500 low sow 10.000

t-t,, days

Fig. 3.14 - Variation of the “delayed elasticity” withtime(“)

Table 3.1 Variation of PC1 and h with humidity of ambient medium and composition of the concrete(“)

Concrete Composition

Relative Humidity ofAmbient Medium

In water- 100%

In Damp Atmosphere;Over Water-go%

Outdoors-70%

Dry Atmosphere:Interior of Building-40%

Stiff ConcreteSlump l/2”-314”

(13-19mm)

P C l

0.60

0.975

1.50

2.25

Plastic Concrete Soft ConcreteSlump 1”-2” Slump 3”-6”(25-51mm) (76-152mm)

P C l P cl

0.80 1 .oo

1.30 1.625

2.00 2.50

3.00 3.75

ThicknessFactor

x

3 0

5

1.5

1

These factors are represented by PC, in Table 3.1

@f- also depends on the theoretical thicknesshth of the structural element in combination withthe relative humidity of the atmosphere. Thesefactors are represented by pc2. The value of #f,at infinity is the product of &, and Bc2 :

Of, =I&, x PC2

The theoretical thickness, hth, is evaluated from:

X2A,hth = CC

where X = theoretical thickness factor, takenfrom Table 3.1A, = area of concrete section, cm2I-c = perimeter of concrete section in contact

with the atmosphere, cm

After evaluating hth as above, the value of PC2can be taken from Fig. 3.15 and the value of@f, can be calculated.

The variation of #f with time is shown in Fig.3.16. The ordinate shows the factor of develop-ment of and the abscissa the time t, in days. Incontrast to delayed elasticity, ed, the time scalein Fig. 3.16 begins at the time the concrete is cast.Therefore, the influence of the age at loading, t,,is obtained from the expression [flf(t)-~rct,b]. Thedependence of the rate of development of @Jr onthe thickness of the member and the relative hu-midity of the environment is indicated in Fig.3.16 by the different curves for various theoreticalthicknesses.

As suggested by Fig. 3.7, loading of concreteat an early age greatly increases the final flow fac-tor, #f. In addition to age at loading, an adjustmentin creep effect calculations may be necessary whena rapid hardening cement is used, or when theprocess of cement hydration is hampered becauseof low temperatures. Such corrections may bemade by calculating a theoretical age for the con-crete by use of the formula:

a ; [T(,., + lo] At’t =

30

where t = theoretical agea = 1 .O for ASTM cement Types I and I IQ = 2.0 for ASTM cement Type II IQI = 3.0 for cement having highly accel-

)

55 1 0 2 0 4 0 60 6 0 2160

h,h, cm 1 cm = 0.39 in.

Fig. 3.15 - Effect of member thickness on “flow”(“)

When concrete cures at 20’ C (68O F) and normalhardening cement is used, theoretical time and realtime are equivalent. Theoretical time and real timeare also equivalent when loading takes place im-mediately after the curing process is over. This is

36

0 . 2 5

00 10 loo 1000 8000

Time t, days 1 cm = 0.39 in.

Fig. 3.16 - Variation of “flow” with time”‘)

normally the case for precast segmental bridges.If the age of loading has been assumed as 7

days in the creep calculation, an equivalent agecan be obtained by:

- curing 7 days at 20’ C and use of Type I or

Type II cement since:1 (20+10)7

= 730

- curing 4 days at 16O C (61° F) and use of Type

I I I cement since: 2(16+10)4= 7

30

- curing 3 days at 13X0 C (56O F) and use of ce-ment having highly accelerated strength

gain since: 3 (13.5 + 10) 3= 7

30

Alternatively, use of normal cement and curing of4 days at 16’ C and 3 days at 13.5’ C gives a theo-retical age of only:

(16 + 10) 4 + (13.5 + 10) 3= 5.5 days, and load-

30

ing should be postponed for 1.5 days.Due to the importance of the creep factor in

design calculations for precast segmental bridgesand the inherent uncertainty in determination ofthe creep factor, it is recommended that calcula-tions be made using values of the creep factor in-creased and decreased 15 percent from the theor-etical value.

37

/38mm). A three-week erection period starts fourweeks after production of the last segment. Thestructure is made continuous by casting a midspansplice one week after completion of segmenterection, and the bridge is erected over water.

The creep factor to be used for the momentredistribution calculations is obtained as follows:

where: #.&, = 0.4fld(t--to) is obtained frOmI Fig. 3.14 at ageof seven days. The delayed elasticity thatoccurs during the week after erectionwhile the structure is not continuousamounts to &(t-t,) = 0.38. Only the re-mainder (l-Pd(t--t,j) = 1.0 - 0.38 = 0.62contributes to the moment redistribution.The value of #r, is calculated from:

#f, = ljcl x&2

&, is taken from Table 3.1 The value is1.3.Theoretical thickness hth = h2Ac/~ =5(0.32) = 1.60 m (5.25 ft.)The corresponding value of Bc2 = 1.12is taken from Fig. 3.15.The values for Sfttj and flfct,, are takenfrom Fig. 3.16. The value of Prctj at t =infinity equals 1. The average age of theconcrete at loading, based on the indi-cated time schedule is 9/2 + 4 + 3 +l =12% weeks, and from Fig. 3.16, the cor-responding value for Pfct,) = 0.3.

Therefore:4 = 0.4 (0.62) + 1.3 x 1.12 (l-0.3)6 = 0.25 + 1.02 = 1.27

Moment redistribution calculations willbe carried out for:

4 Low = 0.85 x 1.27 = 1.074 High = 1.15 x 1.27 = 1.46

3.3.2.6 Influence of Creep on SuperstructureMoments

The theoretical considerations of the influenceof creep in redistribution of moments presented in

*

3.3.2.5 Example Creep Factor Calculations

To provide a numerical example of creep factorcalculations, a three-span example bridge will beassumed which has 44 segments produced at arate of one segment per day over a period of nineweeks. The average concrete thickness is 0.32 m(12.6 in.). Slump of the concrete was 1% in.

Section 3.3.2.1 are applied to actual bridge exam-ples for a variety of loading conditions in thisSection. The effects of dead load, cantilever pre-stress, continuity prestress, and other loadings thatmay cause moment redistribution are treatedseparately. The general procedure is as follows (thestep numbers below do not necessarily relate tothe diagram numbers shown in the various exam-ples) :

Step 1. Bending moments are determined duringthe erection phase.

Step 2. Bending moments are determined in thecontinuous condition (the elastic momentdistribution that would have occurredif the structure had been erected in onesingle step).

Step 3. The difference between the moments ofStep 2 and Step 1 is calculated. This dif-ference is always a moment diagram con-sisting of straight lines, since it is merelythe result of changed fixities (boundaryconditions).

Step 4. The diagram obtained in Step 3 is multi-plied by the factor (l-e-@) and the“creep moments” are obtained.

Step 5. Bending moments of Steps 1 and 4 areadded in order to find the moment dis-tribution at infinity.

It should be noted that at any time betweenerection and infinity, the bending moments in thestructure will be between the values calculated inSteps 1 and 5.

Comparing the examples in Figs. 3.17,3.18, and3.19 it is seen that the final dead load bendingmoments in the structure depend on the order inwhich the joints are closed in the structure. Inthese same figures, it is seen that the magnitude ofthe moment redistribution due to creep also de-pends on the construction sequence and the num-ber of spans in the structure.

Construction Procedure

Structure weighs 5 k/lin. ft. (73 kN/mj

Step 1. Erect cantileversover supports C

k.F-G on false-

P P work,close j o i n t sB and F and re-

i move falseworkP P

Step 3. Concrete spliceat D

Fig. 3.17 (a) - Effect of creep on dead load moments -Example 1

Moment Calculations

-3- Casting of midspansplice completed atjoints B and F.Bending momentsat end of Step 3are as Step 2

-& Elastic distributionof 3 (mid-spansplice completed atDj. Bending mo-ments continuousstructure:

MB = MF = +2985k-ft.MC = ME = -7548K-ft.M ,, = +4702 k-ft.

-5- Difference betweenI

-_ -~~ diagrams 4 and 2:

.,02 ’M = +12250 -7548 = +4702 k-ft.

-6- Creep momentsobtained by

6- Imultiplication

I’ 2351 .-G====-- of diagram 5 by

(1 - e+j = 0.5(for exampleonly)

0800 -7- Dead load mo-ments at infin-

7 -==zx-- ity obtained from2180 I -1351 diagrams 2 and 6:

-lk-ft.= 1.356 kN-m

Fig. 3.17 (b) - Effect of creep on dead load moments -

Example 1

Construction Procedure

Structure weighs 5k/lin.ft. (73 kN/mj

a Step 1. - Erect cantilev-ers over sup-ports C and E.

100 ft. = 30.5 m

ing segmentsbetween ABand FG onfalsework.c l o s e j o i n t s Band F, and re-move false-work.

Fig. 3.18 (a) - Effect of creep on dead load moments -

Example 2

Figs. 3.20 and 3.21 illustrate that the effect ofcreep on the moments resulting from continuitypost-tensioning depends on the construction se-quence and the order in which the tendons arestressed.

I38

Moment Calculations Moment Calculations

- 2 -

- 3 -

-5-

-6-

6 I I’ 212s I

%4&f+-1 k-ft. = 1.356 kNm

B e n d i n g m o m e n t sat C and E; resultof Step 1.

Mc = 12250 k-ft.B e n d i n g m o m e n t snot effected byStep 2.Construction com-pleted. Bendingmoments resultingfrom Step 3:

MB = +1471 k-ft.MC = -12597 k-ft.MD = -347 k-ft.

Elastic distr ibu-tion of bendingmoments in con-tinuous structure:

MB = +2985 k-ft.MC = -7548 k-ft.MD = +4702 k-ft.Difference be-tween diagrams 4and 3M = 4702 + 347 =5049 k-ft.Creep momentsobtained bymultiplication ofdiagram 5 by(l-e+1 = 0.5 (inexample only)M,, = 0.5 x 5049= 2525 k-ft.Dead load mo-ments at infinityobtained from dia-grams 3 and 6

M =+1471+O.! (2525) = 2228k-ft.MC = -12597 +2525 = -10072k-ft.MD = -347 + 2525= +2178 k-ft.

Fig. 3.18 (b) - Effect of creep on dead load moments -Example 2

Construction Procedure

Structure weighs 5kllin.ft. (73 kN/m)

Step 1 - Erect cantileverover support C.

Step 2 - Erect tailspansegment be-

AGC D E F G HI tween A and B

L l i P ll P n P ,gon falsework.

, 100’ , 4.0’ , 1.0’ , - concrete joint

r.,.a t B

- remove false-work

. . ,.;.. .:.P Step 3 - Erect cantilever

over support E: : 1 - concrete joint

at D

h 1P P P Step 4 - Erect cantileverover support G.

A1: -concrete joint

100 ft. = 30.5 mat F.

Step 5 - Erect tailspansegment be-tween H and Ion falsework

-concrete jointat H.

- remove false-work.

Fig. 3.19 (a) - Effect of creep on dead load moments -Example 3

39

-2-

I I

- 3 -

I

- 4 -

- 5 -

Bending momentat support C, re-sult of Step 1

MC = 12250 k-ft.B e n d i n g m o m e n t sat joint B, supportC, result of Step 2.

MB = +1575MC = 12250 k-ft.B e n d i n g m o m e n t sat jo int B , supportsC and E, joint D,result of Step 3

MB = +1575,MC, ME = -12250Mg=O

B e n d i n g m o m e n t sat joint B,supportsC,E,G, joints Dand F, result ofStep 4 MB =+1575, MC, ME,MG = -12250,Mg,MF=OB e n d i n g m o m e n t sresulting from Step5, end of erection.

M =1575-0.3 (38) = +1564k-ft.MC = -12,250 -38 = -12,288 k-ft.MD = +47 k-ft.ME = -12,250 +131 = -12,119k-ft.MF = -178 k-ft.M = - 1 2 2 5 0 -48% = -12;736k-ft.hlkf = +1429 k-ft.Elast ic bendingmoment distribu-tion continuousbridge.Difference be-tween diagrams 5and 6.Creep bendingmoments, ob-tained by multi-plication of dia-gram 7 with factor(1 -e@) (herechosen to be 0.5)Dead load bendingmoments at infin-ity obtained byaddition of dia-grams 5 and 8.

Fig. 3.19 (b) - Effect of creep on dead load moments -Example 3

Construction Procedure

Prestressing forceF,=F2=1000k=F

M = Fe assumed not toA G C D

rr*&mn II. rEWDOY F,- IL*DOW F, g vary with time

fEccentricity e = 3’-0”(0.9 m)

100- Step 1 - Both halves of

the structureerected

1 k=4.448kN is stressedStep 2 - Midspan joint at

C is concreted- midspan conti-

nuity prestressis stressed.

Fig. 3.20 (a) - Effect of creep on moments due to conti-nuity post-tensioning - Example 1

Moment Calculations Moment Calculations

,

-2- Elastic momentdistribution iftendons Fg werestressed in contin-

3- I-3- Difference be-

tween diagrams 1and 2.

-4- Creep bendingmoments obtained

3I - 3 -

.484 F.A-

4- 1I O.Z.?h ’

0.75s F. -5-

s- I(1 I II,I1 + ‘110.242P. O.lo* P.

uous system.

Difference be-tween 1 and 2.

Creep Momentsobtained by multi-plication of 3 byf 1 -a-@) takenas 0.5.Final moments bycontinuity pre-stress Fg, obtainedby addition of 1and 4.

B e n d i n g m o m e n t sresult ing fromStep 2. TendonsFt are stressed inthe continuoussystem and aretherefore notsubject to creepmoment redistri-bu t ion .Final momentsdue to all continu-ity prestress ob-tained by additionof 5 and 6.

4 by multiplication

I O.emf. of 3 b factor(1-e4), taken as0.5.

i’Ey -5- $gaE~,,551.

-6- Elastic bendingmoment distribu-tion by stressingof tendons F2.These tendons arestressed in contin-uous system andtherefore notsubject to creepmoment redistri-bu t ion .

6 I I i II

- 6 -

r= -7- Total bending mo-merits by prestressFt and F2, ob-tained by additionof 3 and 6.

Fig. 3.20 (b) - Effect of creep on moments due to conti-

nuity post-tensioning - Example 1

A a C D E F GISNDON F,.

Construction Procedure

Prestressing force F, =F2 = FEccentricity = eM = Fe assumed not tovary with time

Step 1 - Erect cantileverover supports Cand E

I P P 1 - concrete mid-span joint at D

k n i- stress contin-

uity tendon Fg.

Step 2 - Erect segmentsin tailspan be-tween A and B(F and G)

- stress continuitytendons F t .

Fig. 3.21 (a) - Effect of creep on moments due to conti-

nuity post-tensioning - Example 2

Fig. 3.22 shows the influence of creep on themoments due to the cantilever post-tensioning. Inthis case, the effect of creep is independent of theconstruction sequence since the stressing of thetendons does not change the statical system.

Fig. 3.21 (b) - Effect of creep on moments due to conti-

nuity post-tensioning - Example 2

Construction procedureTENDON F,-

1TENOOH F>-

d r

1I I d Prestressing force = F

10’ , 70’ 30’ (for simplicity assumed

100’ I.0’ 100’ constant over length andtime)

100 ft. = 30.5 m Eccentricity = e

-2- Elastic distribu-

2-F /i,o.m P. 0.335F. tion of bending

I moments by pre-

o.*wJ 5% stress if stressed incontinuous bridge.

-4- Creep bendingmoments due to

o.ss0r. cantilever prestressI obtained by multi-I

l Iplication of dia-gram 3 with factor(l-e+), taken as0.5.

Fig. 3.22 - Effect of creep on moments due to cantilever

post-tensioning

40

3.3.3 Analysis for Superimposed Dead Loadand Live Load

The main loadings on a precast segmental boxgirder bridge, the dead load of the box girdersuperstructure and the prestressing force exertedby the post-tensioning tendons, were discussed inSection 3.3.2 with major emphasis given to mo-ment redistribution resulting from creep. Afterthe structure has been erected and completelypost-tensioned, the response of the superstructureto additional superimposed dead load and to liveload is considered in the same manner as for anycontinuous bridge. The response of the structureto these loads is elastic. The superimposed deadload is subject to additional creep deformation, butthis deformation does not cause significant re-distribution of moments.

Consideration of the effects of live load on thetransverse design moments and the use of trans-verse post-tensioning in deck slabs is considered inSections 3.4 and 3.5, respectively.

3.3.4 Analysis for the Effects of Temperature

The effects of temperature on a precast seg-mental bridge superstructure are similar to thetemperature effects on any bridge superstructurein the longitudinal direction. For illustrative pur-poses, calculations evaluating longitudinal tem-perature effects are presented below. It is noted,however, that the Standard Specifications for High-way Bridges of the American Association of StateHighway Officials’6) permit stress increases of 25to 40 percent for loading combinations that in-clude temperature and shrinkage effects. Since theshrinkage effects are substantially reduced due tothe maturity of the concrete before a continuityconnection is made, the permissible stress increaseis usually substantially more than the actual tem-perature and shrinkage effects on a precast seg-mental box girder superstructure. Furthermore, thelongitudinal thermal stresses are primarily of con-cern relative to the possibility of crack develop-ment at service load (which is accepted as a matterof course in reinforced concrete structures), andthe longitudinal temperature stresses would haveminimal, if any, effect on the strength of thesuperstructure.

The effects of temperature are generally believedto be more significant in the transverse directionwhere temperature stresses may act in combina-tion with the effect of transverse post-tensioningof deck slabs. These effects are considered in Sec-tions 3.4.7 and 3.5, respectively.

(a) shows a structure wherethe top slab temperature is increased At degreeswith respect to the bottom of the section. Thenormal expansion of the top slab is restrainedby the webs and the remainder of the box sec-tion. For purposes of analysis, the deformationof the box section may be considered to be pre-vented by exerting external forces P at the centroidof the top slab level as shown in Fig. 3.23 (a).Concrete stresses in the top slab will be:

f, = EaAtwhere E = modulus of plasticity of concrete

cr = linear coefficient of thermal expan-sion

Under the loading condition in Fig. 3.23(a) thestresses in the webs and bottom slab remain zero.If the area of the top slab is A, the required forceP will be:

P=f,A

In Fig. 3.23(b), external equilibrium is restoredby removing forces P by superimposing forces P’which are equal in magnitude but are in oppositedirections (P = P’). The force P’ may be consideredto act at the centroid of the full cross section asshown in Fig. 3.23 (c) by introducing the moment:

M = P’ (c, - e)

The concrete stresses resulting from the equiva-lent thermal force and moment are shown in Fig.3.23 (d):

f,, = -E&At

fc2 = +EaAt ;

fc3 (top fiber) = +EtitA (c,-e) F

fc3 (bottom fiber) = - EaAtA (c,-e) p

r41

The longitudinal effects of temperature causethe total structure length to increase or decrease,and where there is a temperature difference be-tween the top slab and the remainder of the boxsection, longitudinal bending moments and shearsresult. The change in overall length of structuremay be accommodated by expansion joints, ex-pansion bearing details, and/or flexure of piers.The effects of a temperature differential betweentop and bottom slabs is illustrated for simple spanand continuous bridges.

For consideration of longitudinal temperaturedifferential effects on a simply supported boxgirder bridge, Fig. 3.23

-t

f, = E&t

where E = modulus of elasticity of concrete(Y = linear coefficient of

thermal expansion p’\p’

(4)

+

7

Fig. 3.23 - Analysis for temperature differential between top and bottom slabs

--(4

42

where:+ = tension- = compression6 = total area of sectionI = moment of inertia of section

Applying these equations to the cross sectionand section properties in Fig. 3.24 for a top slabtemperature increase of 18’ F (10’ C), with OL =5.5 x 1 O6 in./in./OF (9.9 x lo6 m/m/‘C), and E =4 x lo6 psi (27.6 x lo3 MPa) [SO00 psi (34.5MPa) concrete], the stresses become:

fCl = - 4000 x 5.5 x 1 O6 x 18 = -0.396 ksi(-2.73 MPa)

fc 2 = +0.396 x 1929.6/3614.4 = + 0.211 ksi(+ 1.46 MPa)

fc3t= +0.396 x 1929.6 (18.5 - 4) x 18.5/1142 x lo3 = + 0.180 ksi (+ 1.24 MPa)

fc3b = -0.396 x 1929.6 (18.5 - 4) (48 -18.5)/1142 x lo3 =-0.286 ksi(-1.97 MPa)

Total top fiber stress: -0.396 + 0.211 + 0.180 =-0.005 ksi (-0.035 MPa)

Total bottom fiber stress: 0.211 - 0.286 = -0.075ksi (-0.518 MPa)

1 ft. = 0.3048 m1 in. = 25.4 mm

Fig. 3.24 - Superstructure cross section assumed for tem-

perature differential analysis

From these calculations it is seen that a tempera-ture increase in the top slab with respect to the re-mainder of the cross section causes very smallcompressive stresses when the superstructure issimply supported.

In the case of continuous superstructures, re-sistance to the rotation at the supports resultingfrom temperature differentials between top andbottom slabs generates additional moments andflexural stresses. For the three span structureshown in Fig. 3.25 (a), the procedure for calcula-tion of temperature moments and stresses is asfollows:1. The continuous superstructure is considered to

be cut over the supports into three simply sup-ported spans as illustrated in Fig. 3.25 lb).The temperature stresses and rotations at sup-ports can then be calculated for equivalentthermal force and moment as for simple spanbridges as described above.

43

M,, shown in Fig. 3.25(cl, required to rejoin the ends of the girdersover the supports are calculated.

3. The total temperature effects on the continuousstructure are obtained by adding the momentsand stresses resulting from the calculations in 1and 2 above.

I!,(b)

“MY UM,U

Fig. 3.25 - Procedure for analysis of a three span structurefor temperature differential stresses

The calculation procedure for continuous super-structures described above in general terms is ap-plied in the following to the continuous bridgewith five equal spans shown in Fig. 3.26 (a).

Proceeding with the first step in the analysis,the superstructure is considered to be cut overeach support, and a constant equivalent thermalmoment, M, is applied over the full length of allgirders as shown in Fig. 3.26 (b). M causes equalrotations at each girder and over the supports. Inorder to rotate the girders back to the same slopesat the supports, bending moments MI and M2must be applied resulting in the moment diagramshown in Fig. 3.26 (c). The total slope at support2 resulting from the constant temperature momentM acting on simple spans l-2 and 2-3 may be cal-culated using moment-area or slope-deflectiontechniques as:

MP MQ MPslope= -+-=-

2EI 2EI El

By the same procedure, the slope due to MI andM2 at support 2 is:

M,n M,Q M,a 2M,11 M,Q

3EI +3EI+-=- -

6EI 3EI + 6EI

Setting the slope due to the temperature momentequal to the slope resulting from M, and M2provides the following:

2M,Q M211 MI1

zl+zEi-=El

L

2. The restraint moments

A A A A I1 2 3 4 5 6

(a)

,I (b)

A A A A A1 2 3 4 5 6

(4

Fig. 3.26 - Moments in a five-span continuous superstruc-

ture due to temperature differentials.

A similar equation is developed for support 3:

M,Q + 5M$? MI1-= -6EI 6EI El

Solving these two equations simultaneously for MIand M2 gives:

M, =gM

EMMz=,~

The total bending moment diagram is, therefore,the sum of the diagrams in Figs. 3.27 (a) and 3.27(b), as shown in Fig. 3.27 (c). The stresses due tothis moment diagram and the axial forces due tothe temperature differential are calculated as fol-lows for span 3-4:

f,, = - 0.396 ksi (-2.73 MPa)f,, = +0.211 ksi (+1.46 MPa)feat= +1/19 x 0.180 = +O.OlO ksi (+0.07

MPa)f c3b =- l/19 x 0.286 = -0.015 ksi (-0.10

MPa)

The combined stresses for span 3-4 are shown inFig. 3.27 (d). The compressive stress of 0.07 ksi(0.52 MPa) calculated for the simple span case,becomes a tensile stress of 0.195 ksi (1.35 MPa)in the continuous case. While this is a significantstress, the magnitude is much less than the 25 to40 percent stress increase for temperature and

shrinkage permitted by the specifications. Further,the stress is less than 50 percent of the modulusof rupture of the concrete so temperature stresseswould not be expected to cause cracking in thesuperstructure.

The moments M, and M2 cause a change in sup-port reactions. For the above example the changein reactions at supports 1, 2, and 3 will be respec-tively +24M/1911, -3OM/19Q, and +6M/19P.

For spans 1, 2, and 3, respectively, and for II =80 ft. (24.4 m) and M = P’(c, - e) = E c@t (c, -e) = 4 x lo6 x 144/1000x 5.5 x 10m6 x 18 x 13.4 x(1.54 - 0.33) = 924 ft. kips (1253 kN-m). Thechanges in support reactions are: +14.6 kips,-18.2 kips, and +3.6 kips (+65.0, -80.9, +16.0kN). The weight of the girder is 3.75 kips/ft.(54.7 kN/m) which provides dead load reactionsat supports 1, 2, and 3 of 119 kips, 339 kips, and292 kips (525, 1503, 1294 kN). Therefore, thechange in dead load reactions due to the tempera-ture differential is, for this structure, on the orderof 12 percent for the exterior support and 1.2 to5.4 percent for interior supports.

0.4

(4

+o 196

Fig. 3.27 - Moments and stresses in a five-span continuous

superstructure due to a temperature differential of 18OF

(IOOC) between top and bottom slabs

3.3.5 Shear Lag

3.3.5.1 Computer Analysis of Shear Lag in Single-Cell Box Girder Bridges

Computer analyses of four single celled boxgirder bridges shown in Fig. 3.28 were performedto provide data on the magnitude of shear lageffects. The computer model assumed rigid dia-phragms at the pier and at abutments. The cross

44

STRUCTURE DEPTH D (‘1, SPAN L if,!A

::150

E150

1500 100 ::

Fig. 3.28 - Superstructure details assumed for computeranalysis of shear lag

sectional dimensions and thicknesses of these four

bridges were intentionally chosen to exaggeratethe shear lag effects. The analyses were performedusing a computer program, MUPDlt8), which isbased on the folded plate method using elasticitytheory. Longitudinal force distributions obtained

from these computer analyses were plotted at vari-ous sections and compared with forces calculatedby elementary beam theory. The ratios betweenthe peak forces found from the MUPDI computeranalyses and the forces at the same points foundby elementary beam theory give a measure of theeffects which are commonly lumped under thedesignation “shear lag”. The forces may be ex-pressed in terms of stresses by dividing by the slabor web thicknesses.

The analyses were performed for four differentloading conditions shown in Fig. 3.29: 1) deadload; 2) prestress; 3) live load’plus impact for max-imum negative moment; 4) live load plus impactfor maximum positive moment. Loadings 5 and 6in Fig. 3.29 were obtained by superposition ofresults for both sides of the bridge in load cases3 and 4, respectively. The combination of fourbridges and four loading conditions required six-teen separate analyses.

Since the major interest in this investigation wasthe ratio of the peak longitudinal forces from theMUPDI analysis to the forces at the same pointsfound by elementary beam theory, these are sum-marized in Tables 3.2 and 3.3. Results are given atfour points on the cross-section a, b, c, d where the

Fig. 3.29 - Loading cases for computer analysis of shearlag

peak forces occur. Results are given at several sec-tions along the span which are deemed important.These include sections at midspan; maximum +M; maximum - M (center support); several sec-tions close to the center support; and sectionswhere concentrated live loads act.

A careful study of Tables 3.2 and 3.3 reveal anumber of important facts. In the following, theratio of the longitudinal force N, obtained fromthe MUPDI analysis to that obtained from ele-mentary beam theory will be called “force ratio”for brevity.

1. Comparing force ratios of structure A with thoseof structure B, they are seen to be very similar.The same is true comparing results for structureC with those of structure D. This indicates theforce ratios are essentially independent of varia-tion in depth for a given span (within the spandepth ratio range between 20 and 30).

2. Comparing force ratios of structures A andB with those of structures C and D, it can be

45

LoadCase

1

DeadLoad

2

Pre-Stress

3

2 LanesLL+lfor- M

4

2 LanesLL+1for+M

5

4 LanesLL+Ifor- M

6

4 LanesLL+Ifor+M

6075144146148150

1 ft.= 0.3048m

Dist. Xfrom

SupportFt.

56.2575144146148150

75135144146148150

7587144146148150

6075144146148150

7587144146148150

xb=Bottom Slab

Table 3.2 Summary of results for longitudinal force ratios for structures A and B

Remark

MAX+MMIDSPAN

M A X - M

MIDSPAN

M A X - M

MIDSPANPT.LOAD

M A X - M

PT.LOADMIDSPAN

M A X - M

MIDSPANPT.LOAD

M A X - M

PT.LOADMIDSPAN

M A X - M

Structure A Structure BL = 150 ft. D = 7.5 ft. L = 150 ft. D = 5.0 ft.

Ratio of N, Ratio of N,MUPDI 3/Beam Analysis MUPDI 3/Beam Analysis

a b C d a b C d

1.04 1.05 1.04 1.06 1.04 1.07 1.04 1.061.04 1.07 1.05 1.07 '1.04 1.07 1.05 1.071.07 1.08 1.07 1.08 1.08 1.11 1.09 1.101.11 1.12 1.11 1.10 1.13 1.16 1.13 1.151.33 1.32 1.37 1.34 1.35 1.37 1.40 1.391.41 1.44 1.51 1.50 1.44 1.46 1.52 1.50

0.84 1.02 0.78 1.02 0.92 1.02 0.91 1.021.02 2.14 1.03 2.11 1.01 0.61 1.02 0.591.07 1.51 1.03 1.55 1.06 3.46 1.06 3.631.05 1.49 1.06 1.54 1.05 3.00 1.06 3.001.07 1.42 1.09 1.45 1.06 2.36 1.08 2.391.09 1.37 1.12 1.41 1.07 1.96 1.10 2.07

1.20 1.17 1.17 1.17 1.12 1.13 1.11 1.131.33 1.38 1.47 1.40 1.33 1.33 1.36 1.351.25 1.28 1.26 1.28 1.23 1.25 1.26 1.251.35 1.32 1.32 1.28 1.32 1.33 1.32 1.311.58 1.49 1.63 1.63 1.63 1.58 1.70 1.611.75 1.69 1.91 1.80 1.81 1.66 1.91 1.74

1.12 1.21 1.21 1.22 1.15 1.18 1.20 1.181.07 1.07 1.08 1.09 1.04 1.07 1.05 1.071.14 1.17 1.08 1.20 1.18 1.26 1.22 1.211.25 1.31 1.23 1.31 1.33 1.32 1.35 1.291.56 1.60 1.60 1.26 1.64 1.60 1.09 1.191.70 1.65 1.76 1.81 1.75 1.68 1.78 1.77

1.10 1.06 1.09 1.07 1.03 1.07 1.04 1.071.11 1.13 1.20 1.13 1.13 1.13 1.14 1.131.09 1.07 1.07 1.08 1.10 1.09 1.10 1.101.15 1.11 1.13 1.08 1.14 1.16 1.14 1.141.29 1.32 1.31 1.35 1.35 1.36 1.39 1.371.40 1.43 1.50 1.48 1.45 1.44 1.52 1.47

1.00 1.07 1.07 1.08 1.04 1.07 1.08 1.071.03 1.02 1.04 1.03 1.00 1.03 1.00 1.041 .oo 1 .oo 0.96 1.03 1.05 1.13 1.08 1.081.06 1.12 1.08 1.13 1.17 1.16 1.18 1.131.28 1.37 1.30 1.37 1.36 1.38 1.39 1.421.35 1.41 1.41 1.50 1.41 1.46 1.43 1.50

46

!

LoadCase

1

DeadLoad

2

Pre-Stress

3

2 LanesLL+Ifor-M

4

2 LanesLL+Ifor+M

5

4 LanesLL+Ifor- M

6

4 LanesLL+Ifor+M

Dist. Xfrom

SupportFt.

112.5150294296298300

150270294296298300

150174294296298300

120150294296298300

150174294296298300

120150294296298300

1 ft. = 0.3048m

~b=Bot+om Slab

Table 3.3 Summary of results for longitudinal force ratios for structures C and D

Remark

MAX+MMIDSPAN

M A X - M

MIDSPAN

M A X - M

MIDSPANPT.LOAD

M A X - M

PT.LOADMIDSPAN

M A X - M

MIDSPANPT.LOAD

M A X - M

PT.LOADMIDSPAN L

M A X - M

Structure C Structure DL=300ft.D=15ft. L=3OOft.D=lOft.

Ratio of N, Ratio of N,MUPDI B/Beam Analysis MUPDI 3/Beam Analysis

a b

0.99 1.010.99 1.021.02 1.021.08 1.121.13 1.191.13 1.20

0.85 1.000.99 1.091 .oo 1.081.00 1.101.02 1.111.02 1.11

1 .oo 1.041.08 1.101.12 1.111.22 1.221.29 1.301.17 1.31

1.04 1.051 .oo 1 .oo1.08 1.101.15 1.241.21 1.321.29 1.29

1.00 1.021.00 1.021.04 1.021.09 1.121.14 1.191.07 1.21

1.00 1.011.00 1.001 .oo 1.031.04 1.141.07 1.201.14 1.19

C d a b C d

1.00 1.02 0.99 1.01 0.99 1.010.99 1.02 0.99 1.01 1 .oo 1.011.02 1.02 1.04 1.04 1.04 1.041.11 1.13 1.10 1.13 1.12 1.131.17 1.22 1.14 1.20 1.18 1.211.18 1.23 1.13 1.20 1.17 1.21

0.77 1.01 0.96 1.00 0.95 1.000.99 1.11 0.99 1.33 0.99 1.271.00 1.09 1.00 1.22 1.00 1.231.01 1.10 1 .oo 1.17 1.01 1.181.03 1.10 1.01 1.12 1.03 1.131.04 1.09 1.01 1.10 1.03 1.09

1 .oo 1.03 1.00 1.02 1.03 1.001.09 1.12 1.05 1.11 1.09 1.091.14 1.11 1.09 1.12 1.10 1.111.24 1.25 1.18 1.17 1.19 1.191.34 1.32 1.26 1.22 1.29 1.251.38 1.37 1.25 1.21 1.29 1.23

1.11 1.04 1.02 1.04 1.05 1.041 .oo 1.02 1.00 1.02 1.00 1.001.10 1.08 1.11 1.09 1.09 1.091.18 1.27 1.20 1.17 1.20 1.181.30 1.36 1.27 1.21 1.27 1.231.39 1.33 1.26 1.20 1.32 1.26

0.98 1.02 1.00 1.01 1.01 1.001.00 1.04 1.00 1.04 1.01 1.031.05 1.02 1.02 1.05 1.04 1.041.12 1.13 1.08 1.10 1.09 1.111.18 1.19 1.13 1.13 1.15 1.161.20 1.23 1.11 1.12 1.14 1.14,

1.04 1.00 1 .oo 1.01 1.01 1.000.99 1.01 0.99 1.02 0.99 1.001.03 1.00 1.05 1.03 1.03 1.031.07 1.15 1.10 1.10 1.10 1.101.15 1.23 1.14 1.13 1.15 1.151.22 1.20 1.13 1.13 1.17 1.16

47

seen that the latter are considerably lower indi-cating that an increase in span results in a de-crease in force ratio. This is logical since it isgenerally recognized that “shear lag” is inverse-ly proportional to the span length to platewidth ratio.

3. For a given structure, considering the dominantforces for any of the loadings, the force ratiosare highest at the center support and drop offrapidly a few feet away. (Note that nearly allforce ratios are less than 1 .lO at 6 ft (1.8 m) fromthe center support.) The dead load longitudinalforce variation across the section of structure f3at 6 ft. away from the support and at the sup-port is shown in Figs. 3.30 and 3.31, respec-tively; and similar drawings are presented forstructure D in Figs. 3.32 and 3.33. The forceratios in the midspan positive moment regionsare much smaller. The force ratios are primarilya function of shear lag, which in turn is a func-tion of the magnitude of the shear, which isgreatest at the center support. The forces canbe expressed in terms of stresses at the variouspoints by dividing by the web or slab thickness,respectively.

4. For the important dead load case 1, the forceratios at the center support ranged from 1.41 to1.52 for structures A and 8, and from 1.13 to1.23 for structures C and D; while at midspan,they ranged from 1.04 to 1.07 for structures Aand 8 and from 0.99 to 1.02 for structures Cand D.

5. The force ratios for the dominant stresses underthe prestress load case 2 were generally muchsmaller than the force ratios for dead load. Forstructures A and B, some high values of force

Fig. 3.30 - Longitudinal force variation structure 6 six feetfrom center support

Fig. 3.31 - Longitudinal force variation in structure 13 atcenter support

635 t

V E R T I C A L

DIMENSION

NOT TO

SCALE FOR

C L A R I T Y

1 ff = 0.3046 mlForce I” k,pr

1 k = 4.446 kN

Fig. 3.32 - Longitudinal force variation in structure Dsix feet from center support

ratio resulted at points b and d due to the rela-tively small absolute value of the force at thosepoints calculated by beam analysis. When com-pared to small initial values of N, from beamanalysis, the values of N, from MUPDI gavelarge force ratios, even though the numericalforce increase was not large. For dominantforces in the top slab, the force ratios for theprestress load case ranged from 1.01 to 1.12 forstructures A and B, and from 0.99 to 1.09 forstructures C and D.

6. As seen in the key to load cases shown in Fig.3.29, loadings 3 and 4 represent 2 lanes of liveloading, plus impact, placed on one half of the

48

3 985’

1) 5.140~

VERTICAL

DIMENSION

NOT TOSCALE FOR

CLARITY

Fig. 3.33 - Longitudinal force variation in structure D

at center support

transverse cross-section. Thus, force ratios forthese loadings reflect not only the effect ofshear lag, but also of eccentric loading. Asmentioned earlier, live load forces are muchsmaller than dead load forces. For load cases 3and 4, force ratios at the center support rangedfrom 1.65 to 1.91 for structures A and B andfrom 1 .17 to 1.39 for structures C and D. Atthe sections where the concentrated live loadsacted (near midspan) the force ratios rangedfrom 1.12 to 1.47 for structures A and B andfrom 1.02 to 1.12 for structures C and D.

7. As seen in the key to load cases shown in Fig.3.29, loadings 5 and 6 represent 4 lanes of liveloading, plus impact, placed symmetrically onthe transverse cross-section. Thus, force ratiosfor these loadings are due only to the effect ofshear lag. Force ratios at the center supportranged from 1.35 to 1.52 for structures A andB, and from 1.07 to 1.23 for structures C and D,which are very similar to the force ratios for thedead load case. At the sections where theconcentrated live loads acted (near midspan) theforce ratios ranged from 1 .OO to 1.20 for struc-tures A and B and from 1.00 to 1.04 for struc-tures C and D.

3.3.5.2 Consideration of Shear Lag in BridgeDesigns

As noted in Section 3.3.5.1, the section param-

eters chosen for the computer analyses were in-tentionally selected to provide an upper bound tothe magnitude of the shear lag effect that couldbe expected in a bridge. The shear lag effect fromthe prestressing counteracts the shear lag due todead load and live load. In this regard, the modelused in the above computer analysis, which con-siders the bridge post-tensioned by continuous ten-dons from end to end of the bridge, probably un-derestimates the actual magnitude of shear lag dueto prestressing in a segmental structure. The use ofpartial length tendons concentrated directly overthe webs in the negative moment area would resultin a higher stress concentration at these pointscounteracting shear lag effects even more thanresults from the continuous tendon assumptionused in the MUPDI analysis.

An important finding from the computer analy-sis was the very limited length of structure inwhich significant shear lag effects were found tooccur. As illustrated in Section 3.3.5.1, the maxi-mum effects are 10 percent only 6 ft. (1.8 m)from the center of the support. In most designs,this would mean that shear lag effects are onlysignificant within the pier section. The computeranalyses also show the most significant effects onthe short span (150 ft.) (45.7 m) structures withhigher width to span ratios.

It is felt that the above discussion of the magni-tude and length of structure affected in conjunc-tion with the specification requirement of zerotensile stress in the top slab under full serviceload, which in itself provides a tensile stress resid-ual capacity in the concrete in excess of 500 psi(3.45 MPa) between service load and the initia-tion of cracking, provide sufficient justification fordisregarding explicit consideration of the shearlag effects in most practical bridge design projects.For shorter span structures (150 ft.) (45.7 m)with wide (40 ft.) (12.2 m) single cell segments,shear lag might be considered in the pier segmentby providing some nominal residual compressivestress under peak negative moments, or by use ofcomputer programs such as MUPDI 3 to evaluatethe magnitude of the shear lag effect.

3.3.6 Ultimate Strength Analysis

Precast segmental bridges erected in cantileverwill normally have excess ultimate strength ca-pacity under full loading conditions because thenegative moment tendons are proportioned tomaintain zero tensile stress in the top slab in any

Moments in f t . -k ips1 ft.-k = 1.356 KN-m

Fig. 3.34 - Ultimate moment curves vs. capacity for a three-span segment of a precast segmental bridgeC2’)

condition of erection or service loading. Therefore,the combination of negative moment tendons andpositive moment continuity tendons will usuallyprovide more than adequate longitudinal momentcapacity to meet the load factor requirementsunder loading conditions which produce maximummoments in the continuous structure.

Under partial loadings which produce maximumpositive moments in one span, a check should bemade to assure that the structure has the negativemoment capacity required in the adjacent un-loaded spans to withstand any moment reversalthat might occur. Additional tendons may be re-quired in the top slab at midspan to assure continu-ity between the top slab negative moment tendons.This check is important to avoid the possibilitythat a negative moment hinge might form in anunloaded span before the sections in the loadedspan have reached their ultimate capacity.

Fig. 3.34 shows ultimate moment curves for athree-span segment of a precast segmental bridge.Curve (a) shows the required moment capacityunder full loading of all spans. Curve (b) shows therequired moment capacity under loading of thecentral span only. Note that negative moment ca-pacity is required at the center of the unloadedspans under the partial loading. The ultimatemoment capacity of the structure is indicated be-tween the shaded areas.

(a)

(b)

Fig. 3.35 - Initial loading and reaction assumption for

transverse analysis

50

(4

.

t

+RI

7

U.4

Xm,+R2) X(R1+R2) X(R, -R2) ‘h(R2-R2)

=P =P

Fig. 3.36 - Non-symmetrical loading and reaction assumption for transverse analysis

51

3.4 Transverse Analysis

3.4.1 General

Transverse moments, shear and axial forces inbox girders are analyzed taking into considerationthe longitudinal geometry, torsional properties,and transverse geometry of the box girder. Inter-mediate diaphrams are generally not required, andthe design method presented in the following sec-tions does not include consideration of them.

3.4.2 Principles

In Fig. 3.35 (a), loading 2P per unit length isassumed to be constant over the length of a simplysupported box girder with section ABCD. Con-sider the corners of the box girder supported asshown in Fig. 3.35 (b). The analysis reduces thento simple case of a frame. This analysis is carriedout and transverse moments, shear and axialforces are calculated. Also the support reactionsR,, Ra, Ra, and R4 are evaluated.

Non-symmetrical loading as indicated in Fig.3.36 (a) would cause bearing forces or supportreactions as shown :

R, > R, and R4 = -Rg

The fact that previously assumed supports are notpresent must be accounted for by subsequentloading of the box girder by forces opposite to

R R,, Ra, and R4. These forces are shown inF/g: 3.36 (b). For a subsequent analysis of the boxgirder by forces RI , R2, RB, and R,,, these loadsare rearranged in symmetrical and antisymmetricalcomponents as shown in Fig. 3.36 (c).

3.4.3 Symmetrical Box Girder Loading

Symmetrical loading of the box girder as shownin Fig. 3.37 (a) causes longitudinal bending andshear that has been accounted for in the calcula-tion of longitudinal prestressing. Transverse mo-ments are, because of the placement of the loadat the webs, secondary in nature and usually neg-ligible. Not negligible, however, are the transverseaxial forces which are: tension in webs, tensionin bottom slab, and compression in the top slab.Top and bottom slab axial forces are a conse-quence of the rate of change of longitudinal shearas is shown in the following. The box girder shownin Fig. 3.37 (b) is cut through the longitudinalcenterline. Support and loading P are indicated.Shear forces T,, TZ, and T3 occur in top slab,web and bottom slab, respectively, in a section of

0 t

IA BP4 P

Id -47

fb)

Fig. 3.37 - Transverse analysis for symmetrical loading

the box. The direction of T, is the same as that ofthe load P. The directions of T, and T3 are asshown, since they must be at right angles to the lon-gitudinal shear forces in top slab and bottom slabcaused by the rate of change of longitudinalbending moments. Over a length L’ the rate ofchange of the shear forces in top slab, web, andbottom slab is T, ‘, T2’, and T3’, respectively.Obviously T2 ‘ equals the vertical load P on L’.However, in the horizontal direction equilibriumcan only be obtained by addition of transverseaxial forces in top slab and bottom slab as shown.These axial forces are equal to rates of change ofshear forces T, and TB, being T, ’ and Ts’ as isshown in Fig. 3.37 (b). T,’ and TB’ are obtainedfrom the rates of change of the shear stress whichmay be calculated as illustrated in Fig. 3.38. Theshear stress diagram over the bottom slab, maxi-mum value 7, is shown in Fig. 3.38 (b). The valueof T may be calculated as:

Pbdz P b z

r=dl=-I

where I is the moment of intertia of the half sec-tion shown. From the distribution of the shear

52

W

(Cl

Fig. 3.38 - Transverse analysis for symmetrical loading

stress over the top and bottom slab as shown inFig. 3.38 (b):

Tn1

=T3

n - dTb2

Substituting the value of 7 from above:

Tr, = T3f - Pb2dz

21

The transverse axial force diagram caused by cen-tral loading of 2P is as indicated in Fig. 3.38 (4.The shortening or elongation of the individualmembers due to axial loads sets up transverse mo-ments which can usually be neglected.

3.4.4 Antisymmetrical Loading

Antisymmetrical loading of the box girder asshown in Fig. 3.39 (a) affects the structure in thefollowing ways:

1. In the transverse direction, transverse bendingand torsional shear are induced.

2. In the longitudinal direction, moments andshear forces are set up acting in the planesof the bottom slab and top slab.

(bl

Fig. 3.39 - Antisymmetrical box girder loading effects

Since the box girder is relatively stiff in thetransverse direction, the response of the structureto upward and downward forces -P and +P is tobalance transversely. This results in transversemoments M, and horizontal and vertical shearforces S,., and S, as shown in Fig. 3.39 (b). Thereare also horizontal and vertical displacements hand v.

These displacements h and v cannot occur with-out the resistance of the top slab and bottom slab(h) and webs (v) in the longitudinal direction.Deflection v of web AD will cause longitudinalbending stresses, compression -T at D and tension+T at A. Because of compatability of strains,equal stresses +T occur in the top slab CD due tohorizontal displacement h as shown in Fig. 3.39(c). This illustrates that, as a result of transversedeformations, bending moments and shear forcesare set up in the longitudinal direction of the boxgirder. The longitudinal forces act in the planes ofthe slabs and webs and, as a result, part of the ex-

53

,rJ

(bl

1 H

Fig. 3.40 - Horizontal forces and shear forces acting onbox girder

ternal load P, say T,‘, is carried by the webs direct-

ly to the supports. At the same time, shear forcesT’,., are acting in the top and bottom slab. The ratioof T’, and T’,, follows directly from the geometryof the box section as a consequence of equalstresses T at the corners.

After having determined the basic consequencesof transverse deformations, the box girder maybe cut at the horizontal neutral axis. Fig. 3.40 (a)shows the top half to the box girder and the hori-zontal forces, discussed up to this point, acting onit. The lack of horizontal equilibrium is restored

by the torsional shear forces. A torsional moment,uniformly applied over the length of the boxgirder, by loads +P and -P per unit length, changesat the rate of MIt per unit length; where M’, =PH. Assuming the concrete thickness d to be smallwith respect to box girder dimensions V and H,the shear forces t, are constant per unit length ofweb or slab. Torsional shear forces, therefore, are

in the webs t’, = t’,,V, and in top and bottomslab t’,, = t’,H as indicated in Fig. 3.40 (b). Thevalue of the various torsional shear forces may becalculated as follows:

t’oM’tzTd=-2VH

t’, = t’,V

f’h = t’, H

where t’, = torsional unit shear force

M’:= torsional shear stress= torsional moment per unit length of

box girdert’, and t’,, = rate of change of torsional shear

force in the web and slab, respec-tively.

3.4.5 Evaluation of the Contributions of Trans-verse Bending, Longitudinal Bending andTorsion to Resistance of AntisymmetricalLoading.

The top half of a box girder section with unitlength L’ is shown in Fig. 3.41 (a) with the hori-zontal forces acting on it. Horizontal equilibriumleads to the expression:

2S,, +T,,‘=t,,’

The left half of the box section with unit lengthL’ illustrated in Fig. 3.41 (b) shows the verticalforces acting on it. Vertical equilibrium leads to:

2S, + T’, + t’, = .P

A complete box section with length L’ is shown inFig. 3.42 (a) with the forces acting on it. Momentequilibrium of the forces in Fig. 3.42 (a) leads tothe expression:

t’,H+t,,‘V+T’,H-T’,V-PH=O

T” t

t I

Fig. 3.41 - Equilibrium of horizontal and vertical forcesunder antisymmetrical loading

54

Fig. 3.42 - Box section equilibrium under antisymmetricalloading

Fig. 3.42 (b) shows a box section with unit lengthL’ indicating displacements h and v and the forcesresisting these displacements. This leads to:

d = web thicknessd, = slab thickness

P = rotation of cornerL’ = unit lengthL = span length

In the longitudinal direction:

EdV3v=crT’,L4 12

/and h = OLT’,, L4

I

Ed, H3-

12

The rate of change of longitudinal shear forcesT’,, and T’, are considered external uniform dis-tributed load. The coefficient (Y equals384L for thedeflection of a simply supported beam.

The relations of S, and S,, and t’, and tIh fol-low from the geometry of the box girder:

S; S;=M,“--Z f)-

fh’ t,’-z-zH V

to ’

The above equations permit solution for all un-knowns.

3.4.6 Example Transverse Analysis Calculations

The box girder section shown in Fig. 3.43 hasa simply supported span of 40.00 m (131.2 ft.)length. The moment of inertia of the full section is2.76m4 (319.5 ft.4). A linear load of 10 t/m(6.8 k/ft.) is present over the full length of the boxgirder. Web and slab thicknesses are 0.3 m (1.0 ft).

Consider the box supported at four corners asshown in Fig. 3.44.

IO t/m

t---lI 15

I ti t 0,3I

4

QJ

1 I -d

0zoo

? 0 . 3

I 1 I ’

6,00

1 ml = 3.28 ft.tt=lOOOkgf1 t/m = 0 678 km

tim

f!q

INote: 10 tonnes 0‘force in the c.g.1.

1

mctnc wonl =1 70 =p 9.8 x ,w Nmtcml

‘loooman tbs SI sysom. Thiranalyar II I” the

_ 570 c.g.*. syrtsml

Fig. 3.43 - Example transverse analysis box girder section

V tc

Fig. 3.44 - Support assumptions for example transverseanalysis

1.72

(a) Moments, t-m/m (b) Axial Forces, t/m

1 I

- 3 . 4 24 +

- 1.15-b. L '

.

1 t/m = 0.678 klft.1 t-m/m = 2.2 k-ft./ft. . b

f

1

892 (cl Support Forces, t/m P1.08

Fig. 3.45 - Moments, axial forces, and support forces for example transverse analysis

FE l-T-[ + p-j + 1 m2 1 ID8 I 5 15 L LB2

Fig. 3.46 - Adjustment of support forces for example transverse analysis

Bending moments, axial forces and supportforces are obtained from a conventional momentdistribution calculation. The resulting diagrams arepresented in Figs. 3.45 (a), 3.45 (b), and 3.45 (c).

The supports not actually present are taken intoaccount by the loads of Fig. 3.46 (a), which inturn are subdivided into the loads of Figs. 3.46(b), 3.46 (cl, and 3.46 (d).

1The central loading of Fig. 3.46 (b) causes

longitudinal bending only. Transverse moments arenegligible. However, axial forces are developedwhich are shown in Fig. 3.47. The transverse axialforce is evaluated as:

(

5 x 0.3 x 2.B52 x 0.85l/2

>= 3.75 t/m

l/2 x 2.76(2.54 k/ft.)

The loading of Fig. 3.46 (c) causes transverse andlongitudinal bending and torsion. In accordancewith Section 3.4.5:

h.and v:

5 ~~“4Oyz$d]v= 384

S” x 1.72 1o.33 =

5x

404

12 x T,’ 12 x T’,

384 - o.3x5.73x1 .7 +0.3x5.7x1.73 1S” = 177.17[$ +G]

= 5.45 T’, + 61.3 T’,

From vertical equilibrium:

3.92 = t,’ + T,’ + 2 S,

From moment equilibrium:

-3 .92 x 5.7 + T,’ x 5.7 - T,,’ x 1.7 + t,’ x 5.7 +fh’ x 1.7 = 0

I 17making use of fy, = -

th 5.7

fh ‘= 3.35 t,’

and as a consequence of equal longitudinal stressesat the corner of the box girder:

0.85T, ’ 2.85Th ’

1 .73 = 5.73Th’= 11.24T,’

substituting in the moment equilibrium equation:

-22.34 - 13.41 T,’ + 11.4 t,’ = 0Solving the above equations:

T’v = 0.026 t/m (18 IbJft.1

T’h = 0.30 t/m (203 IbJft.1

S” = 0.95 t/m (644 Ib./ft.)

t’, = 1.99 t/m (1350 Ib./ft.)

t’h = 6.67 t/m (4520 Ib./ft.)

Corner moments M, = 0.95 x 2.85 = 2.71 t-m/m(5.96 k-ft./ft.)

Resulting bending moment and axial force dia-grams are presented in Figs. 3.48 (a) and 3.48 (b).

Axial forces are obtained from:

top slab:2 x 2.71 = 3.18 t/m (2160 Ib./ft.)

1.7

-check: 3.18 6.67 0.3= t,,’ - Th’ = = 3 18

2

web. 2 x 2.715.7

= 0.95 t/m (644 Ib./ft.) at top

3.92 - 0.95 = 2.97 t/m (2010 Ib./ft.)

at bottom

check: 2.97 - 0.95 = 2.02 = t,’ + T,’

= 1.99 + 0.03

11 t/m = 0.678 k/ft.t/m = 0.678 k/ft.

Fig . 3 .47 - T r a n s v e r s e a x i a l f o r c e s f o r e x a m p l e t r a n s v e r s eana lys is , t /m

57

fSubstituting these values of h and v in the aboveequation:

1 for displacements

(a) Moment, t-m/m

A3-‘*

1 tlm = 0.678 k/ft.1 t-m/m = 2 2 k-ft./ft. (b) Axial

Fig. 3.48 - Bending moment and axial force diagrams re-

sulting from example transverse analysis loading case of

Fig. 3.46 (c)

1 t/m = 0.678 k/ft. 6.48

1 t-m/m = 2.2 k-ft./ft. (a) Moment, t -m/m

- OJ7 an

(b) Axial Force, t/m

Fig. 3.49 - Bending moment and axial force diagrams re-

sulting from example transverse analysis loading case ofFig. 3.46 (d)

A solution for loading case d in Fig. 3.46 is ob-tained in a similar manner. Moment and axial forcediagrams are presented in Figs. 3.49 (a) and 3.49(b), respectively.

The final results of the investigation shown inFigs. 3.50 (a) and 3.50 (b) are obtained by addi-tion of the results given in Figs. 3.45, 3.47, 3.48,and 3.49.

Conclusions from the example transverse analy-sis calculations are as follows:

2 . 5 8 1

i.58(a) Moments, t-m/m

2 2 7

(b) Awal Forces. t/m

Fig. 3.50 - Final moment and axial force diagrams result-ing from example transverse analysis

1. Transverse bending moments are influencedconsiderably by torsion to the extent that maxi-mum moments occur at places other than expectedin the case of a regular frame [compare Figs.3.45 (a) and 3.50 (a).]

2. Transverse axial tensile forces cannot be neglect-ed since they increase the required amount of rein-forcement. These forces are particularly signifi-cant in the bottom slab.

3. Axial compressive forces reduce the requiredamount of reinforcement. This is particularlysignificant in the webs at the connection with thetop slab. At these points, compressive forces arehigh and occur simultaneously with high moments.

4. Corner moments as given in Figs. 3.48 (a) and3.49 (a) caused by loading indicated in Figs.3.46 (c) and 3.46 (d) may be approximatelycalculated as Pe/8 where P is the vertical or hori-zontal force, and e is the width and depth of thebox respectively.

5. When span/depth ratios are constant, longitud-inal bending has very little influence on trans-verse moment distribution.

58

3.4.7 Transverse Temperature Effects

Tensile stresses in the box girder cross sectionmay be generated by the following temperatureeffects:

1. At sections near the supports, the relativelythin top slab may cool much more rapidlythan the thicker bottom slab. This willcause tensile stresses around the exterior ofthe cross section.

2. With strong and prolonged sun radiation onthe bridge surface, the air in the interior of ahollow box girder may become heated toover 100’ F (38’ C). When the outer aircools during the night, the temperature dif-ference between the interior and outer airproduces transverse flexural moments in thewebs and slabs which cause tensile stressesaround the exterior of the cross section.Fig. 3.51 shows the moments and stressesin a single cell box girder at midspan and atthe support for a temperature difference of27O F (15’ C) between the air inside andoutside the box.(12)

3. Thick concrete elements exposed to intensesun radiation are subject to substantial ten-sile stresses when the exterior surfaces cooldue to the lag in response of the interior con-crete to the temperature change.

The significant tensile stresses shown for thebridge section in Fig. 3.51 illustrate the desir-ability of avoiding the use of thick concrete websand slabs which are highly rigid with respect totransverse flexure. The flexural stiffness is, ofcourse, a function of both the thickness and lengthof the structural element. This factor becomesmore significant when the transverse temperaturestresses are combined with the transverse tensilestresses in webs that result from the transversepost-tensioning of deck slabs as discussed in Sec-tion 3.5. The -joint between the web and bottomslab near supports is a point where the combinedtensile stresses may become high, and, at this point,it is particularly important that any cracks whichmay result from the various effects be anticipatedin the design. These tensile stresses and potentialcracks may be accommodated by use of a conser-vative design of nonprestressed shear reinforce-ment, or by the use of prestressed stirrups. Thelatter option has the advantage of providing amuch higher degree of assurance against crackingin the webs.

.

3.5 Analysis and Transverse Post-TensioMgof Deck Slabs

3.5.1 Live Load Plus impact Analysis

Analysis for live load plus impact momentsand shears in deck slabs of precast segmentalbridges requires consideration of the effect of con-centrated loads on variable depth plates whichare integral parts of a tubular frame. Design of suchslabs is accomplished by use of charts of influencesurfaces for variable depth plates.‘gv lo)

For cantilever slab moments, the use of the in-fluence charts simply requires computing the sum-mation of the ordinates of the wheel loads plottedon the influence surface and multiplying by themagnitude of the wheel load to obtain the mo-ment per unit length for the point under considera-tion. For interior span positive moments, theinfluence surfaces are used to determine fixed endmoments for various positions of the load. Thefixed end moments are then used in a frameanalysis to determine the effects of live load onthe frame.

More extensive discussion of calculation of liveload moments using influence surfaces and a de-sign example for a transversely post-tensioned deckare presented in “Post-Tensioned Box GirderBridge Manual” published by the Post-TensioningI nstitute.(lg)

The analysis of two or more box girders con-nected by a common slab requires considerationof the flexural and torsional restraints at supportsas well as the flexural and torsional response ofthe box girders and the connection slabs. Thisanalysis may be accomplished by an extension ofthe analytical procedures described in Section3.4. A detailed procedure to accomplish this analy-sis has been published.“” Alternatively, the analy-sis of single or multiple cell box girder sectionsmay be made by use of one of the available com-puter programs.

3.5.2 Transverse Post-Tensioning of Deck Slabs

Transverse post-tensioning of deck slabs offersthe following advantages in comparison with non-prestressed transverse reinforcement:

1 The deck slab thickness is reduced with re-su lting reductions in concrete quantitiesand dead load moments and shears.

2 Longer slab spans may be achieved whichpermits reduction in the number of websrequired in wide structures. This reducesforming costs and concrete quantities.

59

Mid spancross-section

Supportcross-section

II11 ft. = 0.3048 m1 in. = 25.4 mm1 ft.-k/ft. = 0.45 t-m/m1 psi = 0.0069 MPa

2.82 - 41.51

-

Transverse bending moment in ft-kips/ftfor temperature difference T, - Ti = 27°F (15°C)

Corresponding Point 1’ ”1 2’ 2”

Edge Stresses Span 5564 *220 +485 + 6 8

(psi) Support ?483 f 8 4 +446 +446

- 7.78

Fig. 3.51 - Transverse moments and stresses due to a temperature difference of 27OF between the outer and inner surfaces of abox girder(“)

60

3 A high level of assurance is provided againstthe development of longitudinal cracking inthe deck slab. This provides a more durabledeck with minimal potential maintenancecosts.

4 In the area of top slab anchorages, such asillustrated in Fig. 2.8, transverse compres-sion is helpful in counteracting tensile stressesin the slab which result from concentratedanchorage forces.

5 For wide segments, the use of transversepost-tensioning in the deck slabs usuallyresults in reduced overall structure cost.

Transversely post-tensioned deck slabs also nor-mally have transverse and longitudinal nonpre-stressed reinforcement in the top and bottom ofthe slab. This contributes to the flexural capacityof the slab in ultimate strength calculations andprovides the necessary flexural capacity to permitremoval of the section from the forms and handl-ing prior to stressing of the transverse tendons.The transverse post-tensioning is proportioned tolimit the tensile stresses in the deck slabs to thedesign values. Subsequently, the slab is checked

to see if the combined prestressed and nonpre-stressed reinforcement in the transverse directionis sufficient to meet the load factor requirements.If not, the amount of either the prestressed ornonprestressed reinforcement should be increasedas required.

Tendon profiles for transverse deck slab rein-forcement may vary depending on the type of ten-don material and on other design and constructionrequirements. Tendon geometry used for the Kish-waukee River Bridge is shown in Figs. 3.52 and3.53. Fig. 3.52 illustrates the use of bar tendons,and Fig. 3.53 the geometry proposed in the designdrawings. The placement of the bar tendons inthe center of the slab was selected in this case toprovide a means of support for the longitudinaltendons. While this increased the required amountof transverse post-tensioning by about 30 percent,this increase in cost was offset by reduction inlabor requirements for placement of the longitud-inal tendons. The tendon profile shown in Fig.3.53 was selected to more closely approximatethe moment diagram.

One additional factor that must be consideredwhen transverse post-tensioning of the deck slabis used is the effect of the transverse elastic short-

I

E Sor Qirder(Symm.)

i

Fig. 3.52 - Transverse and longitudinal post-tensioning, Kishwaukee Bridge, Illinois

1 ft. = 0.3048 m1 in. = 25.4 mm

Fig. 3.53 - Transverse tendon geometry from design drawings, Kishwaukee River Bridge, Illinois

ening of the deck slab in generating Wditionaltransverse moments and stresses. The lateral bend-ing of the webs sets up fixed end moments thatmust be distributed throughout the transverseframe. An analysis of this effect on a cross sec-tion of a post-tensioned box girder bridge cast-in-place on falsework is shown in Fig. 3.54.“”For wide sections, such as this, relatively hightensile stresses are generated by the slab short-ening. Even in narrower sections that might beexpected in a precast segmental bridge, this effectmay be substantial and should be considered inthe design. These stresses become highest near pierswhere th& transverse frame elements are thickest.A design check should be made to assure thatstresses resulting from transverse post-tensioningof the deck slab, in conjunction with the transversetemperature stresses discussed in Section 3.4.7,dre not sufficiently high to cause cracking atthe bottom exterior corner as illustrated in Fig.3 55 (“) The magnitude of these stresses and the. .potential for crack development are minimizedby use bf the thinnest possible concrete sectionsconsistent with strength requirements and withsegment design recommendations presented inChapter 2.

3.6 Analysis and Correction of Deformations

3.6.1 General

The development of segmental construction hasmade it economical to build slender concretebridges with long spans. As a result, the magnitudeof the deformations and deflections may be in-creased to such an extent that they require moreattention and usually need adjustment during con-struction. The amount of deformation is furtherincreased by erection of a structure in free can-tilever. The deformations require correction of thegeometry of a structure during segment fabrica-tion which can only be based on an effective pre-diction of the deformations.

Erection of a typical span in a multispan bridgeusually starts at a pier by placing segments alter-nately on both sides in free cantilever until mid-span is reached. The newly erected cantilever isthen connected to the completed part of the struc-ture by casting the midspan splice. This procedureis repeated for each additional span, however, withdifferent resulting deformations since these dependon the statical system in which the addition takesplace. Obviously, this statical system changes

62

V, = 67.197 lb//f 13.12’ 1 3 . 1 2 ' 1 3 . 1 2 ' 1 3 . 1 2 ' 1 3 . 1 2 ' V, = 67,197 lb//f

j-$m3-- ~j+&~--

- - - -

.-. -.

2 't

I

I IMidspan cross-section

1 f t . = 0 . 3 0 4 8 m1 I".= 25.4 mm1 ft.-k/ft = 0.45 t-m/m1 ps, = 0.0069 MPa

Correspondingedge stresses(psi1

PomtMidspanSupport

1’ 1 " 2 ' 2"t295 ?130 t309 t 31

+488 t 54 ?766 +340

Fig. 3.54 - Transverse bending moments due to normal force component of post-tensioning in deck slab”2)

Bridge axis+

Fig. 3.55 - Potential cracking due to temperature stresses

and elastic shortening of slab due to transverse post-tension-ing(12)

numerous times in the construction process. Theanalysis of deformations therefore implies the sum-mation of deformations in all successive inter-mediate phases. This is a tedious and complex,but, nonetheless unavoidable, aspect of the designcalculations.

3.6.2 Analysis

Important contributions to deformations, elasticas well as creep, are made by self weight, prestress-

63

ing (cantilever, continuity, and losses), and deadload. As mentioned above, total deformationsare obtained by summing up the contributions ofeach intermediate phase of construction. Also,the changes occurring after completion of thestructure are added. The various phases are:

Phase A:Phase B,B’:

condition of free cantileverintermediate phases (connection ofa new cantilever to completedstructure)

Phase C: completed structure

Deformations are either hand or computer calcu-lated. In the latter case, the influence of time de-pendent properties such as modulus of elasticityof concrete, influence of creep, shrinkage, andrelaxation losses on tendon forces, and differencesin the creep factors of individual segments can beintegrally entered into the calculations. In the caseof hand calculations, this is not feasible and sim-plifications are needed.

The following sections are based on the assump-tion of hand calculated deformations. It is com-mon practice to consider deformations due tobending moments only, since those by axial andshear forces are usually negligible.

3.6.2.1 Phase A - Free Cantilever

Loading conditions are:1. Elastic deflection due to self weight.2. Elastic deflection due to initial cantilever

prestress.3. Creep deformation of 1 and 2 for the dura-

tion of this phase.

The deflected shape of the completed cantilever iseasily calculated. Elastic deflections due to selfweight and prestress are calculated assuming aYoung’s modulus of elasticity:

E = 33 w3’2 fi

where f’, = cylinder strength of concrete inpsi at the time of erection

w = unit weight of concrete in lb. per cu. ft.E may be assumed constant for precast segments

after the segment age reaches 28 days.

The prestressing force used for the calculation isthe total of initial tendon forces reduced onlyby friction losses and part of the steel relaxationloss. The relaxation loss is evaluated from a relaxa-tion-time curve based on test results by the steelsupplier, or from typical relaxation curves such asgiven in Figs. 3.56 (a) and 3.56 (b), and an esti-mate of the time the cantilever is in phase A.

This time is also needed for the determination ofthe contribution of creep to the deformations.Steel relaxation varies significantly for differentpost-tensioning materials (wire, strand or bar),and low relaxation materials are available (relax-ation losses for low relaxation strand are in therange of 25 percent of the values in Fig. 3.56 (a)).For this reason, use of relaxation curves for thespecific material to be used is recommended.

Although creep starts from erection of the firstsegment onwards, without the use of a computerit is not practical to calculate total creep deforma-tion as the sum of the effects of each successivestep. A reasonable approximation is obtained whenthe completed cantilever is considered to creepduring a time interval which starts when the can-tilever is halfway complete and ends when a con-nection with the completed structure is made.This time interval is different for each canti-lever arm as illustrated by Fig. 3.57.

Creep deformations are obtained by multiplica-tion of the elastic deformations by a creep factor.The creep factor used here is

4 '2'1 = @d, fld(tZpt, ) + @f,[~f,,-~ftJ for part a

4 t4t2 = #d, (3d(t4-‘2) + @fee[oft4 -aft,] for part b

Fig. 3.56 (a) - Relaxation loss curves for stress-relieved strand

I / iiiitiiiiii I iiiiiiiiiii i iiiiiiiiiii i iiiiiwiI ,I,I I I

f,, = 700”.-Ii

30 50TIME-HOURS

YEARS

64

I

(b) - Relaxation loss curves for 150 K 1% in. diameter bars (1030 MPa - 32 mm@)

The sequence of erection and the time schedule

rckx.ed at t2 -closed at t4

must be known or assumed prior to the start of

‘ri time scale “t”

the deformation calculations.

t4to t1 t2 t3

part “a” of cantilever I creeps during interval t2-t,part “b” during t4-t2

hA

Fig. 3.57 - Effect of construction sequence on creep time

interval as a free cantilever

3.6.2.2 Intermediate Phases B,B’

Deformations in this phase are those from:

1. The weight of cast-in-place splices.2. Continuity prestress in the span considered.3. Continuity prestress in the adjacent spans.4. Creep deformation resulting from 2 and 3

above.

The required calculations are simplified if car-ried out for a simply supported span. The effectof fixity may be treated separately and may thenbe added to the simple span calculations. Fig.3.58 illustrates this procedure. Span BC is assumedto be part of a structure with a number of equalspans. After application of continuity prestress,this span is “loaded” with the concentrated load V,the weight of the midspan splice, and the moment-area of the continuity prestress.

Both these loads cause secondary moments,Fig. 3.58 (b), which affect the deformations ofspan BC and all preceding spans. The total elasticdeformation is obtained by summation of the threebending moment diagrams shown in Fig. 3.58 (c)of the simply supported span BC. Creep deforma-tions are found by multiplying the elastic values bya creep factor. The creep influence is limited tothat part of the creep taking place in the periodbetween closing of the splices in spans BC and CDrespectively. The remainder of the creep deforma-tion is assumed to occur in the final continuous

65

I-

TIME IN HOURS

Fig. 3.56

I

lb)

(dJ

A B c D

Fig. 3.58 - Superstructure deformations in phase 8

system. With reference to Fig. 3.57, the creep fac-tor to be used is:

# (t4t2) = @d, fld(t,yt2) + @f, [oft,- “fq

The total deformation is shown in Fig. 3.58 (d)indicating a rotation over pier C, bringing down theforward cantilever arm. Also, this rotation in-creases by creep while the structure is in phase B.Addition of a new span, Fig. 3.58 (e), again causessecondary moments which will affect span BC aswell, Fig. 3.58 (f), and so will the connection ofeach successive span. For this reason, it is easierto calculate the deformation due to secondarymoments after summation of all contributingmoment diagrams. The rotation of each forwardarm, however, must be determined just beforeclosure of the next span.

3.6.2.3 Phase C - Final Continuous System

Deformations in this phase consist of:

1. Elastic and creep deformation by superim-posed dead load.

2. Elastic and creep deformation by prestresslosses.

3. Creep deformations by self weight, cantileverprestress and continuity prestress.

Determination of the elastic deformation bysuperimposed dead load (weight of topping, curbs,railings, etc.) needs no further comment. Thecreep deformation is obtained by multiplicationof the elastic value by @ct, -t,), with t, being thetime of application of the dead load.

For the amount of deformation by prestresslosses, a simplification is made. The total amountof the losses caused by creep, shrinkage and re-laxation is reduced by the part of the relaxationloss deducted in phase A. All other losses are con-sidered to take place in the final system. Thisnegative prestressing force F again causes elasticand creep deformation and is written, therefore, ina simplified form as:

where F i = initial prestressing force

Ff = final prestressing force

t , = time of completion of structure

The determination of the creep deformationsby self weight and prestressing in the completedstructure is based on the solution presented inSection 3.3. Evaluation of the creep deformationsin this phase can be restricted to those occurringin the final system. The creep effects of the inter-mediate phases B,B’ are then neglected; theerror is small, since the most important contri-bution, the creep of the forward cantilever arm,has been taken into account. After a few spanshave been completed, the statical system duringconstruction closely resembles the final com-pleted structure.

3.6.3 Alignment

The need for correction of deformations shouldbe investigated for all precast segmental bridges.The use of match-cast joints makes alignment cor-rections during construction awkward and un-desirable. In the casting yard, corrections are al-ways minor and are easily accommodated by thecasting equipment. Adjustments of alignment canbe made during construction by use of stainlesssteel shims in the joints. The following procedureof alignment correction for a bridge with severalequal spans illustrates the principles. Correctionsconsist of those resulting from deformation, ro-tations, and superimposed curvatures.

66

3.6.3.1 Correction of Deformations

The correction curve of each cantilever armequals the deformation curve but with oppositesign. Typical deflection curves are shown in Fig.3.59. The theoretical curve is approached bystraight lines one or more segments long. Thedifference between a curve and approximatingstraight lines obtained in this way is not visibleprovided the angular changes are kept below 0.001radians as shown.

As indicated in Section 3.6.2.2, the deforma-tion of the forward cantilever arm will be differ-ent from the backward arm, because of differentcreep behavior and the rotation caused by con-tinuity prestress. Although it is possible to makeadditional corrections during casting for forwardand backward cantilever arms, it proves simplerto make such corrections by counter rotations.

correction /

Fig. 3.59 - Typical deflection curves

3.6.3.2 Correction of Rotation

Due to continuity prestressing in the end span,the forward cantilever arm rotates over an angle CYas shown in Fig. 3.60. A similar rotation p occursin the subsequent spans. Starting erection of thefirst cantilever with a counter rotation of ~1 - %(3would bring the forward cantilever arm to a slopeof ‘43 after stressing of the end span continuitytendons. The subsequent span then automaticallystarts with a counter curve of %p as well, and thissituation repeats itself until completion of thestructure as shown in Fig. 3.61.

The continuity prestress obviously affects notonly the forward cantilever arm but also the re-mainder of the completed part of the structure.However, the resulting up and downward curvesfrom this source are usually part of the deforma-tion corrections made in the form. This also ap-plies to the angle changes occurring at the splices.

3.6.3.3 Correction of Superimposed Curvature

The desired alignment of most bridges differsfrom a straight line. Provided the casting forms

,.

*

Fig. 3.60 - Cantilever rotations due to continuity post-tensioning

Fig. 3.61 - Correction for rotations due to continuity

post-tensioning

Fig. 3.62 - Correction for roadway curvature

used are sufficiently adaptable, any shape ofbridge, including vertical curves, horizontal curves,superelevation, etc., can be achieved by superim-posing the difference between the desired curva-ture and the straight axis (the shaded area of Fig.3.62) on the corrections previously described.

3.6.3.4 Example Alignment Calculations

Part of a bridge is shown in Fig. 3.63. The de-flection X of span LM is the value calculated forthe sum of elastic and creep deformations causedby the continuity prestress of all adjacent spans.The camber Y of span MO and the rotation ofthe forward cantilever arm OP are those calculatedfor elastic and creep deformations caused bycontinuity prestress of span MO only. It is clearthat corrections for span MO will be based on areduced camber Y - X. After erection, the de-flected shape of the cantilever arms NOP (support

67

Fig. 3.63 - Example alignment calculations \

Fig. 3.64 - Deflected shape of cantilever after erection

012

Fig. 3.65 - Correction of deflected cantilever geometry toobtain a straight axis

= 0) will be as indicated in Fig. 3.64. The correc-tion to obtain a straight axis, shown shaded in Fig.3.65, is arrived at by:

1. Drawing the deformation line a due to contin-uity prestress in all spans (Y-X in Fig. 3.63).

2. Reducing curve a by the free cantilever de-flection, resulting in curve b.

3. Rotation of the axis by an angle %p.

Verification of this result is illustrated in Fig. 3.66:

1. The correction is introduced with oppositesign in curve d.

2. The free cantilever deflection is superimposedin curve e.

3. The rotation of %(3 is added in curve f. In thissituation the midspan splice is cast.

4. Continuity prestress is added resulting incurve g.

5. Deflection by continuity prestress of all ad-jacent spans results in the final geometry h.

Fig. 3.66 - Summation of geometry corrections

The discontinuity at 0 does not exist since MOis the final bridge axis after step 5, whereas OPshows the situation after step 4 only.

3.6.3.5 Notes on Alignment Calculations

1. With the procedure illustrated in Figs. 3.63through 3.66, only the deformations during con-struction are covered. After completion, addi-tional deformations will occur. These can betreated, if found to be of considerable magni-tude, similar to corrections of superimposedcurvature as described in Section 3.6.3.3.

2. The corrections described are based on deforma-tion calculations. It is essential to check the re-sults of such calculations by field measurements.Such comparative measurements should alwaystake place in the morning at the same hour inorder to minimize the considerable effect ofmovements due to temperature variations.

3.7 Computer Programs

3.7.1 General

In some cases, hand calculations may be suffi-ciently accurate for the final design of a precastsegmental bridge. However, for more complexsuperstructures, the use of a computer program toassist in the analysis becomes most helpful. Fur-ther, the calculation of deflections becomesvery cumbersome by hand unless substantial ap-proximations are introduced, and a computer pro-gram is an invaluable aid in providing a more pre-cise estimate of time-related deflections. Thesources listed below have programs developed oradapted specifically for use in design of precastsegmental bridges. Additional programs undoubt-edly exist that could be used more or less directlyto analyze precast segmental bridges.

68

i.

3.7.2 Sources of Computer Programs

Detailed information on computer programservices may be obtained from the following:

Dyckerhoff & Widmann, Inc.529 Fifth AvenueNew York, New York 10017(2 12) 953-0700

Engineering Computer CorporationP.O. Box 22526Sacramento, California 95831(916) 922-9316

Europe Etudes BC ProgramThe Preston Corporation2426 Cee GeeSan Antonio, Texas 78217(512) 828-6264

Center for Highway ResearchThe University of Texas at AustinAustin, Texas 72717

Segmental Technology and ServicesP.O. Box 50825Indianapolis, Indiana 46520(3 17) 849-9686

University of California at BerkeleyDepartment of Civil EngineeringBerkeley, California 94720

,

CHAPTER 4

FABRICATION, TRANSPORTATIONAND ERECTION OF PRECAST SEGMENTS

4.1 Fabrication of Precast Segments” 4,

4.1 .l General Considerations

During design of a segmental structure, consider-ation should be given to the formwork necessaryto achieve economy and to obtain efficiency inproduction. It is generally preferable to use as fewunits as possible, consistent with economic ship-ping and erection.

In the case of girder segments, economy andspeed of production may be increased by:

1 .

2.

3.

4.

5.

6.7.

8.

9.

10.

11.

Keeping the length of the segments equal andkeeping them straight, even for curved struc-tures.Proportioning the segments or parts of them,such as keys and web stiffeners, in such a waythat easy stripping of the forms is possible.Maintaining a constant web thickness in thelongitudinal direction.Maintaining a constant thickness of the topflange in the longitudinal direction.Keeping the dimensions of the connectionbetween webs and the top flange constant.Bevelling corners to facilitate casting.Avoiding interruptions of the surfaces of websand flanges caused by protruding parts foranchorages, inserts, etc.Using a repetitive pattern, if practical, fortendon and anchorage locations.Minimizing the number of diaphragms andstiffeners.Avoiding dowels which have to pass throughthe forms.Minimizing the number of blockouts.

Variation of the cross section of girder segments isgenerally limited to changing the depth and widthof the webs and the thickness of the bottomflange. Curves in the vertical and horizontal direc-tion and twisting of the structure are easily ac-commodated.

Segmental construction is distinguished by thetype of joint between elements. The followingtypes have been used:

1. Wide (broad) joints (this type of joint is notconsidered in the design procedures presentedin this manual).

2: Match-cast joints.

The precision of line of segments assembledwith wide joints depends mainly on the accuracy

71

of the casting of the joints during erection and lesson the accuracy of the segments. Curvature andtwisting of the structure may be obtained withinthe joint.

The principle of the match-cast joint is that theconnecting surfaces fit each other very accurately,so that only a thin layer of filling material isneeded in the joint. Each segment is cast againstits neighbor. The sharpness of line of the assembledconstruction depends mainly on the accuracy ofthe manufacture of the segments.

4.1.2 Methods of Casting

Segments to be erected with wide joints may becast separately. Match-cast joint members are castby the “long-line” or “short-line” method.

4.1.2.1 The Long-Line Method

Principle-All of the segments are cast, in theircorrect relative position, on a long line. One ormore formwork units move along this line. Theformwork units are guided by a pre-adjusted soffit.An example of this method is shown in Figs. 4.1through 4.3

Advantages-A long line is easy to set up and tomaintain control over the production of thesegments. After stripping the forms it is notnecessary to take away the segments immediately.

Disadvantages-Substantial space may be re-quired for the long line. The minimum length isnormally slightly more than half the length of thelongest span of the structure. It must be con-structed on a firm foundation which will notsettle or deflect under the weight of the segments.In case the structure is curved, the long line mustbe designed to accomodate the curvature. Becausethe forms are mobile, equipment for casting,curing, etc., has to move from place to place.

4.1.2.2 The Short-Line Method

Principle-The segments are cast at the sameplace in stationary forms and against a neighboringelement. After casting, the neighboring element istaken away and the last element is shifted to theplace of the neighboring element, clearing thespace to cast the next element. A horizontal cast-ing operation is illustrated in Figs. 4.4 through 4.6.Segments intended to be used horizontally mayalso be cast vertically. A photograph of a short-line form is presented in Fig. 4.7.

Advantages-The space needed for the short-

R n

Formwork

\ Soffit

Fig. 4.1 - Cross section of formwork using long-line method(14)

/Outside Fotmwork

Inside Formwork

ELEVATION

1 I

PLAN

Fig. 4.2 - Start of casting (long-line method)(14)

ELEVATION

PLAN

Fig. 4.3 - After casting several segments (long-line method)(‘4)

72

AFTER STRIPPING 0 L D DURING CASTING

;’ FORMWORK “,

=+#t+# f# - C A R R I A G E

hJRNBUCKLES’-

Fig. 4.4 - Formwork for short-line method(‘4)

@ido Formwork /Bulkhead

Fig. 4.5 - Just before separation of segments (short-line method)‘14)

Fig. 4.6 -Just before casting next segment (short-line method)(‘4)

73

Fly. 4 7 Shott line form used for Purls Belt Brdges”)

line method is small in comparison to the long-line method, approxim&tefy ttiree times the lengthof a segment. The entire process is centralized.Horizontal and vertieaf c-urves and twisting ofthe structure are obtained by adjusting the po-sition’of the neighboring segment.

Disadvantages-To obtain the desired structuralconfiguration, the neighboring segments must beaccurately positioned.

4.1.3 Formwork

Formwork must be designed to safely supportall loads that might be applied without. undesireddeformations or settlements. Soil stabilizat$n OPthe foundation may be required, or the forr&ork~may be designed so thaf adjustments can be made + .

Special consideration must be given to thoseparts of the forms that have to change in dimen-sions. To facilitate alignment or adjustment, spec-ial equipment such as wedges, screws, or hydraulicjacks should be provided. Anchorages of thetendons and inserts must be designed in such away that their position is rigid during casting.Fittings must not interfere with stripping of theforms. If accelerated steam curing using tempera-

ture in excess of approximately 160’ F (71’ C) isforeseen, the .influences of the deformations of theforms, caused- by heating and cooling, must be.: 1

to compensate for settlement.Since prodUction of, segments is based onreusing‘

the forms as much aspossible,.the formwork must_be sturdy and s$%ai attention must be giLen toconstruction details. Forms must also be easy tohandle. Paste leakage through formwork jointsmust be prevented. This can normally be achievedby using a flexible sealing material. Special atten-tion must be given to the junction of tendonsheathing with the forms. The forms may need to

-* consid&e$‘ig prder to avoid development of cracksin the -concrete. External vibrato& must beattached at locations that will achieve maximumconsolidation and permit easy exchange duringthe casting operations. Internal vibration mayalso be required.

be flexible in order to accomr%date slight dif-ferences of dimensions with the previously castsegment. They must be designed in such a waythat the.. necessary adjustments ior the desiredcamber, curvature and twisting can be ‘achievedaccurately and easily.

Holes for prestressing tendons may be formed by:

1. Rubber hoses which are pulled out after harden-ing of the concrete.

2. Sheathing which remains after hardening of the

concrete. Flexible sheathing made out of spirallywound metal is usually stiffened from the insideby means of dummy cables, rubber or plastichoses, etc., during the casting operation.

3. Rigid sheathing with smooth or corrugated wallsmay be ,used that will not deform significantlyunder the pressure of wet vibrated concrete andfor which there is no danger of perforation.

4. Movable mandrels.

Holes must be accurately positioned, particu-larly when a large number of holes is required.Horizontal and vertical tolerance for tendonholes within the segment should not exceed +%in. (13 mm) from the theoretical location. Ten-don ducts shall be match-cast in alignment atsegment faces.

Formwork that produces typical box girdersegments within the following tolerances is con-sidered good workmanship.

Width of web. . . . . . . . . . . . . . +3/8 in. (10 mm)Depth of bottom slab. . . ~‘~t00in.(13mmt00)Depth of top slab . . . . . . . . . . . &l/4 in. (6 mm)Overall depth of segment. . . . . . *l/4 in. (6 mm)Overall width of segment. . . . . . *l/4 in. (6 mm)Length of match-cast segment. . +_ l/4 in. (6 mm)Diaphragm di’mensions . . . . . . ?1/2 in. (13 mm)Grade of roadway and soffit . . . .+1/8 in (3 mm)Depending upon the detail at bridge piers, the

tolerances for the soffit of a pier segment may needto be limited to *l/16 in. (1.6 mm). The toleranceof a segment should be determined immediatelyafter removing the forms. If specified tolerancesare exceeded, acceptance or rejection should bebased on the effect of the over-tolerance on finalalignment and on whether the effect can be cor-rected in later segments. In match-cast construc-tion, a perfect fit is established between segments.Limits for smoothness and out-of-squareness ofthe joint should be established.

4.1.4 Concrete

Uniform quality of concrete is essential for seg-mental construction. Procedures for obtaininghigh quality concrete are covered in PCI and PCApublications.“6*‘6’ Both normal weight andstructural lightweight concrete can be made con-sistent and uniform with proper mix proportioningand production controls. Ideal concrete for seg-mental construction will have as near as practicalzero slump and 28-day strength greater than thestrength specified by’ structural design. It is rec-ommended that stati&caI,methods be used to eval-uate concrete mixes. *

The methods and procedures used to obtain the

75

characteristics of concrete required by the designmay vary somewhat depending on ‘whether thesegments are cast in the field or in a plant. Theresults will be affected by curing temperatureand type of curing. Liquid or steam curing orelectric heat curing may be used.

A sufficient number of trial mixes must be madeto assure uniformity of strength and modulus ofelasticity at all significant load stages. Carefulselection of aggregates, cement, gdmixtures andwater will improve strength and modulus of elas-ticity and will also reduce shrinkage and creep.Soft aggregates and poor sands must be avoided.Creep and shrinkage data for the aggregates and/orconcrete mixes should be available or should bedetermined by tests.

Corrosive admixtures such as calcium chloridemay not be used. Water-reducing admixtures andalso air-entraining admixtures which improveconcrete resistance to environmental effects suchas deicing salts and freeze and thaw actions arehighly desirable. However, their use must berigidly controlled in order not to increase undesir-able variations in strength and modulus of elastic-ity of concrete. The cement, fine aggregate, coarseaggregate, water and admixture should be com-bined to produce a homogeneous concrete mix-ture of a quality that will conform to the mini-mum field test and structural design requirements.Care is necessary in proportioning concrete mixesto ensure that they meet specified criteria. Reliabledata on the potential of the mix in terms ofstrength gain and creep and shrinkage performanceshould be developed for the basis of improveddesign parameters. Proper vibration should be usedto afford use of lowest slump concrete and toallow for the optimum consolidation of the con-crete.

4.1.5 Joint Surfaces

Requirements concerning surface quality mustbe stricter for match-cast joints than for widejoints filled with mortar or concrete. Surfacesshould be oriented perpendicular to the painpost-tensioning tendons to minimize shearingforces and dislocation in the plane of the jointduring post-tensioning. Inclination with respectto a plane perpendicular to the longitudinal axis ispermitted for joints with assured friction resis-tance. The inclination should generally not exceed20 degrees. Larger inclination, but not more thanapproximately 30 degrees may be permitted if theinclined surface area is located close to the neutralaxis and does not exceed 25 percent of the total

joint’s surface area.For match-cast joints, the surface, including

formed keys, should be even and smooth, to avoidpoint contact and surface crushing or chippingoff of edges during post-tensioning. Holes orsheathing for tendons must be located very pre-cisely when producing segments joined by post-tensioning. Care is required to prevent leakage orpenetration of joint-fil l ing materials into theduct, blocking passage of the tendons.

4.1.6 Bearing Areas

Bearing areas at reactions should be even, with-out ridges, grooves, honeycomb, etc., to assureuniform distribution of bearing forces. It may bedesirable to place bearing elements like pads orsteel plates in the forms before casting. Other-wise, cement mortar or epoxy may be requiredon contact surfaces.

4.2 Handling and Transportation of PrecastSegments” 4,

Segments should be handled carefully in amanner that limits stresses to values compatiblewith the strength and age of the concrete. It shouldbe verified that the segment weights are less thanthe capacity of the lifting equipment. Highway andsite transportation may produce dynamic stresseswhich may be considered by use of an impactcoefficient. Special care of cantilever projections isoften needed to prevent cracking. Location of lift-ing hooks and inserts should be determined care-fully to avoid excessive stresses in the segmentduring handling, and they should have a safetyfactor of 1.75 to 2.00 when all loads and stresseshave been considered. Storage of units at the siteshould be arranged to minimize damage, deflec-tion, twist, and discoloration of the units. Stock-piling should be limited to avoid excessive director eccentric forces. Special precautions may berequired to avoid settlement of foundations madeto support the stored segments. Inserts, anchoragesand other imbedded items may need to be pro-tected from corrosion and from penetration ofwater or snow during cold weather. In cases whereextensive transportation of segments is required,it is recommended that a segment should not beerected before it is certain that the subsequentsegment has been safely transported.

4.3 Methods of Erection’7*20)

4.3.1 Cranes

Mobile cranes moving on land or floating onbarges are commonly used where access is availableas illustrated in Fig. 4.8. Occasionally, a portalcrane straddling the deck has been used withtracks installed on temporary trestles on eitherside of the bridge. The capacities of cranes readilyavailable in the United States and Canada makesthis method of erection more attractive than it isin Europe.

4.3.2 Winch and’ Beam

In this method, illustrated in Fig. 4.9, a liftingdevice attached to an already completed part ofthe deck raises the segments which have beenbrought to the bridge site by land carrier or barge.The segments are lifted into place by winchescarried at deck level on a short cantilever mechan-ism anchored on the bridge. In the first applica-tions of this type of erection in Europe, the seg-ment over the pier had to be placed independently(either cast-in-place or handled by a separatemobile crane). Recently, this drawback has beenovercome. Now the precast pier segment may beplaced on the pier with the same basic equipmentcantilevered temporarily from a tower attachedto the pier.

4.3.3 Launching Gantry

In this method, a special machine travels alongthe completed spans and maintains the work flowat the deck level. The crane gantry, which wasfirst used for the Oleron Viaduct, has contributedsignificantly to the development of precast seg-mental construction. The principle behind seg-mental erection using the crane gantry system isshown in Fig. 4.10. An essential component inthe system is a truss girder which has a length some-what greater than the maximum bridge span. Thesystem consists essentially of:

1. A main truss where the bottom chords act asrolling tracks.

2. Three-leg frames which may or may not be fixedto the main truss. The rear and center framesallow the segments to pass through them longi-tudinally.

3. A trolley which can travel along the girder andis capable of longitudinal, transverse, andvertical movement as well as horizontal rotations.

Fig. 4.8 - Segment erection by crane, Corpus Christi Bridge, Texas

Fig. 4.9 - Winch and beam erection, St. Andre de CubzacBridge, France(‘)

52.00 54.00f ~~106.00 I

t

i 106.00 t

Fig. 4.10 - Operational stages of a launching gantry (firsttype)(‘)

To complete a full construction cycle for a typicalspan, the gantry assumes three successive positions:

1 .

2.

For placing typical segments in cantilever, thecenter leg rests directly over a pier while therear leg is seated towards the end of the pre-viously completed deck cantilever [Fig. 4.10(a)].For placing the segment over the adjacent pier,the girder is moved along the completed deckuntil the ceder leg reaches the end of the can-tilever. The front leg rests on a temporary cor-bel fixed to the pier while the pier segment isplaced and adjusted into position [Fig. 4.10 (b)l .

3. Finally, the segment placing trolley is used as alaunching cradle with the help of an auxiliarytower bearing on the newly placed pier seg-ment. The gantry is then transferred to its initialposition one span further thus allowing the seg-ment placing cycle to repeat itself [Fig. 4.10

(c)l .For structures combining vertical and horizon-

tal curvatures, including variable superelevation,the launching gantry can be designed to followthe geometry of the bridge while maintainingoperational stability and segment placing capa-bility. In the last few years, several importanttechnical improvements have been made in gantrydesign. These advancements are exemplifiedstarting at the Chillon Viaduct in Switzerland,and later at the Saint-Cloud Bridge where 143-ton (130 t) segments were easily placed in a 337ft. (102 m) span with a 1090 ft. (332 m) radiusof curvature (see Figs. 3.4 and 4.11). It should benoted that, on certain structures, a somewhatdifferent approach is used in designing the launch-ing gantry system (see Fig. 4.12). The total lengthof the truss girder is now slightly greater thantwice the maximum span length. In this system,all three gantry supports rest directly over a pier.Although the investment cost is higher in thissystem than in the original concept, this type ofgantry has several advantages:

1. The completed deck carries no gantry reactions.2. Stability against unsymmetrical loading due to

unbalanced cantilever erection may be pro-vided by the gantry.

3. The pier segment may be placed and adjustedduring the normal placing cycle for the preced-ing cantilever spans.

4. Construction time may be further reduced iftwo placing trolleys are used.

In this advanced system, segments may bemoved in place over the completed bridge orbeneath the bridge. This procedure was used on thelarge Rio-Niteroi Bridge where all segments werefloated on pontoons and lifted into place by four540 ft. (164 m) long launching gantries weighing400 tons (363 t) each (see Fig. 4.13). A similarapproach was also used for the 83 South Via-ducts near Paris.

4.3.4 Progressive Placing

The latest development of precast segmentalconstruction embodies the concept of progressiveplacing. This approach actually comes directlyfrom cantilever design. Here, segments are placed

Fig. 4.11 - Launching gantry, St. Cloud Bridge, Parist7)

/ ’F ig . 4 .12 r .Operationat stag& of a launching gantri~

, (second ty&)“‘t‘% */ j: 1 ‘t

continuously from one ‘end ‘of tfie deck to the.,other ‘in’successive Cantilevers.ontlie same side ofthe various piers rather than in b’alan&d’cantilever

at each pier. 7

When the-deck reaches one pier, permanentbearings are installed and construction proceedsto the next span. Some noteworthy advantagesof the method are:

1. The operations are continuous and are per-formed at the deck.level.

2. The method seems to be of interest primarily inthe 100 to 160 ft. (30 to 50 m) span rangewhere conventional cantilever construction’ isnot always economical,

3. During construction, the piers are not subjectedto significant unbalanced moments althoughthe vertical reaction is substantially increased.

One disadvantage of the method is that con-struction of the first sqt2must be carried out with,. .a special’system.

It should also be noted that the stresses in’thedeck are completely reversed duringcanstruetionand after completion,_Conseq~uently, special sta-bilization devices m’ust be used temporarily tokeep. the concrete stresses’ within safe limits andto minimize the amount of temporary prestress.A tower and .guy cable system has been used effea-4tively to control theundesirabfe temporary stresses.

Fig. 4.13 - Launching gantry for Rio-Niteroi Bridge, Brazi117’

Figs. 4.14 and 4.15 show schematically the princi-ple of progressive segment placing together withsome of the construction details.

Fig. 4.14 - Construction sequence (elevation) using pro-gressive segment placingt7)

Fig. 4.15 - Construction sequence (isometric view) usingprogressive segment placing17)

4.3.5 Erection Toleranced’ 4,

Maximum differential between outside faces ofadjacent units in the erected position should notexceed l/4 in. (6 mm). The most important itemof tolerance or acceptance is the final geometry ofthe erected superstructure. The evaluation of thedeck surface of each segment used in the cantileverportions of the bridge superstructure, measuredafter closure sections are in place, must not varyfrom the theoretical profile grade elevation bymore than that specified for the project. Thegradient of the deck surface of each segmentshould not vary from the theoretical profile grad-ient by more than 0.3 percent. More liberal tol-erances may be acceptable if the design incorpo-rates a wearing surface.

4.3.6 Design of Piers and Stability DuringConstruction”’

4.3.6.1 Single Slender Piers

If the piers in the finished structure are designedsolely to transfer the deck loads to the foundations(including horizontal loads), there is the likelihoodthat the piers will be unable to resist the unsym-metrical moments due to the cantilever construc-tion (i.e., with one segment plus the equipmentload). Thus, temporary shoring is often required(see Figs. 4.16 and 4.17) at considerable cost.More recently, the stability of the cantilever under

‘SEGMENT WEIGHTS: 60 TO 40 t

- ?.tAX. STATICAL REACTION IN SUPPORT: ,060 ,

PROVISIONAL SUP

1 t = 1.1 ton1 m = 3.28 ft.

Fig. 4.16 - Stability during construction(‘)

construction has been provided by the equipmentused for placing the segments.

With double piers, two parallel walls make upthe pier structure, which usually rests on a singlefoundation. Such a configuration was successfullyused for a number of European bridges, includingthe Chillon Viaduct illustrated in Fig. 4.18. Stabil-ity during construction is excellent and requireslittle temporary equipment, except for somebracing between the slender walls to prevent elas-tic instability.

4.3.6.2 Moment Resisting Piers

Moment resisting piers are designed to with-stand the unbalanced moments during construc-tion while temporary vertical prestress rods make arigid connection between the deck and the piercap. The Corpus Christi Bridge shown in Fig. 4.19utilized moment resisting piers.

When the ratio between span lengths and pierheight allows it, the rigid connection and thecorresponding frame action may be maintainedpermanently between the deck and piers. Thisframe action is also achieved by use of twin neo-prene bearings which allow for deck expansion.

Fig. 4.17 - Temporary erection shoring at pier, Pierre-Benite Bridge, France(‘)

Fig. 4.18 - Twin piers, Ghillon Viaduct,,Switrer21and(‘j

-- --

Fig. 4.19,- Moment resisting piers, Corpus Christi Bridge, TexaO

Fig. 4.20 - Piers with twin neoprene bearings during con-struction(21)

Flat jacks are usually placed between the pier topand the deck soffits to permit the removal oftemporary bearings and installation of the per-manent ones.

a 3

Fig. 4.21 - Twin neoprene bearings in final structure(2’)

This type of pier detail is shown in Fig. 4.20where the elastomeric bearings are indicated as(1 ), the vertical erection post-tensioning betweenpier and super-structure is shown as (21, and thetemporary concrete bearing pads are shown as (3).After completion of erection and continuity post-tensioning, the vertical post-tensioning at the pierand the temporary concrete bearing pads are re-moved, leaving the neoprene bearings in place asshown in Fig. 4.21.

CHAPTER 5

DESIGN EXAMPLE,NORTH VERNON BRIDGE, INDIANA

5.1 General

The North Vernon Bridge over the MuscatatuckRiver in Indiana was built parallel to an existingreinforced concrete arch bridge with the purposeof doubling the capacity of the existing roadway.The spans were therefore fixed to meet those ofthe arch, as indicated in Fig. 5.1. Cost estimatesfor widening the bridge with another arch provedtoo expensive and led to consideration of bothsteel and concrete alternatives. The presence of aprecast concrete plant in the vicinity of the bridgesite, and the feasibility of segment erection bymobile crane made it possible that even this smallstructure with a total deck area of only 8855 sq.ft. (823 m*) could be built competitively usingprecast segmental construction.

5.2 Structure Dimensions

The total bridge length of 381 ft. (116.04 m)is made up of 2 end cross girders of 5 ft. 3 in. (1.6m), 44 segments of 8 ft. 0 in. (2.44 m) length, 2pier segments of 9 ft. 0 in. (2.74 m) length, and acast-in-place splice of 5 ft. 3 in. (1.6 m). The spanand segment dimensions are shown in Fig. 5.2.In consideration of the length of the main span,the depth of the box girder was selected as 9 ft.0 in. (2.745 m). The resulting span/depth ratio of21 .l is well within the economical limits. The boxgirder dimensions and section properties are pre-sented in Fig. 5.3. These dimensions are constant

,I

I2 3 4 5 6 7 6 9 IO II 12 13 1st l5 I6 I7 I6 I9 20 21 22 23 24 25 26

1 m = 3.28 ft.

Fig. 5.1 - Span arrangement

SPANI

SUPPORT

JOINT NUMBERS

a-AREA A (M2)b-DISTANCE CG TO TOP C, (Mlc-MOMENT OF INERTIA I (MO)d-MOMENT OF RESIST 2, lM3)

Zb lM3)e-KERNEL BEAM Kt IM)

Kb (Mlf -THICKNESS BOTTOM D 041

1.0024.02394.01512.31150.555

1.066 1.1224.423 4.7504.1482 4.23282.6378 2.93060.608 0.7050.956 0.9380.252 0.302

1.1514.9084.2683.08240.740.9250.33

Fig. 5.3 - Cross section dimensions and segment properties

for all segments except for the two segments lo-cated on either side of the two pier segments. Inthese segments, the bottom slab thickness wasincreased from 8 in. (0.20 m) to 13 in. (0.33 m)in order to reduce the compressive stress in thebottom fibers resulting from the negative supportmoments.

2xJ3 9 x 2 . 4 4 9 x 2.44

29.8 I*

29.01

1 m = 3.28 ft.

Fig. 5.2 - Segment dimensions and joint numbers

85

5.3 Order of Erection

The erection sequence for the structure is i nthree steps as indicated in Fig. 5.4.

Step 1: The segmental cantilevers are erectedfrom each pier.

Step 2: The precast end cross girders a r eerected.

Step 3: The midspan splice is cast-in-place.

II

a P B

II S T E P I

u,v,S T E P 2

> S T E P 3

Fig. 5.4 - Erection sequence

5.4 Post-Tensioning Details

Except as noted below, the post-tensioning iscarried out by tendons consisting of twelve % in.diameter 270 k strands (13 mm $I, 1862 MPa)with an ultimate force of 495 kips (2202 kN).All tendons are stressed initially to 70 percent oftheir ultimate force. The effective force level inthe example design calculations at time of pre-stressing is reduced to allow for anchor seating andfriction losses. The final tendon forces after lossesare 60 percent of ultimate or lower. ,

The post-tensioning tendons are arranged ingroups as follows:

Group 1:

Group 2:

Group 3a:

Cantilever post-tensioning consists of26 tendons, 13 in each web (See Fig.5.5).Tail span continuity post-tensioningconsists of 2 tendons, one in each web(See Fig. 5.6).Center span continuity post-tensioningconsists of 8 tendons, 4 in each web,located in the bottom slab at midspanand anchored in the top slab (See Fig.5.7).

G R O U P I

Fig. 5.5 - Cantilever tendon layout

Fig. 5.6 - Tail span continuity tendons

201 202 203 2 0 4 3 b.b -1 \ . . \

Y’- .w-- - - - - - <- - tJ - - - \ I-1 ---l-----------.~--J. 2 0 5. .5 \ . .

t. .,

. . .

- - - t=-- L- -a.-,- ---r-- _.-_ __.

TI

Fig. 5.7 - Center span continuity tendons: Bottom slab (Group 3a)251

Top slab (Group 3b)

86

CANTILEVER TENDONS CENTER SPAN CONTINUITY TENDONS-GROUP

I

CENTER SPAN CONTINUITY~EN D O N S

G R O U P 3 a

Fig. 5.8 - Location of tendons (eccentricities)

fig. 5.9 - Loading for erection moment stability

Group 3b: Center span continuity post-tensioningconsists of four 6-strand tendons lo-cated in the top slab. These tendons areanchored in the pier segments (SeeFig. 5.7).

The precise location of the tendons in the sectionis indicated in Fig. 5.8.

5.5 Design Requirements and Loading*

The design is carried out by elastic methodsto meet the following criteria:

1. Concrete bending stresses within allowable limitsfor 5500 psi (38 MPa) concrete.

2. No tension allowed for combinations of allloadings.*

3. Cracking safety under 110 percent of dead loadand 125 percent of live load.*

4. Ultimate load capacity of 115 percent of deadload and 225 percent of live load.*

TAILS~PAN ~C~NTINUITY TENDON

3b

5. Final tendon forces are 60 percent of ultimateor lower.

The design is carried out for loading by:

1. Dead load during construction2. Initial prestress3. Superimposed permanent loads4. Live loads5. Temperature differential6. Creep under box girder dead load7. Creep under post-tensioning8. Loss of prestress

5.6 Design Procedure

The design of the North Vernon Bridge is pre-sented in accordance with the following steps:

Step 1:

Step 2:

Step 3:

Free cantilever plus initial cantileverGroup 1 post-tensioning. Stress control inall phases of erection.Completion of end span plus initial con-tinuity Group 2 post-tensioning. Stresscontrol.Concreting of midspan splice plus initialcontinuity Group 3 post-tensioning. Stresscontrol.

“The design requirements presented here are those selected for theNorth Vernon Bridge and are generally somewhat more conserva-tive than required by current American Association of State High-way Officials’ Bridge Specifications(6). and the PCI Tentative De-sign and Construction Specifications for Precast Segmental Bridgespresented in Appendix Section A.I.

87

Step 4: Addition of permanent loads. Stress con-trol.

Step 5: Addition of variable loads. Stress control.Step 6: Influence of time.Step 6a: Dead load moment redistribution due to

concrete creep. Stress control.Step 6b: Post-tensioning moment redistribution

due to concrete creep. Stress control.Step 6c: Prestress losses. Stress control.Step 7: Final stress controlStep 8: Transverse section analysis.

Other calculations required to complete thedesign are made by procedures common to con-ventional post-tensional box girder bridges or con-ventional reinforced concrete design and are notpresented here. These calculations relate to thefollowing:

1. Calculation of end cross girder and pier segmentreinforcement.

2. Support forces and bearing requirements.3. Road joint movements.4. Principal shear stresses at service load.5. Ultimate moments, safety to failure.6. Ultimate shear, safety to failure.7. Substructure loading during erection.8. Temporary prestressing of segments during

erection.9. Reinforcement of keys.

In all cases, provision must be made to accom-modate additional temporary erection loads onthe structure, and stress and stability checks mustbe made for the structure under these loadings.Such erection loads can be intentional (for exam-ple, movement of a launching girder over the struc-ture), or unintentional (storage of post-tensioningtendons or a large group of visitors on the struc-ture). Consideration of erection loads has beenomitted in the presentation of this design exam-ple for simplicity.

NOTE:

All of the following design example diagrams anddimensions are in c.g.s. metric units

Dimensions = meters (3.28083 ft)Forces = metric tonnes (2204.62 lb)Bending moments = tonnes x meters (7232.98 ft. I b.)Stress = tonnes/sq. meter (1.422 psi)

The relationship to SI metric units is:Force: 1 t = 9.8 kN = 2204.62 lb.

(1 lb. = 4.448 Newtons)Moment: 1 t-m = 9.8 kN-m = 7232.98 ft.-lb.

(1 ft.-lb. = 1.356 kN-m)Stress: 1 t/m2 = 9.8 kPa = 1.422 Ib./in.2

(1 Ib./in.2 = 6.895 kilopascals)

88

5.6.1 Step 1. Free Cantilever Plus Initial Can-tilever Group 1 Post-Tensioning

In Step 1, stresses are calculated for loading dueto the dead load of the free cantilever box girdersection and the Group 1 cantilever post-tensioning.The post-tensioning is shown in Fig. 5.5 and con-sists of 13 tendons in each web. A check is madefor unbalance during erection. The calculations aremade as follows:

1. Calculate the effect on the supporting struc-ture caused by unbalance of segment x+n+l(See Fig. 5.9) Check stability of the assembly.The stability is in this case assured by placingtwo supports on a wide pier.

2. Calculate concrete stresses in each joint dueto dead load of segments x+n+ 1.

3. Calculate forces in the tendons present inthe segments x to x+n. Consider frictionlosses and, if judged necessary, steel relaxa-tion. Subsequently calculate concrete stressesin each joint due to post-tensioning.

4. Comply with stress limitations for all valuesof n in each joint.

At completion of erection of one cantilever,the bending moments are as shown in Fig. 5.10(only half of the cantilever is shown, the otherhalf is identical):

Diagram 5

Diagram 6

Diagram 7

Diagram 8

Diagram 9

Diagram 10

Box girder dead load bending mo-ments (t-m).Tendon force diagram for Group 1post-tensioning (t).Eccentricity of Group 1 tendons,

(ml.Bending moment diagram due toGroup 1 post-tensioning, diagram6 x 7 (t-m).Bending moment diagram obtainedby multiplication of the tendonforce diagram hy the section modu-lus (moment of resistance in Fig.5.3) and dividing by the sectionarea F/A x Z,. This is the top fibermoment due to the axial compres-sion from post-tensioning (t-m).

Bending moment diagram obtainedby multiplication of the tendon

5

6

7

0

9

IO

force diagram by the section modu-lus of the bottom fiber and dividingby the section area F/A x Zb. Thisis the bottom fiber moment due tothe axial compression from post-tensioning (t-m).

JOINT NUMBERS(See Fig. 5.2)

Fig. 5.10 - Step 1. Free cantilever plus initial cantilevergroup 1 post-tensioning

89

Diagram 11 Check top fiber moments (indirect-(Fig. 5.11) ly checking stresses). Moment dia-

gram (a) is obtained by adding dia-grams 8 and 9 from Fig. 5.10.This is the top fiber moment due tothe combination of bending andaxial force resulting from post-tensioning. Diagram c + a is diagrama reduced by the dead load momentdiagram (diagram 5 in Fig. 5.10).The top fiber compressive stresscontrol limits are indicated by thef’, x Z, diagram. Allowable com-pressive stress at this stage is 2150t/m2. In this case 2150 x 1.422 =3057 psi or approximately 0.55 x5500 = 3025 psi.

Diagram 12 Check bottom fiber moments (indi-rectly checking stresses). Momentdiagram b is obtained by addingdiagrams 8 and 10 from Fig. 5.10.This is the bottom fiber momentdue to the combination of bendingand axial force from post-tension-ing. Diagram c + b is the additionof diagram 5, box girder deadload moment from Fig. 5.10, todiagram b. The bottom fiber com-pressive stress control moment dia-gram based on f, = 0.55 x 5500 =3025 psi, or 2150 t/m2, is also indi-cated in Fig. 5.11 [2150 x 3.0824= 6627 t-m (47,932 ft. kips)] .

I I

12

Fig. 5.11 - Step 1. Check top fiber and bottom fiber

moments

90

5.6.2 Step 2. Completion of Tail Span PlusContinuity Group 2 Post-Tensioning

The completion of the tail span is achieved byaddition of the end span cross girders and installa-tion of the Group 2 post-tensioning shown in Fig.5.6. This post-tensioning consists of one tendon ineach web. For analytical purposes, the changeswith respect to Step 1 are:

1. End cross girder is added2. End support is added3. Continuity Group 2 post-tensioning is installed4. Two supports at piers are replaced by one

support at the center of the pier

With reference to Fig. 5.12, the calculations toaccount for the above changes proceed as follows:

Diagram 1 Determine box girder dead loadbending moment diagram due to in-troduction of end support and endcross girder.Determine force diagram of Group2 post-tensioning tendons and thetendon eccentricities.

Diagram 2

Diagram3

Diagram 4

Diagram 5

Diagram 6

Determine the bending moment dia-gram due to Group 2 tendons.The structure is simply supportedand the bending moment equals theforce multiplied by the eccentricity.The tendon force diagram multi-plied by the top section modulus,Z,, and divided by the sectionarea, A, expresses the axial com-pression due to post-tensioning interms of a top fiber moment (t-m).The tendon force diagram multi-plied by the bottom section mod-ulus, Zb, and divided by the sectionarea, A, expresses the axial com-pression due to post-tensioning interms of a bottom fiber moment(t-m).Add diagrams 3 and 4 to obtaindiagram 6a. This is the combinedaxial (expressed as a moment)and bending moment effect of thepost-tensioning on the top fiber(t-m).

3

4

5

6a

-172

6 b

Add diagrams 3 and 5 to obtain6b. This is the combined axial(expressed as a moment) andbending moment effect of the post-tensioning on the bottom fiber(t-m).

2 3 4 5 6 7 8 8 1 0

Fig. 5.12 - Completion of tail span plus continuity group2 post-tensioning

91

See diagrams of Fig. 5.13 with numbers corres-ponding to those below, and diagrams from previ-ous figures as noted.

Diagram 7 Add bending moment diagrams dueto box girder dead load from Steps1 and 2 (diagram 5 from Fig. 5.10plus diagram 1 from Fig. 5.12)

Diagram 8 Add diagram 11 a of Step 1 todiagram 6a of Step 2.

Diagram 9 Check top fiber moments com-pared to allowable by adding dia-gram 7 and the results of calcula-tion 8 above. As can be seen, thereis a large margin between the maxi-mum permissible moment of 9176t-m and the moment in the struc-ture.

Diagram 10 Add diagram 12b of Step 1 to dia-gram 6b of Step 2.

Diagram 11 Check bottom fiber moments com-pared to allowable by adding dia-gram 7 to the results of calculation10 above. Again the structure mo-ment is much less than the permis-sible value of 6627 t-m.

7

+tSS

9

I I

-I?59

Fig. 5.13 - Step 2 continued. Check top fiber and bottom

fiber moments

92

5.6.3 Step 3. Completion of Center Span

At this stage, the cast-in-place midspan splice iscompleted and continuity post-tensioning inGroups 3a and 3b is placed and stressed. Group 3apost-tensioning consists of four tendons in eachweb which are located in the bottom slab at mid-span. Group 3b post-tensioning consists of four 6-strand top slab tendons. Both Group 3a and Group3b post-tensioning are shown in Fig. 5.7.

The calculation procedure illustrated in Fig.5.14 for this step is as follows:

Diagram 1 Calculate the bending moment dia-gram due to the additional weightof the midspan cast-in-place seg-ment.The tendon force diagram andeccentricities shown in Fig. 5.14are for all tendons in Groups 3aand 3b.

Diagram 2 Determine bending moment dia-grams due to post-tensioning Groups3a and 3b. The post-tensioning isstressed in the continuous system,and the resulting moment diagramsare obtained as follows:2a. Assume hinges at supports onpiers, calculate post-tensioning forcediagram.2b. Calculate the bending momentsdue to post-tensioning Groups 3aand 3b for the hinged span CE(moment = force x eccentricity).2c. Calculate angle of rotation atC and E by the moment diagramobtained in 2b.2d. Calculate the secondary momentrequired to rotate the joint closedat C and E.

Diagram 3

2e. The addition of diagrams 2band 2d is the bending momentdiagram resulting from post-ten-sioning in the continuous system.

Multiply the tendon force diagramof post-tensioning Groups 3a and3b by Z, and divide by the sectionarea, A. This provides an equivalenttop fiber moment diagram to ac-count for the effect of the axialforce.

Diagram 4 Multiply the tendon force diagramof post-tensioning Groups 3a and3b by Zb and divide by the sectionarea, A. This provides an equivalentbottom fiber moment diagram to

Diagram 5

account for the effect of the axialforce.Add diagrams 2e and 3 to obtaindiagram 5a which is the totaleffect of the post-tensioning withrespect to the top fiber, expressedas a moment.Add diagrams 2e and 4 to obtaindiagram 5b which is the totaleffect of the post-tensioning withrespect to the bottom fiber, ex-pressed as a moment.

2 b

d

e

3

4

50

5 b

456!69

Fig. 5.14 - Step 3. Completion of center span

93

Top and bottom fiber stresses are checked in 5.6.4 Step 4. Addition of Superimposed Dead

Fig. 5.15 in terms of moments as follows: Loads

Diagram 6 Check top fiber moment by addi-tion of diagrams 1 and 5a of Step3 to diagram 9 of Step 2. The mo-ments (and stresses) are satisfac-tory in all locations.

Diagram 7 Check bottom fiber moment by ad-dition of diagrams 1 and 5b of Step3 to diagram 11 of Step 2. Againthe moments are well within theallowable values throughout thelength of the structure.

6

Fig. 5.15 - Step 3 continued. Check top fiber and bottomfiber moments

At this stage the effect of permanent superim-imposed dead loads due to addition of curbs,railings and toppings is considered. Permanentsuperimposed loads are treated separately from liveloads because permanent loads cause creep defor-mations of the structure. The amount of the super-imposed dead load is 1.525 t/m (1.03 kip/ft.).With reference to Fig. 5.16, the calculation pro-cedure is as follows:

Diagram 1

Diagram 2

Diagram 3

Calculate bending moments due tosuperimposed loads.Check top fiber moments by add-ing diagram 1 above to diagram 6of Step 3. All top fiber momentsare within the allowable.Check bottom fiber moments byadding diagram 1 above to diagram7 of Step 3. All bottom fiber mo-ments are within the allowable.

Fig. 5.16 - Step 4. Addition of superimposed dead loads.Check top fiber and bottom fiber moments

94

5.6.5 Step. 5. Application of Live Load andTemperature Load

The live load on the structure is HS20-44.The temperature loading consists of a 10’ C(18O F) temperature rise of the top slab withrespect to the webs and the bottom slab for maxi-mum temperature effects and a 5O C (go F) tem-perature decrease of the top slab with respect tothe webs and bottom slab for minimum tempera-ture effects. With the area of the top slab 1.988m* (21.39 ft.*) and modulus of elasticity 3.5 xlo6 t/m* (5 x lo6 psi), the force developed by a1OoC temperature differential with a thermal co-efficient, CY, of 0.00001 m/m/‘C (5.56 x 1O-6in./in./OF) is 695.8 t (1534 kips). The eccentricityof this force with respect to the neutral axis is0.926m (3.04 ft.). The temperature differentialanalysis procedure is presented in Section 3.3.4.The temperature stresses calculated are convertedto equivalent bending moments. As illustrated byFigs. 5.17, 5.18 and 5.19, the calculation proce-dure is as follows:

Diagram 1 Calculate live load positive mo-(Fig. 5.17) ments (diagram la) and negative

moments (diagram 1 b).Diagram 2 Calculate maximum bottom fiber

(Fig. 5.17) temperature moments (2a) andminimum bottom fiber temperaturemoments (2b), and maximum andminimum top fiber temperaturemoments (Figs. 2c and 2d, respec-tively).

Diagram 3 Combine diagrams 1 and 2 to pro-(Fig. 5.18) vide:

3a. Maximum live load momentplus maximum temperature mo-ment bottom fiber.3b. Minimum live load moment andminimum temperature moment topfiber.

Diagram 4(Fig. 5.19)

Diagram 5

2 b

+,*I

+4.

2 c

Check top fiber moments withrespect to allowable by combiningdiagram 2 of Step 4 (Fig. 5.16)with 3a and 3b of Step 5. Allmoments within the allowable.Check bottom fiber moments withrespect to allowable by combiningdiagram 3 of Step 4 (Fig. 5.16)with diagrams 3a and 3b of Step 5.All moments within the allowable.

Fig. 5.17 - Step 5. Application of live load and tempera-ture load

95

3 b

Fig. 5.18 - Step 5 continued. Maximum live load plus

maximum temperature moments on bottom fiber and topfiber

Fig. 5.19 - Step 5 continued. Check top fiber and bottom

fiber moments

96

5.6.6 Step 6. Influence of Time

With passage of time, the moments in the struc-ture are modified due to creep effects on box gird-er dead load moments and post-tensioning mo-ments, and by the effect of prestress losses. Thesethree effects will be considered separately in thefollowing calculations. Step 6a will consider theredistribution of box girder dead load momentsdue to creep, Step 6b will cover the redistributionof the post-tensioning moments due to creep, andStep 6c will consider the effect of prestress losses.

In all of these calculations, high and low valuesof the creep factors will be assumed as follows:

f#l, = 1.41 #* = 1.05(1 -e-@‘I) =0.76 (1 -ee-@2) =0.65

5.6.6.1 Step 6a. Box Girder Dead Load MomentRedistribution Due to Creep

With reference to Fig. 5.20, the calculationprocedure is as follows:

Diagram 1

Diagram 2

Diagram 3

Diagram 4

Calculate box girder dead load mo-ments (not including superimposeddead load) in the continuous struc-tu re.Calculate the box girder dead loadmoments at completion of erec-tion. Add diagram 5, Step 1 todiagram 1, Step 2, and diagram 1,Step 3.The difference between diagrams 1and 2 above is as shown.Diagram 3 is multiplied by the highvalue of the creep factor (1 - e-@l)to provide a high estimate of thebox girder dead load creep momentredistribution.

Diagram 5

60

2

3

4

5

Diagram 3 is multiolied bv the IOW

value of the creep factor Ci - e*2 )to provide a low estimate of thebox girder dead load momentredistribution.

Fig. 5.20 - Step 6. Influence of time. Step 6a. Box girderdead load moment redistribution due to creep

97

5.6.6.2 Step 6b. Post-Tensioning Moment Redis-tribution Due to Creep

Diagram 1(Fig. 5.21)

Diagram 2

Diagram 3

Diagram 4

Diagram 5

Diagram 6

Diagram 7

Diagram 8

Diagram 9

Diagram 10

Diagram 11

The effects of cantilever post-tensioning (Group 1) on the contin-uous structure.The cantilever post-tensioning mo-ments at the end of erection (dia-gram 8 from Step 1, Fig. 5.10).The difference between diagrams 1and 2 above.Multiply diagram 3 by the highvalue of the creep factor (1 - e*l ),giving a high estimate of the canti-lever post-tensioning (Group 1)moment redistribution due to creep.

Multiply diagram 3 by the lowvalue of the creep factor (1 - e-‘#‘2 )giving a low estimate of the canti-lever post-tensioning (Group 1)moment redistribution due to creep.Determine the effect of Group 2continuity post-tensioning on thecontinuous structure.

The effect of Group 2 post-tension-ing during construction (diagram 3,Fig. 5.12).

The difference between diagrams 6and 7, above.

Multiply diagram 8 by the highvalue of the creep factor ( 1 -e-@l 1, giving a high estimate ofthe Group 2 post-tensioning mo-ment redistribution due to creep.

Multiply diagram 8 by the low valueof the creep factor (1 - e+2 1,giving a low estimate of the Group2 post-tensioning moment redistri-bution due to creep.

Combine diagrams 4 and 9 to ob-tain a high value of the total redis-tribution of post-tensioning mo-ments due to creep.

Diagram 12

6 b

2

3

4

5

6+21

7t 21

6

9

IO

I I

1 2

Combine diagrams 5 and 10 to ob-tain a low value of the total redis-tribution of post-tensioning mo-ments due to creep.

Fig. 5.21 - Step 6b. Post-tensioning moment redistribu-

tion due to creep

98

5.6.6.3 Step 6c. Effect of Prestress Losses

Prestress losses due to friction, elastic shorten-ing, shrinkage and creep have been calculated as14 percent of initial forces or 18.610 t/m* (26,460psi).

Diagram 2(Fig. 5.22)

Diagram 3

Diagram 4

Diagram 5Diagram 6

Diagram 7

Group 1 post-tensioning tendonforce diagram multiplied by pre-stress loss percentage.Group 2 post-tensioning tendonforce diagram multiplied by pre-stress loss percentage.Group 3 post-tensioning tendonforce diagram multiplied by pre-stress loss percentage.Diagrams 2,3 and 4 added together.Diagram 5 multipled by 2, anddivided by the section area, A. Thisis the prestress force loss effect onthe top fiber expressed as a mo-

ment.Diagram 5 multiplied by 2, and di-vided by the section area, A. Thisis the prestress force loss effect onthe bottom fiber expressed as amoment .

6I

-30

Fig. 5.22 - Step 6c. Effect of prestress losses

Diagram 8(Fig. 5.23)

Diagram 9

Diagram 10

Diagram 11

Diagram 12

Diagram 13

Group 2 continuity post-tensioningbending moments in continuoussystem multiplied by loss per-centage.Group 1 cantilever post-tensioningbending moments in continuoussystem multiplied by loss per-centage.Group 3 continuity post-tensioningbending moments in continuoussystem multiplied by loss per-centage.Diagrams 8, 9 and 10 added to-gether.Diagram 11 added to diagram 6 toobtain total equivalent top fiberbending moments due to losses.Diagram 11 added to diagram 7 toobtain total equivalent bottom fiberbending moments due to losses.

e -3

g a

‘0 a

II -a

-411 2

13+tD

162021222324252627

Fig. 5.23 - Step 6c continued. Equivalent top fiber and

bottom fiber bending moments due to prestress losses

99

5.6.7 Step 7. Final Stress Control

Diagram 1(Fig. 5.24)

Diagram 2(Fig. 5.24)

Diagram 3(Fig. 5.24

Diagram 4(Fig. 5.24

Calculation of total time-related(maximum and minimum) effectsfrom Steps 6a, 6b and 6c for topfibers.

Calculation of total time-related(maximum and minimum) effectsfrom Steps 6a, 6b and 6c for bot-tom fibers.

Final stress control for the topfiber is evaluated by combiningdiagram 1 above with diagram 4from Step 5 (Fig. 5.19).

Final stress control for the bottomfiber is evaluated by combiningdiagram 2 above with diagram 5from Step 5 (Fig. 5.19).

h

‘I ,. ! .I

11, / 1 ‘,,I’

Fig. 5.24 - Step 7. Final stress control. Top fiber andbottom fiber time-related bending moments

100

p

5.6.8 Step 8. Calculation of Transverse Moments

Transverse moments in the North Vernon Bridgewere calculated by use of a computer programbased on folded plate theory. The calculation pro-cedure divides the box section into longitudinalstrips which may or may not be of constantthickness. This makes it possible to include con-sideration of the areas where slabs or webs arethickened. The length of the strips is taken as thespan length for a simply supported box girder,or as the distance between points of zero moment i’ ‘Pin the case of a continuous box girder.

The results of the analysis are given at the con-nections of the longitudinal strips. The resultsprovide bending moments and axial forces due tobox girder dead load, superimposed dead loads,linear loads (curbs), and live loads. The live loadmay be either uniformly distributed, or one ormore vehicles. In either case, live load momentsare obtained from influence lines calculated foreach section. The uniformly distributed live load ora design vehicle is placed on the influence lines insuch a position as to give maximum positive ornegative moments. Because of the effect of loaddistribution, influence lines for uniformly dis-tributed live loads differ from influence lines forvehicles.

Influence diagrams and moment and axial force+MI

+ve +I.150+Q-+QO88 1-L +o.wa ’

-2.477 - 2 1 7 7

diagrams for the North Vernon Bridge are pre-sented in Figs. 5.25 to 5.31. Size and location oftransverse reinforcement are shown in Fig. 5.32.

AXIAL FORCE DUE TOSELFWEIGHT

Fig. 5.25 - Transverse moments and axial forces due tobox girder dead load

101

4 IO 4

\ -QLlOl I

0 0

A X I A L F O R C E D U ET O T O P P I N G

Fig. 5.26 - Transverse moments and axial forces due tosuperimposed dead load

2 3 ,325 t/m

Fig. 5.27 - Transverse moments and axial forces due to

linear loads (one side only)

102

9

1 1

I1-o.co2I

ISECTION

~ SECTION 2I

/ I9 ‘p g! /-0.024 t on24

1 S ECTION 5;

Fig. 5.28 - Influence lines for vehicle Fig. 5.29 - influence lines for vehicle, continued

103

Fig. 5.30 - Transverse moments and axial forces due to Fig. 5.31 - Transverse moments and axial forces due touniformly distributed live load vehicular loading

104

309

411

i

, II319’ @ 6”

J

/ i3194 @ 6”

,’ / -- -----fi l\,. 1 ft. = 0.3048 m ’

T- 1 in. =f 7+ ,25.4 m m

4 1 3 Cal IO”1’ I

CABLES.

INote: bar size is indicated by the first digit of bar numbers

Fig. 5.32 - Transverse reinforcement details

t

A. APPENDIX

A.1 Tentative Design and Construction Specifica-tions for Precast Segmental Box Girder Bridges.

% The PCI Bridge Committee prepared tentativedesign and construction specifications and accom-panying commentary in 1975 in the form of a pro-posed addition to the AASHTO Standard Specifi-cations for Highway Bridges. They were presentedto the AASHTO Committee on Bridges and Struc-tures for evaluation, and then were published bythe Prestressed Concrete Institute (PC1 JOURNAL,July-August 1975) to develop comments and dis-cussion.

The PCI Bridge Committee evaluated the com-ments received relative to the 1975 tentative speci-fications as well as new information on design andconstruction of precast segmental box girderbirdges, and prepared the following version of thedesign and construction specifications for con-sideration by the AASHTO Subcommittee onBridges at its 1977 Regional Meetings. The speci-fication proposals as presented in this section rep-resent the recommendations of the PCI BridgeCommittee, and may be modified prior to finaladoption as AASHTO Standard Specifications forHighway Bridges.

The specification proposals are presented here ina format utilizing section numbers compatible withthe 1973 AASHTO Standard Specifications forHighway Bridges. Specifically, new sections of the1973 AASHTO Specifications are proposed asfollows:

1.6.25 Precast Segmental Box Girders

2.4.33 (L) Precast Segment Manufacture andErection

2.4.33 (M) Epoxy Bonding Agents for Pre-cast Segmental Box Girders

2.4.33 (N) Inspection of Precast SegmentalBox Girder Jointing Procedures

2.4.33 (0) Epoxy Bonding Agent Tests

1.6.25 Precast Segmental Box Girders

(A) General

Except as otherwise noted in this section, theprovisions of Section 6 - Prestressed Concrete

shall apply to the analysis and design of precastsegmental box girder bridges. Deck slabs withouttransverse post-tensioning shall be designed underthe applicable provisions of Section 5 - ConcreteDesign.

Elastic analysis and beam theory may be used inthe design of precast segmental box girder struc-tures. For box girders of unusual proportions,methods of analysis which consider shear lag*shall be used to determine stresses in the crosssection due to longitudinal bending.

(B) Design of Superstructure

(1) Flexure

The transverse design of precast segments forflexure shall consider the segment as a rigid boxframe. Top slabs shall be analyzed as variable depthsections considering the fillets between the topand webs. Wheel loads shall be positioned to pro-vide maximum moments, and elastic analysis shallbe used to determine the effective longitudinaldistribution of wheel loads for each load location(see Article 1.2.8). Transverse post-tensioning oftop slabs is generally recommended.

In the analysis of precast segmental box girderbridges, no tension shall be permitted at the top ofany joint between segments during any stage oferection or service loading. The allowable stressesat the bottom of the joint shall be as specified inArticle 1.6.6 (B) (2).

(2) Shear

(a) Reinforced keys shall be provided in segmentwebs to transfer erection shear. Possible reverseshearing stresses in the shear keys shall beinvestigated, particularly in segments near apier. At time of erection, the shear stress car-ried by the shear key shall not exceed 2c

(b) Design of web reinforcement for precastsegmental box girder bridges shall be in ac-cordance with the provisions of Article 1.6.13.

(3) Torsion

In the design of the cross section, considerationshall be given to the increase in web shear resultingfrom eccentric loading or geometry of structure.

(4) Deflections

Deflection calculations shall consider dead load,live load, prestressing, erection loads, concretecreep and shrinkage, and steel relaxation.

Deflections shall be calculated prior to manu-facture of segments, based on the anticipated pro-duction and erection schedules. Calculated deflec-tions shall be used as a guide against which erecteddeflection measurements are checked.

‘Defined as non-uniform distribution of bending stress over thecross section.

106

(5) Details

(a) Epoxy bonding agents for match-cast jointsshall be thermosetting 100 percent solidcompositions that do not contain solvent orany non-reactive organic ingredient except forpigments required for coloring. Epoxy bond-ing agents shall be of two components, aresin and a hardener. The two componentsshall be distinctly pigmented, so that mixingproduces a third color similar to the concretein the segments to be joined, and shall bepackaged in pre-proportioned, labeled, ready-to-use containers.

Epoxy bonding agents shall be formulated toprovide application temperature ranges whichwill permit erection of match-cast segments atsubstrate temperatures from 40F (5C) to115F (46C). If two surfaces to be bondedhave different substrate temperatures, theadhesive applicable at the lower temperatureshall be used.

If a project would require or benefit fromerection at concrete substrate temperatureslower than 4OF, the temperature of theconcrete to a depth of approximately 3 in.(76 mm) should be elevated to at least 40F toinsure effective wetting of the surface by theepoxy compound and adequate curing of theepoxy compound in a reasonable length oftime. An artificial environment will have to beprovided to accomplish this elevation intemperature and should be created by anenclosure heated by circulating warm air orby radiant heaters. In any event, localizedheating shall be avoided and the heat shall beprovided in a manner that prevents surfacetemperatures greater than 11OF (43C) duringthe epoxy hardening period. Direct flame jett-ing of concrete surfaces shall be prohibited.

Epoxy bonding agents shall be insensitive todamp conditions during application and, aftercuring, shall exhibit high bonding strengthto cured concrete, good water resistivity, lowcreep characteristics and tensile strengthgreater than the concrete. In addition, theepoxy bonding agents shall function as alubricant during the joining of the match-castsegments being joined, and as a durable,watertight bond at the joint. See Article 2.4.33(M) for epoxy bonding agent specifications.

(b) Articles 1.6.24 (C) and 1.6.24 (F) relating toflange thickness and diaphragms shall notapply to precast segmental box girders.

(C) Design of Substructure

In addition to the usual substructure design con-siderations, unbalanced cantilever moments due tosegment weights and erection loads shall be ac-commodated in pier design or with auxiliary struts.Erection equipment which can eliminate these un-balanced moments may be used.

COMMENTARY

1.6.25 Precast Segmental Box Girders

(A) General

Material strengths and allowable stresses need beno different from other prestressed concretebridges; therefore, current limits in Standard Speci-fications for Highway Bridges should apply. How-ever, higher strength concrete has advantages andshould be used when available. Higher strengthconcrete has more durability, not only because ofthe mix design but also because of the greaterquality control required to produce it.

Precast segmental box girders may be designedby beam theory with consideration of shear lag.Shear lag need only be investigated for segmentswider than 40 ft. (12m) used on 150 ft. (46m)spans or less, because of the shallow depth.

(B) Design of Superstructure

Influence surfaces for design of constant andvariable depth deck slabs have been published(see References 5 and 6, page 109).

The following limitations are recommended:

1. When beam theory is used, single cell boxesshould be no more than 40 ft. (12m) wide, includ-ing cantilevers. For bridges wider than 40 ft.,multiple box cross sections or multiple cell boxesare usually used. Single cell boxes of width greaterthan 40 ft. can be used if carefully analyzed forshear lag to determine the portion of cross sectioncapable of handling longitudinal moment.

2. For maximum economy, the span-to-depthratio for constant depth structures should be 18to 20. However, span-to-depth ratios of 20 to 30have been used when required for clearances oresthetics. The shallower depths require the use ofmore high strength post-tensioning steel which maycause congested cross sections. Variable depthstructures usually have span-to-depth ratios of 18to 20 at the supports and 40 to 50 at midspan.

3. Width-to-depth ratios should also be consid-ered. A shallow box girder that is too wide begins

107

to behave as a slab. No criteria have been estab-lished, but when the width-todepth ratio is greaterthan six, considering the total width of the sectionincluding slab cantilevers, it is recommended thatthe designers use multiple cell boxes or carefullyanalyze the cross section.

4. Proper fillets should be used in the cross sec-tion to allow stress transfer around the box per-imeter and to provide ample room for the largenumber of tendons.

5. Diaphragms should be considered. These areusually required only at piers, abutments, and ex-pansion joints.

6. The thickened bottom slab in pier segments,when required for stresses, should taper down orstep down to the minimum midspan segment bot-tom slab thickness in as short a distance as is prac-tical.

7. Web thicknesses should be chosen for pro-duction ease. If post-tensioning anchorages arelocated in the webs, web thickness may be gov-erned by the anchorage requirements.

8. Permanent access holes into the box sectionshould be limited in size to the minimum func-tional dimension and should be located near pointsof minimum stress.

(C) Design of Substructure

Unbalanced cantilever moments occur duringerection only and are usually greater in magnitudethan service load moments. Wind loads in combi-nation with erection loads could develop criticalstresses and, thus, wind loads should be consid-ered in accordance with Article 1.2.22.

Selected References

The following selected references provide someuseful guidelines in the design and construction ofprecast prestressed segmental box girder bridges:

1. PCI Committee on Segmental Construction,“Recommended Practice for Segmental Con-struction in Prestressed Concrete,” PCI JOUR-NAL, V. 20, No. 2, March-April 1975, pp. 22-41.

2. Muller, Jean, “Ten Years of Experience in Pre-cast Segmental Construction,” PCI JOURNAL,V. 20, No. 1, January-February 1975, pp. 28-61.

3. Swann, R. A., “A Feature Survey of ConcreteBox Spine-Beam Bridges,” Cement and ConcreteAssociation, 52 Grosvenor Gardens, LondonSW1 W OAQ, 1972.

4. Maisel, V. I., and Roll, F., “Methods of Analysisand Design of Concrete Boxbeams with SideCantilevers,” Technical Report No. 42.494,Cement and Concrete Association, 52 GrosvenorGardens, London, SWlW OAQ, November, 1974.

5. Pucher, Adolph, “Influence Surfaces of ElasticPlates,” 4th Edition, 1973 (English), Springer- Verlag New York, Inc.

6. Homberg, Helmut, “Double Webbed Slabs,”(Dalles Nervurees Platten Mit Zwei Stegen),1974 (English), Springer - Verlag New York,Inc.

2.4.33 Prestressed Concrete

(L) Precast Segment Manufacture and Erection

(1) Manufacture of segments

Each segment shall be match-cast with its ad-jacent segments to ensure proper fit during erec-tion. As the segments are match-cast they must beprecisely aligned to achieve the final structuregeometry. During the alignment, adjustments tocompensate for deflections are made.

All tendon ducts are placed during production.The conduit to enclose grouted, post-tensionedtendons shall be mortar tight, made of galvanized,ferrous metal, and may be either rigid with asmooth inner wall, capable of being curved to theproper configuration, or a flexible, interlockingtype. Couplers for either type shall also provide amortar tight connection. Rigid conduit may befabricated with either welded or interlockingseams. Galvanizing of welded seams for rigid con-duit or of conduit couplers will not be required.During placing and finishing of concrete in a seg-ment, inflatable hoses capable of exerting suffi-cient pressure on the inside walls shall be placedinternally in all conduits and shall extend a mini-mum of 2 ft. (0.6m) into the conduit in the pre-viously cast segment. Either type of conduit shallbe capable of withstanding all forces due to con-struction operations without damage. Other typesof conduit and/or internal protection systems arepermitted subject to the approval of the Engineer.

(2) Erection of Segments

Segments are usually erected by the cantilevermethod from each pier without falsework, al-though temporary supports may be used. Withthe approval of the Engineer, other systems oferection may be considered.

Match-cast segments shall be erected usingepoxied joints. Pressure shall be provided on the

108

joint by means of post-tensioning. The pressureshall be as uniform as possible with a minimum of30 psi (0.21 MPa) at any point.

Deflections of cantilevers shall be measured aserection progresses and compared with computeddeflections. Any deviation from the required align-ment shall be corrected by either modifying thesegment geometry during the casting operation orby inserting stainless steel screen wire shims in theepoxy joints during erection. The maximum thick-ness of shims at any joint shall be l/16 in. (1.6mm).Provision shall be made to permit alignment ad-justments of a completed cantilevered portion ofthe box girder before the midspan splice connect-ing adjacent cantilevers is constructed.

(3) Grouting

Grouting of the ducts shall be done in accord-ance with Article 2.4.33 (I). Under normal condi-tions, grouting shall be accomplished within 20calendar days following installation of tendons.For delays beyond 20 days, tendons shall be pro-tected with a water soluble oil or approved equalprotective agent.

Protection of the tendon ducts against splittingfrom freezing of water in ducts must be provideduntil cement grout can be used. Use of some othertype grout should be considered when erecting inthese low temperatures.

(M) Epoxy Bonding Agents for Precast SegmentalBox Girders

All epoxy bonding agents shall meet the require-ments of Article 1.6.25 (B) (5) (a). Two-partepoxy bonding agents shall be supplied to the erec-tion site in sealed containers, pre-proportionedin the proper reacting ratio, ready for combiningand through mixing in accordance with the manu-facturer’s instructions. All containers shall beproperly labeled to designate the resin componentand the hardener component as well as the tem-perature range for its application. The substratetemperature range of 40F to 115F (5C to 46C)may be divided into either two or three applica-tion ranges for bonding agents. Such ranges shalloverlap each other by at least 6F (3C).

Surfaces to which the epoxy material is to beapplied shall be free from oil, laitance, form re-lease agent, or any other material that would pre-vent the material from bonding to the concretesurface. All laitance and other contaminants shallbe removed by light sandblasting or by high pres-sure water blasting with a minimum pressure of5000 psi (35 MPa). Wet surfaces should be driedbefore applying epoxy bonding agents. The sur-face should be at least the equivalent of saturated

109

surface dry (no visible water).Instructions furnished by the supplier for the

safe storage, mixing and handling of the epoxybonding agent shall be followed. The epoxy shallbe thoroughly mixed until it is of uniform color.Use of a proper sized mechanical mixer operatingat no more than 600 RPM will be required. Con-tents of damaged or previously opened containersshall not be used. Mixing shall not start until thesegment is prepared for installation. Application ofthe mixed epoxy bonding agent shall be accordingto the manufacturer’s instructions using trowel,rubber glove or brush on one or both surfaces tobe joined. The coating shall be smooth and uni-form and shall cover the entire surface with a mini-mum thickness of l/16 in. (1.6mm) applied onboth surfaces or l/8 in. (3.2mm) if applied on onesurface. Epoxy should not be placed within 3/8 in.(9.5mm) of prestressing ducts to minimize flowinto the ducts. A discernible bead line must be ob-served on all exposed contact areas after tempo-rary post-tensioning. Erection operations shall becoordinated and conducted so as to complete theoperations of applying the epoxy bonding agentto the segments, erection, assembling, and tem-porary post-tensioning of the newly joined segmentwithin 70 percent of the open time period of thebonding agent.

The epoxy material shall be applied to all sur-faces to be joined within the first half of the geltime, as shown on the containers. The segmentsshall be joined within 45 minutes after applica-tion of the first epoxy material placed and a mini-mum average temporary prestress of 50 psi (0.35MPa) over the cross section should be applied with-in 70 percent of the open time of the epoxy mater-ial. At no point of the cross section shall the tem-porary prestress be less than 30 psi (0.21 MPa).

The joint shall be checked immediately aftererection to verify uniform joint width and properfit. Excess epoxy from the joint shall be removedwhere accessible. All tendon ducts shall be swabbedimmediately after stressing, while the epoxy isstill in the non-gelled condition, to remove orsmooth out any epoxy in the conduit and to sealany pockets or air bubble holes that have formedat the joint.

If the jointing is not completed within 70 per-cent of the open time, the operation shall be ter-minated and the epoxy bonding agent shall becompletely removed from the surfaces. The sur-faces must be prepared again and fresh epoxy shallbe applied to the surface before resuming jointingoperations.

As general instructions cannot cover all situa-

tions, specific recommendations and instructionsshall be obtained in each case from the Engineerin charge.

Epoxy bonding agents shall be tested to deter-mine their workability, gel time, open time, bondand compression strength, shear, and working tem-perature range. See Article 2.4.33 (0) for testmethods and recommended specification limits.The frequency of the tests shall be stated in theSpecial Provisions of the Contract.

The Contractor shall furnish the Engineer sam-ples of the material for testing, and a certificationfrom a reputable independent laboratory indicatingthat the material has passed the required tests.

(N) Inspection of Precast Segmental Box GirderJointing Procedures

In addition to the material acceptance tests,which should be initially performed by a neutraltesting laboratory and then checked by the owners’organization, the owners’ inspector should makeregular checks of the epoxy jointing procedures.Data such as weather, ambient temperature, con-crete surface temperature, adhesive batch number,and the jointing time should be noted. The inspec-tor should frequently sample and record data suchas the observed gel time of the epoxy bondingagent, the surface conditions of the segmentsbeing joined, the adequacy of coverage of the ad-hesive, the amount of material being squeezedfrom the joints, and the approximate open time ofthe epoxy. An approximate determination of theopen time can be noted from behavior of lap jointsamples spread on small cement-asbestos boards.

(0) Epoxy Bonding Agent Tests

Test 1 - Sag Flow of Mixed Epoxy Bonding Agent

This test measures the application workability ofthe bonding agent.

Testing Method: ASTM D 2730 for the desig-nated temperature range.

Specification: ‘Mixed epoxy bonding agent mustnot sag flow at l/8 in. (3.2mm) minimum thick-ness at the designated minimum and maximumapplication temperature range for the class ofbonding agents used.

Test 2 - Gel Time of Mixed Epoxy Bonding Agent

Gel time is determined on samples mixed asspecified in the testing,method. It provides a guidefor the period of time the mixed bonding agentremains workable in the mixing container and dur-ing which it must be applied to the match-cast jojoint surfaces.

Testing Method: ASTM D 2471 (except thatone quart and one gallon quantities shall be tested).

Specification: 30 minutes minimum on onequart (0.95Q) and one gallon (3.79Q) quantitiesat the maximum temperature of the designatedapplication temperature range. (Note: gel time isnot to be confused with open time specified inTest 3).

Test 3 - Open Time of Bonding Agent

This test measures workability of the epoxybonding agent for the erection and post-tensioningoperations. As tested here, open time is defined asthe minimum allowable period of elapsed timefrom the application of the mixed epoxy bondingagent to the precast segments until the two seg-ments have been assembled together and tempo-rarily post-tensioned.

Testing Method: Open time is determined usingtest specimens as detailed in the Tensile BendingTest (Test 4). The epoxy bonding agent, at thehighest specified application temperature, is mixedtogether and applied as instructed in Test 4 to theconcrete prisms which shall also be at the highestspecified application temperature. The adhesivecoated prisms shall be maintained for 60 minutesat the highest specified application temperaturewith the adhesive coated surface or surfaces ex-posed and uncovered before joining together.The assembled prisms are then cured and tested asinstructed in Test 4.

Specification: The epoxy bonding agent is ac-ceptable for the specified application temperatureonly when essentially total fracturing of concretepaste and aggregate occurs with no evidence ofadhesive failure.

Construction situations may sometimes requireapplication of the epoxy bonding agent to theprecast section prior to erecting, positioning andassembling. This operation may require epoxybonding agents having prolonged open time. Ingeneral, where the erection conditions are suchthat the sections to be bonded are prepositionedprior to epoxy application, the epoxy bondingagent shall have a minimum open time of 60 min-utes within the temperature range specified forits application.

Test 4 - Three Point Tensile Bending Test

This test, performed on a pair of concreteprisms bonded together with epoxy bonding agent,determines the bonding strength between thebonding agent and concrete. The bonded concreteprisms are compared to a reference test beam ofconcrete 6x6~18 in. (150x150x460mm).

Testing Method: 6x6x9 in. (150xl50x230mm)concrete prisms of 6000 psi (41 MPa) compressivestrength at 28 days shall be sandblasted on one 6x6

110

in. side to remove mold release agent, laitance,etc., and submerged in clean water at the lowertemperature of the specified application tempera-ture range for 72 hours. Immediately on removingthe concrete prisms from the water, the sand-blasted surfaces shall be air dried for one hour atthe same temperature and 50 percent RH and eachshall be coated with approximately a l/16 in. (1.6mm) layer of the mixed bonding agent. The adhe-sive coated faces of two prisms shall then be placedtogether and held with a clamping force normal tothe bonded interface of 50 psi (0.35 MPa). The as-sembly shall then be wrapped in a damp clothwhich is kept wet during the curing period of24 hours at the lower temperature of the specifiedapplication temperature range.

After 24 hours curing at the lower temperatureof the application temperature range specified forthe epoxy bonding agent, the bonded specimenshall be unwrapped, removed from the clampingassembly and immediately tested. The test shallbe conducted using the standard ASTM C78 testfor flexural strength with third point loading andthe standard MR unit. At the same time the twoprisms are preapred and cured, a companion testbeam shall be prepared of the same concrete,cured for the same period and tested followingASTM C78.

Specification: The epoxy bonding agent is ac-ceptable if the load on the prisms at failure isgreater than 90% of the load on the reference testbeam at failure.

Test 5 - Compression Strength of Cured EpoxyBonding Agent

This test measures the compressive strength ofthe epoxy bonding agent.

Testing Method: ASTM D 695.Specification: Compressive strength at 77F

(25C) shall be 2000 psi (14 MPa) minimum after24 hours cure at the minimum temperature of thedesignated application temperature range and 6000psi (41 MPa) at 48 hours.

Test 6 - Temperature Deflection of Epoxy Bond-

ing Agent

This test determines the temperature at whichan arbitrary deflection occurs under arbitrarytesting conditions in the cured epoxy bondingagent. It is a screening test to establish perform-ance of the bonding agent throughout the erec-

tion temperature range.Testing Method: ASTM D 648.Specification: A minimum deflection tempera-

ture of 122F (5OC) at fiber stress loading of 264psi (1.8 MPa) is required on test specimens cured7 days at 77F (25C).

Test 7 - Compression and Shear Strength of

Cured Epoxy Bonding Agent

This test is a measure of the compressive strengthand shear strength of the epoxy bonding agentcompared to the concrete to which it bonds. The“slant cylinder” specimen with the epoxy bondingagent is compared to a reference test cylinder ofconcrete only.

Testing Method: A test specimen of concreteis prepared in a standard 6x12 in. (15Ox300mm)cylinder mold to have a height at midpoint of 6 in.and an upper surface with a 30-degree slope fromthe vertical. The upper and lower portions of thespecimen with the slant surfaces may be formedthrough the use of an elliptical insert or by sawinga full sized 6x12 in. cylinder. If desired, 3x6 in.(75xl50mm) or 4x8 in. (lOOx200mm) specimensmay be used. After the specimens have been moistcured for 14 days, the slant surfaces shall be pre-pared by light sandblasting, stoning or acid etching,then washing and drying the surfaces, and finallycoating one of the surfaces with a 10 mil (0.25mm)thickness of the epoxy bonding agent under test.The specimens shall then be pressed togetherand held in position for 24 hours. The assemblyshall then be wrapped in a damp cloth which shallbe kept wet during an additional curing period of24 hours at the minimum temperature of thedesignated application temperature range. Thespecimen shall then be tested at 77F (25C) follow-ing ASTM C 39 procedures. At the same time asthe slant cylinder spcimens are made and cured, acompanion standard test cylinder of the same con-crete shall be made, cured for the same period,and tested following ASTM C 39.

Specification: The epoxy bonding agent is ac-ceptable for the designated application tempera-ture range if the load on the slant cylinder speci-ment is greater than 90 percent of the load on thecompanion cylinder. The bond strength on theslant surface (shear), determined by dividing thespecimen test load by the area of the elliptical slantsurface, shall be at least 3000 psi (21 MPa) at 48hours.

111

A.2 Summary of Precast Segmental ConcreteBridges in the United States and Canada WithCross Sections

Note: for metric dimensions1 ft. = 0.3048 m1 in. = 25.4 mm

J

Fig. A.2.1 Lievre River Bridge, QuebecSpans: 130 feet - 260 feet - 120 feetBridge Length: 520 feetSegment Length: 9 feet 6 inches

t-c ROADWAY

Fig. A.2.2 Bear River Bridge, Nova ScotiaEnd Spans: 203 feet 9 inchesInterior Spans: 265 feetBridge Length: 1997.50 feetSegment Length: 14 feet 2 inches

Fig. A.2.3 Corpus Christi, TexasSpans: 100 feet - 200 feet - 100 feetBridge Length: 400 feetTwo Segments WideSegment Length: 10 feet

‘v-0”l- 1

c 23'.5"4

1'.ll'%" 3,-o" l'e 2'-(1-. I- -I " .

6'-6"

Fig. A.2.5 North Vernon, IndianaOver Muscatatuck RiverSpans: 95 feet - 190 feet - 95 feetBridge Length: 380 feetSegment Length: 8 feet

112

,‘.W’ 20’.0”-I

Fig. A.2.4 Vail Pass, ColoradoEnd Spans: 160 feetMain Spans: 210 feetSegment Length: 7 feet 4 inches

Fig. A.26 Kishwaukee River Bridge, Illinois

End Spans: 170 feet

interior Spans: 250 feetNorthbound : 1090 feet

Southbound: 1090 feetSegment Length: 7 feet O-5/8 inches

Fig. A.2.7 Parke County, IndianaBridge Length: 276 feet

Spans: 90 feet - 180 feet - 90 feetSegment Length: 8 feet

4,-O” SPLICE

Fig. A.2.8 Turkey Run, Indiana Fig. A.2.11 Scottdale Bridge, Michigan

Bridge Length: 322 feet Bridge Length: 407 feetSpans: 180 feet - 180 feet Spans: 97 feet - 206.5 feet - 97 feet

Segment Length: 8 feet Segment Length: 8 feet

, ‘-9” lo’.0”

Fig. A.2.9 Pike County, Kentucky

Bridge Length: 372 feetSpans: 93.5 feet - 185 feet - 93.5 feet

Segment Length: 7 feet 10 inches

Fig. A.2.10 Lake Oahe Crossing Missouri River,

North DakotaBridge Length: 3020 feet

Spans: 179 feet - 10 @ 265 feet - 179 feet

Segment Length: 8 feet 4 inches

113

Fig. A.2.12 Illinois River, Illinois

Eastbound: 3329.5 feetWestbound: 3203.5 feetApproach Spans: 175 feet - 230 feet

Main Spans: 390 feet - 550 feet - 390 feet

Segment Length: 10 feet

Fig. A.2.13 Zilwaukee, Michigan

Bridge Over Saginaw RiverBridge Length: 8000 feet

Two segments WideSpans: Variable 155-392 feet

Segment Length: 8 feet to 12 feet

Fig. A.2.14

‘l-3-1,4” ,‘4.11,16’

St. Louis MissouriBridge Length: 405 feetSpans: 100 feet - 200 feet - 100 feet

Segment Length: 9 feet 4 inches

Fig. A.2.15 Akron Bridge, Ohio

Westbound: 3660 feetEastbound: 3646 feet

Spans: Variable 100 to 290 feetSegment Length: 6,7 and 8 feet

Fig. A.2.16 Lake County Ramps, IndianaBridge Length: 6240 feet

(Ramps plus Mainline)

Spans: Variable 100 to 315 feetSegment Length: 7 feet 9 inches

114

A.3 Notation

A =A =A, =E =

Fi =Ff =H =

I =

L =L’ =

M, =

Mcr =

ME =M, =

MI, =

M, =M’, =

N, =

P =

P =

P =

R =R =Sh =s, =St =

s, =

Tw =T, =T2 =T3 =T’, =T’2 =T’, =

T’,, =T’, =

v =

x, =

2, =2, =b =

cross sectional area of segmentarea of top slabarea of concrete section28-day modulus of elasticity of concreteinitial prestressing forcefinal prestressing forcehorizontal distance center to center ofwebsmoment of inertiaspan lengthunit length along spantransverse momentscreep moment resulting from change ofstatical systemerection momentmoment due to loads before change ofstatical system (Fig. 3.10)moment due to same loads, considered toproduce M,, applied to changed staticalsystem (Fig. 3.10)moment at time ttorsional moment per unit length of boxgirderratio of longitudinal forces obtained fromcomputer analysis to forces obtained fromelementary beam theorypost-tensioning forceload causing deflection 6 (Fig. 3.11)loading per unit length (Fig. 3.35)reaction before settlement (Fig. 3.11)support reactions (Fig. 3.36)horizontal shear force in transverse analysisE,h EA, elastic shrinkage restraint forceshrinkage restraint force adjusted for theeffect of creepvertical shear force in transverse analysisambient temperature during At’ daysshear force in top slabshear force in webshear force in bottom slabrate of change of shear force in top slabrate of change of shear force in webrate of change of shear force in bottomslabshear forces in top and bottom slabportion of external load carried to sup-ports by websvertical distance from center of top slabto center of bottom slabincrease in support reaction due to elas-tic and creep deformation (Fig. 3.11)top section modulusbottom section modulushorizontal dimension from centerline ofbox section to centerline of web

c, =c,, =d =

d, =d =

e ==

;I, =

f, =fcb =

h =

h th =

II =

q =

t =

t =

t, =

t’, =

t’, =

t, =

t, =

V =

w =

Z =

AS, =

As h t =

At =

At’ =

a =

a =

a =

a =

P=

P=

P=

B Cl=

Pc2=

distance from centroid to top fiberdistance from centroid to bottom fiberweb thicknessslab thicknessthickness of top and bottom slab (Fig.3.38)eccentricity of post-tensioning forcebase of natural logrithms = 2.718. . .28-day compressive strength of concretetest cylindersconcrete stressbottom fiber compressive stresshorizontal displacement

theoretical thickness of structural elementwith respect to relative humiditycantilever length (Fig. 3.8)uniformly distributed load (Fig. 3.8)theoretical agetheoretical time after casting (days)theoretical age of concrete at time ofloading (days)rate of change of torsional shear force intop and bottom slabsrate of change of torsional shear force inwebstime of completion of the structuretime of application of the dead loadvertical displacementunit weight of concretevertical dimension from centerline of boxsection to centerline of slabmember elongation due to shrinkage re-straint force, Stf,ht 8, member shortening due to shrink-age at time t

temperature differentialnumber of days at ambient temperature Telastic angle change at end of cantilever(Fig. 3.8)a factor used in determining theoreticalage related to the type of cement usedcoefficient of linear thermal expansionrotation of forward cantilever arm adja-cent to end span (Fig. 3.60)angle change due to restraint moment(Fig. 3.8)rotation of corner of box sectionrotation of forward cantilever arm adja-cent to interior span (Fig. 3.60)factor reflecting the influence of the rela-tive humidity of the ambient medium andthe composition of the concrete on Qrfactor reflecting the influence of the rela-tive humidity of the ambient medium andthe theoretical thickness of the concretehth On @r

115

fld(t-t,) = factor variable from zero to unity indi-cating the variation of #d with time

rClfW - Brct,, = factor variable from zero to unityindicating the variation of $f witht ime

6 = elastic deflection (Fig. 3.8)

EC, = creep strainE, = elastic strain

Esh = shrinkage strain at infinity

Esht = shrinkage strain at time tx = factor used in determining the theore-

tical thickness hth (Table 3.1)

P = perimeter of concrete section in contactwith the atmosphere

A. 4 References

1 .

2 .

3 .

4.

5 .

6 .

7 .

8 .

9 .

10.

11.

Kashima, S., and Breen, J. E., “Construction andLoad Tests of a Segmental Precast Box Girder BridgeModel” Research Report 121-5 (s), Center for High-way Research, The University of Texas at Austin,February, 1975.Post-Tensioning Institute, Post-Tensioning Manual,Glenview, Illinois, 1976.Ruesch, H., and Kupfer, H., “Bemessung von Spann-betonbauteilen,” Chapter M, Beton-Kalender, Wil-helm Ernst and Son, Berlin, 1977 (in German).Lin, T. Y., Design of Prestressed Concrete Structures,Second Edition, John Wiley & Sons, Inc., New York,1963.Leonhardt, F., Prestressed Concrete Design and Con-struction, Second Edition, Wilhelm Ernst & Sons,Berlin, Munich, 1964.American Association of State Highway and Trans-portation Officials, Standard Specification for High-way Bridges, Twelfth Edition, 1977, American Asso-ciation of State Highway and Transportation Officials,Washington, D.C.Muller, Jean, “Ten Years of Experience in PrecastSegmental Construction”, Journal of the PrestressedConcrete Institute, Vol. 20, No. 1. January - Feb-ruary, 1975.Scordelis, A. C., “Analysis of Continuous Box GirderBridges”, SESM 67-25, Department of Civil Engineer-ing, University of California, Berkeley, November,1967.Homberg, Helmut, “Fahrbahnplatten. mit Verand-lither Dicke” Springer-Verlag, New York, 1968.Homberg, Helmut, and Ropers, Walter, “Fahrbahn-platten mit Verandlicher Dicke”, Springer-Verlag,New York, 1965.Muller, Jean, “Concrete Bridges Built in Cantilever”,Societe des lngenieurs Civils de France, British Sec-tion, 1963.

a = stress7 = maximum shear stress in bottom slab

[Fig. 3.38(a)]7 = torsional shear stress

4 = ecr/ee, creep factor, also = @d + @f

@t = E,,/E~ at time t

@d = creep due to “delayed elasticity” or re-coverable creep on removal of load

Of = creep due to “flow”, not recoverable

~kt,) = magnitude of the creep factor at time t fora concrete specimen loaded at time t,

@d, = magnitude of “delayed elasticity” atinfinity

@f, = magnitude of “flow” at infinity

12.

1 3 .

1 4 .

15.

1 6 .

17.

18.

1 9 .

20.

21.

Leonhardt, F., and Lipproth, W. “Conclusions Drawnfrom Distress of Prestressed Concrete Bridges” Beton-und Stahlbetonbau, No. 10, Vol. 65, pp. 231-244,Berlin, October, 1970 (in German).Brown, R. C., Jr., Burns, N. H., and Breen, J. E.,“Computer Analysis of Segmentally Erected Pre-cast Prestressed Box Girder Bridges,” Research Re-port 121-4, Center for Highway Research, The Uni-versity of Texas at Austin, November, 1974.PCI Committee on Segmental Construction, “Rec-ommended Practice for Segmental Construction inPrestressed Concrete”, Journal of the PrestressedConcrete Institute, Vol. 20, No. 2, March - April,1975.

Prestressed Concrete Institute, Manual for QualityControl for Plants and Production of Precast Pre-stressed Concrete Products, Prestressed Concrete In-stitute, Chicago, 1977.

Portland Cement Association, Design and Control ofConcrete Mixtures, Eleventh Edition, Portland Ce-ment Association, Skokie Illinois, 1968.Comite’ Europeen du Beton /FIP, Bulletin d’infor-mation No. 111 October, 1975.

Freyermuth, Clifford L., “Design of ContinuousHighway Bridges with Precast, Prestressed ConcreteGirders”, Journal of the Prestressed Concrete Insti-tute, Vol. 14, No. 2, March - April, 1969, pp. 14-39.

Post-Tensioning Institute, Post-Tensioned Box GirderBridge Manual, Post-Tensioning Institute, Glenview,Illinois, 1978.Libby, James R., “Long Span Precast, PrestressedGirder Bridges”, Journal of the Prestressed ConcreteInstitute, Vol. 16, No. 4, July - August, 1971, pp.80-98.Freyssinet International, “Precast Segmental Can-tilever Bridge Construction”, Technical Brochure,May, 1973.

116