NU GIRDER BRIDGE DESIGN AND DETAILING MANUAL · The NU Girder Bridge Design and Detailing Manual documents current best practices for NU Girder bridge designs in Alberta. It is intended

NU GIRDERBridge Design and

Detailing Manual

Volume IManual

Version 1.0

August 2018

i

Alberta Transportation

NU Girder Bridge Design and Detailing Manual

Technical Services BranchAlberta Transportation

© Copyright, August 2018

The Crown in right of the Province of Alberta, as represented by the Minister of Transportation

Permission is given to reproduce all or part of this document without modification. If changes are madeto any part, it should be made clear that that part has been modified.

Alberta Transportation NU GIRDER BRIDGE DESIGN AND DETAILING MANUAL

ii

PREFACE

The NU Girder Bridge Design and Detailing Manual documents current best practices for NU Girder bridgedesigns in Alberta. It is intended to supplement the requirements of the Bridge Structures Design Criteria (BSDC).

The manual focuses on the design and detailing of NU Girder bridges. It also touches on conceptual designissues, drafting standards, and material specifications. As a result, certain components of this manual overlapwith other Department documents. The Department strives to provide consistency between these documents;however, changes to one document might not be immediately reflected in other documents. If a discrepancy isfound, the Consultant should ask the Department for clarification.

This manual includes exceptions, modifications, and clarifications of requirements in the BSDC, but does notcover all possible scenarios. It is not our intent to limit progress or discourage innovation. Consultants areencouraged to consider engineering options they deem appropriate for a specific site. The Department’s DesignException Process must be used to propose an engineering option that does not comply with this manual.

Our primary goal is to bring consistency to the design of NU Girder bridges in Alberta. Items pertaining togeometry, detailing, and materials will help produce a reasonably uniform design product. In the Department'sexperience, these items help reduce design, construction, inspection, and maintenance problems, whileproviding a reasonable balance between safety, quality, and cost.

Approved:

Date: aJohn AlexanderDirector, Bridge Engineering SectionTechnical Services BranchAlberta Transportation

Date: aDes WilliamsonExecutive DirectorTechnical Services BranchAlberta Transportation

john.alexander

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john.alexander

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September 04, 2018

john.alexander

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john.alexander

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September 04, 2018

john.alexander

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iii

ACKNOWLEDGEMENTS

The NU Girder Bridge Design and Detailing Manual was prepared in collaboration with Associated Engineering,Armtec, LaFarge, and Eagle Builders, with significant contributions from the following individuals:

Alberta TransportationJohn AlexanderMike TokarClayton Matwychuk

Associated EngineeringMichael PaulsenBala BalakrishnanJessica GagneKatrin HabelTara Alexander

ArmtecFilip BrogowskiJames Siffledeen

LaFarge CanadaJason RabasseNitesh Patel

Eagle BuildersJason McNuttKevin Kooiker


iv

LIST OF CHANGES

The following page is reserved for documenting changes to this version of the NU Girder Bridge Design andDetailing Manual. When changes are made to the manual, the following actions will be completed:

· The version of the manual will be updated;· A revision triangle will be placed next to the change in the manual;· A basic description and the date of the change will be summarized below.

Document Revision Date Description


v

TABLE OF CONTENTS

PREFACE IIACKNOWLEDGEMENTS IIILIST OF CHANGES IVTABLE OF CONTENTS VLIST OF TABLES VIILIST OF FIGURES VIIILIST OF SAMPLE CALCULATIONS X

1. OVERVIEW 1-12. NU GIRDERS 2-1

NU GIRDERS IN ALBERTA 2-1NU GIRDER APPLICATIONS 2-2FEATURES OF NU GIRDERS 2-3

2.3.1. Typical Features 2-32.3.2. Typical Sections and Spans 2-52.3.3. NU Girder Drawings 2-6

FABRICATION 2-72.4.1. Precast Certification 2-7

3. PRELIMINARY DESIGN CONSIDERATIONS 3-1GENERAL 3-1FABRICATION 3-3BRIDGE GEOMETRY 3-4

3.3.1. Horizontal Profile 3-43.3.2. Vertical Profile 3-53.3.3. Cross-Section Profile 3-53.3.4. Span Arrangement 3-53.3.5. Skew 3-6

BRIDGE ARTICULATION 3-73.4.1. Abutments 3-83.4.2. Piers 3-83.4.3. Bearing Types and Temporary Supports 3-9

GIRDER SELECTION 3-103.5.1. Girder Depth 3-103.5.2. Girder Spacing 3-103.5.3. Post-Tensioning 3-103.5.4. Girder Selection Design Tools 3-11

4. DETAILED DESIGN CONSIDERATIONS 4-1REFERENCES AND STANDARDS 4-4LIMIT STATES 4-4LOADS 4-5

4.3.1. Vehicle Load 4-54.3.2. Temperature Effects 4-54.3.3. Relative Humidity 4-6


vi

MATERIAL PROPERTIES 4-74.4.1. Material Resistance Factors 4-74.4.2. Concrete 4-74.4.3. Reinforcing Steel 4-154.4.4. Prestressing Strand 4-164.4.5. Structural Steel 4-17

EXPECTED LOAD HISTORY 4-184.5.1. Stage 1 - Fabrication 4-184.5.2. Stage 2 - Construction 4-194.5.3. Stage 3 – In-Service 4-19

PRESTRESSED DESIGN CONSIDERATIONS 4-204.6.1. Prestressed Concrete Stress Limits 4-204.6.2. Strand Debonding and Deviation 4-214.6.3. Post-Tensioning Considerations 4-244.6.4. Strand Transfer Length and Development Length 4-314.6.5. Loss of Prestress 4-324.6.6. Effective Modulus and Age-Adjusted Effective Modulus 4-44

PRESTRESSED DESIGN APPROACHES 4-464.7.1. General 4-464.7.2. Simplified Method 4-464.7.3. Detailed Method 4-484.7.4. Restraint Forces 4-53

PRESTRESSED CONCRETE DESIGN LIMIT STATES 4-584.8.1. Limit State Checks 4-594.8.2. Serviceability Limit States 4-604.8.3. Ultimate Limit States 4-704.8.4. End Zone Design 4-774.8.5. Related Elements 4-88

GLOSSARY OF TERMSLIST OF SYMBOLSREFERENCES

APPENDIX A: SECTION PROPERTIESAPPENDIX B: TYPICAL DETAILS DRAWINGSAPPENDIX C: NU GIRDER FABRICATIONAPPENDIX D: SECTION PROPERTIES NOTATION


vii

LIST OF TABLES

Table 4-1 Flow Chart for Detailed Design – Serviceability and Ultimate Limit States Check 4-3

Table 4-2 Effective Temperature 4-5

Table 4-3 Modifications to Effective Temperature 4-5

Table 4-4 Temperature Differential 4-6

Table 4-5 Material Resistance Factors 4-7

Table 4-6 Concrete Classes 4-7

Table 4-7 Reinforcing Steel Grades 4-15

Table 4-8 Steel Grades 4-17

Table 4-9 Expected Load History during Fabrication 4-18

Table 4-10 Expected Load History during Construction 4-19

Table 4-11 Expected Load History in Service 4-19

Table 4-12 Prestressing Tendon Stress Limits 4-20

Table 4-13 Prestressed Concrete Stress Limits 4-21

Table 4-14 Post-Tensioning Design Criteria 4-24

Table 4-15 Prestress Losses for Pretensioned Girders 4-34

Table 4-16 Prestress Losses for Post-Tensioning 4-35

Table 4-17 Friction Factors for Post-Tensioning 4-39

Table 4-18 Fixed End Moments for Creep 4-54

Table 4-19 Fixed End Moments for Shrinkage 4-56

Table 4-20 Limit State Checks at Fabrication 4-59

Table 4-21 Limit State Checks during Construction 4-59

Table 4-22 Limit State Checks in Service 4-60


viii

LIST OF FIGURES

Figure 2-1 Typical NU Girder Highway Overpass – 111 Street over Anthony Henday Drive 2-1

Figure 2-2 Belgravia Overpass – Fox Drive, Edmonton 2-2

Figure 2-3 Pretensioned NU Girder Features 2-3

Figure 2-4 Post-Tensioned NU Girder Features 2-4

Figure 2-5 NU Girder Bottom Flange – Prestressing Strand Grid 2-5

Figure 2-6 NU Girder Series 2-6

Figure 2-7 Completed NU Girder 2-7

Figure 3-1 Anthony Henday Drive over Whitemud Drive Bridge 3-1

Figure 3-2 Horizontal Curve Layout Considerations 3-5

Figure 3-3 Girder End Layouts for Skewed Bridges 3-6

Figure 3-4 Bridge Articulation for a Typical NU Girder Highway Overpass 3-7

Figure 3-5 Examples of Pier Articulation 3-9

Figure 3-6 Typical NU Girder Span Range – Effect of Continuity and Post-Tensioning 3-12

Figure 3-7 Preliminary Selection - Total Number of Strands - NU1600 3-13

Figure 3-8 Preliminary Selection - Total Number of Strands – NU2000 3-14

Figure 3-9 Preliminary Selection - Total Number of Strands – NU2400 3-14

Figure 4-1 NU Girder Bridge Construction 4-1

Figure 4-2 Shrinkage Strain Development with Time 4-10

Figure 4-3 Long-Term View of Shrinkage Strain Development with Time 4-10

Figure 4-4 Creep Coefficient and Creep Strain 4-11

Figure 4-5 Creep Coefficient with Time 4-15

Figure 4-6 Creep Coefficient with Time (Long-Term) 4-15

Figure 4-7 Prestress Relaxation 4-17

Figure 4-8 Example Debonded Strand Pattern 4-22

Figure 4-9 Example Deviated Strand Pattern 4-23

Figure 4-10 Example Splayed Strand Pattern 4-23

Figure 4-11 Example Tendon Profile 4-25

Figure 4-12 Typical Duct Arrangements and Limitations 4-27

Figure 4-13 Eccentricity of Curved Tendons 4-27

Figure 4-14 Strand Development Length 4-32

Figure 4-15 Prestressing Stress Levels – Pretensioned NU Girder 4-38

Figure 4-16 Wobble Friction Losses (Collins & Mitchell, 1997) 4-39


Page ix

Figure 4-17 Applied Stress Varying in Time 4-45

Figure 4-18 Stress Related Strain as a Function of Time 4-45

Figure 4-19 Example of Change of Girder Concrete Stresses Between Transfer and Erection 4-48

Figure 4-20 Example of Change of Deflected Shape Between Transfer and Erection 4-48

Figure 4-21 Positive Sign Convention 4-49

Figure 4-22 Linear Superposition of Load Effects 4-52

Figure 4-23 Two-Span NU Girder Bridge End Slopes and Restraint Moment 4-54

Figure 4-24 Shrinkage Restraint Moment 4-55

Figure 4-25 Two-Span NU Girder Bridge Shrinkage Restraint Moment 4-56

Figure 4-26 34th Street over Whitemud Drive, Edmonton, Alberta 4-58

Figure 4-27 Serviceability Limit State – Typical Design Process 4-61

Figure 4-28 Prestressing Geometry Definitions – Straight Strands 4-64

Figure 4-29 Prestressing Geometry Definitions – Deviated Strands 4-65

Figure 4-30 Example of Mid-Span Deflection for an NU Girder Bridge through Construction 4-67

Figure 4-31 Flexural Capacity – Strain Compatibility 4-71

Figure 4-32 Shear Capacity vs Shear Demand 4-72

Figure 4-33 Modified Compression Field Theory Definitions 4-75

Figure 4-34 Example Stress Flow at NU Girder End 4-77

Figure 4-35 Free-body Diagram of End Region of Beam 4-80

Figure 4-36 Available Development Length at End 4-80

Figure 4-37 End Zone 3D Strut-and-Tie Model 4-83

Figure 4-38 End Zone Bottom Flange Strut-and-Tie Model 4-84

Figure 4-39 General Zone and Local Zone (Clause C8.16.2.1 of the CHBDC) 4-86


x

LIST OF SAMPLE CALCULATIONS

Sample Calculation 1 Effective Temperature Determination 4-6

Sample Calculation 2 Shrinkage Strain Calculation 4-10

Sample Calculation 3 Creep Coefficient Calculation 4-14

Sample Calculation 4 Prestressing Relaxation 4-16

Sample Calculation 5 Post-Tensioning Profile 4-28

Sample Calculation 6 Plant Related Prestress Losses 4-36

Sample Calculation 7 Immediate Post-Tensioning Losses 4-40

Sample Calculation 8 Camber Calculation at Release 4-66

Sample Calculation 9 Camber Calculation at Deck Pour 4-69

Sample Calculation 10 Calculation of Shear Capacity 4-76


Page 1-1

1. OVERVIEW

NU Girders are Alberta Transportation’s preferred shape for medium- and long-span, precast concrete girderbridges. This manual presents best practices for design and detailing of NU Girder bridges in Alberta, along withcomprehensive design examples that include design calculations, code interpretation, and commentary.

This manual provides guidance to bridge engineers on the design and detailing requirements of NU Girderbridges. Its overall purpose is to help consultants produce safe, efficient, and economical NU Girder designs thatmeet the requirements of the Canadian Highway Bridge Design Code (CHBDC) and Alberta Transportation (theDepartment).

Volume I: NU Girder Bridge Design and Detailing

Chapter 2 NU Girders

This chapter provides:

· Context for the use of NU Girders in highway bridges across Alberta· Features of the NU Girder, including typical terminology and definitions, geometry and section

properties· Current Alberta Transportation Typical Details Drawings (Appendix B)· An overview of the fabrication process to produce an NU Girder

Chapter 3 Preliminary Design Considerations

This chapter reviews:

· Preliminary considerations when designing an NU Girder bridge, including girder selection, girderdepth and spacing, and when to consider post-tensioning

· Design guidance on the suitability of girder size, spacing, and number of strands· Bridge geometry, including horizontal alignment, vertical alignment, and skew· Bridge articulation, abutment type, piers, and the effect on NU Girder design· Considerations for girder selection

Chapter 4 Detailed Design Considerations

This chapter covers:

· Design considerations and criteria for completing the design of an NU Girder bridge, including materialproperties, CHBDC interpretation, the Department’s exceptions and variances to CHBDC, best practices,and specific design details

· Limit States applicable to NU Girders· Serviceability Limit States of stress and deformation· Ultimate Limit States flexure and shear

Volume II: Design Examples

Detailed design calculations and instructional commentary are provided for four design examples:

Example 1: Typical two-span highway overpassExample 2: Girder end zone design and detailingExample 3: Single-span integral abutment grade separationExample 4: Multi-span river crossing complete with post-tensioning


Page 2-1

2. NU GIRDERS

2.1. NU GIRDERS IN ALBERTA

The NU Girder is a precast, prestressed concrete bridge I-girder that was developed at the University of Nebraskain the 1990s. Its development was driven by several factors, including limitations with other I-girder shapes. Adistinguishing feature is that the NU Girder takes advantage of advances in precast concrete productiontechnology. The intent was to develop a girder series that was optimized for performance in two-span bridgesand with full-length post-tensioning.

Figure 2-1Typical NU Girder Highway Overpass – 111 Street over Anthony Henday Drive, Edmonton

Alberta engineers recognized the advantages of the new girder series from the early days of their inception. Thefirst bridge constructed using NU Girders in Alberta was the Oldman River Bridge in Taber, built in 2001.

Since then, the NU Girder’s optimized shape and prestressing layout has replaced other precast concrete girdertypes for span lengths of 20 m or greater. NU Girder depths typically vary from 1200 mm to 2800 mm and arefrequently used for spans up to 60 m, which covers most short- and medium-span ranges for bridges.

NU Girders have been used successfully in longer span structures and were extended to 65 m for the Bow RiverBridge on Deerfoot Trail.

Page 2-2

NU GIRDER BRIDGE DESIGN AND DETAILING MANUAL

2.2. NU GIRDER APPLICATIONS

In Alberta, bridges are designed in accordance with the Canadian Highway Bridge Design Code, CSA S6-14(CHBDC) and Alberta Transportation’s Bridge Structures Design Criteria (BSDC) version 8.0. For prestressedconcrete bridges, CHBDC Section 8 Concrete Structures defines specific requirements for the design of structuralcomponents made of cast-in-place and precast concrete reinforced with passive and/or prestressedreinforcement, including pretensioning and post-tensioning.

For over 30 years, Alberta Transportation has updated its bridge design criteria based on extensive design andconstruction experience. In addition to design considerations, the BSDC specify geometry, detailing, andmaterials that are meant to produce consistency in bridge design. A consistent approach to applying the bestpractices in BSDC and in this manual will also simplify construction, reduce maintenance, and extend the servicelife of Alberta’s NU Girder bridges.

A wide variety of precast girder bridges can be designed in accordance with federal and provincial codes andguidelines. Successful designs can be found across Alberta. In highway and urban settings, NU Girder bridgesare most competitive with other bridge types in the span range of 20 m to 60 m. Common bridge configurationsinclude single-span pretensioned concrete girder bridges, multi-span pretensioned girder bridges, and multi-span post-tensioned concrete girder bridges.

Prestressed concrete girders are used in straight and curved bridges, square and skewed bridges, and withconventional, semi-integral, and fully integral abutments. These configurations are not exhaustive; theDepartment encourages continued innovation and progressive designs.

Figure 2-2Belgravia Overpass – Fox Drive, Edmonton

NU Girders have found use in non-conventional configurations, including a trellis bridge arrangement.

Page 2-3

2 - NU GIRDERS

2.3. FEATURES OF NU GIRDERS

NU Girders are prestressed concrete girders, classified as either pretensioned girders or post-tensioned girders.Throughout this manual, pretensioned girders refers to girders that are prestressed by pretensioning only, whilepost-tensioned girders refers to those that are prestressed by both pretensioning and post-tensioning.

In a pretensioned girder (Figure 2-3), the top flange is reinforced with standard reinforcing steel, comprising abasic grid of transverse and longitudinal bars, and four straight prestressing strands.

The web is reinforced with two layers of shear reinforcement that are made of 10M or 15M rebar, or welded wirereinforcement (WWR). Projecting stirrups can be either closed U-Bars or two open hooks. While mostreinforcement in the NU Girder is regular black rebar, the projecting bars are corrosion resistant reinforcement(CRR). Within the web, deviated strands may run between the shear reinforcement.

Typically, the bottom flange is highly reinforced with straight prestressing strands, some of which may bedebonded or deviated. Bottom flange confinement reinforcing consists of the base WWR and a hat bar. At thegirder ends, there is a galvanized shoe plate on the bottom flange, which includes a series of shear studs.

The pretensioned girder shown would have a cast-in-place end diaphragm. In this case, the girder end has ashear key profile, and the portion of the girder end embedded into the diaphragm is also roughened inaccordance with Alberta Transportation’s Standard Specifications for Bridge Construction (SSBC).

Similar pretensioned girders are fabricated with an end block when a conventional abutment with steeldiaphragms is used.

Figure 2-3Pretensioned NU Girder Features

Top flangeprestressing

Shear key profile

Bottom flangeprestressing

Bottom flange reinforcing

Shear reinforcing

Deviated strands

Shoe plate

Projecting stirrups

Page 2-4


In post-tensioned girders (Figure 2-4), one or more ducts run between the web reinforcing. Though notillustrated here, post-tensioning ducts may be combined with deviated strands. The post-tensioning ducts aremade of corrugated galvanized steel.

Typically, when designed to be post-tensioned, NU Girders have reinforced concrete end blocks. The end blocksare reinforced with regular reinforcement and bursting reinforcement, and include block-outs at each anchorlocation.

In post-tensioned bridges, the bursting reinforcement and post-tensioning hardware may also be included in acast-in-place diaphragm. In these cases, there is no end block on the girder, and the post-tensioning ductsextend beyond the girder end.

Figure 2-4Post-Tensioned NU Girder Features

The end regions of NU Girders are highly reinforced, and care should be taken to add or change the reinforcingdetails of the NU Girder Bridge Typical Details Drawings described in Section 2.3.3.

Items not shown above, but typically required, include:

· Lifting hooks, used for handling the girders· Holes through web for end reinforcement, or for interior girder cross-bracing· Inserts for exterior girder cross-bracing· Girder Identification Label – located 1.0 m from the end on the underside of the girder bottom flange

or outside the area of the cast-in-place diaphragm (if girder end is embedded)

Bottom flangeprestressing

Shear reinforcing

End block

Post-tensioning anchorage(bursting reinforcement

not shown)

Projecting endblockstirrups

Shoe plate

Post-tensioning ductEnd block reinforcing

Top flange prestressing

Projectingstirrups

Bottom flangereinforcing

Page 2-5

2 - NU GIRDERS

The Department’s requirements for surface treatment for NU Girder bridges are indicated on Standard DrawingS-1851 and in the SSBC. In general, the outside of exterior girders has a Class 3 bonded finish; all other surfaceshave a Class 1 ordinary surface finish.

In Alberta, NU Girders can be fabricated in depths ranging from 1200 mm to 2800 mm, in increments of 400mm. NU Girders were developed in hard metric units, and as such are often referenced without including theunits (e.g., a 2000 mm deep NU Girder is referred to as an NU2000).

In the development of the NU Girder, the size and shape of the flanges were optimized for a range of criteria(Geren and Tadros 1994) including taking advantage of high-performance concrete. In prestressed concretegirders, the bottom flange is important in determining the maximum achievable span for a specified girderdepth. The size and shape were largely influenced by the ability to fabricate girders in existing plants andmaximize the area of prestressing strand that could be placed within the flange.

Structural efficiency of I-girder shapes improves as web thickness decreases. For the NU Girder series, the webwidth was sized to accommodate both reinforcement and post-tensioning ducts, while maintaining thenecessary cover. For girders without post-tensioning, additional strands that are deviated may be located withinthe web. In Alberta through collaboration with the fabricators a consistent web width of 185 mm is usedregardless of whether the girders are pretensioned or post-tensioned.

For the NU Girder series, a maximum of 72 strands can be accommodated (Figure 2-5). Additionally, four bondedprestressing strands shall be incorporated in the top flange, to assist in controlling stresses at transfer duringtransportation and during construction. Of the 72 strands, up to 26 are located within the web. These 26 strandscan be deviated as necessary for design. If the girders will be post-tensioned, a maximum of four ducts aretypically used, which displaces some of the web prestressing.

Figure 2-5NU Girder Bottom Flange – Prestressing Strand Grid

Page 2-6


See Appendix A – Section Properties for the NU Girder sizes available in Alberta, along with the geometricproperties.

NU1200 NU1600 NU2000 NU2400 . NU2800

Figure 2-6NU Girder Series

Each girder size has a broad range of applicable span lengths and a variety of factors, including loading,transverse girder spacing, and whether the bridge is post-tensioned (Figure 2-6). Chapter 3 reviews design toolsavailable in selecting the appropriate NU Girder size.

Design drawings shall be completed in accordance with the Department’s Engineering Drafting Guidelines forHighway and Bridge Projects which includes drawing layouts, checklists and standard notes requirements.

NU Girders shall also be designed and detailed in accordance with the Department’s NU Girder Bridge TypicalDetails Drawings (Appendix B). Typical Details Drawings are not engineered documents. Rather, they providedirection to Consultants on the Department’s preferred details when completing designs and shall be usedunless the Department’s approval is obtained.

The Typical Details Drawings are provided in Appendix B – Typical Details Drawings.

T-1750-17 NU Girder Bridges Typical Details – Sheet 1 covers girder layouts, girder sections and finishes,and girder elevations.

T-1751-17 NU Girder Bridges Typical Details – Sheet 2 covers cross-section reinforcement for prestressedand post-tensioned girders.

T-1752-17 NU Girder Bridges Typical Details – Sheet 3 covers end details.

T-1753-17 NU Girder Bridges Typical Details – Sheet 4 covers cross-bracing, haunch details, and pierdiaphragm connections.

Page 2-7

2 - NU GIRDERS

2.4. FABRICATION

The fabrication of an NU Girder is a specialized process. Since the use of NU Girders began, the precastingcommunity has worked to improve fabrication efficiency while working with the Province and Consultants inimproving girder designs.

Girder designs affect the entire fabrication process, from preparing the forms to girder stressing and removalwithin a 24-hour period. A successful NU Girder design must also allow for economical fabrication. To use NUGirders successfully and economically, Consultants must have a solid understanding of reinforcing andprestressing details and how designs affect girder fabrication quality and scheduling. This manual incorporateslessons from decades of precast girder fabrication in Alberta.

See Appendix C – Fabrication for an overview of the fabrication process for a typical NU Girder. For a morethorough understanding of the fabrication process, constructability, and indicative pricing, Consultants areencouraged to contact precast Fabricators.

Figure 2-7Completed NU Girder

NU Girder fabrication must be completed by a precast fabricator certified by the Canadian Precast/PrestressedConcrete Institute (CPCI) Certification Program in Group B (Bridge Products) in category B4 or BA4 for all NUGirder types, and in category B3 or B3A for NU Girders with straight strands only.

Cost of NU Girder Fabrication

Market forces that influence the cost of NU Girders include:

Labour – Subtle changes in detailing can substantially increase labour effort in production. Productionrequires a 24-hour turn-around in girder fabrication. Changes or complexity may require undesirableincreases in effort to maintain the production cycle.

Materials – The costs of commodity materials such as reinforcing steel, prestressing strand, and cementused in concrete production are the main contributors to material costs. Due to the multiple materialcomponents, NU Girder costs are buffered from any one commodity price fluctuation.


Page 3-1

3. PRELIMINARY DESIGN CONSIDERATIONS

3.1. GENERAL

The overall objective when designing bridges is to develop cost-effective, functional, aesthetically pleasing, anddurable solutions that will require minimal future maintenance. Preliminary design is a critical step in every bridgeproject. Decisions made in this phase will affect bridge geometry, including girder depth and spacing, bridgeskew and deck geometry, overall length, and span arrangement. Further, the bridge articulation is defined,including determination of fixed and expansion joints, pier connectivity, and abutment configuration.

These decisions affect the overall cost of the project. It is crucial for the Consultant to see the overall picture andoptimize the bridge layout while meeting design requirements and constraints.

NU Girders place specific constraints on bridge designs, which may also be constrained by topography,environmental limitations, or roadway constraints. The final selection of the bridge layout should be the bestsolution to meet all project objectives.

If the girder selection pushes the limits of feasibility during preliminary design, small changes during detaileddesign may require reconfiguration of the entire superstructure. For example, if deeper girders are required, thiscould affect not only the bridge structure itself but the approach road geometry as well. Thus, the Consultant iscautioned when pushing limits of the system during preliminary design, as there are still uncertainties in thedesign.

Figure 3-1Anthony Henday Drive over Whitemud Drive Bridge

Optimizing the Bridge LayoutThe intent of preliminary design is to establish an efficient bridge layout, not just to achieve an efficientgirder design. Consultants are cautioned that the process involves a balance between optimized girderdesign and the transfer of costs onto other aspects of the bridge. This balance shall be considered whendeveloping an optimum bridge layout.

One example could be the use of post-tensioning to eliminate a girder line, which would increase the costand complexity of the girders in fabrication but would also lead to a more efficient and cost-effective bridge.

Page 3-2


This section presents areas of considerations in bridgedesign as they relate to the use of NU Girders. Theseinclude:

FabricationWhen detailing NU Girders, understanding whichelements of design add significant cost and which canbe incorporated or modified at low cost.

For example, although repeatability is important forprecast efficiency, making changes to the number of deviated strands between girders does not significantlyaffect cost. But changing the deviation points will increase cost.

Bridge GeometryWhen determining the bridge profile, understanding the implications of NU Girders on horizontal profile, verticalprofile, cross-section, span arrangement, and skew.

For example, understanding that changes to the NU Girder form drive NU Girder costs. When completing an NUGirder bridge layout for complex geometry, avoid changes to skew and diaphragm locations.

Bridge ArticulationWhen making decisions on the bridge abutment and pier articulation, understanding the effect on NU Girderdesign.

For example, using concrete diaphragms can allow for simplicity in girder design using the diaphragm toaccommodate the bridge skew or small changes in span length.

Girder SelectionWhen selecting a girder section, selecting appropriate prestressing levels for the span and spacing, as well asunderstanding the ranges for optimal use for the various NU Girder sections, depending on span continuity andpost-tensioning use.

For example, avoiding the initial selection of girders at the upper end of their applicable span range, to avoidsignificant challenges controlling stresses during detailed design.

These considerations are discussed in more detail below.

Structures Alternative Report

In Alberta, the Structures Alternative Report isused to document the preliminary design phasein bridge design. The report includes arecommendation on the type of structure to becarried forward to detailed design.

Page 3-3

3 - PRELIMINARY DESIGN CONSIDERATIONS

3.2. FABRICATION

When designing NU Girder bridges and developing the preliminary and detailed design of NU Girders, it isimportant to consider design features that affect fabrication.

SimplicityThe Typical Details Drawings for NU Girders (Appendix B)represent several iterations of design, fabrication, andconsultation with the Precast industry. These details provide acommon, simple approach to detailing NU Girders. Thesedetails have been found to be cost-effective and should formthe basis for NU Girder Design.

RepeatabilityGenerally, maximum repetition makes precast structures costeffective. Consultants should take advantage of repetition,rather than trying to optimize individual girders. This appliesto girder size and layout, but also to concrete mix designs andother aspects that could be optimized.

Within a given span, design each girder to the same sectionand strand pattern. Economy in precasting results from theproduction of identical units. Consultants should aim to keepall girder lengths the same and avoid small increases in lengthto accommodate varying skew. Rather, look to incorporatethese differences into the cast-in-place diaphragms.

ConstructabilityOther important considerations during preliminary design areconstruction aspects such as fabrication, lifting, storage,transport and erection, and onsite construction activities.

Erection and transportation limitations often govern the sizeof girders and can be the decisive factor in the choice ofsystem.

Girder DesignThe following considerations apply when designing NU Girders for any given bridge:

· The cost of changing the forms increases costs more than the actual cost of materials.· Changes can introduce cost and risk of error.· Changes in span length are less expensive to accommodate than changes in girder depth.· Changes in strand patterns are relatively easy to accommodate, although Consultants should minimize

changing locations for hold-down points.· Deviated strands require an extra stage in the stressing operation.· Keep attachments (e.g., for diaphragms) at similar locations to limit modifications of forms.· Avoid skew variations where possible, to avoid changes to the form bulkhead.

Rules of Thumb for Cost-EffectiveNU Girder Designs

Simplicity: Keep it simple. Make use ofproven details.

Repeatability: Repetition and modularitylower the cost.

Constructability: Check freight andinstallation constraints specifically for eachproject.

Reinforcing: Watch the rebar content –100 kilograms per cubic metre is usuallyan indication of good design.

Girder Lines: Fewer lines of girders aremore economical.

Post-Tensioning: Post-tensioning instages can give higher load capacity forthe same depth of girders and result infewer lines of girders but will require moreelaborate onsite construction.

Maintenance: Design with maintenance inmind. Complex designs download costs toconstruction and maintenance.

Concrete Strength in Fabrication

Fabricators in Alberta have developed their concrete mixes to achieve a consistent specified releasestrength of 45 MPa and specified 28-day strength of 70 MPa. As such there is no advantage in specifyinglower release or 28-day strengths. Additionally, Consultants shall not specify strengths greater than thosepresented, as there would be extensive cost implications.

Page 3-4


3.3. BRIDGE GEOMETRY

The overall bridge and headslope geometry (e.g., roadway profile, roadway plan, clear road width, streambedwidth) must comply with the Department’s Bridge Conceptual Design Guidelines and the BSDC. Pinch pointswith the vertical and horizontal clearance envelope often govern the bridge layout. It is often not enough to justconsider the centreline profile. Consideration at the extents of the bridge is necessary (i.e., exterior girder linesand edges of substructure).

Consultants often deal with profile changes by adjusting abutment seat heights at the girder ends as well as inthe haunches. The interaction of horizontal, vertical, and cross-section profiles needs to be carefully establishedwhen determining the girder layout, abutment seat elevations, haunch heights, and other girder layout aspects.In particular, this is a consideration for irregular bridges, to accommodate cross-falls, skews, and vertical roadwayprofiles.

In general, it is preferable for bridges to be on tangent square alignments. Irregular bridges, such as curved,skewed, or flared bridges, require extra design and detailing, and cost more for construction and maintenance.

Curved NU Girders are not available; however, straight NU Girders can be used for horizontally curved bridgesunder certain circumstances. The girder arrangement must take into account the curvature and span length.Chord/curve offsets need to be carefully considered.

The main impact of curvature is typically on the exterior girders where the extent of deck overhang at mid-spanand at piers must be evaluated, and impact on girder design determined. Where curves are tight, the overhanglength may limit girder layout and span lengths. The girder layout at piers should consider overhangs andchanges in girder chord direction (kinks) between girder lines of adjacent spans. These can lead to interferenceand must be considered in the pier diaphragm layout. Transverse load effects of the changes in girder directionat the piers should be considered in the design, in particular in continuous structures, and if the Consultantconsider post-tensioning of the structure.

For curved bridges, the skews between girders and substructure impact girder layout, girder ends, and pier andabutment geometry (see Figure 3-2).

Repetition is key in making precast girders cost-effective. To keep pier and abutment diaphragms at reasonablewidths, girder lengths may need to be varied and girder ends skewed. It is also easier for Fabricators to varygirder length than to change skew angles. Thus, in general, the number of different skew angles should belimited.

However, as the decision regarding layout of the girders directly affect substructure arrangement and cost, theConsultant must consider the costs transferred to the substructure when establishing the girder layout with thegoal of optimizing the overall bridge design.

Page 3-5


Figure 3-2Horizontal Curve Layout Considerations

The profile of the roadway over the bridge may include crest or sag curves. The impact of the vertical alignmenton the NU Girder design is often in bearing elevation and haunch variations. Variations in girder slopes can beaccommodated by setting bearing elevation for each girder and varying the longitudinal slope of the girders.

In special cases, such as low speed environments or for pedestrian bridges, the vertical curve can be significant,which could lead to large variations in haunch heights. Curved bridges with large cross-falls can also result indeep haunches.

Deck cross-sections have a crown or are on a super-elevation; these are usually accommodated by bearingelevation and haunch variations. Transitions in cross-sections create complications for the haunch and deckgeometry.

NU Girders are typically used with spans up to about 60 m, although longer spans can be achieved. Under certaincircumstances, splicing of the NU Girders could be considered. However, this would involve significant additionaldesign, fabrication, and construction considerations and would require Department approval. In general, one-piece girders are more economical than spliced girders.

The BSDC require the same number of girder lines in continuous systems.

Varying skew around a horizontal curve

Constant skew around a horizontal curve

Page 3-6


The span arrangement is often governed by site constraints and can be the determining factor for selecting thebridge system. Without geometric site constraints, the span arrangement ideally follows span length ratiosbetween adjacent spans, as suitable for the chosen bridge articulation. Generally, it is preferable to minimizespan length variations where reasonably possible, to minimize precast costs.

Ideally, continuous spans have similar lengths for all interior spans, with end spans between 0.65 and 0.85 of theinterior span length. Ideal arrangements cannot always be achieved. Where span arrangements are governed byother constraints, the girders should be chosen to best accommodate the required span layout.

Where short end spans are required, the structure should be checked for uplift.

Square girder ends are the most cost-effective and should be used where possible. Where the girder ends areon a skew to the support line, the following shall be considered:

· For small skews (less than 15°): It is preferable to keep girder ends square and deal with skewed end inthe cast-in-place diaphragms.

· For larger skews (15° to 30°), round the skew to the nearest 5°.· For large skews, the skewed flange should be trimmed as shown in Figure 3-3 (B) and Figure 3-3 (C) to

avoid corner spalling, simplify detailing and save on diaphragm depth.

INSERT FIGURE

Figure 3-3Girder End Layouts for Skewed Bridges

For post-tensioned bridges, the anchorage of the post-tensioning needs to be adjusted, as required toaccommodate skewed ends.

(A) Square Girder End (B) Chamfered Flange (C) Skewed Girder End

Page 3-7


3.4. BRIDGE ARTICULATION

The articulation of the structure is the Consultant’s choice and will depend on bridge geometry, site constraints,and system efficiency. The chosen articulation must be suitable for bridge geometry and site constraints. TheDepartment’s preference is that the use of joints and bearings is minimized within guidelines and acceptablestress/deformation limits.

When choosing the bridge articulation, the Consultant shall consider limits given by thermal and other effectsthat cause strains, deformations, or displacements.

Generally, the Consultant has the following choices at abutments and piers:

· Abutments:

o Conventional abutmentso Integral abutments (semi-integral and full integral)

· Piers:

o Diaphragms/girders integral with pierso Diaphragms/girders supported by bearings

Figure 3-4Bridge Articulation for a Typical NU Girder Highway Overpass

BRG ABUT 2

EXP

HWY

FXD

HWY

EXP

BRG ABUT 1PIER & MEDIAN

Page 3-8


Several different criteria are involved in the selection of abutment types, and this design shall be completed inaccordance with the BSDC. Issues that related specifically to NU Girder bridges include:

· Thermal span and selection of cycle control joints· Out-of-plane and skew forces acting on the abutment system· Long-term movements due to creep and shrinkage

Conventional abutments: The BSDC requires open steel diaphragms for conventional abutments, to allow forfuture deck joint inspection and repair. NU Girders used in conventional abutments require an end block andthe prestressing strands at the girder ends need to be adequately protected.

In addition to the thermal span, sizing the deck joints requires consideration of the long-term shortening of thestructure due to creep and shrinkage. Long-term rotations resulting from creep need to be considered whendesigning bearings to have adequate rotational capacity.

Integral abutments: The type of integral abutment will be either semi-integral or fully integral.

NU Girders with semi-integral abutments have bearings at the girder ends. Dependent on the chosen type ofsemi-integral abutments, abutment forces need to be accounted for in the NU Girder design. Semi-integralabutments generally make the structure more durable, since they eliminate deck joints; however, they stillinclude bearings, which will require maintenance over the life of the structure.

Semi-integral abutments have reduced strains/loads on the substructure, when compared to fully integralabutments. Consideration should be given to extend the deck slab beyond the abutment backwall to move thetransition from deck to approach slab beyond the abutment. Where approach slabs terminate above the bearingseat, open steel diaphragms are required to allow for future inspection and repairs.

Fully Integral abutments eliminate joints and bearings. They require full moment and shear connection betweenthe girder ends and the abutment, which can be achieved through shear friction, by extending strands beyondthe girder ends and anchoring them in cast-in-place concrete as well as by reinforcing bars through the websof the NU Girders. This connection is designed with a concrete end diaphragm. The embedment of the NUGirders in the concrete end diaphragm also reduces risks associated with end zone cracking.

The negative moment resistance of NU Girders is small; thus, the continuity needs to be made throughcontinuous reinforcing between the abutment and deck slab. In the horizontal direction, integral abutmentsbear directly against the soil and need to remain within the thermal span limits of the BSDC.

The girders must be supported on temporary bearings until they are made integral with the abutments. Inaccordance with the BSDC, a minimum of 150 mm of concrete is to be cast below the girders.

For both semi-integral and fully integral bridges, time-dependent effects on rotation, shortening, and restraints,resulting from creep and shrinkage need to be considered.

The choice of pier type depends on the topography, span arrangements, and other considerations. The girderscan sit atop of piers on bearings or be made composite with the pier cap through a cast-in-place concretediaphragm.

The BSDC require continuous cast-in-place concrete diaphragms at piers. Where concrete is cast fully aroundgirder ends, the BSDC require a plinth of a height of minimum 150 mm, to allow for sufficient diaphragmconcrete being cast below the girders. The BSDC further require separation of girder ends by at least 300 mm.

It is generally advantageous to make the superstructure at the pier continuous and possibly monolithic with thepier, to improve durability and minimize the use of deck joints and bearings. Where piers are made monolithicwith the superstructure, the impact of thermal and other restraint effects or deformations must be assessed, andthe stiffness of the entire system must be evaluated.

Page 3-9


Fixed Pier/Girder ConnectionAnthony Henday Drive over Wedgewood Creek

Hinged Articulation at Pier111 Street over Anthony Henday Drive

Figure 3-5Examples of Pier Articulation

Longitudinal superstructure continuity at the piers is achieved through a cast-in-place deck and diaphragm andmay also include post-tensioning.

The continuity achieved through cast-in-place concrete pier diaphragms and continuous deck reinforcingprovides continuous behaviour for live loads and superimposed dead loads only. While this method of attainingcontinuity may not be structurally as optimized as a post-tensioned system, it combines many of the advantagesof fully continuous systems without the requirements of post-tensioning. Note that careful crack control of thedeck is required, achieved through reinforcing detailing in the negative moment regions. These systems aresuited for monolithic pier construction or construction with a double bearing line.

Continuity may also be achieved by post-tensioning the girders. Girder shortening and camber effects need tobe considered when laying out the structure, and the Consultant needs to investigate how the post-tensioningprocess affects girder displacements at the piers or builds in restraints. Post-tensioning allows balancing ofmoments and makes the system overall structurally efficient.

A single bearing line may be appropriate; however, this requires approval from the Department. Single bearinglines allow narrower pier caps but will require temporary support for construction. They are only acceptablewhen the bridge is post-tensioned and requires careful detailing.

A broad range of bearings can be used with NU Girder bridges. Bridge articulation, abutment type, and pier typewill affect the demands on the bearings and thus the selection of bearing used in design. In Alberta, laminatedelastomeric bearings are the preferred option. Where these bearings cannot be used, pot bearings should beconsidered.

The bearing design needs to consider all displacements that can occur during construction and under serviceconditions. Longitudinal bearing displacements include not only temperature movements, but also, shrinkage,creep, post-tensioning effects, and settlement. In the transverse direction, the Consultant must assess fixity andrestraints of the substructure.

Plain unreinforced elastomeric bearing pads can be used to support NU Girders on pier caps or abutment seatsduring construction before the girder ends are cast fully into a cast-in-place reinforced concrete diaphragm.

Page 3-10


3.5. GIRDER SELECTION

Girder selection, including choice of depth and spacing, is typically governed by span length, geometricconstraints, and loading. The Consultant should be aware of the trade-off between redundancy and economicsin superstructure design. The weight, depth, and length of girders have an effect on fabrication, transportation,and erection. Consultants need to understand fabrication, transportation, and erection limits, and discussionwith Fabricators is encouraged.

Girder depth is often controlled by vertical clearance requirements to the roadway beneath or minimumhydrotechnical soffit elevation requirements. To minimize approach grades this often leads to requirements fora shallow superstructure, and therefore a high span-to-depth ratio.

Each girder depth has an efficient range. Girder use beyond this range is not ideal as it may lead to high stressesfrom excessive pretensioning resulting in cracks, complicated strand debonding and deviation patterns,congested reinforcing, or other unforeseen consequences. When using NU Girders at the upper end of theirrange, it is recommended to engage Fabricators to identify potential risks and mitigation at an early stage.

When a structure is not controlled by vertical clearance limitations, the optimal girder depth should bedetermined based on the optimal fabrication, transportation, and erection cost. When a structure is controlledby vertical clearance limitations, the following considerations also apply when selecting the girder depth:

· For a given girder depth, it can be advantageous to use the girder to its maximum span, even if moreprestressing strands and reinforcing bars are required.

· By using a girder to its maximum span capability, a longer span can be achieved without increasing thedepth of the superstructure.

For varying span lengths within a structure, it is typically preferred to use the same girder depth consistentlyalong the bridge length, rather than optimizing each span to achieve minimum span-to-depth ratios.

Girder spacing is typically limited by deck design considerations and by the minimum number of girdersrequired. The BSDC require all slab and girder bridges to have a minimum of four girder lines and limits maximumgirder spacing and overhangs to the limits of the empirical deck design method. This can control girder spacingin narrow bridges. For wider bridges, wider girder spacing, within BSDC and CHBDC requirements, can be morecost effective, since the costs of an additional girder line often outweigh the additional deck concrete costs.Efficiency in the number of girder lines needs to be balanced with additional dead loads needed for thickerdecks.

Post-tensioning has been used successfully for many NU Girder bridges in Alberta. Post-tensioned NU Girderbridges provide several advantages including:

· Reducing pretensioning demand on the girders, which can reduce fabrication related cracks· Increasing achievable span for a particular girder section· Allowing for wider girder spacing, with the potential to reduce the total number of girder lines· Increased durability

The benefits should be considered along with the following construction issues:

· Access to install the post-tensioning and carry out the stressing· Limitations on the amount of post-tensioning with respect to stress limits in the strands and in the

girders

Page 3-11


· Additional costs incurred by additional onsite operations· Schedule implications of an additional stage in construction· Challenges in future widening should be considered for bridges with planned widening in the

foreseeable future.

The number of post-tensioning ducts, their profile and post-tensioning forces and stages are determined basedon statics principles and stress limits and follow the same principles as the design of other prestressedcomponents.

The post-tensioning strands are typically stressed in either one or two stages. While multistage post-tensioningallows for a better optimization of the girders, the additional efforts and potential schedule implications mayoutweigh the benefits gained through the multistage stressing. In addition, the post-tensioning cables need tobe protected between first strand installation and final grouting to avoid premature deterioration of the strands.Post-tensioning stages should be assessed on a project basis.

Selecting the optimum girder depth requires an understanding of the range of applicability for NU Girdersections considered. Each girder section has a range of applicability depending on girder spacing, amount ofpretensioning, and whether it is continuous or post-tensioned.

The figures presented in this section are intended for use in girder selection during preliminary design. Thesefigures are based on recent experience and recorded data of over 200 NU Girder bridges constructed withinAlberta and represent what has been successfully designed and constructed. These figures are meant forguidance in preliminary design only and are not meant to be definitive limits on NU Girder use, nor be used asdetailed design tools. NU Girders that fall outside the limits of these figures may be feasible in certain situations,however in these situations the Consultant will need to complete more sufficient calculations during preliminarydesign to confirm the design will work.

Page 3-12


NU Girder Span Range

Figure 3-6 presents the range in span that each NU Girder section can be applied, considering the simply-supported span range, and the effect to which continuity, and post-tensioning can extend the span range. Thisfigure is based on existing structures, and is applicable for average girder spacings of 3.0 m to 3.2 m.

Figure 3-6Typical NU Girder Span Range – Effect of Continuity and Post-Tensioning

Page 3-13


NU Girder Target Pretensioning and Post-Tensioning

The figures below present the total number of prestressing strands that may be expected, dependent on spanlength, and whether the girder is pretensioned only, or pretensioned and post-tensioned. The figures are basedon data gathered from over 200 NU Girder bridges constructed in Alberta. Based on available information,figures have been prepared where sufficient data exists. This includes the NU1600, NU2000 and NU2400.

The figures present an expected total number of strands based on the span length, and whether the structure ispretensioned only, or pretensioned and post-tensioned. The total number of strands includes the strands locatedin the top flange. The expected range is based on an average girder spacing of around 3.0 m to 3.2 m.

The ranges presented in these figures have been found to lead to feasible designs. While designs may becompleted outside of these ranges, Consultants are cautioned that additional effort during preliminary designmay be necessary to confirm feasibility and avoid changes to the structure layout during detailed design.

Figure 3-7 presents the expected total number of strands for the NU1600 series, Figure 3-8 presents the expectedtotal number of strands for the NU2000 series, and Figure 3-9 presents the expected total number of strands forthe NU2400 series.

Figure 3-7Preliminary Selection - Total Number of Strands - NU1600

Page 3-14


Figure 3-8Preliminary Selection - Total Number of Strands – NU2000

Figure 3-9Preliminary Selection - Total Number of Strands – NU2400


Page 4-1

4. DETAILED DESIGN CONSIDERATIONS

Alberta Transportation’s criteria for NU Girder bridge designs include the design considerations and codeinterpretation outlined in this section.

This section presents design considerations in the general order that a Consultant would follow in completingthe detailed design of an NU Girder bridge:

· Establish design criteria:

o Section 4.1 References and Standardso Section 4.2 Limit Stateso Section 4.3 Loadso Section 4.4 Materialso Appendix A NU Girder Section Properties

· Define expected load history for fabrication, construction, and service, as well as the specific limit stateschecks required:

o Section 4.5 Expected Load History

· Design for Serviceability and Ultimate Limit States

o Section 4.6 Prestressed Concrete Design Considerationso Section 4.7 Prestressed Concrete Design Approacheso Section 4.8 Prestressed Concrete Design Limit Stateso Section 4.8.1 Limit State Checkso Section 4.8.2 Serviceability Limit Stateso Section 4.8.3 Ultimate Limit States

Figure 4-1NU Girder Bridge Construction

Page 4-2


This manual focuses on aspects of design that are relevant to NU Girder bridges. Consultants are encouraged toreference relevant Alberta Transportation publications and the Canadian Highway Bridge Design Code CSA S6-14(CHBDC) for guidance on the overall bridge design process.

The manual also assumes that readers understand prestressed concrete design principles. Several references areavailable for additional information on prestressed concrete design:

· Prestressed Concrete Basics, Collins and Mitchell· Concrete Structures Stresses and Deformations, Ghali and Favre· The Design of Prestressed Concrete Bridges, Concepts and Principles, Robert Benaim· Prestressed Concrete Bridges, Christian Menn· CPCI Design Manual

Page 4-3

4 - DETAILED DESIGN CONSIDERATIONS

Example Flow Chart for Serviceability and Ultimate Limit States Checks

Table 4-1Flow Chart for Detailed Design – Serviceability and Ultimate Limit States Check

Step 1: Establish Bridge Design Requirements and Criteria

A. Codes and ReferencesB. Climatic and EnvironmentalC. Section PropertiesD. Material PropertiesE. Geometry

Step 2: Define Expected Load History and Stages of Construction

A. Stage 1: FabricationB. Stage 2: ConstructionC. Stage 3: Service

Step 3: NU Girder Design

A. Prestressed Design Considerationsa. Prestressed Girder Stress Limitsb. Debonding/Deviation

of Strandsc. Post-Tensioning Considerationsd. Transfer Length and

Development lengthe. Loss of Prestressf. Effective Modulus and Age-

Adjusted Effective ModulusB. Serviceability Limit State ChecksC. Ultimate Limit State Checks

Bridge design criteria include preliminary engineering results andcriteria for completing detailed designs.

References:

· Section 4.1 for References and Standards· Section 4.2 for Limit States· Section 4.3 for Loads· Section 4.4 for Materials· Appendix A for NU Girder Section Properties

NU Girder design is an iterative process to establish the optimumprestressing strand layout/post-tensioning layout. The process involvesconsideration of several criteria unique to prestressed concrete. Theseinclude prestressed loss, transfer length, continuity and restraintmoments, and the effects of creep and shrinkage.

NU Girder selection is typically governed by the Serviceability LimitStates, with Ultimate Limit State checks being completed last duringdesign.

References:

· Section 4.6.1 for Prestressed Concrete Stress Limits· Section 4.6.2 for Strand Debonding and Deviation· Section 4.6.3 for Post-Tensioning Considerations· Section 4.6.4 for Transfer Length and Development

Length· Section 4.6.5 for Loss of Prestress· Section 4.6.6 for Effective Modulus and Age-Adjusted

Effective Modulus· Section 4.7 for Prestressed Design Approaches· Section 4.8.2 for Serviceability Limit States· Section 4.8.3 for Ultimate Limit States

Load history provides the basis for analyzing stages of construction anddefining age at loading, age at erection, time of deck pour, post-tensioning stages (if applicable), and application of superimposed deadloads.

References:

· Section 4.5 for Expected Load History

Page 4-4


4.1. REFERENCES AND STANDARDS

Alberta Transportation bridges are designed to the BSDC and are required to meet a minimum design life of 75years. When completing a design in accordance with the Department’s requirements, Consultants must meetadditional criteria.

Consultants shall use the most current version of the following standards and publications for the completionof an NU Girder bridge design. At this manual’s initial publication date, the current reference standards andpublications include:

· Bridge Structure Design Criteria, Version 8.0. (BSDC)· Canadian Highway Bridge Design Code CSA S6-14 (CHBDC)· Bridge Conceptual Design Guidelines, Version 2.0· Engineering Drafting Guidelines for Highway and Bridge Projects, Version 2.1.· Standard Specifications for Bridge Construction, Edition 16, 2017 (SSBC)

4.2. LIMIT STATES

In designing an NU Girder bridge, the Consultant shall check stability and strength in the ultimate limit state(ULS), and cracking, deformations, stresses, and vibration in the serviceability limit state (SLS). It is also necessaryto consider the construction sequence and check the appropriate limit states through construction and intoservice.

When reviewing the design of an NU Girder, the main stages of construction and limit states are:

· Fabrication

o SLS: Stresses in the concrete and prestressing steel at release

· Construction

o SLS: Stresses in the concrete and prestressing steel at various stages, such as deck pour, post-tensioning (if applicable)

o SLS: Deformations (camber prediction and girder shortening)o ULS: Strength and stability under construction loads

· Service

o SLS: Stresses in the concrete and prestressing steel in the short and long term under applicableload combinations

o SLS: Deformations and vibrationo ULS: Strength and stability

Page 4-5


4.3. LOADS

All loads are determined in accordance with Section 3 of CHBDC and BSDC. This includes dead loads, earth loads,secondary prestress loads, and live loads. Loads specific for NU Girder bridges in Alberta are described below.

In Alberta, for highway bridges, the design vehicle is a CL-800 Truck. This corresponds to the CL-W Truck asdefined in the CHBDC, with a total weight of 800 kN. No adjustments are required for the 9 kN/m uniformlydistributed load for lane load.

Temperature effects shall be determined in accordance with Section 3 – Loads of the CHBDC. ClimaticInformation is presented in Annex A3.1 - Climatic and Environmental Data of the CHBDC.

The temperature range that is considered is the difference between the maximum and minimum effectivetemperatures. When determining the effects, NU Girder bridges are classified as Type C Superstructures; as such,they fall within the range summarised in Table 4-2.

Table 4-2Effective Temperature

Maximum effective temperature Minimum effective temperature

10oC above maximum mean daily temperature 5oC below minimum mean daily temperature

Maximum mean daily temperature and minimum mean daily temperature are found in Annex A3.1 - Climaticand Environmental Data of the CHBDC.

Further modifications to the effective temperatures are applied, based on the depth of the structure. Theprovisions in CHBDC allow for a reduction in the effective temperature range with increasing depth (Table 4-3).

Table 4-3Modifications to Effective Temperature

NU Girder Series Structure Depth1 Reduction in maximumeffective temperature, oC

Increase in minimum effectivetemperature, oC

NU1200 1425 mm 4.5oC 6.4oC

NU1600 1825 mm 6.2oC 8.9oC

NU2000 2225 mm 7oC 10oC

NU2400 2625 mm 7oC 10oC

NU2800 3025 mm 7oC 10oC1Structure depth based on 225 mm thick deck, neglecting haunch contribution

Page 4-6


It is necessary to consider thermal gradients through the superstructure. The thermal gradient is defined aspositive when the top surface of the structure is warmer than the bottom surface. For winter conditions, bothpositive and negative differentials shall be considered. For summer conditions, only positive differentials shallbe considered. The provisions from CHBDC are simplified for NU Girder bridges in Table 4-4.

Table 4-4Temperature Differential

Summer ConditionsPositive Temperature Differential

Winter ConditionsPositive or Negative Temperature Differential

10oC 5oC

NU Girders are subject to creep and shrinkage and are affected by relative humidity. The relative humidity canbe found in Annex A3.1 - Climactic and Environmental Data of the CHBDC. The Annual Mean RelativeHumidity is interpolated from the contour map of Canada for the project site.

For most locations in Alberta, an annual mean relative humidity of 50 percent is appropriate.

Sample Calculation 1: Effective Temperature Determination

As an example, calculate the effective temperature for consideration for a NU2000 Girder bridge located inEdmonton, AB.

Example of Effective Temperature Calculation: Edmonton, Alberta

Max Temperature Min Temperature

Mean DailyTemperature

From Figure A3.1.1 of the CHBDCMax Mean Daily Temperature: 27oC

From Figure A3.1.2 of the CHBDCMin Mean Daily Temperature: -41oC

Adjustment forSuperstructure type

Type C: +10 oC Type C: -5 oC

Adjustment forSuperstructure depth

NU2000: -7 oC NU2000: +10 oC

Effective Temperature Max Effective Daily Temperature: 30oC Min Effective Daily Temperature: -36oC

Page 4-7


4.4. MATERIAL PROPERTIES

The materials typically used in NU Girder fabrication, and the mechanical properties to be used for design,include concrete, reinforcing steel, prestressing strand, and structural steel.

Table 4-5Material Resistance Factors

Material Material Resistance Factor

Concrete fc = 0.75

Reinforcement

Reinforcing bars and wire fabric

Prestressing strands

fr = 0.90

fp = 0.95

Structural Steel

Flexure, shear, tension

Compression

Welds

Shear Connectors

fs = 0.95

fs = 0.90

fw = 0.67

fsc = 0.85

In Alberta, Fabricators of NU Girders have developed concrete mixes to meet the specified release strengths andallow for a 24-hour fabrication cycle. The specified strengths that are achievable are summarized below and shallbe used for design of NU Girders in Alberta.

Table 4-6Concrete Classes

Concrete Class Description of Use f'c

NU Girder Concrete Precast NU Girders 70 MPaClass HPC Cast-in-place decks, curbs, barriers, sidewalks and medians

abutment and pier diaphragms; deck joint blockouts;precast concrete partial depth deck panels

45 MPa

CHBDC does not provide guidance for strength gain with time. The following specified strengths shall be usedin design:

NU Girder Specified Strength:

At Transfer: = 45 MPa

At 28 days: = 70 MPa

Page 4-8


In CHBDC the modulus of elasticity of concrete is determined from the following:

= +.

Where:

= specified strength of concrete at 28 days (MPa)

= mass density of concrete (kg/m3)

Prediction of early age stiffness

CHBDC specifies concrete stiffness as a function of specified 28-day strength. However, in the design of NUGirders, it is necessary to predict response at various stages, in particular at early age at release. The followingequation is used to determine the stiffness of concrete:

= 3000 + 6900 2300

.

Where:

= specified strength of concrete at transfer (MPa)

= mass density of concrete (kg/m3)

NU Girder Bridge Design: Concrete Stiffness

The following values are appropriate for use in determining concrete stiffness for use in NU Girder bridgedesign:

Density: It is appropriate to use a mass density of concrete of rc = 2295 kg/m3 when calculating theconcrete stiffness. CHBDC values for unit weight of gc = 24.0 kN/m3 for reinforced concrete and gc = 24.5kN/m3 for prestressed concrete are recommended for calculating self-weight loads.

Note: Fabricator test data shows that concrete stiffness can vary by as much as 15 percent from CHBDCpredictions. Consultants should be aware of and consider this sensitivity in design when appropriate.

NU Girder concrete mixes are normal weight concrete. Therefore, the cracking strength for NU Girder concrete,, is calculated by:

= 0.4

Where:

= specified compressive strength of concrete (MPa)

At transfer, the specified release strength is used to calculate the release cracking strength, .

= 0.4

Where:

= specified compressive strength of concrete at transfer (MPa)

(4-1)

(4-2)

(4-3)

(4-4)

Page 4-9


The thermal coefficient of linear expansion is taken as:

= 10 x 10-6/oC

The consideration of shrinkage is necessary for estimating girder behaviour and overall bridge behaviour, andincludes shrinkage of the NU Girder and differential shrinkage between the deck and girders. Shrinkage isdetermined in accordance CHBDC, where the shrinkage strain, ecs, that develops in a period of time, t-ts iscalculated by:

( − ) = ( − )

Where:

( − )= time varying strain in concrete due to shrinkage

= age of concrete after casting (days)

= age of concrete from when the influence of shrinkage is calculated (days)

( − )= coefficient describing the development with time of shrinkage in concrete

= notional shrinkage coefficient

In this equation, the shrinkage strain that develops over time is a function of the notional shrinkage coefficient,

ecso, and a coefficient bs(t-ts), which describes the development of shrinkage with time.

Notional Shrinkage Coefficient:

= 160 + 50 9 −+

10 10

= −1.55 1− 100

Development of Shrinkage with Time

( − ) =−

350 2100 + ( − )

Where:

= difference between mean concrete strength and specified strength, and is taken as 10 MPa

RH = annual mean relative humidity (%)

= volume per unit length of a concrete section divided by the corresponding surface area in contactwith freely moving air (mm)

The age of concrete from when shrinkage is initially considered to start follows the curing period. NU Girdercuring includes initial curing in the form (approximately 16 hours), followed by 4 days of subsequent curing.Therefore, a value of 5 days for the age of concrete is considered appropriate for calculating the influence ofshrinkage.

(4-5)

(4-7)

(4-6)

(4-8)

Page 4-10


Sample Calculation 2: Shrinkage Strain Calculation

As an example, calculate the shrinkage strain development over time, for a typical NU Girder up to the ageof deck pour, based on the following concrete properties and criteria:

f’c = 70 MPa a = 10 MPa

RH = 50% rv = 86 mm (NU2000)

ts = 5 days t = 180 days

The term bRH is found from Equation (4-7) to be:

= −1.55 1− 100 = −1.55 1−50

100 = −1.356

Then the notional shrinkage coefficient is determined from Equation (4-6) to be:

ε = −1.356 160 + 50 9 −70 + 10

10 10 = −284.8 10

We then determine the term bs(t-ts), which describes the development of shrinkage with time fromEquation (4-8):

( − ) =−

1035.4 + ( − )

The description of shrinkage strain can then be determined from Equation (4-5) to be:

( − ) = −284.8x10−

1035.4 + ( − )

This equation can be graphically depicted to show the development of shrinkage with time, as seen inFigure 4-2 and Figure 4-3.

In our example, we are looking to calculate the shrinkage that has occurred at 180 days. The strain isdetermined from the period where influence of shrinkage is calculated, at ts = 5 days, to the time ofconsideration, t = 180 days.

( − ) = −284.8x10180− 5

1035.4 + (180− 5) = −108.3x10

Figure 4-2Shrinkage Strain Development with Time

Figure 4-3Long-Term View of Shrinkage Strain Development

with Time

(log scale)

Page 4-11


Creep is the increase in strain associated with a sustained compressive stress. It is described by the creepcoefficient, which is the ratio of creep strain to elastic strain. The creep coefficient is used in simplified and refinedanalysis to determine the effects of creep, such as girder camber with time, and restraint forces that developwith time.

Figure 4-4 shows the relationship between the creep coefficient, elastic strain, and creep strain. In this figure, atheoretical creep coefficient is presented, along with an initial, sustained, elastic load applied at time t=0, thatresults in an elastic strain of 100x10-6. The creep strain that results is predicted by the creep coefficient, multipliedby the elastic strain.

Figure 4-4Creep Coefficient and Creep Strain

Creep of concrete is nonlinear with respect to time and with respect to the magnitude of the sustained load.However, when the sustained stress is less than 40 percent of the concrete compressive strength, a nearly linearrelationship exists between sustained stress and creep strain. In the design of NU Girder bridges, bridge codeslimit the magnitude of sustained stress in the concrete to the linear region.

In CHBDC, the creep coefficient is defined as the ratio of creep strain to the elastic strain that results when usingthe stiffness of concrete at 28 days. The provisions below present the CHBDC approach to calculating the creepstrain and calculating the creep coefficient (represented as f28).

Creep Strain

( , ) =( ),

∙ ( , )

Where:

( , ) = creep strain developing over the time period (t,t0)

( ) = sustained stress applied at time t0 (MPa)

, = concrete modulus of elasticity at 28 days (MPa)

( , ) =creep coefficient

(x10

-6)

(4-9)

Page 4-12


Creep Coefficient

The creep coefficient is calculated from the following:

( , ) = ( − )

Where:

= 1 +1 − 100%

0.46 2100

=5.3

( + )10

=1

0.1 + ,.

( − ) =−

+ −

.

Where:

= 150 1 + 1.2 100%2100 + 250

But shall not be taken greater than 1500

In Equation (4-13), t0,ADJ is the adjusted age at loading, which is used to account for the effect of the type ofcement and curing temperature. This is a deviation from CHBDC, with the provisions for determining anappropriate value for t0,ADJ adopted from fib Model Code for Concrete Structures 2010, and based on concretemixes with rapid strength gain. The adopted provisions do not include the additional effects of elevatedtemperatures.

, =9

2 + . + 1

Where:

= 0 for normal cements

= 1 for rapidly hardening cements

For NU Girder concrete mixes, a is taken as 1. For HPC concrete, such as for use in concrete decks, is takenas 0.

Use of Creep in Time-Dependent Analysis

In NU Girder design, early age of loading must be considered. The application of the creep coefficient for agesof loading other than 28 days must be applied correctly to predict the creep strains. A straightforward approachis to use a creep coefficient defined as the ratio of creep strain to the elastic strain at the age of loading , which isrepresented as f0. This is achieved by adjusting f28 and is covered below.

(4-10)

(4-14)

(4-12)

(4-13)

(4-11)

(4-15)

(4-16)

Page 4-13


Using this definition for f0, the creep coefficient is the ratio of creep strain to elastic strain at the time of loading,and is defined below:

( , ) = ε ( , ) ∙( )( )

The creep coefficient is calculated from the following relationship:

( , ) =( ),

( , )

The creep function is also used, as a convenient way to describe the total load-related strain resulting from anapplied unit stress.

( , ) =1( ) +

( , ),

=1( ) +

( , )( )

Or:

( , ) =1 + ( , )

( )To determine the total load-related strain, the creep function is multiplied by the applied sustained stress.

( , ) =( )( )

[1 + ( , )]

Where:

( , )= total load-related strain (elastic and creep) occurring in the time period t-t0

Section 4.6.6 discusses the use of the creep coefficient in more detail as it relates to its use in time-dependentanalysis.

(4-17)

(4-18)

(4-20)

(4-19)

(4-21)

Page 4-14


Sample Calculation 3: Creep Coefficient Calculation

As an example, calculate the creep coefficient development over time, for a typical NU Girder up to the ageof deck pour, based on the following concrete properties and criteria:

f’c = 70 MPa a = 10 MPa

RH = 50% rv = 86 mm (NU2000)

t0 = 0.75 days t = 180 days

Ec,28 = 31896 MPa Ec(t0) = 26937 MPa

The adjusted age at loading is calculated from Equation (4-16) to be:

, = 0.759

2 + 0.75 . + 1 = 3.2

The terms fRH, bf and bt can then be calculated from Equations (4-11) to (4-15) to be:

= 1 +1 − 50

100

0.46 2(86)100

= 1.907

=5.3

8010

= 1.874

=1

0.1 + (3.2) . = 0.732

= 150 1 + 1.250

1002(86)100 + 250 = 508.0

We then determine the term bc(t-t0) which describes the development of creep with time from Equation (4-14):

( − ) =( − )

508.0 + ( − )

.

The creep coefficient can then be determined from Equation (4-10):

( , ) = ( − ) = 1.907 × 1.874 × 0.732( − )

508.0 + ( − )

.

= 2.616( − )

508.0 + ( − )

.

Once the creep coefficient ϕ28 is calculated, Equation (4-18) is used to determine ϕ0, the creep coefficient thatis the ratio of creep strain to elastic strain at the time of loading.

( , ) =( ),

∙ ( , ) = 0.845 ( , )

( , ) = 0.845 ∙ 2.616( − )

508.0 + ( − )

.

= 2.211( − )

508.0 + ( − )

.

This equation can be graphically depicted to show the development of creep with time, as seen in Figure 4-5and Figure 4-6.

In our example, we are looking to calculate the creep coefficient at 180 days for a load that was applied at0.75 days.

(180, 0.75) = 2.211(180− 0.75)

508.0 + (180− 0.75)

.

= 1.477

Page 4-15


Sample Calculation 3: Creep Coefficient Calculation (Continued)

NU Girders in Alberta are fabricated with welded wire reinforcement (WWR) or carbon steel reinforcing, or amixture of the two. Reinforcement that projects from the girder into the deck shall be low carbon/chromiumreinforcing bars. Reinforcement in the deck will be either stainless steel or low carbon/chromium reinforcingbars. See BSDC for reference on selection of reinforcing steel grades for deck reinforcement.

Table 4-7Reinforcing Steel Grades

For the purposes of design, the following properties shall be used:

Carbon steel: fy = 400 MPa.

Stainless Steel: fy = 420 MPa

Low Carbon/Chromium: fy = 500 MPa

WWR: fy = 485 MPa

In CHBDC the modulus of elasticity of reinforcement is taken as:

Es = 200,000 MPa

Description Grades

Top flange reinforcement WWR

Stirrups WWR or carbon steel

Projecting bars Low carbon/chromium

Bottom flange confinement reinforcement WWR and carbon steel

End block reinforcement WWR and carbon steel

Deck and diaphragm reinforcement Stainless steel or low/chromium

Figure 4-6Creep Coefficient with Time (Long-Term)

Figure 4-5Creep Coefficient with Time

(log scale)

Page 4-16


Currently, low carbon/chromium reinforcing is only produced in imperial bar sizes. Stainless steel reinforcing isavailable in both metric and imperial sizes.

Metric 15M bars and imperial #5 bars have cross-sectional areas within 0.5 percent and direct substitution willhave negligible impact on a component’s design.

Prestressing strands used in pretensioning and post-tensioning of NU Girder bridges are 15.2 mm diameter, 7-wire, low-relaxation strand. Prestressing strands shall conform to ASTM A416/A416M Grade 1860 forlow-relaxation strand with a minimum tensile strength of 1860 MPa.

= 1860 MPa

In CHBDC the modulus of elasticity of prestressing strand is taken as:

= 200,000 MPa

In CHBDC the yield strength of prestressing strands is taken as:

= 0.9

In lieu of manufacturer’s data, using a minimum tensile strength of 1860 MPa results in:

= 0.9 = 0.9 × 1860 = 1674

The term relaxation refers to the loss of stress in the prestressing steel when held under a constant strain.

For low-relaxation prestressing strand, CHBDC provides the following equation to estimate relaxation of astressed strand:

∆ =(24 )45 − 0.55

Where:

∆ = loss of prestress (MPa)

= time elapsed since jacking (days)

= stress in tendons at jacking (MPa)

= yield strength of prestressing strands (MPa)

(4-22)

(4-23)

Page 4-17


In NU Girder bridges, there are several elements fabricated from structural steel. This can include cross-bracing,end diaphragms, joints, bridgerail, bearing sole plates, and shoe plates.

All miscellaneous steel that is attached to or embedded into girders and that has exposed faces shall begalvanized. All steel diaphragms, including all associated plates, washers, nuts, and bolts, shall be galvanized.

All structural steel shall meet the following requirements.

Table 4-8Steel Grades

Description Grades

Cross-bracing, diaphragms comprising channels Grade 300W or Grade 350W, and galvanized

Shoe plates, bearing base plates Grade 300W or Grade 350W, and galvanized

Sample Calculation 4: Prestressing Relaxation

As an example, calculate the relaxation of prestressing that occurs between jacking of the strands and transfer.

fsj = 0.75fpu = 1395 MPa fpy = 1674 MPa

t = 0.75 days

The relaxation is calculated from Equation (4-23) to be:

∆ =log(24 )

45 − 0.55 =log(24 ∙ 0.75)

4513951674 − 0.55 1395 = 11.0

As a logarithm-based relationship, a significant amount of relaxation occurs shortly after stressing. The figurebelow shows the relaxation that would occur over one year.

Figure 4-7Prestress Relaxation

Page 4-18


4.5. EXPECTED LOAD HISTORY

Establishing an expected load history during design is necessary for completion of the design of an NU Girderbridge. The milestones established for various stages of the NU Girder bridge construction need to provide aconsistent and realistic basis for design and construction.

The three main stages of an expected load history for an NU Girder are described below. The stages areFabrication, Construction, and Service. Expected load history, prestress loss considerations, and typical loadingconditions are summarized for each stage.

Guidance on expected load history is based on fabrication and construction experiences in Alberta. However, asproject constraints on schedule vary with every project, the Consultant shall develop the load history based onthe specifics of the project and, when necessary, in consultation with the Department.

Table 4-9Expected Load History during Fabrication

Stage 1 – Fabrication

Fabrication comprises the period from initial strand tensioning in the prestressing bed to immediately aftertransfer of the prestressing force to the NU Girder.

Jacking Stress (fsj) will be the target stress applied to the strands in the prestressing bed.

Expected Load history Concrete age at transfer = 0.75 days

Prestress Losses The Fabricator and the Consultant are both responsible for consideration ofprestress loss. In general, the Fabricator is responsible for achieving the stress instrands immediately prior to transfer fsi, and is required to consider all losses upto this point. The Consultant thus considers all prestresses losses occurring at thepoint of transfer, and forward. This delineation of responsibility is covered furtherin Section 4.6.5.2. Prestress losses at this stage of construction include thefollowing:

Fabricator Responsibility:

· Fabrication-specific losses including bed shortening and seating losses· Strand relaxation: Following jacking (and prior to transfer) the strands

will lose stress due to relaxation (REL1)

Consultant Responsibility:

· Elastic Shortening (ES): The girder will shorten due to the initialprestressing force causing a loss of stress in the prestressing strand.

Loading Prestressing force

Self-weight of the NU Girder

Other Considerations The steps in fabrication of a typical NU Girder are summarised in Appendix C.

Consideration of debonding, deflected strands, end zone cracking, developmentlength, etc.

Page 4-19


Table 4-10Expected Load History during Construction

Stage 2 – Construction

Construction comprises the period from fabrication to immediately before the bridge is in Service.

Expected Load history Load history during construction will depend on number of girders and spans,complexity of bridge design (simple or multi-stage PT) and other considerations.It is typical to have a bridge superstructure designed to be completed within oneworking season; however, final superimposed dead loads may be deferred to asecond construction season.

The following are guidelines for the range that may be used during design.

· Age at erection: 60 days to 180 days· Age at deck pour application: 180 days to 360 days· Age at post-tensioning: 90 days to 360 days· Time of Superimposed Dead Loads: 180 days +

Prestress Losses After transfer, NU Girders will undergo creep and shrinkage, and the prestressingstrands will relax. These will be considered following the Simplified Method(Section 4.7.2) or a Detailed Method, as appropriate (Section 4.7.3).

Loading Lifting and Handling

Construction Loads (falsework and construction loading during deck pour)

Concrete Deck (including differential shrinkage)

Superimposed Dead Loads (Barriers, asphalt overlay, etc.)

Post-Tensioning (if applicable)

Table 4-11Expected Load History in Service

Stage 3 – In Service

Following completion of construction, this extends until the end of the service life (75 years).

Expected Load history Load history in service will go from bridge opening to 75 years.

Prestress Losses Similar to the Construction Stage, NU Girders will continue to undergo creep andshrinkage, and the prestressing strands will relax. These will be consideredfollowing the Simplified Method (Section 4.7.2) or a Detailed Method, asappropriate (Section 4.7.3).

Typically, consideration of all losses provides a conservative consideration ofstresses, and so SLS checks are completed considering the long-term prestresslosses.

Loading Live Loads

Thermal Loads

Page 4-20


4.6. PRESTRESSED DESIGN CONSIDERATIONS

The pretensioning limits defined in CHBDC are modified for use in Alberta. The approach adopted is based onlimiting stress in strands immediately prior to transfer, fsi.

The pretensioning steel stress limits to be used for design of NU Girders is summarized below:

Table 4-12Prestressing Tendon Stress Limits

DescriptionStress Limit

%fpu Limit For fpu = 1860 MPa

Pretensioning

Immediately prior to Transfer, fsi 0.75fpu 1395 MPa

Post-Tensioning

At Jacking, fsj 0.80fpu 1488 MPa

At Transfer, fst

At anchorage and couplers Elsewhere

0.70fpu

0.74fpu

1302 MPa1376 MPa

Immediately Prior to Transfer: refers to the moment immediately prior to transfer.

The stress in the strands immediately prior to transfer is specified by the Consultant. Fabricators will include theforce required to compensate for plant-related losses such as relaxation, bed shortening, and seating losses.Therefore, the actual jacking forces experienced in the plant will be higher than the value immediately prior totransfer.

At Jacking: refers to the time of tensioning tendons, immediately before transfer.

For post-tensioning, the specified jacking force includes an allowance to compensate for anchorage slip attransfer.

At Transfer: refers to the time immediately after transfer.

Alberta Approach

The current CHBDC approach to calculating pretensioning steel stresses has led to challenges withinterpretation and application of prestressing tendon stress limits and losses at transfer. Primarily, theprestress losses prior to transfer are in the Fabricator’s control; however, the CHBDC requires Consultantsto consider them.

The approach adopted in this Manual shall be used on Alberta Transportation projects. The terms“at jacking” and “at transfer” are not used when dealing with pretensioning. Rather, the moment ofconsideration is “immediately prior to transfer” and is represented by fsi.

This approach is discussed further in Section 4.6.5.

Page 4-21


The following stress limits on prestressed concrete apply for NU Girder design:

Table 4-13Prestressed Concrete Stress Limits

Description

Stress Limit

(f’ci = 45 MPa)

(f’c = 70 MPa)

At Transfer and During Construction

Compression 0.6f’ci 27.0 MPa

Tension 0.5fcri 1.34 MPaIn Service

Compression – Permanent Loads 0.4f’c 28.0 MPa

Compression – Permanent and Transitory Loads 0.6f’c 42.0 MPa

Tension fcr 3.35 MPa

For pretensioned NU Girder bridges, portions of the structure outside of the girders, such as the deck, are notconsidered prestressed; therefore, crack width limitations from CHBDC shall apply.

For post-tensioned NU Girder bridges, the entire superstructure, including deck, shall be considered prestressedand the limitations above shall apply. In some scenarios, allowing exceedance of the tension limits may beconsidered acceptable for decks, with approval from the Department; however, crack widths, deck reinforcinggrade, and ability to complete a deck rehabilitation shall be thoroughly considered.

Debonding of strands and deviation of strands are used to control stresseswithin a girder, in particular at the ends.

Debonding of strands in NU Girder fabrication is achieved by placing aplastic sheath around the strand for the specified debonding length.

CHBDC specifies that the number of strands where the bonding does notextend to the ends of the girder shall not exceed 25 percent of the total number of strands. The Department hasestablished an exception to this limit, allowing up to 35 percent of strands to be debonded. This requirementapplies to girders with only pretensioning strands, as well as to girders with pretensioning and post-tensioningstrands. For girders with pretensioning and post-tensioning strands, the 35 percent limit shall be applied to thetotal number of pretensioning strands only.

When selecting strand debonding locations and developing a debonding pattern, the following shall be met:

· The number of strands debonded in any one horizontal row shall not exceed 40 percent of the strandsin that row;

· Not more than 40 percent of the debonded strands, or four strands, whichever is greater, shall havethe debonding terminated at any one section;

· Termination sections for debonding shall be at least 60 strand diameters (912 mm) apart longitudinally;

Controlling Girder Stresses

The Department’s preferenceis to begin with debonding asthe method to control girderconcrete stresses.

Page 4-22


· Strands further from the section vertical centreline shall be debonded prior to those nearer thecentreline;

· Debonded strands shall be symmetrically distributed about the centerline of the girder;· Debonded lengths of pairs of strands that are symmetrically positioned about the centerline of the

girder shall be equal; and· Exterior strands in each horizontal row shall be fully bonded and shall not be debonded at any location.

The effect of debonding shall be such that all limit states are satisfied, with consideration of the total developedresistance at any section being investigated.

Some advantages when selecting to debond strands:

· Hold-down points/devices are not required.· The stressing process is simplified.· No repairs are needed to the forms (for removing hold-down devices).· Improved stress distribution at girder ends will reduce cracking.

Some potential disadvantages to consider when selecting to debond strands:

· Fewer strands are available to anchor struts at supports in the end zone· Slightly more complicated for analysis· Leakage into plastic sheath possible if ends of strands are not properly protected

Figure 4-8Example Debonded Strand Pattern

Deviating strands is an effective way to control end stresses, by reducing the eccentricity of the prestressingforce at the girder end. Deviating strands in NU Girders is achieved by using hold-down devices in the forms tocreate a deviated strand profile. Only the strands within the web can be deviated.

The CHBDC’s prescribed limits on deviating strands are related to the maximum number of strands whenbundled. The hold-down devices used in NU Girder fabrication maintain strand spacing of 50 mm; therefore,the CHBDC provisions for bundling do not apply. Rather, the limits on deviating strands are based on practicalconsiderations in fabrication. The Consultant should discuss these practical decisions with fabricators.

The figures below show two arrangements for deviating strands. Figure 4-9 shows a deviated strand profile,where strand groups are deviated. Figure 4-10 shows an example of splaying the strands.

Strands bonded for full length

Debonded for 1.5 m

Debonded for 3.0 m

Debonded for 4.5 m

Page 4-23


The following general considerations are useful for developing a strand deviation pattern:

· Hold-down point force is limited to a safe working load of 213 kN. The unfactored load demand atjacking shall be less than the safe working load. In checking this, it is conservative to use 0.8fpu as themaximum jacking stress when determining the unfactored load demand. For deviated strands, thisforce is related to the angle of deviation. Higher angles of deviation result in higher hold-down forces.

· Strands are deviated in groups, each with an individual hold-down point. Hold-down devices aretypically limited to 12 strands.

· Fewer hold-down points are preferred. The maximum number of deviated strand groups is typically 3on either side of mid-span.

· Splaying of deviated strands at the girder ends can be used to reduce girder end zone cracking. This isaccomplished by increasing strand spacing at the ends by multiples of 50 mm.

· Provide a minimum of 1.0 m between hold-down points.

The Consultant should be aware that the hold-down point locations defined in design will likely change at theshop drawing stage, where the fabricators will need to accommodate the hold-downs within their existingforms. Locations may need to be revised in the order of 500 mm.

Some of the advantages of using deviated strands for stress control:

· Vertical component of prestressing improves shear resistance· Fewer critical locations (compared to debonding locations) to check during design

Some potential disadvantages to consider when selecting to deviate strands:

· Additional steps required during fabrication· May not reduce end zone cracking

Figure 4-9Example Deviated Strand Pattern

Figure 4-10Example Splayed Strand Pattern

Page 4-24


Post-tensioning is another way to control service stresses in NU Girder bridges. Often post-tensioning is usedwhen extending span lengths, reducing the number of girder lines, using a shallower section, or to controlstresses during construction.

When completing the post-tensioning design, the Consultant shall establish the tendon information, tendonprofile, jacking forces, and prestress losses. In design, some of these criteria must be based on typical values, asthe precise values are not known until construction. For example, anchor set depends on the post-tensioninghardware used and the Contractor’s equipment.

In construction, the Contractor will prepare stressing calculations based on the properties of the equipment usedand the materials procured. To achieve the design requirements, the Consultant shall include the designassumptions as part of the construction drawings. The drawings shall include information design criteria, adetailed profile, and a force diagram. The Consultant shall refer to the Engineering Drafting Guidelines forHighway and Bridge Projects for complete requirements. These detailing requirements are discussed further inthe following sections.

The post-tensioning design criteria are summarized on the drawings and include the items in the table below:

Table 4-14Post-Tensioning Design Criteria

Category Design Criteria Details

Material Properties Tendon Number of strands per tendon

Strand Strand properties, size and gradeSee Section 4.3.4

Ducts Material, size, and locations for vents

Design Forces Initial Jacking Force fsj

Wobble Coefficient KSee Section 4.6.5.4

Friction Coefficient m See Section 4.6.5.4

Anchor Set Dependent on anchorage systemSee Section 4.6.5.4 for recommended values

Modulus of Elasticity In construction, this will be based on mill certificates forstrands procured.See Section 4.4.4.2 for recommended values

Sequence Stages Define the post-tensioning stages, including strands tobe jacked to necessary forces for multi-stage stressing.

Limitations Minimum concrete strength prior to completingstressing activities.

Grouting Identify requirements for duct grouting.

Page 4-25


In post-tensioned systems, the tendons are a primary structural component; their failure could result in totalcollapse. Therefore, protection of the tendons is critical. The grout provides the bond to the duct, allowing thesystem to act compositely. The grout also acts as a corrosion protection system. The long-term durability of thesystem requires a successfully completed grouting operation.

The SSBC outlines the requirements for duct inlets and outlets, grout specifications, and grouting operationrequirements. The intent is for complete grout penetration in the ducts and around the tendons, with no voids.Unbonded tendons are not permitted.

The inside cross-sectional area of the duct shall be at least twice the cross-sectional area of the prestressingtendon. Clause 8.4.4.5.2 of the CHBDC states that the inside diameter of a circular duct shall not exceed 40percent of the web thickness. Notwithstanding this clause, the Department has determined that for NU Girdersthe inside duct diameter can be increased to a maximum of 50 percent of the web thickness, provided the insideduct area is greater than 250 percent of the total strand area.

Tendon profiles are developed based on providing a beneficial load case that balances gravity loads. Thetendon eccentricity will produce tension on the top when the tendon eccentricity is below the section centre ofgravity, and tension on the bottom when it is above. In general, the profile is similar to the opposite sign ofthe dead load moment diagram. To produce the desired stress state, the centroid of the post-tensioning willbe near the centroid of the section at simply supported connections, highest over fixed pier locations, andlowest at the locations of maximum bending moment.

Figure 4-11 shows the shape of a post-tensioning tendon, with typical values for low point and inflection pointidentified.

Figure 4-11Example Tendon Profile

Alberta Experience

A successful and common approach to post-tensioning is to use 80 mm outside diameter, 76 mm insidediameter ducts, post-tensioned using 12 - 15.2 mm diameter strands. Consultants who are considering theuse of larger tendons (e.g., 15 - 15.2 mm diameter strands), shall contact a local Fabricator to discussfeasibility and availability of large duct sizes.

Recommendations in this Manual are based on the use of 80 mm outside diameter duct.

0.05L2

to 0.1L2

L1 L2

~0.5L20.05L1

to 0.1L1

~0.4L1

Abut PierPier

Low Point Inflection Point Inflection Point

High Point

End Span Interior Span

0.05L2

to 0.1L2

Page 4-26


The established post-tensioning profile is based on a number of criteria, including number of tendons, spacingrequirements between tendons and between anchorages, and the constraints for duct placement within the NUGirder.

When developing a profile, smooth curves are used. Parabolas are typically used to define the curved profile.The use of parabolas to define the tendon profile is convenient for three reasons:

· In preliminary design, parabolas allow for simple load-balancing equations.· In detailed design, parabolas are convenient for establishing losses as well as forces at the sections

considered.· In fabrication, parabolas allow fabricators to easily determine the duct placement along the web.

The various constraints affecting tendon layout are discussed below.

In developing the profile, several considerations and limits apply for the placement of the post-tensioning ductwithin the girder. These are described below and shown in Figure 4-12.

Clear Distance between Ducts

Clause 8.14.2.2.2 of the CHBDC identifies the minimum clear distance between ducts of 40 mm.

Abutment Ends

The stressing of post-tensioning occurs at abutments, where the post-tensioning anchorage assembly will beincorporated into the girder end block or incorporated into a cast-in-place concrete end-diaphragm. Theminimum spacing between the ducts at the end is dependent on the size of the anchorage assembly and block-out. For typical tendons, a vertical end spacing of 400 mm between centreline of ducts is adequate, with aminimum of 250 mm from the top of the girder flange to the centre of the top duct.

Pier Ends

At piers, the ducts are spliced through the cast-in-place diaphragm. The top duct shall remain beneath the toplayer of top flange reinforcing within the NU Girder, with a minimum distance of 40 mm between top of girderand top of duct. The spacing between ducts shall meet the requirements of minimum clear distance of 40 mmbetween ducts.

For typical 80 mm conduit, this corresponds to a minimum spacing of 120 mm centre-to-centre betweenconduits.

Low Point

At the desired location for maximum eccentricity, the bottom duct can be placed as low as the bottom of thestirrup within the web. Bottom flange hat bars are omitted in the locations where the duct conflicts with thebottom flange hat bar. The spacing between ducts shall meet the requirements of clear distance of 40 mmbetween ducts.

For typical 80 mm conduit, this corresponds to a minimum spacing of 120 mm centre-to-centre betweenconduits.

Page 4-27


Abutment End Low Point Pier End

Figure 4-12Typical Duct Arrangements and Limitations

The tendon profile is used to determine the post-tensioning force effects on the section. The location on thesection where the force is applied will correspond to the centre of the tendon. Tendon profiles in NU Girderbridges are typically curved and, as such, the tendon centroid will not occur at the centre of the duct. Instead, itwill have an eccentricity above or below the duct centroid, depending on the direction of curvature.

CHBDC provides guidance for the eccentricity, based on the diameter of the duct. For NU Girder bridges, typicalduct diameter is 80 mm (76 mm inside diameter) and an eccentricity of 20 mm is used (see Figure 4-13).

Reproduced from CHBDC: Figure 8.2

Figure 4-13Eccentricity of Curved Tendons

Duct Diameter, d (mm) e (mm)

75 < d < 100 20

Rebar alternativefor webreinforcementshown

WWR alternativefor webreinforcementshown

Page 4-28


Sample Calculation 5: Post-Tensioning Profile

As an example, create a tendon profile, for the top tendon in an NU Girder bridge with 53 m long span. Thegirder is an NU2400 with 4 tendons. The girder and bridge geometry is shown below. From here, theabutment overhang, clear span length, and pier diaphragm lengths are shown. Tendon ducts are 80 mmdiameter, with all geometry below defined for the centreline of the tendon.

Span Geometry

Loverhang = 550 mm Lclearspan = L1 = 53000 mm Ldiaphragm = 500 mm

For the purpose of establishing a tendon profile, the profile is based on stationing along the length,beginning at the back of the overhang. Next the low point, and points of inflection are calculated:

Llowpoint = 0.4L1 = 21,200 mm STAlowpoint = Loverhang + Llowpoint = 21,750 mm

Linflection = 0.1L1 = 5300 mm STAinflection = Loverhang + Lclearspan - Linflection = 48,250 mm

Vertical geometry for the tendon will maximize the available drape.For the top tendon the height above the girder soffit at the lowpoint is governed by the spacing between ducts, and clearanceabove the strands in the web (if included). For this example, fourlayers of pretensioning strands are included in the bottom flange.

ylowpoint = 60 mm + 150 mm + 40 mm + (½) 80 mm + 360 mm

ylowpoint = 650 mm

Vertical geometry for the high point is limited by the ductsmaintaining cover under the top mat of girder reinforcement. At thegirder ends, there is 25 mm cover to the top mat of reinforcing with10 mm diameter reinforcing bars. To maintain 40 mm of clearancebetween the ducts and rebar, the centreline of the duct max height iscalculated as:yhighpoint = 2400 mm – 25 mm – 10 mm - 40 mm – (½) 80 mm

yhighpoint = 2285 mm

For the simply supported end, the height of the tendon is taken as 2000 mm. (keeping in mind the centroidof the tendon group is located near the centroid of the composite section).

The tendon profile will be defined by three parabolic curves:

· Curve 1 extends from Abutment 1 to the low point· Curve 2 extends from the low point to the inflection point· Curve 3 extends from the inflection point to the high point.

Abutment Pier550

53000

250 250

500

Girder Bottom Flange

3@12

0

3@50

360

150

60

STA 0

Page 4-29


Sample Calculation 5: Post-Tensioning Profile (Continued)

The following conditions are placed on the profile:· Slopes between Curve 1 and Curve 2 (at the low point) is zero· Slopes between Curve 2 and Curve 3 (at the inflection points) are the same, to maintain a smooth

profile· Slope at end of Curve 3 over the pier (at the high point) is zero

With these boundary conditions, linear algebra can be used to determine the constants for the three curvesdefined by parabolas. For the conditions applied above, the following tendon profile geometry isdetermined:

Tendon Profile Geometryy(x) = ax2+bx+c

Curve Curve 1 Curve 2 Curve 3

Parameter STA = 0 mmto

STA = 21750 mm

STA = 21750 mmto

STA = 48250 mm

STA = 48250 mmto

STA = 53550 mmA 2.85 x 10-6 1.94 x 10-6 -9.70 x 10-6

B -124.0 x 10-3 -84.4 x 10-3 1.04 x 100

C 2.00 x 103 1.57 x 103 -25.5 x 103

The tendon geometry is shown graphically below.

Top Duct - Tendon Profile

The tendon profiles for the other ducts are completed similarly. Locations for low points, inflection pointsand high points should remain constant for any particular girder. As the Consultant completes the design,there is opportunity to refine the profile, for example, by adjusting the location of the low point to matchthe location of maximum moment.

Page 4-30


The sequence of completing the stressing of post-tensioning is an important component of the constructionsequence and staging. Decisions required include the sequence (single-stage and multi-stage) and end-stressingrequirements (single-end and dual-end).

In post-tensioning, the tendons are jacked according to the stressing sequence established by the Consultant.The sequence will need to consider the order of tendon stressing to establish the desired stress state in thesuperstructure.

The Contractor completes a stressing procedure based on the design, which further identifies the specificstressing sequence, stressing system used, initial set requirements, anticipated elongation, and jacking stresses.The procedure is based on the specific anchorage system used by the Contractor and is complete with stressingcalculations.

Single-Stage Post-Tensioning

Single-stage post-tensioning refers to the completion of all post-tensioning during a single stressing event.When constructing NU Girder bridges with single-stage post-tensioning, the deck will be poured prior tocompletion of the post-tensioning application.

In design, the entire post-tensioning force is applied to the composite section.

Multi-Stage Post-Tensioning

Multi-stage post-tensioning refers to the completion of post-tensioning in more than one stage. One commonreason to use multi-stage post-tensioning is to provide additional capacity in the NU Girders for the loadingassociated with the deck pour.

NU Girder bridges with multi-stage post-tensioning typically have more than one span. A frequently used multi-stage approach is to construct the pier diaphragms, then tension around 50 percent of the tendons to their fullvalue, allowing sufficient capacity for the deck pour loads. Following the deck curing, the remaining tendons aretensioned to their full value.

In design, only the second stage of post-tensioning is applied to the composite girder system. The second stageof post-tensioning results in elastic shortening losses in the first stage of post-tensioning, which must beconsidered.

End-Stressing

Dual-end stressing, whereby each tendon is stressed from each end, is typical for NU Girder bridges. Thealternative is to use single-end stressing, where one end is a “dead-end” and is not stressed.

Dual-end stressing provides a means to partially overcome the friction losses along the length of the tendon,and to provide a high tendon stress after jacking. Dual-end stressing is usually necessary for long bridges, where

Design Exception – Multi-Stage Post-Tensioning

The sequence of completing multi-stage post-tensioning by stressing half of the tendons is preferred. Itallows for the tendons to be fully stressed and grouted in accordance with the Standard Specifications forBridge Construction (SSBC).

Another stressing sequence includes stressing all the tendons to around 50 percent of the final jackingforce for the deck pour. After curing, the tendons are restressed to their final values. While this sequencehas the benefit of not resulting in the locked-in elastic losses of the first stage post-tensioning, it doesleave the post-tensioning ungrouted until final stressing occurs. This sequence is not in accordance withthe SSBC, and would require a Design Exception from the Department.

Page 4-31


the cumulative friction and wobble losses can be substantial. If single-end stressing is used, alternating the endof jacking is used to average the friction losses at each end.

The geometric and reinforcing design of the girders and end diaphragms needs to accommodate anchoragesand couplers. From a durability perspective, care must be taken that no water penetrates the post-tensioningducts during construction and that the grout fully fills the tendons. Experience has shown that poorly protectedand grouted ducts lead to premature failures of post-tensioning strands, which is difficult to detect and requirescostly rehabilitation.

The transfer length is the length of strand required for the initial prestressing force (corresponding to the initialprestressing stress fse) to be fully transferred to the concrete. Clause 8.9.1.8 of the CHBDC identifies that thetransfer length, lt, can be taken as:

= 50

Where:

= diameter of the prestressing strand (mm)

During construction and through the life of the bridge, applied loadswill cause the stress in the prestressing strand to increase beyond theinitial prestress levels. As an example, when the deck is poured, theapplied moment on the girder increases and the stress in the strandsincreases to resist the increased moment demand on the section. Abonded development length (referred to as the flexural bond length),beyond the transfer length, is required to develop this increased stressin the prestressing strand.

As discussed in the CHBDC Commentary, the development length, ld, is the sum of the transfer length, lt, andflexural bond length, lb.

= +

The development length of prestressing strand is the length required to develop the ultimate capacity of thestrand. The development length for prestressing strand (including both transfer length and flexural bond length)is defined in Clause 8.15.4 of the CHBDC, and is calculated as:

= 1.5 ′ − 117 + 0.18 −

Where:

= stress in prestressing strand just before transfer (MPa)

= effective stress in prestressing after all loses (MPa)

= stress in prestressing strand at ultimate (MPa)

For Clarification: The use of 50db

for transfer length used inEquation (4-24) is an acceptableapproximate method for calculatingtransfer length. However, thisapproximation is not used in theCHBDC calculation for developmentlength in Equation (4-26).

(4-24)

(4-25)

(4-26)

Page 4-32


In completing the design of an NU Girder at the end regions, or at locations of debonding, it is necessary todetermine the stress in the strand at a location within the development length of a strand when calculating thecontribution from prestressing in shear design. The stress in the strand is assumed to vary linearly from zero atthe start of bond, to fse at the transfer length, and again linearly to fps over the flexural bond length. However, aconservative approach is common practice in Alberta, linearly interpolating between zero and fps over thedevelopment length, as depicted in Figure 4-14.

Figure 4-14Strand Development Length

For debonded strands, where tension at SLS Combination 1 occurs in the concrete component within a distanceof ld from the end of the debonded length, a development length of 2ld shall be used.

Loss of prestress refers to the loss of tension in the prestressing strands. For NU Girders, this loss occurs withboth pretensioning and post-tensioning and begins from the moment of tensioning of the strands in thefabrication plant, or at the moment of jacking of post-tensioning tendons.

By determining the loss of prestress, the effective prestress (fse) can be determined. It is the effective prestressthat is calculated and used at the various stages of construction and in service to determine the stresses in theNU Girder and check service limit states, including cracking and deformation.

The approach currently outlined in CHBDC provides good guidance for post-tensioning applications. Forpretensioning, experience has shown a lack of consistency in application of the stress limits, and responsibilityfor calculation of losses. This manual presents an alternative approach for pretensioning, with clear delineationof responsibility for the consideration of losses. This approach is to be used in the design of NU Girder bridgesin Alberta.

lt lb

ld

fps

fse

Page 4-33


Prestress losses include immediate and short-term losses, and long-term or time-dependent losses. In NU Girderbridges, prestress losses arise from the following sources:

Anchorage Seating (ANC) – Immediate: ANC losses are a mechanical loss of stress. The loss is caused by theslip that anchorage systems require to engage prestressing tendons. ANC losses occur with both pretensioningand post-tensioning.

Elastic Shortening (ES) – Immediate: ES losses are caused by a change in strain in the tendon resulting fromthe shortening of the concrete girder under load. At the moment of transfer, the concrete surrounding thetendon shortens as the prestressing force is applied and, because of strain compatibility, the tendon that isbonded to the concrete will shorten with it.

In the case of post-tensioning, if all tendons are tensioned simultaneously there is no ES loss for the post-tensioning strands; the structure shortens with the application of post-tensioning. However, there will be a lossto the pretensioned strands as a result of the structure’s elastic shortening.

For post-tensioned bridges with staged post-tensioning, there may also be an elastic loss consideration; thesubsequent tensioning in later stages of post-tensioning will result in losses in the post-tensioning tendonstensioned in earlier stages.

Friction (FR) – Immediate: In post-tensioning applications, FR losses in tendon stress are caused by twosources: friction between the tendon and the ducts, and the wobble effect due to unintended deviation of theduct from its specified profile.

Relaxation (REL1, REL2) – Time-dependent: Relaxation refers to the time-dependent reduction of stress intendons.

Shrinkage (SH) – Time-dependent: Shrinkage of the NU Girder concrete will reduce the length of the tendon,resulting in reduced tendon stress.

Creep (CR) – Time-dependent: Creep of the NU Girder concrete will reduce the length of the tendon, resultingin reduced tendon stress.

In pretensioned NU Girders, the responsibility for consideration of prestress loss is with the Fabricator and theConsultant.

Delineation of Responsibility

The current CHBDC approach for determining prestress loss for pretensioned girders require thatConsultants account for strand relaxation in the plant, prior to girder fabrication. This complicatescalculation of the specified jacking stress and can result in uncertainty in the actual stress in theprestressing immediately prior to transfer.

Rather than specify the jacking stress, the approach in Alberta for design is to specify the stressimmediately prior to transfer. This firmly puts the plant losses, including relaxation, in the responsibility ofthe Fabricator, who can then establish a jacking procedure to provide the specified strand stressimmediately prior to transfer. Through discussions with Fabricators, it has been found that the limit of0.75fpu for stress immediately prior to transfer is reasonable to safely achieve and has thus been adopted(see Table 4-12).

Page 4-34


The Fabricator is responsible to achieve the prestress immediately prior to transfer and must consider lossesthat include mechanical plant losses (such as bed shortening and seating losses) and relaxation occurring fromthe moment of jacking until transfer.

The Consultant must consider all losses occurring from the moment of transfer through service.

The delineation of responsibility is outlined in the table below.

Table 4-15Prestress Losses for Pretensioned Girders

Stage Source of Prestress Loss Responsibility

Prio

rto

Tran

sfer

Bed Shortening Fabricator

Anchorage Seating Fabricator

Relaxation (REL1) Fabricator

Prestress immediately prior to transfer: fsi

AtT

rans

fer Elastic Shortening (ES) Consultant

Prestress immediately after transfer: fst

Aft

erTr

ansf

er

Creep (CR) Consultant

Shrinkage (SH) Consultant

Relaxation (REL2) Consultant

Prestress following all losses: fpe

When considering post-tensioning, the responsibility for consideration of prestress loss is with the Contractorand the Consultant.

The Consultant’s post-tensioning design shall include a jacking sequence, jacking stresses, as well as theassumptions for various losses occurring at the time of jacking.

The Contractor shall complete jacking stress calculations, including losses for anchorage seating and friction,based on the actual post-tensioning system used in construction. The jacking stresses established by theContractor are part of the overall post-tensioning procedure used to achieve the desired level of post-tensioning.

Contractors completing post-tensioning work require Certification through the Post-Tensioning Institute, asoutlined in the SSBC.

Page 4-35


Table 4-16 outlines the delineation of responsibility for post-tensioning.

Table 4-16Prestress Losses for Post-Tensioning

Stage Source of Prestress Loss Responsibility

AtJ

acki

ngPrestress at Jacking: fsj

Friction (FR) Contractor / Consultant

Anchorage Seating (ANC) Contractor / Consultant

Elastic Shortening (ES) Contractor / Consultant

Prestress immediately after Transfer: fst

Aft

erTr

ansf

er

Creep (CR) Consultant

Shrinkage (SH) Consultant

Relaxation (REL2) Consultant

Prestress following all losses: fpe

Prestress losses can be divided into two groups. Losses “at transfer” occur up to the time immediately after theprestressing force is applied to the concrete element. Losses “after transfer” begin immediately after transferand continue throughout the life of the structure. The total prestress loss, ∆ , is represented as the sum of theselosses:

∆ = ∆ + ∆

Where:

∆ = loss of prestress (MPa)

∆ = losses up to and including transfer (MPa)

∆ = losses occurring after transfer (MPa)

Losses at transfer include all losses until just after the application offorce on the concrete. This can include losses from anchorageseating (ANC), friction (FR), initial relaxation (REL1) and elasticshortening (ES).

In pretensioned girders, ∆ is comprised of plant losses (seatinglosses, bed shortening, etc), initial relaxation, and elastic shorteningof the girder. By specifying the stress immediately prior to transfer,fsi, the only loss at this stage that the Consultant needs to consideris elastic shortening.

For completeness, an example calculation of the plant losses is included below, demonstrating the losscalculations necessary for consideration by the Fabricator.

For Clarification: Initial relaxation(REL1) is mentioned in this section forcompleteness and historic context.Historically, Consultants haveincluded this loss in their calculations.However, for Alberta Transportationprojects, Fabricators are responsiblefor accounting for this loss.

(4-27)

Page 4-36


Sample Calculation 6: Plant Related Prestress Losses

As an example, calculate the plant related losses for a typical NU Girder. The following calculations are for asingle strand, and are based on the following criteria:

Target strand stress and force, immediately prior transfer (specified by Consultant on the Drawings)

fsi = 0.75fpu = 1395 MPa Fsi = 195.3 kN

Plant Information

Lbed = 40,000 mm Unstressed bed length Lchuck = 100 mm Chuck length

Lhead = 500 mm Stress head length LDE = 5 mm Dead end seating

LLE = 10 mm Live end seating LBS = 10 mm Total bed shortening

trel1 = 0.75 days Assumed time between “lock off” and transfer

Finitial = 40 kN Initial force applied (to remove slack prior to final stressing)

Mill Certificate Information

= 141.6 = 196.3

Stressing Calculations

Fabricator is responsible for overcoming all plant related losses during stressing to achieve the target forceapplied to the girder immediately prior to transfer.

Total strand length that will elongate under stressing:

= + 2( + ) = 40,000 + 2(100 + 500) = 41,200

Calculate stressing force following initial force.

= – = 195.3− 40.0 = 155.3

Total elongation of strand required to achieve design force without any losses:

= ∙∙ =

(155.3)(41,200)(141.6)(196.3) = 230.19

Plant related losses such as relaxation, bed shortening, and seating losses are determined below to addresshow much overpull is needed to achieve the target force.

Relaxation (REL1) is calculated from Equation (4-36):

=(24 )

45 − 0.55

ℎ = 0.9 = (0.9)(1860) = 1674 a

=195.3x10

141.6 = 1379

=log(24 ∙ 0.75)

4513791674 − 0.55 (1379) = 10.53

=(10.53)(141.6)

1000 = 1.491

=(1.491)(41,200)(141.6)(196.3) = 2.210

Page 4-37


With post-tensioning, the losses up to and including transfer include friction, anchor seating, and elasticshortening.

∆ , = + +

Losses after transfer for both pretensioned and post-tensioned girders begins after the application of load andcontinue throughout the life of the structure. This includes losses from creep (CR), shrinkage (SH), and relaxation(REL2).

∆ = + +

Figure 4-15 shows the prestress losses applicable for a conventional pretensioned NU Girder, applicable at mid-span for the girder.

Sample Calculation 6: Plant Related Prestress Losses (Continued)

The length of overpull required to overcome relaxation, bed shortening and seating losses is then calculated:

= + 2 + = 2.210 +102 + 5 = 12.21

Total elongation:

+ = 230.19 + 12.21 = 242.40

Force per mm of elongation:

=155.3

230.19 = 0.675kN/mm

Then the target jacking force is calculated, which will overcome plant losses and relaxation to provide thetarget force immediately prior to transfer:

= 195.3 + (12.21)(0.675) = 203.5 = 203.5× 10

Fabricators typically work to have the maximum force at jacking below 0.78fpu for safety considerations.

= ..

= 1437 ≅ 0.77 < 0.78

(4-28)

(4-29)

Page 4-38


Figure 4-15Prestressing Stress Levels – Pretensioned NU Girder

CHBDC provides provisions for determining prestresses losses. These losses include immediate losses and time-dependent losses.

Immediate losses refer to anchorage seating (ANC), elastic shortening (ES), and friction (FR) losses.

When completing an NU Girder bridge design that does not include post-tensioning, the Consultant considersthe immediate losses caused by elastic shortening only. When a design includes post-tensioning, the Consultantmust consider the additional losses of friction and anchorage seating.

Anchorage Seating (ANC)In post-tensioned applications, the Consultant must include the effects of seating of the post-tensioninganchorage system. The CHBDC Commentary provides guidance on anchorage seating for the basis of design. Ingeneral, post-tensioning of NU Girder bridges uses 12 strand tendons, which can be expected to have 10 mmof anchorage seating.

The slip associated with anchorage seating reduces the strain in the strand, and thus reduces the stress. Thelength of strand affected will be limited by the amount of friction the tendon is subjected to, which is a functionof tendon curvature, wobble, and coefficient of friction.

Determination of anchorage seating losses is best illustrated by example and is shown in Sample Calculation 7.

Dfs2

ES

fsi

Transfer

fst

fse

Jacking

Time (days) (log scale)

Pres

tres

s(M

Pa)

Page 4-39


Friction:In post-tensioning applications, friction losses refer to the losses in tendon stress caused by friction between thetendon and the ducts and by the wobble effect.

Wobble represents the unintended deviation of a prestressing duct from its specified profile, as shown in Figure4-16. When post-tensioning ducts are installed during fabrication, they are supported at discrete locations alongthe girder web and installed to specified tolerances. The wobble effect accounts for the small unintendedchanges in profile and for additional friction that results from fabrication placement and the flexibility of theduct between support locations.

Figure 4-16Wobble Friction Losses (Collins & Mitchell, 1997)

= 1− ( )

Where:

= jacking stress (MPa)

= wobble coefficient, (1/m)

= distance away from the jacking end (m)

= coefficient of friction between the strand and the duct

= vector sum of angular changes in elevation and plan of a prestressing tendon from thejacking point to the point of consideration, x (radians)

Table 4-17Friction Factors for Post-Tensioning

Duct Size Friction Factors

Semi-rigid steel up to 75 mm outside diameter K = 0.005m = 0.20

Semi-rigid steel over 75 mm outside diameter K = 0.003m = 0.20

(4-30)

Page 4-40


Sample Calculation 7: Immediate Post-Tensioning Losses

As an example, calculate the tendon forces applied at jacking, including the immediate prestress losses, forthe post-tensioning tendon profile developed in Sample Calculation 5. The tendon is made up of 12 –15.2 mm diameter low-relaxation strands. The losses considered include anchorage and friction, and arebased on the following criteria:

K = 0.003 m-1 m = 0.20

fsj = 0.80 fpu = 1488 MPa Ep = 200,000 MPa Ap = 12 x 140 mm2 = 1,680 mm2

DANC = 10 mm

For this example, the profile is considered at 10th points.

x 0L 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L 1.0L

x 0 5355 10710 16065 21420 26775 32130 37485 42840 48195 53550

y 2000 1417 998 742 650 699 858 1130 1513 2007 2285

Losses due to friction, calculated according to Equation (4-30), are a function of length along the tendonand the cumulative angle change. From our profile developed in Sample Calculation 5, the slope (dy/dx) ateach point and the cumulative angle change (a) are calculated.

x 0L 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L 1.0L

dy/dx -0.124 -0.094 -0.063 -0.032 -0.002 0.019 0.040 0.061 0.082 0.102 0.000

a 0.000 0.031 0.061 0.092 0.122 0.144 0.164 0.185 0.206 0.227 0.329

By applying Equation (4-30), the losses, FR, at each point away from the location of jacking are calculated.The stress, fsx, at any location due to the jacking stress, is then calculated.

x 0L 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L 1.0L

FR 0 33 65 96 126 154 180 207 232 257 301

fsx 1488 1455 1423 1392 1362 1334 1308 1281 1256 1231 1186

The next step is to determine the anchorage losses. It is helpful to look at the tendon stress graphically whendetermining the anchorage losses. The figure below shows the tendon stress at jacking including frictionlosses. Also shown is the slope of the tendon stress, which is used in determining the anchor set loss.

slope1

Page 4-41


Sample Calculation 7: Immediate Post-Tensioning Losses (Continued)

Anchor set will result in a loss in strain in the tendon. Below, the strain diagram for the tendon is shown, atjacking, and following anchor set. The area shaded represents the anchor set. By knowing the magnitude ofthe anchor seating, the length of tendon affected, xanc set, can be calculated.

Over the length affected, the slope is assumed to be constant. A length of 0.3L is used to calculate slope.

slope =1488 − 1392

16065 = 0.00598 /

=∆

= 18295

And the value of stress in the tendon at the point of anchor influence, fpp, is calculated as:

= − ∙ = 1488− 0.00598 ∙ 18295 = 1379

The tendon stress at each location following anchor set can be calculated. In the table below, the tendonstress following anchor seating is shown, along with the ratio fpi/fpu, which can be compared with the limitsin Table 4-12 to confirm that tendon stress limits are met. The limits are 0.70fpu at anchorages, and 0.74fpu

elsewhere, which are both satisfied.

x 0L 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L 1.0L

fpi 1267 1299 1332 1365 1362 1334 1308 1281 1256 1231 1187

fpi/fpu 0.68 0.70 0.72 0.73 0.73 0.72 0.70 0.69 0.68 0.66 0.64

Lastly, the tendon force diagram is determined, which is included on the design drawings, representing thetendon force at jacking following anchor set.

xanc set

Page 4-42


Elastic Shortening (ES)In prestressed concrete, ES loss is a result of the shortening of the concrete girder under load. At the momentof transfer, the concrete surrounding the tendon shortens as the prestress force is applied. With straincompatibility, the tendon that is bonded to the concrete will shorten with it. The prestress loss can be estimatedusing the following equation:

=

Where:

= modulus of elasticity of the tendons (MPa)

= modulus of elasticity of concrete at transfer (MPa)

= concrete stress at the centre of gravity of tendons due to the prestressing effect attransfer and the self-weight of the member at sections of consideration (MPa)

Time-dependent prestress losses arise from creep (CR), shrinkage (SR), and relaxation (REL1 and REL2). CHBDCprovides a simplified method; the Commentary provides additional direction and resources on detailed time-dependent prestress losses.

It is appropriate to use the simplified method for preliminary and detailed design of NU Girder bridges with asimple expected load history. This includes simple-span and multi-span bridges with pretensioned girders.Special consideration is required to estimate camber (discussed in Section 4.8.2.4). Detailed methods provide ameans of determining losses and estimating camber, while also allow more opportunity for refining designs.

For NU Girder bridges that have a complex expected load history, which may include post-tensioning, a detailedmethod for determining losses is necessary. CHBDC Commentary identifies the age-adjusted effective modulus(AAEM) method as one method appropriate for determining prestress loss in prestressed girder design. TheAAEM method does not directly calculate the losses arising from the various contributing factors, but insteadcompletes a sectional response that includes creep, shrinkage, and relaxation to determine the response of thesection. The Detailed Method is discussed in Section 4.7.3. The simplified provisions from CHBDC are presentedbelow.

Creep (CR) – Time-dependent: Creep of the NU Girder concrete will reduce the length of the tendon, resultingin reduced tendon stress. The amount of long-term prestress loss due to creep can be estimated from thefollowing equations:

= 1.37− 0.77 100( − )

Where:

= annual mean relative humidity (%)

= 2.0

= modulus of elasticity of the tendons (MPa)

= modulus of elasticity of the concrete (MPa)

= concrete stress at the centre of gravity of tendons due to the prestressing effect attransfer and the self-weight of the member at sections of consideration (MPa)

= concrete stress at the centre of gravity of tendons due to all dead loads except thedead load present at transfer at the same section for which fcir is calculated (MPa)

(4-31)

(4-32)

Page 4-43


The term (fcir-fcds) represents the long-term sustained stress in the concrete at the centre of gravity of the tendonsand is calculated by removing the stress resulting from additional dead loads after transfer (fcds) from the stressstate immediately after transfer (fcir). The dead loads include deck pour, asphalt pavement, and othersuperimposed dead loads.

To estimate the prestress loss due to creep at a time other than the long-term losses, the CHBDC Commentaryprovides the following equation:

( ) = 1− . √

Where:

= time after transfer (days)

Shrinkage (SH) – Time-dependent: Shrinkage of the NU Girder concrete will reduce the length of the tendon,resulting in reduced tendon stress.

= (117− 1.05 )

To determine the prestress loss due to shrinkage at a time other than the long-term losses, CHBDC Commentaryprovides the following provision:

( ) = 1− . √

Relaxation (REL1, REL2) – Time-dependent: Relaxation of the prestressing strand will result in a loss of stressof the prestressing. Relaxation is considered in two different stages: relaxation before Transfer (REL1), andrelaxation after Transfer (REL2). Relaxation before transfer is the responsibility of the Fabricator as discussed inSection 4.6.5.2.

Relaxation before transfer can be calculated using the basic equationdescribing relaxation of strands held under constant tension (see alsoSection 4.4.4.4):

=log(24 )

45 − 0.55

Where:

t = time (days) elapsed since jacking, typically taken as 0.75 days for girders fabricated on a24-hour cycle

= stress in tendons at jacking (MPa)

Relaxation occurring after transfer is affected by the shortening of the girder due to creep and shrinkage, andthe same equation is not applicable. Therefore, CHBDC provides the following calculation for relaxation aftertransfer:

= − 0.55 0.34−+

1.25 3 ≥ 0.002

Where:

= stress in tendons immediately after transfer (MPa)

(4-33)

(4-34)

(4-35)

(4-36)

(4-37)

REL1 is the responsibility of theFabricator, with an exampleshown in Sample Calculation 6

Page 4-44


As discussed earlier, the response of prestressed concrete sections is time-dependent because properties of thematerials used vary with time. Specifically, concrete under a sustained load will experience creep, concreteexposed to a drying environment will shrink, and prestressed steel under a sustained tensile load will relax. Whenusing detailed methods of analysis, the effective modulus and age-adjusted effective modulus are usefulmethods of incorporating creep and shrinkage effects. These are presented below.

CHBDC has been developed to allow for linear approximations. By meeting the requirement in this manual andCHBDC, effects such as creep strains can be reasonably assumed to be linearly related to stress. This assumptionof linearity allows the principle of superposition to be used, and a constitutive relationship can be written as:

( ) = ( )1 + ( , )

( ) +1 + ( , )

( )

∆ ( )

( )+ ( , )

This equation can be more simply understood by reviewing each of the terms:

( )1 + ( , )

( )

This term represents the strain developing due to a sustained load sc applied at time ti developing overthe interval (t,ti). The initial elastic strain increases as described by the creep coefficient.

1 + ( , )( )

∆ ( )

( )

This term represents the load related strain that develops due to a varying load Dsc that is slowlyapplied over the interval (t,t). As described below in Section 4.6.6.2, the aging coefficient is used toreplace the need for integration, simplifying this term.

( , )

This term represents the shrinkage strain that develops over the interval (t,ts).

The variation in stress with time and the resultant strain are shown graphically in Figure 4-17 and Figure 4-18.Here, ec(t) is the concrete strain at time t, ( ) and ( )are the stresses at times ti and respectively, ( , )and

( , ) are the creep coefficients at time t for ages of loading of ti and respectively, ( ) and ( ) are theconcrete modulus of elasticity at ages ti and respectively, and ( , )is the shrinkage strain at time t where ts

is the time shrinkage begins. Here the creep coefficient is defined as the ratio of creep strain to initial elasticstrain, consistent with Equation (4-17).

(4-38)

[1]1]]

[2]1]]

[3]1]]

Page 4-45


Time (t)

Stre

ss, s

c(t)

ti t

Dsc(t)

sc(ti)

Figure 4-17Applied Stress Varying in Time

Figure 4-18Stress Related Strain as a Function of Time

In Equation (4-38), Dsc(t) is a stress increment which begins at zero at time ti and gradually increases to its fullvalue at time t. This would correspond to load cases such as differential shrinkage between the deck and girders.

A simplified solution to Equation (4-38) was formalised by Bazant (1972), where the introduction of the agingcoefficient, χ, replaces the integral with an algebraic expression.

( ) = ( ) ∙1 + ( , )

( ) +∆ ( ) ∙1 + ( , )

( ) + ( , )

The aging coefficient is a function of both the stress history and concrete aging properties but can generally betaken constant with little loss in accuracy. The following is recommended for use:

= 0.7

The benefit of the aging coefficient is that the deformation ofconcrete can be written in a linear system of equations, even ifstresses are applied or removed gradually. In essence, the varyingstress is treated as if its full magnitude was applied at time ti, butits effects are reduced by the aging coefficient to account for itsgradual development. The aging coefficient assumes the rate atwhich stress is applied.

The treatment of creep as presented above led to the development of the effective modulus to be used in design.The definition of the effective modulus is the inverse of the creep function. When using the effective modulus,the strains calculated represent the load-related strains.

, ( , ) =1

( , ) =( , )

1 + ( , )

Aging CoefficientConcrete Structures: Stresses andDeformations, Ghali, Favre and Elbadry(2011) provides more information on theuse of the aging coefficient.

(4-39)

(4-40)

(4-41)

Stra

indu

eto

appl

ied

stre

ss

Time (t)ti t

ec(t)-ecs

ec(ti)-ecs

( )− ( , )

( ) − ( , )

TimeTime

Stre

ss

( )

( )

Page 4-46


A second term is also developed, termed the age-adjusted effective modulus. Here, the definition is similar tothe effective modulus but includes the aging coefficient. As discussed above, the aging coefficient accounts forthe rate of application of a gradually introduced load. If the load is applied instantaneously, an aging coefficientof 1 is used, and the age adjusted effective modulus becomes equivalent to the effective modulus.

, ( , ) =( , )

1 + ( , )

4.7. PRESTRESSED DESIGN APPROACHES

In NU Girder bridge design, the girder selection, and prestressing design (including pretensioning and post-tensioning) are typically governed by the Serviceability Limit States (SLS).

In the completion of the prestressing design, calculating the amount of prestressing force is necessary fordetermining the stress in the NU Girder, and completing the SLS checks. From the moment of transfer,prestressing experiences loss of prestress due to several sources previously discussed (such as relaxation, elasticshortening, creep and shrinkage) and as a result, the effective prestress acting on a section will change with time.The effective prestress is also affected by changes to boundary conditions and changes to loading.

There are multiple approaches to completing prestressing design in NU Girder bridges, ranging fromapproximate to highly refined, and the approach selected must be suitable for the complexity of the bridgebeing designed. In this Manual, two approaches are presented:

· Simplified Method· Detailed Method

The simplified method is considered suitable when designing bridges with a simple expected load history, thatdo not involve post-tensioning or multiple changes of boundary conditions. The detailed method is consideredappropriate for any bridge, including those with more complex expected load-histories, changes to boundaryconditions, and with post-tensioning.

The Simplified Method is considered appropriate for NU Girder bridges thathave a simple load history and do not involve post-tensioning or multiplechanges of boundary conditions. Applicable bridge configurations include:

· Single-span NU Girder bridges with a cast-in-place deck· Multi-span NU Girder bridges with cast-in-place deck and

diaphragms

The basic method for checking NU Girder stresses during design involves calculating the girder stresses at criticalsections for key stages of the girder’s service life. As the section remains uncracked, simple elastic theory is usedto calculate stresses caused by applied loads:

Design Examples 1 and 3provide comprehensiveexamples using theSimplified Methoddescribed in this Sectionfor checking stresses.

(4-42)

Page 4-47


Axial Stress:

=

Bending Stresses:

=

Prestressing Bending Stresses:

=∙ ∙

Where:

= Concrete stress (MPa). Calculated for top and bottom fibre, referenced as ft and fbrespectively

= Axial load (N). Typically, this is the effective prestressing force on the section

= Applied moment (N mm). This will be due to self-weight, and applied loads includingthe deck, superimposed dead loads, restraint moments, live loads, and thermal loads

= Distance from extreme fibre to section centroid, for top and bottom fibre referenced asyt and yb respectively (mm)

= Distance from the centroid of the prestressing to the centroid of the section (mm)

= Moment of Inertia of the section (mm4)

When calculating the elastic stresses, the prestressing force applied is the effective prestressing force. Theeffective prestressing force is the force in the prestressing strand after losses are considered.

This method relies on the use of the simplified method of calculating prestress losses, summarised inSection 4.6.5. By following these provisions, the prestress loss at any time can be calculated, and the effectiveprestress can be determined. This provides a simple method for calculating girder stresses.

Mid-Span Girder Stresses at Release

∙ ∙ ∙

PrestressAxial Stresses

PrestressBending Stresses

Self-WeightBending Stresses

Concrete Stress

+ + =

(4-43)

(4-44)

(4-45)

Page 4-48


Several methods of incorporating time-dependent effects into structuralanalysis are available. This manual uses a method termed the Age-AdjustedEffective Modulus (AAEM) Method, adapted from Collins and Mitchell (1987),for incorporating time-dependent effects.

The simplified method discussed earlier calculates the effective prestress anduses this calculation to determine sectional response at critical stages and atcritical locations, with camber calculated independently. By contrast, the refinedmethod approaches the analysis by considering the loads acting on a sectionand using an effective modulus of elasticity for the concrete to account for creep effects. Shrinkage, prestressrelaxation, and other effects (post-tensioning, restraint moments, etc.) are applied as load cases on the section,and the strain and curvature response are calculated. Linear stress–strain relationships allow for determinationof the stress distribution for the concrete and prestressing at the section. Stages in construction are appliedthrough principles of superposition of load-effects. Consideration of multiple sections along a girder allow fornumerical integration of strains to calculate girder shortening, and of curvature to calculate deflected shape.Following this approach has the added benefit of a better prediction of deflected shape and the potential formore accurately determining the positive moment over the pier. There is also an improved appreciation ofstresses and deflection along the girder as shown in the figure below.

Figure 4-19Example of Change of Girder Concrete Stresses Between Transfer and Erection

Using AAEM Method

Figure 4-20Example of Change of Deflected Shape Between Transfer and Erection

Using AAEM Method

Design Example 4provides a comprehensiveexample using thedetailed methoddescribed in this section,for checking stresses andcalculating deformations.

Length along girder

Conc

rete

Stre

ss(M

Pa)

Top Fibre Stress - At Transfer

Top Fibre Stress - At Erection Bottom Fibre Stress - At Erection

Bottom Fibre Stress - At Transfer Allowable Stress Limit

Deflected Shape at ErectionDeflected Shape at Transfer

Length along girder

Def

lect

ion

(mm

)

Page 4-49


This method is identified in Clause C8.7.4.3 of the CHBDCCommentary and is presented as the Detailed Method for treatmentof time-dependent effects. The approach assumes elastic behaviourwith plane-sections theory for uncracked elements. The sectionsbelow outline the basic approach to applying this method to predictthe sectional responses for NU Girder bridges, with time based on theAge-Adjusted Effective Modulus (AAEM) Method.

The section forces considered are the normal force N acting at the reference point and the bending moment M,taken with respect to the reference axis. A positive normal force causes tension and a positive bending momentcauses tension on the bottom fibre. The resulting strain distribution is considered positive, as illustrated in Figure4-21.

Figure 4-21Positive Sign Convention

The first set of section forces considered are those caused by self-weight and are termed N0 and M0. In the casethat the beam is horizontal and statically determinate, the self-weight will not produce an axial load.

The next set of forces to consider is the prestressing. Since the prestressing strands are in one or more layers, itis convenient to define a prestressing force, Pj, for each layer, j. The prestressing strands remain linear–elasticthrough the stressing process, and so the force Pj can be expressed as:

=

Where:

= number of strands in layer j

= area of one prestressing strand (mm2)

= modulus of elasticity of prestressing strand (MPa)

= strain in the prestressing strand of layer j

Another refined method forincluding time-dependent effects ispresented in Concrete Structures:Stresses and Deformations, Ghali,Favre and Elbadry (2011).

Reference Axis

(4-46)

Page 4-50


For the elastic case with only self-weight and prestress acting, the section forces can be written as:

= +

= +

Where:

= −

= −

and ypsj is the distance to the centroid of the prestressing force for layer j.

The response of a section to the loading defined by Equations (4-47) and (4-48) can be described by its straindistribution. For a plane section the strain distribution is linear and is described herein by the strain at thereference axis, eo, and curvature, y. The strain distribution for the section is calculated as:

= +

while the strain in the prestressing layer j is calculated as:

= + +

Then, for a section under a normal axial force, N and moment M, the elastic response at time t is given by:

ε =N

E A

=M

E I

where and are the transformed sectional properties calculated with respect to the reference modulus, Eref. Ingeneral, the NU Girder concrete’s modulus is taken as the reference modulus.

Loss of prestresses is discussed in detail in Section 4.6.5. Prestress levels can be classified as immediate and long-term. Immediate losses include everything up to and including transfer, while long-term losses occur thereafter.

With prestressed concrete, immediate losses include anchor seating, shortening of the stressing bed, andintrinsic relaxation before transfer. At transfer, shortening of the girder results in elastic shortening of the strands.The elastic prestress loss is accounted for by using transformed section properties and ensuring that equilibriumand the compatibility requirements of Equations (4-51) and (4-52) are met.

(4-48)

(4-47)

(4-50)

(4-49)

(4-51)

(4-52)

(4-54)

(4-53)

Page 4-51


Following transfer, concrete creep and shrinkage and strand relaxation result in further prestress loss. Creepand shrinkage cause a shortening of the girder; resultant losses of prestress are calculated consideringequilibrium and compatibility. Relaxation loss is outlined in Section 4.4.4.4. Here, the intrinsic relaxation, Dfpr, iscalculated by adapting Equation (4-23):

∆ =(24 )45 − 0.55

where t is the age in days, fpi is the stress in the steel at time zero and fpy is the yield strength of the prestressingsteel.

Intrinsic relaxation is based on a test where the strand is held at a constant length. To account for the effect ofshortening of the prestressed beam, the intrinsic relaxation is reduced by the relaxation reduction coefficient cr

as described by Ghali et al. (2011), to give the reduced relaxation, ∆ ̅ .

∆ ̅ = ∆

In most practical cases the relaxation reduction coefficient can be taken as 0.8 (Collins and Mitchell 1997).Consultants can refer to either Ghali et al. (2011) or Collins and Mitchell (1997) for further information on thederivation of the relaxation reduction coefficient, and its use.

This method uses the effective modulus to calculate stress-related strains and assumes that any stresses appliedon a section are done so instantaneously. The effect of creep on the section is considered directly proportionalto the creep function, J(t,t0), with free shrinkage and prestress relaxation being treated as forces on the section.The procedure, adapted from Collins and Mitchell (1987), is outlined below.

First, the load is calculated as the sum of applied loads, shrinkage effects, and prestressing.

( , ) = + ( , ) + ( , )

( , ) = + ( , ) + ( , )

Where:

( , ) = , ( , ) ( , )

( , ) = , ( , ) ( , ) −ℎ

2

( , ) = − ,

( , ) = − ,

Where:

= distance from the centroid of the composite section to the top fibre of the deck (mm)

ℎ = thickness of the concrete deck (mm)

The effective modulus of the prestressing, Ep,eff, accounts for relaxation by reducing the elastic modulus of theprestressing steel. It is calculated as:

(4-55)

(4-56)

(4-57)

(4-58)

(4-62)

(4-59)

(4-61)

(4-60)

Page 4-52


, = −∆ ̅

The strain distribution at any time t, after loading at ti is then calculated as:

( , ) =, ( , )

( , ) =, ( , )

where the prime symbol denotes an effective sectional property and is calculated as the transformed sectionproperty with respect to the effective modulus of the concrete, Ec,eff(t,ti). The effective modulus is equal to theinverse of the creep function.

, ( , ) =1

( , ) =( , )

1 + ( , )

Changes in boundary and loading conditions can, in general, be incorporated by satisfying the requirements ofstatic equilibrium and compatibility, and by using the principle of superposition. This is illustrated in Figure 4-22,where a prestressed concrete girder is subjected to load case 1 at t1, and load case 2 at t2. At t1, the load causesan upward deflection, which increases with time. At t2, this load is removed, and its load effects with time areremoved. Also at t2, load case 2 is added. The summation of the separate cases produces a system that meetsthe requirements of static equilibrium and compatibility, while accounting for time-dependent effects. Thismethod of superposition includes the effects of creep recovery under the assumption that creep recovery isproportional to creep.

Mid

-Spa

nD

efle

ctio

n

Time

Load Case 2Sum

Load Case 1

Removal ofLoad Case 1

t1 t2

Figure 4-22Linear Superposition of Load Effects

In using the method of superposition, events are characterised by discrete times. At these times, the previousload case is removed while the new load case is applied. The response of the structure becomes a sum of theseparate responses, whether it be strain distribution, mid-span deflection, or some other desired response.

In some cases, special care must be taken in the way that the requirements are met. For the structure considered,two such cases arise:

· Addition of the deck, which produces composite action and differential shrinkage between the deckand girder

· Formation of a continuity diaphragm

(4-64)

(4-65)

(4-63)

(4-66)

Page 4-53


Composite action can be incorporated into the detailed analysis methods, as described above. In cases whereloads are applied to a composite section, the section properties and material properties are transformed withrespect to a chosen reference modulus, and the analysis is performed as outlined.

Problems arise when loads are applied at times when materials have no definable properties. This is because themethods outlined determine response over time with respect to initial properties. Both the effective and age-adjusted elastic moduli are based on the elastic modulus at the time of loading. Thus, because a deck has zerostiffness when poured, its transformed sectional properties are zero, and the problem becomes ill conditioned.

One way to solve this problem is to choose a time, tc, when composite action is considered to begin. Then loadeffects after this date are determined based on the age of the deck when composite action begins.

Thus, when the deck is poured, its stiffness is neglected until composite action begins. The load is fully carriedby the girder, and the deck is free to shrink. At tc the system is considered to become instantaneously composite.Differential shrinkage between the deck and girder now results in a positive moment acting on the section, whichbegins at zero and gradually increases. This effect is handled differently by each method.

The deck shrinkage is treated as a set of forces acting on the composite section and is added to the otherrestraining forces of Equations (4-57) and (4-58). Then the forces acting on the composite section are:

( , ) = + ( , ) + ( , ) + ( , ) ,

( , ) = + ( , ) + ( , ) + ( , ) ,

When the prestressing force is applied to NU Girders at transfer, the girders deflect elastically, creating the initialcamber. When unrestrained, the camber will increase (increased vertical deflection up) with time due to creep ofthe girder concrete under the prestressing load.

When continuity is created at girder ends (typically by means of a concrete end diaphragm), the end rotation ofthe girders becomes restrained. The bending moment that develops is termed a restraint moment.

Restraint moments are also caused by differential shrinkage between the deck and the girders. When a deck ispoured, it is initially plastic. Following some time, the deck begins to act compositely with the girders. Oncecomposite, the difference between deck concrete shrinkage and the girder shrinkage (differential shrinkage) willresult in a driving force that is restrained at the girder ends.

The CHBDC recognizes that restraint forces (F) can be reduced (F’), to take into account the effect of creep, asdefined in Equation (4-69). AASTHO LRFD further recognizes that restraint forces can be classified as resultingfrom suddenly imposed deformations, or slowly imposed deformations, and can be reduced as defined below:

Restraint Force Reduction for suddenly imposed deformations:

′ = 1 − ( , )

Restraint Force Reduction for slowly imposed deformations:

′ =1 − ( , )

( , )

The PCI Bridge Design Manual (2011) provides a method for calculating restraint moments that arise fromrestraining the end rotation of the NU Girder. The basic method to determine restraint moments involvesallowing rotation to continue past the point of establishing continuity, then determining the moment requiredto restore compatibility of the system.

(4-68)

(4-67)

(4-69)

(4-70)

Page 4-54


Figure 4-23 illustrates the change in end rotation from immediately before continuity (q1) to the point when weare considering the development of the restraint moment (q2) after continuity. The restraint moment thatdevelops restores compatibility. Here the restraint moment MR is required to restore the rotation of qR.=q2-q1.

Figure 4-23Two-Span NU Girder Bridge End Slopes and Restraint Moment

NU Girder bridges remain uncracked and are prismatic with constant section stiffness. The restraint moment torestore continuity becomes a function of the stiffness, length, and angle. Several methods of structural analysisare available to calculate the restraint moment. When using spreadsheets to complete calculations, convenientmethods include The Flexibility Method, or The Moment Distribution Method.

As an example for a symmetric two-span bridge, the restraint moments that develop can be determined fromthe fixed end moments, which are summarized in the table below.

Table 4-18Fixed End Moments for Creep

Creep Fixed End Moments

Left End Span Interior Span Right End SpanLeft Moment 0 2EIθR/L 3EIθR/L

Right Moment -3EIθR/L -2EIθR/L 0

The fixed end moments are based on the following:

= modulus of elasticity for the member being restrained. Typically the NU Girder concrete is usedfor the reference modulus of elasticity (MPa)

= Moment of inertia for the member being restrained (mm4)

= The angle of rotation after the moment of continuity that would occur if the girder end were freeto rotate (radians)

= Length of the span being considered (mm)

When applying fixed end moments, the age-adjusted effective modulus, defined in Section 0 is used for thesection stiffness.

q1 q2

MR

Page 4-55


Shrinkage

For calculating the restraint moment due to differential shrinkage, the internal restraining force required torestore the differential shrinkage between the deck and girders is determined, and the moment resulting fromthat force is applied to the structure. This is illustrated in Figure 4-24.

Figure 4-24Shrinkage Restraint Moment

The calculation for the resultant moment is presented in Equation (4-72). In this equation, the force that developsas a result of the differential shrinkage is based on the age-adjusted elastic modulus for the deck concrete,recognizing that the load is gradually applied, and is reduced due to the effects of creep.

The differential shrinkage is calculated as:

, ( , ) = , ( , )− , ( , )

Where:

= time when the moment due to differential shrinkage is calculated (days)

= time when the deck concrete shrinkage commences (days)

, ( , ) = deck shrinkage occurring in the period (t,t1)

, ( , ) = girder shrinkage occurring in the period (t,t1)

The moment due to the differential shrinkage is then calculated as:

= , , ( , ) , ( , ) −ℎ

2

Where:

= area of the concrete deck (mm2)

, , ( , ) = age adjusted elastic modulus of the deck concrete (MPa)

= distance from the centroid of the composite section to the top fibre of the deck (mm)

ℎ = thickness of the concrete deck (mm)

εs,diff(t,t1)

Centre of gravityof compositesection

ytc

Adeck εs,diff(t,t1)Ec,aa,deck(t,t1)

Strain Restraining Force

hdeck

(4-72)

(4-71)

Page 4-56


This moment is applied along the structure length. Similar to restraint moments that develop due to creep, fixedend moments to restore continuity are determined. The table below summarises the fixed end moments as afunction of the shrinkage moment for a two-span bridge.

Table 4-19Fixed End Moments for Shrinkage

Shrinkage fixed end actions

Left End Span Interior Span Right End Span

Left Moment 0 Ms 1.5Ms

Right Moment -1.5Ms -Ms 0

Figure 4-25Two-Span NU Girder Bridge Shrinkage Restraint Moment

Where

( , ) , = , , ( , ) , ( , ) ,

( , ) , = , , ( , ) , ( , ) ,

Here the subscript D denotes that the property is associated with the deck. The strain distribution at any time tcan then be determined from Equations (4-63) and (4-65), where the effective transformed section properties ofthe girder become the effective transformed section properties of the composite section.

The creation of a diaphragm at a pier, creating continuity, has the effect of restricting end rotation. As a result,the system becomes statically indeterminate, with a restraining moment developing over the pier to maintaincontinuity.

The force method is used to determine the magnitude of the restraint moment, where the system is first freedof its rotational restraint making the system determinate. Over the time period considered, the amount of endrotation of the freed system is calculated. Then the restraint moment required to restore compatibility isdetermined and applied to the structure, restoring compatibility. In the calculation of the restraint moment, theage-adjusted properties of the structure are used.

To incorporate the gradual increase in the restraint moment, Equation (4-39) is adapted, so that only the changein stress over the time period is considered. The change in stress is caused by the development of the restraintmoment.

(4-74)

(4-73)

Page 4-57


( ) = ∆ ( ) ∙1 + ( , )

( )

By its definition, Equation (4-75) implies that a stress increasing from zero to Dsc at time t produces a strain[1+ f(t,tc)] times the instantaneous strain that would occur if the stress were introduced at time tc. Then, thestrain distribution resulting from the restraint load case can be determined as:

( , ) =− ( , )

, ( , ) ̅

( , ) =− ( , )

, ( , ) ̅

Because the structure is no longer determinate, the compatibility condition of end rotation must be invoked tosolve for the magnitude of the restraint moment. For convenience, the diaphragm is considered to be rigid, andthe condition is that, at tc, end rotation of the composite section at the centre pier becomes fixed. Numericalintegration of curvature can be used to provide slope of the section. Then, for times greater than tc, the freerotation is calculated. Iteration can be used to determine the value of the restraint moment required to restorecompatibility.

If the other system is considered free to deform axially, no axial load develops at the diaphragm. The restraintmoment can be termed MR(t,tc), and the load vector for the load case of the restraint moment can be written forconvenience as:

− ( , ) = 0

− ( , ) = − ( , )

(4-75)

(4-77)

(4-76)

(4-79)

(4-78)

Page 4-58


4.8. PRESTRESSED CONCRETE DESIGN LIMIT STATES

NU Girder bridges are designed to satisfy the Limit States established in CHBDC and by the Department. Theserequire that the NU Girder bridge be proportioned to satisfy the Serviceability Limit States including stresses,cracking and vibration, and Ultimate Limit States of strength and stability.

Prestressed concrete design requires specific checks for fabrication, construction, and in service. The Limit Statechecks required are summarized in Section 4.8.1.

The specific requirements for satisfying the Serviceability Limit States and Ultimate Limit States are thenpresented in Section 4.8.2 and Section 4.8.3.

Figure 4-2634th Street over Whitemud Drive, Edmonton, Alberta

Page 4-59


Several limit state checks are required when designing NU Girder bridges. Below, the necessary Limit State checksfor NU Girder bridges are presented during the three main stages of an expected load history: Fabrication,Construction, and Service.

These limit state checks do not include additional checks completed by Contractors and Fabricators, whichinclude fabrication, erection, and handling checks.

Table 4-20Limit State Checks at Fabrication

Table 4-21Limit State Checks during Construction

Stage 1 – Fabrication: Limit State Checks

Serviceability Limit StatesStress limits required during Fabrication include prestressing limits (Table 4-12) and concrete stress limits(Table 4-13). Deformation checks require calculation of camber.

Fabrication Consideration SLS Check

Prestress transfer: Strand stresses Stress: Prestressing limits

Prestress transfer: Concrete maximum compressionand maximum tension

Stress: Concrete stress limits

Prestress transfer: End zone stresses Stress: end zone reinforcing

Immediately after transfer Deformation: Camber

Stage 2 – Construction

Serviceability Limit StatesSLS checks required during Construction will depend on the stages of construction considered. For concretestress limits, see Table 4-13. Deformation checks require calculation of camber at various stages.

Construction Stage SLS Check

Girder erection Deformation: Camber

Before deck casting Deformation: Camber

Immediately after deck castingStress: Concrete stress limitsDeformation: Camber

Immediately after superimposed dead loads Deformation: Camber

Immediately after post-tensioning(if applicable)

Stress: Prestressing limits (for post-tensioning),Concrete stress limitsDeformation: Camber

Ultimate Limit StatesULS checks required during Construction are related to stability of the bridge as a whole, and itscomponents.

Construction Stage ULS Check

Deck pour Girder and cross-bracing capacity

Page 4-60


Table 4-22Limit State Checks in Service

Stage 3 – In Service

Serviceability Limit StateStress limits required during Service include concrete stress limits, cracking, deformation, and vibration.

Service Consideration SLS Check

SLS combinations: concrete stresses incompression and tension

Stress: Concrete stress limits

Long-term deformation Deformation: CamberDeck cracking see Clause 8.12 of the CHBDC (not covered in this manual)Vibration see Clause 3.4.4 of the CHBDC (not covered in this manual)Ultimate Limit StateULS checks required during Service are related to strength. Factored resistance must always exceed totalfactored load effects. For NU Girders, this includes shear capacity and flexural resistance checks for criticallocations.

Service Consideration ULS Check

ULS Combinations: Maximum factored shear Shear capacity at critical locations

ULS Combinations: Maximum factoredbending

Flexural capacity at critical locations

The design of NU Girder bridges requires that the girder design be proportioned to satisfy the requirements forcracking, deformation, stress, and vibration serviceability limit states (SLS).

In addition to the service limit states outlined in CHBDC, the Department requires camber predictions beprovided by the Consultant for the stages of construction, beginning with fabrication through to the end of theservice life of the bridge.

Mid-span stresses are typically the governing criteria for aserviceability limit state that defines the required number ofstrands and the required amount of post-tensioning. While thisis often selected at the preliminary design phase, along with thegirder section, spacing, and post-tensioning requirements, thereis the opportunity to optimize these decisions during thedetailed design process.

The chart in Figure 4-27 outlines the general procedure forcompleting the SLS design of an NU Girder. Throughout thisprocess, the Consultant will have an opportunity to refine the design and is encouraged to engage withfabricators to determine the effects of design decisions on fabrication and constructability.

The process of completing an NU Girderdesign is best illustrated by example.

Volume 2 – Design Examples presentsseveral comprehensive examples usingboth the simplified method and thedetailed method, for checking stressesand calculating deformations.

Page 4-61


Figure 4-27Serviceability Limit State – Typical Design Process

The method of analysis shall be in accordance with Section 5 of the CHBDC and in accordance with BSDC.

The Consultant shall use a design approach appropriate for the level of complexity of the bridge being designed.Section 4.7 presents two approaches for determining prestress losses and completing prestressed concretedesign and are referred to as the Simplified Method and the Detailed Method.

Establish Criteria: Geometry, girder size, material properties, and initial pretensioning and post-tensioning design (number of strands/tendons). This is completed at preliminary design.

SLS checks at transfer: Establish strand debonding patternor deviation layout to satisfy the girder stresses at transfer.

Prestress Losses: Determine long-term and short-term prestressing force losses, using eitherthe simplified or the detailed method outlined in Section 4.7.

During this phase ofdesign, iteration will benecessary to optimizethe pretensioning andpost-tensioning designs.

Updating the short-termand long-termprestressing losses asrequired).

Load Effects: Determine bridge girder load effects for all dead and live loads.

Complete SLS Checks for concrete stresses duringconstruction. This may include multiple stages for post-tensioned bridges.

Complete SLS Check for concrete stresses in-service.

Complete SLS Camber Calculations: Camber calculations for the relevant stages completed.

Prestressing design finalized: Stress immediately before transfer, fpi, established forpretensioning, along with debonding/deviated strand layout. Jacking stress, fsj, established forpost-tensioning, along with tendon profile and stressing sequence and staging.

[1]

[2]

[3]

SLS

Stre

ssCh

ecks

[4]

[5]

[6]

[7]

[8]

Page 4-62


NU Girders are designed to be fully prestressed during their service life, requiring concrete stresses to meet thelimits identified in Section 4.6.1. In general, tensile stresses govern design, limited to 0.5fcri at transfer and fcr inService. During construction, it may be appropriate to consider the age of the girders and use the appropriatemodulus of rupture for the stress check. For bridges that are made continuous through cast-in-placediaphragms, the non-prestressed portion of the bridge will be subjected to tensile stresses, and the CHBDCprovisions for crack control will apply.

The limit state checks outlined in Table 4-20, Table 4-21, and Table 4-22 will require calculating girder stress andconfirming that the design meets the stress requirements identified in Table 4-13.

Critical Sections

It is necessary to check the NU Girder at critical sections and at the necessary stages of construction. Criticalsections are:

· At the girder ends· At mid-span· At location of maximum moment (when it does not correspond with mid-span)· At locations along the girder where changes in strand profile occur (such as locations of debonding or

deviation)

Analysis and Software

CHBDC does not specify a method of analysis for checking the serviceability limit states for an NU Girderbridge design. However, basic flexural theory assumptions must be satisfied, including the following:

· Plane sections remain plane and strains vary linearly over the depth of the section;

· In uncracked sections, stress is linearly proportional to strain;

· Strain changes in bonded reinforcement are equal to strain changes in surrounding concrete;

· Concrete may be assumed to resist tension at sections that are uncracked;

· After cracking, tension in the concrete is neglected.

In addition to these criteria, the analysis must consider the expected load history and time-dependenteffects, including:

· Time-dependent losses of prestressing caused by creep and shrinkage of concrete, and relaxationof tendons;

· Interdependence of these phenomena;

· Elapsed time between stages of construction.

The level of sophistication for analysis must be appropriate for the complexity of the bridge being designed.It is the Consultant’s responsibility to use methods appropriate for completing the design.

Use of Software

Computer software is commonly used in the analysis of NU Girder bridges to determine load effects anddeflections. Some analysis software is capable of completing staged construction with time-dependentconsiderations such as creep, shrinkage and strand relaxation, however in the use of such software theConsultant must be confident in the manner of treatment of these criteria, and ensure the approach isconsistent with good engineering judgement, CHBDC, the Department’s requirements, and this manual.

Page 4-63


Reliable prediction of camber and deflection are required toprovide estimates of haunch thickness and quantity estimatingnecessary to achieve the final design gradeline.

Prediction of camber is a function of several parameters. At themoment of transfer, initial camber prediction requiresconsideration of the debonded strands and deviation ofstrands, transfer lengths, and modulus of elasticity of the NUGirder concrete. With time, creep, shrinkage, and relaxationaffect the camber of prestressed girders. Tadros et al (2011)identified that at release, the modulus of elasticity is the largestcontributor of uncertainty in initial predictions of camber.

A good practice is to obtain a mean prediction of camber. TheConsultant should also recognize that the prediction will havevariability and should complete the design and detailing withtolerance to the range of variability that could be expected.

Camber at Transfer

At transfer, the deformation of the girder is elastic. Basic structural analysis is used to determining the elasticresponse of the NU Girder. These equations can be used to calculate the camber for the various loadings applied,including self-weight, and prestressing (including straight strands, debonded strands, and deviated strands). TheNU Girder remains elastic through the loading; therefore, the principle of superposition is applicable and thecontributions to the deformation are calculated separately and added together, simplifying the analysis.

The methods presented below use transformed section properties. This allows the use of prestressing forceimmediately prior to transfer, and is the method currently promoted by AASHTO LRFD Bridge DesignSpecifications (2017). A common alternative is to use gross-section properties with the prestressing force justafter transfer (as presented in Section 4.6.5.4 for Elastic Losses). However, this approach is not used here. Forfurther discussion on Section Properties, see Appendix D.

The mid-span camber at transfer is the sum of the contributions from self-weight and prestressing:

∆ = ∆ + ∆

Treatment of Self-Weight

Mid-span deflection caused by self-weight of the NU Girder is calculated from the following:

∆ =5

384

Where:

= uniformly distributed load, in this case due to the self-weight of the NU Girder (N/mm)

= length of the girder between support locations (mm)

= modulus of elasticity of concrete at the time of transfer (MPa)

= transformed moment of inertia of the NU Girder (mm4)

Typically, it is reasonable to use the length of the final support locations for the length in this calculation.

Deflected Girder Shape

The method for calculating camber in thissection provides the mid-span camber. Todetermine the camber at locations otherthan mid-span will require an assumptionof the deflected shape.

The deflected shape is often assumed tobe parabolic; however, due to deviatedand debonded strands, it will typically beflatter than a parabola.

For more complex situations, a detailedapproach for determining girderdeflection may be necessary, such as amoment-area method.

(4-80)

(4-81)

Page 4-64


Treatment of Prestressing

The prestressing in an NU Girder may include a combination of deviated strands, debonded strands, and straightstrands. It is convenient to sub-divide the effects of prestressing into groups of strands with the same pattern,and determine the effects of each group.

Tadros et al. (2011) provide a straightforward method for determining the camber of a general strand pattern.This method includes consideration of transfer length, debonding, and strand deviations, and uses moment-area method to calculate the camber caused by prestressing. Tadros identified that neglecting transfer lengthaffects the prediction of camber by less than 1 percent. The method presented below is adapted from the Tadrosmethod, excluding the effects of transfer length and overhang past the point of bearing support.

This method is considered appropriate for most basic situations. However, Consultants should understand thelimitations and use more refined methods where warranted.

Case 1: Straight Strands

The component of mid-span deflection caused by straight strands, bonded or debonded, can be calculated fromthe following equation.

∆ = 8( − 4 )

Where:

∆ = deflection component due to prestressing force at transfer (N/mm)

= prestressing force immediately before transfer (N/mm)

= eccentricity of prestressing (mm)

= debonded length of strand, as distance between the girder end and start of prestressing(mm)

Figure 4-28Prestressing Geometry Definitions – Straight Strands

(4-82)

Page 4-65


Case 2: Deviated Strands

The component of mid-span deflection caused by deviated, fully bonded strands can be calculated from thefollowing equation.

∆ = 8 + ( − )43

Where:

= eccentricity of prestressing at girder end (mm)

= eccentricity of prestressing at centre (mm)

= length of strand deviation measured from end of girder (mm)

Figure 4-29Prestressing Geometry Definitions – Deviated Strands

(4-83)

Page 4-66


Sample Calculation 8: Camber Calculation at Release

As an example, calculate the mid-span camber for an NU2400 Girder based on the following properties andcriteria:

W = -17.8 kN/m L = 48000 mm

Eci = 26937 MPa Iti = 608.11 x 109 mm4

Psi = 193.8 x 103 N/strand

The girder is stressed with 68 strands, comprising the following groups:

Group 1: Straight n = 46 strands, ec = 748 mm

Group 2: Deviated n = 8 strands, ee = -1180 mm ec = 540 mm b=16800 mm



The strands are all fully bonded, and therefore a=0.

The deflection due to self-weight is found from Equation (4-81) to be:

∆ =5 ∙ −17.8 ∙ 48000

384 ∙ 26937 ∙ 608.11 × 10 = −75.1

The deflection due to Group 1 (straight strands) is found from Equation (4-82) to be:

∆ , =46 ∙ 193.8x10 ∙ (748)8 ∙ 26937 ∙ 608.11 × 10

(48000 ) = 117.2

The deflection due to Group 2 (deviated strands) is found from Equation (4-83) to be:

∆ , =8 ∙ 193.8x10 ∙ 480008 ∙ 26937 ∙ 608.11 × 10 540 + (−1180− 540)

4 ∙ 168003 ∙ 48000 = 7.1

Similarly the deflection contributions from Group 3 and 4 can be calculated to be:

∆ , = 14.5

∆ , = 15.8

The mid-span camber at release is then calculated as:

∆ = ∆ + ∆ = 80

The mid-span camber at transfer is thus calculated to be 80 mm

Page 4-67


Long-Term Camber Prediction

Prediction of long-term camber requires consideration of the effects of creep, shrinkage, and relaxation ofprestressing steel, as well as the stages of construction. Figure 4-30 illustrates the changes to mid-span deflectionfor an NU Girder bridge through construction and into service. The main stages shown are release, deck pour,and application of superimposed dead loads.

Figure 4-30Example of Mid-Span Deflection for an NU Girder Bridge through Construction

As previously discussed, creep is the increase in strain caused by a sustained stress. If there were no losses inprestressing force, the increase in mid-span deflection with time could be calculated as the initial cambermultiplied by the creep coefficient for the time period considered. Using the age at loading creep coefficient(defined in Equation (4-17)), the mid-span deflection at a given time due to initial elastic deflection and creepcan be calculated as:

∆ ( , ) = ∆ + ∆ ( , ) = ∆ [1 + ( , )]

Where:

∆ ( , )= total mid-span deflection due to instantaneous deformation and creep over thetime period t1, t0 (mm)

∆ = instantaneous deformation, mid-span camber at transfer (mm)

( , ) = creep coefficient for the time period t1, t0

The effect of prestress loss over time can be treated as a load case to determine the effect on mid-span deflectionas outlined in Tadros (2011).

With this approach, the prestress losses are determined in accordance with Section 4.6.5.4 for the time periodconsidered. However, as prestress losses increase gradually from zero, their effect is reduced by the agingcoefficient, as described in Section 4.6.6.2.

Deck Pour SuperimposedDead Loads

(4-84)

Page 4-68


Prestress losses are applied as a negative load case on the girder, using the elastic properties at time of transfer(t0). The elastic deformation caused by prestress losses is then multiplied by the creep coefficient to account forthe effects of creep but reduced by the aging coefficient to account for the gradual increase in prestressinglosses with time.

∆ ( , ) = ∆ ( ) ∙ 1 + ∙ ( , )

Where:

∆ , = increase in camber due to creep over the time period t1, t0 (mm)

∆ ( )= elastic mid-span deflection due to prestress losses, at transfer (t0) (mm)

= aging coefficient

The total camber is then obtained by superimposing the separate effects.

∆ ( ) = ∆ + ∆ ( , ) + ∆ ( )

∆ ( ) = ∆ ∙ 1 + ( , ) + ∆ ∙ 1 + ∙ ( , )

(4-85)

(4-87)

(4-86)

Page 4-69


Sample Calculation 9: Camber Calculation at Deck Pour

Following from the previous example, calculate the mid-span camber for an NU2400 Girder just before deckpour, based on the following properties and criteria:

Δo=80.0 mm t = 180 days

= 0.74 = 1376 MPa =1860 MPa

Eci = 26937 MPa Ec,28 = 31896 MPa

CR = 175 MPa SH = 54 MPa

REL2 = 17 MPa f0 (180,0.75) = 1.477 (see Sample Calculation 3)

The increase in mid-span camber can be calculated from Equation (4-84):

∆ (180,0.75) = ∆ [1 + ( , )] = 80.0[1 + 1.477] = 198.2

Second, the effects due to prestress are determined. This begins by calculating the amount of prestress loss at180 days, using the ultimate values for creep loss (CR), shrinkage loss (SH) and relaxation (REL2) modified byequations (4-33), and (4-35) for 180 days.

(180) = 1− . √ = −115.2

(180) = 1− . √ = −39.9

The amount of relaxation that occurs by 180 days is taken as a percentage of total relaxation. The percentagetotal relaxation is assumed to be proportional to the percentage of shrinkage and creep losses that haveoccurred by 180 days, compared with total creep and shrinkage losses, and is calculated as:

(180) =(180) + (180)

+ = 0.68 ∙ = −11.5

Total prestress losses at 180 days are thus:

= −115.2− 39.9− 11.5 = −166.6

The loss force per strands is then calculated as:

, = ∙ = −166.6 ∙ 140 = −23.3

The mid-span deflection resulting from each strand group due to losses is then calculated based on theEquations described earlier for each particular strand group. For the straight strands, this is calculated as:

∆ , =,

8( − 4 ) =

46 ∙ −23.3x103 ∙ (748)8 ∙ 26937 ∙ 608.11 × 109 (480002) = −14.1

For the deviated strands, this is calculated as:

∆ , =,

2

8+ ( − )

4 2

3 2

=8 ∙ −23.3x103 ∙ (480002)8 ∙ 26937 ∙ 608.11 × 109 540 + (−1180 − 540)

4(168002)3(480002) = −0.9

∆ , =8 ∙ −23.3x103 ∙ (480002)8 ∙ 26937 ∙ 608.11 × 109 740 + (−980 − 740)

4(144002)3(480002) = −1.7

∆ , =6 ∙ −23.3x103 ∙ (480002)8 ∙ 26937 ∙ 608.11 × 109 915 + (−805 − 915)

4(120002)3(480002) = −2.5

Page 4-70


The design of NU Girder bridges requires that the girder design be proportioned to satisfy the requirements forstrength and stability. In particular, the factored resistance must be greater than the effects of the factored loads.

In calculating the factored flexural resistance of an NU Girder, basic flexural theory applies based on theconditions of equilibrium and strain compatibility. Flexural resistance is calculated in accordance with CHBDC,which identifies the following assumptions for use when determining flexural capacity:

· Strain in the concrete varies linearly over the depth of the section.· Strain compatibility between concrete, reinforcing, and prestressing (i.e. strain changes in the bonded

reinforcement) is assumed to be equal to the strain changes in the surrounding concrete.· Maximum strain in concrete in compression is assumed to be 0.0035.· Stress in reinforcement is taken as the value of stress determined from strain compatibility based on a

stress–strain curve representative of the steel reinforcement used, multiplied by the material resistancefactor.

· Tensile strength of concrete is neglected.· Relationship between concrete strain and stress is based on an equivalent rectangular concrete stress

distribution.

Concrete compressive stress developed is based on the development of a rectangular concrete stress block, witha uniform compressive stress sc distributed over a compression zone bounded by the edges of the cross-section,and a straight-line parallel to the neutral axis with a depth a. The stress block properties are defined as:

sc = a1fcf’c

a= b1c

Where:

a1 = 0.85-0.0015f’c ≥ 0.67

b1 =0.97-0.0025f’c ≥ 0.67

the value for f’c shall correspond to the specified compressive strength of the concrete component beingconsidered, which may be either the deck or the girder, or both (depending on the depth of the stress block).

(4-88)

(4-89)

(4-90)

(4-91)

Sample Calculation 9: Camber Calculation at Deck Pour (Continued)

The effects for other groups are calculated similarly, with the total deflection due to prestress loss is:

∆ = −19.2

By applying Equation (4-87) the effects due to initial elastic deformation, creep, shrinkage and relaxation canbe combined to calculate the mid-span camber at 180 days.

= 1 + ( , ) + (1 + ( , ))

= 80.0(1 + 1.477)− 19.2(1 + 0.7 ∙ 1.477) = 159.1

Page 4-71


The stress in prestressing, , may be determined using a method of strain compatibility. However, when the

ratio of neutral axis to depth of prestressing is less than or equal to 0.5, the stress can be determined

from:

= 1−

Where:

= 0.3 for low-relaxation strands

Figure 4-31 identifies the definitions used in calculating flexural resistance.

Figure 4-31Flexural Capacity – Strain Compatibility

The shear capacity of an NU Girder bridge is determined using the modified compression field theory outlinedin Clause 8.9 of the CHBDC. In this theory, shear resistance is comprised of contributions from concrete, Vc, shearreinforcement, Vs, and the vertical component of any prestressing or post-tensioning, Vp.

dp

b ec

ep

a = b1c

a1fcf’c

Tp =fpfpsAps

Section depth and haunch thickness

Girder ULS design capacity shall be based on a nominal girder section, assuming a deck haunch height of13 mm between the bottom of the deck slab and the top of the precast girder. The theoretical design haunchshould be used for calculation of loads and quantities.

c

N.A.

C=aba1fcf'’c,deck

SectionForces

(4-92)

(for a < tdeck)

Page 4-72


Factored shear resistance, Vr

= + +

Where:

= factored shear resistance provided by tensile stresses in concrete (N)

= factored shear resistance provided by shear reinforcement (N)

= component in the direction of the applied shear of the effective prestressing force, factored by(taken as positive if resisting the applied shear) (N)

When determining the factored shear resistance, the concrete and steel contributions are limited to:

+ ≤ 0.25 ′

Where:

= effective web width within depth (mm)

= effective shear depth (mm)

Figure 4-32 shows a typical shear force diagram for an NU Girder. In this figure, the factored shear resistance isshown with the contributions from Vc, Vs, and Vp, confirming that the resistance is greater than the factored sheardemand.

Figure 4-32Shear Capacity vs Shear Demand

In calculating the contributions from concrete and shear reinforcement, the factor b accounting for the shearresistance of cracked concrete, and the angle of inclination q both need to be determined. The sections belowoutline the method for calculating these factors and determining the shear capacity of an NU Girder.

Length along girder

(4-93)

(4-94)

Page 4-73


The factored shear resistance provided by concrete is determined from:

= 2.5b

Where:

= factor accounting for the shear resistance of concrete

= resistance factor of concrete

= cracking strength of concrete (MPa), which shall be ≤ 3.2 MPa



Effective Shear Depth

The effective shear depth, dv, is taken as the greater of 0.72h or 0.9d. In calculating the effective shear depth, dis taken as the distance from the extreme compression fibre to the centroid of the longitudinal tensionreinforcement in the half-depth of the section containing the flexural tension zone.

For regions in positive bending, the tension reinforcement will correspond to the strands in the bottom flangeand any deviated strands or post-tensioning strands that fall in the half-depth at the section of consideration.

For regions in negative bending, such as over piers in continuous NU Girder bridges, the longitudinal deckreinforcing, top flange prestressing and reinforcing, and any deviated strands or post-tensioning ducts locatedwithin the half section need to be included.

Effective Web Width

The effective web width bv is taken as the minimum web width within the effective shear depth. For NU Girderswithout post-tensioning, bv is taken as the full web width of 185 mm. When considering NU Girder bridges withpost-tensioning, the effect of the ducts in the web must be considered. NU Girders have the post-tensioningfully grouted; therefore, in accordance with Clause 8.9.1.6 of the CHBDC, one-quarter of the diameter of thegrouted duct is subtracted from the web width when determining bv.

The factored shear resistance, Vs, provided by reinforcing steel is determined from:

=

Where:

= resistance factor of reinforcing bars

= specified yield strength of reinforcing bars (MPa)

= area of transverse shear reinforcement perpendicular to the axis of a member within distance s,

(mm2)

= angle of inclination of the principal diagonalcompressive stresses to the longitudinal axis of a member(degrees) (see Section 4.8.3.2.4 below)

= spacing of reinforcing bars (mm)

The application of Equation (4-96) isonly for components with the shearreinforcement located perpendicularto the longitudinal axis, as is the casefor NU Girders.

(4-95)

(4-96)

Page 4-74


It is also necessary to ensure the minimum amount of transverse reinforcement is included in the design. Theminimum area of transverse shear reinforcement is determined from:

≥ 0.15

In designing the shear reinforcement for an NU Girder, the primary method for achieving adequate shearresistance is in the sizing and spacing of the shear stirrups. An efficient design will adjust the spacing of thestirrups to meet the requirements, using a minimum number of spacing changes and a single stirrup bar size.

The contribution to the factored shear resistance provided by pretensioning or post-tensioning is calculated asthe component of pretensioning force in the direction of the applied shear factored by the fp.

= ,

Where:

, = the vertical component of the effective prestressing force

When reviewing sections where the strands have not fully developed, it is necessary to use a reduced value ofprestressing. Section 4.6.4 discusses the transfer length and development length with guidance for determiningthe prestress available in those locations.

In applying the modified compression field theory, the factor b and inclination q need to be calculated todetermine the concrete and transverse steel contributions to shear resistance. It is necessary to follow the generalmethod outlined in CHBDC as prestressed girders are not suitable for the simplified method.

The factor b is calculated as:

b =0.4

1 + 1500

The angle of inclination q is calculated as:

= (29 + 7000 )

Where:

= longitudinal strain

The longitudinal strain, , represents the longitudinal strain atmid-height at the ultimate limit state, and considers bending,shear, prestressing, and axial loads. The longitudinal strain iscalculated as:

=+ − + 0.5 −

2 +

In the complete modified compressionfield theory presented in Clause 8.9 of theCHBDC, a term Sze is included. However,a value of Sze = 300 mm is applicablewhen minimum transverse reinforcementis met, which is necessary for NU Girders.The provisions presented here aresimplifications based on using minimumtransverse reinforcement.

(4-97)

(4-98)

(4-99)

(4-100)

(4-101)

Page 4-75


Where:

= factored shear at a section (N)

= factored coincident moment at a section (Nmm)

= component in the direction of the applied shear of all of the effective prestressing forces crossingthe critical section factored by ∅ (taken as positive if resisting the applied shear) (N)

= factored axial load normal to the cross section occurring simultaneously with , including theeffects of tension due to creep and shrinkage (N)

= area of tendons on the flexural tension side of a member (mm2)

= stress in prestressed reinforcement when stress in the surrounding concrete is zero (MPa)

= modulus of elasticity of reinforcing bars (MPa)

= area of reinforcing bars on the flexural tension half depth of a member (mm2)

= modulus of elasticity of tendons (MPa)

The evaluation of Equation (4-101) is based on the following:

≥ − , ≥ 0 > 0

> 0 , < 0

= 0.7 for bonded tendons outside the transfer length

If < 0 then it may be taken as = 0or =.

, However, shall not be take less

than −0.20 × 10

= area of concrete on the flexural tension side of a member (mm2)

Figure 4-33Modified Compression Field Theory Definitions (Adapted from Clause C8.9.3.8 of the CHBDC Commentary)

0.5h

0.5h

Flexuraltension

side

bv

dvd

A’s A’ps A’c

Flexuralcompressionflange

Flexuraltensionflange

As Aps

Act

Nf

Mf

Vfq

−

( − )

+ 0.5 + 0.5 −

dv

− + 0.5 + 0.5 −

Page 4-76


Sample Calculation 10: Calculation of Shear Capacity

Calculate the factored shear resistance for an NU2400 Girder, based on the following criteria:

Material properties:

= 0.75 f’c = 70 MPa fcr = 3.35 MPa > 3.2 MPa therefore use 3.2 MPa

= 0.90 fy = 400 MPa Es = 200,000 MPa

= 0.95 fpu = 1,860 MPa Ep = 200,000 MPa

Reinforced with 15M stirrups @ 300 O/C at section considered:

Av = 400 mm2 s = 300 mm

Girder is prestressed with 64 strands in bottom flange, 22 of which are deviated. At location considered, thefollowing properties apply:

Vf = 2180 kN Mf = 4,000 kN∙m Vp = 426 kN Nf = 0 kN

Aps = 42 x 140 mm2 = 5,880 mm2 fpo = 0.7fpu = 0.7 x 1,860 MPa = 1,302 MPa

As = 0 mm2 bv = 185 mm dv = 2,070 mm

The longitudinal strain, εx, is found from Equation (4-101), as:

=+ − + 0.5 −

2 +=

4,0002,070 + 2,180 − 426 + 0.5 ∙ 0 − 5,880 ∙ 1,302

2(200,000 ∙ 0 + 200,000 ∙ 5,880 )

= −0.00169 < 0 and as is negative, may be taken as 0.

Then, the factor b is calculated through Equation (4-99):

b =0.4

1 + 1500 =0.4

1 + 1500 ∙ 0 = 0.4

The angle of inclination θ is determined from Equation (4-100), as the following:

= (29 + 7000 ) = 29°

The factored shear resistance can be determined from Equation (4-93) as:

= + +

Where the factored shear resistance provided by concrete is calculated from Equation (4-95):

= 2.5b = 0.25 ∙ 0.4 ∙ 0.75 ∙ 3.2 ∙ 185 ∙ 2,070 = 91.9

And the factored shear resistance provided by reinforcing steel is calculated from Equation (4-96) as:

=cot

=0.90 ∙ 400 ∙ 400 ∙ 2,070 ∙ cot(29°)

300 = 1,793

Finally, the factored shear resistance is found to be:

= + + = 92 + 1,793 + 426 = 2311

Page 4-77


End zones in NU Girders are regions with complex stress states and require attention in addition to the sectionaldesign models used for the remainder of the NU Girder design. The complex stress state is generated by theinteraction of force effects from bearings, transfer of prestressing forces, loads, and if applicable post-tensioningforces.

NU Girder end regions vary due to end block requirements (ends may have the same cross-section as the restof the girder, or have thickened end blocks), bridge articulation (supported on bearings, or integral with aconcrete diaphragm), and they may be pretensioned, or pretensioned and post-tensioned.

The end zone length is considered to be approximately equal to the girder depth and qualifies as a region neara discontinuity (Clause 8.9.2.2 of the CHBDC). The complex stress state in the region leads to tensile stresses overthe height of the girder, which often leads to cracking at the girder ends. Thus, the end zones require carefuldetailing to control cracking and avoid unwanted decreases in durability and/or strength

Figure 4-34 shows an example of the elastic stress flow at an end region for an NU Girder with multiple deviatedstrand groups at the moment of transfer. In this figure, stress contours are presented, with the dark bluerepresenting tensile stresses.

Figure 4-34Example Stress Flow at NU Girder End

Several studies have investigated cracking of end zone regions of precast girders, including NU Girders. Furtherinformation can be found in Marshall and Mattock (1962), Hasenkamp et al. (2008), Tuan et al. (2004), Cook andReponen (2008), Crispino et al. (2009), and NCHRP 654.

Current practice (see Appendix B for Typical Details Drawings) has been found to adequately control crackingin most situations. However, it is critical that the Consultant understand the flow of forces in the end zone of NUGirders, and how to appropriately proportion end zone reinforcement to achieve an acceptable design.

Bottom FlangeStraight Strands

Deviated Strand Group 1

Deviated Strand Group 2

Deviated Strand Group 3Top Flange Straight Strands Stress Contours

(MPa)

- 2.5

0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

22.5

25.0

27.5

30.0

32.5

35.0

Page 4-78


It is important to recognize that some end zone cracking is a result of fabrication methods. Other end zonecracking is a result of the design and therefore the girder end zones need to be adequately designed to accountfor the different support and loading conditions at the abutments and piers at all stages of construction, andthe abutment and pier configurations.

NU Girders without end blocks: Used for pretensioned girders with cast-in-place concrete diaphragms withanchorage of prestressing strands in the flanges and web. These NU Girders can have either straight bottomstrands only or a combination of bottom and deviated or debonded strands. Top strands are required to avoidpremature cracking in the top flange due to potential negative bending moments occurring during handling,transportation, and construction. Spalling forces occur between groups of prestressing strands (Figure 4-25).These cracks most often form at the transition of the bottom flange to the web. Cracks in the web itself are alsofairly common. To address the spalling forces, closely spaced transverse reinforcement (stirrups) are required tocontrol cracking.

NU Girders with end blocks: Used with conventional abutments and may include post-tensioning tendons inaddition to prestressing strands. The widened end zone allows for easier placement of transverse reinforcing.The additional force effects of the post-tensioning need to be considered in the design.

Design of the end zone involves confirming the design hasadequate capacity to satisfy the ultimate limit states, as wellas providing adequate crack control reinforcing.

The design process will include the following steps:

· Shoe plate sizing based on bearing requirements· Shear design in the end-zone, including

anchorage of longitudinal reinforcing and acheck on web crushing

· Determination of the end zone transverse reinforcing requirements, including BSDC and CHBDCrequirements, and anchorage of transverse streel

· Determination of confinement reinforcement in the bottom flange· Shoe plate design.

The first item considered in the end zone design is the shoe plate, which is used to transmit load between thegirders and the substructure. At bearing locations, girder ends shall have cast-in galvanized shoe plates anchoredinto the girders with shear studs. The shoe plate design shall account for the different support conditions at theabutments and piers and shall transfer all vertical and horizontal forces from the girders into the substructure.Sizing of the shoe plate will depend on the bridge articulation and bearing stresses in the concrete.

· NU Girder bridges with fixed or expansion bearings: In these bridges, the shoe plate provides theprimary load-path for loads transmitted to the substructure from the superstructure, and the shoe platewill need to be designed to adequately resist the design loads. The Consultant will also need toproportion the shoe plate size to accommodate the bearing.

· NU Girder bridges with integral abutments: In these bridges, the shoe plate provides the primaryload-path for loads transmitted to the substructure during construction. Following construction of theconcrete diaphragm, the load-path changes, and loads are transferred through the end diaphragm.

Pretensioning Anchorage Zones

The requirements for pretensioninganchorage zones is outlined in Clause 8.16.3of the CHBDC and are similar to AASHTO endzone requirements. Tuan and Tadros (2004)have shown that the CHBDC requirementsappear to be adequate on tests on 2000 mmdeep NU Girders.

Page 4-79


The minimum area for the shoe plate must be checked for adequate bearing resistance. The bearing resistanceof the concrete, Br, is calculated in accordance with Clause 8.8.7 of the CHBDC to be:

= 0.85

Where:


= specified concrete compressive strength (MPa)

= area of the shoe plate bearing area (mm2)

The NU Girder Bridge Typical Details Drawings (Appendix B) provide guidance on the sizing appropriate for NUGirders. Consultants shall use these as the initial basis for shoe plate geometry but must confirm that these meetthe requirements for their design.

The end zone region is defined as a region near a discontinuity in accordance with Clause 8.9.2.2 of the CHBDC,and a strut-and-tie model is required to complete the end zone design. The strut-and-tie model is to becompleted in accordance with Clause 8.10 of the CHBDC. Shear design in the end zone is also checked inaccordance with Clause 8.9 of the CHBDC to confirm adequate shear reinforcing and longitudinal reinforcementanchorage.

When completing these checks, it is necessary to consider the end zone design during construction for adequacyof the reinforcement of the non-composite girder design to support construction loads, including the weight ofthe deck in addition to the design checks of the structure in service.

Shear Reinforcement

Initially, the required shear reinforcement in the end region is determined by following the shear reinforcementdesign outlined in Section 4.8.3.2, and is completed at dv from the end of the beam. Shear capacity needs to bechecked at all critical stages which includes construction stages such as the concrete deck pour, in addition tothe load combinations corresponding to the in-service structure.

Longitudinal Reinforcement

Once the amount of shear reinforcement is determined, the force required to be resisted in the longitudinalreinforcement is determined from Clause 8.9.3.14 of the CHBDC:

= 0.5 + − 0.5 − cot

Where:

= factored axial load normal to the cross section occurring simultaneously with (N)

= factored shear at a section (N)

= factored shear resistance provided by shear reinforcement (N) within a length of cot from theface of support, however ≤


= component in the direction of the applied shear of all of the effective prestressing forces crossingthe critical section factored by (taken as positive if resisting the applied shear) (N)

= angle of inclination of the principal diagonal compressive stresses to the longitudinal axis of amember (degrees)

(4-102)

(4-103)

Page 4-80


The tension force in the reinforcement shall be developed at the point where a line inclined at angle extendingfrom the inside edge of the bearing area intersects the centroid of the reinforcement.

The basis for this equation can be derived by looking at the free-body diagram of the end region, shown in thefigure below.

Figure 4-35Free-body Diagram of End Region of Beam

Clause C8.9.3.11 of CHBDC Commentary

In NU Girders, the available amount of longitudinal reinforcing is usually only provided by the prestressingstrands in the bottom flange. Strands which are debonded do not contribute to the required longitudinalcapacity, and only bonded strands are considered. For this, the level of development of the strands at the frontof the bearing node as shown in Figure 4-36 needs to be determined.

Figure 4-36Available Development Length at End

Clause C5.6.3.4.2 of AASHTO LRFD Bridge Design Specifications (2017)

The amount of force that the longitudinal strands are able to develop depends on the details of the end zonedesign. Bottom strands may project and be bent up (hooked) and cast into the concrete end diaphragm toprovide passive development.

When strands are cut flush to the end of the girder, the available development of force is limited to the reduceddevelopment described in Section 4.6.4.3

Page 4-81


Strut and Tie Model

Web Crushing

The capacity of the web against crushing is checked according to Clause 8.9.3.3 of the CHBDC and is representedby the limit placed on Vc+Vs.

+ ≤ 0.25

Where:

= factored shear resistance provided by tensile stresses in concrete (N)

= factored shear resistance provided by shear reinforcement (N)





Anchorage Zone Reinforcement

The anchorage zone is designed to resist tensile, bursting, and spalling forcesresulting from the prestressing forces applied at the girder end. Transversereinforcement is provided in the form of stirrups. The following requirementsmust be met for the anchorage zone reinforcement.

End Zone Transverse Reinforcement

Clause 8.16.3 of the CHBDC requires the minimum amount of transversereinforcement be placed over a distance 0.25 times the overall girder depth.The minimum area provided by the transverse reinforcement is determinedas:

, = 0.08

Where:

= total ultimate prestressing force of tendons (N)

= resistance factor of reinforcing steel

= yield strength of the reinforcing bars, MPa

In addition, the BSDC requires the following for stirrups for crack control, derived from AASHTO LRFD BridgeDesign Specifications, to be met. This is achieved by limiting the stress in the stirrups in the end zone. The forcein the end zone stirrups, Pr, shall be limited to the following:

The term transversereinforcement is used todescribe the shear and endzone reinforcement, anddescribes the stirrups,which are detailed on thedrawings. The two terms areinterchangeable.

(4-104)

(4-105)

The use of a strut-and-tie model is best presented in a worked example. Design Example 2 presents acomprehensive design of an NU Girder end zone, covering the necessary design checks outlined in thisSection.

Page 4-82


=

Where:

= stress in stirrup steel, not exceeding 140 MPa

= total area of vertical crack control end zone reinforcement (mm2)

In determining the force in the end zone stirrups, Pr shall not be less than 4 percent of the pretensioning forceat transfer.

Stirrup Anchorage

The crack control stirrups shall be anchored beyond the anticipatedextreme top and bottom cracks with sufficient embedment to developat least 210 MPa. Since the crack control reinforcement is required tominimize the crack width, and not for strength, there is no need todevelop the full yield strength beyond the locations of the top andbottom cracks. For NU Girders, the anticipated top and bottom cracksmay be assumed for design to be at the junction between the weband the flanges. Therefore, the crack control stirrup anchorage intothe flanges should be designed for a maximum stress of 210 MPa.

Detailing Stirrups in the End Zone

Experience has shown that cracking is minimized when the first crack control stirrup is placed as close to theend of the girder as possible. Therefore, the end cover for the crack control stirrup shall be 30 mm for exposedgirder ends and 25 mm for girders encased into field cast diaphragms (see BSDC).

Careful reinforcing placement is required in the end zone to avoid congestion and conflicts. Conflicts may becaused by shear studs from sole plates, holes in the web, and location of prestressing strands.

The end zone stirrups shall be detailed to the following requirements, where the more stringent requirementstake precedence:

· The end stirrup shall be placed as close to the girder end as possible.

· The area of stirrups determined in Clause 8.16.3.2 of the CHBDC (Equation (4-105)) shall be distributedof 0.25 times the overall girder depth.

· Half of the end zone stirrups (i.e., 0.5 As) determined in Equation (4-106) shall be concentrated withinthe end h/8 of the girder and the remaining half (i.e., 0.5 As) shall be distributed over a distance fromh/8 to h/2 (where h is the overall depth of the precast girder).

· Reinforcement shall be provided for confinement of the prestressing in the bottom flange over thehorizontal distance of the girder depth, in accordance with Clause 8.16.3.2 of the CHBDC. Thereinforcing shall be shaped to enclose the strands, not to be less than 10M deformed bars, and have aspacing not exceeding 150 mm.

Stirrup Anchorage Requirements

These requirements are based onthe recommendations reported inNCHRP Report 654 Section 3.8:Proposed Revisions to the AASHTOLRFD Bridge Design Specifications(2017).

Pretensioning Anchorage Zone: Bottom Flange Confinement Reinforcement Detailing

Closed ties in the bottom flange are normally fabricated in two pieces with full tension lap splices. The topof the ties can be left open in the mid-span region of the girder wherever there is conflict with post-tensioning cables. Re-entrant corners shall not be used in the stirrup configurations.

(4-106)

Page 4-83


A strut-and-tie model of the bottom flange is proposed in NCHRP 849 Section 2.5.2 to determine theconfinement reinforcing required for horizontal transverse tensile forces in the flange at the bearing. Thehorizontal transverse tensile forces are carried by the top and bottom confinement bars in the bottom flange,and by the shoe plate. Figure 4-37 shows a 3D view of the strut-and-tie model.

Figure 4-37End Zone 3D Strut-and-Tie Model

The approach taken is to model the end of the girder with a 2D strut-and-tie model. For this approach to bevalid, the girder and model must be symmetric about the vertical centreline, and the horizontal strands must besufficient to anchor the inclined strut in the longitudinal direction.

The struts and ties are anchored at nodes corresponding to the centroid of the bonded pretensioning strands.Further, for a 2D model to be applicable, the girder ends must not be skewed. For skewed ends, a 3D strut-and-tie model is completed.

Figure 4-38 shows the formulation of the strut-and-tie model outlined in NCHRP 849, adapted for an NU Girder.

Page 4-84


Geometry Forces

Figure 4-38End Zone Bottom Flange Strut-and-Tie Model

In this model:

= total factored reaction (shear) at the support

= total number of bonded strands at the section

= horizontal width of the shoe plate

ℎ = vertical height of the bottom flange

= total number of bonded strands in one side of the outer portion of the bottom flange (where theouter portion is defined as that extending beyond the projection of the web width

= horizontal distance to the girder centreline of centroid of nf strands in outer portion of the flange

= vertical distance to the girder soffit of centroid of nf strands in the outer portion of the flange

= resistance factor for reinforcing bars

The term cb is calculated to ensure uniform bearing pressure across the width of the bearing and is determinedfrom:

= 2 1− (4-107)

xp

cb

yp

Centroid of strandsin outer portion offlange (fully bondedstrands)

1 −2bb

hb

Page 4-85


From here the tension in the horizontal tie can be calculated from Equation (4-108), and the required steel areato resist the tension tie can be determined:

= +

Shoe Plate Shear Connectors

Shoe plates are connected to the NU Girder by means of shear studs, which transfer the load between the shoeplate and the girder. Shear connector resistance, , is calculated in accordance with Clause 10.11.8.3 of theCHBDC. The capacity of the shear studs is calculated by:

= 0.5 ≤

Where:

= resistance factor for shear connectors

= cross-sectional area of one stud shear connector (mm2)


= modulus of elasticity of concrete (MPa)

= minimum tensile strength of stud steel (MPa)

Shear studs are typically 19 mm diameter studs conforming to CSA W59 Type B Studs, with a minimum tensilestrength of 450 MPa. Shear studs shall have a minimum height of 4 times the diameter of the stud.

When establishing the layout of the shear studs on the shoe plate, the spacing shall not be less than 4 times thediameter of the studs, nor greater than 600 mm. The NU Girder Bridge Typical Details Drawings (see Appendix B)provide guidance on layout.

Shoe Plate to Sole Plate Connection

When connected to a bearing sole plate, the shoe plate must be checked for adequate length for a weldedconnection. The weld capacity is completed in accordance with Clause 10.18.3 of the CHBDC.

A fillet weld connection is typically used, and the capacity of the weld is calculated as the lesser of the capacityof the base material described by Equation (4-110) or the weld material described by Equation (4-111):

= 0.67

Where:

= resistance factor for welds

= area of fusion face (mm2)

= specified minimum tensile strength of base plate / sole plate (MPa)

= 0.67

(4-110)

(4-111)

(4-109)

(4-108)

Page 4-86


Where:

= resistance factor for welds

= size of effective throat area of weld(mm2)

= ultimate strength of weld material, as rated byelectrode classification number (MPa)

A typical shoe plate / sole plate connection would be made of grade300W plate steel for the shoe plates and sole plates, with an ultimate tensile strength, Fu, of 450 MPa. Referringto the Electrode classification for 300W steel in Clause 10.18.3 of the CHBDC provides an ultimate strength ofthe weld material, Xu, of 490 MPa.

In order to compensate for zinc contamination when welding a galvanized plate, the specified weld size shall be2 mm greater than the weld size used in design.

Post-tensioning tendons add to the complex stress state in the end zone. Post-tensioning tendons require designof two regions referred to as the local zone and the general zone, in accordance with Clause 8.16.2.2 and Clause8.16.2.3 of the CHBDC. Figure 4-39 shows the local zone and general zone as defined in CHBDC.

(a) Principal Tensile Stresses (b) Principal compressive Stressesand the General Zone and the Local Zone

Figure 4-39General Zone and Local Zone (Clause C8.16.2.1 of the CHBDC)

Anchorage Zone

The anchorage zone is considered to include the general zone and the local zone. CHBDC identifies theanchorage zone as comprising the full depth of the member in the transverse direction. Anchorage zone size forNU Girders will depend on where the post-tensioning hardware is incorporated:

· For NU Girders with post-tensioning hardware incorporated in the end block, the anchorage zone willbe the full height of the end block.

· For NU Girders with post-tensioning hardware incorporated in a cast-in-place diaphragm, theanchorage zone will be the full height of the concrete diaphragm.

The longitudinal extent of the anchorage zone is between 1.0 and 1.5 times the transverse dimension of theanchorage zone.

Equation (4-110) is a conservativesimplification from CHBDC applicablefor longitudinal fillet weld connectionsbetween shoe plates and sole plates.When more detailed calculations arewarranted, refer to Clause 10.18.3.2.2of the CHBDC

Page 4-87


General Zone Design

The general zone includes the overall anchorage zone and extends the length over which the concentrated post-tensioning anchorage force spreads transversely to a more linear stress distribution. Within the general zone,the assumption of plane sections remaining plane is not valid, and beam theory cannot be used for analysis.

CHBDC identifies three design methods for use in designing the anchorage zone reinforcement, including strut-and-tie method, elastic stress analysis, and the approximate method. It is important to note that the approximatemethod is not appropriate for use for post-tensioned NU Girder bridges.

When used, strut-and-tie models shall be completed in accordance with Clause 8.10 of the CHBDC. Strut-and-tie design is not covered in this manual. Further examples for strut-and-tie designs of end zone regions aregiven in Collins and Mitchell (1997) or NCHRP 356.

Alternatively, reinforcing could be designed based on elastic stress analysis, which gives a good estimate of thestress flow. However, elastic analysis cannot be applied to cracked concrete, and the Consultant needs to takethis into account when designing NU Girder end zones with this method. The effects of the cross-section changesneed to be considered in the analyses, in particular at the bottom flange-to-web transition.

When completing the general zone design, the following shall be met:

Compressive Stresses

The compressive strength in the concrete behind the anchorage devices shall not exceed 0.75fcf’c. Thiscompressive strength limit is applicable to the general zone (i.e. outside of the local zone). The general zone inNU Girders shall be designed to avoid excessive cracking or inelastic rotations.

Bursting Reinforcement

For NU Girders, resistance to bursting forces is provided by closed ties. The design shall meet the followingrequirements, as outlined in Clause 8.16.2.2.3.2 of the CHBDC:

· Reinforcement shall extend over the full width of the component and be anchored as close to the outerfaces of the component as cover requirements permit;

· Reinforcement shall be distributed behind the loaded surface along both sides of the tendon for adistance that is the lesser of 2.5 times the distance from the loaded surface to the centroid of thebursting force, and 1.5 times the corresponding lateral dimension of the section;

· The centroid of the bursting reinforcement shall be at the location of the centroid of the bursting force;

· Spacing of reinforcement shall not exceed the lesser of 24 bar diameters and 300 mm

Spalling and Longitudinal Edge Tension

The spalling force shall not be taken as less than 2 percent of the post-stressing force. Resistance to spallingforces shall be provided by non-prestressed or prestressed reinforcement located close to the longitudinal andtransverse edges of the concrete and shall meet the following requirements:

· Spalling reinforcement shall extend over the full available width and depth of the component;

· Spalling reinforcement between multiple anchorage devices shall tie the anchorage devices together;

· Longitudinal edge tension reinforcement and spalling reinforcement for eccentric anchorage devicesshall be continuous. The reinforcement shall be extended along the tension face over the full length ofthe anchorage zone and along the loaded face from the longitudinal edge to the other side of theeccentric anchorage device or group of anchorage devices.

For multiple anchorages with centre-to-centre spacing of more than 0.4 times the depth of the section, thespalling force shall be determined by analysis.

Page 4-88


Local Zone Design

The local zone is the region surrounding the anchorage device. Local zone reinforcing for post-tensioningtendons is usually based on post-tensioning tendon manufacturer testing and recommendations.

The preceding sections cover the relevant limit states checks for NU Girder design. The design of an NU Girderbridge will include additional items not covered in this manual. The following items are specific to NU Girderbridges, and guidance is found within the NU Girder Bridge Typical Details Drawings. Consultants shall referencethe BSDC and CHBDC when completing the design of these components.

Intermediate Diaphragms

Intermediate diaphragms for NU Girder bridges shall have a maximum spacing of 13.0 m.

For NU1200, intermediate diaphragms may be C-shape (channel) or W-shape sections of at least 1/3 (andpreferably 1/2) the girder depth. For all other NU Girders, intermediate diaphragms shall be X-bracing or K-bracing and top and bottom horizontals shall be provided.

Intermediate diaphragms and NU Girders shall be designed for construction loads during deck concreteplacement in accordance with requirements of Clause 3.16 of the CBHDC and Section 4.10.6 of SSBC. Typically,diaphragms provided shall become part of the permanent structure and be left in place for future maintenance,widening, and rehabilitation. The only exception to this is at the ends of NU Girder bridges with integralabutments where the erection stage diaphragms may be removable.

Diaphragms of exterior NU Girders carrying deck overhangs shall be checked to ensure sufficient strength andstability to handle concentrated loads from deck finishing machines, work bridges, and loads from temporarywalkways outside the edge of the deck slab. Loads assumed for such design shall be based on realistic estimatesfor each bridge and shall be shown on the detailed design drawings, in accordance with the Engineering DraftingGuidelines for Highway and Bridge Projects.

For NU Girder bridges with moderate skews, oversized or slotted holes may be used to accommodate moderatedifferential vertical camber or horizontal sweep between adjacent girders during erection. Oversized or slottedholes shall meet requirements of Clause 10.18 of the CBHDC.

Pier Diaphragms

Pier diaphragms shall be continuous cast-in-place concrete diaphragms and shall be either pinned, fullymonolithic with the pier top, or permit free expansion. Positive moment connections of girder over the piersshall consist of lapped and bent-up prestressing strands or lapped and cast-in hooked reinforcing steel. Theminimum separation between girder ends shall be 300 mm. Where pier diaphragms are not monolithic with thepier top (cap or shaft), the ends of both girders shall be supported on separate reinforced elastomeric pads.Where pier diaphragms are connected monolithically to the pier top (cap or shaft) and are cast around girderends, the girders shall be erected on plain unreinforced elastomeric pads on a minimum 150 mm high plinth, toprovide sufficient clear space between the girder bottom and previously cast concrete, to ensure proper flow ofconcrete under the ends of the girders.

Abutment Diaphragms

Except for integral abutment designs, abutment diaphragms shall be steel brace type, to provide open accessfor inspection and maintenance of bearings and abutment deck joints.

For conventional abutments with deck joints, the superstructure end diaphragm shall be an open steeldiaphragm, to provide access for deck joint inspection and repair. The girder web at abutment ends shall bethickened and designed as part of the abutment steel diaphragm system for transferring laterals loads from thesuperstructure to the substructure.


GLOSSARY OF TERMS

AAEM – Age-Adjusted Elastic Modulus.

AASHTO – American Association of State Highway and Transportation Officials

Anchor — A bolt, stud, or reinforcing bar embedded in concrete.

Anchorage —

(a) In post-tensioning, a device used to anchor a tendon to a concrete member;

(b) In pretensioning, a device used to anchor a tendon until the concrete has reached a predeterminedstrength; and

(c) For reinforcing bars, a length of reinforcement, mechanical anchor, or hook, or a length ofreinforcement combined with a mechanical anchor or a hook.

Anchorage seating — Deformation of anchorage or seating of tendons in anchorage device when prestressingforce is transferred from jack to anchorage device.

At Jacking — At the time of tensioning tendons.

At Transfer — At the time immediately after transfer.

BSDC – Bridge Structures Design Criteria

Camber — The vertical deviation of a bridge member from straight, when viewed in elevation.

CHBDC — Canadian Highway Bridge Design Code

Creep — Time-dependent deformation of concrete under sustained load.

Debonding — Wrapping or sheathing prestressing strand to prevent bond between strand and surroundingconcrete.

Deck — An element of a floor system that carries and distributes wheel loads to the substructure.

Development length — Length of embedded reinforcement required to develop the specified strength of thereinforcement.

Duct — An opening in concrete for internal post-tensioning tendons.

End block — Enlarged end section of a member designed to reduce anchorage stresses.

Grout — A mixture of cementitious material and water, with or without aggregate, proportioned to produce aconsistency without segregation of the constituents, used in post-tensioning.

Intrinsic relaxation — Time-dependent reduction of stress in a prestressing tendon held at constant strain.

Jacking force — The force applied to stress tendons.

Limit states — Those conditions beyond which a structure or component ceases to meet the criteria for whichit was designed.

Post-tensioned girder — Girders which are prestressed by both pretensioning and post-tensioning.

Post-tensioning — A method of prestressing in which the tendons are stressed after the concrete has reacheda predetermined strength.

Prestressing — A load-case applied to an element or structure by means of prestressing strands. Applied eitheras pre-tensioning or post-tensioning.


Prestressed Concrete — Reinforced concrete in which internal stresses have been introduced to reducepotential tensile stresses in concrete resulting from loads.

Pretensioning — A method of prestressing in which the tendons are stressed before the concrete is placed.

Pretensioned girder — Girders which are prestressed by pretensioning only.

Relaxation — The time-dependent reduction of stress in tendons at constant strain.

Serviceability limit states (SLS) — Limit states corresponding to cracking, deformations, stresses and vibration.

Shrinkage — Time-dependent deformation of concrete caused by drying and chemical changes (hydrationprocess).

Spacing — The distance between centrelines of adjacent reinforcing bars, wires, tendons, or anchors.

Span — The distance between centreline of supports or bearing units of a bridge, measured parallel to thecenterline of the bridge.

SSBC – Standard Specifications for Bridge Construction

Strand — A linear component that constitutes all or part of a tendon.

Substructure — That part of a bridge, including abutments and piers, that supports the superstructure.

Superstructure — That part of a bridge that spans water, a roadway, a railway, or another obstruction and issupported by the substructure.

Transfer length — The length over which a prestressing force is transferred to concrete by bond in apretensioned component.

Transverse reinforcement — Reinforcement used to resist shear, torsion, or lateral forces in a structuralcomponent (typically deformed bars bent into U, L, or rectangular shapes and located not parallel to longitudinalreinforcement). Note: The term “stirrups” is usually applied to transverse reinforcement in flexural componentsand the term “ties” to transverse reinforcement in compression components.

Tendon — A high-strength steel element used to impart prestress to concrete.

Wobble — Friction caused by unintended deviation of prestressing sheath or duct from its specified profile oralignment.

WWR — Welded wire reinforcement

Ultimate limit states (ULS) — Limit states corresponding to stability and strength.


LIST OF SYMBOLS

A Transformed section area (mm2)′ Effective transformed section area

Area of the shoe plate bearing area (mm2)Area of concrete on the flexural tension side of a member (mm2)Area of fusion face of a welded section (mm2)Loss of prestress due to slip of post-tensioning tendon at anchorage (MPa)Area of one strand (mm2)Area of tendons on the flexural tension side of a member (mm2)Area of reinforcing bars on the flexural compression side of a member (mm2)Cross-sectional area of one stud shear connector (mm2)Area of transverse shear reinforcement perpendicular to the axis of a member within distances (mm2); (Total area of vertical crack control end zone reinforcement (mm2))Size of effective throat area of weld (mm2)Difference between mean concrete strength and specified strength at 28 days, taken as10MPa; Depth of an equivalent rectangular stress block (mm); Debonding length of strand, asdistance between the girder end and start of prestressing (mm)

Br Factored bearing capacity of concrete (N)In camber calculations, length of strand deviation measured from end of girder (mm)Horizontal width of the shoe plate (mm)Effective web width within effective shear depth (mm)Loss of prestress due to creep of concrete (MPa)Depth of neutral axis (mm)A term used in strut-and-tie design of the end zone to ensure uniform bearing pressure (mm)Nominal diameter of a prestressing strand (mm)Effective shear depth (mm)Modulus of elasticity of concrete (MPa)

, Concrete modulus of elasticity at 28 days (MPa)

, Age-adjusted effective modulus (MPa)

, Effective modulus (MPa)Modulus of elasticity of concrete at transfer (MPa)Modulus of elasticity of the tendons (MPa)

, Effective modulus of prestressing (MPa)Elastic modulus of the prestressing (MPa)Modulus of elasticity of steel reinforcement (MPa)Loss of prestress due to elastic shortening of concrete (MPa)Eccentricity, distance from the centroid of the prestressing to the centroid of the section (mm)In camber calculations, eccentricity of prestressing at mid-span (mm)In camber calculations, eccentricity of prestressing at girder end (mm)

′ Reduced restraint force (N)Total specified strength of tendons (N)


Specified minimum tensile strength of base plate / sole plate (MPa); Minimum tensile strengthof stud steel (MPa)Loss of prestress due to friction (MPa)

, Vertical component of the pretensioning force (N)Concrete stress (MPa). Calculated for top and bottom fibre, referenced as ft and fb respectivelySpecified compressive strength of concrete at 28 days (MPa)Concrete stress at the centre of gravity of tendons due to all dead loads except the dead loadpresent at transfer at the same section or sections for which fcir is calculated (MPa)Specified compressive strength of concrete at transfer (MPa)Concrete stress at the centre of gravity of tendons due to the prestressing effect at transferand the self-weight of the member (MPa)Cracking strength of concrete (MPa)Cracking strength of concrete at transfer (MPa)Stress in the steel at time zero (MPa)Stress in prestressed reinforcement when stress in the surrounding concrete is zero (MPa)

∆ Intrinsic relaxation (MPa)Stress in tendons at the ultimate limit state (MPa)

∆ Loss of prestress (MPa)Yield strength of the prestressing steel (MPa)Specified tensile strength of prestressing steel (MPa)

∆ Loss of prestress (MPa)∆ Losses up to and including transfer (MPa)∆ Losses occurring after transfer (MPa)

Effective stress in tendons after all losses (MPa)Stress in tendons just prior to transfer (MPa)Stress in tendons at jacking (MPa)Stress in tendons immediately after transfer (MPa)

, Stress in stirrup steel, 140 MPaSpecified yield strength of reinforcing bars (MPa)

ℎ Vertical height of the bottom flange (mm)Moment of inertia of the section (mm4)Transformed moment of inertia (mm4)

′ Effective moment of inertia (mm4)Transformed moment of inertia of the NU Girder (mm4)Creep functionWobble coefficient (1/m)Length of the girder between support locations (mm)Flexural bond length (mm)Development length (mm)Transfer length (mm)Applied moment (Nmm)Moment caused by self-weight (Nmm)Factored moment (Nmm)Moment due to prestressing (Nmm)

LIST OF SYMBOLS

Restraint moment (Nmm)Unfactored permanent axial load (N)Factored axial load (N)Axial load caused by self-weight (N)Axial load due to prestressing (N)Total number of bonded strands at the sectionModular ratiototal number of bonded strands in one side of the outer portion of the bottom flangeNumber of strands in layer jAxial load (N)Prestressing force immediately before transfer (N/mm)Prestressing force for each layer j (N)Shear connector resistanceLoss of prestress due to relaxation of prestressing steel before transfer (MPa)Loss of prestress due to relaxation of prestressing steel after transfer (MPa)Annual mean relative humidity (%)Volume per unit length of a concrete section divided by the corresponding surface area incontact with freely moving air (mm)Loss of prestress due to shrinkage of concrete (MPa)Spacing of reinforcing bars (mm)Age of concrete after casting (days); Time (days)

, Adjusted age at loading (days)Age of concrete from when the influence of shrinkage is calculated (days)Factored shear resistance provided by tensile stresses in concrete (N)Factored shear force at a section (N)Prestressing force in the direction of the applied shear factored by (N)Total factored shear resistance of a concrete element (N); Weld resistance (N)Factored shear resistance provided by shear reinforcement (N)Factored reaction (shear) at the support (N)Uniformly distributed load (N/mm)Ultimate strength of weld material (MPa)Distance away from the jacking end in post-tensioning (m)Horizontal distance to the girder centreline of centroid of nf strands (mm)Distance from extreme fibre to section centroid, for top and bottom fibre referenced as yt andyb respectively (mm)Vertical distance to the girder soffit of centroid of nf strands (mm)Distance to the centroid of the prestressing force for layer j (mm)Vector sum of angular changes in elevation and plan of a prestressing tendon profile from thejacking point to the point of consideration, x (radians)Ratio of average stress in a rectangular compression block to the specified concrete strengthThermal coefficient of linear expansionFactor used to account for the shear resistance of cracked concreteFactor used in flexural designCoefficient used in the calculation of creep coefficient


Coefficient used in the calculation ofCoefficient used in the calculation of creep coefficientCoefficient describing the effect of relative humidity on shrinkage in concreteCoefficient describing the development with time of shrinkage in concreteCoefficient used in the calculation of creep coefficientUnit weight of concrete (kN/m3)

∆ Instantaneous deformation, mid-span camber at transfer (mm)∆ ( ) Stress increment (or decrement) which begins at zero at time ti (MPa)∆ Total stress related mid-span deflection due to instantaneous deformation and creep (mm)∆ ( , ) Total stress related mid-span deflection due to instantaneous deformation and creep over the

time period t1, t0 (mm)∆ Mid-span deflection due to prestress losses, at t0 (mm)∆ Mid-span deflection (mm)∆ Deflection due to prestressing force at transfer (N/mm)∆ Mid-span deflection due to self-weight (mm)ε Strainε Strain at the reference axisε Strain in the prestressing strand of layer jε ( , ) Creep strain developing over the time period t, t0

ε Strain at the section centroidε Notional shrinkage coefficientε ( , ) Total load related strain occurring in the time period t, t0

ε Time varying strain in concrete due to shrinkageε Strian in prestressing in layer j immediately prior to transferε Longitudinal strain

Angle of inclination of the principal diagonal compressive stresses to the longitudinal axis ofa member (degrees)Coefficient of friction between the strand and the ductResistance factor of concreteResistance factor of reinforcing barsResistance factor for shear connectorsResistance factor of prestressing strandsResistance factor for weldsCreep Coefficient: Ratio of creep strain to the elastic strain that result when using the stiffnessof concrete at 28 daysCoefficient used in calculation of creep coefficientCreep Coefficient: Ratio of creep strain to the elastic strain at the age of loadingMass density of concrete (kg/m3)Stress in concrete (MPa)Aging coefficientRelaxation reduction coefficientCurvature (1/mm)


REFERENCES

Alberta Transportation (2016). Bridge Conceptual Design Guidelines, Version 2.0.

Alberta Transportation (2017). Bridge Structures Design Criteria (BSDC), Version 8.0

Alberta Transportation (2016). Engineering Drafting Guidelines for Highway and Bridge Projects, Version 2.1.

Alberta Transportation (2013). Standard Specifications for Bridge Construction (SSBC), Edition 16

American Association of State Highway and Transportation Officials (2017). AASHTO LRFD Bridge DesignSpecifications, 8th Edition, 2017.

Bazant, Z. (1972). “Prediction of Concrete Creep Effects Using Age-Adjusted Effective Modulus Method”, ACIJournal, Vol. 69, p. 212-217.

Benaim, R. (2008). The Design of Prestressed Concrete Bridges, Concepts and Principles. London Taylor & Francis.

Canadian Highway Bridge Design Code, CSA S6-14 (CHBDC)

Collins, M.P., Mitchell D. (1987). Prestressed Concrete Basics. Canadian Prestressed Concrete Institute.

Collins, M.P., Mitchell D. (1997). Prestressed Concrete Structures. Response Publications.

International Federation for Structural Concrete (2013). fib Model Code for Concrete Structures 2010. Ernst &Sohn.

Ghali, A., Favre, R., Elbadry, M., (2011). Concrete Structures: Stresses and Deformations: Analysis and Design forSustainability. CRC Press.

Cook, R.A., Reponen, M.J. (2008). “Prevention of splitting failure at ends of prestressed beams during fabrication”Final Report, Report No. BD545 RPWO #30, Florida Univ., Gainesville. Dept. of Civil Engineering.

Crispino E.D., Cousins T.E. and Roberts-Wollmann C. (2009). “Anchorage Zone Design for Pretensioned PrecastBulb-T Bridge Girders in Virginia”, Final Contract Report CTRC 09-CR15, Virginia Transportation Research Council.

CEB181 (1987). “Anchorage Zones of Prestressed Concrete Members”. State-of-the-Art Report, Task Group VI/1“Anchorage Zones”, Comite Euro-International du Beton, Lausanne, Switzerland.

Geren, Lynn K., and Tadros, Maher K., “The NU Precast/Prestressed Concrete Girder Bridge I-Girder Series,” PCIJOURNAL V. 39, No. 3, May-June 1994, pp. 26-39.

Hasenkamp, Christie J.; Badie, Sameh S.; Tuan, Christopher Y.; and Tadros, Maher K. (2008), "Sources of End ZoneCracking of Pretensioned Concrete Girders". Civil Engineering Faculty Proceedings & Presentations.

Marshall W.T. and Mattock A.H. (1962). “Control of Horizontal Cracking in the Ends of Pretensioned PrestressedConcrete Girders”, PCI Journal, 7(5), 56-74.

Menn, C. (1986). Prestressed Concrete Bridges. Springer Science & Business Media.

Precast/Prestressed Concrete Institute (2011). Bridge Design Manual 3rd Edition

Tadros, Maher K., Fawzy, Faten., Hanna, Kromel E. (2011), “Precast, prestressed girder camber variability”, PCIJournal Winter 2011, pp 135- 154.

Transportation Research Board of the National Academies, Washington. D.C. NCHRP Report 654: Evaluation andRepair Procedures for Precast/Prestressed Concrete Girders with Longitudinal Cracking in the Web .

Transportation Research Board of the National Academies, Washington. D.C. NCHRP Report 356: Anchorage ZoneReinforcement for Post-Tensioned Concrete Girders.

Tuan C.Y. Yehia S.A., Jongpitakasseel N., and Tadros M.K. (2004). “End Zone Reinforcement for PretensionedConcrete Girders”, PCI Journal, May-June, 68-82.


A-1

Appendix A: Section Properties

In Alberta, NU Girders are fabricated to the geometric sizes outlined below, ranging from NU1200 to NU2800.The girder shapes defined below conform to typical precast NU Girder forms. The geometric properties definedare for the gross section, and do not consider reinforcing or prestressing.

Figure A-1NU1200 Geometry and Properties

NU1200 Properties

Property Value

Area Ag 505.11 x 103 mm2

Moment of InertiaIg,x 99.28 x 109 mm4

Ig,y 28.56 x 109 mm4

Neutral Axis y 546.2 mm

Volume-to-Surface Area Ratio rv 85 mm


A-2

Figure A2NU1600 Geometry and Properties

NU1600 Properties

Property Value

Area Ag 579.11 x 103 mm2

Moment of Inertia Ig,x 203.42 x 109 mm4

Ig,y 28.77 x 109 mm4




A-3


NU2000 Properties

Property Value

Area Ag 653.11 x 103 mm2


Ig,y 28.98 x 109 mm4




A-4


NU2400 Properties

Property Value

Area Ag 727.11 x 103 mm2


Ig,y 29.19 x 109 mm4

Neutral Axis y 1,106 mm



A-5


NU2800 Properties

Property Value

Area Ag 801.11 x 103 mm2


Ig,y 29.40 x 109 mm4

Neutral Axis y 1,297.6 mm



B-1

Appendix B: Typical Details Drawings

http://www.transportation.alberta.ca/Content/docType30/Production/BridgePrecastGirdersDrawings.pdf.

http://www.transportation.alberta.ca/Content/docType30/Production/BridgePrecastGirdersDrawings.pdf


C-1

Appendix C: NU Girder Fabrication

NU Girder fabrication must be completed by a precast fabricator certified by the Canadian Precast/PrestressedConcrete Institute (CPCI) Certification Program in Group B (Bridge Products) in category B4 or BA4 for all NUGirder types, and in category B3 or B3A for NU Girders with straight strands only. CPCI contains a directory ofCertified Precast Plants, for reference.

Having a thorough understanding of fabrication, transportation, general handling, and erection will aidConsultants in avoiding the challenges that can make precast concrete girder bridges less cost-effective. ThisAppendix is meant to provide a general overview to the fabrication process for NU Girders in Alberta.

NU Girder fabrication is completed on a 24-hour cycle. This process begins with form preparation and iscompleted with girder stressing and removal of the NU girder from the forms.

Form Preparation, Strand and Reinforcement Placement

For the first girder in a series of similar girders, the forms are adjusted for the overall geometry. This includescompletion of necessary adjustments to the bulkheads (including fabrication on new bulkheads if necessary) toaccommodate end geometry (skew). This also includes adjustments to the base for hold-down devices whendeviated strands are used, and adjustments to forms for cross-bracing locations.

Bottom flange reinforcement with Web reinforcement includingDeviated strands Post-tensioning ducts


C-2

Bottom flange reinforcement with Shoe plate installedDebonded strands

End zone reinforcement – No End block End Zone Reinforcement – End Block with PT

Top Flange Following Concrete Pour Top Flange Finishing


C-3

Stressing and Removal from Forms

Following the completion of reinforcing placement and strand stressing, the girder concrete is poured. Formsare opened and girder strand release (or detensioning) commences following achieving the specified strengthat release, f’ci.

Strand release (or detensioning) of the NU Girders may be achieved using hydraulic methods where all strandsare detensioned simultaneously (gang detensioning) or by heat cutting. When completed by heat cutting, thesequence of detensioning is important to maintain symmetric loading and avoid cracking of the girder ends.

Girder Finishing Inspection of girder following removal of forms

Curing, Storage and Transport

During fabrication, two types of curing are completed: curing in the form, and curing after removal from theform.

In the form, additional heat is applied in a controlled manner to raise the ambient temperature. This onlycommences following the initial set of concrete, usually 2 to 4 hours after casting.

After removal from the forms, the girders are cleaned, patched, and finished within a 12-hour period. Within 24hours after removal from the forms, curing continues. The curing following removal from the forms continuesfor a minimum of 4 days, and is either steam curing or by continuous misting or heat.

Girders are stored in plant yard until transported to site. Storage requires that the girders are kept upright, andsupported near the ends on stable foundations.

For long girders, Fabricators will often support the girders at a distance up to 10 percent of the length from theends. This helps with general stability and reduces sweep.


C-4

NU Girder curing in the form NU Girder placed in the steam chamber

Girder Handling in Yard Girder Storage following Curing

NU Girder loaded for transport NU Girder loaded for transport


D-1

Appendix D: Section Properties Notation

In completing NU Girder design, various section properties are referenced. The notation used, and briefdescriptions are summarized in this Appendix.

Gross Section Properties

Gross section properties are specific to a geometric shape, and do not include the additional stiffness ofconstituent materials. Gross section properties are represented by the basic geometric symbols A, B or I, andmay include a subscript for the element. (E.g. INU for the gross moment of inertia for an NU Girder).

Gross section area

Gross section moment of inertia

The geometric properties for the NU Girder Section presented in Appendix B are gross section properties.

Transformed Section Properties

Transformed section properties include the stiffness of the constituent materials comprising a section.Transformed section properties are denoted with tilde character over the geometric property.

A Transformed section area

Transformed moment of inertia

In determining the transformed section properties, one material is transformed into an equivalent amount ofthe other material, with the equivalence based on the modular ratio, n.

=

The modular ratio is based on the reference modulus of elasticity, Eref. Typically, the modulus of elasticity of theNU Girder concrete is chosen as the reference modulus.

The use of the parallel axis theorem is used to calculate the section properties based on the constituent parts.Basic structural analysis references provide background on the calculation of the geometric properties of anarea, establishing the centroid, and calculating the composite section properties. In general, when using theparallel axis theorem to determine the transformed section properties, the contribution of moment of inertia ofprestressing steel and the reinforcing steel is negligible.

Effective Section Properties

Effective section properties refer to a transformed section, where the reference modulus of elasticity is theeffective modulus of elasticity of the concrete Ec,eff. The effective section properties are used in the EffectiveModulus Method when including the effects of creep and shrinkage. Effective section properties are denoted bya prime symbol over the geometric property.

Effective section area

Effective moment of inertia

Documents

NU GIRDER BRIDGE DESIGN AND DETAILING MANUAL · The NU Girder Bridge Design and Detailing Manual documents current best practices for NU Girder bridge designs in Alberta. It is intended