Bridge Superstructure Design

ISO BRG083110M3 Rev. 3

Berkeley, California, USA November 2011 Version 15

CSiBridge



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CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THE DEVELOPMENT AND TESTING OF THIS SOFTWARE. HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON THE ACCURACY OR THE RELIABILITY OF THIS PRODUCT.

THIS PRODUCT IS A PRACTICAL AND POWERFUL TOOL FOR STRUCTURAL DESIGN. HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC ASSUMPTIONS OF THE SOFTWARE MODELING, ANALYSIS, AND DESIGN ALGORITHMS AND COMPENSATE FOR THE ASPECTS THAT ARE NOT ADDRESSED.

THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE CHECKED BY A QUALIFIED AND EXPERIENCED ENGINEER. THE ENGINEER MUST INDEPENDENTLY VERIFY THE RESULTS AND TAKE PROFESSIONAL RESPONSIBILITY FOR THE INFORMATION THAT IS USED.

i

Contents

Bridge Superstructure Design

1 Introduction

1.1 Organization 1-1

1.2 Recommended Reading 1-2

2 Design Prerequisites

2-1 AASHTO LRFD 2-2

2.1.1 Load Pattern Types 2-2

2.1.2 Design Load Combinations 2-3 2.1.3 Default Load Combinations 2-4

2.2 CAN/CSA-S6-S06 2-6

2.2.1 Load Pattern Types 2-6

2.2.2 Design Load Combinations 2-7 2.2.3 Default Load Combinations 2-9 2.3 Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 3-11

2.3.1 Load Pattern Types 3-11

2.3.2 Design Load Combinations 3-13 2.3.3 Default Load Combinations 3-17

ii

3 Determine Live Load Distribution Factors (LLDF)

3.1 AASHTO-LRFD 2007 3-1

3.1.1 Algorithm for Determining Live Load Distribution

Factors (LLDF) 3-2

3.1.2 Determine Live Load Distribution Factors 3-2

3.1.3 Apply LLD Factors 3-4

3.1.3.1 User Specified 3-4

3.1.3.2 Calculated by CSiBridge in Accordance with AASHTO-LFRD 2007 3-4 3.1.3.3 Read Directly from Girder 3-5 3.1.3.4 Uniformly Distribution to Girders 3-5 3.1.4 Generate Virtual Combinations 3-5

3.1.4.1 Stress Check 3-5

3.1.4.2 Shear or Moment Check 3-6 3.1.5 Read Forces/Stresses Directly from Girders 3-6

3.1.5.1 Stress Check 3-6

3.1.5.2 Shear or Moment Check 3-7 3.1.6 LLDF Design Example Using Method 2 3-7

3.2 CAN/CSA-S6-06 3-16

3.2.1 Algorithm for Determining Live Load Distribution

Factors (LLDF) 3-16

3.2.2 Determine Live Load Distribution Factors 3-17

3.2.3 Moment Region 3-18

3.2.4 Apply LLD Factors 3-18

3.2.4.1 User Specified 3-19

3.2.4.2 Calculated by CSiBridge in Accordance

with CAN/CSA-S6-06 3-19

3.2.4.3 Forces Read Directly from Girders 3-19 3.2.4.4 Uniformly Distribution to Girders 3-19 3.2.5 Generate Virtual Combinations 3-20

3.2.5.1 Stress Check 3-20

3.2.5.2 Shear or Moment Check 3-21 3.2.6 Read Forces/Stresses Directly from Girders 3-21

3.2.6.1 Stress Check 3-21

3.2.6.2 Shear or Moment Check 3-21

4 Define a Bridge Design Request

iii

4.2 Check Type 4-3

4.3 Station Range 4-5

4.4 Design Parameters 4-5

4.5 Demand Sets 4-17

4.6 Live Load Distribution Factors 4-17

5 Design Concrete Box Girder Bridges

5.1 AASHTO 5-2

5.1.1 Stress Design AASHTO-STD-2002 5-2 5.1.1.1 Capacity Parameters 5-2

5.1.1.2 Demand Parameters 5-2

5.1.1.3 Algorithm 5-3

5.1.2 Stress Design AASHTO-LFRD-2007 5-3 5.1.2.1 Capacity Parameters 5-3

5.1.2.2 Algorithm 5-3

5.1.2.3 Stress Design Example 5-4 5.1.3 Flexure Design AASHTO-LRFD-2007 5-6 5.1.3.1 Capacity Parameters 5-6

5.1.3.2 Variables 5-6

5.1.3.3 Design Process 5-7

5.1.3.4 Algorithm 5-8

5.1.3.5 Flexure Design Example 5-10 5.1.4 Shear Design AASHTO-LRFD-2007 5-15 5.1.4.1 Capacity Parameters 5-15

5.1.4.2 Variables 5-15

5.1.4.3 Design Process 5-16

5.1.4.4 Algorithm 5-18

5.1.4.5 Shear Design Example 5-24 5.1.5 Principal Stress Design, AASHTO-LRFD-2007 5-31 5.1.5.1 Capacity Parameters 5-31 5.1.5.2 Demand Parameters 5-31 5.1.5.3 Algorithm 5-31 5.2 CAN/CSA-S6-06 5-33 5.2.1 Stress Design 5-33 5.2.2 Flexure Design 5-33 5.2.2.1 Variables 5-34 5.2.2.2 Design Process 5-35

iv 5.2.2.3 Algorithms 5-35 5.2.3 Shear Design 5-38 5.2.3.1 Variables 5-39 5.2.3.2 Design Process 5-40 5.2.3.3 Algorithms 5-42 5.3 Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 5-47 5.3.1 Stress Design 5-47 5.3.2 Flexure Design 5-48 5.3.2.1 Design Process 5-48 5.3.2.2 Algorithms 5-51 5.3.3 Shear Design 5-52 5.3.3.1 Variables 5-54 5.3.3.2 Design Process 5-55 5.3.3.3 Algorithms 5-56

6 Design Multi-Cell Concrete Box Bridges using AMA

6.1 AASHTO-LRFD 2007 6-1 6.1.1 Stress Design 6-2 6.1.2 Shear Design 6-3 6.1.2.1 Variables 6-4 6.1.2.2 Design Process 6-5 6.1.2.3 Algorithms 6-6 6.1.3 Flexure Design 6-10 6.1.3.1 Variables 6-10 6.1.3.2 Design Process 6-11 6.1.3.3 Algorithms 6-12 6.2 CAN/CSA-S6-06 6-14 6.2.1 Stress Design 6-15 6.2.2 Shear Design 6-16 6.2.2.1 Variables 6-16 6.2.2.2 Design Process 6-18 6.2.2.3 Algorithms 6-19 6.2.3 Flexure Design 6-22 6.2.3.1 Variables 6-22 6.2.3.2 Design Process 6-23 6.2.3.3 Algorithms 6-24

v 6.3 Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 6-27 6.3.1 Stress Design 6-27 6.3.2 Flexure Design 6-28 6.3.2.1 Design Process 6-28 6.3.2.2 Algorithms 6-30 6.3.3 Shear Design 6-32 6.3.3.1 Variables 6-33 6.3.3.2 Design Process 6-35 6.3.3.3 Algorithms 6-36

7 Design Algorithms for Precast I and U-Girder Bridges

7.1 AASHTO-LFRD 2007 7-1 7.1.1 Design Stress 7-2 7.1.2 Design Shear 7-2 7.1.2.1 Variables 7-3 7.1.2.2 Design Process 7-5 7.1.2.3 Algorithms 7-5

7.1.2.4 Shear Design Example 7-9

7.1.3 Design of Flexural 7-14

7.1.3.1 Variables 7-15

7.1.3.2 Design Process 7-16

7.1.3.3 Algorithms 7-16

7.1.3.4 Flexure Design Capacity Example 7-19

7.2 CAN/CSA-S6-06 7-23 7.2.1 Stress Design 7-23 7.2.2 Shear Design 7-24 7.2.2.1 Variables 7-25 7.2.2.2 Design Process 7-26 7.2.2.3 Algorithms 7-26 7.2.3 Flexural Design 7-30 7.2.3.1 Variables 7-30 7.2.3.2 Design Process 7-31 7.2.3.3 Algorithms 7-32 7.3 Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 7-35 7.3.1 Stress Design 7-35 7.3.2 Flexure Design 7-36 7.3.2.1 Design Process 7-36 7.3.2.2 Algorithms 7-38

vi

7.3.3 Shear Design 7-39

7.3.3.1 Variables 7-41

7.3.3.2 Design Process 7-42

7.3.3.3 Algorithms 7-43

8 Design Steel I-Beam Bridge with Composite Slab

8.1 Strength Properties 8-1

8.1.1 Yield Moments 8-1

8.1.2 Plastic Moments 8-3

8.1.3 Section Classification and Factors 8-7

8.2 Demand Sets 8-11

8.2.1 Demand Flange Stress fbu and ff 8-12

8.2.2 Demand Flange Lateral Bending Stress f1 8-13

8.2.3 Depth of Web in Compression 8-14

8.3 Strength Design Request 8-15

8.3.1 Flexure 8-15

8.3.2 Shear 8-21

8.4 Service Design Request 8-24

8.5 Web Fatigue Design Request 8-26

8.6 Constructibility Design Request 8-27 8.6.1 Staged (Steel-I Comp Construct Stgd) 8-27 8.6.2 Non-Staged (Steel Comp Construct NonStgd) 8-27 8.6.3 Slab Status vs. Unbraced Length 8-27

8.6.4 Flexure 8-28

8.6.5 Shear 8-30

8.7 Section Optimization 8-33

9 Run a Bridge Design Request

9.1 Description of Example Model 9-2

9.2 Design Preferences 9-3

9.3 Load Combinations 9-3

9.4 Bridge Design Request 9-5

vii

10 Design Output

10.1 Display Results as a Plot 10-1

10.1.1 Additional Display Examples 10-2

10.2 Display Data Tables 10-7

10.3 Advanced Report Writer 10-8

10.4 Verification 10-11

viii

List of Figures

Figure 2-1 Code-Generated Load Combinations for Bridge

Design Form – AASHTO LRFD 2-5

Figure 2-2 Define Load Combinations Form – AASHTO LRFD 2-6 Figure 2-3 Code-Generated Load Combinations for Bridge

Design Form – CAN/CSA-S6-06 2-10

Figure 2-4 Define Load Combinations Form – CAN/CSA-S6-06 2-11 Figure 2-5 Define Code-Generated Load Combinations for

Bridge Design from – Eurocode 2-18

Figure 2-6 Define Load Combination form – Eurocode 2-19

Figure 3-1 General Dimensions 3-8

Figure 3-2 Lever Rule 3-11

Figure 4-1 Bridge Design Request – Concrete Box Girder Bridges 4-2 Figure 4-2 Bridge Design Request – Compost I or U Girder Bridges 4-2 Figure 4-3 Bridge Design Request form – Steel I Beam

with Composite Slab 4-3

Figure 4-4 Superstructure Design Request Parameters form 4-6 Figure 5-1 LRFD 2007 Stress Design, ASSHTO Box Beam,

Type BIII-48 5-4

Figure 5-2 Reinforcement, LRFD 2007 Stress Design AASHTO Box

Beam, Type BIII-48 5-5

Figure 5-3 LRFD 2007 Flexure Design Cross-Section, AASHTO Box

Beam, Type BIII-48 5-11

Figure 5-4 Reinforcement, LRFD 2007 Flexure Design Cross-Section,

AASHTO Box Bea, Type BIII-48 5-11

Figure 5-5 Shear Design Example, AASHTO Box Beam,

Type BIII-48 5-24

Figure 5-6 Shear Design Example Reinforcement, AASHTO Box

Beam, Type BIII-48 5-25

Figure 5-7 Rectangular Stress Distribution,

Eurocode 2 EN 1992-1-1 5-49

Figure 5-8 Idealized and Design Stress-Strain Diagrams for Reinforcing Steel for Tension and Compression,

ix Figure 5-9 Idealized and Design Stress-Strain Diagrams for Prestressing

Steel, Absolute Values are Shown for Tensile Stress and Strain, Eurocode 2 EN 1992-1-1 5-50 Figure 6-1 Rectangular Stress Distribution,

Eurocode 2 EN 1992-1-1 6-29

Figure 6-2 Idealized and Design Stress-Strain Diagrams for Reinforcing Steel for Tension and Compression,

Eurocode 2 EN 1992-1-1 6-29

Figure 6-3 Idealized and Design Stress-Strain Diagrams for Prestressing Steel, Absolute Values are Shown

for Tensile Stress and Strain, Eurocode 2 EN 1992-1-1 6-30

0H

Figure 7-1 Shear design example deck section 7-9

1H

Figure 7-2 Shear design example beam section 7-10

2H

Figure 7-3 Flexure capacity design example deck section 7-19

3H

Figure 7-4 Flexure capacity design example beam section 7-20

4H

Figure 7-5 Rectangular Stress Distribution,

Eurocode 2 EN 1992-1-1 7-37

Figure 7-6 Idealized and Design Stress-Strain Diagrams for Reinforcing Steel for Tension and Compression,

Eurocode 2 EN 1992-1-1 7-37

Figure 7-7 Idealized and Design Stress-Strain Diagrams for Prestressing Steel, Absolute Values are Shown

for Tensile Stress and Strain, Eurocode 2 EN 1992-1-1 7-38 Figure 8-1 Steel I-Beam with Composite Section 8-5 Figure 8-2 Steel I-Beam Composite Section 8-6 Figure 9-1 3D view of example concrete box girder bridge model 9-2

5H

Figure 9-2 Elevation view of example bridge 9-2

6H

Figure 9-3 Plan view of the example bridge 9-3

7H

Figure 9-4 Bridge Design Preferences form 9-3

8H

Figure 9-5 Code-Generated Load Combinations for Bridge Design

form 9-4

9H

Figure 9-6 Define Load Combinations form 9-4

10H

Figure 9- 7 Define Load Combinations form 9-5

11H

Figure 9-8 Perform Bridge Design - Superstructure 9-6

12H

x

Figure 10-1 Plot of flexure check results for the example bridge

design model 10-2

Figure 10-2 Select the location on the beam or slab for which

results are to be displayed 10-3

Figure 10-3 Bridge Concrete Box Deck Section – External

Girders Vertical 10-4

Figure 10-4 Bridge Concrete Box Deck Section – External

Girders Sloped 10-4

Figure 10-5 Bridge Concrete Box Deck Section – External

Girders Clipped 10-4

Figure 10-6 Bridge Concrete Box Deck Section – External

Girders and Radius 10-5

Figure 10-7 Bridge Concrete Box Deck Section – External

Girders Sloped Max 10-5

Figure 10-8 Bridge Concrete Box Deck Section – Advanced 10-6 Figure 10-9 Bridge Concrete Box Deck Section -

AASHTO – PCI – ASBI Standard 10-6

Figure 10-10 Choose Tables for Display form 10-7 Figure 10-11 Design database table for AASHTO LRFD 2007

flexure check 10-8

Figure 10-12 Choose Tables for Export to Access form 10-9 Figure 10-13 Create Custom Report form 10-10 Figure 10-14 An example of the printed output 10-11

1 - 1

Chapter 1

Introduction

As the ultimate versatile, integrated tool for modeling, analysis, and design of bridge structures, CSiBridge can apply appropriate code-specific design processes to concrete box girder bridge design, design when the superstructure includes Precast Concrete Box bridges with a composite slab and steel I-beam bridges with composite slabs. The ease with which these tasks can be accom-plished makes CSiBridge the most productive bridge design package in the industry.

Design using CSiBridge is based on load patterns, load cases, load combina-tions and design requests. The design output can then be displayed graphically and printed using a customized reporting format.

It should be noted that the design of bridge superstructure is a complex subject and the design codes cover many aspects of this process. CSiBridge is a tool to help the user with that process. Only the aspects of design documented in this manual are automated by the CSiBridge design capabilities. The user must check the results produced and address other aspects not covered by CSi-Bridge.

1.1 Organization

• This manual is designed to help you become productive using CSi-Bridge design in accordance with the available codes when modeling

1 - 2 Recommended Reading/Practice

concrete box girder bridges and precast concrete girder bridges. Chap-ter 2 describes code-specific design prerequisites. ChapChap-ter 3 describes Live Load Distribution Factors. Chapter 4 describes defining the de-sign request, which includes the dede-sign request name, a bridge object name (i.e., the bridge model), check type (i.e., the type of design), sta-tion range (i.e., porsta-tion of the bridge to be designed), design parame-ters (i.e., overwrites for default parameparame-ters) and demand sets (i.e., load-ing combinations). Chapter 5 identifies code-specific algorithms used by CSiBridge in completing concrete box girder bridges. Chapter 6 provides code-specific algorithms used by CSiBridge in completing concrete box and multicell box girder bridges. Chapter 7 describes code-speicifc design parameters for precast I and U girder. Chapter 8 explains how to design and optimize a steel I-beam bridge with com-posite slab in accordance with AASHTO LRFD 2008 Edition, Section 6 or Appendix A. Chapter 9 describes how to run a Design Request us-ing an example that applies the AASHTO LRFD 2007 code, and Chap-ter 10 describes design output for the example in ChapChap-ter 9, which can be presented graphically as plots, in data tables, and in reports generat-ed using the Advancgenerat-ed Report Writer feature.

1.2 Recommended Reading/Practice

It is strongly recommended that you read this manual and review any applica-ble “Watch & Learn” Series™ tutorials, which are found on our web site, http://www.csiberkeley.com, before attempting to design a concrete box girder or precast concrete bridge using CSiBridge. Additional information can be found in the on-line Help facility available from within the software’s main menu.

ASHTO LRFD 2007 2 - 1

Chapter 2

Define Loads and Load Combinations

This chapter describes the steps that are necessary to define the loads and load combinations that the user intends to use in the design of the bridge superstruc-ture. The user may define the load combinations manually or have CSiBridge automatically generate the code generated load combinations. The appropriate design code may be selected using the Design/Rating > Superstructure De-sign > Preference command. Currently, the AASHTO STD 2002 and AASH-TO LRFD 2007 design codes (Section 2.1), the CAN/CSA-S6-06 code for concrete bridges only (Section 2.2), and Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 code (Section 3.3) are supported by CSiBridge.

For referring to pertinent sections of the corresponding code, a unique prefix is assigned for each code.

 Reference to the AASHTO LRFD 2007 code is identified with the prefix “AASHTO.”

 Reference to the CAN/CSA S6-06 code is identified with the prefix “CSA.”

 Reference to the Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 code is identified as “EN 1992-1-1.”

When the code generated load combinations are going to be used, it is impor-tant for users to define the load pattern type in accordance with the applicable

2 - 2 ASHTO LRFD 2007

code. The load pattern type can be defined using the Loads > Load Patterns command. The user options for defining the load pattern types are summarized in the Tables 2-1 and 2-2 for the AASHTO LRFD code, Tables 2-5 and 2-6 for the CAN/CSA-S6-06 code, and Table 2-9 and 2-10 for Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005.

2.1

ASHTO LRFD 2007

2.1.1 Load Pattern Types

Tables 2-1 and 2-2 show the permanent and transient load pattern types that can be defined in CSiBridge. The tables also show the AASHTO abbreviation and the load pattern descriptions. Users may choose any name to identify a load pattern type.

Table 2-1 PERMANENT Load Pattern Types Used in the AASHTO-LRFD 2007 Code CSiBridge

Load Pattern Type

AASHTO

Reference Description of Load Pattern

CREEP CR Force effects due to creep

DOWNDRAG DD Downdrag force

DEAD DC Dead load of structural components and

non-structural attachments

SUPERDEAD DW Superimposed dead load of wearing surfaces

and utilities

BRAKING BR Vehicle braking force

HORIZ. EARTH PR EH Horizontal earth pressures

LOCKED IN EL Misc. locked-in force effects resulting from the

construction process

EARTH SURCHARGE ES Earth surcharge loads

VERT. EARTH PR EV Vertical earth pressure

PRESTRESS PS Hyperstatic forces from post-tensioning

Table 2-2 TRANSIENT Load Pattern Types Used in the AASHTO LRFD 2007 Design Code CSiBridge

Load Pattern Type

AASHTO

Reference Description of Load Pattern

BRAKING BR Vehicle braking force

CENTRIFUGAL CE Vehicular centrifugal loads

VEHICLE COLLISION CT Vehicular collision force

ASHTO LRFD 2007 2 - 3

Table 2-2 TRANSIENT Load Pattern Types Used in the AASHTO LRFD 2007 Design Code CSiBridge

Load Pattern Type

AASHTO

Reference Description of Load Pattern

QUAKE EQ Earthquake

FRICTION FR Friction effects

ICE IC Ice loads

- IM Vehicle Dynamic Load Allowance

BRIDGE LL LL Vehicular live load

LL SURCHARGE LS Live load surcharge

PEDESTRIAN LL PL Pedestrian live load

SETTLEMENT SE Force effects due settlement

TEMP GRADIENT TG Temperature gradient loads

TEMPERATURE TU Uniform temperature effects

STEAM FLOW WA Water load and steam pressure

WIND–LIVE LOAD WL Wind on live load

WIND WS Wind loads on structure

2.1.2 Design Load Combinations

The code generated design load combinations make use of the load pattern types noted in Tables 2-1 and 2-2. Table 2-3 shows the load factors and combi-nations that are required in accordance with the AASHTO LRFD 2007 code. Table 2-3 Load Combinations and Load Factors Used in the AASHTO LRFD 2007 Code

Load Combo Limit State DC DD DW EH EV ES EL PS CR SH LL IM CE BR PL LS WA WS WL FR TU TG SE EQ IC CT CV Str I γP 1.75 1.00 - - 1.00 0.5/1.20 γTG γSE - - - - Str II γP 1.35 1.00 - - 1.00 0.5/1.20 γTG γSE - - - - Str III γP - 1.00 1.40 - 1.00 0.5/1.20 γTG γSE - - - - Str IV γP - 1.00 - - 1.00 0.5/1.20 - - - - - Str V γP 1.35 1.00 0.40 1.00 1.00 0.5/1.20 γTG γSE - - - - Ext Ev I γP γEQ 1.00 - - 1.00 - - 1.00 - - -

2 - 4 ASHTO LRFD 2007

Table 2-3 Load Combinations and Load Factors Used in the AASHTO LRFD 2007 Code

Load Combo Limit State DC DD DW EH EV ES EL PS CR SH LL IM CE BR PL LS WA WS WL FR TU TG SE EQ IC CT CV Ext Ev II γP 0.5 1.00 - - 1.00 - - - 1.00 1.00 1.00 Serv I 1.00 1.00 1.00 0.30 1.00 1.00 0.5/1.20 γTG γSE - - - - Serv II 1.00 1.30 1.00 - - 1.00 0.5/1.20 - - - - - Serv III 1.00 0.80 1.00 - - 1.00 0.5/1.20 γTG γSE - - - - Serv IV 1.00 1.00 1.00 0.70 - 1.00 0.5/1.20 - 1.00 - - - - Fatigue-LL, IM & CE Only - 0.75 - - - - - - - - - - -

Table 2-4 shows the maximum and minimum factors for the permanent loads in accordance with the AASHTO LRFD 2007 code.

Table 2-4 Load Factors for Permanent Loads,

γ

_P, Used in the AASHTO LRFD 2007 Code Type of Load Load Factor Maximum Minimum DC DC: Strength IV only 1.25 1.50 0.90 0.90 DD: Downdrag 1.40 0.25

DW: Wearing Surfaces and Utilities 1.50 0.65

EH: Horizontal Earth Pressure 1.50 0.90

EL: Locked in Construction Stresses 1.00 1.00

EV: Vertical Earth Pressure 1.35 1.00

ES: Earth Surcharge 1.50 0.75

Two combinations for each permanent load pattern are required because of the maximum and minimum factors. When the default load combinations are used, CSiBridge automatically creates both load combinations (one for the maximum and one for the minimum factor), and then automatically creates a third combi-nation that represents an enveloped combicombi-nation of the max/min combos.

ASHTO LRFD 2007 2 - 5

2.1.3 Default Load Combinations

Default design load combinations can be activated using the Design/Rating > Load Combinations > Add Default command. Users can set the load combi-nations by selecting the “Bridge” option. Users may select the desired limit states and load cases using the Code Generated Load Combinations for Bridge Design form. The form shown in Figure 2-1 illustrates the options when the AASHTO LRFD 2007 code has been selected for design.

Figure 2-1 Code-Generated Load Combinations for Bridge Design Form – AASHTO LRFD

After the desired limit states and load cases have been selected, CSiBridge will generate all of the code-required load combinations. These can be viewed us-ing the Home > Display > Show Tables command or by usus-ing the Show/Modify button on the Define Combinations form, which is shown in Figure 2-2.

2 - 6 CAN/CSA-S6-06

Figure 2-2 Define Load Combinations Form – AASHTO LRFD

The load combinations denoted as Str-I1, Str-I2, and so forth refer to Strength I load combinations. The load case StrIGroup1 is the name given to enveloped load combination of all of the Strength I combinations. Enveloped load combi-nations will allow for some efficiency later when the bridge design requests are defined (see Chapter 4).

2.2

CAN/CSA-S6-06

2.2.1 Load Pattern Types

Tables 2-5 and 2-6 show the permanent, transient, and exceptional load pattern types that can be defined in CSiBridge. The tables also show the CSA abbrevi-ation and the load pattern descriptions. Users may choose any name to identify a load pattern type.

Table 2-5 PERMANENT Load Pattern Types Used in the CAN/CSA-S6-06 Code CSiBridge

Load Pattern Type CSA Description of Load Pattern

CREEP K Force effects due to creep

DEAD D Dead load of structural components and

CAN/CSA-S6-06 2 - 7

Table 2-5 PERMANENT Load Pattern Types Used in the CAN/CSA-S6-06 Code CSiBridge

Load Pattern Type CSA Description of Load Pattern

HORIZ. EARTH PR E Horizontal earth pressures

EARTH SURCHARGE E Earth surcharge loads

PRESTRESS P Hyperstatic forces from post-tensioning

Table 2-6 TRANSIENT Load Pattern Types Used in the CAN/CSA-S6-06 Design Code CSiBridge

Load Pattern Type CSA Description of Load Pattern

VEHICLE COLLISION H Vehicular collision force

VESSEL COLLISION H Vessel collision force

QUAKE EQ Earthquake

FRICTION K Friction effects

ICE F Ice loads

- IM Vehicle Dynamic Load Allowance

BRIDGE LL L Vehicular live load

SETTLEMENT S Force effects due settlement

TEMP GRADIENT K Temperature gradient loads

TEMPERATURE K Uniform temperature effects

STEAM FLOW F Water load and steam pressure

WIND–LIVE LOAD V Wind on live load

WIND W Wind loads on structure

2.2.2 Design Load Combinations

The code generated design load combinations make use of the load pattern types noted in Tables 2-5 and 2-6. Table 2-7 shows the load factors and com-binations that are required in accordance with the CAN/CSA-S6-06 code.

Table 2-7 Load Combinations and Load Factors Used in the CAN/CSA-S6-06 Code

Permanent Loads Transitory Loads Exceptional Loads

Loads D E P L1 K W V S EQ F A H

Fatigue limit state

2 - 8 CAN/CSA-S6-06

Table 2-7 Load Combinations and Load Factors Used in the CAN/CSA-S6-06 Code

Permanent Loads Transitory Loads Exceptional Loads

Loads D E P L1 _{K W V S EQ F A H} Serviceability limit states SLS Combination 1 1.00 1.00 1.00 0.90 0.80 0 0 1.00 0 0 0 0 SLS Combination 22 0 0 0 0.90 0 0 0 0 0 0 0 0 Ultimate limit states3 ULS Combination 1 αD αE αP 1.70 0 0 0 0 0 0 0 0 ULS Combination 2 αD αE αP 1.60 1.15 0 0 0 0 0 0 0 ULS Combination 3 αD αE αP 1.40 1.00 0.504 0.50 0 0 0 0 0 ULS Combination 4 αD αE αP 0 1.25 1.654 0 0 0 0 0 0 ULS Combination 5 αD αE αP 0 0 0 0 0 1.00 0 0 0 ULS Combination 65 αD αE αP 0 0 0 0 0 0 1.30 0 0 ULS Combination 7 αD αE αP 0 0 0.904 0 0 0 0 1.30 0 ULS Combination 8 αD αE αP 0 0 0 0 0 0 0 0 1.00 ULS Combination 9 1.35 αE αP 0 0 0 0 0 0 0 0 0

1 For the construction live load factor, see CSA Clause 3.16.3. 2. For superstructure vibration only.

3. For ultimate limit states, the maximum or minimum values of specified in Table CSA Table 3.2 shall be used. 4. For wind loads determined from wind tunnel tests, the load factors shall be specified in CSA Clause 3.10.5.2. 5. For long spans, it is possible that a combination of ice load F and wind load W will require investions.

Table 2-8 shows the maximum and minimum factors for the permanent loads in accordance with the AASHTO LRFD 2007 code. Table 2-4b shows the maximum and minimum factors for the permanent loads in accordance with the CAN/CSA-S6-06 code.

Table 2-8 Load Factors for Permanent Loads, Earth Pressure, and Hydrostatic Pressure and Prestress, αE and αP Used in the CAN/CSA-S6-06 Code

Dead Load Maximum αD Minimum αD

Factory-produced components, excluding wood 1.10 0.95 Cast-in-place concrete, wood, and all non-structural

compo-nents 1.20 0.90

Wearing surfaces, based on nominal or specified thickness 1.50 0.65 Earth fill, negative skin friction on piles 1.25 0.80

CAN/CSA-S6-06 2 - 9

Table 2-8 Load Factors for Permanent Loads, Earth Pressure, and Hydrostatic Pressure and Prestress, αE and αP Used in the CAN/CSA-S6-06 Code

Dead load in combination with earthquakes Maximum αD Minimum αD

All dead loads for ULS Combination 5 (see CSA Table 3.1) 1.25 0.80

Earth pressure and hydrostatic pressure Maximum αE Minimum αE

Passive earth pressure, considered as a load 1.25 0.50 At-rest earth pressure

Active earth pressure Backfill pressure Hydrostatic pressure

Prestress _{Maximum αP Minimum αP}

Secondary prestress effects 1.05 0.95

Two combinations for each permanent load pattern are required because of the maximum and minimum factors. When the default load combinations are used, CSiBridge automatically creates both load combinations (one for the maximum and one for the minimum factor), and then automatically creates a third combi-nation that represents an enveloped combicombi-nation of the max/min combos.

2.2.3 Default Load Combinations

Default design load combinations can be activated using the Design/Rating > Load Combinations > Add Default command. Users can set the load combi-nations by selecting the “Bridge” option. Users may select the desired limit states and load cases using the Code Generated Load Combinations for Bridge Design form. The form shown in Figure 2-3 illustrates the options when the CAN/CSA-S6-06 code has been selected for design.

2 - 10 CAN/CSA-S6-06

Figure 2-3 Code-Generated Load Combinations for Bridge Design form –

CAN/CSA-S6-06

After the desired limit states and load cases have been selected, CSiBridge will generate all of the code-required load combinations. These can be viewed us-ing the Home > Display > Show Tables command or by usus-ing the Show/Modify button on the Define Combinations form, which is shown in Figure 2-4.

Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 2 - 11

Figure 2-4 Define Load Combinations form – CAN/CSA-S6-06

The load combinations denoted as ULS1-1, ULS1-2, and so forth refer to Ulti-mate I load combinations. The load case ULS1Group1 is the name given to en-veloped load combination of all of the Ultimate I combinations. Enen-veloped load combinations will allow for some efficiency later when the bridge design requests are defined (see Chapter 4).

2.3

Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005

2.3.1 Load Pattern Types

Table 2-9 Permanent Actions, Table 2-10 Prestress and Table 2-11 Variable Actions show the load pattern type and Eurocode description as well as the Eu-rocode abbreviation. Users may choose any name to identify a load pattern type

2 - 12 Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005

Table 2-9 Permanent Actions CSiBridge Load Pattern Type

Eurocode

Abbreviations Description of Load Pattern

General Permanent Actions General Permanent Actions

DEAD G

DEADMANUFACTURE G

DEADWEARING G

Geotechnical Permanent Actions Geotechnical Permanent Actions

DEADWATER Ggeo

DOWNDRAG Ggeo

VERTICALEARTHPRESSURE Ggeo

Uneven Settlements - Linear analysis Uneven Settlements - Linear analysis

SETTLEMENT Gset_L

Table 2-10 Prestress CSiBridge Load Pattern Type

Eurocode

Reference Description of Load Pattern

Prestress PT Prestress

PRESTRESS

Table 2-11 Variable Actions

CSiBridge

Load Pattern Type AbbreviationsEurocode Description of Load Pattern

Traffic Actions

EURO LOADMODEL1 CHARACTER LM1_Char Load Model 1 w ith combination of

Tandem System and UDL system without introducing psi factor

EURO LOADMODEL1 FREQUENT LM1_Freq Load Model 1 w ith combination of

Tandem System and UDL system introducing psi factors

EURO LOADMODEL2 LM2 Load Model 2

EURO LOADMODEL3 LM3 Load Model 3

EURO LOADMODEL4 LM4 Load Model 4

PEDESTRIANLL FCT Footway and Cycle Tracks

PEDESTRIANLLREDUCED FCTr Footway and Cycle Tracks reduced

value Horizontal Traffic Actions

BRAKING HTA Traction and Braking

CENTRIFUGAL C Centrifugal Force

Other Actions

WIND W Wind Load

WINDONLIVELOAD Wt Wind with Traffic

TEMPERATURE T

TEMPERATUREGRADIENT TG

SNOW S Snow with H < 1000m

SNOWHIGHALTITUDE S Snow with H > 1000m

Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 2 - 13

Table 2-11 Variable Actions

CSiBridge

Load Pattern Type AbbreviationsEurocode Description of Load Pattern

Geotechnical Variable Actions Geotechnical Variable Actions

HORIZONTALEARTHPRESSURE Qgeo BOUYANCY Qgeo WATERLOADPRESSURE Qgeo EARTHHYDROSTATIC Qgeo EARTHSURCHARGE Qgeo ACTIVEEARTHPRESSURE Qgeo Earthquake Load QUAKE E Accidental loads IMPACT A VEHICLECOLLISION A VESSELCOLLISION A

2.3.2 Design Combinations

Table 2-12 Permanent Actions, Table 2-10 Prestress and Table 2-11 Variable Actions show the load pattern type and Eurocode description as well as the Eu-rocode abbreviation. Users may choose any name to identify a load pattern type

1. Combination Groups

Table 2-12 Ultimate Limit State Design Situation

Combination Group Abbreviation

Persistent and Transient – EQU (A)

Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(A)

EQU

Persistent and Transient – EQU+STR (A)

Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(A) NOTE 2

EQU+STR

Persistent and Transient – STR/GEO (B1)

Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(B) (first table)

2 - 14 Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005

Table 2-12 Ultimate Limit State Design Situation

Combination Group Abbreviation

Persistent and Transient – STR/GEO (B2-a)

Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(B) (second table)

STR/GEO-B2-a

Persistent and Transient – STR/GEO (B2-b)

Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(B) (second table)

STR/GEO-B2-b

Persistent and Transient – STR/GEO (C)

Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(C)

STR/GEO-C Persistent and Transient – STR/GEO (C) + Factors (B)

Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(C) for geotechnical actions and Table A2.4 (B) for non geotechnical actions.

STR/GEO-C+B

Seismic

Combinations of actions for seismic design situations Eq. 6.12

SEIS Accidental

Combinations of actions for accidental design situations Eq. 6.11

ACC

Table 2-13 Serviceability Limit State design situation

Combination Group Abbreviation

Characteristic

Characteristic combination of actions Eq.6.14

CARAC Frequent

Frequent combination of actions Eq. 6.15

FREQ Quasi-permanent

Quasi-permanent combination of actions Eq. 6.16

Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 2 - 15

Table 2-14 Combination Factors (Ref. Table A2.1)

Ψ0 : Used for combination of variable action

Ψ1 : Used for combination of frequent value of variable action

Ψ2 : Used for combination for quasi-permanent value of variable action

Load Name Ψ0 Ψ1 Ψ2

Load Model 1 – Tandem System 0.75 0.75 0.0

Load Model 1 – UDL System 0.4 0.4 0.0

Load Model 2 0.0 0.75 0.0

Load Model 3 0.0 0.0 0.0

Load Model 4 0.0 0.75 0.0

Footways and Cycle Tracks 0.0 0.0 0.0

Footways and Cycle Tracks reduced value 0.4 0.4 0.0

Wind (Persistent design situations) 0.6 0.2 0.0

Wind with traffic 0.0 0.0 0.0

Snow H < 1000 m 0.7 0.5 0.0

Snow H > 1000 m 0.7 0.5 0.2

Thermal action (Temperature) 0.6 0.6 0.5

Construction Loads 1.0 1.0

Table 2-15 Partial Factors

Load Name EQU EQU + STR

STR/ GEO-B1

STR/

GEO-B2a GEO-B2b STR/ GEO-C STR/ GEO-C+B STR/

SEIS, ACC CARAC,

FREQ, QUAS max min max min max min max min max min max min max min General Perma-nent Actions 1.05 0.95 1.35 1.15 1.35 1 1.15 1 1 1 1.35 1 1 1 Geotechnical Permanent Actions 1.05 0.95 1.35 1.15 1.35 1 1.15 1 1 1 1.35 1 1 1 Uneven Settle-ments - Linear analysis 1.05 0.95 1.35 1.15 1.20 0 1.02 0 1 0 1.20 0 1 0 Prestress ϒ P ϒ P ϒ P ϒ P ϒ P ϒ P ϒ P ϒ P ϒ P ϒ P ϒ P ϒ P 1 1 Traffic Actions 1.35 0 1.35 0 1.35 0 1.35 0 1.15 0 1.50 0 1 0 Horizontal Traffic Actions 1.35 0 1.35 0 1.35 0 1.35 0 1.15 0 1.50 0 1 0 Other Actions 1.50 0 1.50 0 1.50 0 1.50 0 1.30 0 1.50 0 1 0 Geotechnical Variable Actions 1.50 0 1.50 0 1.50 0 1.50 0 1.30 0 1.30 0 1 0 Seismic 1 1 Accidental 1 1

2 - 16 Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005

Tables 2-16 Load Combinations

A. For (1) EQU, (2) EQU+STR, (3) STR/GEO-B2b, (4) STR/GEO-C, (5) STR/GEO-C+B and (6) CARAC (Characteristic) (EN1990, Eq. 6.10, 6.10b and 6.14)

Leading Variable

Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A

1. gr1a 1 1 1 1 Ψ0 Ψ0 Ψ0 2. gr1b 1 1 1 3. gr2 1 1 1 1 Ψ0 Ψ0 4. gr3 1 1 1 Ψ0 Ψ0 5. gr4 1 1 1 1 Ψ0 Ψ0 6. gr5 1 1 1 Ψ0 Ψ0 7. W 1 1 1 Ψ0 Ψ0 Ψ0 8. Wt, required: gr1a 1 1 1 Ψ0 Ψ0 Ψ0 9. T 1 1 Ψ0 1 Ψ0 Ψ0 10. T, required: gr1a 1 1 1 Ψ0 1 Ψ0 11. Qgeo 1 1 Ψ0 Ψ0 Ψ0 1 12. Qgeo, required: gr1a 1 1 1 Ψ0 1 Ψ0 1 13. N 1 1 Ψ0 Ψ0 1 Ψ0

Note: 1. Bold characters indicate that the possibility of non-existence of the associated load group will be considered. 2. If the leading action is not involved in a load combination, the corresponding load combination will not be

gen-erated

B. For (1) STR/GEO-B1 and(2) STR/GEO-B2a (EN1990, Eq. 6.10) Leading Variable

Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A

1. Required: gr1a 1 1 1 Ψ0 Ψ0 Ψ0 Ψ0

1 1 Ψ0 Ψ0 Ψ0 Ψ0

C. For QUAS (EN1990, 6.16) Leading Variable

Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A

1. Required: gr1a 1 1 1 Ψ2 Ψ2 Ψ2 Ψ2

1 1 Ψ2 Ψ2 Ψ2 Ψ2

D. For SEIS (EN1990, Eq. 6.12) Leading Variable

Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A

Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 2 - 17 E. For ACC (EN1990, Eq. 6.11)

Main Variable Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A

1. A 1 1 Ψ2 Ψ2 Ψ2 1 2. gr1a 1 1 1 Ψ2 Ψ2 1 3. gr1b 1 1 Ψ1 1 4. gr4 1 1 Ψ1 Ψ2 Ψ2 1 5. W 1 1 Ψ1 Ψ2 Ψ2 Ψ2 1 6. T 1 1 Ψ2 Ψ2 1 7. Qgeo 1 1 Ψ2 Ψ2 Ψ2 1 8. N 1 1 Ψ2 Ψ1 Ψ2 1

F. For FREQ (EN1990, Eq. 6.15) Leading Variable

Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A

1. gr1a 1 1 1 Ψ2 Ψ2 Ψ0 2. gr1b 1 1 Ψ1 3. gr4 1 1 Ψ1 Ψ2 Ψ2 4. W 1 1 Ψ1 Ψ2 Ψ2 Ψ2 5. T 1 1 Ψ2 Ψ2 6. Qgeo 1 1 Ψ2 Ψ1 7. N 1 1 Ψ2 Ψ1 Ψ2

2.3.3 Default Load Combinations

Default design load combinations can be activated using the Design/Rating >Load Combinations > Add Default command. Users can set the load com-binations by selecting the “Bridge” option. Users may select the desired limit states and load cases using the Code Generated Load Combinations for Bridge Design form. The form shown in Figure 2-6 illustrates the options when the Eurocode code has been selected for design.

2 - 18 Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005

Figure 2-5 Define Code-Generated Load Combinations for Bridge Design form – Eurocode

Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 2 - 19

Figure 2-6 Define Load Combination form - Eurocode

The load combinations denoted as EQU-1, EQU-2, and so forth refer to Persis-tent and Transient load combinations 1 and 2. The load case EQUGroup1 is the name given to enveloped load combination of all of the EQU Persistent and Transient combinations. Enveloped load combinations will allow for some ef-ficiency later when the bridge design requests are defined (see Chapter 4).

AASHTO LRFD 2007 3 - 1

Chapter 3

Determine Live Load Distribution Factors

This chapter describes the algorithms used by CSiBridge to determine the live load distribution factors used to assign live load demands to individual girders. An explanation is given with respect to how the distribution factors are applied in a shear, stress, and moment check in accordance with the AASHTO LRFD 2007 code (Section 3.1), the CAN/CSA-S6-06 code (Section 3.2), and the Eu-rocode 2 EN 1992-1:2004 and EN 1992-2:2005 code (Section 3.3).

For referring to pertinent sections of the corresponding code, a unique prefix is assigned for each code.

 Reference to the AASHTO LRFD 2007 code is identified with the prefix “AASHTO.”

 Reference to the CAN/CSA S6-06 code is identified with the prefix “CSA.”

 Reference to the Eurocode 2 EN 1992-1:2004 and EN 1992-2:2005 code is identified as “EN 1992-1-1.”

For the AASHTO LRFD and CAN/CSA-S6-06 codes, the live load distribution factors are applicable only to superstructures with a deck that includes precast I or U girders with composite slabs. For Eurocode 2 EN 1992-1:2004 and EN 1992-2:2005 code, the live load distribution factors are applicable to

super-3 - 2 AASHTO LRFD 2007

structures with a deck that includes multi-cell concrete box, precast I or U gird-ers with composite slabs, or steel I girdgird-ers with composite slabs.

3.1

AASHTO LRFD 2007

This section explains the how the live load distribution factors are applied in a shear, stress, and moment check in accordance with the AASHTO LRFD 2007 code.

Legend:

Girder = beam + tributary area of composite slab

Section Cut = all girders present in the cross-section at the cut location

3.1.1 Algorithm for Determining Live Load Distribution

Fac-tors (LLDF)

CSiBridge gives the user a choice of four methods to address distribution of live load to individual girders.

Method 1 – The LLD factors are specified directly by the user.

Method 2 – CSiBridge calculates the LLD factors by following procedures outlined in AASHTO LRFD Section 4.6.2.2.

Method 3 – CSiBridge reads the calculated live load demands directly from in-dividual girders (available only for Area models).

Method 4 – CSiBridge distributes the live load uniformly to all girders.

It is important to note that to obtain relevant results, the definition of a Moving Load case must be adjusted depending on which method is selected.

 When the LLD factors are user specified or specified in accordance with the code (Method 1 or 2), only one lane with a MultiLane Scale Factor = 1 should be loaded into a Moving Load cases included in the demand set com-binations.

 When CSiBridge reads the LLD factors directly from individual girders (Me-thod 3, applicable to area and solid models only) or when CSiBridge applies

AASHTO LRFD 2007 3 - 3 the LLD factors uniformly (Method 4), multiple traffic lanes with relevant Multilane Scale Factors should be loaded in accordance with code require-ments.

3.1.2 Determine Live Load Distribution Factors

At every section cut, the following geometric information is evaluated to de-termine the LLD factors.

 span lengththe length of span for which moment or shear is being calcu-lated

 the number of girders

 girder designationthe first and last girder are designated as exterior girders and the other girders are classified as interior girders

 roadway widthmeasured as the distance between curbs/barriers; medians are ignored

 overhangconsists of the horizontal distance from the centerline of the exte-rior web of the left exteexte-rior beam at deck level to the inteexte-rior edge of the curb or traffic barrier

 the beamsincludes the area, moment of inertia, torsion constant, center of gravity

 the thickness of the composite slab t1 and the thickness of concrete slab haunch t2

 the tributary area of the composite slabwhich is bounded at the interior girder by the midway distances to neighboring girders and at the exterior girder; includes the entire overhang on one side, and is bounded by the mid-way distances to neighboring girder on the other side

 Young’s modulus for both the slab and the beamsangle of skew support. CSiBridge then evaluates the longitudinal stiffness parameter, Kg, in accor-dance with AASHTO LRFD 4.6.2.2 (eq. 4.6.2.2.1-1). The center of gravity of the composite slab measured from the bottom of the beam is calculated as the sum of the beam depth, thickness of the concrete slab haunch t2, and one-half

3 - 4 AASHTO LRFD 2007

the thickness of the composite slab t1. Spacing of the girders is calculated as the average distance between the centerlines of neighboring girders.

CSiBridge then verifies that the selected LLD factors are compatible with the type of model: spine, area, or solid. If the LLD factors are read by CSiBridge directly from the individual girders, the model type must be area or solid. This is the case because with the spine model option, CSiBridge models the entire cross section as one frame element and there is no way to extract forces on in-dividual girders. All other model types and LLDF method permutations are al-lowed.

3.1.3 Apply LLD Factors

The application of live load distribution factors varies, depending on which method has been selected: user specified; in accordance with code; directly from individual girders; or uniformly distributed onto all girders.

3.1.3.1 User Specified

When this method is selected, CSiBridge reads the girder designations (i.e., exterior and interior) and assigns live load distribution factors to the individual girders accordingly.

3.1.3.2 Calculated by CSiBridge in Accordance with AASHTO

LRFD 2007

When this method is selected, CSiBridge considers the data input by the user for truck wheel spacing, minimum distance from wheel to curb/barrier and multiple presence factor for one loaded lane.

Depending on the section type, CSiBridge validates several section parameters against requirements specified in the code (AASHTO LRFD Tables 4.6.2.2.2b-1, 4.6.2.2.2d-4.6.2.2.2b-1, 4.6.2.2.3a-1 and 4.6.2.2.3b-1). When any of the parameter val-ues are outside the range required by the code, the section cut is excluded from the Design Request.

At every section cut, CSiBridge then evaluates the live load distribution factors for moment and shear for exterior and interior girders using formulas specified

AASHTO LRFD 2007 3 - 5 in the code (AASHTO LRFD Tables 4.6.2.2.2b-1, 4.6.2.2.2d-1, 4.6.2.2.3a-1 and 4.6.2.2.3b-1). After evaluation, the LLDF values are assigned to individual girders based on their designation (exterior, interior). The same value equal to the average of the LLDF calculated for the left and right girders is assigned to both exterior girders. Similarly, all interior girders use the same LLDF equal to the average of the LLDF of all of the individual interior girders.

3.1.3.3 Forces Read Directly from Girders

When this method is selected, CSiBridge sets the live load distribution factor for all girders to 1.

3.1.3.4 Uniformly Distributed to Girders

When this method is selected, the live load distribution factor is equal to 1/n where n is the number of girders in the section. All girders have identical LLD factors disregarding their designation (exterior, interior) and demand type (shear, moment).

3.1.4 Generate Virtual Combinations

When the method for determining the live load distribution factors is user-specified, code-user-specified, or uniformly distributed (Methods 1, 2 or 4), CSi-Bridge generates virtual load combination for every valid section cut selected for design. The virtual combinations are used during a stress check and check of the shear and moment to calculate the forces on the girders. After those forces have been calculated, the virtual combination are deleted. The process is repeated for all section cuts selected for design.

Four virtual COMBO cases are generated for each COMBO that the user has specified in the Design Request (see Chapter 4). The program analyzes the de-sign type of each load case present in the user specified COMBO and multip-lies all non-moving load case types by 1/ n (where n is the number of girders) and the moving load case type by the section cut values of the LLD factors (ex-terior moment, ex(ex-terior shear, in(ex-terior moment and in(ex-terior shear LLD factors). This ensures that dead load is shared evenly by all girders, while live load is distributed based on the LLD factors.

3 - 6 AASHTO LRFD 2007

The program then completes a stress check and a check of the shear and the moment for each section cut selected for design.

3.1.4.1 Stress Check

At the Section Cut being analyzed, the girder stresses at all stress output points are read from CSiBridge for every virtual COMBO generated. To ensure that live load demands are shared equally irrespective of lane eccentricity by all girders, CSiBridge uses averaging when calculating the girder stresses. It cal-culates the stresses on a beam by integrating axial and M3 moment demands on all the beams in the entire section cut and dividing the demands by the number of girders. Similarly, P and M3 forces in the composite slab are integrated and stresses are calculated in the individual tributary areas of the slab by dividing the total slab demand by the number of girders.

When stresses are read from analysis into design, the stresses are multiplied by

n (where n is number of girders) to make up for the reduction applied in the

Virtual Combinations.

3.1.4.2 Shear or Moment Check

At the Section Cut being analyzed, the entire section cut forces are read from CSiBridge for every Virtual COMBO generated. The forces are assigned to in-dividual girders based on their designation. (Forces from two virtual Combina-tionsone for shear and one for momentgenerated for exterior beam are as-signed to both exterior beams, and similarly, Virtual Combinations for interior beams are assigned to interior beams.)

3.1.5 Read Forces/Stresses Directly from Girders

When the method for determining the live load distribution is based on forces read directly from the girders, the method varies based on which Design Check has been specified in the Design Request (see Chapter 4).

3.1.5.1 Stress Check

At the Section Cut being analyzed, the girder stresses at all stress output points are read from CSiBridge for every COMBO specified in the Design Request.

AASHTO LRFD 2007 3 - 7 CSiBridge calculates the stresses on a beam by integrating axial, M3 and M2 moment demands on the beam at the center of gravity of the beam. Similarly P, M3 and M2 demands in the composite slab are integrated at the center of gravi-ty of the slab tributary area.

3.1.5.2 Shear or Moment Check

At the Section Cut being analyzed, the girder forces are read from CSiBridge for every COMBO specified in the Design Request. CSiBridge calculates the demands on a girder by integrating axial, M3 and M2 moment demands on the girder at the center of gravity of the girder.

3.1.6 LLDF Design Example Using Method 2

The AASHTO-LRFD Specifications allow the use of advanced methods of analysis to determine the live load distribution factors. However, for typical bridges, the specifications list equations to calculate the distribution factors for different types of bridge superstructures. The types of superstructures covered by these equations are described in AASHTO LRFD Table 4.6.2.2.1-1. From this table, bridges with concrete decks supported on precast concrete I or bulb-tee girders are designated as cross-section “K.” Other tables in AASHTO LRFD 4.6.2.2.2 list the distribution factors for interior and exterior girders in-cluding cross-section “K.”

The distribution factor equations are largely based on work conducted in the NCHRP Project 12-26 and have been verified to give accurate results com-pared to 3-dimensional bridge analysis and field measurements. The multiple presence factors are already included in the distribution factor equations except when the tables call for the use of the lever rule. In these cases, the computa-tions need to account for the multiple presence factors. The user is providing those as part of the Design Request definition together with wheel spacing, curb to wheel distance and lane width.

Notice that the distribution factor tables include a column with the heading “range of applicability.” The ranges of applicability listed for each equation are based on the range for each parameter used in the study leading to the devel-opment of the equation. When any of the parameters exceeds the listed value in

3 - 8 AASHTO LRFD 2007

the “range of applicability” column, CSiBridge reports the incompliance and excludes the section from design.

AASHTO LRFD Article 4.6.2.2.2d of the specifications states: “In beam-slab bridge cross-sections with diaphragms or cross-frames, the distribution factor for the exterior beam shall not be taken less than that which would be obtained by assuming that the cross-section deflects and rotates as a rigid cross-section.” This provision was added to the specifications because the original study that developed the distribution factor equations did not consider intermediate diaph-ragms. Application of this provision requires the presence of a sufficient num-ber of intermediate diaphragms whose stiffness is adequate to force the cross section to act as a rigid section. For prestressed girders, different jurisdictions use different types and numbers of intermediate diaphragms. Depending on the number and stiffness of the intermediate diaphragms, the provisions of AASH-TO LRFD 4.6.2.2.2d may not be applicable. If the user specifies option “Yes” in the “Diaphragms Present” option the program follows the procedure outlined in the provision AASHTO LRFD 4.6.2.2.2d.

For this example, one deep reinforced concrete diaphragm is located at the midspan of each span. The stiffness of the diaphragm was deemed sufficient to force the cross-section to act as a rigid section; therefore, the provisions of AASHTO LRFD S4.6.2.2.2d apply.

AASHTO LRFD 2007 3 - 9 Required information:

AASHTO Type I-Beam (28/72)

Noncomposite beam area, Ag = 1,085 in 2 Noncomposite beam moment of inertia, Ig = 733,320 in

4

Deck slab thickness, ts = 8 in.

Span length, L = 110 ft.

Girder spacing, S = 9 ft.-8 in.

Modulus of elasticity of the beam, EB = 4,696 ksi Modulus of elasticity of the deck, ED = 3,834 ksi C.G. to top of the basic beam = 35.62 in. C.G. to bottom of the basic beam = 36.38 in. 1. Calculate n, the modular ratio between the beam and the deck.

n = EB E D (AASHTO LRFD 4.6.2.2.1-2) = 4 696 3834 = 1.225

2. Calculate eg, the distance between the center of gravity of the noncompo-site beam and the deck. Ignore the thickness of the haunch in determin-ing eg

eg = NAYT + ts 2 = 35.62 + 8 2 = 39.62 in. 3. Calculate Kg, the longitudinal stiffness parameter.

Kg =

(

)

2 g

n I+Ae (4.6.2.2.1-1)

= 1.225 733 320 1 085 39.62_ + ( )2_=2 984 704 in4

4. Interior girder. Calculate the moment distribution factor for an interior beam with two or more design lanes loaded using AASHTO LRFD Ta-ble S4.6.2.2.2b-1. DM =

(

) (

)

(

)

0.1 0.6 0.2 ₃ 0.075+ S 9.5 S L Kg 12.0Lts

(

) (

0.6

)

0.2

{

( )( )3

}

0.1 0.075 9.667 9.5 9.667 110 2 984 704 12 110 8  = + _{ }   = 0.796 lane (eq. 1)

3 - 10 AASHTO LRFD 2007

5. In accordance with AASHTO LRFD 4.6.2.2.2e, a skew correction factor for moment may be applied for bridge skews greater than 30 degrees. The bridge in this example is skewed 20 degrees, and therefore, no skew correction factor for moment is allowed.

Calculate the moment distribution factor for an interior beam with one design lane loaded using AASHTO LRFD Table 4.6.2.2.2b-1.

DM =

(

) (

)

(

)

0.1 0.4 0.3 ₃ 0.06+ S 14 S L Kg 12.0Lts =

(

) (

)

{

( )( )

}

0.1 0.4 0.3 3 0.06+ 9.667 14 9.667 110 _2984704 12 100 8 _   = 0.542 lane (eq. 2)

Notice that the distribution factor calculated above for a single lane loaded already includes the 1.2 multiple presence factor for a single lane, therefore, this value may be used for the service and strength limit states. However, multiple presence factors should not be used for the fatigue limit state. Therefore, the multiple presence factor of 1.2 for the single lane is required to be removed from the value calculated above to deter-mine the factor used for the fatigue limit state.

6. Skew correction factor for shear.

In accordance with AASHTO LRFD 4.6.2.2.3c, a skew correction factor for support shear at the obtuse corner must be applied to the distribution factor of all skewed bridges. The value of the correction factor is calcu-lated using AASHTO LRFD Table 4.6.2.2.3c-1.

SC =

(

)

0.3 3 1.0+0.20 12.0Lts Kg tanθ =

(

( )( )

)

0.3 3 1.0+0.20 12.0 110 8 2 984 704 tan 20 = 1.047

7. Calculate the shear distribution factor for an interior beam with two or more design lanes loaded using AASHTO LRFD Table S4.6.2.2.3a-1.

DV =

(

) (

)

2 0.2+ S 12 − S 35

AASHTO LRFD 2007 3 - 11 = 0.2+

(

9.667 12

) (

− 9.667 35

)

2

= 0.929 lane

Apply the skew correction factor:

DV = 1.047 0.929( )=0.973 lane (eq. 4)

8. Calculate the shear distribution factor for an interior beam with one de-sign lane loaded using AASHTO LRFD Table S4.6.2.2.3a-1.

DV = 0.36+

(

S 25.0

)

= 0.36+

(

9.667 25.0

)

= 0.747 lane

Apply the skew correction factor:

DV = 1.047 0.747( )

= 0.782 lane (eq. 5)

9. From (1) and (2), the service and strength limit state moment distribution factor for the interior girder is equal to the larger of 0.796 and 0.542 lane. Therefore, the moment distribution factor is 0.796 lane.

From (4) and (5), the service and strength limit state shear distribution factor for the interior girder is equal to the larger of 0.973 and 0.782 lane. Therefore, the shear distribution factor is 0.973 lane.

10. Exterior girder

11. Calculate the moment distribution factor for an exterior beam with two or more design lanes using AASHTO LRFD Table 4.6.2.2.2d-1.

DM = eDVinterior

e = 0.77+de 9.1

where de is the distance from the centerline of the exterior girder to the inside face of the curb or barrier.

3 - 12 AASHTO LRFD 2007

e = 0.77 + 1.83/9.1 = 0.97

DM = 0.97(0.796) = 0.772 lane (eq. (7)

12. Calculate the moment distribution factor for an exterior beam with one design lane using the lever rule in accordance with AASHTO LRFD Ta-ble 4.6.2.2.2d-1.

Figure 3-2 Lever Rule

DM =

[

(3.5 6+ )+3.5 9.667 1.344 wheels 2

]

=

= 0.672 lane (eq. 8)

Notice that this value does not include the multiple presence factor, therefore, it is adequate for use with the fatigue limit state. For service

AASHTO LRFD 2007 3 - 13 and strength limit states, the multiple presence factor for a single lane loaded needs to be included.

DM = 0.672 1.2 ( )

= 0.806 lane (eq. 9) (Strength and Service)

13. Calculate the shear distribution factor for an exterior beam with two or more design lanes loaded using AASHTO LRFD Table 4.6.2.2.3b-1.

DV = eDVinterior where: e = 0.6+de10 = 0.6 1.83 10+ = 0.783 DV = 0.783 0.973 ( ) = 0.762 lane (eq. 10)

14. Calculate the shear distribution factor for an exterior beam with one design lane loaded using the lever rule in accordance with AASHTO LRFD Table 4.6.2.2.3b-1. This value will be the same as the moment distribution factor with the skew correction factor applied.

DV = 1.047 0.806( )

= 0.845 lane (eq. 12) (Strength and Service) Notice that AASHTO LRFD 4.6.2.2.2d includes additional requirements for the calculation of the distribution factors for exterior girders when the girders are connected with relatively stiff cross-frames that force the cross-section to act as a rigid section. As indicated in the introduction, these provisions are applied to this example; the calculations are shown below.

15. Additional check for rigidly connected girders (AASHTO LRFD 4.6.2.2.2d)

3 - 14 AASHTO LRFD 2007

The multiple presence factor, m, is applied to the reaction of the exterior beam (AASHTO LRFD Table 3.6.1.1.2-1)

m1 = 1.20

m2 = 1.00

m3 = 0.85

R = NL Nb+Xext

( )

∑ ∑

e x2 (4.6.2.2.2d-1) where:

R = reaction on exterior beam in terms of lanes NL = number of loaded lanes under consideration

e = eccentricity of a design truck or a design land load from

the center of gravity of the pattern of girders (ft.)

x = horizontal distance from the center of gravity of the

pat-tern of girders to each girder (ft.)

Xext = horizontal distance from the center of gravity of the pat-tern to the exterior girder (ft.) See Figure 1 for dimen-sions.

One lane loaded (only the leftmost lane applied):

R = 1 6+24.167 21( ) _2 24.1672

(

( )2 +(14.52)2+(4.8332)2

)

_ = 0.1667 + 0.310

= 0.477 (Fatigue)

Add the multiple presence factor of 1.2 for a single lane: R = 1.2 0.477 ( )

= 0.572 (Strength) Two lanes loaded:

AASHTO LRFD 2007 3 - 15 = 0.333 + 0.443

= 0.776

Add the multiple presence factor of 1.0 for two lanes loaded: R = 1.0 0.776 ( )

= 0.776 (Strength) Three lanes loaded:

R =

( )

(

( )2 ( )2 ( )2

)

3 6+24.167 21 9 3+ − _2 24.1672 + 14.52 + 4.8332 _ = 0.5 + 0.399

= 0.899

Add the multiple presence factor of 0.85 for three or more lanes loaded: R = 0.85 0.899 ( )

= 0.764 (Strength)

These values do not control over the distribution factors summarized in Design Step 16.

16. From (7) and (9), the service and strength limit state moment distribution factor for the exterior girder is equal to the larger of 0.772 and 0.806 lane. Therefore, the moment distribution factor is 0.806 lane.

From (10) and (12), the service and strength limit state shear distribution factor for the exterior girder is equal to the larger of 0.762 and 0.845 lane. Therefore, the shear distribution factor is 0.845 lane.