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Bridge Superstructure Design AASHTO 2014

CSiBridge

Bridge Superstructure Design AASHTO 2014

ISO BRG102816M8 Rev. 0 Proudly developed in the United States of America October 2016

Copyright

Copyright Computers & Structures, Inc., 1978-2016 All rights reserved. The CSI Logo and CSiBridge are registered trademarks of Computers & Structures, Inc. Watch & LearnTM is a trademark of Computers & Structures, Inc. Adobe and Acrobat are registered trademarks of Adobe Systems Incorported. AutoCAD is a registered trademark of Autodesk, Inc. The computer program CSiBridge and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest with Computers & Structures, Inc. Unlicensed use of these programs or reproduction of documentation in any form, without prior written authorization from Computers & Structures, Inc., is explicitly prohibited.

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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.

Contents

Bridge Superstructure Design 1 Introduction

1.1 Organization 1-1

1.2 Recommended Reading/Practice 1-2

2 Define Loads and Load Combinations

2.1 Load Pattern Types 2-1

2.2 Design Load Combinations 2-4

2.2.1 AASHTO LRFD Code 2-4

2.2.2 AASHTO LRFD Code with Caltrans Amendments 2-4

2.2.3 AASHTO LRFD Code with PennDOT Amendments 2.4

2.3 Default Load Combinations 2-9

i

CSiBridge Superstructure Design

3 Live Load Distribution

3.1 Methods for Determining Live Load Distribution 3-1

3.2 Determine Live Load Distribution Factors 3-2

3.3 Apply LLD Factors 3-3

3.3.1 User Specified 3-4 3.3.2 Calculated by CSiBridge in Accordance

with AASHTO LFRD 3-4 3.3.3 Forces Read Directly from Girders 3-4 3.3.4 Uniformly Distribution to Girders 3-4

3.4 Generate Virtual Combinations 3-5

3.4.1 Stress Check 3-5 3.4.2 Shear or Moment Check 3-6

3.5 Read Forces/Stresses Directly from Girders 3-6

3.5.1 Stress Check 3-6 3.5.2 Shear or Moment Check 3-6

3.6 LLD Factor Design Example Using Method 2 3-7

4 Define a Bridge Design Request

4.1 Name and Bridge Object 4-4

4.2 Check Type 4-4

4.3 Station Range 4-6

4.4 Design Parameters 4-6

4.5 Demand Sets 4-18

4.6 Live Load Distribution Factors 4-18

ii

Contents

5 Design Concrete Box Girder Bridges

5.1 Stress Design AASHTO LFRD 5-2

5.1.1 Capacity Parameters 5-2 5.1.2 Algorithm 5-2 5.1.3 Stress Design Example 5-2

5.2 Flexure Design AASHTO LRFD 5-5

5.2.1 Capacity Parameters 5-5 5.2.2 Variables 5-5 5.2.3 Design Process 5-6 5.2.4 Algorithm 5-7 5.2.5 Flexure Design Example 5-10

5.3 Shear Design AASHTO LRFD 5-15

5.3.1 Capacity Parameters 5-15 5.3.2 Variables 5-15 5.3.3 Design Process 5-17 5.3.4 Algorithm 5-18 5.3.5 Shear Design Example 5-24

5.4 Principal Stress Design, AASHTO LRFD 5-31

5.4.1 Capacity Parameters 5-31 5.4.2 Demand Parameters 5-31

6 Design Multi-Cell Concrete Box Bridges using AMA

6.1 Stress Design 6-2

6.2 Shear Design 6-3

6.2.1 Variables 6-4 6.2.2 Design Process 6-5 6.2.3 Algorithms 6-6

6.3 Flexure Design 6-10

6.3.1 Variables 6-10 6.3.2 Design Process 6-11 6.3.3 Algorithms 6-12

iii


7 Design Precast Concrete Girder Bridges

7.1 Stress Design 7-1

7.2 Shear Design 7-2

7.2.1 Variables 7-3 7.2.2 Design Process 7-5 7.2.3 Algorithms 7-5 7.2.4 Shear Design Example 7-9

7.3 Flexure Design 7-14

7.3.1 Variables 7-15 7.3.2 Design Process 7-16 7.3.3 Algorithms 7-16 7.3.4 Flexure Capacity Design Example 7-20

8 Design Steel I-Beam Bridge with Composite Slab

8.1 Section 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 8-12

8.2.1 Demand Flange Stresses fbu and ff 8-13 8.2.2 Demand Flange Lateral Bending Stress f1 8-14 8.2.3 Depth of the Web in Compression 8-15 8.2.4 Moment Gradient Modifier Cb 8-16

8.3 Strength Design Request 8-16

8.3.1 Flexure 8-16 8.3.2 Shear 8-24

8.4 Service Design Request 8-26

8.5 Web Fatigue Design Request 8-28

8.5.1 Web Fatigue 8-28

iv

Contents

8.5.2 Flange Fatigue 8-29

8.6 Constructability Design Request 8-29

8.6.1 Staged (Steel I Comp Construct Stgd) 8-29 8.6.2 Non-staged (Steel I Comp Construct Non-staged) 8-30 8.6.3 Slab Status vs Unbraced Length 8-30 8.6.4 Flexure 8-31 8.6.5 Shear 8-33

8.7 Section Optimization 8-35

8.8 PennDOT Amendments for DM-4 8-36

9 Design Steel U-Tub Bridge with Composite Slab

9.1 Section Properties 9-1

9.1.1 Yield Moments 9-1 9.1.2 Plastic Moments 9-2 9.1.3 Section Classification and Factors 9-7

9.2 Demand Sets 9-9

9.2.1 Demand Flange Stresses fbu and ff 9-10 9.2.2 Demand Flange Lateral Bending Stress f1 9-11 9.2.3 Depth of the Web in Compression 9-12

9.3 Strength Design Request 9-13

9.3.1 Flexure 9-13 9.3.2 Shear 9-16

9.4 Service Design Request 9-19

9.5 Web Fatigue Design Request 9-20

9.6 Constructability Design Request 9-22

9.6.1 Staged (Steel-U Comp Construct Stgd) 9-22 9.6.2 Non-staged (Steel-U Comp Construct NonStgd) 9-22 9.6.3 Slab Status vs Unbraced Length 9-22

v


9.6.4 Flexure 9-23 9.6.5 Shear 9-27

9.7 Section Optimization 9-30

10 Run a Bridge Design Request

10.1 Description of Example Model 10-2

10.2 Design Preferences 10-3

10.3 Load Combinations 10-3

10.4 Bridge Design Request 10-5

10.5 Start Design/Check of the Bridge 10-6

11 Display Bridge Design Results

11.1 Display Results as a Plot 11-1

11.1.1 Additional Display Examples 11-2

11.2 Display Data Tables 11-7

11.3 Advanced Report Writer 11-8

11.4 Verification 11-11

Bibliography

vi

Chapter 1 Introduction

As the ultimate versatile, integrated tool for modeling, analysis, and design of bridge structures, CSiBridge can apply appropriate code-specific design pro-cesses to concrete box girder bridge design, design when the superstructure in-cludes Precast Concrete Box bridges with a composite slab and steel I-beam or U-tub bridges with composite slabs. The ease with which these tasks can be ac-complished 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 CSiBridge.

1.1 Organization This manual is designed to help you become productive using CSiBridge de-sign in accordance with the available codes when modeling concrete box girder

1 - 1

CSiBridge Bridge Superstructure Design

bridges and precast concrete girder bridges. Chapter 2 describes code-specific design prerequisites. Chapter 3 describes Live Load Distribution Factors. Chapter 4 describes defining the design request, which includes the design re-quest name, a bridge object name (i.e., the bridge model), check type (i.e., the type of design), station range (i.e., portion of the bridge to be designed), design parameters (i.e., overwrites for default parameters) 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 multi-cell 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 composite slab. Chapter 9 describes how to design and opti-mize a steel U-beam bridge with composite slab. Chapter 10 describes how to run a Design Request using an example that applies the AASHTO LRFD code, and Chapter 11 describes design output for the example in Chapter 10, which can be presented graphically as plots, in data tables, and in reports generated using the Advanced 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.csiamerica.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 softwares main menu.

1 - 2 Recommended Reading/Practice

http://www.csiamerica.com/

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 Design > Preference command.

When the code generated load combinations are going to be used, it is important for users to define the load pattern type in accordance with the applicable code. The load pattern type can be defined using the Loads > Load Patterns com-mand. The user options for defining the load pattern types are summarized in the Tables 2-1 and 2-2 for the AASHTO LRFD code.

2.1 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 pat-tern type.

Load Pattern Types 2 - 1


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

Load Pattern Type AASHTO

Reference Description of Load Pattern Creep CR Force effects due to creep

Downdrag DD Downdrag force

Dead, Dead Manufacture, Water DL

DC Dead load of structural components and non-structural attachments

Wearing Surface DW Superimposed dead load of wearing surfaces and utilities

Hor Eearth Pr, Hydrostatic, Passive Earth Pr, Active Earth Pr

EH Horizontal earth pressures

Locked In EL Misc. locked-in force effects resulting from the construction process

Earth Surchr ES Earth surcharge loads

Ver Earth Pr EV Vertical earth pressure

Prestress, Hyperstatic

PS Hyperstatic forces from post-tensioning

Shrinkage SH Force effects due to shrinkage

Table 2-2 TRANSIENT Load Pattern Types Used in the AASHTO LRFD 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

Vessel Collision CV Vessel collision force

Quake EQ Earthquake

Friction FR Friction effects

Ice IC Ice loads

Impact IM Vehicle Dynamic Load Allowance

Vehicle Live LL Vehicular live load

Permit Veh Live LL-P Permit Vehicular live load

Vehicle Fatigue LL-F Fatigue Vehicular live load

Vehicle Deflection LL-D Deflection Vehicular live load

2 - 2 Load Pattern Types

Chapter 2 - Define Loads and Load Combinations

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

CSiBridge Load Pattern Type

AASHTO Reference Description of Load Pattern

LL Surchr LS Live load surcharge

PedestrianLL PL Pedestrian live load

Settlement SE Force effects due settlement

Temp Grad TG Temperature gradient loads

Temperature TU Uniform temperature effects

Water Pr, Stream Flow Bouyancy

WA Water load and stream pressure

Wind - Live Load WL Wind on live load

Wind WS Wind loads on structure

2 - 3


2.2 Design Load Combinations 2.2.1 AASHTO LRFD Code

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 combinations that are required in accordance with the AASHTO LRFD code.

Tables 2-4 and 2-5 shows the maximum and minimum factors for the permanent loads in accordance with the AASHTO LRFD code.

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 combination of the max/min combos.

2.2.2 AASHTO LRFD Code with Caltrans Amendments Table 2-6 shows the load factors and combinations that are required in accord-ance with the AASHTO LRFD code with Caltrans amendments.

2.2.3 AASHTO LRFD Code with PennDOT Amendments Table 2-7 and 2-8 show the load factors and live load vehicles for steel and con-crete girder bridges, respectively, that are required in accordance with the AASHTO LRFD code with PennDOT amendments.

2 - 4 Design Load Combinations


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

TU

SE

EQ

IC

CT

CV

Str I P 1.75 1.00 - - 1.00 0.50/ 1.20

TG SE - - - -

Str II P 1.35 1.00 - - 1.00 0.50/ 1.20

TG SE - - - -

Str III P - 1.00 1.40 - 1.00 0.50/ 1.20

TG SE - - - -

Str IV P - 1.00 - - 1.00 0.50/ 1.20

- - - - - -

Str V P 1.35 1.00 0.40 1.00 1.00 0.50/ 1.20

TG SE - - - -

Ext Ev I P EQ 1.00 - - 1.00 - - - 1.00 - - -

Ext Ev II P 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 1.00/ 1.20

TG SE - - - -

Serv II 1.00 1.30 1.00 - - 1.00 1.00/ 1.20

- - - - -

Serv III 1.00 0.80 1.00 - - 1.00 1.00/ 1.20

TG SE - - - -

Serv IV 1.00 - 1.00 0.70 - 1.00 1.00/ 1.20

- 1.00 - - - -

Fatigue I LL, IM & CE Only

- 1.50 - - - - - - - - - - -

Fatigue II LL, IM & CE Only

- 0.75 - - - - - - - - - - -

Design Load Combinations 2 - 5


Table 2-4 Load Factors for Permanent Loads, P , AASHTO LRFD Code

Type of Load Load Factor

Maximum Minimum DC: Components and Attachments DC: Strength IV only

1.25 1.50

0.90 0.90

DD: Downdrag Piles, Tomlinson Method Piles, Method Drilled Shafts, ONeill and Reese (1999) Method

1.40 1.05 1.25

0.25 0.30 0.35

DW: Wearing Surfaces and Utilities 1.50 0.65 EH: Horizontal Earth Pressure

Active At-Rest AEP for Anchored Walls

1.50 1.35 1.35

0.90 0.90 N/A

EL: Locked in Construction Stresses 1.00 1.00 EV: Vertical Earth Pressure

Overall Stability Retaining Walls and Abutments Rigid Buried Structure Rigid Frames Flexible Buried Structures other than Metal Box Culverts Flexible Metal Box Culverts

1.00 1.35 1.30 1.35 1.95 1.50

N/A 1.00 0.90 0.90 0.90 0.90

ES: Earth Surcharge 1.50 0.75

Table 2-5 Load Factors for Permanent Loads due to Superimposed Deformations, P , AASHTO LRFD Code

Bridge Component

PS CR, SH Superstructures, Segmental Concrete Substructures supporting Segmental Super-structures

1.0

See Table 2-5, DC

Concrete Superstructures, non-segmental 1.0 1.0 Substructures supporting non-segmental Superstructures

Using Ig Using Ieffective

0.5 1.0

0.5 1.0

Steel Substructures 1.0 1.0



Table 2-6 Load Combinations and Load Factors Used in the AASHTO LRFD Code with Caltrans Amendments

Load Combo Limit State

DC DD DW EH EV ES EL PS CR SH

LL IM CE BR PL LS

LL-P IM CE

WA

WS

WL

FR

TU

TU

SE

EQ

IC

CT

CV

Str I P 1.75 - 1.00 - - 1.00 0.50/ 1.20

TG SE - - - -

Str II P - 1.35 1.00 - - 1.00 0.50/ 1.20

TG SE - - - -

Str III P - - 1.00 1.40 - 1.00 0.50/ 1.20

TG SE - - - -

Str IV P - - 1.00 - - 1.00 0.50/ 1.20

- - - - - -

Str V P 1.35 - 1.00 0.40 1.00 1.00 0.50/ 1.20

TG SE - - - -

Ext Ev I 1.00 EQ - 1.00 - - 1.00 - - - 1.00 - - -

Ext Ev II 1.00 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 1.00/ 1.20

TG SE - - - -

Serv II 1.00 1.30 - 1.00 - - 1.00 1.00/ 1.20

- - - - -

Serv III 1.00 0.80 - 1.00 - - 1.00 1.00/ 1.20

TG SE - - - -

Serv IV 1.00 - - 1.00 0.70 - 1.00 1.00/ 1.20

- 1.00 - - - -

Fatigue I LL, IM & CE Only

- 1.75 - - - - - - - - - - - -

Fatigue II LL-P, IM & CE Only

- - 1.00 - - - - - - - - - - -

Design Load Combinations 2 - 7


Table 2-7 Load factors and Live Load Vehicles for Steel Girder Bridge Used in the AASHTO LRFD Code with PennDOT Amendments

Load Combination Limit State DC DW

LL IM CE BR LS

PL WS Design LL Vehicle (Load Type)

Str I 1.25/0.90 1.50/0.65 1.75 - - PHL-93 (LL)

Str IP 1.25/0.90 1.50/0.65 1.35 1.75 - PHL-93 (LL)

Str IA 1.25/0.90 1.50/0.65 1.35 - - PHL-93 (LL)

Str II 1.25/0.90 1.50/0.65 1.35 - - P-82 (LL-P)

Str III 1.25/0.90 1.50/0.65 - - 1.40 -

Str IV 1.5 1.50/0.65 - - - - Str V 1.25/0.90 1.50/0.65 1.35 - 0.40 PHL-93 (LL)

Serv II 1.00 1.00 1.30 - - PHL-93 (LL)

Serv IIA 1.00 1.00 1.00 - - PHL-93 (LL) Serv IIB 1.00 1.00 1.00 - - P-82 (LL-P)

Fatigue I (infinite) LL, IM & CE Only

- - 1.50 - - HS20-30(LL-F)

Fatigue II (finite) LL, IM & CE Only

- - 0.75 - - HS20-30(LL-F)

DEFL LL, IM CE & BR Only

- - 1.00 - - PenDOT Defl Trk (LL-D)

Const/ Uncured Slab 1.25 1.50/0.65 1.50 - 1.25 User Defined (LL)



Table 2-8 Load factors and Live Load Vehicles for Prestressed Concrete Girder Bridge Used in the AASHTO LRFD Code with PennDOT Amendments

Load Combination Limit State DC DW

LL IM CE BR LS

PL CR SH Design LL Vehicle

(Load Type)

Str I 1.25/0.90 1.50/0.65 1.75 - 0.5 PHL-93 (LL)

Str IP 1.25/0.90 1.50/0.65 1.35 1.75 0.5 PHL-93 (LL)

Str IA 1.25/0.90 1.50/0.65 1.35 - 0.5 PHL-93 (LL)

Str II 1.25/0.90 1.50/0.65 1.35 - 0.5 P-82 (LL-P)

Serv I 1.00 1.00 1.00 - 1.00 PHL-93 (LL)

Serv I with PL 1.00 1.00 0.80 1.00 1.00 PHL-93 (LL) Serv III 1.00 1.00 0.80 - 1.00 PHL-93 (LL)

Serv III with PL 1.00 1.00 0.65 1.00 1.00 PHL-93 (LL)

Serv IIIA 1.00 1.00 1.00 - - Controlling PHL-93 (LL) or P-82 (LL-P)

Serv IIIB 1.00 1.00 1.00 - - Controlling PHL-93 (LL) or P-82 (LL-P)

Fatigue I (infinite) LL, IM & CE Only

- - 1.50 - - HS20-30(LL-F)

DEFL LL, IM CE & BR Only

- - 1.00 - - PenDOT Defl Trk (LL-D)

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 Design option, and then choose the amend-ments from the dropdown box if needed. Users may select the desired limit states and load cases using the Code Generated Load Combinations for Bridge Design form. The forms shown in Figure 2-1 to Figure 2-3 illustrate the options when the AASHTO LRFD code with or without amendments has been selected for design.

Default Load Combinations 2 - 9


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

AASHTO LRFD

2 - 10 Default Load Combinations


Figure 2-2 Code-Generated Load Combinations for Bridge Design Form AASHTO LRFD with PennDOT Amendments for Steel Girders



Figure 2-3 Code-Generated Load Combinations for Bridge Design Form AASHTO LRFD with PennDOT Amendments for Concrete Girders

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 using the Home > Display > Show Tables command or by using the Show/Modify button on the Define Combinations form, which is shown in Figure 2-4.

2 - 12 Default Load Combinations


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).


Chapter 3 Live Load Distribution

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.

The live load distribution factors derived using the code-based Method 2 de-scribed in Section 3.1 of this manual are applicable only to superstructures of the following types: precast I- or U-girders with composite slabs, steel I-girders with composite slabs, and multi-cell concrete box girders. These deck section types may also have the live loads distributed based on Methods 1, 3 or 4 de-scribed in Section 3.1 of this manual. Legend: Girder = beam + tributary area of composite slab Section Cut = all girders present in the cross-section at the cut location LLD = Live Load Distribution

3.1 Methods for Determining Live Load Distribution 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.

3 - 1


Method 2 CSiBridge calculates the LLD factors by following procedures out-lined 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 (Method 3, applicable to area and solid models only) or when CSiBridge ap-plies the LLD factors uniformly (Method 4), multiple traffic lanes with rele-vant Multilane Scale Factors should be loaded in accordance with code re-quirements.

3.2 Determine Live Load Distribution Factors At every section cut, the following geometric information is evaluated to de-termine the LLD factors.

span lengththe length of span for which moment or shear is being calculat-ed

the number of girders

girder designationthe first and last girder are designated as exterior girders and the other girders are classified as interior girders

roadway widthmeasured as the distance between curbs/barriers; medians are ignored

3 - 2 Determine Live Load Distribution Factors

Chapter 3 - Live Load Distribution

overhangconsists of the horizontal distance from the centerline of the exte-rior web of the left exterior beam at deck level to the interior edge of the curb or traffic barrier

the beamsincludes 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 slabwhich 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

Youngs modulus for both the slab and the beamsangle of skew support.

CSiBridge then evaluates the longitudinal stiffness parameter, Kg, in accord-ance 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 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 LLD factor method permutations are allowed.

3.3 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.

Apply LLD Factors 3 - 3


3.3.1 User Specified When this method is selected, CSiBridge reads the girder designations (i.e., ex-terior and interior) and assigns live load distribution factors to the individual girders accordingly.

3.3.2 Calculated by CSiBridge in Accordance with AASHTO LRFD 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-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 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 LLD factor values are assigned to indi-vidual girders based on their designation (exterior, interior). The same value equal to the average of the LLD factors calculated for the left and right girders is assigned to both exterior girders. Similarly, all interior girders use the same LLD factors equal to the average of the LLD factors of all of the individual in-terior girders.

3.3.3 Forces Read Directly from Girders When this method is selected, CSiBridge sets the live load distribution factor for all girders to 1.

3.3.4 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

3 - 4 Apply LLD Factors


factors disregarding their designation (exterior, interior) and demand type (shear, moment).

3.4 Generate Virtual Combinations When the method for determining the live load distribution factors is user-specified, code-specified, or uniformly distributed (Methods 1, 2 or 4), CSiBridge generates virtual load combination for every valid section cut se-lected 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 combinations 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 multi-plies 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, exterior shear, interior moment and interior shear LLD factors). This ensures that dead load is shared evenly by all girders, while live load is distributed based on the LLD factors.

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

3.4.1 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.

Generate Virtual Combinations 3 - 5


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.

3.4.2 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-tionsone for shear and one for momentgenerated for exterior beam are as-signed to both exterior beams, and similarly, Virtual Combinations for interior beams are assigned to interior beams.)

3.5 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).

3.5.1 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. 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.

3.5.2 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 - 6 Read Forces/Stresses Directly from Girders


3.6 LLD Factor 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 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 dia-phragms. Application of this provision requires the presence of a sufficient number of intermediate diaphragms whose stiffness is adequate to force the cross section to act as a rigid section. For prestressed girders, different jurisdic-tions use different types and numbers of intermediate diaphragms. Depending on the number and stiffness of the intermediate diaphragms, the provisions of

LLD Factor Design Example Using Method 2 3 - 7


AASHTO 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.

Figure 3-1 General Dimensions

Required information:

AASHTO Type I-Beam (28/72) Noncomposite beam area, Ag = 1,085 in2 Noncomposite beam moment of inertia, Ig = 733,320 in4 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.

3 - 8 LLD Factor Design Example Using Method 2


n = B DE E (AASHTO 2014 4.6.2.2.1-2)

= 4696 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 + 2st = 35.62 + 8 2 = 39.62 in.

3. Calculate Kg, the longitudinal stiffness parameter.

Kg = ( )2gn I Ae+ (4.6.2.2.1-1)

= ( )2 41.225 733 320 1 085 39.62 2 984 704 in + =

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 = ( ) ( ) ( )0.10.6 0.2 30.075 9.5 12.0g sS S L K Lt+

( ) ( ) ( )( ){ } 0.10.6 0.2 30.075 9.667 9.5 9.667 110 2 984 704 12 110 8 = + = 0.796 lane (eq. 1)

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 = ( ) ( ) ( )0.10.4 0.3 30.06 14 12.0g sS S L K Lt+

= ( ) ( ) ( )( ){ } 0.10.4 0.3 30.06 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 load-ed 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 = ( )0.331.0 0.20 12.0 tans gLt K +

= ( )( )( )0.331.0 0.20 12.0 110 8 2 984 704 tan20+ = 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 = ( ) ( )20.2 12 35S S+

= ( ) ( )20.2 9.667 12 9.667 35+

= 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 25.0S+

= ( )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 9.1de+

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

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 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 10de+

= 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)

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 = ( ) 2L b extN N X e x+ (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 = ( ) ( ) ( ) ( )( )2 2 21 6 24.167 21 2 24.1672 14.52 4.8332 + + + = 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:

R = ( ) ( ) ( ) ( )( )2 2 22 6 24.167 21 9 2 24.1672 14.52 4.8332 + + + + = 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 23 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.

Table 3-1 Summary of Service and Strength Limit State Distribution Factors -- AASHTO LRFD

Load Case

Moment interior beams

Moment exterior beams

Shear interior beams

Shear exterior beams

Distribution factors from Tables in 4.6.2.2.2

Multiple lanes load-ed 0.796 0.772 0.973 0.762

Single lane loaded 0.542 0.806 0.782 0.845

Additional check for rigidly connected girders

Multiple lanes load-ed NA 0.776 NA 0.776

Single lane loaded NA 0.572 NA 0.572

Design Value 0.796 0.806 0.973 0.845 Value reported by CSiBridge 0.796 0.807 0.973 0.845


Chapter 4 Define a Bridge Design Request

This chapter describes the Bridge Design Request, which is defined using the Design/Rating > Superstructure Design > Design Requests command.

Each Bridge Design Request is unique and specifies which bridge object is to be designed, the type of check to be performed (e.g., concrete box stress, pre-cast composite stress, and so on), the station range (i.e., the particular zone or portion of the bridge that is to be designed), the design parameters (i.e., param-eters that may be used to overwrite the default values automatically set by the program) and demand sets (i.e., the load combination[s] to be considered). Multiple Bridge Design Requests may be defined for the same bridge object.

Before defining a design request, the applicable code should be specified using the Design/Rating > Superstructure > Preferences command. Currently, the AASHTO STD 2002, AASHTO LRFD 2007, AASHTO LRFD 2012, CAN/CSA S6, EN 1992, and Indian IRC codes are available for the design of a concrete box girder; the AASHTO 2007 LRFD, AASHTO LRFD 2012, AASHTO LRFD 2014, CAN/CSA S6, EN 1992, and Indian IRC codes are available for the design of a Precast I or U Beam with Composite Slab; the AASHTO LFRD 2007, AASHTO LRFD 2012, AASHTO LRFD 2014, CAN/CSA S6, and EN 1992-1-1 are available for Steel I-Beam with Compo-site Slab superstructures; and the AASHTO LRFD 2012 and AASHTO LRFD 2014 are available for a U tub bridge with a composite slab.

Name and Bridge Object 4 - 1


Figure 4-1 shows the Bridge Design Request form when the bridge object is for a concrete box girder bridge, and the check type is concrete box stress. Figure 4-2 shows the Bridge Design Request form when the bridge object is for a Composite I or U girder bridge and the check type is precast composite stress. Figure 4-3 shows the Bridge Design Request form when the bridge object is for a Steel I-Beam bridge and the check type is composite strength.

Figure 4-1 Bridge Design Request - Concrete Box Girder Bridges

4 - 2 Name and Bridge Object

Chapter 4 - Define a Bridge Design Request

Figure 4-2 Bridge Design Request - Composite I or U Girder Bridges

Figure 4-3 Bridge Design Request Steel I Beam with Composite Slab

Name and Bridge Object 4 - 3


4.1 Name and Bridge Object Each Bridge Design Request must have unique name. Any name can be used.

If multiple Bridge Objects are used to define a bridge model, select the bridge object to be designed for the Design Request. If a bridge model contains only a single bridge object, the name of that bridge object will be the only item avail-able from the Bridge Object drop-down list.

4.2 Check Type The Check Type refers to the type of design to be performed and the available options depend on the type of bridge deck being modeled.

For a Concrete Box Girder bridge, CSiBridge provides the following check type options:

AASHTO STD 2002

Concrete Box Stress

AASHTO LRFD

Concrete Box Stress

Concrete Box Flexure

Concrete Box Shear and Torsion

Concrete Box Principal

CAN/CSA S6, and EN 1992-1-1 and IRC: 112

Concrete Box Stress


Concrete Box Shear

For Multi-Cell Concrete Box Girder bridge, CSiBridge provides the following check type options:

4 - 4 Name and Bridge Object


AASHTO LRFD, CAN/CSA S6, EN 1992-1-1, and IRC: 112

Concrete Box Stress


Concrete Box Shear

For bridge models with precast I or U Beams with Composite Slabs, CSiBridge provides three check type options, as follows:

AASHTO LRFD, CAN/CSA S6, EN 1992-1-1, and IRC: 112

Precast Comp Stress

Precast Comp Shear

Precast Comp Flexure

For bridge models with steel I-beam with composite slab superstructures, CSiBridge provides the following check type option:

AASHTO LRFD

Steel Comp Strength

Steel Comp Service

Steel Comp Fatigue

Steel Comp Constructability Staged

Steel Comp Constructability NonStaged

EN 1994-2:2005

Steel Comp Ultimate

Steel Comp Service Stresses

Steel Comp Service Rebar


Check Type 4 - 5



For bridge models with steel U-tub with composite slab superstructures, CSiBridge provides the following check type option:

AASHTO LRFD

Steel Comp Strength

Steel Comp Service

Steel Comp Fatigue



The bold type denotes the name that appears in the check type drop-down list. A detailed description of the design algorithm can be found in Chapter 5 for concrete box girder bridges, in Chapter 6 for multi-cell box girder bridges, in Chapter 7 for precast I or U beam with composite slabs, and in Chapter 8 for steel I-beam with composite slab.

4.3 Station Range The station range refers to the particular zone or portion of the bridge that is to be designed. The user may choose the entire length of the bridge, or specify specific zones using station ranges. Multiple zones (i.e., station ranges) may be specified as part of a single design request.

When defining a station range, the user specifies the Location Type, which de-termines if the superstructure forces are to be considered before or at a station point. The user may choose the location type as before the point, after the point, or both.

4.4 Design Parameters Design parameters are overwrites that can be used to change the default values set automatically by the program. The parameters are specific to each code,

4 - 6 Station Range


deck type, and check type. Figure 4-4 shows the Superstructure Design Re-quest Parameters form.

Figure 4-3 Superstructure Design Request Parameters form

Table 4-1 shows the parameters for concrete box girder bridges. Table 4-2 shows the parameters for multi-cell concrete box bridges. Table 4-3 shows the parameters applicable when the superstructure has a deck that includes precast I or U girders with composite slabs. Table 4-4 shows the parameters applicable when the superstructure has a deck that includes steel I-beams.

Table 4-1 Design Request Parameters for Concrete Box Girders AASHTO STD 2002

Concrete Box Stress Resistance Factor - multiplies both compression and tension stress limits Multiplier on cf to calculate the compression stress limit

Multiplier on sqrt( cf ) to calculate the tension stress limit, given in the units specified

The tension limit factor may be specified using either MPa or ksi units for cf and the resulting tension limit

Design Parameters 4 - 7


Table 4-1 Design Request Parameters for Concrete Box Girders

AASHTO LRFD Concrete Box Stress

Concrete Box Stress, PhiC, - Resistance Factor that multi-plies both compression and tension stress limits

Concrete Box Stress Factor Compression Limit - Multiplier on cf to calculate the compression stress limit

Concrete Box Stress Factor Tension Limit Units - Multiplier on sqrt( cf ) to calculate the tension stress limit, given in the units specified

Concrete Box Stress Factor Tension Limit - The tension limit factor may be specified using either MPa or ksi units for cf and the resulting tension limit

Concrete Box Shear Concrete Box Shear, PhiC, - Resistance Factor that multi-plies both compression and tension stress limits

Concrete Box Shear, PhiC, Lightweight Resistance Factor that multiplies nominal shear resistance to obtain factored resistance for light-weight concrete

Include Resal (Hunching-girder) shear effects Yes or No. Specifies whether the component of inclined flexural com-pression or tension, in the direction of the applied shear, in variable depth members shall or shall not be considered when determining the design factored shear force in accord-ance with Article 5.8.6.2.

Concrete Box Shear Rebar Material - A previously defined rebar material label that will be used to determine the area of shear rebar required

Longitudinal Torsional Rebar Material - A previously defined rebar material that will be used to determine the area of lon-gitudinal torsional rebar required


Concrete Box Flexure, PhiC, - Resistance Factor that multi-plies both compression and tension stress limits

Concrete Box Principal

See the Box Stress design parameter specifications

CAN/CSA S6 Concrete Box Stress Multi-Cell Concrete Box Stress Factor Compression Limit -

Multiplier on cf to calculate the compression stress limit

Multi-Cell Concrete Box Stress Factor Tension Limit - The tension limit factor may be specified using either MPa or ksi units for cf and the resulting tension limit

Concrete Box Shear Phi Concrete c -- Resistance factor for concrete (see CSA

4 - 8 Design Parameters


Table 4-1 Design Request Parameters for Concrete Box Girders Clause 8.4.6)

Phi PT p -- Resistance factor for tendons (see CSA Clause 8.4.6)

Cracking Strength Factor Multiplies sqrt( cf ) to obtain cracking strength

EpsilonX Negative Limit -- Longitudinal negative strain limit (see Clause 8.9.3.8)

EpsilonX Positive Limit -- Longitudinal positive strain limit (see Clause 8.9.3.8)

Tab slab rebar cover Distance from the outside face of the top slab to the centerline of the exterior closed transverse torsion reinforcement

Web rebar cover Distance from the outside face of the web to the centerline of the exterior closed transverse torsion re-inforcement

Bottom Slab rebar cover Distance from the outside face of the bottoms lab to the centerline of the exterior closed trans-verse torsion reinforcement

Shear Rebar Material A previously defined rebar material label that will be used to determine the required area of transverse rebar in the girder

Longitudinal Rebar Material A previously defined rebar material that will be used to determine the required area of longitudinal rebar in the girder


Phi Concrete c -- Resistance factor for concrete (see CSA Clause 8.4.6)

Phi Pt p -- Resistance factor for tendons (see CSA Clause 8.4.6)

Phi Rebar s -- Resistance factor for reinforcing bars (see CSA Clause 8.4.6)

Eurocode EN 1992 Concrete Box Stress Compression limit Multiplier on fc k to calculate the com-

pression stress limit Tension limit Multiplier on fc k to calculate the tension

stress limit Concrete Box Shear Gamma C for Concrete Partial factor for concrete. Gamma C for Rebar Partial safety factor for reinforcing

steel. Gamma C for PT Partial safety factor for prestressing

steel. Angle Theta The angle between the concrete compression

strut and the beam axis perpendicular to the shear force.



Table 4-1 Design Request Parameters for Concrete Box Girders The value must be between 21.8 degrees and 45 degrees.

Factor for PT Duct Diameter Factor that multiplies post-tensioning duct diameter when evaluating the nominal web thickness in accordance with section 6.2.3(6) of the code. Typical values 0.5 to 1.2.

Factor for PT Transmission Length Factor for the trans-mission length of the post tensioning used in shear re-sistance equation 6.4 of the code. Typical value 1.0 for post tensioning.

Inner Arm Method The method used to calculate the inner lever arm z of the section (integer).

Inner Arm Limit Factor that multiplies the depth of the sec-tion to get the lower limit of the inner lever arm z of the sec-tion.

Effective Depth Limit Factor that multiplies the depth of the section to get the lower limit of the effective depth to the ten-sile reinforcement d of the section.

Type of Section Type of section for shear design. Determining Factor Nu1 Method that will be used to calcu-

late the 1 factor. Factor Nu1 1 factor Determining Factor AlphaCW Method that will be used to

calculate the cw factor. Factor AlphaCW cw factor Factor Fywk Multiplier of vertical shear rebar characteristic

yield strength to obtain a stress limit in shear rebar used in 6.10.aN. Typical value 0.8 to 1.0.

Shear Rebar Material A previously defined material label that will be used to determine the required area of transverse rebar in the girder.

Longitudinal Rebar Material A previously defined material that will be used to determine the required area of longitudi-nal rebar in the girder.


Gamma c for Concrete Partial safety factor for concrete.

Gamma c for Rebar Partial safety factor for reinforcing steel.

Gamma c for PT Partial safety factor for prestressing steel. PT pre-strain Factor to estimate pre-strain in the post-

tensioning. Multiplies fpk to obtain the stress in the tendons after losses. Typical value between 0.4 and 0.9.



Table 4-2 Design Request Parameters for Multi-Cell Concrete Box

AASHTO LRFD

Multi-Cell Concrete Box Stress

Multi-Cell Concrete Box Stress, PhiC, - Resistance Factor that multiplies both compression and tension stress limits

Multi-Cell Concrete Box Stress Factor Compression Limit - Multiplier on cf to calculate the compression stress limit

Multi-Cell Concrete Box Stress Factor Tension Limit Units - Multiplier on sqrt ( )cf to calculate the tension stress limit, given in the units specified


Multi-Cell Concrete Box Shear

Multi-Cell Concrete Box Shear, PhiC, - Resistance Factor that multiplies both compression and tension stress limits

Multi-Cell Concrete Box Shear, PhiC, Lightweight Re-sistance Factor that multiplies nominal shear resistance to obtain factored resistance for light-weight concrete

Negative limit on strain in nonprestressed longitudinal rein-forcement in accordance with section 5.8.3.4.2; Default Value = -0.4x10-3, Typical value(s): 0 to -0.4x10-3

Positive limit on strain in nonprestressed longitudinal rein-forcement - in accordance with section 5.8.3.4.2; Default Value = 6.0x10-3, Typical value(s): 6.0x10-3

PhiC for Nu - Resistance Factor used in equation 5.8.3.5-1; Default Value = 1.0, Typical value(s): 0.75 to 1.0

Phif for Mu - Resistance Factor used in equation 5.8.3.5-1; Default Value = 0.9, Typical value(s): 0.9 to 1.0

Specifies which method for shear design will be used ei-ther Modified Compression Field Theory (MCFT) in accord-ance with 5.8.3.4.2 or Vci Vcw method in accordance with 5.8.3.4.3. Currently only the MCFT option is available.

A previously defined rebar material label that will be used to determine the required area of transverse rebar in the girder.

A previously defined rebar material that will be used to de-termine the required area of longitudinal rebar in the girder

Multi-Cell Concrete Box Flexure

Multi-Cell Concrete Box Flexure, PhiC, - Resistance Factor that multiplies both compression and tension stress limits

CAN/CSA S6



Table 4-2 Design Request Parameters for Multi-Cell Concrete Box Multi-Cell Concrete Box Stress

Multi-Cell Concrete Box Stress Factor Compression Limit - Multiplier on cf to calculate the compression stress limit


Multi-Cell Concrete Box Shear

Highway Class The highway class shall be determined in accordance with CSA Clause 1.4.2.2, Table 1.1 for the av-erage daily traffic and average daily truck traffic volumes for which the structure is designed




Cracking Strength Factor -- Multiplies sqrt( cf ) to obtain cracking strength



Shear Rebar Material A previously defined rebar material that will be used to determine the required area of trans-verse rebar in the girder

Longitudinal Rebar Material A previously defined rebar material that will be used to determine the required area of longitudinal rebar in the girder

Multi-Cell Concrete Box Flexure

Highway Class The highway class shall be determined in accordance with CSA Clause 1.4.2.2, Table 1.1 for the av-erage daily traffic and average daily truck traffic volumes for which the structure is designed




Eurocode EN 1992 Multi-Cell Concrete Box Stress

Compression limit Multiplier on fc k to calculate the com-pression stress limit



Table 4-2 Design Request Parameters for Multi-Cell Concrete Box Tension limit Multiplier on fc k to calculate the tension

stress limit Multi-Cell Concrete Box Shear

Gamma C for Concrete Partial factor for concrete.

Gamma C for Rebar Partial safety factor for reinforcing steel.

Gamma C for PT Partial safety factor for prestressing steel.

Angle Theta The angle between the concrete compression strut and the beam axis perpendicular to the shear force. The value must be between 21.8 degrees and 45 degrees.

Factor for PT Duct Diameter Factor that multiplies post-tensioning duct diameter when evaluating the nominal web thickness in accordance with section 6.2.3(6) of the code. Typical values 0.5 to 1.2.

Factor for PT Transmission Length Factor for the trans-mission length of the post tensioning used in shear re-sistance equation 6.4 of the code. Typical value 1.0 for post tensioning.





late the 1 factor. Factor Nu1 1 factor Determining Factor AlphaCW Method that will be used to




Longitudinal Rebar Material A previously defined material that will be used to determine the required area of longitudi-nal rebar in the girder.



Table 4-2 Design Request Parameters for Multi-Cell Concrete Box Multi-Cell Concrete Box Flexure



Gamma c for PT Partial safety factor for prestressing steel. PT pre-strain Factor to estimate pre-strain in the post-

tensioning. Multiplies fpk to obtain the stress in the tendons after losses. Typical value between 0.4 and 0.9.

Table 4-3 Design Request Parameters for Precast I or U Beams AASHTO LRFD Precast Comp Stress

Precast Comp Stress, PhiC, - Resistance Factor that multi-plies both compression and tension stress limits

Precast Comp Stress Factor Compression Limit - Multiplier on fc to calculate the compression stress limit

Precast Comp Stress Factor Tension Limit Units - Multiplier on sqrt(fc) to calculate the tension stress limit, given in the units specified

Precast Comp Stress Factor Tension Limit - The tension limit factor may be specified using either MPa or ksi units for fc and the resulting tension limit

Precast Comp Shear

PhiC, - Resistance Factor that multiplies both compression and tension stress limits

PhiC, Lightweight Resistance Factor that multiplies nominal shear resistance to obtain factored resistance for light-weight concrete

Negative limit on strain in nonprestressed longitudinal rein-forcement in accordance with section 5.8.3.4.2; Default Value = -0.4x10-3, Typical value(s): 0 to -0.4x10-3



Table 4-3 Design Request Parameters for Precast I or U Beams

Positive limit on strain in nonprestressed longitudinal rein-forcement - in accordance with section 5.8.3.4.2; Default Val-ue = 6.0x10-3, Typical value(s): 6.0x10-3

PhiC for Nu - Resistance Factor used in equation 5.8.3.5-1; Default Value = 1.0, Typical value(s): 0.75 to 1.0

Phif for Mu - Resistance Factor used in equation 5.8.3.5-1; Default Value = 0.9, Typical value(s): 0.9 to 1.0

Specifies what method for shear design will be used - either Modified Compression Field Theory (MCFT) in accordance with 5.8.3.4.2 or Vci Vcw method in accordance with 5.8.3.4.3 Currently only the MCFT option is available.

A previously defined rebar material label that will be used to determine the required area of transverse rebar in the girder

A previously defined rebar material that will be used to deter-mine the required area of longitudinal rebar in the girder


Precast Comp Flexure, PhiC, - Resistance Factor that multi-plies both compression and tension stress limits

CAN/CSA S6 Precast Comp Stress

Precast Comp Stress Factor Compression Limit - Multiplier on fc to calculate the compression stress limit

Precast Comp Stress Factor Tension Limit - The tension limit factor may be specified using either MPa or ksi units for fc and the resulting tension limit

Precast Comp Shear

Highway Class The highway class shall be determined in accordance with CSA Clause 1.4.2.2, Table 1.1 for the aver-age daily traffic and average daily truck traffic volumes for which the structure is designed




Cracking Strength Factor -- Multiplies sqrt( cf ) to obtain cracking strength



Shear Rebar Material A previously defined rebar material label that will be used to determine the required area of trans-verse rebar in the girder.



Table 4-3 Design Request Parameters for Precast I or U Beams

Longitudinal Rebar Material A previously defined rebar ma-terial that will be used to determine the required area of longi-tudinal rebar n the girder


Highway Class The highway class shall be determined in accordance with CSA Clause 1.4.2.2, Table 1.1 for the aver-age daily traffic and average daily truck traffic volumes for which the structure is designed




Eurocode EN 1992 Precast Comp Stress

Compression limit Multiplier on fc k to calculate the com-pression stress limit

Tension limit Multiplier on fc k to calculate the tension stress limit

Precast Comp Shear

Gamma C for Concrete Partial factor for concrete.

Gamma C for Rebar Partial safety factor for reinforcing steel.

Gamma C for PT Partial safety factor for prestressing steel. Angle Theta The angle between the concrete compression

strut and the beam axis perpendicular to the shear force. The value must be between 21.8 degrees and 45 degrees.

Factor for PT Transmission Length Factor for the transmis-sion length of the post tensioning used in shear resistance equation 6.4 of the code. Typical value 1.0 for post tension-ing.





late the 1 factor. Factor Nu1 1 factor



Table 4-3 Design Request Parameters for Precast I or U Beams Determining Factor AlphaCW Method that will be used to




Longitudinal Rebar Material A previously defined material that will be used to determine the required area of longitudinal rebar in the girder.




Gamma c for PT Partial safety factor for prestressing steel.

PT pre-strain Factor to estimate pre-strain in the post-tensioning. Multiplies fpk to obtain the stress in the tendons af-ter losses. Typical value between 0.4 and 0.9.

Table 4-4 Design Request Parameters for Steel I-Beam AASHTO LRFD Steel I-Beam - Strength

Resistance factor Phi for flexure Resistance factor Phi for shear Do webs have longitudinal stiffeners? Use Stage Analysis load case to determine stresses on com-

posite section? Multiplies short term modular ratio (Es/Ec) to obtain long-term

modular ratio Use AASHTO, Appendix A to determine resistance in nega-

tive moment regions? Steel I Beam Comp -Service

Use Stage Analysis load case to determine stresses on com-posite section?

Shored Construction? Does concrete slab resist tension? Multiplies short term modular ratio (Es/Ec) to obtain long-term

modular ratio



Table 4-4 Design Request Parameters for Steel I-Beam Steel-I Comp - Fatigue

There are no user defined design request parameters for fatigue

Steel I Comp Construct Stgd

Resistance factor Phi for flexure

Resistance factor Phi for shear Resistance factor Phi for Concrete in Tension Do webs have longitudinal stiffeners?

Concrete modulus of rupture factor in accordance with

AASHTO LRFD Section 5.4.2.6, factor that multiplies sqrt of f'c to obtain modulus of rupture, default value 0.24 (ksi) or 0.63 (MPa), must be > 0

The modulus of rupture factor may be specified using either MPa or ksi units

Steel I Comp Construct Non Stgd

Resistance factor Phi for flexure

Resistance factor Phi for shear Resistance factor Phi for Concrete in Tension Do webs have longitudinal stiffeners? Concrete modulus of rupture factor in accordance with

AASHTO LRFD Section 5.4.2.6, factor that multiplies sqrt of f'c to obtain modulus of rupture, default value 0.24 (ksi) or 0.63 (MPa), must be > 0

The modulus of rupture factor may be specified using either MPa or ksi units

4.5 Demand Sets A demand set name is required for each load combination that is to be consid-ered in a design request. The load combinations may be selected from a list of user defined or default load combinations that are program determined (see Chapter 2).

4.6 Live Load Distribution Factors When the superstructure has a deck that includes precast I or U girders with composite slabs or multi-cell boxes, Live Load Distribution Factors can be specified. LLD factors are described in Chapter 3.

4 - 18 Demand Sets

Chapter 5 Design Concrete Box Girder Bridges

This chapter describes the algorithms applied in accordance with the AASHTO LRFD 2014 (AASHTO LRFD) for design and stress check of the superstruc-ture of a concrete box type bridge deck section.

When interim revisions of the codes are published by the relevant authorities, and (when applicable) they are subsequently incorporated into CSiBridge, the program gives the user an option to select what type of interims shall be used for the design. The interims can be selected by clicking on the Code Prefer-ences button.

In CSiBridge, when distributing loads for concrete box design, the section is always treated as one beam; all load demands (permanent and transient) are distributed evenly to the webs for stress and flexure and proportionally to the slope of the web for shear. Torsion effects are always considered and assigned to the outer webs and the top and bottom slabs.

With respect to shear and torsion check, in accordance with AASHTO Article 5.8.6, torsion is considered.

The user has an option to select No Interims or YYYY Interims on the Bridge Design Preferences form. The form can be opened by clicking the Code Preferences button.

5 - 1


The revisions published in the 2015 interims were incorporated into the Flex-ure Design.

5.1 Stress Design AASHTO LRFD

5.1.1 Capacity Parameters PhiC Resistance Factor; Default Value = 1.0, Typical value: 1.0 The compression and tension limits are multiplied by the C factor

FactorCompLim cf multiplier; Default Value = 0.4; Typical values: 0.4 to 0.6. The cf is multiplied by the FactorCompLim to obtain the compression limit.

FactorTensLim cf multiplier; Default Values = 0.19 (ksi), 0.5(MPa);

Typical values: 0 to 0.24 (ksi), 0 to 0.63 (MPa). The cf is multiplied by the FactorTensLim to obtain the tension limit.

5.1.2 Algorithm The stresses are evaluated at three points at the top fiber and three points at the bottom fiber: extreme left, Bridge Layout Line, and extreme right. The stresses assume linear distribution and take into account axial (P) and both bending moments (M2 and M3).

The stresses are evaluated for each demand set (Chapter 4). If the demand set contains live load, the program positions the load to capture extreme stress at each of the evaluation points.

Extremes are found for each point and the controlling demand set name is rec-orded.

The stress limits are evaluated by applying the Capacity Parameters (see Sec-tion 5.2.1).

5 - 2 Stress Design AASHTO LRFD

Chapter 5 - Design Concrete Box Girder Bridges

5.1.3 Stress Design Example Cross Section: AASHTO Box Beam, Type BIII-48 as shown in Figure 5-1

Figure 5-1 AASHTO LRFD Stress Design, AASHTO Box Beam, Type BIII-

48 Concrete unit weight, wc = 0.150 kcf Concrete strength at 28 days, cf = 5.0 ksi Design span = 95.0 ft Prestressing strands: in. dia., seven wire, low relaxation Area of one strand = 0.153 in2 Ultimate strength fpu = 270.0 ksi Yield strength fpy = 0.9 ksi fpu = 243 ksi Modulus of elasticity, Ep = 28500 ksi

Stress Design AASHTO LRFD 5 - 3


Figure 5-2 Reinforcement, AASHTO LRFD Stress Design

AASHTO Box Beam, Type BIII-48 Reinforcing bars: yield strength, fy = 60.0 ksi

Section Properties A = area of cross-section of beam = 826 in2 h = overall depth of precast beam = 39 in I = moment of inertia about centroid of the beam = 170812 in4 yb,yt = distance from centroid to the extreme

bottom (top) fiber of the beam = 19.5 in

Demand forces from Dead and PT (COMB1) at station 570: P = 856.51 kip M3 = 897.599 kip-in

Top fiber stress =

3top top856.51 897.59919.5 0.9344 ksi826 170812

P M yA I

= = =

5 - 4 Stress Design AASHTO LRFD


Bottom fiber stress =

3bot bot856.51 897.59919.5 1.139ksi826 170812

P M yA I

= + = + =

Stresses reported by CSiBridge: top fiber stress envelope = 0.9345 ksi

bottom fiber stress envelope = 1.13945 ksi

5.2 Flexure Design AASHTO LRFD

5.2.1 Capacity Parameters PhiC Resistance Factor; Default Value = 1.0, Typical value: 1.0 The nominal flexural capacity is multiplied by the resistance factor to obtain factored resistance.

5.2.2 Variables APS Area of PT in the tension zone

AS Area of reinforcement in the tension zone

Aslab Area of the slab

bslab Effective flange width = horizontal width of the slab, measured from out to out

bwebeq Equivalent thickness of all webs in the section

dP Distance from the extreme compression fiber to the centroid of the pre-stressing tendons

dS Distance from the extreme compression fiber to the centroid of rebar in the tension zone

fps Average stress in prestressing steel (AASHTO LRFD eq. 5.7.3.1.1-1)

fpu Specified tensile strength of prestressing steel (area weighted average of all tendons in the tensile zone)

Flexure Design AASHTO LRFD 5 - 5


fpy Yield tensile strength of prestressing steel (area weighted average of all tendons in the tensile zone)

fy Yield strength of rebar

k PT material constant (AASHTO LRFD eq. 5.7.3.1.1-2)

Mn Nominal flexural resistance

Mr Factored flexural resistance

tslabeq Equivalent thickness of the slab

1 Stress block factor, as specified in AASHTO LRFD 2015 Interim Sec-tion 5.7.2.2.

1 Stress block factor, as specified in AASHTO LRFD Section 5.7.2.2.

Resistance factor for flexure

5.2.3 Design Process The derivation of the moment resistance of the section is based on the approx-imate stress distribution specified in AASHTO LRFD Article 5.7.2.2. The nat-ural relationship between concrete stress and strain is considered satisfied by an equivalent rectangular concrete compressive stress block of 1 over a zone bounded by the edges of the cross-section and a straight line located par-allel to the neutral axis at the distance a = 1c from the extreme compression fiber. If the AASHTO LRFD 2015 interim is selected the factor 1 is taken as 0.85 for specified compressive strengths not exceeding 10.0 ksi. For specified concrete compressive strengths exceeding 10.0ksi, 1is reduced at rate of 0.02 for each 1.0ksi of strength in excess of 10.0ksi, except that 1 is not taken less than 0.75. For AASHTO LRFD no interim the 1is always taken as 0.85 inde-pendent of concrete compressive strength. The factor The distance c is meas-ured perpendicular to the neutral axis. The factor 1 is taken as 0.85 for con-crete strengths not exceeding 4.0 ksi. For concrete strengths exceeding 4.0 ksi, 1 is reduced at a rate of 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi, except that 1 is not to be taken to be less than 0.65.

5 - 6 Flexure Design AASHTO LRFD


The flexural resistance is determined in accordance with AASHTO LRFD Par-agraph 5.7.3.2. The resistance is evaluated for bending about horizontal axis 3 only. Separate capacity is calculated for positive and negative moment. The capacity is based on bonded tendons and mild steel located in the tension zone as defined in the Bridge Object. Tendons and mild steel reinforcement located in the compression zone are not considered. It is assumed that all defined ten-dons in a section, stressed or not, have fpe (effective stress after loses) larger than 0.5 fpu (specified tensile strength). If a certain tendon should not be consid-ered for the flexural capacity calculation, its area must be set to zero.

The section properties are calculated for the section before skew, grade, and superelevation have been applied. This is consistent with the demands being reported in the section local axis. It is assumed that the effective width of the flange (slab) in compression is equal to the width of the slab.

5.2.4 Algorithm At each section:

All section properties and demands are converted from CSiBridge model units to N, mm.

The equivalent slab thickness is evaluated based on the slab area and slab width, assuming a rectangular shape.

slabslabeq

slab

Atb

=

The equivalent web thickness is evaluated as the summation of all web hori-zontal thicknesses.

web

webeq web1

n

b b=

The 1 stress block factor is evaluated in accordance with AASHTO LRFD 5.7.2.2 based on section cf

For AASHTO LRFD 2015 Interim

Flexure Design AASHTO LRFD 5 - 7


> 10.0, 1 = 0.85 10

1.00.02; 0.75

else 1 = 0.85

For AASHTO LRFD No Interim

1 = 0.85

The 1 stress block factor is evaluated in accordance with AASHTO LRFD 5.7.2.2 based on section cf

If cf > 28 MPa, then 128max 0.85 0.05; 0.65 ;

7cf =

else 1 0.85. =

The tendon and rebar location, area, and material are read. Only bonded ten-dons are processed; unbonded tendons are ignored.

Tendons and rebar are split into two groups depending on which sign of mo-ment they resistnegative or positive. A tendon or rebar is considered to re-sist a positive moment when it is located outside of the top fiber compression stress block and is considered to resist a negative moment when it is located outside of the bottom fiber compression stress block. The compression stress block extends over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = 1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis.

For each tendon group, an area weighted average of the following values is determined:

sum of the tendon areas, APS

distance from the extreme compression fiber to the centroid of prestress-ing tendons, dP

specified tensile strength of prestressing steel, fpu

constant k (AASHTO LRFD eq. 5.7.3.1.1-2)

5 - 8 Flexure Design AASHTO LRFD


For each rebar group, the following values are determined:

sum of the tension rebar areas, As

distance from the extreme compression fiber to the centroid of the ten-sion rebar, ds

The distance c between the neutral axis and the compressive face is evaluated in accordance with (AASHTO LRFD eq. 5.7.3.1.1-4).

1 1 slab

PS PU s s

puc PS

p

A f A fc ff b kA

d

+=

+

The distance c is compared against requirement of Section 5.7.2.1 to verify if stress in mild reinforcement fs can be taken as equal to fy. The limit on ratio c/ds is calculated depending on what kind of code and its interim are speci-fied in the Bridge Design Preferences form as shown in the table below:

Code AASHTO LRFD 2012 No Interims

AASHTO LRFD 2012 with 2013 Interims or

later

0.6 0.0030.003 +

where the compression control strain limit is per AASHTO LRFD 2013 Interims table C5.7.2.1-1 When the limit is not satisfied the stress in mild reinforcement fs is re

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