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Bridge Superstructure Design AASHTO 2012

CSiBridge®

Bridge Superstructure Design AASHTO 2012

ISO BRG102816M7 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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DISCLAIMER

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.

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 2-3

2.3 Default Load Combinations 2-5

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

i

CSiBridge Superstructure Design

3.3.2 Calculated by CSiBridge in Accordance with AASHTO LFRD 2012 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

5 Design Concrete Box Girder Bridges

5.1 Stress Design AASHTO LFRD-2012 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-2012 5-5

5.2.1 Capacity Parameters 5-5 5.2.2 Variables 5-5 5.2.3 Design Process 5-6

ii

Contents

5.2.4 Algorithm 5-7 5.2.5 Flexure Design Example 5-10

5.3 Shear Design AASHTO LRFD-2012 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-2012 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

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

iii


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 Fatigue Design Request 8-28

8.5.1 Web Fatigue 8-28 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 8-32

8.7 Section Optimization 8-35

iv

Contents

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 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

v


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 bridges with composite slabs. The ease with which these tasks can be accom-plished makes CSiBridge the most productive bridge design package in the in-dustry.

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 2007 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 gen-erated 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 software’s 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 De-sign > Preference command.

When the code generated load combinations are going to be used, it is im-portant for users to define the load pattern type in accordance with the applica-ble code. The load pattern type can be defined using the Loads > Load Pat-terns command. The user options for defining the load pattern types are sum-marized 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 pattern type.

Load Pattern Types 2 - 1


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

VESSEL COLLISION CV Vessel collision force

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 - 2 Load Pattern Types

Chapter 2 - Define Loads and Load Combinations

2.2 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

LL IM CE

WA

WS

WL

FR

TU

TU

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 1.00 γEQ - 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

γTG γSE - - - -

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

γTG γSE - - - -

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

- 1.00 - - - -

Fatigue I-LL, IM & CE Only

- 0.875/1.75

- - - - - - - - - - - -

Fatigue II-LL, IM

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

Design Load Combinations 2 - 3


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, Pγ , AASHTO LRFD 2007 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, α Tomlinson Method Piles, λ Method Drilled Shafts, O’Neill 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, Pγ , AASHTO LRFD 2007 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 Superstruc-tures

Using Ig Using Ieffective

0.5

0.5

2 - 4 Design Load Combinations


Table 2-5 Load Factors for Permanent Loads due to Superimposed Deformations, Pγ , AASHTO LRFD 2007 Code

Bridge Component

PS CR, SH 1.0 1.0

Steel Substructures 1.0 1.0 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.

2.3 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.

Default Load Combinations 2 - 5


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 using the Show/Modify button on the Define Combinations form, which is shown in Figure 2-2.

2 - 6 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).

Default Load Combinations 2 - 7

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

Young’s modulus for both the slab and the beamsangle of skew support.

CSiBridge then evaluates the longitudinal stiffness parameter, Kg, in accord-ance with AASHTO 2012 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 2012 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 2012 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 2012 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 individu-al 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 as-signed 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 interior 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-2012 Specifications allow the use of advanced methods of anal-ysis to determine the live load distribution factors. However, for typical bridg-es, the specifications list equations to calculate the distribution factors for dif-ferent types of bridge superstructures. The types of superstructures covered by these equations are described in AASHTO 2012 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 2012 4.6.2.2.2 list the distribution factors for interior and exterior girders including 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 2012 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 2012 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 2012 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 2012 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 2012 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 2012 Table 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 2012 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 2012 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 2012 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 2012 Table 4.6.2.2.3c-1.

SC = ( )0.331.0 0.20 12.0 tans gLt K θ+

= ( )( )( )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 2012 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 2012 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 2012 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 2012 Table 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 2012 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 2012 Table 4.6.2.2.3b-1. This value will be the same as the moment dis-tribution factor with the skew correction factor applied.

DV = ( )1.047 0.806

= 0.845 lane (eq. 12) (Strength and Service)

Notice that AASHTO 2012 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 2012 4.6.2.2.2d)

The multiple presence factor, m, is applied to the reaction of the exterior beam (AASHTO 2012 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 2012

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, 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, AASH-TO LRFD 2012, CAN/CSA S6, and EN 1992-1-1 are available for Steel I-Beam with Composite Slab superstructures; and the AASHTO LRFD 2012 is 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 2007

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 2007, 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 2007, 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 2007 and 2012

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

Steel Comp Constructability Staged

Check Type 4 - 5


Steel Comp Constructability NonStaged

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

4 - 6 Station Range


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 2007 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 ϕc -- 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 ϕp -- 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 ϕc -- Resistance factor for concrete (see CSA Clause 8.4.6)

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

Phi Rebar ϕs -- 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 η1 factor. Factor Nu1 – η1 factor Determining Factor AlphaCW – Method that will be used to

calculate the αcw factor. Factor AlphaCW – αcw 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 2007

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 η1 factor. Factor Nu1 – η1 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 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 f′c to calculate the compression stress limit

Precast Comp Stress Factor Tension Limit Units - Multiplier on sqrt(f′c) 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 f′c 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 f′c 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 f′c 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 η1 factor. Factor Nu1 – η1 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 2007 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 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 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 2012 for design and stress check of the superstructure 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 “2013 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 2013 interims were incorporated into the Flex-ure Design.

5.1 Stress Design AASHTO LRFD-2012

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 φC 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-2012

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 LRFD 2012 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: ½ 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-2012 5 - 3


Figure 5-2 Reinforcement, LRFD 2012 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 top

856.51 897.59919.5 0.9344 ksi826 170812

P M yA I

− −σ = − = − = −

5 - 4 Stress Design AASHTO LRFD-2012


Bottom fiber stress =

3bot bot

856.51 897.59919.5 1.139ksi826 170812

P M yA I

− −σ = + = + = −

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

bottom fiber stress envelope = −1.13945 ksi

5.2 Flexure Design AASHTO LRFD-2012

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-2012 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-2012 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-2012 eq. 5.7.3.1.1-2)

Mn Nominal flexural resistance

Mr Factored flexural resistance

tslabeq Equivalent thickness of the slab

β1 Stress block factor, as specified in AASHTO-2012 Section 5.7.2.2.

φ 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-2012 Article 5.7.2.2. The natu-ral relationship between concrete stress and strain is considered satisfied by an equivalent rectangular concrete compressive stress block of 0.85 cf ′ 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 = β1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis. The factor β1 is taken as 0.85 for concrete strengths not exceeding 4.0 ksi. For concrete strengths exceeding 4.0 ksi, β1 is reduced at a rate of 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi, except that β1 is not to be taken to be less than 0.65.

The flexural resistance is determined in accordance with AASHTO-2012 Para-graph 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.

5 - 6 Flexure Design AASHTO LRFD-2012


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 β1 stress block factor is evaluated in accordance with AASHTO-2012 5.7.2.2 based on section cf ′

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

7cf ′ − β = −

else 1 0.85.β =

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 = β1c 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-2012 eq. 5.7.3.1.1-2)

= −

2 1.04 py

pu

fk

f

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-2012 eq. 5.7.3.1.1-4).

1 slab0.85

PS PU s s

puc PS

p

A f A fcf

f b kAd

+=

′β +

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 interims are specified in the Bridge Design Preferences form as shown in the table below:



Code AASHTO LRFD 2012 No Interims

AASHTO LRFD 2012 with 2013 Interims

𝑐𝑐𝑑𝑑𝑠𝑠

≤ 0.6 0.0030.003 + 𝜀𝜀𝑐𝑐𝑐𝑐

where the compression control strain limit 𝜀𝜀𝑐𝑐𝑐𝑐 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 reduced to satisfy the requirement of Section 5.7.2.1.

The distance c is compared to the equivalent slab thickness to determine if the section is a T-section or rectangular section.

– If 1 slabeq ,c tβ > the section is a T-section.

If the section is a T-section, the distance c is recalculated in accordance with (AASHTO-2012 eq. 5.7.3.1.1-3).

( )slab webeq slabeq

1 webeq

0.85

0.85

PS PU s s c

puc PS

pt

A f A f f b b tc

ff b kA

y

′+ − −=

′ β +

Average stress in prestressing steel fps is calculated in accordance with (AASHTO-2012 eq. 5.7.3.1.1-1).

= − 1PS PU

p

cf f kd

Nominal flexural resistance Mn is calculated in accordance with (AASHTO-2012 eq. 5.7.3.2.2-1).

– If the section is a T-section,

( ) slabeq1 1 1slab webeq slabeq0.85 ;

2 2 2 2n PS PS p S s s ctc c cM A f d A f d f b b t

β β β ′= − + − + − −

else



1 1

2 2n PS PS p S s sc cM A f d A f d .β β = − + −

Factored flexural resistance is obtained by multiplying Mn by φ.

Mr = φMn

Extreme moment M3 demands are found from the specified demand sets and the controlling demand set name is recorded.

5.2.5 Flexure Design Example Cross Section: AASHTO Box Beam, Type BIII-48, as shown in Figure 5-3.

Concrete unit weight, wc = 0.150 kcf Concrete strength at 28 days, cf ′ = 5.0 ksi (~34.473 MPa) Design span = 95.0 ft Prestressing strands: ½ 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 = 28 500 ksi

Reinforcing bar yield strength, fy = 60.0 ksi



Figure 5-3 LRFD 2012 Flexure Design Cross-Section, AASHTO Box Beam, Type BIII-48

Figure 5-4 Reinforcement, LRFD 2012 Flexure Design

Cross-Section, AASHTO Box Beam, Type BIII-48



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

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

slabslabeq

slab

48 5.5 5.5in48

Atb

×= = =

Value reported by CSiBridge = 5.5 in

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

web

webeq web1

5 5 10 inn

b b= = + =∑


Tendons are split into two groups depending on which sign of moment they resistnegative or positive. A tendon is considered to resist a positive mo-ment 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 lo-cated parallel to the neutral axis at the distance a = β1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis.


– sum of the tendon areas, ( ) 2bottom 0.153 6 23 4.437inPTA = + =



Value reported by CSiBridge = 4.437 in2

– distance from the center of gravity of the tendons to the extreme com-

pression fiber, bottom23 2 6 439 36.586 in

23 6PTy × + ×= − =

+

Value reported by CSiBridge = 19.5 + 17.0862 = 36.586 in

– specified tensile strength of prestressing steel, 270 kippuf =

Value reported by CSiBridge = 270 kip

– constant k (AASHTO-2012 eq. 5.7.3.1.1-2)

2432 1.04 2 1.04 0.28270

py

pu

fk

f = − = − =

Value reported by CSiBridge = 0.28

The β1 stress block factor is evaluated in accordance with AASHTO-2012 5.7.2.2 based on section .cf ′

– If cf ′ > 28 MPa, then

128max 0.85 0.05;0.65

734.473 28max 0.85 0.05;0.65 0.80376

7

cf ′ − β = −

− = − =

Value calculated by CSiBridge = 0.8037 (not reported)

The distance c between the neutral axis and the compressive face is evaluated in accordance with (AASHTO-2012 eq. 5.7.3.1.1-4).

1 slab

27036.586

0.85

4.437 270 6.91in0.85 5 0.8037 48 0.28 4.437

PT pu

puc PT

pt

A fc

ff b kA

y

=′β +

×= =

× × × + ×

Value calculated by CSiBridge = 6.919 in (not reported)



The distance c is compared to the equivalent slab thickness to determine if the section is a T-section or a rectangular section.

– If 1 slabeq 6.91 0.80376 5.56 in 5.5inc tβ > → × = > , the section is a T-section.

Value reported by CSiBridge, section = T-section

– If the section is a T-section, the distance c is recalculated in accordance with (AASHTO-2012 eq. 5.7.3.1.1-3).

slab webeq slabeq

1 webeq

27036.586

0.85 ( )

0.85

4.437 270 0.85 5(48 10)5.5 7.149in0.85 5 0.8037 10 0.28 4.437

PT pu c

puc PT

pt

A f f b b tc

ff b kA

y

′− −= =

′β +

× − × −=

× × × + ×



7.1491 270 1 0.28 255.23ksi36.586ps pu

pt

cf f ky

= − = − =

Value reported by CSiBridge = 255.228 ksi

Nominal flexural resistance Mn is calculated in accordance with (AASHTO-2012 5.7.3.2.2-1).

– If the section is a T-section, then

( )

( )

slabeq1 1slab webeq slabeq0.85

2 2 27.149 0.803764.437 255.228 36.586

27.149 0.80376 5.50.85 5 48 10 5.5

2 238287.42 kip-in

n PT ps PT ctc cM A f y f b b t

β β ′= − + − −

× = × × − +

× × − −

=

Value calculated by CSiBridge = 38287.721 kip-in (not reported)




1.0 38287.42 38287.42 kip-inr nM M= φ = × = Value reported by CSiBridge = 38287.721 kip-in

5.3 Shear Design AASHTO LRFD-2012

5.3.1 Capacity Parameters PhiC – Resistance Factor; Default Value = 0.9, Typical value: 0.7 to 0.9. The nominal shear capacity of normal weight concrete sections is multiplied by the resistance factor to obtain factored resistance.

PhiC (Lightweight) – Resistance Factor for light-weight concrete; Default Val-ue = 0.7, Typical values: 0.7 to 0.9. The nominal shear capacity of light-weight concrete sections is multiplied by the resistance factor to obtain factored re-sistance.

Include Resal (haunched girder) Shear Effect – Typical value: Yes. Specifies whether the component of inclined flexural compression or tension, in the di-rection of the applied shear, in variable depth members shall or shall not be considered when determining the design factored shear force.

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 label that will be used to determine the required area of longitudinal torsional rebar.

5.3.2 Variables A Gross area of the section

AO Area enclosed by the shear flow path, including the area of holes, if any

Al Area of longitudinal torsion reinforcement

Shear Design AASHTO LRFD-2012 5 - 15


Avsweb Area of shear reinforcement in web per unit length

Avtweb Area of transverse torsion reinforcement in web per unit length

b Minimum horizontal gross width of the web (not adjusted for ducts)

bv Minimum effective horizontal width of the web adjusted for the pres-ence of ducts

be Minimum effective normal width of the shear flow path adjusted to ac-count for the presence of ducts

dv Effective vertical height of the section = max(0.8×h, distance from the extreme compression fiber to the center of gravity of the tensile PT)

CGtop, CGbot Distance from the center of gravity of the section to the top and bottom fiber

h Vertical height of the section

ph Perimeter of the polygon defined by the centroids of the longitudinal chords of the space truss resisting torsion

uuuu TMVP ,, 32, Factored demand forces and moments per section

t Minimum normal gross width of the web (not adjusted for ducts) = ( )webcosb α

tv Minimum effective normal width of the web = ( )webcosvb α

αweb Web angle of inclination from the vertical

φ Resistance factor for shear

κweb Distribution factor for the web

λ Normal or light-weight concrete factor

5 - 16 Shear Design AASHTO LRFD-2012


5.3.3 Design Process The shear resistance is determined in accordance with AASHTO-2012 Para-graph 5.8.6 (Shear and Torsion for Segmental Box Girder Bridges). The proce-dure is not applicable to discontinuity regions and applies only to sections where it is reasonable to assume that plane sections remain plane after loading. The user should select for design only those sections that comply with the pre-ceding assumptions by defining appropriate station ranges in the Bridge Design Request (see Chapter 4).

If the option to consider real effects is activated, the component of the inclined flexural compression or tension in the direction of the demand shear in variable depth members is considered when determining the design section shear force (AASHTO-2012 Paragraph 5.8.6.1).

The section design shear force is distributed into individual webs assuming that the vertical shear that is carried by a web decreases with increased inclination of the web from vertical. Section torsion moments are assigned to external webs and slabs.

The rebar area and ratio are calculated using measurements normal to the web. Thus, vertical shear forces are divided by cos(alpha_web). The rebar area cal-culated is the actual, normal cross-section of the bars. The rebar ratio is calcu-lated using the normal width of the web, tweb = bweb × cos(alpha_web).

The effects of ducts in members are considered in accordance with paragraph 5.8.6.1 of the code. In determining the web or flange effective thickness, be, one-half of the diameter of the ducts is subtracted. All defined tendons in a sec-tion, stressed or not, are assumed to be grouted. Each tendon at a section is checked for presence in the web or flange, and the minimum controlling effec-tive web and flange thicknesses are evaluated.

The tendon duct is considered as having effect on the web or flange effective thickness even if only part of the duct is within the element boundaries. In such cases, the entire one-half of the tendon duct diameter is subtracted from the el-ement thickness.

If several tendon ducts overlap in one flange or web (when projected on the horizontal axis for flange, or when projected on vertical axis for the web), the diameters of ducts are added for the sake of evaluation of the effective thick-



ness. In the web, the effective web thickness is calculated at the top and bottom of each duct; in the flange, the effective thickness is evaluated at the left and right sides of the duct.

The Shear and Torsion Design is completed first on a per web basis. Rebar needed for individual webs is then summed and reported for the entire section. The D/C ratio is calculated for each web. Then the shear area of all webs is summed and the entire section D/C is calculated. Therefore, the controlling section D/C does not necessarily match the controlling web D/C (in other words, other webs can make up the capacity for a “weak” web).

5.3.4 Algorithm All section properties and demands are converted from CSiBridge model

units to N, mm.

If the option to consider resal effects is activated, the component of the in-clined flexural compression or tension in the direction of the demand shear in variable depth members is evaluated as follows:

– Inclination angles of the top and bottom slabs are determined

slab top2 slab top1slab top

2 1arctan

y yStat Stat

− α = −

slabbot2 slabbot1slabbot

2 1arctan

y yStat Stat

− α = −

where

slab top2 slab top1,y y vertical coordinate of the center of gravity of the top slab at stations 1 and 2. The y origin is assumed to be at the top of the section and the + direction is up.

1 2,Stat Stat stations of adjacent sections. When the section being analyzed is “Before,” the current section station is Stat2; when the section being analyzed is “After,” the current section station is Stat1. Therefore, the statement 1 2Stat Stat< is always valid.

The magnitudes of normal forces in slabs are determined as follows:



3slab top slab top slab top

3

u uP MP A dA I

= −

3slabbot slabbot slabbot

3

u uP MP A dA I

= +

where slab top slabbot,d d are distances from the center of gravity of the section to the center of gravity of the slab (positive).

The magnitudes of vertical components of slab normal forces are determined as follows:

resal top slab top slab toptanP P α=

resalbot slabbot slabbottanP P α=

On the basis of the location and inclination of each web, the per-web demand values are evaluated.

Location Outer Web Inner Web

Vuweb Tuweb Vuweb Tuweb

Shear and Torsion Check

2 resal top resalbot

web

abs( )cos

uV P P κα

+ + × Abs(Tu)


web

abs( )cos

uV P P κα

+ + × 0

where ( )( )web

web webweb1

cos | |

cos | |n

ακ

α=∑

Evaluate effective thicknesses:

Evaluate dv bv be tv

– If bv ≤ 0, then

web web flag flagWebPassFlag 2, 0; 0; 0; 2; 2vs vt vs vtD A A A AC

= = = = = =

proceed to report web results

– If be < 0, then SectionPassFlag = 2.



Evaluate design :cf ′

cf ′ min( ,cf ′ 8.3 MPa)

Evaluate the stress variable K:

– Calculate the extreme fiber stress:

bot bot3

33P M CGA I

σ = + top top3

33P M CGA I

σ = − ( )tens top botmax ,σ = σ σ

– If tens 0.5 ,ccf ′>σ then K = 1; else

| |

1 ,0.166 c

PAK

f= +

′×

where K < 2.

Evaluate Vc per web (shear capacity of concrete):

web 0.1663 .c c v vV K f b d′= λ (AASHTO-2012 5.8.6.5-3)

Evaluate Vs per web (shear force that is left to be carried by rebar):

web webweb .u c

sV VV − φ

=φ

– If web 0,sV < then web 0;vsA =

else webweb .s

vsy v

VAf d

=

Verify the minimum reinforcement requirement:

– If web 0.35vs yA t f< (AASHTO-2012 eq. 5.8.2.5-2), then

web 0.35vs yA t f= and webflag 0;sA =

else webflag 1.vsA =

Evaluate the nominal capacities:



web webs vs y vV A f d=

web web webn c sV V V= +

Evaluate the shear D/C for the web:

web

web.

u

s v v c

VDC b d f

φ = ′

Evaluate Tcr (AASHTO-2012 eq. 5.8.6.3-2):

00.166 2 .cr c eT K f A b′=

Evaluate torsion rebar:

– If web1 ,3u crT T< φ then:

flag 0vtA =

web 0vtA =

0lA =

Torsion Effects Flag = 0;

else:

flag 1vtA =

webweb

0 2u

vty

TAA f

=φ

web

0 long2u h

ly

T pAA f

=φ

Torsion Effects Flag = 1.

Evaluate the combined shear and torsion D/C for the web:



web web

0

web

2 .1.25

u u

v v e

t c

V TD b d A bC f

+φ φ =

′

Evaluate the controlling D/C for the web:

– If web web

,s t

D DC C

>

then Ratio Flag = 0;

else

Ratio Flag = 1

web webmax , .

s t

D D DC C C

=

– If 1,DC> then Web Pass Flag = 1;

else

Web Pass Flag = 0.

Assign web rebar flags where the rebar flag convention is:

Flag = 0 – rebar governed by minimum code requirement

Flag = 1 – rebar governed by demand

Flag = 2 – rebar not calculated since the web bv< 0

Flag = 3 – rebar not calculated since the web is not part of the shear flow path for torsion

Evaluate entire section values:

section webc cV V=∑

section webs sV V=∑

section webn nV V=∑

section webvs vsA A=∑



section webvt vtA A=∑

sectionl lA A=

Evaluate entire section D/C:

web web1

web

1

section.

n uv

v vn

v

s c

Vtb dtD

C f

φ

= ′

∑∑

This is equivalent to:

web

1

sec

| |un

v v

s tion c

Vt dD

C f

φ = ′

∑

and

web0

1

section

| | | |2

.1.25

u un

ev v

t c

V TA bt dD

C f

+φφ =

′∑

Evaluate controlling D/C for section:

– If section section

,s t

D DC C

>

then Ratio Flag = 0 else Ratio Flag = 1

section sectionmax , .

s t

D D DC C C

=

– If 1,DC> then Section Pass Flag = 1;

else

Section Pass Flag = 0.

Assign section design flags where flag convention is:



Flag = 0 – Section Passed all code checks

Flag = 1 – Section D/C > 1

Flag = 2 – Section be < 0 (section invalid)

5.3.5 Shear Design Example Cross Section: AASHTO Box Beam, Type BIII-48, as shown in Figure 5-5.

Figure 5-5 Shear Design Example, AASHTO Box Beam, Type BIII-48

φ = 0.9 Concrete unit weight, wc = 0.150 kcf λ = 1.0 Concrete strength at 28 days, f ′c = 5.0 ksi (~34.473 MPa) Design span = 95.0 ft Prestressing strands: ½ in. dia., seven wire, low relaxation Area of one strand = 0.153 in2 Ultimate strength fpu = 270.0 ksi Yield strength fpy = 0.9 fpu = 243 ksi Modulus of elasticity, Ep = 28500 ksi

Reinforcing bars: yield strength, fy = 60.0 ksi (~413.68 MPa)



Section Properties A = area of cross-section of beam = 826 in2 (~532902 mm2) h = overall depth of precast beam = 39 in (~990.6 mm) I = moment of inertia about

centroid of the beam = 170812 in4 (~71097322269 mm4) yb,yt = distance from centroid to the

extreme bottom (top) fiber of the beam = 19.5 in (~495.3 mm)

Aslabtop= Aslabbot = 48×5.5 = 264 in2 (~170322 mm2) Ao = (48 − 5) × (39 − 5.5) = 1440.5 in2 (~929353 mm2) Ph = 2 × (48 − 5 + 39 − 5.5) = 153 in (~3886.2 mm)

Demand forces from Dead and PT (COMB1) at station 114 before: P = −800 kip (~ −3560 E+03 N) M3 = −7541 kip-in (~ −852 E+06 Nmm) V2 = −33 kip (~ −148.3 E+03 N) T = 4560 kip-in (515.2 E+06 Nmm)

Figure 5-6 Shear Design Example Reinforcement

AASHTO Box Beam, Type BIII-48




On the basis of the location and inclination of each web, the per-web demand values are evaluated.

Location Outer Web Inner Web

Vuweb Tuweb Vuweb Tuweb

Shear and Torsion Check


web

abs( )cos

abs(148.3E 03 0 0) 1 74151.9cos0

uV P P

N

+ + × κ=

α+ + + ×

=

Abs(Tu)=515.2E+06 N/A 0 N/A

where ( )( )

( )( )

webweb web 2

web1 1

cos | | cos | 0 |0.5

cos | | cos | 0 |n

ακ = = =

α∑ ∑

Evaluate the effective shear flow path thicknesses:

firstweb lastweb topslab botslabmin( , , , )min(127,127,139.7,139.7) 127mm

e v vb t t t t=

= =

Evaluate the effective web width and normal thickness:

Since the web is vertical, bv = tv = 127 mm.

Evaluate the effective depth:

Since M3 < 0 then

bot topmax(0.8 , )max(0.8 990.6,495.3 419.1) 914.4mm

v PTd h y y= +

= × + =

Evaluate design :cf ′

( ) ( )′ ′= = =min ,8.3MPa min 34.473,8.3MPa 5.871c cf f

Evaluate stress variable K:

Calculate the extreme fiber stress



bot bot3 3560E 03 852 E 06 495.3 12.616MPa.

33 532902 71097322269P M CGA I

− + − +σ = + = + = −

top top3 3560E 03 852 E 06 495.3 0.745MPa

33 532902 71097322269P M CGA I

− + − +σ = − = − = −

tens top botmax( , ) max( 12.61, 0.745) 0.745MPaσ = σ σ = − − = −

If tens 0.5 ,cf ′σ > then K = 1→ false;

else

− +

= + = + =×′×

| 3560E 03 || |5329021 1 2.8

0.166 5.8710.166 c

PAK

f

where K < 2; therefore K = 2.

Evaluate Vc per web (shear capacity of concrete; AASHTO-2012 5.8.6.5-3):

web 0.1663 0.1663 2 1.0 5.871 127 914.4226781N.

c c v vV K f b dλ ′= = × × × × ×

=

Evaluate Vs per web (shear force that is left to be carried by the rebar):

web webweb

74151.9 0.9 226781 144392N.0.9

u cs

V VV − φ − ×= = = −

φ

If web 0,sV < then web 0vsA = → true;

else webweb .s

vsy v

VAf d

=

Verify minimum reinforcement requirement:

– If web 0.35vs yA t f< (AASHTO-2012 eq. 5.8.2.5-2), then → true

2web

0.35 1270.35 0.10745mm / mm413.68vs yA t f ×

= = = and webflag 0;sA =

else webflag 1.vsA =

Evaluate the nominal capacities:



web web 0.10745 413.68 914.4 40645Ns vs y vV A f d= = × × =

web web web 226781 40645 267426Nn c sV V V= + = + =

Evaluate the shear D/C for the web:

web

web

74151.90.9 0.1208

127 914.4 5.871

u

s v v c

VDC b d f

φ = = = × × ′

Evaluate Tcr (AASHTO-2012 eq. 5.8.6.3-2):

00.166 2 0.166 2 5.871 2 929353 127460 147 419 Nmm

cr c eT K f A b′= = × × × × ×

=

Evaluate the torsion rebar:

– If web1 1515.2E6 0.9 460E63 3u crT T< φ => < × → false, then:

flag 1vtA =

2webweb

0

515.2E6 0.7444mm / mm2 0.9 929352 2 413.68

uvt

y

TAA f

= = =φ × × ×

2web

0 long

515.2E6 3886.2 2893mm2 0.9 929352 2 413.68

u hl

y

T pAA f

×= = =φ × × ×

Torsion Effects Flag = 1.

Evaluate the combined shear and torsion D/C for the web:

web web

0

web

74151.9 515.2E62 0.9 127 914.4 0.9 2 929352 127

1.25 5.8711.250.427.

u u

v v e

t c

V TD b d A bC f

+ +φ φ × × × × ×= = × ′

=



Evaluate the controlling D/C for the web:

– If web web

,s t

D DC C

>

then Ratio Flag = 0 → false;

else

Ratio Flag =1 → true

( )web web

max , max 0.1208, 0.427 0.427.s t

D D DC C C

= = =

– If 1,DC

> then Web Pass Flag =1 → true;

else

Web Pass Flag = 0.

Assign web rebar flags where rebar flag convention is:

Flag = 0 – rebar governed by minimum code requirement

Flag = 1 – rebar governed by demand => true

Flag = 2 – rebar not calculated since web bv< 0

Flag = 3 – rebar not calculated since the web is not part of the shear flow path for torsion.

Evaluate the entire section values:

section web 2 226781 453562Nc cV V= = × =∑

section web 2 40645 81290Ns sV V= = × =∑

section web 2 267426 534852 Nn nV V= = × =∑ 2

section web 2 0.10745 0.2149 mm / mmvs vsA A= = × =∑ 2

section web 2 0.7444887 1.48898mm / mmvt vtA A= = × =∑ 2

section 2893mml lA A= =



Evaluate entire section D/C:

web web1

web

1

section.

n uv

v vn

v

s c

Vtb dtD

C f

φ

= ′

∑∑ This is equivalent to:

web 2

1 1

section

| | 148.3E30.9 127 914.4

0.12085.871

un

v v

s c

Vt dD

C f

φ × = = = ′

∑ ∑

and

web0

1

section

2

1

| | | |2

1.25148.3E3 515.2E6

0.9 2 929352 1270.9 127 914.40.427.

1.25 5.871

u un

ev v

t c

V TA bt dD

C f

+φφ =

′

+× × ××

= =×

∑

∑

Evaluate the controlling D/C for the section:

– If section section

,s t

D DC C

>

then Ratio Flag = 0 → false;

else Ratio Flag = 1 →true

( )section section

max , max 0.1208,0.427 0.427.s t

D D DC C C

= = =

– If 1,DC> then SectionPassFlag = 1 → true;

else

Section Pass Flag = 0.



Assign the section design flags where the flag convention is:

Flag = 0 – Section Passed all code checks → true

Flag = 1 – Section D/C >1

Flag = 2 – Section be < 0 (section invalid)

5.4 Principal Stress Design, AASHTO LRFD-2012

5.4.1 Capacity Parameters PhiC – Resistance Factor; Default Value = 1.0, Typical value: 1.0. The compression and tension limits are multiplied by the φC 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 tension limit.

5.4.2 Demand Parameters FactorCompLim – Percentage of the basic unit stress for compression service design; Default value = 1.0; Typical values 1.0 to 1.5. The demand compres-sive stresses are divided by the FactorCompLim factor. This way the control-ling stress can be selected and compared against one compression limit.

FactorTensLim – Percentage of the basic unit stress for tension service design; Default value = 1.0; Typical values 1.0 to 1.5. The demand tensile stresses are divided by the FactorCompLim factor. This way the controlling stress can be selected and compared against one tension limit.

Principal Stress Design, AASHTO LRFD-2012 5 - 31

Chapter 6 Design Multi-Cell Concrete Box Bridges using AMA

This chapter describes the algorithms used by CSiBridge for design checks when the superstructure has a deck that includes cast-in-place multi-cell con-crete box design and uses the Approximate Method of Analysis, as described in the AASHTO LRFD 2012 code.


For MulticellConcBox design in CSiBridge, each web and its tributary slabs are designed separately. Moments and shears due to live load are distributed to individual webs in accordance with the factors specified in AASHTO-2012 Ar-ticles 4.6.2.2.2 and 4.6.2.2.3 of the code. To control if the section is designed as “a whole-width structure” in accordance with AASHTO-2012 Article 4.6.2.2.1 of the code, select “Yes” for the “Diaphragms Present” option. When CSiBridge calculates the Live Load Distribution (LLD) factors, the section and span qualification criteria stated in AASHTO-2012 4.6.2.2 are verified and non-compliant sections are not designed.

Stress Design 6 - 1


When determining the D over C ratio per AASHTO LRFD Article 5.8.3.4.2, the shear design request ignores torsion.



6.1 Stress Design The following parameters are considered during stress design: PhiC – Resistance Factor; Default Value = 1.0, Typical value: 1.0. The com-pression and tension limits are multiplied by the φC factor.

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

FactorTensLim – cf ' multiplier; Default Value = 0.19 (ksi), 0.5(MPa); Typi-cal values: 0 to 0.24 (ksi), 0 to 0.63 (MPa). The cf ' is multiplied by the Fac-torTensLim to obtain tension limit.

The stresses are evaluated at three points at the top fiber of the top slab and three points at the bottom fiber of the bottom slab: the left corner, the center-line web and the right corner of the relevant slab tributary area. The location is labeled in the output plots and tables. See Chapter 9, Section 9.1.1.

Concrete strength cf ′ is read at every point, and compression and tension limits are evaluated using the FactorCompLim - cf ′ multiplier and FactorTensLim -

cf ' multiplier.

The stresses assume linear distribution and take into account axial (P) and ei-ther both bending moments (M2 and M3) or only P and M3, depending on which method for determining LLD factors have been specified in the Design Request (see Chapters 3 and 4).

6 - 2 Stress Design

Chapter 6 - Design Multi-Cell Concrete Box Bridges using AMA

The stresses are evaluated for each demand set (Chapter 4). Extremes are found for each point and the controlling demand set name is recorded.

The stress limits are evaluated by applying the preceding parameters.

6.2 Shear Design The following parameters are considered during shear design:

PhiC – Resistance Factor; Default Value = 0.9, Typical values: 0.7 to 0.9. The nominal shear capacity of normal weight concrete sections is multiplied by the resistance factor to obtain factored resistance.


Check Sub Type – Typical value: MCFT. Specifies which method for shear de-sign will be used: either Modified Compression Field Theory (MCFT) in ac-cordance with AASHTO-2012 Section 5.8.3.4.2; or the Vci/Vcw method in ac-cordance with AASHTO-2012 Section 5.8.3.4.3. Currently only the MCFT op-tion is available.

Negative limit on strain in nonprestressed longitudinal reinforcement in ac-cordance with AASHTO-2012 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 reinforcement in accord-ance with AASHTO-2012 Section 5.8.3.4.2; Default Value = 6.0x10−3, Typical value: 6.0x10−3.

PhiC for Nu – Resistance Factor used in AASHTO-2012 Equation 5.8.3.5-1; Default Value = 1.0, Typical values: 0.75 to 1.0.

Phif for Mu – Resistance Factor used in AASHTO-2012 Equation 5.8.3.5-1; Default Value = 0.9, Typical values: 0.9 to 1.0.

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

Shear Design 6 - 3


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

6.2.1 Variables cA Area of concrete on the flexural tension side of the member

psA Area of prestressing steel on the flexural tension side of the member

vlA Area of nonprestressed steel on the flexural tension side of the mem-ber at the section under consideration

VSA Area of transverse shear reinforcement per unit length

minVSA Minimum area of transverse shear reinforcement per unit length in accordance with AASHTO-2012 Equation 5.8.2.5

a Depth of equivalent stress block in accordance with AASHTO-2012 Section 5.7.3.2.2. Varies for positive and negative moment.

b Minimum web width

bv Effective web width adjusted for presence of prestressing ducts in accordance with AASHTO-2012 Section 5.8.2.9

girderd Depth of the girder

otPTbd Distance from the top of the top slab to the center of gravity of the tendons in the bottom of the precast beam

vd Effective shear depth in accordance with AASHTO-2012 5.8.2.9

cE Young’s modulus of concrete

pE Prestressing steel Young’s modulus

sE Reinforcement Young’s modulus

puf Specified tensile strength of the prestressing steel

6 - 4 Shear Design


uM Factored moment at the section

uN Applied factored axial force, taken as positive if tensile

Vp Component in the direction of the applied shear of the effective pre-stressing force; if Vp has the same sign as Vu, the component is resist-ing the applied shear.

uV Factored shear demand per girder excluding force in tendons

cV2 Shear in the Section Cut excluding the force in tendons

2TotV Shear in the Section Cut including the force in tendons

sε Strain in nonprestressed longitudinal tension reinforcement (AASH-TO-2012 eq. 5.8.3.4.2-4)

ε εLimitPos LimitNeg,s s = Max and min value of strain in nonprestressed longitudinal tension reinforcement as specified in the Design Request

Vϕ Resistance factor for shear

Pϕ Resistance factor for axial load

Fϕ Resistance factor for moment

6.2.2 Design Process The shear resistance is determined in accordance with AASHTO-2012 para-graph 5.8.3.4.2 (derived from Modified Compression Field Theory). The pro-cedure assumes that the concrete shear stresses are distributed uniformly over an area bv wide and dv deep, that the direction of principal compressive stresses (defined by angle θ and shown as D) remains constant over dv, and that the shear strength of the section can be determined by considering the biaxial stress conditions at just one location in the web. For design, the user should select on-ly those sections that comply with these assumptions by defining appropriate station ranges in the Design Request (see Chapter 4).

Shear Design 6 - 5


The effective web width is taken as the minimum web width, measured parallel to the neutral axis, between the resultants of the tensile and compressive forces as a result of flexure. In determining the effective web width at a particular lev-el, one-quarter the diameter of grouted ducts at that level is subtracted from the web width.

All defined tendons in a section, stressed or not, are assumed to be grouted. Each tendon at a section is checked for presence in the web, and the minimum controlling effective web thicknesses are evaluated.

The tendon duct is considered to have an effect on the web effective thickness even if only part of the duct is within the web boundaries. In such cases, the en-tire one-quarter of the tendon duct diameter is subtracted from the element thickness.

If several tendon ducts overlap in one web (when projected on the vertical ax-is), the diameters of the ducts are added for the sake of evaluation of the effec-tive thickness. The effective web thickness is calculated at the top and bottom of each duct.

Shear design is completed on a per-web basis. Please refer to Chapter 3 for a description of the live load distribution to individual girders.

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

For every COMBO specified in the Design Request that contains envelopes, a new force demand set is generated. The new force demand set is built up from the maximum tension values of P and the maximum absolute values of V2 and M3 of the two StepTypes (Max and Min) present in the envelope COMBO case. The StepType of this new force demand set is named ABS and the signs of the P, V2 and M3 are preserved. The ABS case follows the industry practice where sections are designed for extreme shear and moments that are not neces-sarily corresponding to the same design vehicle position. The section cut is de-signed for all three StepTypes in the COMBOMax, Min and ABSand the controlling StepType is reported.

6 - 6 Shear Design


In cases where the demand moment < − ×u u p vM V V d , two new force demand

sets are generated where pos posu u p vM V V d= − and neg neg .u u p vM V V d= − The acro-

nyms “-CodeMinMuPos” and “-CodeMinMuNeg” are added to the end of the StepType name. The signs of the P and V2 are preserved.

The component in the direction of the applied shear of the effective prestress-ing force, positive if resisting the applied shear, is evaluated:

2 2Tot

girders

cp

V VVn−

=

The depth of the equivalent stress block ‘a’ for both positive and negative mo-ment is evaluated in accordance with AASHTO-2012 Equation 5.7.3.1.1.

Effective shear depth is evaluated.

If Mu > 0, then ( )girder bot botmax 0.72 , 0.9 , 0.5 .v PT PTd d d d a= × × − ×

If Mu < 0, then

girder girder compslab girder compslabmax 0.72 ,0.9 ( 0.5 ),( 0.5 ) 0.5 .vd d d d d d a= × × − × − × − ×

The demand/capacity ratio (D/C) is calculated based on the maximum permis-sible shear capacity at a section in accordance with AASHTO-2012 Section 5.8.3.2-2.

0.25 '

up

V

c v

V VDC f b d

−φ

=× × ×

(AASHTO-2012 5.8.3.2-2)

Evaluate the numerator and denominator of (AASHTO-2012 eq. 5.8.3.4.2-4).

numerator 0.5 0.7us u u p ps pu

V

MN V V A f

dε = + × + − − × ×

denominators p ps s vlE A E Aε = × + ×

Adjust denominator values as follows.

Shear Design 6 - 7


If εsdenominator = 0 and εsnumerator > 0, then εs = εsLimitPos and

numerator

.

sp ps

svl

s

E AA

E

ε− ×

ε=

If εsnumerator <0, then denominators p ps s vl c cE A E A E Aε = × + × + ×

Evaluate (eq. 5.8.3.4.2-4).

numerator

denominator

ss

s

εε =

ε

Check if axial tension is large enough to crack the flexural compression face of the section.

If > ×girder

0 52uc

N . f ' ,A

then 2 .s sε = ×ε

Check against the limit on the strain in nonprestressed longitudinal tension re-inforcement specified in the Design Request, and if necessary, recalculate how much longitudinal rebar is needed to reach the EpsSpos tension limit.

LimitNegmax( , )s s sε = ε ε and LimitPosmin( , )s s sε = ε ε

Evaluate the angle θ of inclination of diagonal compressive stresses as deter-mined in AASHTO-2012 Article 5.8.3.4.

18 29 3500 45s≤ + ×ε ≤ (AASHTO-2012 5.8.3.4)

Evaluate the factor indicating the ability of diagonally cracked concrete to transmit tension and shear, as specified in AASHTO-2012 Article 5.8.3.4.

4.81 750 s

β =+ ×ε

(AASHTO-2012 5.8.3.4)

Evaluate the nominal shear resistance provided by tensile stresses in the con-crete (AASHTO-2012 eq. 5.8.3.3-3).

0.083 'c c vV f b d= ×β×λ× × ×

6 - 8 Shear Design


Evaluate how much shear demand is left to be carried by rebar.

uS p c

s

VV V V= − −ϕ

If 0<SV , then 0;VSA = else

θ

=× ×

1tan

sVS

y v

VA .f d

(AASHTO-2012 eq. 5.8.3.3-4)

Check against minimum transverse shear reinforcement.

If 0.5 ,u s c pV V V> ×φ × + then min0.083 'c

VSy

f bA

f×λ ×

= in accord-

ance with (AASHTO-2012 eq. 5.8.2.5-1); else min 0.VSA =

If 0,SV < then min ;VS VSA A= else minmaxVS VS VSA (A ,A ).=

Recalculate Vs in accordance with (AASHTO-2012 eq. 5.8.3.3-4).

1 .tanS VS y vV A f d= × × ×

θ

Evaluate the longitudinal rebar on the flexure tension side in accordance with (AASHTO-2012 eq. 5.8.3.5-1).

req

0.5 min ,10.5

tan

uUP S

U SUSL p ps

v f P y

VV V VM NA E A

d f

− − ×

φ φ = + × + − × × ×φ φ θ = reqmax( , )VL VL SLA A A

Assign longitudinal rebar to the top or bottom side of the girder based on the moment sign.

If 0,UM < then =CompSlabVL U VLA A and BeamBotFlange 0,VLA =

else =CompSlab 0VL UA and BeamBotFlange .VL VLA A=

Shear Design 6 - 9


6.3 Flexure Design The following parameter is used in the design of flexure: PhiC – Resistance Factor; Default Value = 1.0, Typical value(s): 1.0. The nom-inal flexural capacity is multiplied by the resistance factor to obtain factored resistance

6.3.1 Variables APS Area of the PT in the tension zone


slabA Tributary area of the slab

a Depth of the equivalent stress block in accordance with AASHTO-2012 5.7.3.2.2

slabb Effective flange width = horizontal width of the slab tributary area, measured from out to out

webeqb Thickness of the beam web

dP Distance from the extreme compression fiber to the centroid of the prestressing tendons in the tension zone

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

psf Average stress in prestressing steel (AASHTO-2012 eq. 5.7.3.1.1-1)

puf Specified tensile strength of prestressing steel (area weighted aver-

age of all tendons in the tensile zone)

pyf Yield tensile strength of prestressing steel (area weighted average of

all tendons are in the tensile zone)


6 - 10 Flexure Design



nM Nominal flexural resistance

rM Factored flexural resistance

slabeqt Thickness of the composite slab

β1 Stress block factor, as specified in AASHTO-2012 Section 5.7.2.2


6.3.2 Design Process The derivation of the moment resistance of the section is based on approximate stress distribution specified in AASHTO-2012 Article 5.7.2.2. The natural rela-tionship between concrete stress and strain is considered satisfied by an equiva-lent rectangular concrete compressive stress block of 0.85 cf ′ 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 = β1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis. The factor β1 is taken as 0.85 for concrete strengths not exceeding 4.0 ksi. For concrete strengths ex-ceeding 4.0 ksi, β1 is reduced at a rate of 0.05 for each 1.0 ksi of strength in ex-cess of 4.0 ksi, except that β1 is not to be taken to be less than 0.65.

The flexural resistance is determined in accordance with AASHTO-2012 para-graph 5.7.3.2. The resistance is evaluated only for bending about horizontal ax-is 3. Separate capacity is calculated for positive and negative moment. The ca-pacity 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 tendons 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 considered 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 are 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.

Flexure Design 6 - 11


6.3.3 Algorithms At each section:


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

slabslabeq

slab

Atb

=

β1 stress block factor is evaluated in accordance with AASHTO-2012 5.7.2.2 based on section cf ′ .

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

7cf ′ − = −

β

else 1 0 85β = . .

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 the sign of moment they resistnegative or positive. A tendon or rebar is considered to resist 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 ex-tends 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 = β1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis.


sum of the tendon areas, APS

center of gravity of the tendons, dP

specified tensile strength of prestressing steel puf



constant k (AASHTO-2012 eq. 5.7.3.1.1-2)

2 1.04 py

pu

fk

f

= −

For each rebar group, the following values are determined:

sum of tension rebar areas, As

distance from the extreme compression fiber to the centroid of the tension rebar, ds

Positive moment resistance – first it is assumed that the equivalent compres-sion stress block is within the top slab. Distance c between the neutral axis and the compressive face is calculated in accordance with (AASHTO-2012 eq. 5.7.3.1.1-4)

1 slab0.85

PS PU s s

puc PS

p

A f A fcf

f b kAd

+=

′β +




𝑐𝑐𝑑𝑑𝑠𝑠

≤ 0.6 0.0030.003 + 𝜀𝜀𝑐𝑐𝑐𝑐

where the compression control strain limit 𝜀𝜀𝑐𝑐𝑐𝑐 is per AASHTO LRFD 2013 In-terims table C5.7.2.1-1 When the limit is not satisfied the stress in mild reinforcement fs is reduced to satisfy the requirement of Section 5.7.2.1.

The distance c is compared to the equivalent slab thickness to determine if the section is a T-section or rectangular section.



If 1 slabeq ,c tβ > the section is a T-section.

If the section is a T-section, the distance c is recalculated in accordance with (AASHTO-2012 eq. 5.7.3.1.1-3).


1 webeq

0.85

0.85

PS PU s s c

puc PS

pt

A f A f f b b tc

ff b kA

y

′+ − −=

′ β +


= − 1PS PU

p

cf f kd

Nominal flexural resistance Mn is calculated in accordance with (AASHTO-2012 eq. 5.7.3.2.2-1).

If the section is a T-section, then



β β β ′= − + − + − −

else

1 1 .2 2n PS PS p S s s

c cM A f d A f dβ β = − + −


r nM M= ϕ


The process for evaluating negative moment resistance is analogous.


Chapter 7 Design Precast Concrete Girder Bridges

This chapter describes the algorithms used by CSiBridge for design and stress check when the superstructure has a deck that includes precast I or U girders with composite slabs in accordance with the AASHTO LRFD 2012 code.




7.1 Stress Design The following parameters are considered during stress design:

Stress Design 7 - 1


PhiC – Resistance Factor; Default Value = 1.0, Typical value: 1.0. The com-pression and tension limits are multiplied by the φC factor.

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

FactorTensLim – f ' c multiplier; Default Value = 0.19 (ksi), 0.5(MPa); Typ-ical values: 0 to 0.24 (ksi), 0 to 0.63 (MPa). The f ' c is multiplied by the FactorTensLim to obtain tension limit.

The stresses are evaluated at three points at the top fiber of the composite slab: the left corner, the centerline beam and the right corner of the composite slab tributary area. The locations of stress output points at the slab bottom fiber and the beam top and bottom fibers depend on the type of precast beam present in the section cut. The locations are labeled in the output plots and tables.

Concrete strength cf ′ is read at every point and compression and tension limits are evaluated using the FactorCompLim – cf ′ multiplier and FactorTensLim –

f ' c multiplier.

The stresses assume linear distribution and take into account axial (P) and ei-ther both bending moments (M2 and M3) or only P and M3, depending on which method for determining the LLD factor has been specified in the Design Request (see Chapters 3 and 4).

The stresses are evaluated for each demand set (Chapter 4). Extremes are found for each point and the controlling demand set name is recorded.

The stress limits are evaluated by applying the preceding Parameters.

7.2 Shear Design The following parameters are considered during shear design:

PhiC – Resistance Factor; Default Value = 0.9, Typical values: 0.7 to 0.9. The nominal shear capacity of normal weight concrete sections is multiplied by the resistance factor to obtain factored resistance.

7 - 2 Shear Design

Chapter 7 - Design Precast Concrete Girder Bridges


Check Sub Type – Typical value: MCFT. Specifies which method for shear de-sign will be used: Modified Compression Field Theory (MCFT) in accordance with AASHTO LRFD section 5.8.3.4.2; or the Vci/Vcw method in accordance with AASHTO LRFD section 5.8.3.4.3. Currently, only the MCFT option is available.

Negative limit on strain in nonprestressed longitudinal reinforcement in ac-cordance with AASHTO 2012 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 reinforcement in accord-ance with AASHTO 2012 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 of the code; Default Value = 1.0, Typical values: 0.75 to 1.0.

Phif for Mu – Resistance Factor used in AASHTO-2012 equation 5.8.3.5-1; De-fault Value = 0.9, Typical values: 0.9 to 1.0.

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 label that will be used to determine the required area of longitudinal rebar in the girder

7.2.1 Variables a Depth of the equivalent stress block in accordance with AASHTO-

2012 section 5.7.3.2.2. Varies for positive and negative moment.

Ac Area of concrete on the flexural tension side of the member

Aps Area of prestressing steel on the flexural tension side of the member

AVS Area of transverse shear reinforcement per unit length

Shear Design 7 - 3


AVSmin Minimum area of transverse shear reinforcement per unit length in accordance with (AASHTO-2012 eq. 5.8.2.5)

Avl Area of nonprestressed steel on the flexural tension side of the mem-ber at the section under consideration

b Minimum web width of the beam

dv Effective shear depth in accordance with AASHTO-2012 section 5.8.2.9

dgirder Depth of the girder

dcompslab Depth of the composite slab (includes concrete haunch t2)

dPTBot Distance from the top of the composite slab to the center of gravity of the tendons in the bottom of the precast beam

Ec Young’s modulus of concrete

Ep Prestressing steel Young’s modulus

Es Reinforcement Young’s modulus

fpu Specified tensile strength of prestressing steel

Mu Factored moment at the section

Nu Applied factored axial force, taken as positive if tensile

V2c Shear in Section Cut, excluding the force in the tendons

V2tot Shear in Section Cut, including the force in the tendons

Vp Component in the direction of the applied shear of the effective pre-stressing force; if Vp has the same sign as Vu, the component is resist-ing the applied shear.

Vu Factored shear demand per girder, excluding the force in the tendons

εs Strain in nonprestressed longitudinal tension reinforcement (AASH-TO-2012 eq. 5.8.3.4.2-4)

7 - 4 Shear Design


εsLimitPos, εsLimitNeg = Max and min value of strain in nonprestressed longitudinal tension reinforcement as specified in the Design Request

φV Resistance factor for shear

φP Resistance factor for axial load

φF Resistance factor for moment

7.2.2 Design Process The shear resistance is determined in accordance with AASHTO-2012 para-graph 5.8.3.4.2 (derived from Modified Compression Field Theory). The pro-cedure assumes that the concrete shear stresses are distributed uniformly over an area bv wide and dv deep, that the direction of principal compressive stresses (defined by angle θ and shown as D) remains constant over dv, and that the shear strength of the section can be determined by considering the biaxial stress conditions at just one location in the web. The user should select for design on-ly those sections that comply with these assumptions by defining appropriate station ranges in the Design Request (see Chapter 4).

It is assumed that the precast beams are pre-tensioned, and therefore, no ducts are present in webs. The effective web width is taken as the minimum web width, measured parallel to the neutral axis, between the resultants of the ten-sile and compressive forces as a result of flexure.

Shear design is completed on a per-girder basis. Please refer to Chapter 3 for a description of the live load distribution to individual girders.

7.2.3 Algorithms All section properties and demands are converted from CSiBridge model

units to N, mm.

For every COMBO specified in the Design Request that contains envelopes, two new force demand sets are generated. The new force demand sets are built up from the maximum tension values of P and the maximum and mini-mum values of V2 and minimum values of M3 of the two StepTypes (Max and Min) present in the envelope COMBO case. The StepType of these new

Shear Design 7 - 5


force demand sets are named MaxM3MinV2 and MinM3MaxV2, respective-ly. The signs of all force components are preserved. The two new cases are added to comply with industry practice where sections are designed for ex-treme shear and moments that are not necessarily corresponding to the same design vehicle position. The section cut is designed for all four StepTypes in the COMBOMax, Min, MaxM3MinV2, and MinM3MaxV2and the con-trolling StepType is reported.

In cases where the demand moment < − ×u u p vM V V d , two new force demand sets are generated where pos posu u p vM V V d= − and neg neg .u u p vnM V V d= − − The

acronyms “-CodeMinMuPos” and “-CodeMinMuNeg” are added to the end of the StepType name. The signs of the P and V2 are preserved. The compo-nent in the direction of the applied shear of the effective prestressing force, positive if resisting the applied shear, is evaluated:

2 2tot

girders

cp

V VVn−

=

Depth of equivalent stress block ‘a’ for both positive and negative moment is evaluated in accordance with (AASHTO-2012 eq. 5.7.3.1.1).

Effective shear depth is evaluated.

If Mu > 0, then ( )girder bot botmax 0.72 ,0.9 , 0.5 .v PT PTd d d d a= × × − ×

If Mu < 0, then

( ) ( )girder girder compslab girder compslabmax 0.72 ,0.9 0.5 , 0.5 0.5 .vd d d d d d a = × × − × − × − ×

If < − ×u u p vM V V d , then ( )u u p vM V V d .= − ×

The demand/capacity (D/C) ratio is calculated based on the maximum per-missible shear capacity at a section in accordance with AASHTO-2012 5.8.3.2-2.

0.25 '

up

V

c v

V VDC f b d

−φ

=× × ×

(AASHTO-2012 5.8.3.2-2)

7 - 6 Shear Design


Evaluate the numerator and denominator of (AASHTO-2012 eq. 5.8.3.4.2-4):

numerator 0.5 0.7us u u p ps pu

V

MN V V A f

dε = + × + − − × ×

denominators p ps s vlE A E Aε = × + ×

Adjust denominator values as follows

If denominator 0sε = and numerator 0,sε > then LimitPoss sε = ε and

numeratorsp ps

svl

s

E AA .

E

− ×=

εε

If numerator 0,sε < then denominator .s p ps s vl c cE A E A E Aε = × + × + ×

Evaluate (AASHTO-2012 eq. 5.8.3.4.2-4):

numerator

denominator

ss

s

εε =

ε


If > ×girder

0 52uc

N . f ' ,A

then 2 .s sε = ×ε

Check against the limit on the strain in nonprestressed longitudinal tension reinforcement specified in the Design Request, and if necessary, recalculate how much longitudinal rebar is needed to reach the EpsSpos tension limit.

( )LimitNegmax ,s s sε = ε ε and ( )LimitPosmin ,s s sε = ε ε

Evaluate the angle θ of inclination of diagonal compressive stresses as de-termined in AASHTO-2012 Article 5.8.3.4.

18 29 3500 45s≤ + ×ε ≤ (AASHTO-2012 5.8.3.4)

Shear Design 7 - 7


Evaluate the factor indicating the ability of diagonally cracked concrete to transmit tension and shear, as specified in AASHTO-2012 Article 5.8.3.4.

4.81 750 s

β =+ ×ε

(AASHTO-2012 5.8.3.4)

Evaluate nominal shear resistance provided by tensile stresses in the concrete AASHTO-2012 eq. 5.8.3.3-3.

0.083 'c c vV f b d= ×β×λ× × ×

Evaluate how much shear demand is left to be carried by rebar.

uS p c

s

VV V V= − −ϕ

If 0SV ,< then = 0,VSA

else .1

tan

sVS

y v

VAf d

=× ×

θ

(AASHTO-2012 eq. 5.8.3.3-4)


If 0.5 ,u s c pV V V> ×φ × + then min0.083 'c

VSy

f bA

f×λ ×

= in accord-

ance with (AASHTO-2012 eq. 5.8.2.5-1); else min 0.VSA =

If 0SV ,< then minVS VSA A= , else minmax( , ).VS VS VSA A A=


1tanS VS y vV A f d= × × ×

θ

Evaluate longitudinal rebar on flexure tension side in accordance with (AASHTO-2012 eq. 5.8.3.5-1).

7 - 8 Shear Design


req

0.5 min ,10.5

tan

uUP S

U SUSL p ps

v f P y

VV V VM NA E A

d f

− − ×

φ φ = + × + − × × ×φ φ θ reqmax( , )VL VL SLA A A=

Assign longitudinal rebar to the top or bottom side of the girder based on moment sign.

If 0UM ,< then CompSlabUVL VLA A= and BeamBotFlange 0;VLA =

else CompSlabU 0VLA = and BeamBotFlange =VL VLA A .

7.2.4 Shear Design Example The girder spacing is 9'-8". The girder type is AASHTO Type VI Girders, 72-inch-deep, 42-inch-wide top flange and 28-inch-wide bottom flange (AASHTO 28/72 Girders). The concrete deck is 8 inches thick, with the haunch thickness assumed = 0.

Figure 7-1 Shear design example deck section

Materials

Concrete strength Prestressed girders 28-day strength, cf ′ = 6 ksi, Girder final elastic modulus, Ec = 4,415 ksi Deck slab: 4.0 ksi, Deck slab elastic modulus, Es = 3,834 ksi

Shear Design 7 - 9


Reinforcing steel Yield strength, fy = 60 ksi

Figure 7-2 Shear design example beam section

Prestressing strands 0.5-inch-diameter low relaxation strands Grade 270 Strand area, Aps = 0.153 in2 Steel yield strength, fpy = 243 ksi Steel ultimate strength, fpu = 270 ksi Prestressing steel modulus, Ep = 28,500 ksi

Basic beam section properties

Depth = 72 in. Thickness of web = 8 in. Area, Ag = 1,085 in2

7 - 10 Shear Design


Ac = Area of concrete on the flexural tension side of the member (bordered at mid depth of the beam + slab height) = 551 in2

Moment of inertia, Ig = 733,320 in4 N.A. to top, yt = 35.62 in. N.A. to bottom, yb = 36.38 in. P/S force eccentricity e = 31.380 in.

In accordance with AASHTO-2012 2012 4.6.2.6, the effective flange width of the concrete deck slab is taken as the tributary width. For the inte-rior beam, the bslab = 9'-8" = 116 in.

Demands at interior girder Section 2 = station 10’, after girder Section 2, Vu = 319.1 kip; Mu = 3678 kip-ft

The component in the direction of the applied shear of the effective prestress-

ing force, positive if resisting the applied shear, is evaluated:

2 2tot

girders

−= c

pV VV

n Vp = 0 since no inclined tendons are present.

Depth of equivalent stress block ‘a’ for both positive and negative moment is evaluated in accordance with (AASHTO-2012 eq. 5.7.3.1.1).

Effective shear depth is evaluated:

Since Mu > 0, then (for calculation of the depth of the compression block, refer to the Flexure example in Section 7.3 of this manual)

( )( )

girder bot bot max 0.72 , 0.9 , 0.5

max 0.72 80", 0.9 75", 75" 0.5 5.314 0.85v PT PTd d d d a= × × − ×

= × × − × ×

( )max 57 6" 67 5" 72 74" 72 74"= =vd . , . , . .

Value reported by CSiBridge = 72.74"

Check if u u p vM V V d< − ×

( )= × = > − × =3,678 12 44,136 kip-in 319 0 72.74 23,204 kip-inuM

Shear Design 7 - 11


D/C is calculated based on the maximum permissible shear capacity at a sec-tion in accordance with AASHTO-2012 5.8.3.2-2.

319 00.9 0.406

0.25 ' 0.25 6 8 72.74

up

V

c v

V VDC f b d

− −φ

= = =× × × × × ×


Evaluate the numerator and denominator of (AASHTO-2012 eq. 5.8.3.4.2-4)

numerator 0.5 0.7

3678 12 0.5 0 319 0 6.73 0.7 270 346.2 kip72.74

us u u p ps pu

V

MN V V A f

dε = + × + − − × ×

×= + × + − − × × = −

2denominator 28500 ksi 6.73 in 191805 kips p ps s vlE A E Aε = × + × = × =

Adjust denominator values as follows

If denominator 0sε = and numerator 0,sε > then LimitPoss sε = ε and

numeratorsp ps

svl

s

E AA

E

ε− ×

ε= is not applicable.

If numerator 0,sε < then

denominator

28500 6.73 4415 551.4 26 263 461 kips p ps s vl c cE A E A E Aε = × + × + ×

= × + × =

Evaluate (AASHTO-2012 eq. 5.8.3.4.2-4)

numerator

denominator

346.2 1.318E-42626346

ss

s

ε −ε = = = −

ε

Value reported by CSiBridge = −1.318E-4


7 - 12 Shear Design


If girder

0.52 ' ,uc

N fA

> × then 2s sε = ×ε ; this is not applicable since Nu = 0.

Check against the limit on strain in nonprestressed longitudinal tension rein-forcement as specified in the Design Request, and recalculate Avl.

( ) ( )LimitPosmax , max 1.318E-4, 1.318E-4 4 1.318E-4s s sε = ε ε = − − − = −

Evaluate angle θ of inclination of diagonal compressive stresses as deter-mined in AASHTO-2012 Article 5.8.3.4.

18 29 3500 45s≤ θ = + ×ε ≤ 29 3500 1.318E-4 28.5degθ = + ×− = Value reported by CSiBridge = 28.5 deg

Evaluate factor indicating ability of diagonally cracked concrete to transmit tension and shear as specified in AASHTO-2012 Article 5.8.3.4.

4.8 4.8 5.32651 750 1 750 1.318E-4s

β = = =+ ×ε + ×−


Evaluate nominal shear resistance provided by tensile stresses in the concrete (AASHTO-2012 eq. 5.8.3.3-3).

0.0316 '

0.0316 5.32 1.0 6 8 72.74 239.92 kipc c vV f b d= ×β×λ× × ×

= × × × × × =

Value reported by CSiBridge = 240.00 kip

Evaluate how much shear demand is left to be carried by rebar:

319 0 239.6 114.8 kip0.9

uS p c

s

VV V Vφ

= − − = − − =


If 0,SV < then 0;VSA = else

Shear Design 7 - 13


2114.8 1.43E-2 in /in1 160 72.74

tan tan28.5

sVS

y v

VAf d

= = =× × × ×

θ

(AASHTO-2012 eq. 5.8.3.3-4)


If 0.5 319.1 kip 0.5 239.6 119.8 kipu s c pV V V> ×φ × + − > > × = is true,

2min

0.0316 ' 0.0316 1.0 6 8 0.01032in /in60

cVS

y

f bA

f×λ × × ×

= = =

(AASHTO-2012 eq. 5.8.2.5-1) If 0SV ,< then min ;VS VSA A= else ( )= = 2

minmax , 1.43E-2in /2VS VS VSA A A

Value reported by CSiBridge = 1.43E-2in2/in


1 10.0143 60 72.74 114.9kiptan tan28.5S VS y vV A f d= × × × = × × × =

θ


Evaluate longitudinal rebar on flexure tension side in accordance with AASHTO-2012 eq. 5.8.3.5-1:

req

2

0.5 min ,10.5

tan

319 0 0.5 114.93678 12 0 10.9 0.5 28500 6.73 3176.3 in72.74 0.9 1.0 tan28.5 60

uUP S

U S SUSL p ps

v f P y

VV V VM NA E A

d f

− − ×

φ φ = + × + − × × ×φ φ θ

− − × × = + × + − × × = − ×

Value reported by CSiBridge = 0.00 in2 → no additional longitudinal re-bar is required in the beam bottom flange.

7.3 Flexure Design The following parameter is used in the design of flexure:



PhiC – Resistance Factor; Default Value = 1.0, Typical value: 1.0. The nomi-nal flexural capacity is multiplied by the resistance factor to obtain factored re-sistance

7.3.1 Variables APS Area of PT in the tension zone


Aslab Tributary area of the slab

a Depth of the equivalent stress block in accordance with AASHTO-2012 5.7.3.2.2.

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

bwebeq Thickness of the beam web

dP Distance from the extreme compression fiber to the centroid of the prestressing tendons in the tension zone

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

fps Average stress in prestressing steel (AASHTO-2012 eq. 5.7.3.1.1-1)

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

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



Mn Nominal flexural resistance

Mr Factored flexural resistance



tslabeq Thickness of the composite slab

β1 Stress block factor, as specified in AASHTO-2012 Section 5.7.2.2


7.3.2 Design Process The derivation of the moment resistance of the section is based on approximate stress distribution specified in AASHTO-2012 Article 5.7.2.2. The natural rela-tionship between concrete stress and strain is considered satisfied by an equiva-lent rectangular concrete compressive stress block of 0.85 cf ′ 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 = β1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis. The factor β1 is taken as 0.85 for concrete strengths not exceeding 4.0 ksi. For concrete strengths ex-ceeding 4.0 ksi, β1 is reduced at a rate of 0.05 for each 1.0 ksi of strength in ex-cess of 4.0 ksi, except that β1 is not to be taken to be less than 0.65.

The flexural resistance is determined in accordance with AASHTO-2012 para-graph 5.7.3.2. The resistance is evaluated only for bending about horizontal ax-is 3. Separate capacity is calculated for positive and negative moment. The ca-pacity 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 tendons 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 considered 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 are 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.

7.3.3 Algorithms At each section:




The β1 stress block factor is evaluated in accordance with AASHTO-2012 5.7.2.2 based on section .cf ′

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

7cf ′ − β = −

else β1 = 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 what 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 it is considered to resist a negative moment when it is locat-ed 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 = β1c from the extreme compression fiber. The distance c is measured perpendicu-lar to the neutral axis.


– sum of the tendon areas, APS

– center of gravity of the tendons, dP

– specified tensile strength of prestressing steel puf

– constant k (eq. 5.7.3.1.1-2)

2 1.04 py

pu

fk

f

= −

For each rebar group the following values are determined:

– sum of tension rebar areas, As



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

Positive moment resistance – First it is assumed that the equivalent compres-sion stress block is within the top slab. Distance c between the neutral axis and the compressive face is calculated in accordance with (AASHTO-2012 eq. 5.7.3.1.1-4)

1 slab0.85

+=

′β +

PS PU s s

puc PS

p

A f A fc ff b kA

d




Ratio limit 𝑐𝑐𝑑𝑑𝑠𝑠≤ 0.6 0.003

0.003 + 𝜀𝜀𝑐𝑐𝑐𝑐

where the compression control strain limit 𝜀𝜀𝑐𝑐𝑐𝑐 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 reduced to satisfy the requirement of Section 5.7.2.1.The distance c is compared to the slab thickness. If the distance to the neutral axis c is larger than the compo-site slab thickness, the distance c is re-evaluated. For this calculation, the beam flange width and area are converted to their equivalents in slab con-crete by multiplying the beam flange width by the modular ratio between the precast girder concrete and the slab concrete. The web width in the equation for c is substituted for the effective converted girder flange width. The dis-tance c is recalculated in accordance with (AASHTO-2012 eq. 5.7.3.1.1-3).


1 webeq

0.85

0.85

′+ − −=

′ β +

PS PU s s c

puc PS

pt

A f A f f b b tc f

f b kAy



If the calculated value of c exceeds the sum of the deck thickness and the equivalent precast girder flange thickness, the program assumes the neutral axis is below the flange of the precast girder and recalculates c. The term

( )0.85 c wf b b′ − in the calculation is broken into two terms, one refers to the contribution of the deck to the composite section flange and the second refers to the contribution of the precast girder flange to the composite girder flange.

Average stress in prestressing steel fps is calculated in accordance with AASHTO-2012 5.7.3.1.1-1.

= − 1PS PU

p

cf f kd

Nominal flexural resistance Mn is calculated in accordance with AASHTO-2012 5.7.3.2.2-1.

– If the section is a T-section, then



β β β ′= − + − + − −

else 1 1

2 2n PS PS p S s sc cM A f d A f dβ β = − + −


r nM M= ϕ


The process for evaluating negative moment resistance is analogous, except that calculation of positive moment resistance is not applicable.



7.3.4 Flexure Capacity Design Example

Figure 7-3 Flexure capacity design example deck section

Girder spacing: 9'-8"

Girder type: AASHTO Type VI Girders, 72 inches deep, 42-inch-wide top flange, and 28-inch-wide bottom flange (AASHTO 28/72 Girders)

Concrete deck: 8 inches thick, haunch thickness assumed = 0



Figure 7-4 Flexure capacity design example beam section

Materials

Concrete strength Prestressed girders 28-day strength, ′cf = 6 ksi, Girder final elastic modulus, Ec = 4,696 ksi Deck slab = 4.0 ksi, Deck slab elastic modulus, Es = 3,834 ksi Reinforcing steel yield strength, fy = 60 ksi Prestressing strands 0.5-inch-diameter low relaxation strands Grade 270 Strand area, Aps = 0.153 in2



Steel yield strength, fpy = 243 ksi Steel ultimate strength, fpu = 270 ksi Prestressing steel modulus, Ep = 28,500 ksi

Basic beam section properties

Depth = 72 in. Thickness of web = 8 in. Area, Ag = 1,085 in2 Moment of inertia, Ig = 733,320 in4 N.A. to top, yt = 35.62 in. N.A. to bottom, yb = 36.38 in. P/S force eccentricity e = 31.380 in.

In accordance with AASHTO-2012 2007 paragraph 4.6.2.6, the effective flange width of the concrete deck slab is taken as the tributary width.

For the interior beam, the bslab = 9'-8" = 116 in.

Tendons are split into two groups depending on which sign of moment they resistnegative or positive. A tendon is considered to resist a positive moment when it is located outside of the top fiber compression stress block and is con-sidered 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 par-allel to the neutral axis at the distance a = β1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis.


– sum of tendon areas 2

bottom 44 0.153 6.732 inPTA = × = Value reported by CSiBridge = 6.732 in2

– distance from center of gravity of tendons to extreme compression fiber

( )bottom12 2 12 4 10 6 6 8 4 1072 8 75 in

12 12 10 6 4PTy × + × + × + × + ×= + − =

+ + + +

– specified tensile strength of prestressing steel 270 kippuf = Value reported by CSiBridge = 270 kip



– constant k (AASHTO-2012 eq. 5.7.3.1.1-2) 2432 1.04 2 1.04 0.28270

py

pu

fk

f = − = − =


β1 stress block factor is evaluated in accordance with AASHTO-2012 5.7.2.2 based on the composite slab cf ′

β1 shall be taken as 0.85 for concrete strength not exceeding 4.0 ksi. If cf ′ > 4 ksi, then β1 shall be reduced at a rate of 0.05 for each 1.0 ksi of

strength in excess of 4.0 ksi. Since ′cf = 4 ksi, β1 = 0.85. Value calculated by CSiBridge = 0.85 (not reported)

The distance c between neutral axis and the compressive face is evaluated in accordance with AASHTO-2012 5.7.3.1.1-4.

bottom

1 slab bottombottom

0.85

6.732 * 270 5.314 in2700.85 4 0.85 116 0.28 6.73275

PT pu

puc PT

PT

A fc

ff b k A

y

×=

′× ×β × + × ×

= =× × × + × ×

Value calculated by CSiBridge = 5.314 in

The distance c is compared to the composite slab thickness to determine if the c needs to be re-evaluated to include the precast beam flange in the equivalent compression block.

Since c = 5.314 in < 8 in, the c is valid.

Average stress in prestressing steel fps is calculated in accordance with AASHTO-2012 5.7.3.1.1-1.

bottom

5.3141 270 1 0.28 264.64 ksi75ps pu

PT

cf f ky

= − = × − × =

Value reported by CSiBridge = 264.643 ksi

Nominal flexural resistance Mn is calculated in accordance with AASHTO-2012 5.7.3.2.2-1.



Since the section is rectangular,

1bottom bottom

5.314 0.856.732 264.64 752 2

129593.17 12 10799.4 kip-ft

n PT ps PTcM A f y β × = − = × × −

= =

Value calculated by CSiBridge = 107 99 kip-ft (not reported)


0.9 10799.4 9719.5 kip-ftr nM M= φ = × = Value reported by CSiBridge = 9719.5 kip-ft (116633.5 kip-in)


Chapter 8 Design Steel I-Beam Bridge with Composite Slab

This chapter describes the algorithms CSiBridge applies when designing steel I-beam with composite slab superstructures in accordance with, the AASHTO LRFD 2012.

8.1 Section Properties

8.1.1 Yield Moments

8.1.1.1 Composite Section in Positive Flexure The positive yield moment, My, is determined by the program in accordance with AASHTO LRFD 2012 Section D6.2.2 using the following user-defined input, which is part of the Design Request (see Chapter 4 for more information about Design Request).

Mdnc = The user specifies in the Design Request the name of the combo that represents the moment caused by the factored permanent load applied before the concrete deck has hardened or is made composite.

Mdc = The user specifies in the Design Request the name of the combo that represents the moment caused by the remainder of the factored perma-nent load (applied to the composite section).

The program solves for MAD from the following equation,

8- 1


dnc dc ADyt

NC LT ST

M M MFS S S

= + + (AASHTO 2012 D6.2.2-1)

and then calculates yield moment based on the following equation

y dnc dc ADM M M M= + + (AASHTO-2012 D6.2.2-2)

where

SNC = Noncomposite section modulus (in.3)

SLT = Long-term composite section modulus (in.3)

SST = Short-term composite section modulus (in.3)

My is taken as the lesser value calculated for the compression flange, Myc, or the tension flange, Myt. The positive My is calculated only once based on Mdnc and Mdc demands specified by the user in the Design Request. It should be noted that the My calculated in the procedure described here is used by the program only to determine Mnpos for a compact section in positive bending in a continuous span, where the nominal flexural re-sistance may be controlled by My in accordance with (AASHTO-2012 eq. 6.10.7.1.2-3).

1.3n h yM R M≤

8.1.1.2 Composite Section in Negative Flexure For composite sections in negative flexure, the procedure described for positive yield moment is followed, except that the composite section for both short-term and long-term moments consists of the steel section and the longitudinal rein-forcement within the tributary width of the concrete deck. Thus, SST and SLT are the same value. Also, Myt is taken with respect to either the tension flange or the longitudinal reinforcement, whichever yields first.

The negative My is calculated only once based on the Mdnc and Mdc demands specified by the user in the Design Request. It should be noted that the My cal-culated in the procedure described here is used by the program solely to deter-mine the limiting slenderness ratio for a compact web corresponding to 2Dcp /tw in (AASHTO-2012 eq. A6.2.1-2).

8 - 2 Section Properties

Chapter 8 - Design Steel I-Beam Bridge with Composite Slab

( )

λ = ≤ λ

−

2

0.54 0.09cp

yc cprwpw D

cp

h y

EF D

DMR M

(AASHTO-2012 A6.2.1-2)

and web plastification factors in (AASHTO-2012 eqs. A.6.2.2-4 and A6.2.2-5).

( )

( )

λ − λ = − − ≤ λ − λ

1 1 c

c

w pw Dh yc p ppc

p rw yc ycpw D

R M M MR

M M M

(AASHTO-2012 A.6.2.2-4)

( )

( )

λ − λ = − − ≤ λ − λ

1 1 c

c

w pw Dh yt p ppt

p rw yt ytpw D

R M M MR

M M M

(AASHTO-2012 A6.2.2-5)

8.1.2 Plastic Moments

8.1.2.1 Composite Section in Positive Flexure The positive plastic moment, Mp, is calculated as the moment of the plastic forces about the plastic neutral axis. Plastic forces in the steel portions of a cross-section are calculated using the yield strengths of the flanges, the web, and reinforcing steel, as appropriate. Plastic forces in the concrete portions of the cross-section that are in compression are based on a rectangular stress block with the magnitude of the compressive stress equal to 0.85 .cf ′ Concrete in ten-sion is neglected. The position of the plastic neutral axis is determined by the equilibrium condition that there is no net axial force. In calculating Mp for positive moment, the contribution of the rebar in the deck is ignored.

The plastic moment of a composite section in positive flexure is determined by:

• Calculating the element forces and using them to determine if the plastic neu-tral axis is in the web, top flange, or concrete deck

• Calculating the location of the plastic neutral axis within the element deter-mined in the first step

• Calculating Mp.

Section Properties 8 - 3


Equations for the various potential locations of the plastic neutral axis (PNA) are given in Table 8-1.

Table 8-1 Calculation of PNA and Mp for Sections in Positive Flexure

Case PNA Condition Y and Mp

I In Web Pt + Pw ≥ Pc + Ps + Prb + Pn ( ) [ ]

− − − − = +

= + − + + + + + 22

12

2

t c s rt rb

w

wp s s rt rt rb rb c c t t

D P P P P PYP

PM Y D Y P d P d P d P d PdD

II In Top Flange

Pt + Pw + Pc ≥ Ps + Prb + Pn ( ) [ ]

+ − − −= +

= + − + + + + + 22

12

2

c w t s rt rb

c

cp c s s n n rb rb w w t t

c

t P P P P PYP

PM Y t Y P d P d P d P d Pdt

III

Concrete Deck

Below Prb

Pt + Pw + Pc ≥

2

rbct

Ps + Prb + Pn

( )

[ ]

+ + − −=

= + + + + +

2

2

c w t rt rbs

s

sp rt rt rb rb c c w w t t

s

P P P P PY tP

Y PM P d P d P d P d Pdt

IV Concrete Deck at

Prb

Pt + Pw + Pc + Prb ≥ rb

s

ct

Ps + Pn [ ]2

2

rb

sp rt rt c c w w t t

s

Y c

Y PM P d P d P d Pdt

=

= + + + +

V

Concrete Deck

Above Prb and Below

Prt

Pt + Pw + Pc + Prb ≥ rt

s

ct

Ps + Pn

( )

[ ]2

2

rb c w t rts

s


s

P P P P PY tP


+ + + − =

= + + + + +

VI Concrete Deck at

Prt

Pt + Pw + Pc + Prb + Pn ≥ rt

s

ct

Ps [ ]2

2

rt

sp rb rb c c w w t t

s

Y c


=

= + + + +





VII

Concrete Deck

Above Prt

Pt + Pw + Pc + Prb + Prt < rt

s

ct

Ps

( )

[ ]2

2

rb c w t rts

s


s

P P P P PY tP


+ + + + =

= + + + + +

Next the section is checked for ductility requirement in accordance with equa-tion 6.10.7.3. In checking the ductility per 6.10.7.3, the depth of the haunch is neglected.

Dp ≤ 0.42Dt

where Dp is the distance from the top of the concrete deck to the neutral axis of the composite section at the plastic moment, and Dt is the total depth of the composite section. At the section where the ductility requirement is not satis-fied, the plastic moment of a composite section in positive flexure is set to ze-ro.

Figure 8-1 Plastic Neutral Axis Cases -- Positive Flexure

sb

st

ct

tt

cb

tb

wtD

rtA rbArtP

tP

wPcPrbP

sP

CASE I CASE II CASES III-VII

PNA

PNA PNA

Y Y

Y

rtC

rbC

sb

st

ct

tt

cb

tb

wtD

rtA rbArtP

tP

wPcPrbP

sP

CASE I CASE II CASES III-VII

PNA

PNA PNA

Y Y

Y

rtC

rbC



8.1.2.2 Composite Section in Negative Flexure The plastic moment of a composite section in negative flexure is calculated by an analogous procedure. Equations for the two cases most likely to occur in practice are given in Table 8-2. The plastic moment of a noncomposite section is calculated by eliminating the terms pertaining to the concrete deck and longi-tudinal reinforcement from the equations in Tables 8-1 and 8-2 for composite sections.

Table 8-2 Calculation of PNA and Mp for Sections in Negative Flexure


I In Web Pc + Pw ≥ Pt + Prb + Pn ( ) [ ]22

12

2

c t rt rb

w

wp n n rb rb t t l l

D P P P PYP

PM Y D Y P d P d Pd PdD

− − − = +

= + − + + + +

II In Top Flange Pc + Pw + Pt ≥ Prb + Pn

( ) [ ]22

12

2

l w c rt rb

t

tp l n n rb rb w w c c

l

t P P P PYP

PM Y t Y P d P d P d P dt

− − − = +

= + − + + + +

Figure 8-2 Plastic Neutral Axis Cases -- Negative Flexure

rtPrbP

tP

wP

cP

st

tt

ct

D

cb

cb

wt

rtA rbA

PNAY

CASE V

CASE I CASE II

PNAY

rtPrbP

tP

wP

cP

st

tt

ct

D

cb

cb

wt

rtA rbArtA rbA

PNAYPNAY

CASE V

CASE I CASE II

PNAYPNA

Y



in which

Prt = Fyrt Art

Ps = 0.85 cf ′ bsts

Prb = Fyrb Arb

Pc = Fycbctc

Pw = Fyw Dtw

Pt = Fyt bttt

In the equations for Mp given in Tables 8-1 and 8-2, d is the distance from an element force to the plastic neutral axis. Element forces act at (a) mid-thickness for the flanges and the concrete deck, (b) mid-depth of the web, and (c) center of reinforcement. All element forces, dimensions, and distances are taken as positive. The conditions are checked in the order listed in Tables 8-1 and 8-2.

8.1.3 Section Classification and Factors

8.1.3.1 Compact or Non-Compact − Positive Flexure The program determines if the section can be qualified as compact based on the following criteria:

the specified minimum yield strengths of the flanges do not exceed 70.0 ksi,

the web satisfies the requirement of AASHTO-2012 Article (6.10.2.1.1),

150w

Dt

≤

the section satisfies the web slenderness limit,

2

3.76 .cp

w yc

D Et F

≤ (AASHTO-2012 6.10.6.2.2-1)

The program does not verify if the composite section is kinked (chorded) con-tinuous or horizontally curved.



8.1.3.2 Design in Accordance with Appendix A The program determines if a section qualifies to be designed using Appendix A of the AASHTO-2012 Edition based on the following criteria:

• the Design Request Parameter “Use Appendix A?” is set to Yes (see Chapter 4 for more information about setting parameters in the Design Request),

• the specified minimum yield strengths of the flanges do not exceed 70.0 ksi,

• the web satisfies the noncompact slenderness limit,

2 5.7c

w yc

D Et F

< (AASHTO-2012 6.10.6.2.3-1)

• the flanges satisfy the following ratio,

0.3.yc

yt

II

≥ (AASHTO-2012 6.10.6.2.3-2)

The program does not verify if the composite section is kinked (chorded) con-tinuous or horizontally curved.

8.1.3.3 Hybrid Factor Rh − Composite Section Positive Flexure For rolled shapes, homogenous built-up sections, and built-up sections with a higher-strength steel in the web than in both flanges, Rh is taken as 1.0. Other-wise the hybrid factor is taken as:

( )+ β ρ −ρ

=+ β

312 312 2hR (AASHTO-2012 6.10.1.10.1-1)

where

ρ = the smaller of and 1.0yw nF f

β =2 n w

fn

D tA

(AASHTO-2012 6.10.1.10.1-2)

Afn = bottom flange area



Dn = the distance from the elastic neutral axis of the cross-section to the inside face of bottom flange

Fn = fy of the bottom flange

8.1.3.4 Hybrid Factor Rh − Composite Section Negative Flexure For rolled shapes, homogenous built-up sections, and built-up sections with a higher-strength steel in the web than in both flanges, Rh is taken as 1.0. Other-wise the hybrid factor is taken as:

( )+ β ρ −ρ

=+ β

312 312 2hR (AASHTO-2012 6.10.1.10.1-1)

where

β =2 n w

fn

D tA

(AASHTO-2012 6.10.1.10.1-2)


Afn = Flange area on the side of the neutral axis corresponding to Dn. If the top flange controls, then the area of longitudinal rebar in the slab is included in calculating Afn.

Dn = The larger of the distances from the elastic neutral axis of the cross-section to the inside face of either flange. For sections where the neutral axis is at the mid-depth of the web, this dis-tance is from the neutral axis to the inside face of the flange on the side of the neutral axis where yielding occurs first.

Fn = fy of the controlling flange. When the top flange controls, then Fn is equal to the largest of the minimum specified yield strengths of the top flange or the longitudinal rebar in the slab.

8.1.3.5 Hybrid Factor Rh – Non Composite Section For rolled shapes, homogenous built-up sections, and built-up sections with a higher-strength steel in the web than in both flanges, Rh is taken as 1.0. Other-wise the hybrid factor is taken as:



( )+ β ρ −ρ

=+ β

312 312 2hR (AASHTO-2012 6.10.1.10.1-1)

where


β =2 n w

fn

D tA

(AASHTO-2012 6.10.1.10.1-2)

Afn = Flange area on the side of the neutral axis corresponding to Dn.

Dn = The larger of the distances from the elastic neutral axis of the cross-section to the inside face of either flange. For sections where the neutral axis is at the mid-depth of the web, this dis-tance is from the neutral axis to the inside face of the flange on the side of the neutral axis where yielding occurs first.

Fn = fy of the controlling flange.

8.1.3.6 Web Load-Shedding Factor Rb When checking constructability in accordance with the provisions of AASH-TO-2012 Article 6.10.2.1 or for composite sections in positive flexure, the Rb factor is taken as equal to 1.0. For composite sections in negative flexure, the Rb factor is taken as:

21 1.01200 300

wc

wc cb rw

a w

a DRt

λ = − − ≤ +

(AASHTO-2012 6.10.1.10.2)

where

λ = 5.7rwyc

EF

(AASHTO-2012 6.10.1.10.2-4)

2 c wwc

fc fc

D tab t

= (AASHTO LRFD 2008 6.10.1.10.2-5)



When the user specifies the Design Request parameter “Do webs have longitu-dinal stiffeners?” as yes, the Rb factor is set to 1.0 (see Chapter 4 for more in-formation about specifying Design Request parameters).

8.1.3.7 Unbraced Length Lb and Section Transitions The program assumes that the top flange is continuously braced for all Design Requests, except for Constructability. For more information about flange lat-eral bracing in a Constructability Design Request, see Section 8.6 of this man-ual.

The unbraced length Lb for the bottom flange is equal to the distance between the nearest downstation and upstation qualifying cross diaphragms or span support as defined in the Bridge Object. Some of the diaphragm types available in CSiBridge may not necessarily provide restraint to the bottom flange. The program assumes that the following diaphragm qualifies as providing lateral restraint to the bottom flange: single beam, all types of chords and braces ex-cept V braces without bottom beams.

For unbraced lengths where the member is nonprismatic, the lateral torsional buckling resistance of the compression flange at each section within the un-braced length is taken as the smallest resistance within the unbraced length un-der consideration and the moment gradient modifier Cb is taken as 1.0.

For unbraced lengths containing a transition to a smaller section at a distance less than or equal to 20% of the unbraced length from a brace point, the lateral torsional buckling resistance is determined assuming the transition to the smaller section does not exist provided that the lateral moment of inertia of the flange of the smaller section is equal to or larger than 0.5 times the correspond-ing value in the larger section. The algorithm does not distinguish at which brace point the moment demand is smaller and applies the exception at both brace points. It is the responsibility of the user to pay special attention to the section transition within the 20% of the unbraced length from the brace point and to follow the guidelines in AASHTO LRFD C6.10.8.2.3.

For this algorithm to be effective, it is necessary to have bridge section cuts at each nonprismatic girder-section transition. This can be assured by using the local section cuts feature when updating the linked model to create additional local section cuts for each girder of steel I-girder bridge sections. Such girder-only section cuts will be created at changes in the steel I-girder section, at stag-



gered diaphragms (cross frames), and at splice locations wherever a full-width section cut does not exist.

8.2 Demand Sets Demand Set combos (at least one is required) are user-defined combinations based on LRFD combinations (see Chapter 4 for more information about speci-fying Demand Sets). The demands from all specified demand combos are en-veloped and used to calculate D/C ratios. The way the demands are used de-pends on if the design parameter "Use Stage Analysis?” is set to Yes or No.

If “Use Stage Analysis? = Yes,” the program reads the stresses on beams and slabs directly from the section cut results. The program assumes that the effects of the staging of loads applied to non-composite versus composite sections, as well as the concrete slab material time dependent properties, were captured by using the Nonlinear Staged Construction load case available in CSiBridge.

Note that the Design Request for staged constructability check (Steel-I Comp Construct Stgd) allows only Nonlinear Staged Construction load cases to be used as Demand Sets.

If “Use Stage Analysis? = No,” the program decomposes load cases present in every demand set combo to three Bridge Design Action categories: non-composite, composite long term, and composite short term. The program uses the load case Bridge Design Action parameter to assign the load cases to the appropriate categories. A default Bridge Design Action parameter is assigned to a load case based on its Design Type. However, the parameter can be over-written: click the Analysis > Load Cases > {Type} > New command to dis-play the Load Case Data – {Type} form; click the Design button next to the Load case type dropdown list; under the heading Bridge Design Action, select the User Defined option and select a value from the list. The assigned Bridge Designed Action values are handled by the program in the following manner:

Table 8-3 Bridge Design Action

Bridge Design Action Value Specified by the User

Bridge Design Action Category Used in the Design Algorithm

Non-Composite Non-Composite

Long-Term Composite Long-Term Composite

8 - 12 Demand Sets


Short-Term Composite Short-Term Composite

Staged Non-Composite

Other Non-Composite

8.2.1 Demand Flange Stresses fbu and ff Evaluation of the flange stress, fbu, calculated without consideration of flange lateral bending is dependent on setting the Design Request parameter “Use Stage Analysis?” If the “Use Stage Analysis? = No,” then

NC LTC STCbu

comp steel LTC STC

P M M MfA S S S

= + + +

where MNC is the demand moment on the non-composite section, MLTC is the demand moment on the long-term composite section, and MSTC is the demand moment on the short-term composite section.

The short-term section modulus for positive moment is calculated by trans-forming the concrete deck using the steel-to-concrete modular ratio. The modu-lar ratio (n) is calculated as a decimal number expressed as n= Es/Ec and used without rounding. The long-term section modulus for positive moment is cal-culated using a modular ratio factored by n, where n is specified in the Design Parameter as the “Modular ratio long-term multiplier.” The effect of compres-sion reinforcement is ignored. For negative moment, the concrete deck is as-sumed cracked and is not included in the section modulus calculations while tension reinforcement is accounted for.

If “Use Stage Analysis? = Yes,” then the fbu stresses on each flange are read di-rectly from the section cut results. The program assumes that the effects of the staging of loads applied to non-composite versus composite sections, as well as the concrete slab material time dependent properties, were captured by using the Nonlinear Staged Construction load case available in CSiBridge.

In the Strength Design Check, the program verifies the sign of the stress in the composite slab, and if stress is positive (tension), the program assumes that the entire section cut demand moment is carried by the steel section only. This is to reflect the fact that the concrete in the composite slab is cracked and does not

Demand Sets 8 - 13


contribute to the resistance of the section. Flange stress ff , used in the Service Design Check, is evaluated in the same manner as stress fbu, with one excep-tion. When the Steel Service Design Request parameter “Does concrete slab re-sist tension?” is set to Yes, the program uses section properties based on a transformed section that assumes the concrete slab to be fully effective in both tension and compression.

In the Constructability checks, the program proceeds based on the status of the concrete slab. When no slab is present or the slab is non-composite, the fbu stresses on each flange are read directly from the section cut results. When the slab status is composite, the program verifies the sign of the stress in the com-posite slab, and if stress is positive (tension), the program assumes that the en-tire section cut demand moment is carried by the steel section only. This is to reflect the fact that the concrete in the composite slab is cracked and does not contribute to the resistance of the section.

8.2.2 Demand Flange Lateral Bending Stress fl The flange lateral bending stress fl is evaluated only when all of the following conditions are met:

“Steel Girders” has been selected for the deck section type (Components > Superstructure Item > Deck Sections command) and the Girder Modeling In Area Object Models – Model Girders Using Area Objects option is set to “Yes” on the Define Bridge Section Data – Steel Girder form.

The bridge object is modeled using Area Objects. This option can be set us-ing the Bridge > Update command to display the “Update Bridge Structural Model“ form; then select the Update as Area Object Model option.

Set the Live Load Distribution to Girders method to “Use Forces Directly from CSiBridge” on the Bridge Design Request – Superstructure – {Code} form, which displays when the Design/Rating > Superstructure Design > Design Requests command is used (see Chapter 3 for more information about Live Load Distribution). Since there is no live load used in the Con-structability design, request this setting does not apply in that case.

In all other cases, the flange lateral bending stress is set to zero. The fl stresses on each flange are read directly from the section cut results.

8 - 14 Demand Sets


8.2.3 Depth of the Web in Compression For composite sections in positive flexure, the depth of the web in compression is computed using the following equation:

0cc fc

c t

fD d tf f

= − ≥ + (AASHTO-2012 D6.3-1)

Figure 8-3 Web in Compression – Positive Flexure where

fc = Sum of the compression-flange stresses caused by the different loads, i.e., DC1, the permanent load acting on the noncomposite section; DC2, the permanent load acting on the long-term composite section; DW, the wear-ing surface load; and LL+IM; acting on their respective sections. fc is taken as negative when the stress is in compression. Flange lateral bending is dis-regarded in this calculation.

ft = Sum of the tension-flange stresses caused by the different loads. Flange lat-eral bending is disregarded in this calculation.

For composite sections in negative flexure, Dc is computed for the section con-sisting of the steel girder plus the longitudinal reinforcement, with the excep-tion of the following. For composite sections in negative flexure at the Service Design Check Request where the concrete deck is considered effective in ten-sion for computing flexural stresses on the composite section (Design Parame-ter “Does concrete slab resist tension?” = Yes), Dc is computed from AASH-TO-2012 Eq. D 6.3.1-1. For this case, the stresses fc and ft are switched, the signs shown in the stress diagram are reversed, tfc is the thickness of the bottom flange, and Dc instead extends from the neutral axis down to the top of the bot-tom flange.

Demand Sets 8 - 15


8.2.4 Moment Gradient Modifier Cb When the design request parameter ‘Method for determining moment gradient factor Cb‘ is set to ‘Program Determined’, then for each demand set the stresses defined in AASHTO LRFD section 6.10.8.2.3 fmid, f0,f1 and f2 at the unbraced segment are determined by interpolation of demands at nearest section cuts. The designer should be aware that live load moments at neighboring section cuts within the unbraced segment are not necessarily controlled by the same load pattern and as a result the moment gradient calculation may be impacted. The moment gradient modifier Cb is then calculated as:

8.3 Strength Design Request The Strength Design Check calculates at every section cut positive flexural capacity, negative flexural capacity, and shear capacity. It then compares the capacities against the envelope of demands specified in the Design Request.

8.3.1 Flexure

8.3.1.1 Positive Flexure – Compact The nominal flexural resistance of the section is evaluated as follows:

If Dp ≤ 0.1 Dt, then Mn = Mp; otherwise

1.07 0.7 pn p

t

DM M

D

= −

(AASHTO-2012 6.10.7.1.2-2)

8 - 16 Strength Design Request


In a continuous span, the nominal flexural resistance of the section is deter-mined as

Mn ≤ 1.3RhMy

where Rh is a hybrid factor for the section in positive flexure.

The demand over capacity ratio is evaluated as

113DoverC max ,

0.6

u xtl

f n yf

M f S fM F

+ = φ

8.3.1.2 Positive Flexure – Non-Compact Nominal flexural resistance of the top compression flange is taken as:

Fnc = RbRhFyc (AASHTO-2012 6.10.7.2.2-1)

Nominal flexural resistance of the bottom tension flange is taken as:

Fnt = RhFyt (AASHTO-2012 6.10.7.2.2-1)


113DoverC max , ,

0.6

bubu l

f nt f nc yf

f f f fF F F

+ = φ φ

8.3.1.3 Negative Flexure in Accordance with Article 6.10.8 The local buckling resistance of the compression flange Fnc(FLB) as specified in AASHTO-2012 Article 6.10.8.2.2 is taken as:

If λf ≤ λ pf, then Fnc = RbRhFyc. (6.10.8.2.2-1)

Otherwise

λ − λ

= − − λ − λ 1 1 yr f pf

nc b h ych yc rf pf

FF R R F

R F (6.10.8.2.2-2)

in which

Strength Design Request 8 - 17


λ =2

fcf

fc

bt

(6.10.8.2.2-3)

0.38pfyc

EF

λ = (6.10.8.2.2-4)

0.56rfyr

EF

λ = (6.10.8.2.2-5)

Fyr = Compression-flange stress at the onset of nominal yielding within the cross-section, including residual stress effects, but not includ-ing compression-flange lateral bending, taken as the smaller of 0.7Fyc and Fyw, but not less than 0.5 Fyc.

The lateral torsional buckling resistance of the compression flange Fnc(LTB) as specified in AASHTO-2012 Article (6.10.8.2.3) is taken as follows:

If Lb ≤ Lp, then Fnc = RbRhFyc. (6.10.8.2.3-1)

If Lp < Lb ≤ Lr, then

1 1 yr b pnc b b h yc b h yc

h yc r p

F L LF C R R F R R F

R F L L −

= − − ≤ − (6.10.8.2.3-2)

If Lb > Lr, then Fnc = Fcr ≤ RbRhFyc (6.10.8.2.3-3)

in which

unbraced length, 1.0 ,b p t r tyc yr

E EL L r L rF F

= = = π

Cb = moment gradient modifier

2

2b b

crb

t

C R EFLr

π=

(6.10.8.2.3-8)



112 13

fct

c w

fc fc

br

D tb t

= +

(6.10.8.2.3-9)

The nominal flexural resistance of the bottom compression flange is taken as the smaller of the local buckling resistance and the lateral torsional buckling resistance:

( ) ( )FLB LTBmin ,nc nc ncF F F=

The nominal flexural resistance of the top tension flange is taken as:

φ f h yfR F (6.10.8.1.3-1)


1

1

13DoverC max , ,

0.6

bubu

f m f h yf yc

f f f fF R F F

+ = φ φ

8.3.1.4 Negative Flexure in Accordance with Appendix A6 Sections that satisfy the following requirement qualify as compact web sec-tions:

( )2

cp

cppw D

w

Dt

≤ λ (AASHTO-2012 A6.2.1-2)

where

( ) 2

0.54 0.09cp

yc cppw D

cp

h y

EF D

DMR M

λ = ≤

−

(AASHTO-2012 A6.2.1-2)

5.7rwyc

EF

λ = (AASHTO-2012 A6.2.1-3)



Dc = depth of the web in compression in the elastic range

Dcp = depth of the web in compression at the plastic moment

Then web plastification factors are determined as

ppc

yc

MR

M= (AASHTO-2012 A6.2.1-4)

ppt

yt

MR

M= (AASHTO-2012 A6.2.1-5)

Sections that do not satisfy the requirement for compact web sections, but for which the web slenderness satisfies the following requirement:

w rwλ < λ (AASHTO-2012 A6.2.2-1)

where

2 cw

w

Dt

λ = (AASHTO-2012 A6.2.2-2)

5.7rwyc

EF

λ = (AASHTO-2012 A6.2.2-3)

The web plastification factors are taken as:

( )

( )1 1 c

c

w pw Dh yc p ppc

p tw yc ycpw D

R M M MR

M M M

λ − λ = − − ≤ λ − λ

(AASHTO-2012 A6.2.2-4)

( )

( )1 1 c

c

w pw Dh yt p ppt

p rw yt ytpw D

R M M MR

M M M

λ − λ = − − ≤ λ − λ

(AASHTO-2012 A6.2.2-5)

where



( ) ( )c c

crwpw D pw D p

cp

DD

λ = λ ≤ λ

(AASHTO-2012 A6.2.2-6)

The local buckling resistance of the compression flange MncFLB as specified in AASHTO-2012 Article A6.3.2 is taken as:

If ,f pfλ ≤ λ then nc pc ycM R M= (AASHTO-2012 A6.3.2-1)

Otherwise 1 1 yr xc f pfnc pc yc

pc yc rf pf

F SM R M

R M λ − λ

= − − λ − λ (AASHTO-2012 A6.3.2-2)

in which

2fc

ffc

bt

λ = (AASHTO-2012 A6.3.2-3)

0.38pfyc

EF

λ = (AASHTO-2012 A6.3.2-4)

0.95 crf

yr

EkF

λ = (AASHTO-2012 A6.3.2-5)

For built-up sections, 4

c

w

kDt

= (AASHTO-2012 A6.3.2-6)

For rolled shapes (eFramePropType =SECTION_I as defined in API function SapObject.SapModel.PropFrame.GetNameList; PropType argument)

kc = 0.76

The lateral torsional buckling resistance of the compression flange MncLTB as specified in AASHTO-2012 Article A6.3.3 is taken as Mnc = RpcMyc:

If ,b pL L≥ then .nc pc ycM R M= (AASHTO-2012 A6.3.3-1)

If ,p b rL L L< ≤ then



1 1 yr xc b pnc b pc yc pc yc

pc yc r p

F S L LM C R M R M

R M L L −

= − − ≤ −

(AASHTO-2012 A6.3.3-2)

If ,b rL L> then nc cr xc pc ycM F S R M= ≤ (AASHTO-2012 A6.3.3-3)

in which

unbraced length,bL =

1.0p tyc

EL rF

= (AASHTO-2012 A6.3.3-4)

2

1.95 1 1 6.76 yr xcr t

yr xc

FE J S hL rF S h E J

= + +

(AASHTO-2012 A6.3.3-5)

Cb = moment gradient modifier

( )( )

22

2 1 0.078bcr b t

xcb t

C E JF L rS hL r

π= + (AASHTO-2012 A6.3.3-8)

3 33

1 0.63 1 0.633 3 3

fc ft fc ft ft ftw

fc ft

b t t b t tDtJb b

= + − + −

(AASHTO-2012 A6.3.3-9)

112 13

fct

c w

fc fc

br

D tb t

= +

(AASHTO-2012 A6.3.3-10)

The nominal flexural resistance of the bottom compression flange is taken as the smaller of the local buckling resistance and the lateral torsional buckling resistance:

( ) ( )FLB LTBmin ,nc nc ncM M M=



The nominal flexural resistance of the top tension flange is taken as:

f pt ytR Mφ


11

13DoverC max , ,

0.6

xcu

f nc f pt yt yc

Mu f S M fM R M F

+ = φ φ

8.3.1.5 Net Section Fracture All tension flanges are checked for net section fracture per AASHTO-2012 sec-tion 6.10.1.8. The net area of the tension flange is evaluated as follows:

𝐴𝐴𝑛𝑛 = 𝑟𝑟𝑠𝑠𝑠𝑠𝑠𝑠𝐴𝐴𝑔𝑔

Where rspl is a ratio defined by the user in the Splice definition (Bridge > Span Items > Optimize > Splices) command and Ag is the gross flange area. The demand over capacity ratio is calculated as follows:

𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑟𝑟𝐷𝐷 = 𝑓𝑓𝑏𝑏𝑏𝑏𝑚𝑚𝑚𝑚𝑛𝑛�𝑓𝑓𝑦𝑦;0.84𝐴𝐴𝑛𝑛𝐴𝐴𝑔𝑔

𝑓𝑓𝑏𝑏� (AASHTO-2012 6.10.1.8-1)

8.3.1.6 Shear Connectors The program calculates the total nominal shear force Pnom as specified in AASHTO-2012 Article 6.10.10.4.2. The user can use the Pnom value to deter-mine the minimum number of shear connectors n as defined in AASHTO-2012 eq. 6.10.10.4.1-2.

𝑃𝑃𝑛𝑛𝑛𝑛𝑚𝑚 = �𝑃𝑃𝑡𝑡2 + 𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟2

where

𝑃𝑃𝑡𝑡 = 𝑃𝑃𝑠𝑠 + 𝑃𝑃𝑛𝑛

𝑃𝑃𝑠𝑠 = min (0.85𝑓𝑓′𝑐𝑐𝑏𝑏𝑠𝑠𝑠𝑠𝑟𝑟𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑟𝑟𝑠𝑠;𝑓𝑓𝑦𝑦𝑦𝑦𝐷𝐷𝑡𝑡𝑦𝑦 + 𝑓𝑓𝑦𝑦𝑡𝑡𝑏𝑏𝑓𝑓𝑡𝑡𝑡𝑡𝑓𝑓𝑡𝑡 + 𝑓𝑓𝑦𝑦𝑐𝑐𝑏𝑏𝑓𝑓𝑐𝑐𝑡𝑡𝑓𝑓𝑐𝑐)

𝑃𝑃𝑛𝑛 = min (0.45𝑓𝑓′𝑐𝑐𝑏𝑏𝑠𝑠𝑠𝑠𝑟𝑟𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑟𝑟𝑠𝑠;𝑓𝑓𝑦𝑦𝑦𝑦𝐷𝐷𝑡𝑡𝑦𝑦 + 𝑓𝑓𝑦𝑦𝑡𝑡𝑏𝑏𝑓𝑓𝑡𝑡𝑡𝑡𝑓𝑓𝑡𝑡 + 𝑓𝑓𝑦𝑦𝑐𝑐𝑏𝑏𝑓𝑓𝑐𝑐𝑡𝑡𝑓𝑓𝑐𝑐)



𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟 =𝑃𝑃𝑡𝑡𝐿𝐿𝑎𝑎𝑎𝑎𝑎𝑎ℎ𝑅𝑅

AASHTO-2012 6.10.10.4.2-1 to 9)

Larch is calculated as 50% of girder span length and R is the radius of the girder.

8.3.2 Shear When processing the Design Request from the Design module, the program as-sumes that there are no vertical stiffeners present and classifies all web panels as unstiffened. If the shear capacity calculated based on this classification is not sufficient to resist the demand specified in the Design Request, the program recommends minimum stiffener spacing to achieve a Demand over Capacity ratio equal to 1. The recommended stiffener spacing is reported in the result ta-ble under the column heading d0req.

In the Optimization form (Design/Rating > Superstructure Design > Opti-mize command), the user can specify stiffeners locations and the program re-calculates the shear resistance. In that case the program classifies the web pan-els as interior or exterior and stiffened or unstiffened based on criteria specified in AASHTO-2012 section 6.10.9.1e. It should be noted that stiffeners are not modeled in the Bridge Object and therefore adding/modifying stiffeners does not affect the magnitude of the demands.

8.3.2.1 Nominal Resistance of Unstiffened Webs The nominal shear resistance of unstiffened webs is taken as:

n pV CV= (AASHTO-2012 6.10.9.2-1)

in which

0.58p yw wV F Dt= (AASHTO-2012 6.10.9.2-2)

C = the ratio of the shear-buckling resistance to the shear yield strength that is determined as follows:

If 1.12 ,w yw

D Ekt F

≤ then C = 1.0.

(AASHTO-2012 6.10.9.3.2-4)



If 1.12 1.40 ,yw w yw

Ek D EkF t F

< ≤ then 1.12 .yw

w

EkCD Ft

=

(AASHTO-2012 6.10.9.3.2-5)

If 1.40 ,w yw

D Ekt F

> then 21.57 ,

yw

w

EkCFD

t

=

(AASHTO-2012 6.10.9.3.2-6)

in which 255 .c

kdD

= +

(AASHTO-2012 6.10.9.3.2-7)

8.3.2.2 Nominal Resistance of Stiffened Interior Web Panels The nominal shear resistance of an interior web panel and with the section at the section cut proportioned such that:

( )2 2.5w

fc fc ft ft

Dtb t b t

≤+

(AASHTO-2012 6.10.9.3.2-1)

is taken as

( )

2

0.87 1

1n p

o

CV V CdD

−= +

+

(AASHTO-2012 6.10.9.3.2-2)

in which 0.58p yw wV F Dt= (AASHTO-2012 6.10.9.3.2-3)

where

do = transverse stiffener spacing.

Otherwise, the nominal shear resistance is taken as follows:

( )

2

0.87 1

1

n p

o o

CV V Cd dD D

−= + + +

(AASHTO-2012 6.10.9.3.2-8)



8.3.2.3 Nominal Resistance of End Panels The nominal shear resistance of a web end panel is taken as:

Vn = Vcr = CVp (AASHTO-2012 6.10.9.3.3-1)

in which

0.58 .p yw wV F Dt= (AASHTO-2012 6.10.9.3.3-2)


=φ

DoverC .u

v n

VV

8.4 Service Design Request The Service Design Check calculates at every section cut stresses ff at the top steel flange of the composite section and the bottom steel flange of the compo-site section and compares them against limits specified in AASHTO-2012 Sec-tion 6.10.4.2.2.

For the top steel flange of composite sections:

DoverC0 95

f

h yf

f.

. R F= (AASHTO-2012 6.10.4.2.2-1)

For the bottom steel flange of composite sections:

2DoverC0 95

lf

h yf

ff.

. R F

+= (AASHTO-2012 6.10.4.2.2-2)

For both steel flanges of noncomposite sections:

2DoverC0 80

lf

h yf

ff.

. R F

+= (AASHTO-2012 6.10.4.2.2-3)

The flange stresses are derived in the same way as fbu stress demands (see Sec-tion 8.2.1 of this manual). The user has an option to specify if the concrete slab

8 - 26 Service Design Request


resists tension or not by setting the “Does concrete slab resist tension?” Design Request parameter. It is the responsibility of the user to verify if the slab quali-fies, in accordance with “Does concrete slab resist tension?” Section 6.10.4.2.1, to resist tension.

For compact composite sections in positive flexure used in shored construction, the longitudinal compressive stress in the concrete deck, determined as speci-fied in AASHTO-2012 Article 6.10.1.1.1d, is checked against 0.6 .cf ′

DoverC = fdeck/0.6 cf ′

Except for composite sections in positive flexure in which the web satisfies the requirement of AASHTO-2012 Article 6.10.2.1.1, all section cuts are checked against the following requirement:

DoverC c

crw

fF

= (AASHTO-2012 6.10.2.2-4)

where:

fc = Compression-flange stress at the section under consideration due to de-mand loads calculated without consideration of flange lateral bending.

Fcrw = Nominal bend-buckling resistance for webs without longitudinal stiffen-ers determined as specified in AASHTO-2012 Article 6.10.1.9

20 9

crw

w

. EkFDt

=

(AASHTO-2012 6.10.1.9.1-1)

but not to exceed the smaller of RhFyc and Fyw/0.7. In which

k = bend buckling coefficient

( )29

c

kD D

= (AASHTO-2012 6.10.1.9.1-2)

where

Service Design Request 8 - 27


Dc = Depth of the web in compression in the elastic range determined as spec-ified in AASHTO-2012 Article D6.3.1.

When both edges of the web are in compression, k is taken as 7.2.

The highest Demand over Capacity ratio together with controlling equation is reported for each section cut.

8.5 Fatigue Design Request

8.5.1 Web Fatigue Web Fatigue Design Request is used to calculate the Demand over Capacity ra-tio as defined in AASHTO-2012 Section 6.10.5.3 – Special Fatigue Require-ment for Webs. The requirement is applicable to interior panels of webs with transverse stiffeners. When processing the Design Request from the Design module, the program assumes that there are no vertical stiffeners present and classifies all web panels as unstiffened. Therefore, when the Design Request is completed from the Design module, the Design Result Status table shows the message text “No stiffeners defined – use optimization form to define stiffen-ers.”

In the Optimization form (Design/Rating > Superstructure Design > Opti-mize command), the user can specify stiffener locations, and then the program can recalculate the Web Fatigue Request. In that case the program classifies the web panels as interior or exterior and stiffened or unstiffened based on criteria specified in AASHTO-2012 Section 6.10.9.1. It should be noted that stiffeners are not modeled in the Bridge Object and therefore adding/modifying stiffeners does not affect the magnitude of the demands.

DoverC u crV V= (AASHTO-2012 6.10.5.3-1)

where

Vu = Shear in the web at the section under consideration due to demand speci-fied in the Design Request demand set combos. If the live load distribu-tion to girders method “Use Factor Specified by Design Code” is select-ed in the Design Request, the program adjusts for the multiple presence factor to account for the fact that fatigue load occupies only one lane (AASHTO-2012 Section 3.6.1.4.3b) and multiple presence factors shall

8 - 28 Fatigue Design Request


not be applied when checking for the fatigue limit state (AASHTO-2012 Section 3.6.1.1.2).

Vcr = Shear-buckling resistance determined from AASHTO-2012 eq. 6.10.9.3.3-1 (see Section 8.3.2.3 of this manual)

8.5.2 Flange Fatigue For every demand set the top and bottom flange tensile stress range due to ver-tical bending and bottom flange tensile stress range due to lateral bending are calculated at every section cut. The tensile stress ranges can be used by the user to verify AASHTO-2012 load induced fatigue criteria specified in article 6.6.1.2.2.

The flange stresses are derived in the same way as fbu stress demands (see Sec-tion 8.2.1 of this manual). The tensile stress range for a particular demand set is calculated as delta between maximum tensile stress and minimum tensile stress. If the minimum stress is compressive and the maximum stress is tensile the stress range is set equal to the maximum stress, if both maximum and min-imum stresses are compressive the stress range is set equal to zero. If demand set does not contain an envelope of values the stress range is also set to zero.

8.6 Constructability Design Request

8.6.1 Staged (Steel-I Comp Construct Stgd) This request enables the user to verify the superstructure during construction using a Nonlinear Staged Construction load case. The use of nonlinear staged analysis allows the user to define multiple snapshots of the structure during construction where parts of the bridge deck may be at various completion stag-es. The user can control which stages the program will include in the calcula-tions of controlling demand over capacity ratios.

For each section cut specified in the Design Request, the constructability de-sign check loops through the Nonlinear Staged Construction load case output steps that correspond to Output Labels specified in the Demand Set. At each step the program determines the status of the concrete slab at the girder section cut. The slab status can be non present, present non-composite, or composite.

Constructability Design Request 8 - 29


The Staged Constructability Design Check accepts Area Object models. The Staged Constructability Design Check cannot be run on Solid or Spine models.

8.6.2 Non-Staged (Steel-I Comp Construct NonStgd) This request enables the user to verify Demand over Capacity ratios during construction without the need to define and analyze a Nonlinear Staged Con-struction load case. For each section cut specified in the Design Request the Constructability Design Check loops through all combos specified in the De-mand Set list. At each combo the program assumes the status of the concrete slab as specified by the user in the Slab Status column. The slab status can be non-composite or composite and applies to all the section cuts.

The Non-Staged Constructability Design Check accepts all Bridge Object Structural Model Options available in the Update Bridge Structural Model form (Bridge > Update > Structural Model Options option).

8.6.3 Slab Status vs. Unbraced Length On the basis of the slab status, the program calculates corresponding positive flexural capacity, negative flexural capacity, and shear capacity. Next the pro-gram compares the capacities against demands specified in the Demand Set by calculating the Demand over Capacity ratio. The controlling Demand Set and Output Label on a girder basis are reported for every section cut.

When the slab status is composite, the program assumes that the top flange is continuously braced. When slab status in not present or non-composite, the program treats both flanges as discretely braced. It should be noted that the program does not verify the presence of diaphragms at a particular output step. It assumes that anytime a steel beam is activated at a given section cut that the unbraced length Lb for the bottom flange is equal to the distance between the nearest downstation and the upstation qualifying cross diaphragms or span ends as defined in the Bridge Object. The program assumes the same Lb for the top flange. In other words the unbraced length Lb is based on the cross diaphragms that qualify as providing restraint to the bottom flange. Some of the diaphragm types available in CSiBridge may not necessarily provide restraint to the top flange. It is the user’s responsibility to provide top flange temporary bracing at the diaphragm locations before slabs acting compositely.

8 - 30 Constructability Design Request


8.6.4 Flexure

8.6.4.1 Positive Flexure Non Composite The Demand over Capacity ratio is evaluated as:

comp topcomp top comp tens bot

top top top bot

13max , , ,

bu lbu l bu bu l

f h yc f nc f crw f h yt

f ff f fD f fC R F F F R F

+ + += φ φ φ φ

where Fnctop is the nominal flexural resistance of the discretely braced top flange determined as specified in AASHTO LRFD Article 6.10.8.2 (also see Section 8.3.1.3 of this manual) and Fcrwtop is the nominal bend–buckling re-sistance for webs specified in AASHTO LRFD Article 6.10.1.9.1 for webs without longitudinal stiffeners.

20 9

crw

w

. EkFDt

=

(AASHTO-2012 6.10.1.9.1-1)

but not to exceed the smaller of RhFyc and Fyw /0.7

where

29

c

kDD

=

When both edges of the web are in compression, k = 7.2.

8.6.4.2 Positive Flexure Composite The demand over capacity ratio is evaluated as:

comp comp tens bot

top top bot

max , ,bu bu bu l

f h yc f crw f h yt

f f f fD CR F F R F

+= φ φ φ

where Fcrwtop is nominal bend-buckling resistance for webs specified in AASHTO LRFD Article 6.10.1.9.1 for webs without longitudinal stiffeners (also see Section 8.6.4.1 of this manual).



8.6.4.3 Negative Flexure Non Composite The Demand over Capacity ratio is evaluated as:

comp botcomp bot comp tens top

bot bot bot top

13max , , ,

bu lbu l bu bu l

f h yc f nc f crw f h yt

f ff f f f fD C

R F F F R F

+ + += φ φ φ φ

where Fncbot is the nominal flexural resistance of the discretely braced bottom flange determined as specified in AASHTO LRFD Article 6.10.8.2 (also see Section 8.3.1.3 of this manual) and Fcrwbot is nominal bend-buckling resistance for webs specified in AASHTO LRFD Article 6.10.1.9.1 for webs without lon-gitudinal stiffeners (also see Section 8.6.4.1 of this manual).

8.6.4.4 Negative Flexure Composite The demand over capacity ratio is evaluated as:

+ += φ φ φ φ φ

comp botcomp bot comp tens deck

bot bot bot top

13max , , , ,

bu lbu l bu bu

f h yc f nc f crw f h yt t r

f ff f f f fD CR F F F R F f

where Fncbot is the nominal flexural resistance of the discretely braced bottom flange determined as specified in AASHTO LRFD Article 6.10.8.2 (also see Section 8.3.1.3 of this manual), Fcrwbot is the nominal bend–buckling resistance for webs specified in AASHTO LRFD Article 6.10.1.9.1 for webs without lon-gitudinal stiffeners (also see Section 8.6.4.1 of this manual), and fdeck is the de-mand tensile stress in the deck and fr is the modulus of rupture of concrete as determined in AASHTO LRFD Article 5.4.2.6.

8.6.5 Shear When processing the Design Request from the Design module, the program as-sumes that there are no vertical stiffeners present and classifies all web panels as unstiffened. If the shear capacity calculated based on this classification is not sufficient to resist the demand specified in the Design Request and the con-trolling D over C ratio is occurring at a step when the slab status is composite, the program recommends minimum stiffener spacing to achieve a Demand over Capacity ratio equal to 1. The recommended stiffener spacing is reported in the result table under the column heading d0req.



In the Optimization form (Design/Rating > Superstructure Design > Opti-mize command), the user can specify stiffener locations and then the program can recalculate the shear resistance. In that case the program classifies the web panels as interior or exterior and stiffened or unstiffened based on criteria spec-ified in Section 6.10.9.1 of the code. It should be noted that stiffeners are not modeled in the Bridge Object and therefore adding/modifying stiffeners does not affect the magnitude of the demands. Adding stiffeners also does not in-crease capacity of sections cuts where the concrete slab status is other than composite.

8.6.5.1 Non Composite Sections The nominal shear resistance of a web end panel is taken as:

n cr PV V CV= = (AASHTO-2012 6.10.9.3.3-1)

in which

0.58 .p yw wV F Dt= (AASHTO-2012 6.10.9.3.3-2)

The Demand over Capacity ratio is evaluated as

DoverC u

v n

VV

=φ

8.6.5.2 Composite Section

8.6.5.2.1 Nominal Resistance of Unstiffened Webs The nominal shear resistance of unstiffened webs is taken as:

n pV CV= (AASHTO-2012 6.10.9.2-1)

in which

0.58p yw wV F Dt= (AASHTO-2012 6.10.9.2-2)




If 1.12 ,w yw

D Ekt F

≤ then C = 1.0. (AASHTO-2012 6.10.9.3.2-4)

If 1.12 1.40 ,yw w yw

Ek D EkF t F

< ≤ then 1.12 .yw

w

EkCD Ft

=

AASHTO-2012 (6.10.9.3.2-5)

If 1.40 ,w yw

D Ekt F

> then 21.57 ,

yw

w

EkCFD

t

=

AASHTO-2012 (6.10.9.3.2-6)

in which 255 .c

kdD

= +

(AASHTO-2012 6.10.9.3.2-7)

8.6.5.2.2 Nominal Resistance of Stiffened Interior Web Panels The nominal shear resistance of an interior web panel, with the section at the section cut proportioned such that

( )2 2.5,w

fc fc ft ft

Dtb t b t

≤+

(AASHTO-2012 6.10.9.3.2-1)

is taken as

( )

2

0.87 1

1n p

o

CV V CdD

−= +

+

(AASHTO-2012 6.10.9.3.2-2)

in which 0.58p yw wV F Dt= (AASHTO-2012 6.10.9.3.2-3)

where





( )

2

0.87 1

1

n p

o o

CV V Cd dD D

−= + + +

(AASHTO-2012 6.10.9.3.2-8)

8.6.5.2.3 Nominal Resistance of End Panels The nominal shear resistance of a web end panel is taken as:

n cr PV V CV= = (AASHTO-2012 6.10.9.3.3-1)

in which

0.58 .p yw wV F Dt= (AASHTO-2012 6.10.9.3.3-2)


DoverC u

v n

VV

=φ

8.7 Section Optimization After at least one Steel Design Request has been successfully processed, CSiBridge enables the user to open a Steel Section Optimization module. The Optimization module allows interactive modification of steel plate sizes and definition of vertical stiffeners along each girder and span. It recalculates re-sistance “on the fly” based on the modified section without the need to unlock the model and rerun the analysis. It should be noted that in the optimization process the demands are not recalculated and are based on the current CSiBridge analysis results.

The Optimization form allows simultaneous display of three versions of section sizes and associated resistance results. The section plate size versions are “As Analyzed,” “As Designed,” and “Current.” The section plots use distinct colors for each version – black for As Analyzed, blue for As Designed, and red for Current. When the Optimization form is initially opened, all three versions are identical and equal to “As Analyzed.”

Two graphs are available to display various forces, moments, stresses, and rati-os for the As Analyzed or As Designed versions. The values plotted can be

Section Optimization 8 - 35


controlled by clicking the “Select Series to Plot” button. The As Analyzed se-ries are plotted as solid lines and the As Designed series as dashed lines.

To modify steel plate sizes or vertical stiffeners, a new form can be displayed by clicking on the Modify Section button. After the section modification is completed, the Current version is shown in red in the elevation and cross sec-tion views. After the resistance has been recalculated successfully by clicking the Recalculate Resistance button, the Current version is designated to As De-signed and displayed in blue.

After the section optimization has been completed, the As Designed plate sizes and materials can be applied to the analysis bridge object by clicking the OK button. The button opens a new form that can be used to Unlock the existing model (in that case all analysis results will be deleted) or save the file under a new name (New File button). Clicking the Exit button does not apply the new plate sizes to the bridge object and keeps the model locked. The As Designed version of the plate sizes will be available the next time the form is opened, and the Current version is discarded.

8 - 36 Section Optimization

Chapter 9 Design Steel U-Tub Bridge with Composite Slab

This chapter describes the algorithms CSiBridge applies when designing steel U-tub with composite slab superstructures in accordance with the AASHTO LRFD.

9.1 Section Properties

9.1.1 Yield Moments

9.1.1.1 Composite Section in Positive Flexure The positive yield moment, My, is determined by the program in accordance with section D6.2.2 of the code using the following user-defined input, which is part of the Design Request (see Chapter 4 for more information about Design Request).

Mdnc = The user specifies in the Design Request the name of the combo that represents the moment caused by the factored permanent load applied before the concrete deck has hardened or is made composite.

Mdc = The user specifies in the Design Request the name of the combo that represents the moment caused by the remainder of the factored perma-nent load (applied to the composite section).

The program solves for MAD from the following equation,

9- 1


dnc dc ADyt

NC LT ST

M M MFS S S

= + + (D6.2.2-1)

and then calculates yield moment based on the following equation

y dnc dc ADM M M M= + + (D6.2.2-2)

where

SNC = Noncomposite section modulus (in.3)

SLT = Long-term composite section modulus (in.3)

SST = Short-term composite section modulus (in.3)

My is taken as the lesser value calculated for the compression flange, Myc, or the tension flange, Myt. The positive My is calculated only once based on Mdnc and Mdc demands specified by the user in the Design Request. It should be noted that the My calculated in the procedure described here is used by the program only to determine Mnpos for compact sections in positive bending in a continu-ous span, where the nominal flexural resistance may be controlled by My in ac-cordance with (eq. 6.10.7.1.2-3).

1.3n h yM R M≤

9.1.1.2 Composite Section in Negative Flexure For composite sections in negative flexure, the procedure described for positive yield moment is followed, except that the composite section for both short-term and long-term moments consists of the steel section and the longitudinal rein-forcement within the tributary width of the concrete deck. Thus, SST and SLT are the same value. Also, Myt is taken with respect to either the tension flange or the longitudinal reinforcement, whichever yields first. The negative My is cal-culated only once based on the Mdnc and Mdc demands specified by the user in the Design Request.

9.1.2 Plastic Moments

9.1.2.1 Composite Section in Positive Flexure The positive plastic moment, Mp, is calculated as the moment of the plastic forces about the plastic neutral axis. Plastic forces in the steel portions of a


Chapter 9 - Design Steel U-Tub Bridge with Composite Slab

cross-section are calculated using the yield strengths of the flanges, the web, and reinforcing steel, as appropriate. Plastic forces in the concrete portions of the cross-section that are in compression are based on a rectangular stress block with the magnitude of the compressive stress equal to 0.85 .cf ′ Concrete in ten-sion is neglected. The position of the plastic neutral axis is determined by the equilibrium condition, where there is no net axial force. In calculating Mp for positive moment, the contribution of the rebar in the deck is ignored.

The plastic moment of a composite section in positive flexure is determined by:

• Calculating the effective width of bottom flange per 6.11.1.1

• Calculating the element forces and using them to determine if the plastic neu-tral axis is in the web, top flange, or concrete deck;

• Calculating the location of the plastic neutral axis within the element deter-mined in the first step;

and

• Calculating Mp.

Equations for the various potential locations of the plastic neutral axis (PNA) are given in Table 9-1.



I In Web Pt + Pw ≥ Pc + Ps + Prb + Pn ( ) [ ]22

12

2

t c s rt rb

w

wp s s rt rt rb rb c c t t

D P P P P PYP

PM Y D Y P d P d P d P d PdD

− − − − = +

= + − + + + + +

II In Top Flanges

Pt + Pw + Pc ≥ Ps + Prb + Pn ( ) [ ]22

12

2

c w t s rt rb

c

cp c s s n n rb rb w w t t

c

t P P P P PYP

PM Y t Y P d P d P d P d Pdt

+ − − −= +

= + − + + + + +





III

Concrete Deck

Below Prb

Pt + Pw + Pc ≥ 2

rbct

Ps + Prb + Pn ( )

[ ]2

2

c w t rt rbs

s


s

P P P P PY tP


+ + − −=

= + + + + +

IV Concrete Deck at

Prb Pt + Pw + Pc + Prb ≥ rb

s

ct

Ps + Pn [ ]

2

2

rb

sp rt rt c c w w t t

s

Y c


=

= + + + +

V

Concrete Deck

Above Prb and Below

Prt

Pt + Pw + Pc + Prb ≥ rt

s

ct

Ps + Pn ( )

[ ]2

2

rb c w t rts

s


s

P P P P PY tP


+ + + − =

= + + + + +

VI Concrete Deck at

Prt Pt + Pw + Pc + Prb + Pn ≥ rt

s

ct

Ps [ ]

2

2

rt

sp rb rb c c w w t t

s

Y c


=

= + + + +

VII

Concrete Deck

Above Prt

Pt + Pw + Pc + Prb + Prt < rt

s

ct

Ps ( )

[ ]2

2

rb c w t rts

s


s

P P P P PY tP


+ + + + =

= + + + + +



Figure 9-1 Plastic Neutral Axis Cases – Positive Flexure

Prt = Fyrt Art

Ps = 0.85 cf ′ bsts

Prb = Fyrb Arb

Pc = 2 Fycbctc

Pw = (2 Fyw Dtw)/cos αweb

Pt = Fyt bttt where bt is effective width of bottom flange per 6.11.1.1

Next the section is checked for ductility requirement in accordance with equa-tion 6.10.7.3. In checking the ductility per 6.10.7.3, the depth of the haunch is neglected.

Dp ≤ 0.42Dt

where,

Dp is the distance from the top of the concrete deck to the neutral axis of the composite section at the plastic moment.

Dt is the total depth of the composite section.

At the section where the ductility requirement is not satisfied, the plastic mo-ment of a composite section in positive flexure is set to zero.

9.1.2.2 Composite Section in Negative Flexure The plastic moment of a composite section in negative flexure is calculated by an analogous procedure. Equations for the two cases most likely to occur in

rt A rb A rt P

t P

w P c P

rb P s P

CASE I CASE II CASES III - VII

PNA

PNA PNA Y

Y

Y

rt C

rb C



practice are given in Table 9-2. The plastic moment of a noncomposite section is calculated by eliminating the terms pertaining to the concrete deck and longi-tudinal reinforcement from the equations for composite sections.

Table 9-2 Calculation of PNA and Mp for Sections in Negative Flexure


I In Web Pc + Pw ≥ Pt + Prb + Pn ( ) [ ]22

12

2

c t rt rb

w

wp n n rb rb t t l l

D P P P PYP

PM Y D Y P d P d Pd PdD

− − − = +

= + − + + + +

II In Top Flange Pc + Pw + Pt ≥ Prb + Pn

( ) [ ]22

12

2

l w c rt rb

t

tp l n n rb rb w w c c

l

t P P P PYP

PM Y t Y P d P d P d P dt

− − − = +

= + − + + + +

Figure 9-2 Plastic Neutral Axis Cases – Negative Flexure

Prt = Fyrt Art

Ps = 0

Prb = Fyrb Arb

Pc = Fycbctc where bc is effective width of bottom flange per 6.11.1.1

rtPrbP

tP

wP

cP

rtA rbA

PNAY

CASE I CASE II

PNAY

rtPrbP

tP

wP

cP

rtA rbArtA rbA

PNAYPNAY

CASE I CASE II

PNAYPNA

Y



Pw = (2Fyw Dtw)/cos αweb

Pt = 2Fyt bttt

In the equations for Mp, d is the distance from an element force to the plastic neutral axis. Element forces act at (a) mid-thickness for the flanges and the concrete deck, (b) mid-depth of the web, and (c) center of reinforcement. All element forces, dimensions, and distances are taken as positive. The conditions are checked in the order listed.

9.1.3 Section Classification and Factors

9.1.3.1 Compact or Non-Compact - Positive Flexure The program determines if the section can be qualified as compact based on the following criteria:

• the bridge is not horizontally curved

• the specified minimum yield strengths of the flanges do not exceed 70.0 ksi,

• the web satisfies the requirement of Article (6.11.2.1.2),

150w

Dt

≤

• the section satisfies requirements of 6.11.2.3

• the box flange is fully effective as specified in 6.11.1.1

• the section satisfies web slenderness limit

2

3.76 .cp

w yc

D Et F

≤ (6.11.6.2.2-1)

The user can control in the design request parameters how the program shall determine if the bridge is straight or horizontally. If the “Determined by pro-gram” option is selected the algorithm checks for radius of the layout line at every valid section cut. If the radius is a definite number the bridge is classified as horizontally curved.



9.1.3.2 Hybrid Factor Rh – Positive Flexure For homogenous built-up sections, and built-up sections with a higher-strength steel in the web than in both flanges, Rh is taken as 1.0. Otherwise the hybrid factor is taken as:

( )312 3

12 2hRβ ρ ρ

β+ −

=+

(6.10.1.10.1-1)

where

2 n w

fn

D tA

β = (6.10.1.10.1-2)

the smaller of and 1.0yw nF fρ =

Afn = bottom flange area.

Dn = the larger of the distances from the elastic neutral axis of the cross-section to the inside face of either flange. For sections where the neu-tral axis is at the mid-depth of the web, Dn is the distance from the neutral axis to the inside face of the flange on the side of the neutral axis where yielding occurs first.

Fn = fy of the bottom flange.

9.1.3.3 Web Load-Shedding Factor Rb – Positive Flexure For composite sections in positive flexure, the Rb factor is taken as equal to 1.0.

9.1.3.4 Web Load-Shedding Factor Rb – Negative Flexure For composite sections in negative flexure, the Rb factor is taken as:

21 1.01200 300

wc

wc cb rw

a w

a DRt

λ = − − ≤ + (6.10.1.10.2)

where

5.7rwyc

EF

λ = (6.10.1.10.2-4)



2 c wwc

fc fc

D tab t

= (6.10.1.10.2-5)

When the user specifies the design request parameter “Do webs have longitu-dinal stiffeners?” as yes, the Rb factor is set to 1.0 (see Chapter 4 for more in-formation about specifying Design Request parameters).

9.2 Demand Sets Demand Set combos (at least one required) are user-defined combination based on LRFD combinations (see Chapter 4 for more information about specifying Demand Sets). The demands from all specified demand combos are enveloped and used to calculate D/C ratios. The way the demands are used depends on if the parameter "Use Stage Analysis?” is set to Yes or No.

If “Yes,” the program reads the stresses on beams and slabs directly from the section cut results. The program assumes that the effects of the staging of loads applied to non-composite versus composite section and the concrete slab mate-rial time dependent properties were captured by using the nonlinear stage anal-ysis load case available in CSiBridge.

If “Use Stage Analysis? = No,” the program decomposes load cases present in every demand set combo to three Bridge Design Action categories: non-composite, composite long term, and composite short term. The program uses the load case Bridge Design Action parameter to assign the load cases to the appropriate categories. A default Bridge Design Action parameter is assigned to a load case based on its Design Type. However, the parameter can be overwritten: click the Analysis > Load Cases > {Type} > New command to display the Load Case Data – {Type} form; click the Design button next to the Load case type drop down list, under the heading Bridge Design Action select the User Defined option and select a value from the list. The assigned Bridge Designed Action values are handled by the program in the following manner:


Bridge Design Action Value specified by the user

Bridge Design Action Category used in the design algorithm

Non-Composite Non-Composite

Demand Sets 9 - 9



Bridge Design Action Value specified by the user

Bridge Design Action Category used in the design algorithm

Long-Term Composite Long-Term Composite Short-Term Composite Short-Term Composite

Staged Non-Composite Other Non-Composite

9.2.1 Demand Flange Stresses fbu and ff Evaluation of the flange stress, fbu, calculated without consideration of flange lateral bending is dependent on setting the “Use Stage Analysis?” design re-quest parameter.

If the “Use Stage Analysis? = No,” then

NC LTC STCbu

comp steel LTC STC

P M M MfA S S S

= + + +

where,

MNC is the demand moment on the noncomposite section.

MLTC is the demand moment on the long-term composite section.

MSTC is the demand moment on the short-term composite section.

The short term section modulus for positive moment is calculated by trans-forming the concrete deck using steel to concrete modular ratio. The modular ratio (n) is calculated as a decimal number expressed as n=Es/Ec and used without rounding. The long term section modulus for positive moment is using a modular ratio factored by n, where n is specified in the “Modular ratio long term multiplier” Design Parameter. The effect of compression reinforcement is ignored. For negative moment, the concrete deck is assumed cracked and is not included in the section modulus calculations, whereas tension reinforcement is taken into account.

9 - 10 Demand Sets


The effective width of bottom flange per 6.11.1.1. is used to calculate the stresses. However, when design request parameter “Use Stage Analysis? = Yes,” then the fbu stresses on both top and bottom flanges are read directly from the section cut results. In that case the stresses are calculated based on gross section; the use of effective section properties cannot be accommodated with this option. Therefore, if the section bottom flange does not satisfy criteria of 6.11.1.1 as being fully effective, the design parameter "Use Stage Analysis?” should be set to No.

When “Use Stage Analysis? = Yes,” the program assumes that the effects of the staging of loads applied to non-composite versus composite sections and the concrete slab material time dependent properties were captured by using the Nonlinear Staged Construction load case available in CSiBridge. The “Modular ratio long-term multiplier.” is not used in this case.

The program verifies the sign of the stress in the composite slab, and if stress is positive (tension), the program assumes that the entire section cut demand moment is carried by the steel section only. This is to reflect the fact that the concrete in the composite slab is cracked and does not contribute to the re-sistance of the section.

Flange stress ff used in the Service design check is evaluated in the same man-ner as the stress fbu, with one exception. When the Design Parameter “Does concrete slab resist tension?” in the Steel Service Design request is set to “Yes,” the program uses section properties based on a transformed section as-suming the concrete slab to be fully effective in both tension and compression.

9.2.2 Demand Flange Lateral Bending Stress fl The top flange lateral bending stress fl is evaluated only for constructability de-sign check when slab status is ‘non-composite” and when all of the following conditions are met:

“Steel Girders” has been selected for the deck section type (Components > Superstructure Item > Deck Sections command) and the Girder Modeling In Area Object Models – Model Girders Using Area Objects option is set to “Yes” on the Define Bridge Section Data – Steel Girder form.

Demand Sets 9 - 11


The bridge object is modeled using Area Objects. This option can be set us-ing the Bridge > Update command to display the “Update Bridge Structural Model“ form; then select the Update as Area Object Model option.

In all other cases, the top flange lateral bending stress is set to zero. The fl stresses on each top flange are read directly from the section cut results and the maximum absolute value stress from the two top flanges is reported.

9.2.3 Depth of the Web in Compression For composite sections in positive flexure, the depth of web in compression is computed using the following equation:

0cc fc

c t

fD d tf f− = − ≥ +

(D6.3.1-1)

Figure 9-3 Web in Compression – Positive Flexure

where,

fc = sum of the compression-flange stresses caused by the different loads, i.e., DC1, the permanent load acting on the noncomposite section; DC2, the permanent load acting on the long-term composite section; DW, the wear-ing surface load; and LL+IM acting on their respective sections. fc is tak-en as negative when the stress is in compression. Flange lateral bending is disregarded in this calculation.

9 - 12 Demand Sets


ft = the sum of the tension-flange stresses caused by the different loads. Flange lateral bending is disregarded in this calculation.

For composite sections in negative flexure, DC is computed for the section con-sisting of the steel U-tub plus the longitudinal reinforcement, with the excep-tion of the following. For composite sections in negative flexure at the Service Design Check Request where the concrete deck is considered effective in ten-sion for computing flexural stresses on the composite section (Design Parame-ter “Does concrete slab resist tension?” = Yes), DC is computed from (eq. D 6.3.1-1). For this case, the stresses fc and ft are switched, the signs shown in the stress diagram are reversed, tfc is the thickness of the bottom flange, and DC in-stead extends from the neutral axis down to the top of the bottom flange.

9.3 Strength Design Request The strength design check calculates at every section cut positive flexural ca-pacity, negative flexural capacity, and shear capacity. It then compares the ca-pacities against the envelope of demands specified in the design request.

9.3.1 Flexure

9.3.1.1 Positive Flexure – Compact The nominal flexural resistance of the section is evaluated as follows:

If Dp ≤ 0.1 Dt, then Mn = Mp, otherwise

1.07 0.7 pn p

t

DM M

D

= −

(6.10.7.1.2-2)

In a continuous span the nominal flexural resistance of the section is deter-mined as

Mn ≤ 1.3RhMy

where Rh is a hybrid factor for the section in positive flexure.


𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 =𝑀𝑀𝑢𝑢

∅𝑓𝑓𝑀𝑀𝑛𝑛



9.3.1.2 Positive Flexure – Non-Compact Nominal flexural resistance of the top compression flanges is taken as:

Fnc = RbRhFyc (6.11.7.2.1-1)


Fnt = RhFytΔ (6.10.7.2.1-2)

Where

∆= �1 − 3�𝑓𝑓𝑣𝑣𝐹𝐹𝑦𝑦𝑦𝑦

�2

Where 𝑓𝑓𝑣𝑣 = 𝑇𝑇2𝐴𝐴0𝑡𝑡𝑓𝑓𝑓𝑓

is St. Venant torsional shear stress in the flange due to the

factored loads and A0 is enclosed area within the box section


𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = 𝑚𝑚𝑚𝑚𝑚𝑚 �𝑓𝑓𝑏𝑏𝑢𝑢𝑡𝑡𝑏𝑏𝑛𝑛𝑏𝑏∅𝑓𝑓𝐹𝐹𝑛𝑛𝑡𝑡

,𝑓𝑓𝑏𝑏𝑢𝑢𝑦𝑦𝑏𝑏𝑏𝑏𝑏𝑏∅𝑓𝑓𝐹𝐹𝑛𝑛𝑦𝑦

�

9.3.1.3 Negative Flexure Nominal flexural resistance of continuously braced top flange in tension is tak-en as:

Fnt = RhFyt (6.11.8.3)

Nominal flexural resistance of the bottom unstiffened compression flange is taken as:

𝐹𝐹𝑛𝑛𝑦𝑦 = 𝐹𝐹𝑦𝑦𝑏𝑏�1− � 𝑓𝑓𝑣𝑣𝜙𝜙𝑣𝑣𝐹𝐹𝑓𝑓𝑣𝑣

�2 (6.11.8.2.2-1)

In which:

𝐹𝐹𝑦𝑦𝑏𝑏 = nominal axial compression buckling resistance of the flange un-der compression alone calculated as follows:



• If 𝜆𝜆𝑓𝑓 ≤ 𝜆𝜆𝑏𝑏, then:

𝐹𝐹𝑦𝑦𝑏𝑏 = 𝑅𝑅𝑏𝑏𝑅𝑅ℎ𝐹𝐹𝑦𝑦𝑦𝑦Δ (6.11.8.2.2-2)

• If 𝜆𝜆𝑏𝑏 ≤ 𝜆𝜆𝑓𝑓 ≤ 𝜆𝜆𝑟𝑟, then:

𝐹𝐹𝑦𝑦𝑏𝑏 = 𝑅𝑅𝑏𝑏𝑅𝑅ℎ𝐹𝐹𝑦𝑦𝑦𝑦 �Δ − �Δ − Δ−0.3Rh

� �λf−λpλr−λp

�� (6.11.8.2.2-3)

• If 𝜆𝜆𝑓𝑓 ≤ 𝜆𝜆𝑟𝑟, then:

𝐹𝐹𝑦𝑦𝑏𝑏 = 0.9𝐸𝐸𝑅𝑅𝑏𝑏𝑘𝑘𝜆𝜆𝑓𝑓2 (6.11.8.2.2-4)

𝐹𝐹𝑦𝑦𝑣𝑣 = nominal shear buckling resistance of the flange under shear alone calculated as follows:

• If 𝜆𝜆𝑓𝑓 ≤ 1.12�𝐸𝐸𝑘𝑘𝑠𝑠𝐹𝐹𝑦𝑦𝑓𝑓

, then:

𝐹𝐹𝑦𝑦𝑣𝑣 = 0.58𝐹𝐹𝑦𝑦𝑦𝑦 (6.11.8.2.2-5)

• If 1.12�𝐸𝐸𝑘𝑘𝑠𝑠𝐹𝐹𝑦𝑦𝑓𝑓

< 𝜆𝜆𝑓𝑓 ≤ 1.40�𝐸𝐸𝑘𝑘𝑠𝑠𝐹𝐹𝑦𝑦𝑓𝑓

, then:

𝐹𝐹𝑦𝑦𝑣𝑣 =0.65�𝐹𝐹𝑦𝑦𝑓𝑓𝐸𝐸𝑘𝑘𝑠𝑠

𝜆𝜆𝑓𝑓 (6.11.8.2.2-6)

• If 𝜆𝜆𝑓𝑓 > 1.40�𝐸𝐸𝑘𝑘𝑠𝑠𝐹𝐹𝑦𝑦𝑓𝑓

, then:

𝐹𝐹𝑦𝑦𝑏𝑏 = 0.9𝐸𝐸𝑘𝑘𝑠𝑠𝜆𝜆𝑓𝑓2 (6.11.8.2.2-7)

𝜆𝜆𝑓𝑓 = slenderness ratio for the compression flange

= 𝑏𝑏𝑓𝑓𝑓𝑓𝑡𝑡𝑓𝑓𝑓𝑓

(6.11.8.2.2-8)

𝜆𝜆𝑏𝑏 = 0.57�𝐸𝐸𝑘𝑘𝐹𝐹𝑦𝑦𝑓𝑓Δ

(6.11.8.2.2-9)



𝜆𝜆𝑟𝑟 = 0.95�𝐸𝐸𝑘𝑘𝐹𝐹𝑦𝑦𝑦𝑦

(6.11.8.2.2-10)

Δ = �1 − 3 � 𝑓𝑓𝑣𝑣𝐹𝐹𝑦𝑦𝑓𝑓�2 (6.11.8.2.2-11)

𝑓𝑓𝑣𝑣 = St. Venant torsional shear stress in the flange due to the factored loads at the section under consideration (ksi)

= 𝑇𝑇2𝐴𝐴0𝑡𝑡𝑓𝑓𝑓𝑓

(6.11.8.2.2-12)

𝐹𝐹𝑦𝑦𝑟𝑟 = smaller of the compression-flange stress at the onset of nominal yielding, with consideration of residual stress effects, or the specified minimum yield strength of the web (ksi)

= (Δ − 0.3)𝐹𝐹𝑦𝑦𝑦𝑦 (6.11.8.2.2-13)

k = plate-buckling coefficient for uniform normal stress

= 4.0

ks = plate-buckling coefficient for shear stress

= 5.34


𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = 𝑚𝑚𝑚𝑚𝑚𝑚 �𝑓𝑓𝑏𝑏𝑢𝑢𝑡𝑡𝑏𝑏𝑛𝑛𝑏𝑏∅𝑓𝑓𝐹𝐹𝑛𝑛𝑡𝑡

,𝑓𝑓𝑏𝑏𝑢𝑢𝑦𝑦𝑏𝑏𝑏𝑏𝑏𝑏∅𝑓𝑓𝐹𝐹𝑛𝑛𝑦𝑦

�

9.3.2 Shear When processing the design request from the Design module, the program as-sumes that no vertical stiffeners are present and classifies all web panels as un-stiffened. If the shear capacity calculated based on this classification is not suf-ficient to resist the demand specified in the design request, the program rec-ommends minimum stiffener spacing to achieve a demand over capacity ratio equal to 1. The recommended stiffener spacing is reported in the result table under the column heading d0req.



In the Optimization form (Design/Rating > Superstructure Design > Opti-mize command), the user can specify stiffener locations and the program recal-culates the shear resistance. In that case the program classifies the web panels as interior or exterior and stiffened or unstiffened based on criteria specified in Section 6.10.9.1 of the code. It should be noted that stiffeners are not modeled in the Bridge Object and therefore adding/modifying stiffeners does not affect the magnitude of the demands.

9.3.2.1 Nominal Resistance of Unstiffened Webs In the following equations D is taken as depth of the web plate measured along the slope and each web demand over capacity ratio is calculated based on shear due to factored loads taken as

𝑉𝑉𝑢𝑢𝑢𝑢 =𝑉𝑉𝑢𝑢

cos𝛼𝛼𝑤𝑤𝑏𝑏𝑏𝑏

Where Vu is vertical shear due to the factored loads on one inclined web and αweb is the angle of inclination of the web plate to the vertical. The Vui value is reported in the result tables.

The nominal shear resistance of unstiffened webs is taken as:

n pV CV= (6.10.9.2-1)

in which

0.58p yw wV F Dt= (6.10.9.2-2)


If 1.12 ,w yw

D Ekt F

≤ then C = 1.0. (6.10.9.3.2-4)

If 1.12 1.40 ,yw w yw

Ek D EkF t F

< ≤ then 1.12 .yw

w

EkCD Ft

= (6.10.9.3.2-5)



If 1.40 ,w yw

D Ekt F

> then 21.57 ,

yw

w

EkCFD

t

=

(6.10.9.3.2-6)

in which 255 .c

kdD

= +

(6.10.9.3.2-7)

9.3.2.2 Nominal Resistance of Stiffened Interior Web Panels The nominal shear resistance of an interior web panel and with the section at the section cut proportioned such that

( )

2 2.5w

fc fc ft ft

Dtb t b t

≤+

(6.10.9.3.2-1)

is taken as

( )

2

0.87 1

1n p

o

CV V CdD

−= +

+

(6.10.9.3.2-2)

in which 0.58p yw wV F Dt= (6.10.9.3.2-3)

where



( )

2

0.87 1

1

n p

o o

CV V Cd dD D

−= + + +

(6.10.9.3.2-8)

9.3.2.3 Nominal Resistance of End Panels The nominal shear resistance of a web end panel is taken as:

n cr pV V CV= = (6.10.9.3.3-1)



in which

0.58 .p yw wV F Dt= (6.10.9.3.3-2)

9.3.2.4 Torsion Effects For all single box sections, horizontally curved section, and multiple box sec-tions in bridges not satisfying the requirements of Article 6.11.2.3, or with bot-tom flange that is not fully effective according to the provisions of Article 6.11.1.1 Vui is taken as the sum of the flexural and St. Venant torsional shears. The St. Venant torsional shear is calculated as:

𝑉𝑉𝑡𝑡𝑏𝑏𝑟𝑟 = 𝑓𝑓𝑣𝑣𝐴𝐴𝑤𝑤𝑏𝑏𝑏𝑏

𝑤𝑤ℎ𝐷𝐷𝐷𝐷𝐷𝐷 𝑓𝑓𝑣𝑣 =𝑇𝑇

2𝐴𝐴0𝑡𝑡𝑤𝑤


𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 =𝑉𝑉𝑢𝑢𝑢𝑢∅𝑣𝑣𝑉𝑉𝑛𝑛

9.4 Service Design Request The service design check calculates at every section cut stresses ff at top steel flange of composite section, bottom steel flange of composite section and com-pares them against limits specified in Section 6.10.4.2.2 of the code.

For the top and bottom steel flange of composite sections:

𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = 𝑓𝑓𝑓𝑓0.95𝑅𝑅ℎ𝐹𝐹𝑦𝑦𝑓𝑓

(6.10.4.2.2-2)

The flange stresses are derived in the same way as fbu stress demands (see Sec-tion 9.2 of this manual). The user has an option to specify whether concrete slab resists tension or not by setting the design request parameter “Does con-crete slab resist tension?”. It is the responsibility of the user to verify if the slab qualifies per Section 6.10.4.2.1 of the code to resist tension.

Service Design Request 9 - 19


For compact composite sections in positive flexure utilized in shored construc-tion, the longitudinal compressive stress in the concrete deck, determined as specified in Article 6.10.1.1.1d, is checked against 0.6f′c.

DoverC = fdeck/0.6f’c

Except for composite sections in positive flexure in which the web satisfies the requirement of Article 6.10.2.1.1, all section cuts are shall checked against the following requirement:

DoverC = 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑦𝑦𝑐𝑐

(6.10.4.2.2-4)

where:

fc - compression-flange stress at the section under consideration due to demand loads calculated without consideration of flange lateral bending

Fcrw - nominal bend-buckling resistance for webs without longitudinal stiffeners determined as specified in Article 6.10.1.9

𝐹𝐹𝑦𝑦𝑟𝑟𝑤𝑤 = 0.9𝐸𝐸𝑘𝑘

� 𝐷𝐷𝑡𝑡𝑐𝑐�2 (6.10.1.9.1-1)

but not to exceed the smaller of RhFyc and Fyw/0.7. In which

k=bend buckling coefficient

𝑘𝑘 = 9

�𝐷𝐷𝑓𝑓𝐷𝐷 �2 (6.10.1.9.1-2)

where Dc= depth of the web in compression in the elastic range determined as specified in Article D6.3.1 of the code.

When both edges of the web are in compression, k is taken as 7.2.

The highest demand over capacity ratio together with controlling equation is reported for each section cut.

9.5 Web Fatigue Design Request Web Fatigue Design Request is used to calculate the demand over capacity ra-tio as defined in Section 6.10.5.3 of the code – Special Fatigue Requirement for

9 - 20 Web Fatigue Design Request


Webs. The requirement is applicable to interior panels of webs with transverse stiffeners. When processing the design request from the Design module, the program assumes that there are no vertical stiffeners present and classifies all web panels as unstiffened. Therefore when the design request is completed from the Design module the Design Result Status table shows message text – “No stiffeners defined – use optimization form to define stiffeners”.

In the Optimization form (Design/Rating > Superstructure Design > Optimize command), the user can specify stiffeners locations and the program recalcu-lates the Web Fatigue Request. In that case the program classifies the web pan-els as interior or exterior and stiffened or unstiffened based on criteria specified in Section 6.10.9.1 of the code. It should be noted that stiffeners are not mod-eled in the Bridge Object and therefore adding/modifying stiffeners does not affect the magnitude of the demands.

In the following equations D is taken as depth of the web plate measured along the slope and each web demand over capacity ratio is calculated based on shear due to factored loads taken as




For all single box sections, horizontally curved section, and multiple box sec-tions in bridges not satisfying the requirements of Article 6.11.2.3, or with bot-tom flange that is not fully effective according to the provisions of Article 6.11.1.1 Vui is taken as the sum of the flexural and St. Venant torsional shears. The St. Venant torsional shear is calculated as:




If live load distribution to girders method “Use Factor Specified by Design Code” is selected in the design request the program adjusts for the multiple presence factor to account for the fact that fatigue load occupies only one lane

Web Fatigue Design Request 9 - 21


(code Section 3.6.1.4.3b) and multiple presence factors shall not be applied when checking for fatigue limit state (code Section 3.6.1.1.2).

Vcr = shear-buckling resistance determined from eq. 6.10.9.3.3-1 (see Section 9.3.2.3 of this manual)

DoverC=Vui/Vcr (6.10.5.3-1)

9.6 Constructability Design Request

9.6.1 Staged (Steel-U Comp Construct Stgd) This request enables the user to verify the superstructure during construction by utilizing the Nonlinear Staged Construction load case. The use of nonlinear staged analysis allows the user to define multiple snapshots of the structure during construction where parts of the bridge deck may be at various comple-tion stages. The user has a control of which stages the program will include in the calculations of controlling demand over capacity ratios.

For each section cut specified in the design request the constructability design check loops through the Nonlinear Staged Construction load case output steps that correspond to Output Labels specified in the Demand Set. At each step the program determines the status of the concrete slab at the girder section cut. The slab status can be non-composite or composite.

The Staged Constructability design check accepts the following Bridge Object Structural Model Options: - Area Object Model - Solid Object Model The Staged Constructability design check cannot be run on Spine models.

9.6.2 Non-staged (Steel-U Comp Construct NonStgd) This request enables the user to verify demand over capacity ratios during con-struction without the need to define and analyze Nonlinear Staged Construction load case. For each section cut specified in the design request the constructabil-ity design check loops through all combos specified in the Demand Set list. At each combo the program assumes the status of the concrete slab as specified by the user in the Slab Status column. The slab status can be non-composite or composite and applies to all the section cuts.



The Non-Staged Constructability design check accepts all Bridge Object Struc-tural Model Options available in Update Bridge Structural Model form. (Bridge > Update > Structural Model Options option)

9.6.3 Slab Status vs Unbraced Length Based on the slab status the program calculates corresponding positive flexural capacity, negative flexural capacity, and shear capacity. Next the program compares the capacities against demands specified in the Demand Set by calcu-lating the demand over capacity ratio. The controlling Demand Set and Output Label on girder basis are reported for every section cut.

When slab status is composite the program assumes that both top and bottom flanges are continuously braced. When slab status in not present or non-composite the program treats both top flanges as discretely braced. It should be noted that the program does not verify presence of diaphragms at a particular output step. It assumes that anytime a steel beam is activated at a given section cut that the unbraced length Lb for the top flanges is equal to distance between the nearest downstation and upstation qualifying cross diaphragms or span ends as defined in the Bridge Object. In other words the unbraced length Lb is based on the cross diaphragms that qualify as providing restraint to the bottom flange. Some of the diaphragm types available in CSiBridge may not necessarily pro-vide restraint to the top flanges. It is the user responsibility to provide top flanges temporary bracing at the diaphragm locations prior to the slab acting compositely.

9.6.4 Flexure

9.6.4.1 Positive Flexure Non Composite The local buckling resistance of the top compression flange Fnc(FLB) as specified in Article 6.10.8.2.2 is taken as:

If λf ≤ λ pf, then Fnc = RbRhFyc. (6.10.8.2.2-1)

Otherwise

1 1 yr f pfnc b h yc

h yc rf pf

FF R R F

R Fλ λλ λ

− = − − −

(6.10.8.2.2-2)

in which



2

fcf

fc

bt

λ = (6.10.8.2.2-3)

0.38pfyc

EF

λ = (6.10.8.2.2-4)

0.56rfyr

EF

λ = (6.10.8.2.2-5)

Fyr = compression-flange stress at the onset of nominal yielding within the cross-section, including residual stress effects, but not including compression-flange lateral bending, taken as the smaller of 0.7Fyc and Fyw, but not less than 0.5 Fyc

The lateral torsional buckling resistance of the top compression flange Fnc(LTB) as specified in Article (6.10.8.2.3) is taken as follows:

If Lb ≤ Lp, then Fnc = RbRhFyc. (6.10.8.2.3-1)

If Lp < Lb ≤ Lr, then

1 1 .yr b pnc b b h yc b h yc

h yc r p

F L LF C R R F R R F

R F L L −

= − − ≤ − (6.10.8.2.3-2)

If Lb > Lr, then Fnc = Fcr ≤ RbRhFyc. (6.10.8.2.3-3)

in which

unbraced length, 1.0 ,b p t r tyc yr

E EL L r L rF F

π= = =

Cb = 1 (moment gradient modifier)

2

2b b

crb

t

C R EFLr

π=

(6.10.8.2.3-8)



112 13

fct

c w

fc fc

br

D tb t

= +

(6.10.8.2.3-9)

The nominal flexural resistance of the top compression flange is taken as the smaller of the local buckling resistance and the lateral torsional buckling re-sistance:

( ) ( )FLB LTBmin ,nc nc ncF F F=


Fnt = RhFytΔ (6.10.7.2.1-2)

Where


�2





𝐷𝐷/𝐷𝐷 = max�𝑓𝑓𝑏𝑏𝑢𝑢𝑦𝑦𝑏𝑏𝑏𝑏𝑏𝑏 + 𝑓𝑓𝑙𝑙𝑡𝑡𝑏𝑏𝑏𝑏𝜙𝜙𝑓𝑓 𝑅𝑅ℎ 𝐹𝐹𝑦𝑦𝑦𝑦𝑡𝑡𝑏𝑏𝑏𝑏

,𝑓𝑓𝑏𝑏𝑢𝑢𝑦𝑦𝑏𝑏𝑏𝑏𝑏𝑏 + 1

3𝑓𝑓𝑙𝑙𝑡𝑡𝑏𝑏𝑏𝑏𝜙𝜙𝑓𝑓 𝐹𝐹𝑛𝑛𝑦𝑦𝑡𝑡𝑏𝑏𝑏𝑏

,𝑓𝑓𝑏𝑏𝑢𝑢𝑦𝑦𝑏𝑏𝑏𝑏𝑏𝑏𝜙𝜙𝑓𝑓 𝐹𝐹𝑦𝑦𝑟𝑟𝑤𝑤𝑡𝑡𝑏𝑏𝑏𝑏

,𝑓𝑓𝑙𝑙𝑡𝑡𝑏𝑏𝑏𝑏

0.6 𝐹𝐹𝑦𝑦𝑡𝑡𝑏𝑏𝑏𝑏,

𝑓𝑓𝑏𝑏𝑢𝑢𝑡𝑡𝑏𝑏𝑛𝑛𝑏𝑏𝜙𝜙𝑓𝑓 𝑅𝑅ℎ 𝐹𝐹𝑛𝑛𝑡𝑡𝑏𝑏𝑏𝑏𝑡𝑡

�

Where Fcrwtop is nominal bend–bucking resistance for webs specified in AASHTO LRFD Article 6.10.1.9.1 for webs without longitudinal stiffeners.

𝐹𝐹𝑦𝑦𝑟𝑟𝑤𝑤 = 0.9𝐸𝐸𝑘𝑘

� 𝐷𝐷𝑡𝑡𝑐𝑐�2 (6.10.1.9.1-1)

but not to exceed the smaller of RhFyc and Fyw /0.7

where 𝑘𝑘 = 9

�𝐷𝐷𝑓𝑓𝐷𝐷 �2 . When both edges of the web are in compression then k=7.2



9.6.4.2 Positive Flexure Composite Nominal flexural resistance of the top compression flanges is taken as:

Fnctop= RhFycΔ (6.11.3.2.-3)

Where


�2





Fntbot = RhFytΔ (6.11.3.2.-3)

Where

∆= �1 − 3�𝑓𝑓𝑣𝑣𝐹𝐹𝑦𝑦𝑡𝑡

�2

Where 𝑓𝑓𝑣𝑣 = 𝑇𝑇2𝐴𝐴0𝑡𝑡𝑓𝑓𝑡𝑡



The demand over capacity ratio is evaluated as:

𝐷𝐷/𝐷𝐷 = max�𝑓𝑓𝑏𝑏𝑢𝑢𝑦𝑦𝑏𝑏𝑏𝑏𝑏𝑏𝜙𝜙𝑓𝑓 𝐹𝐹𝑛𝑛𝑦𝑦𝑡𝑡𝑏𝑏𝑏𝑏

,𝑓𝑓𝑏𝑏𝑢𝑢𝑡𝑡𝑏𝑏𝑛𝑛𝑏𝑏𝜙𝜙𝑓𝑓 𝐹𝐹𝑛𝑛𝑡𝑡𝑏𝑏𝑏𝑏𝑡𝑡

�

9.6.4.3 Negative Flexure Non Composite The demand over capacity ratio is evaluated as:

𝐷𝐷/𝐷𝐷 = max�𝑓𝑓𝑏𝑏𝑢𝑢𝑦𝑦𝑏𝑏𝑏𝑏𝑏𝑏

𝜙𝜙𝑓𝑓 𝐹𝐹𝑛𝑛𝑦𝑦𝑏𝑏𝑏𝑏𝑡𝑡,𝑓𝑓𝑏𝑏𝑢𝑢𝑡𝑡𝑏𝑏𝑛𝑛𝑏𝑏 + 𝑓𝑓𝑙𝑙𝑡𝑡𝑏𝑏𝑏𝑏𝜙𝜙𝑓𝑓 𝑅𝑅ℎ 𝐹𝐹𝑦𝑦𝑡𝑡𝑡𝑡𝑏𝑏𝑏𝑏

,𝑓𝑓𝑙𝑙𝑡𝑡𝑏𝑏𝑏𝑏

0.6 𝐹𝐹𝑦𝑦𝑡𝑡𝑏𝑏𝑏𝑏�



Where Fnctbot is nominal flexural resistance of the continuously braced unstiff-ened bottom flange determined as specified in AASHTO LRFD Article 6.11.8.2.2-1 (also see Section 9.3.1.3 of this manual).

9.6.4.4 Negative Flexure Composite The demand over capacity ratio is evaluated as:

𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = 𝑚𝑚𝑚𝑚𝑚𝑚 �𝑓𝑓𝑏𝑏𝑢𝑢𝑦𝑦𝑏𝑏𝑏𝑏𝑏𝑏

∅𝑓𝑓𝐹𝐹𝑛𝑛𝑦𝑦𝑏𝑏𝑏𝑏𝑡𝑡,

𝑓𝑓𝑏𝑏𝑢𝑢𝑡𝑡𝑏𝑏𝑛𝑛𝑏𝑏∅𝑓𝑓𝑅𝑅ℎ 𝐹𝐹𝑦𝑦𝑡𝑡𝑡𝑡𝑏𝑏𝑏𝑏𝛥𝛥

,𝑓𝑓𝑑𝑑𝑏𝑏𝑦𝑦𝑘𝑘𝜙𝜙𝑡𝑡 𝑓𝑓𝑟𝑟

�

Where Fnctbot is nominal flexural resistance of the continuously braced unstiff-ened bottom flange determined as specified in AASHTO LRFD Article 6.11.8.2.2-1 (also see Section 9.3.1.3 of this manual), and

∆= �1 − 3�𝑓𝑓𝑣𝑣𝐹𝐹𝑦𝑦𝑡𝑡

�2

Where 𝑓𝑓𝑣𝑣 = 𝑇𝑇2𝐴𝐴0𝑡𝑡𝑓𝑓𝑡𝑡


factored loads and A0 is enclosed area within the box section and fdeck is de-mand tensile stress in the deck and fr is modulus of rupture of concrete as de-termined in AASHTO LRFD Article 5.4.2.6

9.6.5 Shear When processing the design request from the Design module, the program as-sumes that there are no vertical stiffeners present and classifies all web panels as unstiffened. If the shear capacity calculated based on this classification is not sufficient to resist the demand specified in the design request and the con-trolling demand over capacity ratio is occurring at step when the slab status is composite, the program recommends minimum stiffener spacing to achieve a demand over apacity ratio equal to 1. The recommended stiffener spacing is re-ported in the result table under the column heading d0req.

In the Optimization form (Design/Rating > Superstructure Design > Opti-mize command), the user can specify stiffeners locations and the program re-calculates the shear resistance. In that case the program classifies the web pan-els as interior or exterior and stiffened or unstiffened based on criteria specified in Section 6.10.9.1 of the code. It should be noted that stiffeners are not mod-



eled in the Bridge Object and therefore adding/modifying stiffeners does not affect the magnitude of the demands. Adding stiffeners also does not increase capacity of sections cuts where concrete slab status is other then composite.

In the following equations D is taken as depth of the web plate measured along the slope and each web demand over capacity ratio is calculated based on shear due to factored loads taken as




9.6.5.1 Torsion Effects For all single box sections, horizontally curved section, and multiple box sec-tions in bridges not satisfying the requirements of Article 6.11.2.3, or with bot-tom flange that is not fully effective according to the provisions of Article 6.11.1.1 Vui is taken as the sum of the flexural and St. Venant torsional shears. The St. Venant torsional shear is calculated as:




9.6.5.2 Non Composite Sections The nominal shear resistance of a web end panel is taken as:

𝑉𝑉𝑛𝑛 = 𝑉𝑉𝑦𝑦𝑟𝑟 = 𝐷𝐷𝑉𝑉𝑏𝑏 (6.10.9.3.3-1)

in which

0.58 .p yw wV F Dt= (6.10.9.3.3-2)


DoverC u

v n

VVφ

=



9.6.5.3 Composite Sections

9.6.5.3.1 Nominal Resistance of Unstiffened Webs The nominal shear resistance of unstiffened webs is taken as:

n pV CV= (6.10.9.2-1)

in which

0.58p yw wV F Dt= (6.10.9.2-2)


If 1.12 ,w yw

D Ekt F

≤ then C = 1.0. (6.10.9.3.2-4)

If 1.12 1.40 ,yw w yw

Ek D EkF t F

< ≤ then 1.12 .yw

w

EkCD Ft

= (6.10.9.3.2-5)

If 1.40 ,w yw

D Ekt F

> then 21.57 ,

yw

w

EkCFD

t

=

(6.10.9.3.2-6)

in which 255 .c

kdD

= +

(6.10.9.3.2-7)

9.6.5.3.2 Nominal Resistance of Stiffened Interior Web Panels The nominal shear resistance of an interior web panel and with the section at the section cut proportioned such that:

( )

2 2.5w

fc fc ft ft

Dtb t b t

≤+

(6.10.9.3.2-1)

is taken as



( )

2

0.87 1

1n p

o

CV V CdD

−= +

+

(6.10.9.3.2-2)

in which 0.58p yw wV F Dt= (6.10.9.3.2-3)

where



( )

2

0.87 1

1

n p

o o

CV V Cd dD D

−= + + +

(6.10.9.3.2-8)

9.6.5.3.3 Nominal Resistance of End Panels The nominal shear resistance of a web end panel is taken as:

𝑉𝑉𝑛𝑛 = 𝑉𝑉𝑦𝑦𝑟𝑟 = 𝐷𝐷𝑉𝑉𝑏𝑏 (6.10.9.3.3-1)

in which

0.58 .p yw wV F Dt= (6.10.9.3.3-2)


DoverC u

v n

VVφ

=

9.7 Section Optimization After at least one Steel Design Request has been successfully processed, CSiBridge enables the user to open a Steel Section Optimization module. The Optimization module allows interactive modification of certain steel plate siz-es, materials, and definition of vertical stiffeners along each girder and span. The U tub section plate parameters that are available for modification are:



Top flange – thickness, width and material

Webs –thickness, material

Bottom flange – thickness, material

The program recalculates resistance “on the fly” based on the modified section without the need to unlock the model and rerun the analysis. It should be noted that in the optimization process the demands are not recalculated and are based on the current CSiBridge analysis results.

The Optimization form allows simultaneous display of three versions of section sizes and associated resistance results. The section plate size versions are “As Analyzed,” “As Designed,” and “Current.” The section plots use distinct colors for each version – black for As Analyzed, blue for As Designed, and red for Current. When the Optimization form is initially opened, all three versions are identical and equal to “As Analyzed.”

Two graphs are available to display various forces, moments, stresses, and rati-os for the As Analyzed or As Designed versions. The values plotted can be controlled by clicking the “Select Series to Plot” button. The As Analyzed se-ries are plotted as solid lines and the As Designed series as dashed lines.

To modify steel plate sizes or vertical stiffeners, a new form can be displayed by clicking on the Modify Section button. After the section modification is completed, the Current version is shown in red in the elevation and cross sec-tion views. After the resistance has been recalculated successfully by clicking the Recalculate Resistance button, the Current version is designated to As De-signed and displayed in blue.

After the section optimization has been completed, the As Designed plate sizes and materials can be applied to the analysis bridge object by clicking the OK button. The button opens a new form that can be used to Unlock the existing model (in that case all analysis results will be deleted) or save the file under a new name (New File button). Clicking the Exit button does not apply the new plate sizes to the bridge object and keeps the model locked. The As Designed version of the plate sizes will be available the next time the form is opened, and the Current version is discarded.

Section Optimization 9 - 31


The previously defined stiffeners can be recalled in the Steel Beam Section Variation form by clicking the Copy/Reset/Recall button in the top menu of the form. The form can be displayed by clicking on the Modify Section but-ton.


Chapter 10 Run a Bridge Design Request

This chapter identifies the steps involved in running a Bridge Design Request. (Chapter 4 explains how to define the Request.) Running the Request applies the following to the specified Bridge Object:

Program defaults in accordance with the selected codethe Preferences

Type of design to be performedthe check type (Section 4.2.1)

Portion of the bridge to be designedthe station ranges (Section 4.1.3)

Overwrites of the Preferencesthe Design Request parameters (Section 4.1.4)

Load combinationsthe demand sets (Chapter 2)

Live Load Distribution factors, where applicable (Chapter 3)

For this example, the AASHTO LRFD 2007 code is applied to the model of a concrete box-girder bridge shown in Figure 10-1.

It is assumed that the user is familiar with the steps that are necessary to create a CSiBridge model of a concrete box girder bridge. If additional assistance is needed to create the model, a 30-minute Watch and Learn video entitled, ”Bridge – Bridge Information Modeler” is available at the CSI website

10 - 1


www.csiamerica.com. The tutorial video guides the user through the creation of the bridge model referenced in this chapter.

Figure 10-1 3D view of example concrete box girder bridge model

10.1 Description of Example Model The example bridge is a two-span prestressed concrete box girder bridge with the following features:

Abutments: The abutments are skewed by 15 degrees and connected to the bottom of the box girder only.

Prestress: The concrete box girder bridge is prestressed with four 10-in2 tendons (one in each girder) and a jacking force of 2160 kips per tendon.

Bents: The one interior bent has three 5-foot-square columns.

Deck: The concrete box girder has a nominal depth of 5 feet. The deck has a parabolic variation in depth from 5 feet at the abutments to a maximum of 10 feet at the interior bent support.

Spans: The two spans are each approximately 100 feet long.

Figure 10-2 Elevation view of example bridge

10 - 2 Description of Example Model

Chapter 10 - Run a Bridge Design Request

Figure 10-3 Plan view of the example bridge

10.2 Design Preferences Use the Design/Rating > Superstructure Design > Preferences command to select the AASHTO LRFD 2007 design code. The Bridge Design Preferences form shown in Figure 10-4 displays.

Figure 10-4 Bridge Design Preferences form

10.3 Load Combinations For this example, the default design load combinations were activated using the Design/Rating > Load Combinations > Add Defaults command. After the Bridge Design option has been selected, the Code-Generated Load Combina-tions for Bridge Design form shown in Figure 10-5 displays. The form is used

Design Preferences 10 - 3


to specify the desired limit states. Only the Strength II limit state was selected for this example. Normally, several limit states would be selected.

Figure 10-5 Code-Generated Load Combinations for Bridge Design form

The defined load combinations for this example are shown in Figure 10-6.

Figure 10-6 Define Load Combinations form

10 - 4 Load Combinations

Chapter 10 - Run a Bridge Design Request

The Str-II1, Str-II2 and StrIIGroup1 designations for the load combinations are specified by the program and indicate that the limit state for the combinations is Strength Level II.

10.4 Bridge Design Request After the Design/Rating > Superstructure Design > Design Request com-mand has been used, the Bridge Design Request form shown in Figure 10-7 displays.

Figure 10- 7 Define Load Combinations form

The name given to this example Design Request is FLEX_1, the Check Type is for Concrete Box Flexure and the Demand Set, DSet1, specifies the combi-nation as StrII (Strength Level II).

Bridge Design Request 10 - 5


The only Design Request Parameter option for a Concrete Box Flexural check type is for PhiC. A value of 0.9 for PhiC is used.

10.5 Start Design/Check of the Bridge After an analysis has been run, the bridge model is ready for a design/check. Use the Design/Rating > Superstructure Design > Run Super command to start the design process. Select the design to be run using the Perform Bridge Design form shown in Figure 10-8:

Figure 10-8 Perform Bridge Design - Superstructure

The user may select the desired Design Request(s) and click on the Design Now button. A plot of the bridge model, similar to that shown in Figure 10-9, will display.

If several Design Requests have been run, the individ-ual Design Requests can be selected from the Design Check options drop-down list. This plot is described further in Chapter 11.

Figure 10-9 Plot of flexure check results

10 - 6 Start Design/Check of the Bridge

Chapter 11 Display Bridge Design Results

Bridge design results can be displayed on screen and as printed output. The on-screen display can depict the bridge response graphically as a plot or in data tables. The Advanced Report Writer can be used to create the printed output, which can include the graphical display as well as the database tables.

This chapter displays the results for the example used in Chapter 10. The model is a concrete box girder bridge and the code applied is AASHTO LRFD 2007. Creation of the model is shown in a 30-minute Watch and Learn video on the CSI website, www.csiamerica.com.

11.1 Display Results as a Plot To view the forces, stresses, and design results graphically, click the Home > Display > Show Bridge Superstructure Design Results command, which will display the Bridge Object Response Display form shown in Figure 11-1.

The plot shows the design results for the FLEX_1 Design Request created using the process described in the preceding chapters. The demand moments are en-veloped and shown in the blue region, and the negative capacity moments are shown with a brown line. If the demand moments do not exceed the capacity moments, the superstructure may be deemed adequate in response to the flexure Design Request. Move the mouse pointer onto the demand or capacity plot to view the values for each nodal point. Move the pointer to the capacity moment

Display Results as a Plot 11 - 1


at station 1200 and 536981.722 kip-in is shown. A verification calculation that shows agreement with this CSiBridge result is provided in Section 11.4.

Figure 11-1 Plot of flexure check results for the example bridge design model

11.1.1 Additional Display Examples Use the Home > Display > Show Bridge Forces/Stresses command to select, on the example form shown in Figure 11-2, the location along the top or bottom portions of a beam or slab for which stresses are to be displayed. Figures 11-3 through 11-9 illustrate the left, middle, and right portions as they apply to Mul-ticell Concrete Box Sections. Location 1, as an example, refers to the top left se-lection option while location 5 would refer to the bottom center selection option. Locations 1, 2, and 3 refer to the top left, top center, and top right selection op-tion while locations 4, 5, and 6 refer to the bottom left, bottom center, and bot-tom right selection options.

11 - 2 Display Results as a Plot

Chapter 11 - Display Bridge Design Results

Figure 11-2 Select the location on the beam or slab for which results are to be displayed

Figure 11-3 Bridge Concrete Box Deck Section - External Girders Vertical

Top slab cut line

Bottom slab cut line

Centerline of the web Centerline of the web

1 2 3

4 5 6

4

5 6

1 2 3

Display Results as a Plot 11- 3


Figure 11-4 Bridge Concrete Box Deck Section - External Girders Sloped

Figure 11-5 Bridge Concrete Box Deck Section - External Girders Clipped

Top slab cut


Centerline of the web

4

5 6

1 2 3 1 2 3

4 5 6 Centerline of the web

Top slab cut


1 2 3

4

5 6


4 5 6


1 2 3



Figure 11-6 Bridge Concrete Box Deck Section - External Girders and Radius

Figure 11-7 Bridge Concrete Box Deck Section - External Girders Sloped Max

Centerline of the web Centerline of the web 4 5 6

1 2 1 2

6

3

5 4

1 2 3

4, 5 6

Top slab cut


Centerline of the web Centerline of the web

1 2 3 1 2 3

4 5 6

4

5 6


Top slab cut line


3

Display Results as a Plot 11- 5


Figure 11-8 Bridge Concrete Box Deck Section - Advanced

Figure 11-9 Bridge Concrete Box Deck Section - AASHTO - PCI - ASBI Standard


Top slab cut line

Top slab cut line


1 2 3



1 2 3

4

5 6


1 2 3

4 5 6

4

5 6



11.2 Display Data Tables To view design results on screen in tables, click the Home > Display > Show Tables command, which will display the Choose Tables for Display form shown in Figure 11-10. Use the options on that form to select which data results are to be viewed. Multiple selection may be made.

Figure 11-10 Choose Tables for Display form

When all selections have been made, click the OK button and a database table similar to that shown in Figure 11-11 will display. Note the drop-down list in the upper right-hand corner of the table. That drop-down list will include the various data tables that match the selections made on the Choose Tables for Display form. Select from that list to change to a different database table.

Display Data Tables 11- 7


Figure 11-11 Design database table for AASHTO LRFD 2007 flexure check

The scroll bar along the bottom of the form can be used to scroll to the right to view additional data columns.

11.3 Advanced Report Writer The File > Report > Create Report command is a single button click output option but it may not be suitable for bridge structures because of the size of the document that is generated. Instead, the Advanced Report Writer feature within CSiBridge is a simple and easy way to produce a custom output report.

To create a custom report that includes input and output, first export the files us-ing one of the File > Export commands: Access; Excel; or Text. When this command is executed, a form similar to that shown in Figure 11-12 displays.

11 - 8 Advanced Report Writer


Figure 11-12 Choose Tables for Export to Access form

This important step allows control over the size of the report to be generated. Export only those tables to be included in the final report. However, it is possi-ble to export larger quantities of data and then use the Advanced Report Writer to select only specific data sets for individual reports, thus creating multiple smaller reports. For this example, only the Bridge Data (input) and Concrete Box Flexure design (output) are exported.

After the data tables have been exported and saved to an appropriate location, click the File > Report > Advanced Report Writer command to display a form similar to that show in Figure 11-13. Click the appropriate button (e.g., Find existing DB File, Convert Excel File, Convert Text File) and locate the ex-ported data tables. The tables within that Database, Excel, or Text file will be listed in the List of Tables in Current Database File display box.

Advanced Report Writer 11- 9


Figure 11-13 Create Custom Report form

Select the tables to be included in the report from that display box. The selected items will then display in the Items Included in Report display box. Use the var-ious options on the form to control the order in which the selected tables appear in the report as well as the headers (i.e., Section names), page breaks, pictures, and blanks required for final output in .rft, .txt, or .html format.

After the tables have been selected and the headers, pictures, and other format-ting items have been addressed, click the Create Report button to generate the report. The program will request a filename and the path to be used to store the report. Figure 11-14 shows an example of the printed output generated by the Report Writer.

11 - 10 Advanced Report Writer


Figure 11-14 An example of the printed output

11.4 Verification As a verification check of the design results, the output at station 1200 is exam-ined. The following output for negative bending has been pulled from the ConBoxFlexure data table, a portion of which is shown in Figure 11-10:

Demand moment, “DemandMax” (kip-in) = −245973.481

Resisting moment, “ResistingNeg” (kip-in) = 536981.722

Total area of prestressing steel, “AreaPTTop” (in2) = 20.0

Top k factor, “kFactorTop” = 0.2644444

Neutral axis depth, c, “CDistForNeg” (in) = 5.1286

Effective stress in prestressing, fps, “EqFpsForNeg” (kip/in2) = 266.7879

A hand calculation that verifies the results follows:

For top k factor, from (eq. 5.7.3.1.1-2),

245 12 1 04 2 1 04 0 26444270

PY

PU

f .k . . .f

= − = − =

(Results match)

Verification 11- 11


For neutral axis depth, from (AASHTO LRFD eq. 5.7.3.1.1-4),


1 webeq

0.85,

0.85

PT PU c

PUc PT

PT

A f f b b tc ff b kA

Yβ

′− −=

′ + for a T-section

1 webeq

,0.85

PT PU

PUc PT

PT

A fc ff b kAY

β=

′ + when not a T-section

20.0(270) 5.12862700.85(4)(0.85)(360) 0.26444(20)114

c = = +

(Results match)

For effective stress in prestressing, from (AASHTO LRFD eq. 5.7.3.1.1-1),

5 12861 270 1 0 26444 266 788144PS PU

PT

c .f f k . .Y

= − = − =

(Results match)

For resisting moment, from (AASHTO LRFD eq. 5.7.3.2.2-1),

( ) slabeq1 1SLAB webeq slabeq0.85

2 2 2β β ′= − + − −

N PT PS PT c

tc cM A f Y f b b t

1

2β = −

N PT PS PT

cM A f Y , when the box section is not a T-section

NM = − =

5.1286(0.85)20.0(266.788) 144 596646.52

kip-in

R NM Mφ= = =0.85(596646.5) 536981.8 kip-in (Results match)

The preceding calculations are a check of the flexure design output. Other de-sign results for concrete box stress, concrete box shear, and concrete box princi-pal have not been included. The user is encouraged to perform a similar check of these designs and to review Chapters 5, 6, and 7 for a detailed descriptions of the design algorithms.

11 - 12 Verification

Bibliography

ACI, 2007. Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08), American Concrete Institute, P.O. Box 9094, Farmington Hills, Michigan.

AASHTO, 2007. AASHTO LRFD Bridge Design Specifications — Customary U.S. Units, 4th Edition, 2008 Interim Revision, American Association of State Highway and Transportation Officials, 444 North Capitol Street, NW, Suite 249, Washington, D.C. 20001.

AASHTO, 2009. AASHTO Guide Specifications for LRFD Seismic Bridge Design. American Association of Highway and Transportation Offi-cials, 444 North Capital Street, NW Suite 249, Washington, DC 20001.

AASHTO 2012. AASHTO LRFD Bridge Design Specifications — U.S. Units, 6th Edition, American Association of State High way and Transportation Officials, 2012.

Canadian Standards Association (CSA), 2006. Canadian Highway Bridge De-sign Code. Canadian Standards Association, 5060 Spectrum Way, Suite 100, Mississauga, Ontario, Canada, L4W 5N6. November.

EN 1994-2:2005, Eurocode 4: Design of composite steel and concrete struc-tures, Part 2: Composite Bridges, European Committee for Standardi-zation, Management Centre: rue de Stassart, 36 B-1050 Brussels.

Bibliography - 1

SAFE Reinforced Concrete Design

Indian Roads Congress (IRC), May 2010: Standard Specifications and Code of Practice for Road Bridges, Section V, Steel Road Bridges. Kama Koti Marg, Sector 6, RK Puram, New Delhi- 110 022.

R - 2

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