Bsd Aashto Lrfd 2012

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Bridge Superstructure Design

AASHTO 2012


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CSiBridge® 2015


AASHTO 2012

ISO BRG072314M8 Rev. 0 Proudly developed in the United States of America July 2014


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Copyright

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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.

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Contents


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 Distribut ion

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

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CSiBridge Superstructure Design

3.3.2 Calculated by CSiBridge in Accordance

with AASHTO LFRD 2012 3-43.3.3 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


5.2.2 Variables 5-5

5.2.3 Design Process 5-6

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Contents

5.2.4 Algorithm 5-7

5.2.5 Flexure Design Example 5-10

5.3 Shear Design AASHTO LRFD-2012 5-15


5.3.2 Variables 5-15


5.3.4 Algorithm 5-18

5.3.5 Shear Design Example 5-24

5.4 Principal Stress Design, AASHTO LRFD-2012 5-31


5.4.2 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


6.2.3 Algorithms 6-6

6.3 Flexure Design 6-10



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 7-57.2.3 Algorithms 7-5

7.2.4 Shear Design Example 7-9

7.3 Flexure Design 7-14

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CSiBridge Superstructure Design


7.3.2 Design Process 7-167.3.3 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 8-11

8.2.1 Demand Flange Stresses f bu and f f 8-12

8.2.2 Demand Flange Lateral Bending

Stress f 1 8-13

8.2.3 Depth of the Web in Compression 8-14

8.3 Strength Design Request 8-15

8.3.1 Flexure 8-15

8.3.2 Shear 8-22

8.4 Service Design Request 8-24

8.5 Web Fatigue Design Request 8-26

8.6 Constructability Design Request 8-27

8.6.1 Staged (Steel I Comp Construct Stgd) 8-27

8.6.2 Non-staged (Steel I Comp Construct

Non-staged) 8-27

8.6.3 Slab Status vs Unbraced Length 8-28

8.6.4 Flexure 8-28

8.6.5 Shear 8-30

8.7 Section Optimization 8-33

9 Design Steel U-Tub Bridge with Composite Slab

9.1 Section Properties 9-1

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Contents

9.1.1 Yield Moments 9-1

9.1.2 Plastic Moments 9-29.1.3 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

10.5 Start Design/Check of the Bridge 10-6

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Chapter 1Introduction

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

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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

multicell box girder bridges. Chapter 7 describes code-speicifc design parame-

ters 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 optimize a steel U-beam bridge with composite slab. Chapter 10 describeshow 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 generated using the Advanced Report Writer feature.

1.2 Recommended Reading/Practice

It is strongly recommended that you read this manual and review any applica-

ble “Watch & Learn” Series™ tutorials, which are found on our web site,

http://www.csiamerica.com, before attempting to design a concrete box girder

or precast concrete bridge using CSiBridge. Additional information can befound in the on-line Help facility available from within the software’s main

menu.

1 - 2 Recommended Reading/Practice

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Chapter 2Define 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 applicable 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


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CSiBridge Brid ge Superstructure Design

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

CSiBridgeLoad Pattern Type AASHTOReference 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 surfacesand utilities

BRAKING BR Vehicle braking force

HORIZ. EARTH PR EH Horizontal earth pressures

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

CSiBridgeLoad Pattern Type

AASHTOReference 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


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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

LoadComboLimit

State

DCDDDWEHEVESELPSCR

SH

LLIMCEBRPLLS

LLIMCE WA WS WL FR TU TU SE EQ IC CT CV

Str I γ P 1.75 - 1.00 - - 1.00 0.5/

1.20

γ TG γ SE - - - -

Str II γ P - 1.35 1.00 - - 1.00 0.5/

1.20

γ TG γ SE - - - -

Str III γ P - - 1.00 1.40 - 1.00 0.5/

1.20

γ TG γ SE - - - -

Str IV γ P - - 1.00 - - 1.00 0.5/

1.20

- - - - - -

Str V γ P 1.35 - 1.00 0.40 1.00 1.00 0.5/

1.20

γ TG γ SE - - - -

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

Ext EvII 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

γ TG γ SE - - - -

Serv II 1.00 1.30 - 1.00 - - 1.00 1.00/

1.20

- - - - -

Serv III 1.00 0.80 - 1.00 - - 1.00 1.00/

1.20

γ TG γ SE - - - -

Serv IV 1.00 - - 1.00 0.70 - 1.00 1.00/

1.20

- 1.00 - - - -

FatigueI-LL, IM& CEOnly

- 0.875/1.75

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

FatigueII-LL, IM

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

Design Load Combinations 2 - 3


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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,P

γ , 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

CulvertsFlexible Metal Box Culverts

1.00

1.35

1.30

1.35

1.95

1.50

N/A

1.00

0.90

0.90

0.90

0.90

ES: Earth Surcharge 1.50 0.75

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

γ ,

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


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

γ ,

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


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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


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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


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Chapter 3Live 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 ofthe following types: precast I- or U-girders with composite slabs, steel I-girders

with composite slabs, and multi-cell concrete box girders. These deck sectiontypes 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.

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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 combinations.

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 Distr ibution Factors

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

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

ed

the number of girders

girder designation the first and last girder are designated as exterior girders

and the other girders are classified as interior girders

roadway width measured as the distance between curbs/barriers; medians

are ignored

3 - 2 Determine Live Load Distribution Factors


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Chapter 3 - Live Load Distributio n

overhang consists 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 curbor traffic barrier

the beams includes the area, moment of inertia, torsion constant, center of

gravity

the thickness of the composite slab t1 and the thickness of concrete slab

haunch t2

the tributary area of the composite slab which is bounded at the interior

girder by the midway distances to neighboring girders and at the exterior

girder; includes the entire overhang on one side, and is bounded by the mid-

way distances to neighboring girder on the other side

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

CSiBridge then evaluates the longitudinal stiffness parameter, Kg, in 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 CSiBridgedirectly 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; directlyfrom individual girders; or uniformly distributed onto all girders.

Apply LLD Fac tors 3 - 3


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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 AASHTOLRFD 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 equalto 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


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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


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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 theVirtual 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-

tions one for shear and one for moment generated for exterior beam are as-

signed to both exterior beams, and similarly, Virtual Combinations for interior

beams are assigned to interior beams.)

3.5 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 Directl y from Girders


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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


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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 procedureoutlined 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, I g = 733,320 in4

Deck slab thickness, t s = 8 in.

Span length, L = 110 ft.

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

Modulus of elasticity of the beam, E B = 4,696 ksi

Modulus of elasticity of the deck, E D = 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


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n = B D E 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

noncomposite beam and the deck. Ignore the thickness of the haunch in

determining eg

eg = NAYT + 2st = 35.62 + 8 2 = 39.62 in.

3. Calculate K g, the longitudinal stiffness parameter.

K g = ( )2gn I Ae+ (4.6.2.2.1-1)

= ( )2 41.225 7 33 320 1 0 85 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.

D M = ( ) ( ) ( )0.10.6 0.2 3

0.075 9.5 12.0g sS S L K Lt +

( ) ( ) ( )( ){ } 0.1

0.6 0.2 3

0.075 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.

D M = ( ) ( ) ( )0.10.4 0.3 3

0.06 14 12.0g sS S L K Lt +

= ( ) ( ) ( )( ){ } 0.1

0.4 0.3 3

0.06 9.667 14 9.667 110 2984704 12 100 8 +

= 0.542 lane (eq. 2)



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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.

S C = ( )0.3

31.0 0.20 12.0 tans g Lt K θ +

= ( )( )( )0.3

31.0 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 = ( ) ( )2

0.2 12 35S S + −

= ( ) ( )2

0.2 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+



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= 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.

D M = e DV interior

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

D M = 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.



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Figure 3-2 Lever Rule

D M

= ( )[ ]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.

D M = ( )0.672 1.2

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

13. Calculate the shear distribution factor for an exterior beam with two ormore design lanes loaded using AASHTO 2012 Table 4.6.2.2.3b-1.

DV = e DV interior



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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 = ( ) 2 L b ext N N X e x+ ∑ ∑ (4.6.2.2.2d-1)where:



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R = reaction on exterior beam in terms of lanes

N L = 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.)

X ext = 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)



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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 Distribut ion Factors -- AASHTO 2012

Load Case

Momentinteriorbeams

Momentexteriorbeams

Shearinteriorbeams

Shearexteriorbeams

Distribution factors fromTables 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 rigidlyconnected 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 byCSiBridge 0.796 0.807 0.973 0.845



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Chapter 4Define 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,

AASHTO 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 Bri dge Object 4 - 1


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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. Figure4-2 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


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Chapter 4 - Define a Bridge Design Request


Request - Composite I or

U Girder Bridges


Request – Steel I Beamwith Composite Slab

Name and Bridge Object 4 - 3


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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 availableoptions 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


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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


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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 valuesset 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


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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


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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 Factorthat multiplies nominal shear resistance to obtain factoredresistance 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, invariable depth members shall or shall not be consideredwhen determining the design factored shear force in accord-ance with Article 5.8.6.2.

Concrete Box Shear Rebar Material - A previously definedrebar 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 BoxFlexure

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

Concrete BoxPrincipal

See the Box Stress design parameter specifications

CAN/CSA S6

Concrete Box Stress Multi-Cell Concrete Box Stress Factor Compression Limit -


Multi-Cell Concrete Box Stress Factor Tension Limit - Thetension 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


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Clause 8.4.6)

Phi PT ϕp -- Resistance factor for tendons (see CSA Clause8.4.6)

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 thetop slab to the centerline of the exterior closed transversetorsion reinforcement

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

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

Shear Rebar Material – A previously defined rebar materiallabel that will be used to determine the required area oftransverse rebar in the girder

Longitudinal Rebar Material – A previously defined rebarmaterial that will be used to determine the required area oflongitudinal rebar in the girder

Concrete BoxFlexure

Phi Concrete ϕc -- Resistance factor for concrete (see CSAClause 8.4.6)

Phi Pt ϕp -- Resistance factor for tendons (see CSA Clause8.4.6)

Phi Rebar ϕs -- Resistance factor for reinforcing bars (seeCSA Clause 8.4.6)

Eurocode EN 1992

Concrete Box Stress Compression limit – Multiplier on f c k to calculate the com-pression stress limit

Tension limit – Multiplier on f c k to calculate the tensionstress 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 compressionstrut and the beam axis perpendicular to the shear force.



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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 webthickness 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 posttensioning.

Inner Arm Method – The method used to calculate the innerlever 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 thesection 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 characteristicyield strength to obtain a stress limit in shear rebar used in6.10.aN. Typical value 0.8 to 1.0.

Shear Rebar Material – A previously defined material labelthat will be used to determine the required area of transverserebar in the girder.

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

Concrete BoxFlexure

Gamma c for Concrete – Partial safety factor for concrete.

Gamma c for Rebar – Partial safety factor for reinforcingsteel.

Gamma c for PT – Partial safety factor for prestressing steel.

PT pre-strain – Factor to estimate pre-strain in the post-tensioning. Multiplies f pk to obtain the stress in the tendonsafter losses. Typical value between 0.4 and 0.9.



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

Multi-Cell Concrete

Box Stress Multi-Cell Concrete Box Stress Factor Compression Limit -


Multi-Cell Concrete Box Stress Factor Tension Limit - Thetension limit factor may be specified using either MPa or ksi

units for ′cf and the resulting tension limit

Multi-Cell ConcreteBox Shear

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




Cracking Strength Factor -- Multiplies sqrt( ′cf ) to obtain

cracking strength


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

Shear Rebar Material – A previously defined rebar materialthat 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 oflongitudinal rebar in the girder

Multi-Cell ConcreteBox Flexure

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




Eurocode EN 1992

Multi-Cell ConcreteBox Stress

Compression limit – Multiplier on f c k to calculate the com-pression stress limit



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

Tension limit – Multiplier on f c k to calculate the tensionstress limit

Multi-Cell ConcreteBox Shear

Gamma C for Concrete – Partial factor for concrete.

Gamma C for Rebar – Partial safety factor for reinforcingsteel.

Gamma C for PT – Partial safety factor for prestressingsteel.

Angle Theta – The angle between the concrete compressionstrut 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 webthickness 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 posttensioning.








Determining Factor AlphaCW – Method that will be used to

calculate the αcw factor.



Shear Rebar Material – A previously defined material labelthat will be used to determine the required area of transverse

rebar in the girder.

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



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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 - eitherModified Compression Field Theory (MCFT) in accordancewith 5.8.3.4.2 or Vci Vcw method in accordance with 5.8.3.4.3Currently only the MCFT option is available.

A previously defined rebar material label that will be used todetermine 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 CompFlexure

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

CAN/CSA S6

Precast CompStress

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 CompShear

Highway Class – The highway class shall be determined inaccordance 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


EpsilonX Positive Limit -- Longitudinal positive strain limit (seeClause 8.9.3.8)

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



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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

Precast CompFlexure

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




Eurocode EN 1992 Precast CompStress

Compression limit – Multiplier on f c k to calculate the com-pression stress limit

Tension limit – Multiplier on f c k to calculate the tension stresslimit

Precast CompShear

Gamma C for Concrete – Partial factor for concrete.

Gamma C for Rebar – Partial safety factor for reinforcingsteel.

Gamma C for PT – Partial safety factor for prestressing steel.

Angle Theta – The angle between the concrete compressionstrut and the beam axis perpendicular to the shear force. Thevalue 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 resistanceequation 6.4 of the code. Typical value 1.0 for post tension-ing.










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Determining Factor AlphaCW – Method that will be used tocalculate the αcw factor.



Shear Rebar Material – A previously defined material labelthat will be used to determine the required area of transverserebar in the girder.

Longitudinal Rebar Material – A previously defined materialthat will be used to determine the required area of longitudinalrebar in the girder.

Precast Comp

Flexure

Gamma c for Concrete – Partial safety factor for concrete.

Gamma c for Rebar – Partial safety factor for reinforcingsteel.

Gamma c for PT – Partial safety factor for prestressing steel.

PT pre-strain – Factor to estimate pre-strain in the post-tensioning. Multiplies f pk 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 flexur e 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-termmodular 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-termmodular ratio



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

Steel-I Comp -Fatigue

There are no user defined design request parameters forfatigue

Steel I CompConstruct Stgd

Resistance factor Phi for flexure

Resistance factor Phi for shear

Resistance factor Phi for Concrete in Tension


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) or0.63 (MPa), must be > 0

The modulus of rupture factor may be specified using either

MPa or ksi units

Steel I CompConstruct Non Stgd

Resistance factor Phi for flexure

Resistance factor Phi for shear

Resistance factor Phi for Concrete in Tension


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) or0.63 (MPa), must be > 0

The modulus of rupture factor may be specified using eitherMPa 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


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Chapter 5Design 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 theBridge Design Preferences form. The form can be opened by clicking the Code

Preferences button.

5 - 1


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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 – c f ′ multiplier; Default Value = 0.4; Typical values: 0.4 to

0.6. The c f ′ is multiplied by the FactorCompLim to obtain the compressionlimit.

FactorTensLim – c f ′ multiplier; Default Values = 0.19 (ksi), 0.5(MPa);

Typical values: 0 to 0.24 (ksi), 0 to 0.63 (MPa). The c f ′ is multiplied by theFactorTensLim to obtain the tension limit.

5.1.2 Algori thm

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 stressesassume 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


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Chapter 5 - Design Concrete Box Girder Brid ges

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, c f ′ = 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 f pu = 270.0 ksi

Yield strength f py = 0.9 ksi

f pu = 243 ksi

Modulus of elasticity, E p = 28500 ksi

Stress Design AASHTO LRFD-2012 5 - 3


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Figure 5-2 Reinforcement, LRFD 2012 Stress Design

AASHTO Box Beam, Type BIII-48

Reinforcing bars:

yield strength, f y = 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 0.9344ksi

826 170812

P M y

A I

− −σ = − = − = −

5 - 4 Stress Design AASHTO LRFD-2012


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Bottom fiber stress =

3 bot bot 856.51 897.59919.5 1.139ksi826 170812

P M y A 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

d P Distance from the extreme compression fiber to the centroid of the pre-

stressing tendons

d S Distance from the extreme compression fiber to the centroid of rebar in

the tension zone

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

f pu Specified tensile strength of prestressing steel (area weighted average

of all tendons in the tensile zone)

Flexure Design AASHTO LRFD-2012 5 - 5


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f py Yield tensile strength of prestressing steel (area weighted average of all

tendons in the tensile zone)

f y Yield strength of rebar

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

M n Nominal flexural resistance

M r Factored flexural resistance

t slabeq 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 c f ′ over azone 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 f pe (effective stress after loses) larger

than 0.5 f pu (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


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The section properties are calculated for the section before skew, grade, and

superelevation have been applied. This is consistent with the demands beingreported 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 Algori thm

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 slabwidth, assuming a rectangular shape.

slabslabeq

slab

At

b=

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

zontal thicknesses.

web

webeq web

1

n

b b= ∑

The β1 stress block factor is evaluated in accordance with AASHTO-2012

5.7.2.2 based on section c f ′

– If c f ′ > 28 MPa, then 1

28max 0.85 0.05; 0.65 ;

7c f ′ − 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 resist negative 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



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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 astraight 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, d P

–

specified tensile strength of prestressing steel, f pu

–

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

= −

2 1.04

py

pu

f k

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, d s

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

pu

c PS

p

A f A f c

f f b kA

d

+=

′β +

The distance c is compared against requirement of Section 5.7.2.1 to verify if

stress in mild reinforcement f s can be taken as equal to f y. The limit on ratio

c/d s is calculated depending on what kind of code interims are specified inthe Bridge Design Preferences form as shown in the table below:

5 - 8 Flexure Design AASHTO LRFD-2012


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Code AASHTO LRFD 2012

No Interims

AASHTO LRFD 2012

with 2013 Interims

≤ 0.6

0.003

0.003 +

where the compression control strain limit is per AASHTO LRFD 2013

Interims table C5.7.2.1-1

When the limit is not satisfied the stress in mild reinforcement f s is reduced to

satisfy the requirement of Section 5.7.2.1.

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

– If 1 slabeq ,c t β > 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

pu

c PS

pt

A f A f f b b t c

f f b kA

y

′+ − −=

′ β +

Average stress in prestressing steel f ps is calculated in accordance with

(AASHTO-2012 eq. 5.7.3.1.1-1).

= −

1PS PU

p

c f f k

d

Nominal flexural resistance M n is calculated in accordance with (AASHTO-

2012 eq. 5.7.3.2.2-1).

– If the section is a T-section,

( ) slabeq 1 1 1

slab webeq slabeq 0.85 ;2 2 2 2

n PS PS p S s s c

t c c c M A f d A f d f b b t β β β ′= − + − + − −

else



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1 1

2 2

n PS PS p S s s

c c M A f d A f d .

β β = − + −

Factored flexural resistance is obtained by multiplying M n by φ.

M r = φ M n

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, c f ′ = 5.0 ksi (~34.473 MPa)

Design span = 95.0 ft

Prestressing strands: �

Documents

Bsd Aashto Lrfd 2012