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Bridge Superstructure Design Eurocode

CSiBridge®

Bridge Superstructure Design Eurocode

ISO BRG102816M11 Rev. 1 Proudly developed in the United States of America February 2017

Copyright

Copyright Computers & Structures, Inc., 1978-2017 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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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 2-2

2.3 Default Load Combinations 2-7

3 Live Load Distribution

3.1 Methods for Determining Live Load Distribution 3-1

3.2 Determination of Live Load Distribution Factors 3-2

3.3 Apply LLD Factors 3-3

3.3.1 User Specified (Method 1) 3-3 3.3.2 Forces Read Directly from Girders

i

CSiBridge Superstructure Design

(Method 2) 3-4 3.3.3 Uniformly Distributed to Girders (Method 3) 3-4

3.4 Generate Virtual Combinations (Method 1 and 3) 3-4

3.4.1 Stress Check (Methods 1 and 3) 3-4 3.4.2 Shear or Moment Check

(Methods 1 and 3) 3-5

3.5 Read Forces/Stresses Directly from Girders (Method 2) 3-5

3.5.1 Stress Check (Method 2) 3-5 3.5.2 Shear or Moment Check (Method 2) 3-6

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 5-1

5.2 Flexure Design 5-1

5.2.1 Design Process 5-3 5.2.2 Algorithms 5-5

5.3 Shear Design 5-7

5.3.1 Variables 5-9 5.3.2 Design Process 5-10 5.3.3 Algorithm 5-11

ii

Contents

6 Design Multi-Cell Concrete Box Bridges using AMA





6.3.1 Variables 6-8 6.3.2 Design Process 6-10 6.3.3 Algorithm 6-10

7 Design Concrete Slab Bridges





7.3.1 Variables 7-8 7.3.2 Design Process 7-9 7.3.3 Algorithms 7-10

7.4 Crack Width Design 7-13

7.4.1 Variables 7-14 7.4.2 Algorithms 7-14

8 Design Precast Concrete Girder Bridges





iii


8.3.1 Variables 8-8 8.3.2 Design Process 8-9 8.3.3 Algorithms 8-10

9 Design Steel I-Beam Bridge with Composite Slab

9.1 Section Properties 9-1

9.1.1 Yield Moments 9-1 9.1.2 Plastic Moments 9-3 9.1.3 Classification of Cross-Sections 9-7 9.1.4 Effective Section Properties 9-9 9.1.5 Unbraced Length L and Section Transitions 9-12 9.1.6 Lateral Torsional Buckling 9-12

9.2 Design Request Parameters 9-14


9.3.1 Demand Flange Stresses fbu and ff 9-18

9.4 Ultimate Design Request 9-19

9.4.1 Bending 9-20 9.4.2 Shear 9-24

9.5 Service Stress Design Request 9-26

9.5.1 Positive Bending 9-26 9.5.2 Negative Bending 9-26

9.6 Service Rebar Design Request 9-27

9.6.1 Minimum Rebar 9-27 9.6.2 Control of Cracking 9-26

9.7 Constructability Design Request 9-29

9.7.1 Staged (Steel-I Comp Construct Stgd) 9-29 9.7.2 Non-staged (Steel-I Comp Construct NonStgd) 9-29 9.7.3 Slab Status vs Unbraced Length 9-30 9.7.4 Algorithm 9-30

iv

Contents

9.8 Section Optimization 9-31

10 Design Steel U-Tub Bridge with Composite Slab

10.1 Section Properties 10-1

10.1.1 Yield Moments 10-1 10.1.2 Plastic Moments 10-3 10.1.3 Classification of Cross-Sections 10-7 10.1.4 Effective Section Properties 10-9 10.1.5 Unbraced Length L and Section Transitions 10-12 10.1.6 Lateral Torsional Buckling 10-13

10.2 Design Request Parameters 10-15


10.3.1 Demand Flange Stresses fbu 10-19

10.4 Ultimate Design Request 10-20

10.4.1 Bending 10-21 10.4.2 Shear 10-25

10.5 Service Stress Design Request 10-27

10.5.1 Positive Bending 10-27 10.5.2 Negative Bending 10-28

10.6 Service Rebar Design Request 10-29

10.6.1 Minimum Rebar 10-29 10.6.2 Control of Cracking 10-30

10.7 Constructability Design Request 10-30

10.7.1 Staged (Steel I Comp Construct Stgd) 10-30 10.7.2 Non-staged (Steel I Comp Construct NonStgd) 10-31 10.7.3 Slab Status vs Unbraced Length 10-31 10.7.4 Algorithm 10-32

10.8 Section Optimization 10-32

v


11 Run a Bridge Design Request

11.1 Description of Example Model 11-2

11.2 Design Preferences 11-3

11.3 Load Combinations 11-3

11.4 Bridge Design Request 11-5

11.5 Start Design/Check of the Bridge 11-6

12 Display Bridge Design Results

12.1 Display Results as a Plot 12-1

12.1.1 Additional Display Examples 12-2

12.2 Display Data Tables 12-7

12.3 Advanced Report Writer 12-8

12.4 Verification 12-11

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. Currently, the Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 codes are supported by CSiBridge.

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 through 2-3 for the Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005.

2.1 Load Pattern Types Table 2-1 Permanent Actions, Table 2-2 Prestress and Table 2-3 Variable Ac-tions show the load pattern type and Eurocode description as well as the Euro-code abbreviation. Users may choose any name to identify a load pattern type.

Load Pattern Types 2 - 1


Table 2-1 Permanent Actions CSiBridge

Load Pattern Type Eurocode

Abbreviations Description of Load Pattern General Permanent Actions General Permanent Actions DEAD G DEADMANUFACTURE G DEADWEARING G Geotechnical Permanent Actions Geotechnical Permanent Actions DEADWATER Ggeo DOWNDRAG Ggeo VERTICALEARTHPRESSURE Ggeo Uneven Settlements - Linear analysis Uneven Settlements - Linear analysis SETTLEMENT Gset_L

Table 2-2 Prestress CSiBridge

Load Pattern Type Eurocode Reference Description of Load Pattern

Prestress PT Prestress PRESTRESS

Table 2-3 Variable Actions CSiBridge


Abbreviations Description of Load Pattern Traffic Actions EURO LOADMODEL1 CHARACTER LM1_Char Load Model 1 with combination of

Tandem System and UDL system without introducing psi factor

EURO LOADMODEL1 FREQUENT LM1_Freq Load Model 1 with combination of Tandem System and UDL system introducing psi factors

EURO LOADMODEL2 LM2 Load Model 2 EURO LOADMODEL3 LM3 Load Model 3 EURO LOADMODEL4 LM4 Load Model 4 PEDESTRIANLL FCT Footway and Cycle Tracks PEDESTRIANLLREDUCED FCTr Footway and Cycle Tracks reduced

value Horizontal Traffic Actions BRAKING HTA Traction and Braking CENTRIFUGAL C Centrifugal Force Other Actions WIND W Wind Load WINDONLIVELOAD Wt Wind with Traffic TEMPERATURE T TEMPERATUREGRADIENT TG SNOW S Snow with H < 1000m SNOWHIGHALTITUDE S Snow with H > 1000m CONSTRUCTION C Construction load

2 - 2 Load Pattern Types

Chapter 2 - Define Loads and Load Combinations

Table 2-3 Variable Actions CSiBridge


Abbreviations Description of Load Pattern Geotechnical Variable Actions Geotechnical Variable Actions HORIZONTALEARTHPRESSURE Qgeo BOUYANCY Qgeo WATERLOADPRESSURE Qgeo EARTHHYDROSTATIC Qgeo EARTHSURCHARGE Qgeo ACTIVEEARTHPRESSURE Qgeo Earthquake Load QUAKE E Accidental loads IMPACT A VEHICLECOLLISION A VESSELCOLLISION A

2.2 Design Combinations Table 2-1 Permanent Actions, Table 2-2 Prestress and Table 2-3 Variable Ac-tions show the load pattern type and Eurocode description as well as the Euro-code abbreviation. Users may choose any name to identify a load pattern type

1. Combination Groups

Table 2-4 Ultimate Limit State Design Situation Combination Group Abbreviation Persistent and Transient – EQU (A) Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(A)

EQU

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

EQU+STR

Persistent and Transient – STR/GEO (B1) Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(B) (first table)

STR/GEO-B1

Design Combinations 2 - 3


Table 2-4 Ultimate Limit State Design Situation Combination Group Abbreviation Persistent and Transient – STR/GEO (B2-a) Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(B) (sec-ond table)

STR/GEO-B2-a

Persistent and Transient – STR/GEO (B2-b) Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(B) (sec-ond table)

STR/GEO-B2-b

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

STR/GEO-C

Persistent and Transient – STR/GEO (C) + Factors (B) Combinations of actions in persistent and transient design situations from Eq. 6.10 with the partial factors specified in Table A2.4(C) for geotechnical actions and Table A2.4 (B) for non geotechnical actions.

STR/GEO-C+B

Seismic Combinations of actions for seismic design situations Eq. 6.12

SEIS

Accidental Combinations of actions for accidental design situations Eq. 6.11

ACC

Table 2-5 Serviceability Limit State design situation

Combination Group Abbreviation

Characteristic Characteristic combination of actions Eq.6.14

CARAC

Frequent Frequent combination of actions Eq. 6.15

FREQ

Quasi-permanent Quasi-permanent combination of actions Eq. 6.16

QUASI

2 - 4 Design Combinations


Table 2-6 Combination Factors (Ref. Table A2.1)

Ψ0 : Used for combination of variable action

Ψ1 : Used for combination of frequent value of variable action

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

Load Name Ψ0 Ψ1 Ψ2 Load Model 1 – Tandem System 0.75 0.75 0.0 Load Model 1 – UDL System 0.4 0.4 0.0 Load Model 2 0.0 0.75 0.0 Load Model 3 0.0 0.0 0.0 Load Model 4 0.0 0.75 0.0 Footways and Cycle Tracks 0.0 0.0 0.0 Footways and Cycle Tracks reduced value 0.4 0.4 0.0 Wind (Persistent design situations) 0.6 0.2 0.0 Wind with traffic 0.0 0.0 0.0 Snow H < 1000 m 0.7 0.5 0.0 Snow H > 1000 m 0.7 0.5 0.2 Thermal action (Temperature) 0.6 0.6 0.5 Construction Loads 1.0 1.0

Table 2-7 Partial Factors

Load Name EQU EQU + STR

STR/ GEO-B1

STR/ GEO-B2a

STR/ GEO-B2b

STR/ GEO-C

STR/ GEO-C+B

SEIS, ACC CARAC, FREQ, QUAS

max min max min max min max min max min max min max min General Perma-nent Actions 1.05 0.95 1.35 1.15 1.35 1 1.15 1 1 1 1.35 1 1 1

Geotechnical Permanent Actions 1.05 0.95 1.35 1.15 1.35 1 1.15 1 1 1 1.35 1 1 1

Uneven Settle-ments - Linear analysis

1.05 0.95 1.35 1.15 1.20 0 1.02 0 1 0 1.20 0 1 0

Prestress Pϒ Pϒ Pϒ Pϒ Pϒ Pϒ Pϒ Pϒ Pϒ Pϒ Pϒ Pϒ 1 1 Traffic Actions 1.35 0 1.35 0 1.35 0 1.35 0 1.15 0 1.50 0 1 0 Horizontal Traffic Actions

1.35 0 1.35 0 1.35 0 1.35 0 1.15 0 1.50 0 1 0

Other Actions 1.50 0 1.50 0 1.50 0 1.50 0 1.30 0 1.50 0 1 0 Geotechnical Variable Actions

1.50 0 1.50 0 1.50 0 1.50 0 1.30 0 1.30 0 1 0

Seismic 1 1 Accidental 1 1

Design Combinations 2 - 5


Tables 2-8 Load Combinations A. For (1) EQU, (2) EQU+STR, (3) STR/GEO-B2b, (4) STR/GEO-C, (5) STR/GEO-C+B and (6) CARAC (Characteristic)

(EN1990, Eq. 6.10, 6.10b and 6.14) Leading Variable

Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A 1. gr1a 1 1 1 1 Ψ0 Ψ0 Ψ0 2. gr1b 1 1 1 3. gr2 1 1 1 1 Ψ0 Ψ0 4. gr3 1 1 1 Ψ0 Ψ0 5. gr4 1 1 1 1 Ψ0 Ψ0 6. gr5 1 1 1 Ψ0 Ψ0 7. W 1 1 1 Ψ0 Ψ0 Ψ0 8. Wt, required: gr1a 1 1 1 Ψ0 Ψ0 Ψ0 9. T 1 1 Ψ0 1 Ψ0 Ψ0 10. T, required: gr1a 1 1 1 Ψ0 1 Ψ0 11. Qgeo 1 1 Ψ0 Ψ0 Ψ0 1 12. Qgeo, required: gr1a 1 1 1 Ψ0 1 Ψ0 1 13. N 1 1 Ψ0 Ψ0 1 Ψ0

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

erated

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

Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A 1. Required: gr1a 1 1 1 Ψ0 Ψ0 Ψ0 Ψ0 1 1 Ψ0 Ψ0 Ψ0 Ψ0

C. For QUAS (EN1990, 6.16) Leading Variable

Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A 1. Required: gr1a 1 1 1 Ψ2 Ψ2 Ψ2 Ψ2

1 1 Ψ2 Ψ2 Ψ2 Ψ2

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

Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A E 1 1 Ψ0 Ψ0 Ψ0 1

2 - 6 Design Combinations


E. For ACC (EN1990, Eq. 6.11)

Main Variable Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A 1. A 1 1 Ψ2 Ψ2 Ψ2 1 2. gr1a 1 1 1 Ψ2 Ψ2 1 3. gr1b 1 1 Ψ1 1 4. gr4 1 1 Ψ1 Ψ2 Ψ2 1 5. W 1 1 Ψ1 Ψ2 Ψ2 Ψ2 1 6. T 1 1 Ψ2 Ψ2 1 7. Qgeo 1 1 Ψ2 Ψ2 Ψ2 1 8. N 1 1 Ψ2 Ψ1 Ψ2 1

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

Actions G PT LM1-c LM1-f LM2 LM3 LM4 FCT FCTr HTA W Wt T N Qgeo E A 1. gr1a 1 1 1 Ψ2 Ψ2 Ψ0 2. gr1b 1 1 Ψ1 3. gr4 1 1 Ψ1 Ψ2 Ψ2 4. W 1 1 Ψ1 Ψ2 Ψ2 Ψ2 5. T 1 1 Ψ2 Ψ2 6. Qgeo 1 1 Ψ2 Ψ1 7. N 1 1 Ψ2 Ψ1 Ψ2

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

Default Load Combinations 2 - 7


Figure 2-1 Define Code-Generated Load Combinations for Bridge Design form – Eurocode

2 - 8 Default Load Combinations


Figure 2-2 Define Load Combination form - Eurocode

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

Default Load Combinations 2 - 9

Chapter 3 Live Load Distribution

This chapter describes the algorithms used by CSiBridge that can be used to control assignment of 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.

Live load distribution factors can be used to control sharing of live load de-mands by individual girders in spine models that use single frame objects to model an entire cross-section. The use of live load distribution factors is also allowed on area and solid object models.

Legend: Girder = beam + tributary area of composite slab or web + tributary area of top and bottom 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 three 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 reads the calculated live load demands directly from in-dividual girders (available only for Area or Solid models).

Method 3 – CSiBridge distributes the live load uniformly into 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 (Method 1), the number of loaded lanes and MultiLane Scale Factors included in the demand set combinations should correspond to the assumptions based on which the LLD factor was derived. (For example when factors based on AASHTO LRFD code are used only one lane with a MultiLane Scale Factor = 1 should be loaded into Mov-ing Load cases included in the demand set combinations. The vehicle classes defined in the moving load case shall comprise the truck and lane load as de-fined in LRFD clause 5.7.1.2.1.2 or 5.7.1.4.1.2.)

When CSiBridge reads the demands directly from individual girders (Method 2, applicable to area and solid models only) or when CSiBridge applies the LLD factors uniformly (Method 3), multiple traffic lanes with relevant Mul-tilane Scale Factors should be loaded in accordance with code requirements.

3.2 Determination of Live Load Distribution Factors The Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 codes do not give specific guidance on how to calculate Live Load Distribution factors for exte-rior and interior beams. Other bridge codes, such as AASHTO LRFD or CAN/CSA S6, specify comprehensive methods for determining LLD factors for various types of cross-sections. The LLD factors typically are dependent on the following parameters:

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

the number of girders

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

roadway width and spacing of girders

3 - 2 Determination of 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 the neighboring girder on the other side

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

If the live load demands are to be read by CSiBridge directly from the individ-ual girders (Method 2; see the next subsection), 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 individual 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 (Method 1); directly from individual girders (Method 2); or uniformly distributed onto all girders (Method 3).

3.3.1 User Specified (Method 1) 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.

Apply LLD Factors 3 - 3


3.3.2 Forces Read Directly from Girders (Method 2) When this method is selected, CSiBridge sets the live load distribution factor for all girders to 1.

3.3.3 Uniformly Distributed to Girders (Method 3) When this method is selected, the live load distribution factor is equal to 1/n where n is the number of girders in the section. All girders have identical LLD factors disregarding their designation (exterior, interior) and demand type (shear, moment).

3.4 Generate Virtual Combinations (Methods 1 and 3) When the method for determining the live load distribution is user-specified or uniformly distributed (Methods 1 or 3), CSiBridge generates virtual load com-bination for every valid section cut selected for design. The virtual combina-tions are used during a stress check and check of the shear and moment to cal-culate the forces on the girders. After those forces have been calculated, the virtual combinations are deleted. The process is repeated for all section cuts se-lected 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 (Methods 1 and 3) 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

3 - 4 Generate Virtual Combinations (Methods 1 and 3)

Chapter 3 - Live Load Distribution

live load demands are shared equally irrespective of lane eccentricity by all girders, CSiBridge uses averaging when calculating the girder stresses. It cal-culates the stresses on a beam by integrating axial and M3 moment demands on all the beams in the entire section cut and dividing the demands by the number of girders. Similarly, P and M3 forces in the composite slab are integrated and stresses are calculated in the individual tributary areas of the slab by dividing the total slab demand by the number of girders.

When stresses are read from analysis into design, the stresses are multiplied by n (where n is number of girders) to make up for the reduction applied in the Virtual Combinations.

3.4.2 Shear or Moment Check (Methods 1 and 3) 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 momentgenerated for exterior beam are assigned to both exterior beams, and similarly, Virtual Combinations for interi-or beams are assigned to interior beams.)

3.5 Read Forces/Stresses Directly from Girders (Method 2) 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 (Method 2) 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.

Read Forces/Stresses Directly from Girders (Method 2) 3 - 5


3.5.2 Shear or Moment Check (Method 2) At the Section Cut being analyzed, the girder forces are read from CSiBridge for every COMBO specified in the Design Request (see Chapter 4). 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 (Method 2)

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 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 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 Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 for design and stress check of the superstructure of a concrete box type bridge deck section. For referring to per-tinent sections of the corresponding code, a unique prefix is assigned for each code.

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 EN 1992-1-1, Section 6.3 torsion is considered.

5 - 1


5.1 Stress Design The following design parameters are defined by the user in the Design Request (see Chapter 4): – FactorCompLim – fck multiplier; Default Value = 0.6. The fck is multiplied by

the FactorCompLim to obtain the concrete compression limit.

– FactorTensLim - fctk multiplier; Default Value = 0.4. The fctk is multiplied by the FactorTensLim to obtain the concrete 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 locations are labeled in the output plots and tables.

Concrete compressive and tensile strengths are read at every point, and com-pression and tension limits are evaluated using the FactorCompLim − fck mul-tiplier and the FactorTensLim − fctk multiplier.

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.

5.2 Flexure Design The following design parameters are defined by the user in the Design Request (see Chapter 4):

– γc– Partial safety factor for concrete; Default Value = 1.5.

– γsreb– Partial safety factor for reinforcing steel; Default Value = 1.15.

– γsPT – Partial safety factor for prestressing steel; Default Value = 1.15.

– εprePT – Factor to estimate pre-strain in PT. Multiplies fpk to obtain stress in tendons after losses. Typical values are between 0.4 and 0.9

5 - 2 Stress Design

Chapter 5 - Design Concrete Box Girder Bridges

5.2.1 Design Process The derivation of the moment resistance of the section is based on assumptions specified in Section 6.1 of the code:

– Plane sections remain plane.

– The strain in bonded reinforcement or bonded prestressing tendons, whether in tension or in compression, is the same as that in the surrounding concrete.

– The tensile strength of the concrete is ignored.

The stresses in the concrete in compression are derived from the rectangular design stress/strain relationship given in EN 1992-1-1 clause 3.1.7 (Figure 5-1).

Figure 5-1 Rectangular Stress Distribution, Eurocode 2 EN 1992-1-1

The factor λ, defining the effective height of the compression zone, and the factor η, defining the effective strength, follow from:

λ = 0.8 for fck ≤ 50 MPa (EN 1992-1-1 3.19) λ = 0.8 − (fck − 50)/400 for 50 < fck ≤ 90 MPa (EN 1992-1-1 3.20) and η = 1.0 for fck ≤ 50 MPa (EN 1992-1-1 3.21) η = 1.0 − (fck − 50)/200 for 50< fck ≤ 90 MPa (EN 1992-1-1 3.22)

3cuε

sε

cdtη

As

d

x λx

Fs

Ac

Flexure Design 5 - 3


The stresses in the reinforcing or prestressing steel are derived from the de-sign curves in EN 1992-1-1, Figures 3.8 and 3.10 (Figures 5-2 and 5-3).

– The initial strain in prestressing tendons is taken into account when assessing the stresses in the tendons. CSiBridge determines the initial strain by multi-plying the prestressing steel tensile strength fpk by the user-specified factor εprePT and dividing it by Young’s modulus.

Figure 5-2 Idealized and Design Stress-Strain Diagrams for Reinforcing Steel for Tension and Compression

Eurocode 2 EN 1992-1-1

B

A

B

A Idealized

Design

σ

( )t y kk f f=

yk skf γ

ykkf

yd sf E udε ukε ε

yd yk sf f= γykf

ykkf

5 - 4 Flexure Design


Figure 5-3 Idealized and Design Stress-Strain Diagrams for Prestressing Steel, Absolute Values are Shown for Tensile Stress and Strain

Eurocode 2 EN 1992-1-1

– The limit on the mean compressive strain in accordance with EN 1992-1-1, clause 6.1 (5) for a section in concentric loadings is not considered in the CSiBridge algorithm.

5.2.2 Algorithms At each section:

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

slabslabeq

slab

Atb

=

– The tendon and rebar locations, areas, and materials are read. Only bonded tendons are processed; unbonded tendons are ignored.

– The section properties are calculated for the section before skew, grade, and superelevation have been applied. This is consistent with the demands being

B

A

B

A Idealized

Design

σ

pk sk γ

pd pf E udε ukε ε

0.1pd p k sf f= γ0.1p kf

pkk



reported in the section local axis. The entire top and bottom slabs are consid-ered effective in compression.

The ultimate moment resistance of a section is determined using the strain compatibility method and an iterative approach. The following steps are used:

1) The position of the neutral axis is assumed, and the strains in individual re-bar and tendons are calculated. Bars and tendons within the concrete com-pression zone are ignored.

2) The distance x from the extreme compression fiber to the neutral axis is compared to the equivalent slab thickness tslabeq to determine if the section is a T-section or rectangular section. If λx > tslabeq, the section is a T-section.

3) The steel stresses appropriate to the calculated steel strains are calculated from the stress-strain idealization.

4) The concrete stresses appropriate to the strains associated with the assumed neutral axis depth are calculated from the stress-strain idealization.

5) The net tensile and compressive forces at the section are calculated. If these are not equal (the acceptance criterion is [ ]{ }conc rebar conc0.001*PTabs F F F F− + <= ),

the neural axis depth is adjusted accordingly, and the procedure returns to Step 1.

6) When the net tensile force is equal to the net compressive force, the mo-ments are taken about the center of gravity of the concrete compressive block to determine the ultimate moment resistance.

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 compres-sion zone are not considered. It is assumed that all defined tendons in a section, stressed or not, have effective stress after loses equal to εprePT * fpk. If a certain tendon should not be considered for the flexural capacity calculation, its area must be set to zero.



5.3 Shear Design The following design parameters are defined by the user in the Design Request (see Chapter 4):

– γc – Partial safety factor for concrete; Default Value = 1.5.

– γsreb – Partial safety factor for reinforcing steel; Default Value = 1.15.

– γsPT – Partial safety factor for prestressing steel; Default Value = 1.15.

– angle θ – The angle between concrete compression strut and the beam axis perpendicular to the shear force.

– Factor Duct Dia – Factor that multiplies PT duct diameter when evaluating the effective web thickness bw in accordance with EN 1992-1-1, clause 6.2.3 (6).

– αl – Factor for the transmission length of PT, used in shear resistance equa-tion (EN 1992-1-1 6.4).

– Inner Arm Method – The method used to calculate the inner lever arm z of the section. Options are based on defined PT; based on defined rebar; based on defined PT and rebar; multiplier of section depth.

– Inner Arm Limit – The factor that multiplies the depth of the section to get the lower limit of the inner lever arm z of the section (z ≥ Inner Arm Limit * Section Depth).

– Effective depth limit – The factor that multiplies the depth of the section to get the lower limit of the effective depth to the tensile reinforcement d of the section (d = Effective depth limit * Section Depth).

– Type of section – The type of section for shear design; options are program determined; prestressed; non-prestressed. If the program determined option is used and at least one bonded tendon (regardless if stressed or not) is defined in the section cut, the section is classified as prestressed.

– Determining Factor ν1 – The method used to calculate the factor ν1; options are program determined or user defined. If the program determined option is

Shear Design 5 - 7


used, the algorithm assumes the factor ν1 = ν, where ν is determined as fol-lows:

( )0.6 1 in MPa250

ckck

fv f = −

If the design stress of the shear reinforcement is below 80% of the character-istic yield stress fyk, ν1 is taken as:

ν1 = 0.6 for fck ≤ 60 MPa (EN 1992-1-1 6.10.aN)

ν1 = 0.9 – fck / 200 > 0.5 for fck ≥ 60 MPa (EN 1992-1-1 6.10.bN)

– Factor ν1 – User defined value of factor ν1.

– Determining Factor αcw – The method to calculate the factor αcw . Options are program determined or user defined. If the program determined option is used, the algorithm assumes the factor αcw as follows:

( )

( )

1.0 for non-prestressed structures1 for 0 0.25

1.25 for 0.25 0.5

2.5 1 for 0.5 1.0

cp cd cp cd

cd cp cd

cp cd cd cp cd

f f

f f

f f f

+ σ < σ ≤

< σ <

−σ < σ ≤

– Factor αcw– The user defined value for factor αcw used to take account of compression in the shear area.

– Factor fywk – The multiplier of the vertical shear rebar characteristic yield strength to obtain a stress limit in the shear rebar used in equation (EN 1992-1-1 6.10aN). The typical value is in the range of 0.8 to 1.0.

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

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

5 - 8 Shear Design


5.3.1 Variables Ak Area enclosed by the centerlines of the connecting exterior webs and

top and bottom slabs, including inner hollow area

Arebarbot, Arebartop Area of reinforcing steel on the flexural tension side of the member

APTbot, APTtop Area of prestressing steel on the flexural tension side of the member

Ast Area of required closed transverse torsion reinforcement per unit length in accordance with EN 1992-1-1, clause 6.3 (3)

Asw Area of transverse shear reinforcement per unit length

Aswmin Minimum area of transverse shear reinforcement per unit length in accordance with EN 1992-1-1, clause 9.2.2 (5)

b Minimum web width

bw Effective web width adjusted for the presence of prestressing ducts in accordance with EN 1992-1-1, clause 6.2.3 (6)

d Effective section depth

girderd Depth of girder

dPTBot Distance from the top fiber to the center of prestressing steel near the bottom fiber

dPTTop Distance from the bottom fiber to the center of prestressing steel near the top fiber

fcd Design compression strength of concrete

fyd Design yield strength of steel reinforcement

fyk Characteristic yield strength of steel reinforcement

MEd Ultimate design moment demand per section cut

NEd Applied factored axial force per section cut, taken as positive if compression

Shear Design 5 - 9


TEd Ultimate design torsion per section cut

VEd Ultimate design shear force demand per section cut excluding 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 VEd, the component is re-sisting the applied shear.

cV2 Shear in section cut excluding force in tendons

2TotV Shear in section cut including force in tendons

z Inner arm length

5.3.2 Design Process The shear resistance is determined in accordance with EN 1992-1-1, clause 6.2. The procedure assumes that the concrete shear stresses are distributed uniform-ly over an area b wide and d deep, that the direction of principal compressive stresses (defined by angle θ) remains constant over d, and that the shear strength of the section can be determined by considering the biaxial stress con-ditions at just one location in the web. For design, the user should select only those sections that comply with these assumptions by defining appropriate sta-tion ranges in the Design Request (see Chapter 4).

The effective web width is taken as the minimum web width, measured parallel to the neutral axis. In determining the effective web width at a particular level, a fraction of the diameter of grouted ducts at that level is subtracted from the web width. The fraction is defined in the design parameter Factor Duct Dia.

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 fraction of the tendon duct diameter is subtracted from the element thick-ness.

5 - 10 Shear Design


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.

The Shear and Torsion Design is completed on a per web basis. The D/C ratio is calculated and the required area of rebar is reported for each web. The sec-tion 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 αweb. The rebar area calculated is the actual, normal cross-section of the bars.

5.3.3 Algorithm 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 necessarily corresponding to the same design vehicle position. The section cut is designed for all three StepTypes in the COMBOMax, Min and ABSand the controlling StepType is reported.

On the basis of the location and inclination of each web, the per-web demand values are evaluated as shown in the following table:

Location Outer Web Inner Web

VEd TEd VEd TEd

Shear and Torsion

2 web

webcoscV κα

TEd 2 web

webcoscV κα

0

Shear Design 5 - 11


Check

where ( )( )web

web webweb1

cos | |

cos | |n

ακ

α=∑

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 web

webcosc

pV V

V− κ

=α

Demand moment per web is calculated as

sec

web

fEd

MM

n=

− Inner lever arm z is determined based on the stress-strain compatibility method described in Section 5.2.2 of this manual. The calculated inner arm z is compared against the minimum threshold specified in the design parameter Inner Arm Lim-it as z ≥ Inner Arm Limit * Section Depth.

The effective depth of section d of prestressed sections is determined as fol-lows:

If MEd > 0, d = max(Effective depth limit * dgirder , dPTbot) If MEd < 0, d = max(Effective depth limit * dgirder , dPTtop)

The effective depth of section d of non-prestressed sections is determined as follows:

If MEd > 0, then d = max(Effective depth limit * dgirder , drebarbot) If MEd < 0, then d = max(Effective depth limit * dgirder, drebartop)

The reinforcement ratio ρ1 of prestressed sections is determined as follows:

If MEd > 0, then ρ1 = min(0.02, APTbot /bwd) If MEd < 0, then ρ1 = min(0.02, APTtop /bwd)

The reinforcement ratio ρ1 of non-prestressed sections is determined as fol-lows:

5 - 12 Shear Design


If MEd > 0, then ρ1 = min(0.02, Arebarbot /bwd) If MEd < 0, then ρ1 = min(0.02, Arebartop /bwd)

The shear resistance without shear reinforcement of non-prestressed mem-bers or prestressed single span members in regions cracked in bending is de-termined as:

( )1 3, , 1 1100Rd c Rd c ck cp wV C k f k b d = ρ + σ

with a minimum of

( ), min 1Rd c cp wV V k b d= + σ

where:

fck is in MPa

12001 2.0 with in mmk dd

= + ≤

In prestressed continuous or uncracked single span members the shear re-sistance without shear reinforcement is determined as:

( )2, 1

wRd c ctd cp ctd

I bV f fS⋅

= + α σ

where

I is the second moment of area.

bw is the width of the cross-section at the centroidal axis, allowing for the presence of ducts, in accordance with equations (EN 1992-1-1 6.16 and 6.17).

S is the first moment of area above and about the centroidal axis.

σcp is the concrete compressive stress at the centroidal axis caused by axial loading and/or prestressing. ( )in MPa, 0 in compressioncp Ed c EdN A Nσ = >

Shear Design 5 - 13


αl is the factor for transmission length of PT, defined in the Design Parame-ters.

Ratio of VEd over VRd,c is calculated as

,,

Ratio EdEd Rd c

Rd c

VV V

V=

The design value of maximum shear force that can be sustained by the sec-tion cut, limited by crushing of the compression strut, is evaluated as:

( ),max 1 cot tanRd cw w cdV b z v f= α θ + θ

Ratio of VEd over VR,max is calculated as

,max,max

Ratio EdEd R

R

VV V

V=

If VEd > VRd,c and the design parameter Factor fywk < 0.8, then the area of re-quired vertical shear reinforcement per unit length is calculated as:

( ) cot

Edsw

ywk ywk

VAs Factor f z f

=θ

If VEd > VRd,c and the design parameter Factor fywk ≥ 0.8, then the area of re-quired vertical shear reinforcement per unit length is calculated as:

cot

Edsw

ywd

VAs z f

=θ

The minimum area of vertical shear reinforcement per unit length is calculat-ed as:

min 0.08 cksw

yk

fA bs f

=

The area of required longitudinal reinforcement is calculated as:

5 - 14 Shear Design


0.5 cotEdsl

yld

VAf

θ=

The maximum resistance of a member subjected to torsion as limited by the capacity of the concrete struts is evaluated as:

,max ,2 sin cosRd cw cd k ef iT v f A t= α θ θ

where tef,i is checked for effective outer web width, and top and bottom slab widths.

The combined shear and torsion demand/capacity ratio (D/C) is calculated based on web effective width to avoid crushing in accordance with equation 6.3.1 of the code:

,max ,max

Shear and Torsion Ed Ed

Rd R

T VDC T V= +

The torsion demand/capacity ratio (D/C) is calculated based on slab thick-ness to avoid crushing in accordance with Section 8.9.3.18 of the code:

,max

Torsion Ed

Rd

TDC T=

The maximum value of the D/C for Shear and Torsion at webs and Torsion at slabs is reported in the result table in a column labeled “RatioTandV.”

The required area of two link legs per unit length of transverse reinforcement for torsion is calculated as:

2 cot

st Ed

t k yd

A Ts A f

=θ

The required area longitudinal reinforcement per unit length for torsion is calculated as:

1

1 2 cots Ed

k yd

A Ts A f

=θ

Shear Design 5 - 15

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


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 live load distribution method specified in the Design Request (Chapter 4). Torsion effects are ignored.

6.1 Stress Design The following design parameters are defined by the user in the design request:

Stress Design 6 - 1


– FactorCompLim – fck multiplier; Default Value = 0.6. The fck is multiplied by the FactorCompLim to obtain concrete compression limit.

– FactorTensLim - fctk multiplier; Default Value = 0.4. The fctk is multiplied by the FactorTensLim to obtain concrete 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 locations are labeled in the output plots and tables.

Concrete compressive and tensile strengths are read at every point, and com-pression and tension limits are evaluated using the FactorCompLim - fck multi-plier and FactorTensLim - fctk 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 has been specified in the design re-quest (see Chapters 3 and 4).



6.2 Flexure Design The following design parameters are defined by the user in the Design Request:



– γsPT– Partial safety factor for prestressing steel; Default Value = 1.15.

– εprePT– Factor to estimate pre-strain in PT. Multiplies fpk to obtain stress in tendons after losses. Typical values between 0.4 and 0.9.


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

6.2.1 Design Process The derivation of the moment resistance of the section is based on assumptions specified in Section 6.1:

– Plane sections remain plane.

– The strain in bonded reinforcement or bonded prestressing tendons, whether in tension or in compression, is the same as that in the surrounding concrete.

– The tensile strength of the concrete is ignored.

– The stresses in the concrete in compression are derived from the rectangular design stress/strain relationship given in EN 1992-1-1 clause 3.1. (Figure 6.1). The factor λ, defining the effective height of the compression zone and the factor η, defining the effective strength, follow from:

λ = 0.8 for fck ≤ 50 MPa (EN 1992-1-1 3.19) λ = 0.8 − (fck − 50)/400 for 50 < fck ≤ 90 MPa (EN 1992-1-1 3.20) and η = 1.0 for fck ≤ 50 MPa (EN 1992-1-1 3.21) η = 1.0 − (fck -50)/200 for 50< fck ≤90 MPa (EN 1992-1-1 3.22)

Figure 6-1 Rectangular Stress Distribution, Eurocode 2 EN 1992-1-1

– The stresses in the reinforcing or prestressing steel are derived from the de-sign curves in EN 1992-1-1, Figures 3.2 and 3.3 (Figures 6-2 and 6-3).

Ac

As Fs

d

x λx

3cuε

sε

cdtη



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

Eurocode 2 EN 1992-1-1:2004

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

Eurocode 2 EN 1992-1-1:2004

– The initial strain in prestressing tendons is taken into account when assessing the stresses in the tendons. CSiBridge determines the initial strain by

B

A

B

A Idealized

Design

σ

( )t y kk f f=

yk skf γ

ykkf


yd yk sf f= γykf

ykkf

B

A

B

A Idealized

Design

σ

pk sk γ



pkk



multiplying the prestressing steel tensile strength fpk by thr user specified factor εprePT and dividing it by Young’s modulus

– The limit on mean compressive strain in accordance with EN 1992-1-1, clause 6.1 (5) for sections in concentric loadings is not considered in the CSiBridge algorithm.

6.2.2 Algorithms At each section and each web:

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

slabslabeq

slab

Atb

=

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

– The section properties are calculated for the section before skew, grade, and superelevation are applied. This is consistent with the demands being report-ed in the section local axis. The entire top and bottom slab tributary areas are considered as effective in compression.

The ultimate moment resistance of a section is determined using the strain compatibility method and an iterative approach. The following steps are used:

1) The position of neutral axis is assumed, and strains in individual rebars and tendons are calculated. Bars and tendons within the concrete compression zone are ignored.

2) The distance x from the extreme compression fiber to the neutral axis is compared to the equivalent slab thickness tslabeq to determine if the section is a T-section or a rectangular section. If λ x > tslabeq, the section is a T-section.






the neural axis depth is adjusted accordingly, and the procedure returns to Step 1.


The resistance is evaluated only for bending about horizontal axis 3. 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 compres-sion zone are not considered. It is assumed that all defined tendons in a section, stressed or not, have effective stress after loses equal to εprePT * fpk. If a certain tendon should not be considered for the flexural capacity calculation, its area must be set to zero.

6.3 Shear Design The following design parameters are defined by the user in the design request:

− γc– Partial safety factor for concrete; Default Value = 1.5.

− γsreb– Partial safety factor for reinforcing steel; Default Value = 1.15.

− γsPT– Partial safety factor for prestressing steel; Default Value = 1.15.

− angle θ - The angle between concrete compression strut and the beam axis perpendicular to the shear force.

− Factor Duct Dia - Factor that multiplies PT duct diameter when evaluating effective web thickness bw in accordance with EN 1992-1-1, clause 6.2.3 (6).

− αl - Factor for the transmission length of PT, used in shear resistance equa-tion (EN 1992-1-1 6.4).

6 - 6 Shear Design


− Inner Arm Method - Method that will be used to calculate the inner lever arm z of the section. Options are based on defined PT; based on defined rebar; based on defined PT and rebar; multiplier of section depth.

− Inner Arm Limit - Factor that multiplies the depth of the section to get the lower limit of the inner lever arm z of the section. (z ≥ Inner Arm Limit * Section Depth).

− Effective depth limit - Factor that multiplies the depth of the section to get the lower limit of the effective depth to the tensile reinforcement d of the section (d = Effective depth limit * Section Depth).

− Type of section – Type of section for shear design; options are program de-termined; prestressed; non-prestressed. If the program determined option is used and at least one bonded tendon (regardless if it is stressed or not) is defined in the section cut, the section is classified as prestressed.

− Determining Factor ν1 - Method that will be used to calculate the factor ν1; options are program determined or user defined. If the program determined option is used, the algorithm assumes the factor ν1 = ν; where ν is deter-mined as follows:

( )0.6 1 in MPa

250ck

ckfv f = −

If the design stress of the shear reinforcement is below 80% of the charac-teristic yield stress fyk, ν1 is taken as:

ν1 = 0.6 for fck ≤ 60 MPa (EN 1992-1-1 6.10.aN)


− Factor ν1 – user defined value of factor ν1

− Determining Factor αcw - Method that will be used to calculate the factor αcw . Options are program determined or user defined. If the program de-termined option is used, the algorithm assumes the factor αcw as follows:

Shear Design 6 - 7


( )

( )


1.25 for 0.25 0.5

2.5 1 for 0.5 1.0

cp cd cp cd

cd cp cd

cp cd cd cp cd

f f

f f

f f f

+ σ < σ ≤

< σ <

−σ < σ ≤

− Factor αcw- User defined value for factor αcw used to take account of com-pression in the shear area.

− Factor fywk - Multiplier of vertical shear rebar characteristic yield strength to obtain a stress limit in shear rebar used in equation (EN 1992-1-1 6.10aN). Typical values 0.8 to 1.0.

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








b Minimum web width

6 - 8 Shear Design


bw Effective web width adjusted for presence of prestressing ducts in accordance with EN 1992-1-1, clause 6.2.3 (6)


girderd Depth of the girder

dPTbot Distance from the top fiber to the center of the prestressing steel near the bottom fiber.

dPTtop Distance from the bottom fiber to the center of the prestressing steel near the top fiber

fcd Design compression strength of the concrete

fyd Design yield strength of the steel reinforcement

fyk Characteristic yield strength of the steel reinforcement

MEd Ultimate design moment demand

NEd Applied factored axial force, taken as positive in compression

VEd Ultimate design shear force demand per web excluding force in ten-dons

Vp Component in the direction of the applied shear of the effective pre-stressing force; if Vp has the same sign as VEd, the component is re-sisting the applied shear.

cV2 Shear in the section cut excluding force in tendons.

2TotV Shear in the section cut including force in tendons.

z Inner arm length.

6.3.2 Design Process The shear resistance is determined in accordance with EN 1992-1-1, clause 6.2. The procedure assumes that the concrete shear stresses are distributed uniform-ly over an area b wide and d deep, that the direction of principal compressive

Shear Design 6 - 9


stresses (defined by angle θ) remains constant over d, and that the shear strength of the section can be determined by considering the biaxial stress con-ditions at just one location in the web. For design, the user should select only those sections that comply with these assumptions by defining appropriate sta-tion ranges in the Design Request (see Chapter 4).

The effective web width is taken as the minimum web width, measured parallel to the neutral axis. In determining the effective web width at a particular level, a fraction of the diameter of grouted ducts at that level is subtracted from the web width. The fraction is defined in the design parameter Factor Duct Dia.

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 fraction of the tendon duct diameter is subtracted from the element thick-ness.

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.

The Shear Design is completed on a per web basis. The D/C ratio is calculated and the required area of rebar is reported for each web. For a description of dis-tribution of live and other loads into individual webs, please refer to Chapter 3. Section torsion moments are ignored.

6.3.3 Algorithm 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

6 - 10 Shear Design


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 necessarily corresponding to the same design vehicle position. The section cut is designed for all three StepTypes in the COMBOMax, Min and ABSand the controlling StepType is reported.

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

web

cp

V VVn−

=

Inner lever arm z is determined based on stress strain compatibility method described in Section 6.2.2 of this manual. The calculated inner arm z is com-pared against the minimum threshold specified in the design parameter Inner Arm Limit as z ≥ Inner Arm Limit * Section Depth.

The effective depth of the section d of the prestressed sections is determined as follows:

If MEd > 0, then d = max(Effective depth limit * dgirder , dPTbot) If MEd < 0, then d = max(Effective depth limit * dgirder, dPTtop)

The effective depth of the section d of the non-prestressed sections is deter-mined as follows:



If MEd > 0, then ρ1 = min(0.02, APTbot / bwd) If MEd < 0, then ρ1 = min(0.02, APTtop / bwd)

The reinforcement ratio ρ1 of non-prestressed sections is determined as fol-lows :

If MEd > 0, then ρ1 = min(0.02, Arebarbot / bwd) If MEd < 0, then ρ1 = min(0.02, Arebartop / bwd)

Shear Design 6 - 11




with a minimum of


where:

fck is in MPa


= + ≤


( )2, 1

wRd c ctd cp ctd

I bV f fS⋅

= + α σ

where

I is the second moment of area

bw is the width of the cross-section at the centroidal axis, allowing for the presence of ducts, in accordance with equations (EN 1992-1-1 6.16 and 6.17).

S is the first moment of area above and about the centroidal axis

σcp is the concrete compressive stress at the centroidal axis caused by axial loading and/or prestressing ( )in MPa, 0 in compressioncp Ed c EdN A Nσ = >

αl is the factor for transmission length of PT, defined in the design parameters

Ratio of VEd over VRd,c is calculated as:

6 - 12 Shear Design


,,

Ratio EdEd Rd c

Rd c

VV V

V=

The design value of the maximum shear force that can be sustained by the web, limited by crushing of the compression strut, is evaluated as:


Ratio of VEd over VR,max is calculated as:

,max,max

Ratio EdEd R

R

VV V

V=

If VEd > VRd,c and the design parameter Factor fywk < 0.8, then the area re-quired of vertical shear reinforcement per unit length is calculated as:

( ) cot

Edsw

ywk ywk

VAs Factor f z f

=θ

If VEd > VRd,c and the design parameter Factor fywk ≥ 0.8, then the area re-quired of vertical shear reinforcement per unit length is calculated as:

cot

Edsw

ywd

VAs z f

=θ


min 0.08 cksw

yk

fA bs f

=


0.5 cotEdsl

yld

VAf

θ=

Shear Design 6 - 13

Chapter 7 Design Concrete Slab Bridges

This chapter describes the algorithms applied in accordance with the Eurocode 2 EN 1992-1:2004 and EN 1992-2:2005 for design of the superstructure of a concrete slab type bridge deck section.

In CSiBridge, when distributing loads for concrete slab design, the section is always treated as a single beam. All load demands (permanent and transient) are integrated on the entire cross section for stress, flexure, shear and crack width design. Torsion effects are ignored.

7.1 Stress Design The following design parameters are defined by the user in the design request: – FactorCompLim – fck multiplier; Default Value = 0.6. The fck is multiplied

by the FactorCompLim to obtain concrete compression limit

– FactorTensLim - fctk multiplier; Default Value = 0.4; The fctk is multiplied by the FactorTensLim to obtain concrete tension limit

The stresses are evaluated at three points at the top fiber of the slab (points marked red - the left corner, the centerline slab and the right corner) and five points at the bottom fiber of the slab (points marked blue - the most left edge,

Stress Design 7 - 1


the left most bottom corner, the centerline slab and the right most bottom corner and the most right edge). The location is labeled in the output plots and tables.

Concrete compressive and tensile strengths are read at every point, and compres-sion and tension limits are evaluated using the FactorCompLim - fck multiplier and FactorTensLim - fctk multiplier.

The stresses are evaluated for each demand set. If the demand set contains live load, the program positions the load to capture extreme stress at each of the eval-uation points.


7.2 Flexure Design The following design parameters are defined by the user in the design request:




– εprePT– Factor to estimate pre-strain in PT. Multiplies fpk to obtain stress in tendons after losses. Typical value between 0.4-0.9


- Plane sections remain plane.


Chapter 7 - Design Concrete Slab Bridges

- The strain in bonded reinforcement or bonded prestressing tendons, whether in tension or in compression, is the same as that in the surrounding concrete.

- The tensile strength of the concrete is ignored.

- The stresses in the concrete in compression are derived from the rectangu-lar design stress/strain relationship given in 3.1.7, Figure 3.5. The factor λ, defining the effective height of the compression zone and the factor η, de-fining the effective strength, follow from:

λ = 0,8 for fck ≤50 MPa (3.19) λ = 0,8- (fck -50)/400 for 50 < fck ≤ 90 MPa (3.20) and η = 1,0 for fck ≤ 50 MPa (3.21) η = 1,0- (fck -50)/200 for 50< fck ≤90 MPa (3.22)

Figure 3.5: Rectangular stress distribution

- The stresses in the reinforcing or prestressing steel are derived from the de-sign curves in 7.2 (Figure 3.8) and 3.3 (Figure 3.10).



- The initial strain in prestressing tendons is taken into account when as-sessing the stresses in the tendons. CSiBridge determines the initial strain



by multiplying the prestressing steel tensile strength fpk by user specified factor εprePT and dividing it by Young’s modulus.

- The limit on mean compressive strain per paragraph (5) of Section 6 for section in concentric loadings is not considered in the CSiBridge algo-rithm.

7.2.2 Algorithms At each section:

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

slabslabeq

slab

Atb

=

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

– 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. The entire slab width is considered as ef-fective in compression.

The ultimate moment resistance of a section is determined by using strain com-patibility method, by iterative approach. The following steps are used:

1) Position of neutral axis is assumed and strains in individual rebars and tendons are calculated. Bars and tendons falling within the concrete compression zone are ignored.

2) Calculate from the stress-strain idealization the steel stresses appropri-ate to the calculated steel strains.

3) Calculate from the stress-strain idealization the concrete stresses ap-propriate to the strains associated with the assumed neutral axis depth.

4) Calculate the net tensile and compressive forces at the section. If these are not equal (the acceptance criteria is abs {Fconc-[Frebar+FPT]}<= 0.001*Fconc), the neural axis depth is adjusted accordingly and the pro-cedure returns to step 1.



5) When the net tensile force is equal to the net compressive force, the moments are taken about the cg of the concrete compressive block to determine the ultimate moment resistance.

The resistance is evaluated only for bending about horizontal axis 3. Separate ca-pacity is calculated for positive and negative moment. The capacity is based on bonded tendons and mild steel located in tension zone as defined in the Bridge Object. Tendons and mild steel reinforcement located in compression zone are not considered. It is assumed that all defined tendons in a section, stressed or not, have effective stress after loses equal to εprePT * fpk. If a certain tendon should not be considered for the flexural capacity calculation, its area must be set to zero.





− angle θ - The angle between concrete compression strut and the beam axis perpendicular to the shear force.

− αl - Factor for transmission length of PT, used in shear resistance equation 6.4.

− Inner Arm Method - Method that will be used to calculate the inner lever arm z of section. Options are: based on defined PT; based on defined rebar; based on defined PT and rebar; multiplier of section depth.

− Inner Arm Limit - Factor that multiplies depth of section to get lower limit of the inner lever arm z of section. (z ≥ Inner Arm Limit * Section Depth).

− Effective depth limit - Factor that multiplies depth of section to get lower limit of the effective depth to tensile reinforcement d of section. (d = Effec-tive depth limit * Section Depth).

− Type of section – Type of section for shear design; options are: program determined; prestressed; non-prestressed. If program determined and at

7 - 6 Shear Design


least one bonded tendon (regardless if stressed or not) is defined in the sec-tion cut the section is classified as prestressed.

− Determining Factor ν1 - Method that will be used to calculate the factor ν1; options are: program determined; user defined. If program determined the algorithm assumes the factor ν1 = ν; where ν is determined as follows:

𝑣𝑣 = 0.6 �1− 𝑓𝑓𝑐𝑐𝑐𝑐250

� (𝑓𝑓𝑐𝑐𝑐𝑐 in MPa)

If the design stress of the shear reinforcement is below 80% of the characteris-tic yield stress fyk, ν1 is taken as:

ν1 = 0,6 for fck ≤ 60 MPa (6.10.aN)

ν1 = 0,9 – fck /200 > 0,5 for fck ≥ 60 MPa (6.10.bN)

− Factor ν1 – user defined value of factor ν1

− Determining Factor αcw - Method that will be used to calculate the fac-tor αcw . Options are: program determined; user defined. If program de-termined the algorithm assumes the factor αcw as follows:

1.0 for non-prestressed structures

�1 + 𝜎𝜎𝑐𝑐𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐� for 0 < 𝜎𝜎𝑐𝑐𝑐𝑐 ≤ 0.25𝑓𝑓𝑐𝑐𝑐𝑐

1.25 for 0.25 𝑓𝑓𝑐𝑐𝑐𝑐 < 𝜎𝜎𝑐𝑐𝑐𝑐 ≤ 0.5𝑓𝑓𝑐𝑐𝑐𝑐

2.5(1− 𝜎𝜎𝑐𝑐𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐

for 0.5𝑓𝑓𝑐𝑐𝑐𝑐) < 𝜎𝜎𝑐𝑐𝑐𝑐 ≤ 1.0𝑓𝑓𝑐𝑐𝑐𝑐

− Factor αcw- user defined value for factor αcw used to take account of compression in the shear area

− 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 Design 7 - 7


− 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 la-bel that will be used to determine the required area of longitudinal re-bar in the girder.

7.3.1 Variables VEd Ultimate design shear force demand per section cut excluding force

in tendons.

NEd Applied factored axial force per section cut, taken as positive if com-pression.

MEd Ultimate design moment demand per section cut.

TEd Ultimate design torsion per section cut.

cV2 Shear in section cut excluding force in tendons.

2TotV Shear in section cut including force in tendons.

Vp Component in the direction of the applied shear of the effective pre-stressing force; if Vp has the same sign VEd as the component is re-sisting the applied shear.

d Effective section depth.

z Inner arm length.

girderd Depth of slab.

b Slab width.

bw Effective slab width – the value is set equal to b - the adjustment for presence of prestressing ducts in accordance with Section 6.2.3 (6) of the code is not carried out.

dPTTop Distance from bottom fiber to center of prestressing steel near the top fiber.

7 - 8 Shear Design


dPTBot Distance from top fiber to center of prestressing steel near the bottom fiber.

APrebarBot, ARebarTop Area of reinforcing steel on the flexural tension side of the member.

APTBot, APTTop Area of prestressing steel on the flexural tension side of the member.

Asw Area of transverse shear reinforcement per unit length.

Aswmin Minimum area of transverse shear reinforcement per unit length in accordance with Section 9.2.2 (5) of the code.

fcd Design compression strength of concrete.

fyd Design yield strength of steel reinforcement.

fyk Characteristic yield strength of steel reinforcement.

7.3.2 Design Process The shear resistance is determined in accordance with section 6.2 of the EN 1992-1-1:2004. The procedure assumes that the concrete shear stresses are dis-tributed uniformly over an area b wide and d deep, that the direction of princi-pal compressive stresses (defined by angle θ) remains constant over d, and that the shear strength of the section can be determined by considering the biaxial stress conditions at just one location in the slab. For design, the user should se-lect only those sections that comply with these assumptions by defining appro-priate station ranges in the Design Request (see Chapter 4).

The effective slab width is taken as the equivalent slab width, measured paral-lel to the neutral axis. In determining the effective slab width at a particular level, a fraction of the diameter of grouted ducts at that level is not subtracted from the slab width.

The Shear Design is completed on per entire section basis. The D/C ratio is cal-culated and the required area of rebar is reported for the section

Shear Design 7 - 9


7.3.3 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 enve-lopes, 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 necessarily corresponding to the same design ve-hicle position. The section cut is designed for all three StepTypes in the COMBOMax, Min and ABSand the controlling StepType is reported.

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

𝑉𝑉𝑐𝑐 = 𝑉𝑉2𝑐𝑐 − 𝑉𝑉2𝑡𝑡𝑡𝑡𝑡𝑡

– Inner lever arm z is determined based on stress strain compatibility method described in section 7.2.2 of this manual. The calculated inner arm z is compared against the minimum threshold specified in the de-sign parameter Inner Arm Limit as z ≥ Inner Arm Limit * Section Depth.

The effective depth of section d of prestressed sections is determined as follows :

If MEd > 0, then d=max(Effective depth limit * dgirder , dPTBot) If MEd < 0, then d=max(Effective depth limit * dgirder , dPTTop)

The effective depth of section d of non-prestressed sections is determined as follows :

If MEd > 0, then d=max(Effective depth limit * dgirder , drebarBot) If MEd < 0, then d=max(Effective depth limit * dgirder , drebarTop)


7 - 10 Shear Design


If MEd > 0, then ρ1=min(0.02, APTBot /bwd) If MEd < 0, then ρ1=min(0.02, APTTop /bwd)

The reinforcement ratio ρ1 of non-prestressed sections is determined as fol-lows :

If MEd > 0, then ρ1=min(0.02, ArebarBot /bwd) If MEd < 0, then ρ1=min(0.02, Arebartop /bwd)

The shear resistance without shear reinforcement of a non-prestressed members or prestressed single span members in regions cracked in bending is determined as:

𝑉𝑉𝑅𝑅𝑐𝑐,𝑐𝑐 = [𝐶𝐶𝑅𝑅𝑐𝑐,𝑐𝑐𝑘𝑘�100𝜌𝜌1𝑓𝑓𝑐𝑐𝑐𝑐�13+� 𝑘𝑘1𝜎𝜎𝑐𝑐𝑐𝑐]𝑏𝑏𝑤𝑤𝑑𝑑

with a minimum of

𝑉𝑉𝑅𝑅𝑐𝑐,𝑐𝑐 = [𝑣𝑣𝑚𝑚𝑚𝑚𝑚𝑚 + 𝑘𝑘1𝜎𝜎𝑐𝑐𝑐𝑐]𝑏𝑏𝑤𝑤𝑑𝑑

where:

𝑓𝑓𝑐𝑐𝑐𝑐is in MPa

𝑘𝑘1 = 1 + �200𝑐𝑐≤ 2.0 with d in mm


𝑉𝑉𝑅𝑅𝑐𝑐,𝑐𝑐 =𝐼𝐼𝑏𝑏𝑤𝑤𝑆𝑆 �(𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐)2 + 𝛼𝛼1𝜎𝜎𝑐𝑐𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐

where:

𝐼𝐼 is the second moment of inertia

𝑏𝑏𝑤𝑤 is the width of the cross-section at the centroidal axis, allowing for the presence of ducts in accordance with Expressions (6.16) and (6.17)

𝑆𝑆 is the first moment of area above and about the centroidal axis

Shear Design 7 - 11


𝜎𝜎𝑐𝑐𝑐𝑐 is the compressive stress at the centroidal axis due to axial load-ing and/or prestressing (𝜎𝜎𝑐𝑐𝑐𝑐 = 𝑁𝑁𝐸𝐸𝑐𝑐 𝐴𝐴𝑐𝑐⁄ in MPa, 𝑁𝑁𝐸𝐸𝑐𝑐 > 0 in com-pression)

αl - Factor for transmission length of PT, defined in design parameters

Ratio of Ved over VRd,c is calculated as

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑉𝑉𝐸𝐸𝑐𝑐𝑉𝑉𝑅𝑅,𝑐𝑐𝑐𝑐 =|𝑉𝑉𝐸𝐸𝑐𝑐|𝑉𝑉𝑅𝑅,𝑐𝑐𝑐𝑐

The design value of maximum shear force that can be sustained by the sec-tion cut, limited by crushing of the compression strut is evaluated as:

𝑉𝑉𝑅𝑅𝑐𝑐 =𝛼𝛼𝑐𝑐𝑤𝑤𝑏𝑏𝑤𝑤𝑧𝑧𝑓𝑓𝑐𝑐𝑐𝑐

(𝑐𝑐𝑅𝑅𝑅𝑅𝑐𝑐 + 𝑅𝑅𝑅𝑅𝑡𝑡𝑐𝑐)

Ratio of Ved over VR,max is calculated as:

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑉𝑉𝐸𝐸𝑐𝑐𝑉𝑉𝑅𝑅,𝑚𝑚𝑚𝑚𝑚𝑚 =|𝑉𝑉𝐸𝐸𝑐𝑐|𝑉𝑉𝑅𝑅,𝑚𝑚𝑚𝑚𝑚𝑚

If Ved > VRd,c and the design parameter Factor fywk <0.8 then the area re-quired of vertical shear reinforcement per unit length is calculated as:

𝐴𝐴𝑠𝑠𝑤𝑤𝑠𝑠

=|𝑉𝑉𝐸𝐸𝑐𝑐|

(𝐹𝐹𝑅𝑅𝑐𝑐𝑅𝑅𝑅𝑅𝐹𝐹𝑓𝑓𝑦𝑦𝑤𝑤𝑐𝑐) 𝑧𝑧 𝑓𝑓𝑦𝑦𝑤𝑤𝑐𝑐 cot𝑐𝑐

If Ved > VRd,c and the design parameter Factor fywk ≥ 0.8 then the area re-quired of vertical shear reinforcement per unit length is calculated as:

𝐴𝐴𝑠𝑠𝑤𝑤𝑠𝑠

=|𝑉𝑉𝐸𝐸𝑐𝑐|

𝑧𝑧 𝑓𝑓𝑦𝑦𝑤𝑤𝑐𝑐 cot𝑐𝑐

The minimum area of vertical shear reinforcement per unit length is calcu-lated as: 𝐴𝐴𝑠𝑠𝑤𝑤𝑚𝑚𝑚𝑚𝑚𝑚

𝑠𝑠=

0.08 �𝑓𝑓𝑐𝑐𝑐𝑐𝑓𝑓𝑦𝑦𝑐𝑐

𝑏𝑏

The area of required longitudinal reinforcement is calculated as

7 - 12 Shear Design


𝐴𝐴𝑠𝑠𝑐𝑐 =0.5𝑉𝑉𝐸𝐸𝑐𝑐 cot𝑐𝑐

𝑓𝑓𝑦𝑦𝑐𝑐𝑐𝑐

The shear demand/capacity ratio (D/C) is calculated based on slab effective width to avoid crushing in accordance with equation 6.3.1 of the code:

𝑆𝑆ℎ𝑒𝑒𝑅𝑅𝐹𝐹 𝑅𝑅𝑡𝑡𝑑𝑑 𝑇𝑇𝑅𝑅𝐹𝐹𝑠𝑠𝑅𝑅𝑅𝑅𝑡𝑡𝐷𝐷𝐶𝐶

=|𝑉𝑉𝐸𝐸𝑐𝑐|𝑉𝑉𝑅𝑅,𝑚𝑚𝑚𝑚𝑚𝑚

7.4 Crack Width Design The following design parameters are defined by the user in the design request:




– kt - factor dependent on the duration of the load per EN 7.3.4. Typical val-ues 0.6 for short term, 0.4 for long term.

– k1 - coefficient which takes account of the bond properties of the bonded reinforcement per EN 7.11. Typical values 0.8 for high bond bars, 1.6 for effectively plain surface.

– k2 - coefficient which takes account of the distribution of strain per EN 7.11. Typical values 0.5 for bending, 1.0 for pure tension.

– k3 - coefficient k3 per EN 7.11. Typical values 3.4

– k4 - coefficient k4 per EN 7.11. Typical values 0.425.

– 𝜉𝜉1 - adjusted ratio of bond strength taking into account the difference of prestressing and reinforcing steel per EN 7.5. Typical values 0.1-1.0

– Cover Method - Method that will be used to calculate the rebar cover to the longitudinal reinforcement; options are: program determined; user defined. If program determined the algorithm calculates the cover based on the position of the longitudinal rebar in the section and the bar diame-ter.

Crack Width Design 7 - 13


7.4.1 Variables

Esk –Longitudinal reinforcement modulus of elasticity

Espk –Prestressing tendons modulus of elasticity

Ecm –Concrete modulus of elasticity

fctd – Design value of concrete tensile strength

𝜙𝜙s – Diameter of longitudinal tensile rebar

cOD – Cover to the tensile longitudinal rebar

7.4.2 Algorithms 𝜌𝜌𝑟𝑟𝑟𝑟𝑟𝑟 =

𝐴𝐴𝑠𝑠𝑏𝑏𝑑𝑑

𝜌𝜌𝑃𝑃𝑃𝑃 =𝐴𝐴𝑠𝑠𝑐𝑐𝑏𝑏𝑑𝑑

𝜇𝜇′ =𝐴𝐴𝑠𝑠′

𝑏𝑏𝑑𝑑�1 −

𝐸𝐸𝑐𝑐𝑚𝑚𝐸𝐸𝑠𝑠𝑐𝑐

�

𝜂𝜂 =𝐸𝐸𝑠𝑠𝑐𝑐𝐸𝐸𝑐𝑐𝑚𝑚

𝜂𝜂𝑠𝑠𝑐𝑐 =𝐸𝐸𝑠𝑠𝑐𝑐𝑐𝑐𝐸𝐸𝑐𝑐𝑚𝑚

7 - 14 Crack Width Design


∝= ��𝜂𝜂(𝜌𝜌𝑟𝑟𝑟𝑟𝑟𝑟 + 𝜇𝜇′) + 𝜂𝜂𝑠𝑠𝑐𝑐𝜌𝜌𝑃𝑃𝑃𝑃�2 + �𝜇𝜇′

𝑑𝑑′

𝑑𝑑+ 𝜌𝜌𝑟𝑟𝑟𝑟𝑟𝑟�2𝜂𝜂 + 2𝜂𝜂𝑠𝑠𝑐𝑐𝜌𝜌𝑃𝑃𝑃𝑃 �1 −

𝑅𝑅𝑑𝑑�

− 𝜂𝜂(𝜌𝜌𝑟𝑟𝑟𝑟𝑟𝑟 + 𝜇𝜇′) − 𝜂𝜂𝑠𝑠𝑐𝑐𝜌𝜌𝑃𝑃𝑃𝑃

∝ 𝑑𝑑 =∝ 𝑑𝑑

Rebar based moment of inertia

𝐼𝐼𝑠𝑠 = (1−∝) �1 −∝3�𝐴𝐴𝑠𝑠𝑑𝑑2 + �∝ −

𝑑𝑑′

𝑑𝑑 ��∝3−𝑑𝑑′

𝑑𝑑 ��1 −

𝐸𝐸𝑐𝑐𝑚𝑚𝐸𝐸𝑠𝑠𝑐𝑐

�𝐴𝐴𝑠𝑠′ 𝑑𝑑2

+ (𝑑𝑑 − 𝑅𝑅−∝ 𝑑𝑑) �𝑑𝑑 − 𝑅𝑅 −∝ 𝑑𝑑

3�𝐸𝐸𝑠𝑠𝑐𝑐𝑐𝑐𝐸𝐸𝑠𝑠𝑐𝑐

𝐴𝐴𝑠𝑠𝑐𝑐

Stress in rebar

𝜎𝜎𝑠𝑠 =−𝑁𝑁𝑐𝑐

∝ 𝑑𝑑𝑏𝑏𝜂𝜂 + 𝐴𝐴𝑠𝑠 + 𝐴𝐴𝑠𝑠′

−𝑁𝑁𝑐𝑐(𝑑𝑑 − 𝑅𝑅−∝ 𝑑𝑑)(𝑑𝑑−∝ 𝑑𝑑)

𝐼𝐼𝑠𝑠+𝑀𝑀𝑟𝑟𝑐𝑐(𝑑𝑑−∝ 𝑑𝑑)

𝐼𝐼𝑠𝑠

Crack control width per EN 1992-1-1 Section 7.3.4

ℎ𝑐𝑐,𝑟𝑟𝑓𝑓𝑓𝑓 = 𝑚𝑚𝑅𝑅𝑡𝑡 �2.5(ℎ − 𝑑𝑑) ; (ℎ−∝𝑐𝑐)3

; ℎ2� effective height per Figure 7.1

𝐴𝐴𝑐𝑐,𝑟𝑟𝑓𝑓𝑓𝑓 = ℎ𝑐𝑐,𝑟𝑟𝑓𝑓𝑓𝑓𝑏𝑏

𝜌𝜌𝑐𝑐,𝑟𝑟𝑓𝑓𝑓𝑓 = 𝐴𝐴𝑠𝑠+ξ12𝐴𝐴𝑠𝑠𝑐𝑐

𝐴𝐴𝑐𝑐,𝑒𝑒𝑒𝑒𝑒𝑒 per equation 7.10

∆𝜀𝜀 = 𝑚𝑚𝑅𝑅𝑚𝑚�𝜎𝜎𝑠𝑠−𝑐𝑐𝑡𝑡

𝑒𝑒𝑐𝑐𝑡𝑡𝑐𝑐𝜌𝜌𝑐𝑐,𝑒𝑒𝑒𝑒𝑒𝑒

�1+𝐸𝐸𝑠𝑠𝑐𝑐𝐸𝐸𝑐𝑐𝑐𝑐

𝜌𝜌𝑐𝑐,𝑒𝑒𝑒𝑒𝑒𝑒�

𝐸𝐸𝑠𝑠𝑐𝑐 ; 0.6 𝜎𝜎𝑠𝑠

𝐸𝐸𝑠𝑠𝑐𝑐� strain delta per eq 7.9

𝑠𝑠𝑟𝑟,𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑘𝑘3𝑐𝑐𝑂𝑂𝑂𝑂 + 𝑐𝑐1𝑐𝑐2𝑐𝑐4𝜙𝜙𝑠𝑠𝜌𝜌𝑐𝑐,𝑒𝑒𝑒𝑒𝑒𝑒

maximum crack spacing per eq. 7.11

𝑤𝑤𝑐𝑐 = 𝑚𝑚𝑅𝑅𝑚𝑚�0 ; 𝑠𝑠𝑟𝑟,𝑚𝑚𝑚𝑚𝑚𝑚∆𝜀𝜀� crack width per equation 7.8

Crack Width Design 7 - 15

Chapter 8 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 Eurocode 2 EN 1992-1-1:2004 and EN 1992-2:2005 code.


For PrecastComp design in CSiBridge each beam and its tributary composite slab is designed separately. Moments and shears due to live load are distributed to individual beans in accordance with the live load distribution method speci-fied in the Design Request. Torsion effects are ignored.

8.1 Stress Design The following design parameters are defined by the user in the design request: – FactorCompLim – fck multiplier; Default Value = 0.6. The fck is multiplied by

the FactorCompLim to obtain concrete compression limit.

Stress Design 8 - 1


– FactorTensLim - fctk multiplier; Default Value = 0.4. The fctk is multiplied by the FactorTensLim to obtain concrete 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 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 compressive and tensile strengths are read at every point, and com-pression and tension limits are evaluated using the FactorCompLim - fck multi-plier and FactorTensLim - fctk 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 has been specified in the design re-quest (see Chapters 3 and 4).



8.2 Flexure Design The following design parameters are defined by the user in the design request:




– εprePT– Factor to estimate pre-strain in PT. Multiplies fpk to obtain stress in tendons after losses. Typical values are between 0.4 and 0.9.


Chapter 8 - Design Precast Concrete Girder Bridges


− Plane sections remain plane.

− The strain in bonded reinforcement or bonded prestressing tendons, whether in tension or in compression, is the same as that in the surrounding concrete.

− The tensile strength of the concrete is ignored.

− The stresses in the concrete in compression are derived from the rectangular design stress/strain relationship given in EN 1992-1-1 clause 3.1.7 (Figure 8.5). The factor λ, defining the effective height of the compression zone and the factor η, defining the effective strength, follow from:

λ = 0.8 for fck ≤ 50 MPa (EN 1992-1-1 3.19) λ = 0.8 − (fck − 50)/400 for 50 < fck ≤ 90 MPa (EN 1992-1-1 3.20)

and η = 1.0 for fck ≤ 50 MPa (EN 1992-1-1 3.21) η = 1.0 − (fck − 50)/200 for 50 < fck ≤90 MPa (EN 1992-1-1 3.22)

Figure 8-1 Rectangular Stress Distribution, Eurocode 2 EN 1992-1-1:2004

Ac

As Fs

d

x λx

3cuε

sε

cdtη



– The stresses in the reinforcing or prestressing steel are derived from the de-sign curves in EN 1992-1-1 Figures 3.8 and 3.10 (Figures 8.6 and 8.7).

Figure 8-2 Idealized and Design Stress-Strain Diagrams for Reinforcing Steel for Tension and Compression

Eurocode 2 EN 1992-1-1:2004

Figure 8-3 Idealized and Design Stress-Strain Diagrams for Prestressing Steel, Absolute Values are Shown for Tensile Stress and Strain

Eurocode 2 EN 1992-1-1:2004

− The initial strain in prestressing tendons is taken into account when assessing the stresses in the tendons. CSiBridge determines the initial strain by multi-

B

A

B

A Idealized

Design

σ

( )t y kk f f=

yk skf γ

ykkf


yd yk sf f= γykf

ykkf

B

A

B

A Idealized

Design

σ

pk sk γ



pkk



plying the prestressing steel tensile strength fpk by user specified factor eprePT

and dividing it by Young’s modulus.

− The limit on mean compressive strain in accordance with EN 1992-1-1, clause 6.1 (5) for sections in concentric loading is not considered in the CSiBridge algorithm.

8.2.2 Algorithms At each section and each beam:

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

slabslabeq

slab

Atb

=

– The tendon and rebar locations, areas, and materials are read. Only bonded tendons are processed; unbonded tendons are ignored.

– The section properties are calculated for the section before skew, grade, and superelevation are applied. This is consistent with the demands being report-ed in the section local axis. The entire composite slab tributary width is con-sidered as effective in compression.

The ultimate moment resistance of a section is determined by using strain compatibility method, by iterative approach. The following steps are used:

1) The position of the neutral axis is assumed and strains in individual rebars and tendons are calculated. Bars and tendons falling within the concrete compression zone are ignored.

2) The distance x from the extreme compression fiber to the neutral axis is compared to the equivalent slab thickness tslabeq to determine if the section is a T-section or rectangular section. If λ x > tslabeq the section is a T-section.






the neural axis depth is adjusted accordingly and the procedure returns to Step 1.


The resistance is evaluated only for bending about horizontal axis 3. Separate capacity is calculated for positive and negative moment. The capacity is based on bonded tendons and mild steel located in tension zone as defined in the Bridge Object. Tendons and mild steel reinforcement located in compression zone are not considered. It is assumed that all defined tendons in a section, stressed or not, have effective stress after loses equal to εprePT * fpk. If a certain tendon should not be considered for the flexural capacity calculation, its area must be set to zero.


− γc– Partial safety factor for concrete; Default Value = 1.5.

− γsreb– Partial safety factor for reinforcing steel; Default Value = 1.15.


− angle θ - The angle between the concrete compression strut and the beam ax-is perpendicular to the shear force.

− αl - Factor for the transmission length of PT, used in shear resistance equa-tion (EN 1992-1-1 6.4).

− Inner Arm Method - Method that will be used to calculate the inner lever arm z of section. Options are based on defined PT; based on defined rebar; based on defined PT and rebar; multiplier of section depth.

8 - 6 Shear Design


− Inner Arm Limit - Factor that multiplies the depth of the section to get the lower limit of the inner lever arm z of the section (z ≥ Inner Arm Limit * Sec-tion Depth).

− Effective depth limit - Factor that multiplies the depth of the section to get the lower limit of the effective depth to tensile reinforcement d of the section (d = Effective depth limit * Section Depth).

− Type of section – Type of section for shear design; options are program de-termined; prestressed; non-prestressed. If the program determined option is used and at least one bonded tendon (regardless if stressed or not) is defined in the section cut, the section is classified as prestressed.

− Determining Factor ν1 - Method that will be used to calculate the factor ν1; options are program determined or user defined. If the program determined option is used, the algorithm assumes the factor ν1 = ν; where ν is determined as follows:

( )0.6 1 in MPa

250ck

ckfv f = −

If the design stress of the shear reinforcement is below 80% of the character-istic yield stress fyk, ν1 is taken as:

ν1 = 0.6 for fck ≤ 60 MPa (EN 1992-1-1 6.10.aN)


− Factor ν1 – user defined value of factor ν1.

− Determining Factor αcw - Method that will be used to calculate the factor αcw . Options are program determined or user defined. If the program determined option is used, the algorithm assumes the factor αcw as follows:

( )

( )


1.25 for 0.25 0.5

2.5 1 for 0.5 1.0

cp cd cp cd

cd cp cd

cp cd cd cp cd

f f

f f

f f f

+ σ < σ ≤

< σ <

−σ < σ ≤

Shear Design 8 - 7


− Factor αcw- user defined value for factor αcw used to take account of compres-sion in the shear area.

− Factor fywk - Multiplier of vertical shear rebar characteristic yield strength to obtain a stress limit in shear rebar used in equation (EN 1992-1-1 6.10aN). Typical values are 0.8 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.








b Minimum web width of the beam


girderd Depth of girder

dPTbot Distance from top fiber to center of prestressing steel near the bottom fiber

8 - 8 Shear Design


dPTtop Distance from bottom fiber to center of prestressing steel near the top fiber

fcd Design compression strength of concrete

fyd Design yield strength of steel reinforcement

fyk Characteristic yield strength of steel reinforcement

MEd Ultimate design moment demand

NEd Applied factored axial force, taken as positive if compression

VEd Ultimate design shear force demand per beam excluding force in tendons

Vp Component in the direction of the applied shear of the effective pre-stressing force; if Vp has the same sign as VEd the component is re-sisting the applied shear.

cV2 Shear in section cut excluding force in tendons.

V2tot Shear in section cut including force in tendons.

z Inner arm length.

8.3.2 Design Process The shear resistance is determined in accordance with EN 1992-1-1, clause 6.2. The procedure assumes that the concrete shear stresses are distributed uniform-ly over an area b wide and d deep, that the direction of principal compressive stresses (defined by angle θ) remains constant over d, and that the shear strength of the section can be determined by considering the biaxial stress con-ditions at just one location in the web. For design, the user should select only those sections that comply with these assumptions by defining appropriate sta-tion 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.

Shear Design 8 - 9


The Shear Design is completed on a per beam basis. The D/C ratio is calculat-ed and the required area of rebar is reported for each beam. For a description of distribution of live and other loads into individual beams, please refer to Chap-ter 3. Section torsion moments are ignored.

8.3.3 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 necessarily corresponding to the same design vehicle position. The section cut is designed for all three StepTypes in the COMBOMax, Min and ABSand the controlling StepType is reported.

− 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

web

cp

V VVn−

=

− Inner lever arm z is determined based on the stress-strain compatibility meth-od described in Section 8.1.2 of this manual. The calculated inner arm z is compared against the minimum threshold specified in the design parameter Inner Arm Limit as z ≥ Inner Arm Limit * Section Depth.

The effective depth of the section d of the prestressed sections is determined as follows:

If MEd > 0, then d = max(Effective depth limit * dgirder , dPTbot) If MEd < 0, then d = max(Effective depth limit * dgirder, dPTtop)

8 - 10 Shear Design


The effective depth of the section d of the non-prestressed sections is deter-mined as follows:



If MEd > 0, then ρ1 = min(0.02, APTbot /bwd) If MEd < 0, then ρ1 = min(0.02, APTtop /bwd)

The reinforcement ratio ρ1 of non-prestressed sections is determined as fol-lows:

If MEd > 0, then ρ1 = min(0.02, Arebarbot /bwd) If MEd < 0, then ρ1 = min(0.02, Arebartop /bwd)



with a minimum of


where:

fck is in MPa


= + ≤

In prestressed continuous or uncracked single span members, the shear re-sistance without shear reinforcement is determined as:

( )2, 1

wRd c ctd cp ctd

I bV f fS⋅

= + α σ

Shear Design 8 - 11


where

I is the second moment of area

bw is the width of the cross-section at the centroidal axis, allowing for the presence of ducts, in accordance with equations (EN 1992-1-1 6.16 and 6.17)

S is the first moment of area above and about the centroidal axis

σcp is the concrete compressive stress at the centroidal axis caused by axial loading and/or prestressing ( )in MPa, 0 in compressioncp Ed c EdN A Nσ = >

αl - Factor for transmission length of PT, defined in design parame-ters

Ratio of VEd over VRd,c is calculated as

,,

Ratio EdEd Rd c

Rd c

VV V

V=

The design value of maximum shear force that can be sustained by the web, limited by crushing of the compression strut, is evaluated as:


Ratio of VEd over VR,max is calculated as

,max,max

Ratio EdEd R

R

VV V

V=

If VEd > VRd,c and the design parameter Factor fywk < 0.8, then the required ar-ea of vertical shear reinforcement per unit length is calculated as:

( ) cot

Edsw

ywk ywk

VAs Factor f z f

=θ

8 - 12 Shear Design


If VEd > VRd,c and the design parameter Factor fywk ≥ 0.8, then the required ar-ea of vertical shear reinforcement per unit length is calculated as:

cot

Edsw

ywd

VAs z f

=θ


min 0.08 cksw

yk

fA bs f

=


0.5 cotEdsl

yld

VAf

θ=

Shear Design 8 - 13

Chapter 9 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 Eurocode 4 EN 1994-2:2005 code (Part 2).

9.1 Section Properties

9.1.1 Yield Moments

9.1.1.1 Composite Section in Positive Flexure The depth of web in compression that is used in section classification is derived based on positive yield moment, My .The positive yield moment is determined by the program using the following user-defined input, which is part of the Ultimate Design Request (see Chapter 4 for more information about Design Requests).

Mdnc = The user specifies in the Design Request the name of the combo that represents the moment caused by the 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 permanent load (applied to the composite section).

9 - 1


The program solves for MAD from the following equation,

dnc dc ADyt

NC LT ST

M M MFS S S

= + +

and then calculates yield moment based on the following equation

y dnc dc ADM M M M= + +

where

SNC = Noncomposite section modulus

SLT = Long-term composite section modulus

SST = Short-term composite section modulus

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 to determine only the depth of web in compression that is used in classification of webs in accordance with EN 1993-1-1:2005 Table 5.2 for positive bending in the Ultimate Design Check.

Since for Staged and Non-Staged Constructability Design Checks it is difficult to obtain built-up elastic stresses, for the sake of classification of the web it is assumed that the depth of the web in compression for positive bending is based on all stresses being applied to non-composite sections because this produces the greatest depth of web in compression.

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 reinforcement 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. Concrete tension capacity is ignored.

9 - 2 Section Properties

Chapter 9 - Design Steel I-Beam Bridge with Composite Slab

For the sake of classification of the web, the depth of the web in compression for negative bending is based on all stresses being applied to the composite section because this produces the greatest depth of web in compression. This assumption applies to all design checks.

9.1.2 Plastic Moments

9.1.2.1 Composite Section in Positive Flexure The positive plastic moment, Mpl,Rd, 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. The plastic force in the effective width of the composite slab that is in compression is based on a rectangular stress block with the magnitude of the compressive stress equal to 0.85fcd. Concrete in ten-sion is neglected. The position of the plastic neutral axis is determined by the equilibrium condition such that there is no net axial force.

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

Calculate the element forces and use them to determine if the plastic neutral axis is in the web, top flange, or concrete deck.

Calculate the location of the plastic neutral axis within the element deter-mined in the first step.

Calculate Mpl,Rd.

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

Section Properties 9 - 3


Table 9-1 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

12

t c s rt rb

w

D P P P P PYP

− − − − = +

( ) [ ]22

2w

p s s rt rt rb rb c c t tPM Y D Y P d P d P d P d PdD = + − + + + + +

II In Top Flange

Pt + Pw + Pc ≥ Ps + Prb + Pn

12c w t s rt rb

c

t P P P P PYP

+ − − −= +

( ) [ ]22

2c

p c s s n n rb rb w w t tc

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

( ) c w t rt rbs

s

P P P P PY tP

+ + − −=

[ ]2

2s

p rt rt rb rb c c w w t ts

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

rbY c=

[ ]2

2s

p rt rt c c w w t ts

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

( ) rb c w t rts

s

P P P P PY tP

+ + + − =

[ ]2

2s



= + + + + +

VI Concrete Deck at

Prt

Pt + Pw + Pc + Prb + Pn ≥ rt

s

ct

Ps

rtY c=

[ ]2

2s

p rb rb c c w w t ts


= + + + +

VII

Concrete Deck

Above Prt

Pt + Pw + Pc + Prb + Prt < rt

s

ct

Ps

( ) rb c w t rts

s

P P P P PY tP

+ + + + =

[ ]2

2s



= + + + + +



Figure 9-1 Plastic Neutral Axis Cases

in which

Prt = Fyrt Art

Ps = 0.85fcdbsts

Prb = Fyrb Arb

Pc = Fycbctc

Pw = Fyw Dtw

Pt = Fyt bttt

Next the section is checked for ductility requirement in accordance with EN 4 1994-2:2005 6.2.1.2(2). For structural steel grades of web or bottom flanges where fyd > 355 MPa, the MRd is taken as:

Mpl = β Mpl,Rd

where β is the reduction factor given in Figure 9-2. When the value of plx h is greater than 0.4, the section is classified as Class 3 or higher, and the plastic moment of a composite section in positive flexure is set to zero.

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



Figure 9-2 Composite Positive PNA Limits

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 practice are given in Table 9-2. The plastic moment of a non-composite section is calculated by eliminating the terms pertaining to the concrete deck from the equations in Table 9-1.

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


I In Web Pc + Pw ≥ Pt + Prb + Pn 1

2c t rt rb

w

D P P P PYP

− − − = +

( ) [ ]22

2w

p n n rb rb t t l lPM Y D Y P d P d Pd PdD = + − + + + +

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

12l w c rt rb

t

t P P P PYP

− − − = +

( ) [ ]22

2t

p l n n rb rb w w c cl

PM Y t Y P d P d P d P dt = + − + + + +




in which

Prt = Fyrt Art

Ps = 0.85fcdbsts

Prb = Fyrb Arb

Pc = Fycbctc

Pw = Fyw Dtw

Pt = Fyt bttt

In the equations for Mp given in Tables 9-1 and 9-2, 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 9-1 and 9-2.

9.1.3 Classification of Cross-Sections At each section cut the steel beam section is classified in accordance with EN 1993-1-1:2005 Section 5.5. The classification is carried out separately for posi-tive and negative bending for both composite and non-composite sections. The classification of a cross-section depends on the width to thickness ratio of the parts subject to compression. A cross-section is classified according to the highest (least favorable) class of its compression parts.

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



9.1.3.1 Composite Positive Bending The resistance of the top flange is assumed as not being limited by its local buckling resistance since it is restrained by effective attachment to a concrete flange by shear connectors. The spacing of connectors is assumed to be in accordance with Section 6.6.5.5 of the code, and the top flange is always classified as Class 1.

When classifying the web, it is first assumed that the section satisfies require-ments for Class 1 or 2, and the depth of web in compression is based on the plastic range of the composite section for positive moment. When the web does not satisfy requirements for Class 1 or 2 or when the entire composite section does not satisfy requirements of EN 1994-2:2005 Section 6.2.1.2, the section is classified as Class 3. In the next step, the web is verified for Class 3, where the depth of web in compression is based on positive yield moment. See Section 9.1.1.1 of this manual for derivation of the yield moment for positive bending of a composite section. When the web does not satisfy requirements for Class 3, the section is classified as Class 4.

The bottom flange is always in tension and therefore does not have an effect on the classification of the section.

9.1.3.2 Non-Composite Positive Bending The top flange is in compression and is not restrained by the composite slab. Its resistance may be limited by its local buckling resistance. The flange is classi-fied in accordance with Table 5.2 of EN 1993-1-1:2005 as subject to compres-sion.

When classifying the web, it is first assumed that the section satisfies requirements for Class 1 or 2, and the depth of the web in compression is based on the plastic range of the steel beam section for positive moment. When the web does not satisfy requirements for Class 1 or 2 or when the entire composite section does not satisfy requirements of EN 1994-2:2005 Section 6.2.1.2, the section is classified as Class 3. In the next step, the web is verified for Class 3, where the depth of web in compression is based on the neutral axis of the steel beam. When the web does not satisfy requirements for Class 3, the section is classified as Class 4.

The bottom slab classification follows the same procedure as is outlined in Sec-tion 9.1.3.1 of this manual.



9.1.3.3 Composite Negative Bending The top flange is always in tension and therefore does not have an effect on the classification of the section.

When classifying the web, it is first assumed that the section satisfies requirements for Class 1 or 2, and the depth of web in compression is based on the plastic range for negative moment. When the web does not satisfy requirements for Class 1 or 2, the section is classified as Class 3. In the next step, the web is verified for Class 3, where the depth of the web in compression is based on the negative yield moment. See Section 9.1.1.2 of this manual for derivation of the yield moment for negative bending of a composite section. When the web does not satisfy requirements for Class 3, the section is classified as Class 4.

The bottom flange is in compression and unrestrained. The bottom flange resistance may be limited by its local buckling resistance and is classified in accordance with Table 5.2 of EN 1993-1-1:2005 as subject to compression.

9.1.3.4 Non-Composite Negative Bending The classification of top and bottom flanges follows the same procedure as out-lined in Section 9.1.3.3 of this manual.

When classifying the web, it is first assumed that the section satisfies requirements for Class 1 or 2, and the depth of the web in compression is based on the plastic range of the steel beam for negative moment. When the web does not satisfy requirements for Class 1 or 2, the section is classified as Class 3. In the next step, the web is verified for Class 3, where the depth of the web in compression is based on the position of the neutral axis of the steel beam. When the web does not satisfy requirements for Class 3, the section is classified as Class 4.

9.1.4 Effective Section Properties For each section the effective plate sizes, effective area, and moments of inertia of the steel beam and composite section are calculated in accordance with EN 1993-1-5:2006.

9.1.4.1 Effective Section Composite Positive Bending The top flange effective area is equal to the gross area.



The web flange effective area for plate buckling is derived in accordance with Table 4.1 of EN 1993-1-5:2006, assuming a depth of the web in compression based on positive yield moment. See Section 9.1.1.1 of this manual for deriva-tion of yield moments for positive bending of composite sections.

The bottom flange is checked for shear lag in accordance with Section 3 of EN 1993-1-5:2006. The shear lag at the ultimate limit state is determined as the elastic shear lag effect as determined for serviceability and fatigue limit states in accordance with Section 3.3 (1) of EN 1993-1-5:2006.

Figure 9-4 Determination of β Factors for Shear Lag Effects

For flanges where b0 > Le/50 (where b0 is taken as the flange outstand, and Le is the length between points of zero bending moment) the effective width beff for shear lag under elastic conditions is determined from:

0effb b= β (EN 1993-1-5:2006 (3.1))



where β is determined in accordance with EN 1993-1-5:2006 Table 3.1. For the bottom flange in positive bending, the formula for hogging bending is used.

9.1.4.2 Effective Section Non-Composite Positive Bending The top flange effective area for plate buckling is derived in accordance with Table 4.2 of EN 1993-1-5:2006, assuming the uniform compression in the flange ψ = 1 and the buckling factor kσ = 0.43.

The web flange effective area for plate buckling is derived in accordance with Table 4.1 of EN 1993-1-5:2006, assuming a depth of the web in compression based on the neutral axis of the steel beam.

The bottom flange is checked for shear lag in accordance with the procedure outlined in Section 9.1.4.1 of this manual.

9.1.4.3 Effective Section Composite Negative Bending The top flange is checked for shear lag in accordance with the procedure out-lined in Section 9.1.4.1 of this manual. The factor β is determined in accord-ance with EN 1993-1-5:2006 Table 3.1. For the top flange in negative bending, the formula for hogging bending is used.

The web flange effective area for plate buckling is derived in accordance with Table 4.1 of EN 1993-1-5:2006, assuming that the depth of the web in com-pression is based on negative yield moment. See Section 9.1.1.2 of this manual for derivation of yield moments for negative bending of composite sections.

The bottom flange effective area for plate buckling is derived in accordance with Table 4.2 of EN 1993-1-5:2006, assuming uniform compression in the flange ψ = 1 and the buckling factor kσ = 0.43.

9.1.4.4 Effective Section Non-Composite Positive Bending The top flange is checked for shear lag in accordance with the procedure out-lined in Section 9.1.4.1 of this manual. The factor β is determined in accord-ance with EN 1993-1-5:2006 Table 3.1. For the top flange in negative bending, the formula for hogging bending is used.

The web flange effective area for plate buckling is derived in accordance with Table 4.1 of EN 1993-1-5:2006, assuming a depth of the web in compression based on the steel beam neutral axis.



The bottom flange effective area for plate buckling is derived in accordance with Table 4.2 of EN 1993-1-5:2006, assuming the uniform compression in the flange ψ = 1 and the buckling factor kσ = 0.43.

9.1.5 Unbraced Length L and Section Transitions The program assumes that the top flange is continuously braced for all Design Requests, except Constructability. For more information on flange lateral bracing in the Constructability Design Requests, see Section 9.7.3 of this manual.

The unbraced length L for the bottom flange is equal to the distance between the nearest downstation and the upstation qualifying cross diaphragms or span end, 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 beams and all types of chords and braces except V braces without bottom beams.

The program calculates demands and capacities pertaining to a given section cut at a given station without considering the section transition within the un-braced length. It does not search for the highest demands versus the smallest resistance within the unbraced length as the code suggests. It is the responsibil-ity of the user to pay special attention to section transition within unbraced lengths and to follow the guidelines in the code.

9.1.6 Lateral Torsional Buckling The program calculates buckling verification at every section cut. It is the re-sponsibility of the user to verify if the section cut locations correspond to EN 1993-2 clause 6.3.4.2(7), which allows the buckling verification to be per-formed at a distance of 0.25Lk (i.e., 25% of the effective length) from the end with the larger moment.

From EN 1993-2 clause 6.3.4.2(7) assuming factor γ = 0

( ) 1.51 0.44 1m = + + µ Φ (EN 1993-2 eq.(6.14))

2 1V Vµ =



( ) ( )2 12 1 1M MΦ = − + µ for M2 > 0

For each demand set, the applied bending moments M1 and M2 and shears V1 and V2 at each end of equivalent strut are read from the section cuts located at the nearest downstation and upstation diaphragms. The factors μ and ϕ are de-rived in the following algorithm:

If M1 > = 0 or M2 > = 0, then MomRat = 0 else MomRat = Min(M2 / M1, M1 / M2).

If V1 = 0, then μ = 0 else μ = Abs(V2 / V1).

If μ > 1, then μ = 1 / μ

ϕ = 2 * (1 − MomRat) / (1 + μ) m = 1 + 0.44 * (1 + μ) * ϕ ^ 1.5.

It is possible to combine equations (6.10) and (6.12) of EN 1993-2 to produce a single formula for slenderness, taking Af = btf for the flange area, as follows:

( ) ( )( )2

32 2crit

3 1 3

12

f wc y wc f yeff yLT

f

f

A A f L A A f EmA fL

b tN m EIbt

+ +λ = = =

π π

so

1.103 13

y wcLT

f

f ALb Em A

λ = +

where

Awc = web compression zone. The depth of the web in compression is based on negative yield moment. See Section 9.1.1.2 of this manual for derivation of the yield moment for negative bending of the composite section.



L = unbraced length

b = bottom flange width

Af = bottom flange area

The slenderness parameter is compared against the limit set in clause 6.3.2.2(4) of EN 1993-1-1: 0.2.LTλ ≤

If the limit is satisfied, the reduction factor χLT is set to 1.0. If the limit is not satisfied, the section is checked for lateral torsional buckling. Based on the ra-tio h/b, the relevant buckling curve is selected from Table 6.4 in clause 6.3.2.2 of EN 1993-1-1, and the imperfection factor for the lateral torsional buckling curve αLT is determined from Table 6.3 of EN 1993-1-1. From equation (6.56) in EN 1993-1-1 clause 6.3.2.2, the reduction factor χLT is determined as fol-lows:

2 2

1LT

LT LT LT

χ =Φ + Φ −λ

but χLT ≤ 1.0

where

( ) 20.5 1 0.2LT LT LT LT Φ = + α λ − + λ .

9.2 Design Request Parameters The following Design Request parameters are available for user control:

Partial factor γc for concrete, default value = 1.5

Partial factor γc for rebar, default value = 1.15

Partial factor γo for structural steel, default value = 1.0

Partial factor γ1 for structural steel, default value = 1.1

Partial factor γ2 for structural steel, default value = 1.25

k1 – concrete service compression stress limit factor k1 in accordance with EN 1992-1-1 7.2(2), default value = 0.6

9 - 14 Design Request Parameters


k3 – reinforcement service tensile stress limit factor k3 in accordance with EN 1992-1-1 7.2(5), default value = 0.8

Method to evaluate distance bo, Specified Distance for bo and Multiplier of steel top flange width - these three design parameters give users control over how to determine the distance b0 between the centers of the outstand shear connectors used in calculation of the effective width of the compo-site slab in accordance with EN 1994-2:2005 Section 5.4.1.2.

Figure 9-5 Determination of Effective Flange Width

The b0 is determined based on the selected method. Note that the multi-plier is always used to determine the minimum b0 in both methods.

The available methods are as follows:

1) Multiplier of top flange width: b0 = multiplier × top flange width

2) Specified distance from the outside edge of the steel top flange: b0 = max(multiplier × top flange width, top flange width – 2 × distance)

Slenderness limit 1LT0 for lateral torsional buckling in accordance with EN 1993-1-1 6.3.2.3 (1), default value = 0.2.

Use Stage Analysis to determine stresses on composite section, Yes or No

Design Request Parameters 9 - 15


Modular ratio n (=Es/Ec) is the multiplier used to determine long-term com-posite section properties, default value = 3.0.

End post type – in accordance with EN 1993-1-5 Figure 5.1, the end post type is used to evaluate the contribution from the web χw to shear buckling re-sistance.

Figure 9-6 End Post Support Types

Use EN 1994-2 5.5.2 (3) to check Class 3 web – instructs the program to check cross-sections with a Class 3 web and Class 1 or 2 flanges if they may be classified as Class 2 cross-sections with an effective web in ac-cordance with Section 6.2.2.4 of the code (hole in the web method).

Design crack width in accordance with EN 1994-2, Table 7.1.

Effective concrete tensile strength is the mean value of the tensile strength of the concrete, effective at the time when cracks may first be expected to occur. Values of fct,eff may be taken as those for fctm, based on the defined concrete material of the concrete slab. Alternatively when the age of the concrete at cracking cannot be established with confidence as being less than 28 days, a minimum tensile strength of 3 N/mm2 may be adopted in accordance with EN 1994-2 (7.1)

k coefficient that allows for the effect of non-uniform self-equilibrating stresses in accordance with EN 1994-2 (7.1), default value = 0.8



ks coefficient that allows for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection in accordance with EN 1994-2 (7.1), default value = 0.9

9.3 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 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 stresses are calculated based on gross section; the use of effective section properties cannot be accommodated for this option. Therefore, if the section is classified as Class 4, the section is flagged as invalid and skipped. To design Class 4 sections, the design parameter "Use Stage Analysis?” should be set to No. 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.

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.

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, select the User Defined option for the Bridge Design Action, and select a value from the list. The assigned Bridge Design Action values are handled by the program in the following manner:

Demand Sets 9 - 17


Table 9-3 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 Short-Term Composite Short-Term Composite

Staged Non-Composite Other Non-Composite

9.3.1 Demand Flange Stresses fbu Evaluation of the flange stress, fbu, is dependent on the setting for the Design Request parameter “Use Stage Analysis?”:

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

comp steel

NC LTC STCbu

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 long-term section modulus for positive moment uses a modular ratio factored by n, where n is specified in the Design Parameters as the “Modular ratio long-term multiplier.” The effect of compression reinforcement is ignored. For negative moment, the concrete deck is assumed cracked and is not included in the sec-tion modulus calculations, while tension reinforcement is accounted for.

For sections classified as Class 4, the effective section properties as evaluated in Section 9.1.4 of this manual are used to calculate stresses; all other section classes use gross section properties

If “Use Stage Analysis? = Yes,” then the fbu stresses on each flange are read di-rectly from the section cut results. The stresses are calculated based on gross

9 - 18 Demand Sets


section; the use of effective section properties cannot be accommodated with this option. Therefore, if the section is classified as Class 4, the section is flagged as invalid and skipped. To design Class 4 sections, the design parame-ter "Use Stage Analysis?” should be set to No. The program assumes that the effects of the staging of loads applied to non-composite versus composite sec-tions and the concrete slab material time dependent properties are 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 contribute to the resistance of the section.

In Constructability checks, the program proceeds based on the status of the concrete slab. When the slab is not present or is non-composite, the fbu stresses on each flange are read directly from the section cut results. When the slab sta-tus is composite, the program verifies the sign of the stress in the composite slab, and if stress is positive (tension), the program assumes that the entire sec-tion 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 contrib-ute to the resistance of the section.

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. In that case stresses are calculated based on gross sec-tion; the use of effective section properties cannot be accommodated for this Design Request. Therefore, if the section is classified as Class 4, the section is flagged as invalid and skipped. To design Class 4 sections, the non-staged con-structability Design Request (Steel-I Comp Construct NonStgd) can be used.

9.4 Ultimate Design Request The Strength Design Check calculates at every section cut positive bending ca-pacity, negative bending capacity, shear capacity, positive bending shear inter-action, and negative bending shear interaction. It then compares the capacities against the envelope of demands specified in the Design Request.

Ultimate Design Request 9 - 19


9.4.1 Bending

9.4.1.1 Positive Bending – Class 1 and 2 The demand over capacity ratio is evaluated as

,

DoverC .Ed

pl Rd

MM

=

It should be noted that the additional rule in accordance with EN 1994-2-2005 Section 6.2.1.3 (2) is not verified. It is up to the user to ensure that for a con-tinuous beam, MEd does not exceed 0.9 Mpl,Rd at any cross-section in Class 1 or 2 in sagging bending with the concrete slab in compression where both of the following conditions are present:

the cross-section in hogging bending at or near an adjacent support is in Class 3 or 4, and

the ratio of lengths of the spans adjacent to that support (shorter/longer) is less than 0.6.

9.4.1.2 Positive Bending Shear Interaction – Class 1 and 2 Where the vertical shear force VEd exceeds half the shear resistance VRd, given by Vpl,Rd in EN 1994-2-2005 Section 6.2.2.2 or Vb,Rd in Section 6.2.2.3, whichever is smaller, allowance is made for its effect on the resistance moment. The influ-ence of the vertical shear on the resistance to bending is taken into account by a reduced design steel strength (1 − ρ) fyd of the web where:

( )22 1Ed RdV Vρ = − (EN 1994-2 2005 (6.5))

9 - 20 Ultimate Design Request


Figure 9-7 Shear Effects on Resisting Moments

The demand over capacity ratio is calculated as follows:

, RedDoverC Ed

pl Rd

MM

=

9.4.1.3 Positive Bending – Class 3 For derivation of stresses fbu in flanges see Section 9.3.1 of this manual. The demand over capacity ratio is calculated as follows:

Top Bot deck

Top Bot deckDoverC max , ,bu bu

yd yd cd

f f ff f f

=

9.4.1.4 Positive Bending Shear Interaction – Class 3 In accordance with EN 1993-1-2006, Section 7.1 (1),

if η3 exceeds 0.5 and ,1

,

,f Rd

pl Rd

MM

η ≥ where 1,

Ed

pl Rd

MM

η ≥ and 1,

,Ed

bw Rd

VV

η ≥

the design resistance to bending moment is reduced to allow for the shear force. The demand over capacity ratio is calculated as follows:

( )2,1 3

,

DoverC 1 2 1f Rd

pl Rd

MM

= η + − η −

where



Mf,Rd is the design plastic moment of resistance of the section consisting of the effective area of the flanges;

Mpl,Rd is the design plastic resistance of the cross-section consisting of the ef-fective area of the flanges and the fully effective web irrespective of its section class.

9.4.1.5 Positive Bending - Class 4 If the Design Request parameter “Use Stage Analysis? = No,” the fbu stresses on each flange are calculated based on the effective section properties (see Sec-tion 9.3.1 of this manual). The demand over capacity ratio is calculated as fol-lows:

Top Bot deck


yd yd cd

f f ff f f

=

If the Design Request parameter “Use Stage Analysis? = Yes,” the sections classified as Class 4 are flagged as invalid and skipped.

9.4.1.6 Positive Bending Shear Interaction – Class 4 The demand over capacity ratio is calculated using a procedure similar to that used for Class 3 sections (see Section 9.4.1.4 of this manual), although the de-sign plastic moments of resistance Mf,Rd and Mpl,Rd are based on the effective area of the flanges.

( )2,1 3

,

DoverC 1 2 1f Rd

pl Rd

MM

= η + − η −

9.4.1.7 Negative Bending – Class 1 and 2 The demand over capacity ratio is evaluated as

,DoverC Ed

LT pl Rd

MM

=χ

For derivation of lateral torsional buckling reduction factor χLT, see Section 9.1.6 of this manual.



9.4.1.8 Negative Bending Shear Interaction – Class 1 and 2 The demand over capacity ratio is calculated using a procedure similar to that used for positive bending (see Section 9.4.1.2 of this manual), although the de-sign plastic moment of resistance Mpl,RdRed is based on negative bending and the effects of lateral torsional bucking are considered.

, RedDoverC Ed

LT pl Rd

MM

=χ

9.4.1.9 Negative Bending – Class 3 For derivation of stresses fbu in flanges, see Section 9.3.1 of this manual. The demand over capacity ratio is calculated as follows:

Top Bot deck


yd LT yd cd

f f ff f f

= χ

9.4.1.10 Negative Bending Shear Interaction – Class 3 The demand over capacity ratio is calculated using a procedure similar to that used for positive bending (see Section 9.4.1.4 of this manual), although the de-sign plastic moments of resistance Mpl,Rd is based on negative bending.

( )2,1 3

,

DoverC 1 2 1f Rd

pl Rd

MM

= η + − η −

9.4.1.11 Negative Bending – Class 4 If the Design Request parameter “Use Stage Analysis? = No,” the fbu stresses on each flange are calculated based on the effective section properties (see Sec-tion 9.3.1 of this manual). The demand over capacity ratio is calculated as fol-lows:

Top Bot deck


yd LT yd cd

f f ff f f

= χ




9.4.1.12 Negative Bending Shear Interaction – Class 4 The demand over capacity ratio is calculated using a procedure similar to that used for Class 3 sections (see Section 9.4.1.4 of this manual), although the de-sign plastic moments of resistance Mf,Rd and Mpl,Rd are based on negative bend-ing and the effective area of the flanges.

( )2,1 3

,

DoverC 1 2 1f Rd

pl Rd

MM

= η + − η −

9.4.2 Shear When processing the Design Request from the Design module, the program as-sumes vertical stiffeners are present at supports only, and no intermediate ver-tical stiffeners are present.

In the Optimization form (Design/Rating > Superstructure Design > Optimize command), the user can specify stiffener locations. The program recalculates the shear resistance based on the defined stiffener layout. 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.

9.4.2.1 Design Shear Resistance From clause 6.2.6(6) of EN 1993-1-1, resistance to shear buckling should be checked if

72w

w

ht

ε>

η EN 1993-1-1, eq. (6.22)

where the value η = 1.20 is used for steel grades up to and including S460. For higher steel grades, η = 1.00 is used, in accordance with EN 1993-1-5 Section 5.1.2 Note 2 and 235 .yf=ε

If the resistance to shear buckling does not control the design, shear resistance is based on shear plastic resistance given by:

( ), ,

0

3v ybw Rd pl Rd

M

A fV V

γ= = EN 1993-1-1, eq. (6.18)



When resistance to shear buckling must be checked:

the slenderness is obtained from EN 1993-1-5 equation (5.5) for stiffeners at supports only,

,86.4

ww

ht

=λε

the slenderness is obtained from EN 1993-1-5 equation (5.6) for transverse stiffeners at supports and intermediate transverse stiffeners,

,37.4

ww

ht k

=τ

λε

where

( )( )

2

2

5.34 4.00 when 1

4.00 5.34 when 1w w

w w

k h a a h

k h a a hτ

τ

= + ≥

= + < EN 1993-1-5 (eq A.5)

a is the distance between transverse stiffeners.

The design resistance of the web is given by

,13

w yw wbw Rd

M

f h tV

χ

γ= EN 1993-1-5 (eq 5.2)

where the contribution from the web χw to shear buckling resistance is in ac-cordance with EN 1993-1-5 Table 5.1.

Table 9-13

Rigid end post Non-rigid end post

0.83wλ < η η η

0.83 1.08wη≤ λ < 0.83 wλ 0.83 wλ

1.08wλ ≥ ( )1.37 0.7 w+ λ 0.83 wλ



The contribution from the flanges and composite slab is always ignored. The demand to capacity ratio is evaluated as

,DoverC .ed

bw Rd

VV

=

9.5 Service Stress Design Request The service design check calculates at every section cut the stresses fbu at the top steel flange of the composite section, the bottom steel flange of the compo-site section, the shear stress and principal stress at the web, and the compres-sion stress at the top of the composite slab. It then compares them against lim-its specified in EN 1993-2 Section 7.3.

9.5.1 Positive Bending For the derivation of stresses fbu in flanges, see Section 9.3.1 of this manual. The shear stress in the web is derived as:

,ser .EdEd

w

VA

τ =

The principal stress is derived as follows:

2 2Princ ,ser ,ser3Ed Edσ = σ + τ

The demand over capacity ratio is calculated as follows, in accordance with EN 1993-2 Section 7.3:

Top ,serBot deck Princ

webTop Bot 1 deck webDoverC max , , , ,

3

bu Edbu

yyd yd cd y

f f fff f f f

τ σ =

κ

where k1 is the concrete service compression stress limit factor, in accordance with EN 1992-1-1 7.2(2).

9 - 26 Service Stress Design Request


9.5.2 Negative Bending The stresses in the steel section are derived using a procedure similar to that used in Section 9.5.1 of this manual. Stress in rebar is calculated at the top most rebar level, and the concrete slab tension capacity is ignored. Stresses in reinforcement increase as a result of the effects of tension stiffening of concrete between cracks. Δσs is calculated from:

0.4 ctms

st s

f∆σ =

α ρ (EN 1994-2 eq.(7.5))

12 2

sAI

A Iα = (EN 1994-2 eq.(7.6))

A, I are the area and second moment of area, respectively, of the effective composite section neglecting concrete in tension and profiled sheeting, if any;

A2, I2 are the corresponding properties of the structural steel section.

The demand over capacity ratio is calculated as follows in accordance with EN 1993-2 Section 7.3:

rebar+Top ,serBot Princ

webTop Bot 3 rebar webDoverC max , , , ,

3

sEdbu Edbu

yyd yd y y

ff fff f k f f

∆σ

τ σ =

where k3 is the reinforcement service tensile stress limit factor in accordance with EN 1992-1-1 7.2(5).

9.6 Service Rebar Design Request The Service Rebar Design Request checks each section for two conditions: minimum rebar, in accordance with EN 1994-2 Section 7.4.2, and control of cracking resulting from direct loading, in accordance with EN 1994-2 Section 7.4.3.

Service Rebar Design Request 9 - 27


9.6.1 Minimum Rebar When determining the minimum rebar, the program calculates factor kc

( )o

1 0.3 1.01 2c

c

kh z

= + ≤+

(EN 1994-2 eq.(7.2))

where

hc is the thickness of concrete slab

zo is the vertical distance between the centroids of the uncracked concrete slab and the uncracked composite section, calculated using the modular ratio n0 for short-term loading;

If no rebar is defined in the slab, the rebar stress σs is determined from Table 7.2 of EN 1994-2 for the design crack width specified in the Design Request parameter. For a design crack width > 0.2mm, the rebar stress σs is assumed as the min(fy,360MPa), and for a design crack width = 0.2mm, the rebar stress σs is assumed as the min(fy,280MPa).

If rebar is defined in the slab, the rebar stress σs is read from EN 1994-2 Table 7.1 based on the maximum diameter defined at the section and the specified design crack width.

The area of minimum reinforcement is calculated as

,eff .s s c ct cd sA k k k f A= σ (EN 1994-2 eq.(7.1))

When no rebar is defined at the section cut, the maximum bar diameter and the maximum bar spacing are read from Tables 7.1 and 7.2 of EN 1994-2 based on the rebar stress σs and the defined design crack width. The maximum rebar spacing reported is the smaller value of the required bar spacing to provide the calculated minimum reinforcement or the maximum spacing in accordance with Table 7.2 of EN 1994-2. The demand over capacity ratio is arbitrarily set to 1E7.

When rebar is defined at the section cut, the demand over capacity is evaluated as the ratio of the area per unit width of the required minimum reinforcement versus the provided reinforcement. Maximum rebar spacing is read from Table

9 - 28 Service Rebar Design Request


7.2 of EN 1994-2 based on the rebar stress σs and the specified design crack width.

9.6.2 Control of Cracking The stress in rebar resulting from tension stiffening, Δσs, is calculated using the same procedure as outlined in Section 9.5.2 of this manual. For each de-mand set, the stress at the rebar level is calculated. The demand over capacity ratio is reported as the ratio of the maximum bar diameter provided in the top half of the composite slab and the maximum bar diameter, as specified in EN 1994-2 Table 7.1 for the defined design crack width. When no rebar is defined at the section cut, the Δσs and the demand over capacity ratio are set to zero.

9.7 Constructability Design Request

9.7.1 Staged (Steel-I Comp Construct Stgd) This request enables the user to verify the superstructure during construction by using the Nonlinear Staged Construction load case. The nonlinear staged analysis allows the user to define multiple snapshots of the structure during construction, when parts of the bridge deck may be at various completion stag-es. The user controls which stages the program will include in the calculations of the 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.

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.

The section stresses are calculated based on gross section; the use of effective section properties cannot be accommodated for this design request. Therefore,

Constructability Design Request 9 - 29


if the section is classified as Class 4, the section is flagged as invalid and skipped. To design Class 4 sections, the non-staged constructability design re-quest (Steel-I Comp Construct NonStgd) can be used.

9.7.2 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 Construction load case. For each section cut specified in the design request the constructability 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 the Update Bridge Structural Model form (Bridge > Update > Structural Model Options option).

9.7.3 Slab Status vs. Unbraced Length Based on the slab status the program calculates corresponding positive bending capacity, negative bending capacity, shear capacity, and positive and negative bending versus shear interaction. Next the program compares the capacities against demands specified in the Demand Set by calculating the Demand over Capacity ratio. The controlling Demand Set and the Output Label on a girder-by-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 the slab status is 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 any time a steel beam is activated at a given section cut, the un-braced length L for the bottom flange is equal to the distance between the near-est downstation and upstation qualifying cross diaphragms or the span ends as defined in the Bridge Object. The program assumes the same unbraced length L for the top flange. In other words, the unbraced length L 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 re-straint to the top flange. It is the user’s responsibility to provide top flange

9 - 30 Constructability Design Request


temporary bracing at the diaphragm locations prior to the slab acting compos-itely.

9.7.4 Algorithm When the slab status is composite, the staged and non-staged design checks follow the procedure outlined in Section 9.4 of this manual. When the slab status is non-composite, the section resisting demands consists of the steel beam only. Because of the fact that the top flange is not continuously braced, the section is reclassified, and the effective area of the top flange is recalculated. In addition to the checks described in section 9.4 of this manual, the top flange is also checked for lateral torsional buckling.

9.8 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 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 the 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 ratios 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 series is 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 the Modify Section button. After the section modification has been completed, the Current version is shown in red in the elevation and cross-

Section Optimization 9 - 31


section views. After the resistance has been recalculated successfully by clicking the Recalculate Resistance button, the Current version is designated As Designed 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. 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 button.

9 - 32 Section Optimization

Chapter 10 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 Eurocode 4 EN 1994-2:2005 code (Part 2).

10.1 Section Properties

10.1.1 Yield Moments

10.1.1.1 Composite Section in Positive Flexure The depth of web in compression that is used in section classification is de-rived based on positive yield moment, My .The positive yield moment is deter-mined by the program using the following user-defined input, which is part of the Ultimate Design Request (see Chapter 4 for more information about Design Requests).

Mdnc = The user specifies in the Design Request the name of the combo that represents the moment caused by the 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 permanent load (applied to the composite section).

10 - 1


The program solves for MAD from the following equation,

dnc dc ADyt

NC LT ST

M M MFS S S

= + +

and then calculates yield moment based on the following equation

y dnc dc ADM M M M= + +

where

SNC = Noncomposite section modulus

SLT = Long-term composite section modulus

SST = Short-term composite section modulus

My is taken as the lesser value calculated for the compression flanges, 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 not-ed that the My calculated in the procedure described here is used by the pro-gram to determine only the depth of web in compression that is used in classi-fication of webs in accordance with EN 1993-1-1:2005 Table 5.2 for positive bending in the Ultimate Design Check.

Since for Staged and Non-Staged Constructability Design Checks it is difficult to obtain built-up elastic stresses, for the sake of classification of the web it is assumed that the depth of the web in compression for positive bending is based on all loads being applied to non-composite sections because this produces the greatest depth of web in compression.

10.1.1.2 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 flanges or the longitudinal reinforcement, whichever yields first. Concrete tension capaci-ty is ignored.


Chapter 10 - Design Steel U-Tub Bridge with Composite Slab

For the sake of classification of the web, the depth of the web in compression for negative bending is based on all loads being applied to the composite sec-tion because this produces the greatest depth of web in compression. This as-sumption applies to all design checks.

10.1.2 Plastic Moments

10.1.2.1 Composite Section in Positive Flexure The positive plastic moment, Mpl,Rd, 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 webs, and reinforcing steel, as appropriate. The plastic force in the effective width of the composite slab that is in compression is based on a rectangular stress block with the magnitude of the compressive stress equal to 0.85fcd. Concrete in ten-sion is neglected. The position of the plastic neutral axis is determined by the equilibrium condition such that there is no net axial force.

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

• Calculate the element forces and use them to determine if the plastic neu-tral axis is in the webs, top flanges, or concrete deck.

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

• Calculate Mpl,Rd.

Equations for the various potential locations of the plastic neutral axis (PNA) are given in Table 10-1.



Table 10-1 Calculation of PNA and Mp for Sections in Positive Flexure


I In Web Pt + Pw ≥ Pc + Ps + Prb + Pn

12

t c s rt rb

w

D P P P P PYP

− − − − = +

( ) [ ]22

2w

p s s rt rt rb rb c c t tPM Y D Y P d P d P d P d PdD = + − + + + + +

II In Top Flange

Pt + Pw + Pc ≥ Ps + Prb + Pn

12c w t s rt rb

c

t P P P P PYP

+ − − −= +

( ) [ ]22

2c

p c s s n n rb rb w w t tc

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

( ) c w t rt rbs

s

P P P P PY tP

+ + − −=

[ ]2

2s



= + + + + +

IV Concrete Deck at

Prb

Pt + Pw + Pc + Prb ≥ rb

s

ct

Ps + Pn

rbY c=

[ ]2

2s

p rt rt c c w w t ts


= + + + +

V

Concrete Deck

Above Prb and Below

Prt

Pt + Pw + Pc + Prb ≥ rt

s

ct

Ps + Pn

( ) rb c w t rts

s

P P P P PY tP

+ + + − =

[ ]2

2s



= + + + + +

VI Concrete Deck at

Prt

Pt + Pw + Pc + Prb + Pn ≥ rt

s

ct

Ps

rtY c=

[ ]2

2s

p rb rb c c w w t ts


= + + + +

VII

Concrete Deck

Above Prt

Pt + Pw + Pc + Prb + Prt < rt

s

ct

Ps

( ) rb c w t rts

s

P P P P PY tP

+ + + + =

[ ]2

2s



= + + + + +



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

Figure 10-1 Plastic Neutral Axis Cases — Positive Flexure

in which

Prt = Fyrt Art

Ps = 0.85 fcd bs ts

Prb = Fyrb Arb

Pc = 2 Fyc bc tc

Pw = (2 Fyw D tw) / cos αweb

Pt = Fyt bt tt where bt is effective width of bottom flange

Next the section is checked for ductility requirement in accordance with EN 4 1994-2:2005 6.2.1.2(2). For structural steel grades of web or bottom flanges where fyd > 355 MPa, the MRd is taken as:

Mpl = β Mpl,Rd

where β is the reduction factor given in Figure 10-2. When the value of plx h is greater than 0.4, the section is classified as Class 3 or higher, and the plastic moment of a composite section in positive flexure is set to zero.



Figure 10-2 Composite Positive PNA Limits

10.1.2.2 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 10-2. The plastic moment of a non-composite sec-tion is calculated by eliminating the terms pertaining to the concrete deck and longitudinal reinforcement from the equations for composite sections.

Table 10-2 Calculation of PNA and Mp for Sections in Negative Flexure


I In Web Pc + Pw ≥ Pt + Prb + Pn 1

2c t rt rb

w

D P P P PYP

− − − = +

( ) [ ]22

2w

p n n rb rb t t l lPM Y D Y P d P d Pd PdD = + − + + + +

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

12l w c rt rb

t

t P P P PYP

− − − = +

( ) [ ]22

2t

p l n n rb rb w w c cl

PM Y t Y P d P d P d P dt = + − + + + +




in which

Prt = Fyrt Art

Ps = 0 Prb = Fyrb Arb

Pc = Fyc bc tc where bc is effective width of bottom flange

Pw = (2 Fyw D tw)/cos αweb

Pt = 2 Fyt bt tt

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.

10.1.3 Classification of Cross-Sections At each section cut the steel beam section is classified in accordance with EN 1993-1-1:2005 Section 5.5. The classification is carried out separately for posi-tive and negative bending for both composite and non-composite sections. The classification of a cross-section depends on the width to thickness ratio of the parts subject to compression. A cross-section is classified according to the highest (least favorable) class of its compression parts.


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


10.1.3.1 Composite Positive Bending The resistance of the top flange is assumed as not being limited by its local buckling resistance since it is restrained by effective attachment to a concrete flange by shear connectors. The spacing of connectors is assumed to be in ac-cordance with Section 6.6.5.5 of the code, and the top flange is always classi-fied as Class 1.

When classifying the web, it is first assumed that the section satisfies require-ments for Class 1 or 2, and the depth of web in compression is based on the plastic range of the composite section for positive moment. When the web does not satisfy requirements for Class 1 or 2 or when the entire composite section does not satisfy requirements of EN 1994-2:2005 Section 6.2.1.2, the section is classified as Class 3. In the next step, the web is verified for Class 3, where the depth of web in compression is based on positive yield moment. See Section 10.1.1 of this manual for derivation of the yield moment for positive bending of a composite section. When the web does not satisfy requirements for Class 3, the section is classified as Class 4.


10.1.3.2 Non-Composite Positive Bending The top flange is in compression and is not restrained by the composite slab. Its resistance may be limited by its local buckling resistance. The flange is classi-fied in accordance with Table 5.2 of EN 1993-1-1:2005 as subject to compres-sion.

When classifying the web, it is first assumed that the section satisfies require-ments for Class 1 or 2, and the depth of the web in compression is based on the plastic range of the steel beam section for positive moment. When the web does not satisfy requirements for Class 1 or 2 or when the entire composite sec-tion does not satisfy requirements of EN 1994-2:2005 Section 6.2.1.2, the sec-tion is classified as Class 3. In the next step, the web is verified for Class 3, where the depth of web in compression is based on the neutral axis of the steel beam. When the web does not satisfy requirements for Class 3, the section is classified as Class 4.




10.1.3.3 Composite Negative Bending The top flange is always in tension and therefore does not have an effect on the classification of the section.

When classifying the web, it is first assumed that the section satisfies require-ments for Class 1 or 2, and the depth of web in compression is based on the plastic range for negative moment. When the web does not satisfy requirements for Class 1 or 2, the section is classified as Class 3. In the next step, the web is verified for Class 3, where the depth of the web in compression is based on the negative yield moment. See Section 10.1.1.2 of this manual for derivation of the yield moment for negative bending of a composite section. When the web does not satisfy requirements for Class 3, the section is classified as Class 4.

The bottom flange is in compression and unrestrained. The bottom flange re-sistance may be limited by its local buckling resistance and is classified in ac-cordance with Table 5.2 of EN 1993-1-1:2005 as part subject to compression.

10.1.3.4 Non-Composite Negative Bending The classification of top and bottom flanges follows the same procedure as out-lined in Section 10.1.3.3 of this manual.

When classifying the web, it is first assumed that the section satisfies require-ments for Class 1 or 2, and the depth of the web in compression is based on the plastic range of the steel beam for negative moment. When the web does not satisfy requirements for Class 1 or 2, the section is classified as Class 3. In the next step, the web is verified for Class 3, where the depth of the web in com-pression is based on the position of the neutral axis of the steel beam. When the web does not satisfy requirements for Class 3, the section is classified as Class 4.

10.1.4 Effective Section Properties For each section the effective plate sizes, effective area, and moments of inertia of the steel beam and composite section are calculated in accordance with EN 1993-1-5:2006.

10.1.4.1 Effective Section Composite Positive Bending The top flange effective area is equal to the gross area.



The web effective area for plate buckling is derived in accordance with Table 4.1 of EN 1993-1-5:2006, assuming a depth of the web in compression based on positive yield moment. See Section 10.1.1 of this manual for derivation of yield moments for positive bending of composite sections.

The bottom flange is checked for SLS and ULS shear lag and plate buckling ef-fects in accordance with Section 3 and 4 of EN 1993-1-5:2006.

Figure 10-4 Determination of β Factors for Shear Lag Effects

For flanges where b0 > Le/50 (where b0 is taken as half the distance between webs, and Le is the length between points of zero bending moment) the effec-tives width beff for shear lag under elastic conditions is determined from:

0effb b= β (EN 1993-1-5:2006 (3.1))



where β and κ are determined in accordance with EN 1993-1-5:2006 Table 3.1. For the bottom flange in positive bending, the formula for hogging bending is used.

The shear lag effective area at the ultimate limit state for negative bending is determined per EN 1993-1-5:2006 Section 3.3 Note 3 allowing for limited plastic strains.

𝐴𝐴𝑒𝑒𝑒𝑒𝑒𝑒 = 𝐴𝐴𝑐𝑐,𝑒𝑒𝑒𝑒𝑒𝑒𝛽𝛽𝜅𝜅 ≥ 𝐴𝐴𝑐𝑐,𝑒𝑒𝑒𝑒𝑒𝑒𝛽𝛽

(for positive bending the Ac,eff is set equal to Aeff)

Where per EN 1993-1-5: 2006 Section 4.4

Ac,eff = ρ Ac

where ρ is the reduction factor for buckling of plate elements without longitu-dinal stiffeners. 𝜌𝜌 = 1,0 for �̅�𝜆𝑝𝑝 ≤ 0,673

𝜌𝜌 = 𝜆𝜆�𝑝𝑝−0,055(3+𝜓𝜓)𝜆𝜆�𝑝𝑝2

≤ 1,0 for �̅�𝜆𝑝𝑝 ≤ 0,673

Where assuming the uniform compression in the bottom flange ψ = 1 and

�̅�𝜆𝑝𝑝 = �𝑓𝑓𝑦𝑦𝜎𝜎𝑐𝑐𝑐𝑐

=𝑏𝑏�𝑡𝑡

28,4𝜀𝜀�𝑘𝑘𝜎𝜎

and buckling factor kσ=4.0 per Table 4.1 in EN 1993-1-5:2006 and

𝜀𝜀 = �235

𝑓𝑓𝑦𝑦[ 𝑁𝑁𝑚𝑚𝑚𝑚2]

10.1.4.2 Effective Section Non-Composite Positive Bending The top flanges effective area for plate buckling is derived in accordance with Table 4.2 of EN 1993-1-5:2006, assuming the uniform compression in the flange ψ = 1 and the buckling factor kσ = 0.43.



The web effective area for plate buckling is derived in accordance with Table 4.1 of EN 1993-1-5:2006, assuming a depth of the web in compression based on the neutral axis of the steel beam.


10.1.4.3 Effective Section Composite Negative Bending The top flange is checked for shear lag in accordance with the procedure out-lined in Section 10.1.4 of this manual. The factor β is determined in accordance with EN 1993-1-5:2006 Table 3.1. For the top flange in negative bending, the formula for hogging bending is used.

The web effective area for plate buckling is derived in accordance with Table 4.1 of EN 1993-1-5:2006, assuming that the depth of the web in compression is based on negative yield moment. See Section 10.1.1.2 of this manual for deri-vation of yield moments for negative bending of composite sections.

The bottom flange is checked for shear lag and buckling in accordance with the procedure outlined in Section 10.1.4.1 of this manual.

10.1.4.4 Effective Section Non-Composite Negative Bending The top flange is checked for shear lag in accordance with the procedure out-lined in Section 10.1.4.1 of this manual. The factor β is determined in accord-ance with EN 1993-1-5:2006 Table 3.1. For the top flange in negative bending, the formula for hogging bending is used.

The web effective area for plate buckling is derived in accordance with Table 4.1 of EN 1993-1-5:2006, assuming a depth of the web in compression based on the steel beam neutral axis.


10.1.5 Unbraced Length L and Section Transitions The program assumes that the top flange is continuously braced for all Design Requests, except Constructability when slab status is equal to ‘Non-composite’. For more information on flange lateral bracing in the Constructa-bility Design Requests, see Section 10.7.3 of this manual.



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

The program calculates demands and capacities pertaining to a given section cut at a given station without considering the section transition within the un-braced length. It does not search for the highest demands versus the smallest resistance within the unbraced length as the code suggests. It is the responsibil-ity of the user to pay special attention to section transition within unbraced lengths and to follow the guidelines in the code.

10.1.6 Lateral Torsional Buckling The program calculates buckling verification at every section cut. It is the re-sponsibility of the user to verify if the section cut locations correspond to EN 1993-2 clause 6.3.4.2(7), which allows the buckling verification to be per-formed at a distance of 0.25Lk (i.e., 25% of the effective length) from the end with the larger moment.

From EN 1993-2 clause 6.3.4.2(7) assuming factor γ = 0

( ) 1.51 0.44 1m = + + µ Φ (EN 1993-2 eq.(6.14))

2 1V Vµ =

( ) ( )2 12 1 1M MΦ = − + µ for M2 > 0

For each demand set, the applied bending moments M1 and M2 and shears V1 and V2 at each end of equivalent strut are read from the section cuts located at the nearest downstation and upstation diaphragms. The factors μ and ϕ are de-rived in the following algorithm:

If M1 > = 0 or M2 > = 0, then MomRat = 0 else MomRat = Min(M2 / M1, M1 / M2).



If V1 = 0, then μ = 0 else μ = Abs(V2 / V1).

If μ > 1, then μ = 1 / μ

ϕ = 2 * (1 − MomRat) / (1 + μ) m = 1 + 0.44 * (1 + μ) * ϕ ^ 1.5.

It is possible to combine equations (6.10) and (6.12) of EN 1993-2 to produce a single formula for slenderness, taking Af = btf for the flange area, as follows:

( ) ( )( )2

32 2crit

3 1 3

12

f wc y wc f yeff yLT

f

f

A A f L A A f EmA fL

b tN m EIbt

+ +λ = = =

π π

so

1.103 13

y wcLT

f

f ALb Em A

λ = +

where

Awc = web compression zone. The depth of the web in compression is based on positive yield moment. See Section 10.1.1 of this manual for deriva-tion of the yield moment for positive bending of the composite section.

L = unbraced length

b = bottom flange width

Af = bottom flange area

The slenderness parameter is compared against the limit set in clause 6.3.2.2(4) of EN 1993-1-1: 0.2.LTλ ≤

If the limit is satisfied, the reduction factor χLT is set to 1.0. If the limit is not satisfied, the section is checked for lateral torsional buckling. Based on the ra-tio h/b, the relevant buckling curve is selected from Table 6.4 in clause 6.3.2.2



of EN 1993-1-1, and the imperfection factor for the lateral torsional buckling curve αLT is determined from Table 6.3 of EN 1993-1-1. From equation (6.56) in EN 1993-1-1 clause 6.3.2.2, the reduction factor χLT is determined as fol-lows:

2 2

1LT

LT LT LT

χ =Φ + Φ −λ but χLT ≤ 1.0

where

( ) 20.5 1 0.2LT LT LT LT Φ = + α λ − + λ .

10.2 Design Request Parameters The following Design Request parameters are available for user control:

Partial factor γc for concrete, default value = 1.5

Partial factor γc for rebar, default value = 1.15

Partial factor γo for structural steel – yielding, local instability, default val-ue = 1.0

Partial factor γ1 for structural steel-resistance of members

to instability, default value = 1.1

k1 – concrete service compression stress limit factor k1 in accordance with EN 1992-1-1 7.2(2), default value = 0.6

k3 – reinforcement service tensile stress limit factor k3 in accordance with EN 1992-1-1 7.2(5), default value = 0.8

Method to evaluate distance bo, Specified Distance for bo and Multiplier of steel top flange width - these three design parameters give users control over how to determine the distance b0 between the centers of the outstand shear connectors used in calculation of the effective width of the composite slab in accordance with EN 1994-2:2005 Section 5.4.1.2.

Design Request Parameters 10 - 15


Figure 10-5 Determination of Effective Flange Width

The b0 is determined based on the selected method. Note that the multi-plier is always used to determine the minimum b0 in both methods.

The available methods are as follows:

1) Multiplier of top flange width: b0 = multiplier × top flange width

2) Specified distance from the outside edge of the steel top flange: b0 = max(multiplier × top flange width, top flange width – 2 × distance)

Slenderness limit 1LT0 for lateral torsional buckling in accordance with EN 1993-1-1 6.3.2.3 (1), default value = 0.2.

Use Stage Analysis to determine stresses on composite section, Yes or No

Modular ratio n (=Es/Ec) is the multiplier used to determine long-term com-posite section properties, default value = 3.0.

End post type – in accordance with EN 1993-1-5 Figure 5.1, the end post type is used to evaluate the contribution from the web χw to shear buckling re-sistance.



Figure 10-6 End Post Support Types

Use EN 1994-2 5.5.2 (3) to check Class 3 web – instructs the program to check cross-sections with a Class 3 web and Class 1 or 2 flanges if they may be classified as Class 2 cross-sections with an effective web in accordance with Section 6.2.2.4 of the code (hole in the web method).

Design crack width in accordance with EN 1994-2, Table 7.1.

Effective concrete tensile strength is the mean value of the tensile strength of the concrete, effective at the time when cracks may first be expected to occur. Values of fct,eff may be taken as those for fctm, based on the defined concrete ma-terial of the concrete slab. Alternatively when the age of the concrete at crack-ing cannot be established with confidence as being less than 28 days, a mini-mum tensile strength of 3 N/mm2 may be adopted in accordance with EN 1994-2 (7.1)

k coefficient that allows for the effect of non-uniform self-equilibrating stresses in accordance with EN 1994-2 (7.1), default value = 0.8

ks coefficient that allows for the effect of the reduction of the normal force of the concrete slab due to initial cracking and local slip of the shear connection in accordance with EN 1994-2 (7.1), default value = 0.9

10.3 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 10 - 17


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 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 stresses are calculated based on gross section; the use of effective section properties cannot be accommodated for this option. Therefore, if the section is classified as Class 4, the section is flagged as invalid and skipped. To design Class 4 sections or sections where gross and effective areas are not equal, the design parameter "Use Stage Analy-sis?” should be set to No. Note that the Design Request for staged constructa-bility check (Steel-U Comp Construct Stgd) allows only Nonlinear Staged Construction load cases to be used as Demand Sets.

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.

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 drop down list, select the User Defined option for the Bridge Design Action, and select a value from the list. The assigned Bridge Design Action values are handled by the program in the following manner:




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

10 - 18 Demand Sets





Staged Non-Composite Other Non-Composite

10.3.1 Demand Flange Stresses fbu Evaluation of the flange stress, fbu, is dependent on the setting for the Design Request parameter “Use Stage Analysis?”:

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

comp steel

NC LTC STCbu

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 long-term section modulus for positive moment uses a modular ratio factored by n, where n is specified in the Design Parameters as the “Modular ratio long-term multiplier.” The effect of compression reinforcement is ignored. For negative moment, the concrete deck is assumed cracked and is not included in the sec-tion modulus calculations, while tension reinforcement is accounted for.

For sections classified as Class 4, the effective section properties as evaluated in Section 10.1.4 of this manual are used to calculate stresses. All other section classes use ULS effective section properties for Ultimate check and SLS effec-tive properties for Service and Rebar checks.

If “Use Stage Analysis? = Yes,” then the fbu stresses on each flange are read di-rectly from the section cut results. The stresses are calculated based on gross section; the use of effective section properties cannot be accommodated with this option. Therefore, if the section is classified as Class 4, the section is

Demand Sets 10 - 19


flagged as invalid and skipped. To design Class 4 sections or sections where gross and effective areas are not equal, the design parameter "Use Stage Analy-sis?” should be set to No. 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 are 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 contribute to the resistance of the section.

In Constructability checks, the program proceeds based on the status of the concrete slab. When the slab is not present or is non-composite, the fbu stresses on each flange are read directly from the section cut results. When the slab sta-tus is composite, the program verifies the sign of the stress in the composite slab, and if stress is positive (tension), the program assumes that the entire sec-tion 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 contrib-ute to the resistance of the section.

Note that the Design Request for staged constructability check (Steel-U Comp Construct Stgd) allows only Nonlinear Staged Construction load cases to be used as Demand Sets. In that case stresses are calculated based on gross sec-tion; the use of effective section properties cannot be accommodated for this Design Request. Therefore, if the section is classified as Class 4, the section is flagged as invalid and skipped. To design Class 4 sections or sections where gross and effective areas are not equal, the non-staged constructability Design Request (Steel-U Comp Construct NonStgd) can be used.

10.4 Ultimate Design Request The Strength Design Check calculates at every section cut positive bending ca-pacity, negative bending capacity, shear capacity, positive bending shear inter-action, and negative bending shear interaction. It then compares the capacities against the envelope of demands specified in the Design Request.



10.4.1 Bending

10.4.1.1 Positive Bending – Class 1 and 2 The demand over capacity ratio is evaluated as

,

DoverC .Ed

pl Rd

MM

=

It should be noted that the additional rule in accordance with EN 1994-2-2005 Section 6.2.1.3 (2) is not verified. It is up to the user to ensure that for a con-tinuous beam, MEd does not exceed 0.9 Mpl,Rd at any cross-section in Class 1 or 2 in sagging bending with the concrete slab in compression where both of the following conditions are present:

• the cross-section in hogging bending at or near an adjacent support is in Class 3 or 4, and

• the ratio of lengths of the spans adjacent to that support (shorter/longer) is less than 0.6.

10.4.1.2 Positive Bending Shear Interaction – Class 1 and 2 Where the vertical shear force VEd that includes shear from torsional effects (see Section 10.4.2.1 of this manual for evaluation of torsional shear) exceeds half the shear resistance VRd, given by Vpl,Rd in EN 1994-2-2005 Section 6.2.2.2 or Vb,Rd

in Section 6.2.2.3, whichever is smaller, allowance is made for its effect on the resistance moment. The influence of the vertical shear on the resistance to bending is taken into account by a reduced design steel strength (1 − ρ) fyd of the web where:

( )22 1Ed RdV Vρ = − (EN 1994-2 2005 (6.5))



Figure 10-7 Shear Effects on Resisting Moments

The demand over capacity ratio is calculated as follows:

, RedDoverC Ed

pl Rd

MM

=

10.4.1.3 Positive Bending – Class 3 For derivation of stresses fbu in flanges see Section 10.3.1 of this manual. The demand over capacity ratio is calculated as follows:

Top Bot deck


yd yd cd

f f ff f f

=

10.4.1.4 Positive Bending Shear Interaction – Class 3 In accordance with EN 1993-1-2006, Section 7.1 (1),

if η3 exceeds 0.5 and ,1

,

,f Rd

pl Rd

MM

η ≥ where 1,

Ed

pl Rd

MM

η ≥ and 1,

,Ed

bw Rd

VV

η ≥

where the vertical shear force VEd includes shear from torsional effects (see Section 10.4.2.1 for evaluation of torsional shear) the design resistance to bending moment is reduced to allow for the shear force. The demand over ca-pacity ratio is calculated as follows:

( )2,1 3

,

DoverC 1 2 1f Rd

pl Rd

MM

= η + − η −



where

Mf,Rd is the design plastic moment of resistance of the section consisting of the effective area of the flanges;

Mpl,Rd is the design plastic resistance of the cross-section consisting of the ef-fective area of the flanges and the fully effective web irrespective of its section class.

10.4.1.5 Positive Bending - Class 4 If the Design Request parameter “Use Stage Analysis? = No,” the fbu stresses on each flange are calculated based on the effective section properties (see Sec-tion 10.1.4 of this manual). The demand over capacity ratio is calculated as fol-lows:

Top Bot deck


yd yd cd

f f ff f f

=


10.4.1.6 Positive Bending Shear Interaction – Class 4 The demand over capacity ratio is calculated using a procedure similar to that used for Class 3 sections (see Section 10.4.1.4 of this manual), although the de-sign plastic moments of resistance Mf,Rd and Mpl,Rd are based on the effective area of the flanges.

( )2,1 3

,

DoverC 1 2 1f Rd

pl Rd

MM

= η + − η −

10.4.1.7 Negative Bending – Class 1 and 2 The demand over capacity ratio is evaluated as

,DoverC Ed

LT pl Rd

MM

=χ

Where lateral torsional buckling reduction factor χLT is taken as equal to 1.



10.4.1.8 Negative Bending Shear Interaction – Class 1 and 2 The demand over capacity ratio is calculated using a procedure similar to that used for positive bending (see Section 10.4.1.2 of this manual), although the design plastic moment of resistance Mpl,RdRed is based on negative bending and the lateral torsional buckling reduction factor χLT is taken as equal to 1.

, RedDoverC Ed

LT pl Rd

MM

=χ

10.4.1.9 Negative Bending – Class 3 For derivation of stresses fbu in flanges see Section 10.3.1 of this manual. The lateral torsional buckling reduction factor χLT is taken as equal to 1 and the de-mand over capacity ratio is calculated as follows:

Top Bot deck


yd LT yd cd

f f ff f f

= χ

10.4.1.10 Negative Bending Shear Interaction – Class 3 The demand over capacity ratio is calculated using a procedure similar to that used for positive bending (see Section 10.4.1.4 of this manual), although the design plastic moments of resistance Mpl,Rd is based on negative bending.

( )2,1 3

,

DoverC 1 2 1f Rd

pl Rd

MM

= η + − η −

10.4.1.11 Negative Bending – Class 4 If the Design Request parameter “Use Stage Analysis? = No,” the fbu stresses on each flange are calculated based on the effective section properties (see Sec-tion 10.3.1 of this manual). The lateral torsional buckling reduction factor χLT is taken as equal to 1 and the demand over capacity ratio is calculated as follows:

Top Bot deck


yd LT yd cd

f f ff f f

= χ




10.4.1.12 Negative Bending Shear Interaction – Class 4 The demand over capacity ratio is calculated using a procedure similar to that used for Class 3 sections (see Section 10.4.1.4 of this manual), although the de-sign plastic moments of resistance Mf,Rd and Mpl,Rd are based on negative bend-ing and the effective area of the flanges.

( )2,1 3

,

DoverC 1 2 1f Rd

pl Rd

MM

= η + − η −

10.4.2 Shear When processing the Design Request from the Design module, the program as-sumes vertical stiffeners are present at supports only, and no intermediate ver-tical stiffeners are present.

In the Optimization form (Design/Rating > Superstructure Design > Opti-mize command), the user can specify stiffener locations. The program recalcu-lates the shear resistance based on the defined stiffener layout. It should be not-ed that stiffeners are not modeled in the Bridge Object, and therefore, add-ing/modifying stiffeners does not affect the magnitude of the demands.

10.4.2.1 Design Shear Resistance From clause 6.2.6(6) of EN 1993-1-1, resistance to shear buckling should be checked if

72w

w

ht

ε>

η EN 1993-1-1, eq. (6.22)

where the value η = 1.20 is used for steel grades up to and including S460. For higher steel grades, η = 1.00 is used, in accordance with EN 1993-1-5 Section 5.1.2 Note 2 and 235 .yf=ε

If the resistance to shear buckling does not control the design, shear resistance is based on shear plastic resistance given by:

( ), ,

0

3v ybw Rd pl Rd

M

A fV V

γ= = EN 1993-1-1, eq. (6.18)



When resistance to shear buckling must be checked:

• the slenderness is obtained from EN 1993-1-5 equation (5.5) for stiffeners at supports only,

,86.4

ww

ht

=λε

• the slenderness is obtained from EN 1993-1-5 equation (5.6) for transverse stiffeners at supports and intermediate transverse stiffeners,

,37.4

ww

ht k

=τ

λε

where

( )( )

2

2

5.34 4.00 when 1

4.00 5.34 when 1w w

w w

k h a a h

k h a a hτ

τ

= + ≥

= + < EN 1993-1-5 (eq A.5)

a is the distance between transverse stiffeners.

The design resistance of the web is given by

,13

w yw wbw Rd

M

f h tV

χ

γ= EN 1993-1-5 (eq 5.2)

where the contribution from the web χw to shear buckling resistance is in ac-cordance with EN 1993-1-5 Table 5.1.



Table 10-4

Rigid end post Non-rigid end post

0.83wλ < η η η

0.83 1.08wη≤ λ < 0.83 wλ 0.83 wλ

1.08wλ ≥ ( )1.37 0.7 w+ λ 0.83 wλ

The St. Venant torsional shear stress in the web is determined as:

𝑓𝑓𝑣𝑣 =𝑇𝑇

2𝐴𝐴𝑜𝑜𝑡𝑡𝑤𝑤

Where Ao is enclosed area within the box section. Shear force per web resulting from the torsional stress is evaluated as:

𝑉𝑉𝑡𝑡𝑜𝑜𝑐𝑐 = 𝑓𝑓𝑣𝑣𝐴𝐴𝑤𝑤𝑒𝑒𝑤𝑤

The contribution from the flanges and composite slab is always ignored. The demand to capacity ratio is evaluated as

𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 =𝑉𝑉𝑒𝑒𝑒𝑒 + 𝑉𝑉𝑡𝑡𝑜𝑜𝑐𝑐𝑉𝑉𝑤𝑤𝑤𝑤,𝑅𝑅𝑒𝑒

10.5 Service Stress Design Request The service design check calculates at every section cut the stresses fbu at the top steel flange of the composite section, the bottom steel flange of the compo-site section, the shear stress and principal stress at the web, and the compres-sion stress at the top of the composite slab. It then compares them against lim-its specified in EN 1993-2 Section 7.3.

10.5.1 Positive Bending For the derivation of stresses fbu in flanges, see Section 10.3.1 of this manual. The shear stress in the web where the vertical shear force VEd includes shear from torsional effects (see Section 10.4.2.1 for evaluation of torsional shear) is derived as:

Service Stress Design Request 10 - 27


,ser .EdEd

w

VA

τ =

The principal stress is derived as follows:

2 2Princ ,ser ,ser3Ed Edσ = σ + τ

The demand over capacity ratio is calculated as follows, in accordance with EN 1993-2 Section 7.3:

Top ,serBot deck Princ

webTop Bot 1 deck webDoverC max , , , ,

3

bu Edbu

yyd yd cd y

f f fff f f f

τ σ =

κ

where k1 is the concrete service compression stress limit factor, in accordance with EN 1992-1-1 7.2(2).

10.5.2 Negative Bending The stresses in the steel section are derived using a procedure similar to that used in Section 10.3.1 of this manual. Stress in rebar is calculated at the top most rebar level, and the concrete slab tension capacity is ignored. Stresses in reinforcement increase as a result of the effects of tension stiffening of concrete between cracks. Δσs is calculated from:

0.4 ctms

st s

f∆σ =

α ρ (EN 1994-2 eq.(7.5))

12 2

sAI

A Iα = (EN 1994-2 eq.(7.6))

A, I are the area and second moment of area, respectively, of the effective composite section neglecting concrete in tension and profiled sheeting, if any;

A2, I2 are the corresponding properties of the structural steel section.

The demand over capacity ratio is calculated as follows in accordance with EN 1993-2 Section 7.3:

10 - 28 Service Stress Design Request


rebar+Top ,serBot Princ

webTop Bot 3 rebar webDoverC max , , , ,

3

sEdbu Edbu

yyd yd y y

ff fff f k f f

∆σ

τ σ =

where k3 is the reinforcement service tensile stress limit factor in accordance with EN 1992-1-1 7.2(5).

10.6 Service Rebar Design Request The Service Rebar Design Request checks each section for two conditions: minimum rebar, in accordance with EN 1994-2 Section 7.4.2, and control of cracking resulting from direct loading, in accordance with EN 1994-2 Section 7.4.3.

10.6.1 Minimum Rebar When determining the minimum rebar, the program calculates factor kc

( )o

1 0.3 1.01 2c

c

kh z

= + ≤+

(EN 1994-2 eq.(7.2))

where

• hc is the thickness of concrete slab

• zo is the vertical distance between the centroids of the uncracked concrete slab and the uncracked composite section, calculated using the modular ratio n0 for short-term loading;

If no rebar is defined in the slab, the rebar stress σs is determined from Table 7.2 of EN 1994-2 for the design crack width specified in the Design Request parameter. For a design crack width > 0.2mm, the rebar stress σs is assumed as the min(fy,360MPa), and for a design crack width = 0.2mm, the rebar stress σs is assumed as the min(fy,280MPa).

If rebar is defined in the slab, the rebar stress σs is read from EN 1994-2 Table 7.1 based on the maximum diameter defined at the section and the specified design crack width.

Service Rebar Design Request 10 - 29


The area of minimum reinforcement is calculated as

,eff .s s c ct cd sA k k k f A= σ (EN 1994-2 eq.(7.1))

When no rebar is defined at the section cut, the maximum bar diameter and the maximum bar spacing are read from Tables 7.1 and 7.2 of EN 1994-2 based on the rebar stress σs and the defined design crack width. The maximum rebar spacing reported is the smaller value of the required bar spacing to provide the calculated minimum reinforcement or the maximum spacing in accordance with Table 7.2 of EN 1994-2. The demand over capacity ratio is arbitrarily set to 1E7.

When rebar is defined at the section cut, the demand over capacity is evaluated as the ratio of the area per unit width of the required minimum reinforcement versus the provided reinforcement. Maximum rebar spacing is read from Table 7.2 of EN 1994-2 based on the rebar stress σs and the specified design crack width.

10.6.2 Control of Cracking The stress in rebar resulting from tension stiffening, Δσs, is calculated using the same procedure as outlined in Section 10.3.1 of this manual. For each de-mand set, the stress at the rebar level is calculated. The demand over capacity ratio is reported as the ratio of the maximum bar diameter provided in the top half of the composite slab and the maximum bar diameter, as specified in EN 1994-2 Table 7.1 for the defined design crack width. When no rebar is defined at the section cut, the Δσs and the demand over capacity ratio are set to zero.

10.7 Constructability Design Request

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

10 - 30 Constructability Design Request


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.

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.

The section stresses are calculated based on gross section; the use of effective section properties cannot be accommodated for this design request. Therefore, if the section is classified as Class 4, the section is flagged as invalid and skipped. To design Class 4 sections or sections where gross and effective areas are not equal, the non-staged constructability design request (Steel-U Comp Construct NonStgd) can be used.

10.7.2 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 a Nonlinear Staged Construc-tion load case. For each section cut specified in the design request the construc-tability 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 the Update Bridge Structural Model form (Bridge > Update > Structural Model Options option).

10.7.3 Slab Status vs. Unbraced Length Based on the slab status the program calculates corresponding positive bending capacity, negative bending capacity, shear capacity, and positive and negative bending versus shear interaction. Next the program compares the capacities

Constructability Design Request 10 - 31


against demands specified in the Demand Set by calculating the Demand over Capacity ratio. The controlling Demand Set and the Output Label on a girder-by-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 the slab status is not present or non-composite, the program treats the top 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 any time a steel beam is activated at a given section cut, the un-braced length L for the top flanges is equal to the distance between the nearest downstation and upstation qualifying cross diaphragms or the span ends as de-fined in the Bridge Object. Some of the diaphragm types available in CSiBridge may not necessarily provide restraint to the top flange. It is the us-er’s responsibility to provide top flange temporary bracing at the diaphragm lo-cations prior to the slab acting compositely.

10.7.4 Algorithm When the slab status is composite, the staged and non-staged design checks follow the procedure outlined in Section 10.4 of this manual. When the slab status is non-composite, the section resisting demands consists of the steel beam only. Because of the fact that the top flange is not continuously braced, the section is reclassified, and the effective area of the top flange is recalculat-ed. In addition to the checks described in Section 10.4 of this manual, the top flange is also checked for lateral torsional buckling.

10.8 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 the section sizes and associated resistance results. The section plate size versions

10 - 32 Section Optimization


are “As Analyzed,” “As Designed,” and “Current.” The section plots use dis-tinct 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 is 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 the Modify Section button. After the section modification has been completed, the Current version is shown in red in the elevation and cross-section views. After the resistance has been recalculated successfully by click-ing the Recalculate Resistance button, the Current version is designated As Designed 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. The previously defined stiffeners can be re-called 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 dis-played by clicking on the Modify Section button.

Section Optimization 10 - 33

Chapter 11 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 11-1.

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

11 - 1


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

Figure 11-1 3D view of example concrete box girder bridge model

11.1 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 11-2 Elevation view of example bridge

11 - 2 Description of Example Model

Chapter 11 - Run a Bridge Design Request

Figure 11-3 Plan view of the example bridge

11.2 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 11-4 displays.

Figure 11-4 Bridge Design Preferences form

11.3 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 11-5 displays. The form is used

Design Preferences 11 - 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 11-5 Code-Generated Load Combinations for Bridge Design form

The defined load combinations for this example are shown in Figure 11-6.

Figure 11-6 Define Load Combinations form

11 - 4 Load Combinations

Chapter 11 - 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.

11.4 Bridge Design Request After the Design/Rating > Superstructure Design > Design Request com-mand has been used, the Bridge Design Request form shown in Figure 11-7 displays.

Figure 11-7 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 11 - 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.

11.5 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 11-8:

Figure 11-8 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 11-9, 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 12.

Figure 11-9 Plot of flexure check results

11 - 6 Start Design/Check of the Bridge

Chapter 12 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 11. 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.

12.1 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 12-1.

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 envel-oped 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 Re-quest. Move the mouse pointer onto the demand or capacity plot to view the val-ues for each nodal point. Move the pointer to the capacity moment at station 1200

Display Results as a Plot 12 - 1


and 536981.722 kip-in is shown. A verification calculation that shows agreement with this CSiBridge result is provided in Section 12.4.

Figure 12-1 Plot of flexure check results for the example bridge design model

12.1.1 Additional Display Examples Use the Home > Display > Show Bridge Forces/Stresses command to select, on the example form shown in Figure 12-2, the location along the top or bottom por-tions of a beam or slab for which stresses are to be displayed. Figures 12-3 through 12-9 illustrate the left, middle, and right portions as they apply to Multicell Con-crete Box Sections. Location 1, as an example, refers to the top left selection op-tion 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 option while locations 4, 5, and 6 refer to the bottom left, bottom center, and bottom right se-lection options.

12 - 2 Display Results as a Plot

Chapter 12 - Display Bridge Design Results

Figure 12-2 Select the location on the beam or slab for which results are to be displayed

Figure 12-3 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 12- 3


Figure 12-4 Bridge Concrete Box Deck Section - External Girders Sloped

Figure 12-5 Bridge Concrete Box Deck Section - External Girders Clipped

Top slab cut line


Centerline of the web

4

5 6

1 2 3 1 2 3

4 5 6 Centerline of the web

Top slab cut line


1 2 3

4

5 6


4 5 6


1 2 3



Figure 12-6 Bridge Concrete Box Deck Section - External Girders and Radius

Figure 12-7 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 line


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 12- 5


Figure 12-8 Bridge Concrete Box Deck Section - Advanced

Top slab cut line


1 2 3


1 2 3

4

5 6


1 2 3

4 5 6



Figure 12-9 Bridge Concrete Box Deck Section - AASHTO - PCI - ASBI Standard

12.2 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 12-10. Use the options on that form to select which data results are to be viewed. Multiple selection may be made.


Top slab cut line


4

5 6

Display Data Tables 12- 7


Figure 12-10 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 12-11 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.

12 - 8 Display Data Tables


Figure 12-11 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.

12.3 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 using one of the File > Export commands: Access; Excel; or Text. When this com-mand is executed, a form similar to that shown in Figure 12-12 displays.

Advanced Report Writer 12- 9


Figure 12-12 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 possible 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 12-13. Click the appropriate button (e.g., Find ex-isting DB File, Convert Excel File, Convert Text File) and locate the exported 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.

12 - 10 Advanced Report Writer


Figure 12-13 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 vari-ous 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 formatting 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 12-14 shows an example of the printed output generated by the Report Writer.

Advanced Report Writer 12- 11


Figure 12-14 An example of the printed output

12.4 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 12-10:

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)

12 - 12 Verification


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

( )slab webeq slabeq

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 design results for concrete box stress, concrete box shear, and concrete box principal have not been included. The user is encouraged to perform a similar check of these designs and to review Chapters 5, 7, and 8 for a detailed descriptions of the design algorithms.

Verification 12- 13

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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