ISO BRG083110M2 Berkeley, California, USA
Version 15 August 2010
CSiBridge
COPYRIGHT
Copyright Computers & Structures, Inc., 1978-2010 All rights reserved.
The CSI Logo® is a registered trademark of Computers & Structures, Inc. CSiBridgeTM and Watch & LearnTM are trademarks of Computers & Structures, Inc. Adobe® and Acrobat® are registered trademarks of Adobe Systems Incorported. AutoCADTM is a registered trademark of Autodesk, Inc.
The computer program CSiBridgeTM
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.
No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior explicit written permission of the publisher.
Further information and copies of this documentation may be obtained from: Computers & Structures, Inc.
1995 University Avenue
Berkeley, California 94704 USA Phone: (510) 649-2200
FAX: (510) 649-2299
e-mail: [email protected] (for general questions)
e-mail: [email protected] (for technical support questions) web: www.csiberkeley.com
DISCLAIMER
CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THE DEVELOPMENT AND TESTING OF THIS SOFTWARE. HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON THE ACCURACY OR THE RELIABILITY OF THIS PRODUCT.
THIS PRODUCT IS A PRACTICAL AND POWERFUL TOOL FOR STRUCTURAL DESIGN. HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC ASSUMPTIONS OF THE SOFTWARE MODELING, ANALYSIS, AND DESIGN ALGORITHMS AND COMPENSATE FOR THE ASPECTS THAT ARE NOT ADDRESSED.
THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE CHECKED BY A QUALIFIED AND EXPERIENCED ENGINEER. THE ENGINEER MUST INDEPENDENTLY VERIFY THE RESULTS AND TAKE PROFESSIONAL RESPONSIBILITY FOR THE INFORMATION THAT IS USED.
i
Contents
Bridge Superstructure Design
1 Introduction
1.1 Organization 1-1
1.2 Recommended Reading 1-2
2 Design Prerequisites
2-1 Load Pattern Types 2-1
2.2 Design Load Combinations 2-3
2.3 Default Load Combinations 2-4
3 Determine Live Load Distribution Factors (LLDF)
3.1 Algorithm for Determining Live Load Distribution
Factors (LLDF) 3-1
3.2 Determine Live Load Distribution Factors 3-2
3.3 Apply LLD Factors 3-3
3.3.1 User Specified 3-4
3.3.2 Calculated by CSiBridge in Accordance with Code 3-4 3.3.3 Read Directly from Girder 3-4 3.3.4 Uniformly Distribution to Girders 3-4
CSiBridge Superstructure Design
ii
3.4 Generate Virtual Combinations 3-5
3.4.1 Stress Check 3-5
3.4.2 Shear or Moment Check 3-6
3.5 Read Forces/Stresses Directly from Girders 3-6
3.5.1 Stress Check 3-6
3.5.2 Shear or Moment Check 3-6
3.6 LLDF Design Example Using Method 2 3-7
4 Define a Bridge Design Request
4.1 Name and Bridge Object 4-3
4.2 Check Type 4-3
4.3 Station Range 4-5
4.4 Design Parameters 4-5
4.5 Demand Sets 4-10
4.6 Live Load Distribution Factors 4-10
5 Design Concrete Box Girder Bridges
5.1 Stress Design AASHTO-STD-2002 5-1
5.1.1 Capacity Parameters 5-1
5.1.2 Demand Parameters 5-2
5.1.3 Algorithm 5-2
5.2 Stress Design AASHTO-LFRD-2007 5-2
5.2.1 Capacity Parameters 5-2
5.2.2 Algorithm 5-3
5.2.3 Stress Design Example 5-3
5.3 Flexure Design AASHTO-LRFD-2007 5-6
5.3.1 Capacity Parameters 5-6
5.3.2 Variables 5-6
5.3.3 Design Process 5-7
5.3.4 Algorithm 5-8
5.3.5 Flexure Design Example 5-10
5.4 Shear Design AASHTO-LRFD-2007 5-14
5.4.1 Capacity Parameters 5-14
5.4.2 Variables 5-15
5.4.3 Design Process 5-16
iii
5.4.5 Shear Design Example 5-24
5.5 Principal Stress Design AASHTO-LRFD-2007 5-31
5.5.1 Capacity Parameters 5-31
5.5.2 Demand Parameters 5-31
5.5.3 Algorithm 5-31
6 Design Multi-Cell Concrete Box Bridges using AMA
6.1 Stress Design 6-2 6.2 Shear Design 6-3 6.2.1 Variables 6-4 6.2.2 Design Process 6-5 6.2.3 Algorithms 6-6 6.3 Flexure Design 6-10 6.3.1 Variables 6-10 6.3.2 Design Process 6-11 6.3.3 Algorithms 6-11
7 Design Algorithms for Precast I and U-Girder Bridges
7.1 Design Stress 7-1
7.2 Design Shear 7-2
7.2.1 Variables 7-3
7.2.2 Design Process 7-5
7.2.3 Algorithms 7-5
7.2.4 Shear Design Example 7-8
7.3 Design of Flexural 7-14
7.3.1 Variables 7-14
7.3.2 Design Process 7-15
7.3.3 Algorithms 7-16
7.3.4 Flexure Design Capacity Example 7-18
8 Design Steel I-Beam Bridge with Composite Slab
8.1 Strength Properties 8-1
8.1.1 Yield Moments 8-1
8.1.2 Plastic Moments 8-3
8.1.2 Section Classification Factors 8-7
CSiBridge Superstructure Design
iv
8.2.1 Demand Flange Stress fbu and ff 8-10
8.2.2 Demand Flange Lateral Bending Stress f1 8-11 8.2.3 Depth of Web in Compression 8-11
8.3 Strength Design Request 8-13
8.3.1 Flexure 8-13
8.3.2 Shear 8-19
8.4 Service Design Request 8-21
8.5 Web Fatigue Design Request 8-23
8.6 Section Optimization 8-24
9 Run a Bridge Design Request
9.1 Description of Example Model 9-2
9.2 Design Preferences 9-3
9.3 Load Combinations 9-3
9.4 Bridge Design Request 9-5
9.5 Start Design/Check of Structure 9-6
10 Design Output
10.1 Display Results as a Plot 10-1
10.1.1 Additional Display Examples 10-2
10.2 Display Data Tables 10-7
10.3 Advanced Report Writer 10-8
10.4 Verification 10-11
v
List of Figures
Figure 2-1 Code-Generated Load Combinations for Bridge
Design Form 2-5
Figure 2-2 Define Load Combinations form 2-6
Figure 3-1 General Dimensions 3-8
Figure 3-2 Lever Rule 3-11
Figure 4-1 Bridge Design Request – Concrete Box Girder Bridges 4-2 Figure 4-2 Bridge Design Request – Compost I or U Girder Bridges 4-2 Figure 4-3 Bridge Design Request form – Steel I Beam
with Composite Slab 4-3
Figure 4-4 Superstructure Design Request Parameters form 4-5 Figure 5-1 LRFD 2007 Stress Design, ASSHTO Box Beam,
Type BIII-48 5.4
Figure 5-2 Reinforcement, LRFD 2007 Stress Design AASHTO Box
Beam, Type BIII-48 5-4
Figure 5-3 LRFD 2007 Flexure Design Cross-Section, AASHTO Box
Beam, Type BIII-48 5-10
Figure 5-4 Reinforcement, LRFD 2007 Flexure Design Cross-Section,
AASHTO Box Bea, Type BIII-48 5-10
Figure 5-5 Shear Design Example, AASHTO Box Beam,
Type BIII-48 5-24
0
Figure 7-1 Shear design example deck section 7-10
1
Figure 7-2 Shear design example beam section 7-10
2
Figure 7-3 Flexure capacity design example deck section 7-20
3
Figure 7-4 Flexure capacity design example beam section 7-20 Figure 8-1 Steel I-Beam with Composite Section 8-5 Figure 8-2 Steel I-Beam Composite Section 8-6 Figure 9-1 3D view of example concrete box girder bridge model 7-2
5
Figure 9-2 Elevation view of example bridge 7-2
6
Figure 9-3 Plan view of the example bridge 7-3
7
Figure 9-4 Bridge Design Preferences form 9-3
8
Figure 9-5 Code-Generated Load Combinations for Bridge Design form 9-4
CSiBridge Superstructure Design
vi
9
Figure 9-6 Define Load Combinations form 9-4
1
Figure 9- 7 Define Load Combinations form 9-5
1
Figure 9-8 Perform Bridge Design - Superstructure 9-6
1
Figure 9-9 Plot of flexure check results 9-6 Figure 10-1 Plot of flexure check results for the example bridge
design model 10-2
Figure 10-2 Select the location on the beam or slab for which
results are to be displayed 10-3
Figure 10-3 Bridge Concrete Box Deck Section – External
Girders Vertical 10-3
Figure 10-4 Bridge Concrete Box Deck Section – External
Girders Sloped 10-4
Figure 10-5 Bridge Concrete Box Deck Section – External
Girders Clipped 10-4
Figure 10-6 Bridge Concrete Box Deck Section – External
Girders and Radius 10-5
Figure 10-7 Bridge Concrete Box Deck Section – External
Girders Sloped Max 10-5
Figure 10-8 Bridge Concrete Box Deck Section – Advanced 10-6 Figure 10-9 Bridge Concrete Box Deck Section -
AASHTO – PCI – ASBI Standard 10-6
Figure 10-10 Choose Tables for Display form 10-7 Figure 10-11 Design database table for AASHTO LRFD 2007
flexure check 10-8
Figure 10-12 Choose Tables for Export to Access form 10-9 Figure 10-13 Create Custom Report form 10-10 Figure 10-14 An example of the printed output 10-11
1 - 1
Chapter 1
Introduction
As the ultimate versatile, integrated tool for modeling, analysis, and design of bridge structures, CSiBridge can apply the AASHTO STD 2002 or AASHTO LRFD 2007 code to concrete box girder bridge design or the AASHTO 2007 LRFD code for design when the superstructure includes Pre-cast Concrete Box bridges with a composite slab. Additionally, steel I-beam bridges with composite slabs may be designed in accordance with the AASHTO 2007 code. The ease with which these tasks can be accomplished makes CSiBridge the most productive bridge design package in the industry. Design using CSiBridge is based on load patterns, load cases, load combina-tions and design requests. The design output can then be displayed graphically and printed using a customized reporting format.
It should be noted that the design of bridge superstructure is a complex subject and the design codes cover many aspects of this process. CSiBridge is a tool to help the user with that process. Only the aspects of design documented in this manual are automated by the CSiBridge design capabilities. The user must check the results produced and address other aspects not covered by CSi-Bridge.
CSiBridge Bridge Superstructure Design
1 - 2 Organization
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 bridges and precast concrete girder bridges. Chapter 2 describes design prereq-uisites. Chapter 3 describes Live Load Distribution Factors. Chapter 4 de-scribes defining the design request, which includes the design request name, a bridge object name (i.e., the bridge model), check type (i.e., the type of de-sign), station range (i.e., portion of the bridge to be designed), design parame-ters (i.e., overwrites for default parameparame-ters) and demand sets (i.e., loading combinations). Chapters 5 and 6 provide the algorithms used by CSiBridge in completing concrete box and multicell box girder bridges. Chapter 7 describes design parameters for precast I and U girder in accordance with the AASHTO code. Chapter 8 explains how to design and optimize a steel I-beam bridge with composite slab. Chapter 9 describes how to run a Design Request, and Chapter 10 describes design output, which can be presented graphically as plots, in data tables, and in reports generated using the Advanced Report Writer feature.
1.2
Recommended Reading/Practice
It is strongly recommended that you read this manual and review any applica-ble “Watch & Learn” Series™ tutorials, which are found on our web site, http://www.csiberkeley.com, before attempting to design a concrete box girder or precast concrete bridge using CSiBridge. Additional information can be found in the on-line Help facility available from within the software’s main menu.
Load Pattern Types 2 - 1
Chapter 2
Define Loads and Load Combinations
This chapter describes the steps that are necessary to define the loads and load combinations that the user intends to use in the design of the bridge superstruc-ture. The user may define the load combinations manually or have CSiBridge automatically generate the code generated load combinations. The appropriate design code may be selected using the Design/Rating > Superstructure
De-sign > Preference command. Currently, the AASHTO STD 2002 and
AASHTO LRFD 2007 design codes are supported by CSiBridge.
When the code generated load combinations are going to be used, it is impor-tant for users to define the load pattern type in accordance with the applicable code. The load pattern type can be defined using the Loads > Load Patterns command. The user options for defining the load pattern types are summarized in the Tables 2-1 and 2-2.
2.1
Load Pattern Types
Tables 2-1 and 2-2 show the permanent and transient load pattern types that can be defined in CSiBridge. The tables also show the AASHTO abbreviation and the load pattern descriptions. Users may choose any name to identify a load pattern type.
CSiBridge Bridge Superstructure Design
2 - 2 Load Pattern Types
Table 2-1 PERMANENT Load Pattern Types Used in the AASHTOLRFD 2007 Code CSiBridge
Load Pattern Type Reference AASHTO Description of Load Pattern
CREEP CR Force effects due to creep
DOWNDRAG DD Downdrag force
DEAD DC Dead load of structural components and
non-structural attachments
SUPERDEAD DW Superimposed dead load of wearing surfaces
and utilities
BRAKING BR Vehicle braking force
HORIZ. EARTH PR EH Horizontal earth pressures
LOCKED IN EL Misc. locked-in force effects resulting from the
construction process
EARTH SURCHARGE ES Earth surcharge loads
VERT. EARTH PR EV Vertical earth pressure
PRESTRESS PS Hyperstatic forces from post-tensioning
Table 2-2 TRANSIENT Load Pattern Types Used in the AASHTO LRFD 2007 Design Code CSiBridge
Load Pattern Type
AASHTO
Reference Description of Load Pattern
BRAKING BR Vehicle braking force
CENTRIFUGAL CE Vehicular centrifugal loads
VEHICLE COLLISION CT Vehicular collision force
VESSEL COLLISION CV Vessel collision force
QUAKE EQ Earthquake
FRICTION FR Friction effects
ICE IC Ice loads
- IM Vehicle Dynamic Load Allowance
BRIDGE LL LL Vehicular live load
LL SURCHARGE LS Live load surcharge
PEDESTRIAN LL PL Pedestrian live load
SETTLEMENT SE Force effects due settlement
TEMP GRADIENT TG Temperature gradient loads
TEMPERATURE TU Uniform temperature effects
STEAM FLOW WA Water load and steam pressure
WIND–LIVE LOAD WL Wind on live load
Design Load Combinations 2 - 3
2.2
Design Load Combinations
The code generated design load combinations make use of the load pattern types noted in Tables 2-1 and 2-2. Table 2-3 shows the load factors and com-binations that are required in accordance with the AASHTO LRFD 2007 code. Table 2-3 Load Combinations and Load Factors Used in the AASHTO LRFD 2007 Code
Load Combo Limit State DC DD DW EH EV ES EL PS CR SH LL IM CE BR PL LS WA WS WL FR TU TG SE EQ IC CT CV Str I P
1.75 1.00 - - 1.00 0.5/1.20 TG
SE - - - - Str II P
1.35 1.00 - - 1.00 0.5/1.20 TG
SE - - - - Str III P
- 1.00 1.40 - 1.00 0.5/1.20 TG
SE - - - - Str IV P
- 1.00 - - 1.00 0.5/1.20 - - - - - Str V P
1.35 1.00 0.40 1.00 1.00 0.5/1.20 TG
SE - - - - Ext Ev I P
EQ 1.00 - - 1.00 - - 1.00 - - - Ext Ev II P
0.5 1.00 - - 1.00 - - - 1.00 1.00 1.00 Serv I 1.00 1.00 1.00 0.30 1.00 1.00 0.5/1.20 TG
SE - - - - Serv II 1.00 1.00 1.00 - - 1.00 0.5/1.20 - - - - - Serv III 1.00 1.00 1.00 - - 1.00 0.5/1.20 TG
SE - - - - Serv IV 1.00 1.00 1.00 0.70 - 1.00 0.5/1.20 - 1.00 - - - - Fatigue- LL, IM & CE Only - 0.75 - - - - - - - -Table 2-4 shows the maximum and minimum factors for the permanent loads in accordance with the AASHTO LRFD 2007 code.
CSiBridge Bridge Superstructure Design
2 - 4 Default Load Combinations
Table 2-4 Load Factors for Permanent Loads,
P, Used in the AASHTO LRFD 2007 Code Load FactorType of Load Maximum Minimum
DC DC: Strength IV only 1.25 1.50 0.90 0.90 DD: Downdrag 1.40 0.25
DW: Wearing Surfaces and Utilities 1.50 0.65
EH: Horizontal Earth Pressure 1.50 0.90
EL: Locked in Construction Stresses 1.00 1.00
EV: Vertical Earth Pressure 1.35 1.00
ES: Earth Surcharge 1.50 0.75
Two combinations for each permanent load pattern are required because of the maximum and minimum factors. When the default load combinations are used, CSiBridge automatically creates both load combinations (one for the maximum and one for the minimum factor), and then automatically creates a third combi-nation that represents an enveloped combicombi-nation of the max/min combos.
2.3
Default Load Combinations
Default design load combinations can be activated using the Design/Rating >
Load Combinations > Add Default command. Users can set the load
combi-nations by selecting the “Bridge” option. The users may select the desired limit states and load cases using the Code Generated Load Combinations for Bridge Design form shown in Figure 2-1.
Default Load Combinations 2 - 5
Figure 2-1 Code-Generated Load Combinations for Bridge Design form
After the desired limit states and load cases have been selected, CSiBridge will generate all of the code-required load combinations. These can be viewed us-ing the Home > Display > Show Tables command or by usus-ing the
Show/Modify button on the Define Combinations form, which is shown in
CSiBridge Bridge Superstructure Design
2 - 6 Default Load Combinations
Figure 2-2 Define Load Combinations form
The load combinations denoted as Str-I1, Str-I2, and so forth refer to Strength I load combinations. The load case StrIGroup1 is the name given to enveloped load combination of all of the Strength I combinations. Enveloped load combi-nations will allow for some efficiency later when the bridge design requests are defined (see Chapter 4).
Algorithm for Determining Live Load Distribution Factors (LLDF) 3 - 1
Chapter 3
Determine Live Load Distribution Factors
This chapter describes the algorithms used by CSiBridge to determine the live load distribution factors used to assign live load demands to individual girders. An explanation is given with respect to how the distribution factors are applied in a shear, stress, and moment check in accordance with the AASHTO LRFD 2007 code. The live load distribution factors are applicable only to superstruc-tures that have a deck that includes precast I or U girders with composite slabs. Legend:
Girder = beam + tributary area of composite slab
Section Cut = all girders present in the cross-section at the cut location
3.1
Algorithm for Determining Live Load Distribution
Fac-tors (LLDF)
CSiBridge gives the user a choice of four methods to address distribution of live load to individual girders.
Method 1 – The LLD factors are specified directly by the user.
Method 2 – CSiBridge calculates the LLD factors by following procedures outlined in AASHTO LRFD Section 4.6.2.2.
CSiBridge Bridge Superstructure Design
3 - 2 Determine Live Load Distribution Factors
Method 3 – CSiBridge reads the calculated live load demands directly from in-dividual girders (available only for Area or Solid models).
Method 4 – 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 or specified in accordance with the code (Method 1 or 2), only one lane with a MultiLane Scale Factor = 1 should be loaded into a Moving Load cases included in the demand set com-binations.
When CSiBridge reads the LLD factors directly from individual girders (Method 3, applicable to area and solid models only) or when CSiBridge ap-plies the LLD factors uniformly (Method 4), multiple traffic lanes with rele-vant Multilane Scale Factors should be loaded in accordance with code re-quirements.
3.2
Determine Live Load Distribution Factors
At every section cut, the following geometric information is evaluated to de-termine the LLD factors.
span lengththe length of span for which moment or shear is being calcu-lated
the number of girders
girder designationthe first and last girder are designated as exterior girders and the other girders are classified as interior girders
roadway widthmeasured as the distance between curbs/barriers; medians are ignored
overhangconsists of the horizontal distance from the centerline of the exte-rior web of the left exteexte-rior beam at deck level to the inteexte-rior edge of the curb or traffic barrier
Apply LLD Factors 3 - 3
the beamsincludes the area, moment of inertia, torsion constant, center of gravity
the thickness of the composite slab t1 and the thickness of concrete slab haunch t2
the tributary area of the composite slabwhich is bounded at the interior girder by the midway distances to neighboring girders and at the exterior girder; includes the entire overhang on one side, and is bounded by the mid-way distances to neighboring girder on the other side
Young’s modulus for both the slab and the beamsangle of skew support. CSiBridge then evaluates the longitudinal stiffness parameter, Kg, in accor-dance with AASHTO LRFD 4.6.2.2 (eq. 4.6.2.2.1-1). The center of gravity of the composite slab measured from the bottom of the beam is calculated as the sum of the beam depth, thickness of the concrete slab haunch t2, and one-half the thickness of the composite slab t1. Spacing of the girders is calculated as the average distance between the centerlines of neighboring girders.
CSiBridge then verifies that the selected LLD factors are compatible with the type of model: spine, area, or solid. If the LLD factors are read by CSiBridge directly from the individual girders, the model type must be area or solid. This is the case because with the spine model option, CSiBridge models the entire cross section as one frame element and there is no way to extract forces on in-dividual girders. All other model types and LLDF method permutations are al-lowed.
3.3
Apply LLD Factors
The application of live load distribution factors varies, depending on which method has been selected: user specified; in accordance with code; directly from individual girders; or uniformly distributed onto all girders.
CSiBridge Bridge Superstructure Design
3 - 4 Apply LLD Factors
3.3.1 User Specified
When this method is selected, CSiBridge reads the girder designations (i.e., exterior and interior) and assigns live load distribution factors to the individual girders accordingly.
3.3.2 Calculated by CSiBridge in Accordance with Code
When this method is selected, CSiBridge considers the data input by the user for truck wheel spacing, minimum distance from wheel to curb/barrier and multiple presence factor for one loaded lane.
Depending on the section type, CSiBridge validates several section parameters against requirements specified in the code (Tables 4.6.2.2.2b-1, 4.6.2.2.2d-1, 4.6.2.2.3a-1 and 4.6.2.2.3b-1). When any of the parameter values are outside the range required by the code, the section cut is excluded from the Design Re-quest.
At every section cut, CSiBridge then evaluates the live load distribution factors for moment and shear for exterior and interior girders using formulas specified in the code (Tables 4.6.2.2.2b-1, 4.6.2.2.2d-1, 4.6.2.2.3a-1 and 4.6.2.2.3b-1). After evaluation, the LLDF values are assigned to individual girders based on their designation (exterior, interior). The same value equal to the average of the LLDF calculated for the left and right girders is assigned to both exterior gird-ers. Similarly, all interior girders use the same LLDF equal to the average of the LLDF of all of the individual interior girders.
3.3.3 Forces Read Directly from Girders
When this method is selected, CSiBridge sets the live load distribution factor for all girders to 1.
3.3.4 Uniformly Distributed to Girders
When this method is selected, the live load distribution factor is equal to 1/n where n is the number of girders in the section. All girders have identical LLD factors disregarding their designation (exterior, interior) and demand type (shear, moment).
Generate Virtual Combinations 3 - 5
3.4
Generate Virtual Combinations
When the method for determining the live load distribution factors is user-specified, code-user-specified, or uniformly distributed (Methods 1, 2 or 4), CSi-Bridge generates virtual load combination for every valid section cut selected for design. The virtual combinations are used during a stress check and check of the shear and moment to calculate the forces on the girders. After those forces have been calculated, the virtual combination are deleted. The process is repeated for all section cuts selected for design.
Four virtual COMBO cases are generated for each COMBO that the user has specified in the Design Request (see Chapter 4). The program analyzes the de-sign type of each load case present in the user specified COMBO and 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, ex(ex-terior shear, in(ex-terior moment and in(ex-terior shear LLD factors). This ensures that dead load is shared evenly by all girders, while live load is distributed based on the LLD factors.
The program then completes a stress check and a check of the shear and the moment for each section cut selected for design.
3.4.1 Stress Check
At the Section Cut being analyzed, the girder stresses at all stress output points are read from CSiBridge for every virtual COMBO generated. To ensure that live load demands are shared equally irrespective of lane eccentricity by all girders, CSiBridge uses averaging when calculating the girder stresses. It cal-culates the stresses on a beam by integrating axial and M3 moment demands on all the beams in the entire section cut and dividing the demands by the number of girders. Similarly, P and M3 forces in the composite slab are integrated and stresses are calculated in the individual tributary areas of the slab by dividing the total slab demand by the number of girders.
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
CSiBridge Bridge Superstructure Design
3 - 6 Read Forces/Stresses Directly from Girders
3.4.2 Shear or Moment Check
At the Section Cut being analyzed, the entire section cut forces are read from CSiBridge for every Virtual COMBO generated. The forces are assigned to in-dividual girders based on their designation. (Forces from two virtual Combina-tionsone for shear and one for momentgenerated for exterior beam are as-signed to both exterior beams, and similarly, Virtual Combinations for interior beams are assigned to interior beams.)
3.5
Read Forces/Stresses Directly from Girders
When the method for determining the live load distribution is based on forces read directly from the girders, the method varies based on which Design Check has been specified in the Design Request (see Chapter 4).
3.5.1 Stress Check
At the Section Cut being analyzed, the girder stresses at all stress output points are read from CSiBridge for every COMBO specified in the Design Request. CSiBridge calculates the stresses on a beam by integrating axial, M3 and M2 moment demands on the beam at the center of gravity of the beam. Similarly P, M3 and M2 demands in the composite slab are integrated at the center of grav-ity of the slab tributary area.
3.5.2 Shear or Moment Check
At the Section Cut being analyzed, the girder forces are read from CSiBridge for every COMBO specified in the Design Request. CSiBridge calculates the demands on a girder by integrating axial, M3 and M2 moment demands on the girder at the center of gravity of the girder.
LLDF Design Example Using Method 2 3 - 7
3.6
LLDF Design Example Using Method 2
The AASHTO-LRFD Specifications allow the use of advanced methods of analysis to determine the live load distribution factors. However, for typical bridges, the specifications list equations to calculate the distribution factors for different types of bridge superstructures. The types of superstructures covered by these equations are described in Table 4.6.2.2.1-1. From this table, bridges with concrete decks supported on precast concrete I or bulb-tee girders are des-ignated as cross-section “K.” Other tables in 4.6.2.2.2 list the distribution fac-tors for interior and exterior girders including cross-section “K.”
The distribution factor equations are largely based on work conducted in the NCHRP Project 12-26 and have been verified to give accurate results com-pared to 3-dimensional bridge analysis and field measurements. The multiple presence factors are already included in the distribution factor equations except when the tables call for the use of the lever rule. In these cases, the computa-tions need to account for the multiple presence factors. The user is providing those as part of the Design Request definition together with wheel spacing, curb to wheel distance and lane width.
Notice that the distribution factor tables include a column with the heading “range of applicability”. The ranges of applicability listed for each equation are based on the range for each parameter used in the study leading to the devel-opment of the equation. When any of the parameters exceeds the listed value in the “range of applicability” column, CSiBridge reports the incompliance and excludes the section from design.
Article 4.6.2.2.2d of the specifications states: “In beam-slab bridge cross-sections with diaphragms or cross-frames, the distribution factor for the exte-rior beam shall not be taken less than that which would be obtained by assum-ing that the cross-section deflects and rotates as a rigid cross-section.” This provision was added to the specifications because the original study that devel-oped the distribution factor equations did not consider intermediate dia-phragms. Application of this provision requires the presence of a sufficient number of intermediate diaphragms whose stiffness is adequate to force the cross section to act as a rigid section. For prestressed girders, different jurisdic-tions use different types and numbers of intermediate diaphragms. Depending on the number and stiffness of the intermediate diaphragms, the provisions of 4.6.2.2.2d may not be applicable. If the user specifies option “Yes” in the
CSiBridge Bridge Superstructure Design
3 - 8 LLDF Design Example Using Method 2
“Diaphragms Present” option the program follows the procedure outlined in the provision 4.6.2.2.2d.
For this example, one deep reinforced concrete diaphragm is located at the midspan of each span. The stiffness of the diaphragm was deemed sufficient to force the cross-section to act as a rigid section; therefore, the provisions of S4.6.2.2.2d apply.
Required information:
AASHTO Type I-Beam (28/72)
Noncomposite beam area, Ag = 1,085 in
2
Noncomposite beam moment of inertia, Ig = 733,320 in
4
Deck slab thickness, ts = 8 in.
Span length, L = 110 ft.
Girder spacing, S = 9 ft.-8 in. Modulus of elasticity of the beam, EB = 4,696 ksi Modulus of elasticity of the deck, ED = 3,834 ksi C.G. to top of the basic beam = 35.62 in. C.G. to bottom of the basic beam = 36.38 in.
LLDF Design Example Using Method 2 3 - 9
1. Calculate n, the modular ratio between the beam and the deck.
n = EB E (4.6.2.2.1-2) D
= 4696 3834 = 1.225
2. Calculate eg, the distance between the center of gravity of the noncompo-site beam and the deck. Ignore the thickness of the haunch in determin-ing eg
eg = NAYT + ts 2 = 35.62 + 8 2 = 39.62 in.
3. Calculate Kg, the longitudinal stiffness parameter.
Kg = n I
Ae2g
(4.6.2.2.1-1)= 1.225 733 320 1 085 39.62 22 984 704 in4
4. Interior girder. Calculate the moment distribution factor for an interior beam with two or more design lanes loaded using Table S4.6.2.2.2b-1.
DM =
0.1 0.6 0.2 3 0.075 S 9.5 S L Kg 12.0Lts
0.6
0.2
3
0.1 0.075 9.667 9.5 9.667 110 2 984 704 12 110 8 = 0.796 lane (eq. 1)5. In accordance with 4.6.2.2.2e, a skew correction factor for moment may be applied for bridge skews greater than 30 degrees. The bridge in this example is skewed 20 degrees, and therefore, no skew correction factor for moment is allowed.
Calculate the moment distribution factor for an interior beam with one design lane loaded using Table 4.6.2.2.2b-1.
DM =
0.1 0.4 0.3 3 0.06 S 14 S L Kg 12.0Lts =
0.1 0.4 0.3 3 0.06 9.667 14 9.667 110 2984704 12 100 8 CSiBridge Bridge Superstructure Design
3 - 10 LLDF Design Example Using Method 2
= 0.542 lane (eq. 2)
Notice that the distribution factor calculated above for a single lane loaded already includes the 1.2 multiple presence factor for a single lane, therefore, this value may be used for the service and strength limit states. However, multiple presence factors should not be used for the fatigue limit state. Therefore, the multiple presence factor of 1.2 for the single lane is required to be removed from the value calculated above to deter-mine the factor used for the fatigue limit state.
6. Skew correction factor for shear.
In accordance with 4.6.2.2.3c, a skew correction factor for support shear at the obtuse corner must be applied to the distribution factor of all skewed bridges. The value of the correction factor is calculated using Table 4.6.2.2.3c-1. SC =
0.3 3 1.00.20 12.0Lts Kg tan =
0.3 3 1.00.20 12.0 110 8 2 984 704 tan 20 = 1.0477. Calculate the shear distribution factor for an interior beam with two or more design lanes loaded using Table S4.6.2.2.3a-1.
DV = 0.2
S 12
S 35
2= 0.2
9.667 12
9.667 35
2 = 0.929 laneApply the skew correction factor:
DV = 1.047 0.929 0.973 lane (eq. 4) 8. Calculate the shear distribution factor for an interior beam with one
de-sign lane loaded using Table S4.6.2.2.3a-1.
LLDF Design Example Using Method 2 3 - 11
= 0.36
9.667 25.0
= 0.747 laneApply the skew correction factor:
DV = 1.047 0.747
= 0.782 lane (eq. 5)
9. From (1) and (2), the service and strength limit state moment distribution factor for the interior girder is equal to the larger of 0.796 and 0.542 lane. Therefore, the moment distribution factor is 0.796 lane.
From (4) and (5), the service and strength limit state shear distribution factor for the interior girder is equal to the larger of 0.973 and 0.782 lane. Therefore, the shear distribution factor is 0.973 lane.
10. Exterior girder
CSiBridge Bridge Superstructure Design
3 - 12 LLDF Design Example Using Method 2
11. Calculate the moment distribution factor for an exterior beam with two or more design lanes using Table 4.6.2.2.2d-1.
DM = eDVinterior
e = 0.77de 9.1
where de is the distance from the centerline of the exterior girder to the inside face of the curb or barrier.
e = 0.77 + 1.83/9.1 = 0.97
DM = 0.97(0.796) = 0.772 lane (eq. (7) 12. Calculate the moment distribution factor for an exterior beam with one
design lane using the lever rule in accordancd with Table 4.6.2.2.2d-1.
DM =
3.5 6 3.5 9.667 1.344 wheels 2
= 0.672 lane (eq. 8)
Notice that this value does not include the multiple presence factor, therefore, it is adequate for use with the fatigue limit state. For service and strength limit states, the multiple presence factor for a single lane loaded needs to be included.
DM = 0.672 1.2
= 0.806 lane (eq. 9) (Strength and Service) 13. Calculate the shear distribution factor for an exterior beam with two or
more design lanes loaded using Table 4.6.2.2.3b-1.
DV = eDVinterior where:
e = 0.6de10 = 0.6 1.83 10 = 0.783
LLDF Design Example Using Method 2 3 - 13
DV = 0.783 0.973
= 0.762 lane (eq. 10)
14. Calculate the shear distribution factor for an exterior beam with one de-sign lane loaded using the lever rule in accordancd with Table 4.6.2.2.3b-1. This value will be the same as the moment distribution factor with the skew correction factor applied.
DV = 1.047 0.806
= 0.845 lane (eq. 12) (Strength and Service) Notice that 4.6.2.2.2d includes additional requirements for the calcula-tion of the distribucalcula-tion factors for exterior girders when the girders are connected with relatively stiff cross-frames that force the cross-section to act as a rigid section. As indicated in the introduction, these provisions are applied to this example; the calculations are shown below.
15. Additional check for rigidly connected girders (4.6.2.2.2d)
The multiple presence factor, m, is applied to the reaction of the exterior beam (Table 3.6.1.1.2-1) m1 = 1.20 m2 = 1.00 m3 = 0.85 R = NL NbXext
e x2 (4.6.2.2.2d-1) where:R = reaction on exterior beam in terms of lanes
NL = number of loaded lanes under consideration
e = eccentricity of a design truck or a design land load from the center of gravity of the pattern of girders (ft.)
x = horizontal distance from the center of gravity of the pat-tern of girders to each girder (ft.)
CSiBridge Bridge Superstructure Design
3 - 14 LLDF Design Example Using Method 2
Xext = horizontal distance from the center of gravity of the pat-tern to the exterior girder (ft.) See Figure 1 for dimen-sions.
One lane loaded (only the leftmost lane applied):
R = 1 624.167 21 2 24.1672
214.522 4.83322
= 0.1667 + 0.310= 0.477 (Fatigue)
Add the multiple presence factor of 1.2 for a single lane: R = 1.2 0.477
= 0.572 (Strength) Two lanes loaded:
R = 2 624.167 21 9 2 24.1672
214.522 4.83322
= 0.333 + 0.443= 0.776
Add the multiple presence factor of 1.0 for two lanes loaded: R = 1.0 0.776
= 0.776 (Strength) Three lanes loaded:
R =
2 2 2
3 624.167 21 9 3 2 24.1672 14.52 4.8332 = 0.5 + 0.399
= 0.899
LLDF Design Example Using Method 2 3 - 15
R = 0.85 0.899 = 0.764 (Strength)
These values do not control over the distribution factors summarized in Design Step 16.
16. From (7) and (9), the service and strength limit state moment distribution factor for the exterior girder is equal to the larger of 0.772 and 0.806 lane. Therefore, the moment distribution factor is 0.806 lane.
From (10) and (12), the service and strength limit state shear distribution factor for the exterior girder is equal to the larger of 0.762 and 0.845 lane. Therefore, the shear distribution factor is 0.845 lane.
Table 3.1 Summary of Service and Strength Limit State Distribution Factors
Load Case Moment interior beams Moment exterior beams Shear interior beams Shear exterior beams Multiple lanes loaded 0.796 0.772 0.973 0.762 Distribution factors from
Tables in 4.6.2.2.2
Single lane loaded 0.542 0.806 0.782 0.845 Multiple lanes loaded NA 0.776 NA 0.776 Additional check for rigidly
connected girders Single lane loaded NA 0.572 NA 0.572
Design Value 0.796 0.806 0.973 0.845
Name and Bridge Object 4 - 1
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., pa-rameters 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 or AASHTO LRFD 2007 code is available for the design of a concrete box girder, the AASHTO 2007 LRFD code is available for the design of a Precast I or U Beam with Composite Slab, and the AASHTO LFRD 2007 for Steel I-Beam with Composite Slab superstructures.
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.
4 - 2 Name and Bridge Object
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
Chapter 4 - Define a Bridge Design Request
Name and Bridge Object 4 - 3
Figure 4-3 Bridge Design Request - Steel I Beam with Composite Slab
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:
4 - 4 Check Type
AASHTO STD 2002 Concrete Box Stress AASHTO LRFD 2007
Concrete Box Stress Concrete Box Flexure
Concrete Box Shear and Torsion Concrete Box Principal
For Multi-Cell Concrete Box Girder bridge, CSiBridge provides the following check type options:
Concrete Box Stress Concrete Box Flexure Concrete Box Shear
For bridge models with precast I or U Beams with Composite Slabs, CSi-Bridge provides three check type options, as follows:
AASHTO LRFD 2007 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 Steel Comp Strength
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 4 - Define a Bridge Design Request
Station Range 4 - 5
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 Pa-rameters form.
4 - 6 Design Parameters
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 f to calculate the compression stress limit c Multiplier on sqrt( f ) to calculate the tension stress limit, given c
in the units specified
The tension limit factor may be specified using either MPa or ksi units for f and the resulting tension limit c
AASHTO LRFD 2007
Concrete Box Stress Concrete Box Stress, PhiC, - Resistance Factor that multiplies both compression and tension stress limits
Concrete Box Stress Factor Compression Limit - Multiplier on f c
to calculate the compression stress limit
Concrete Box Stress Factor Tension Limit Units - Multiplier on sqrt( f ) to calculate the tension stress limit, given in the units c specified
Concrete Box Stress Factor Tension Limit - The tension limit fac-tor may be specified using either MPa or ksi units for f and the c resulting tension limit
Concrete Box Shear Concrete Box Shear, PhiC, - Resistance Factor that multiplies 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. Speci-fies whether the component of inclined flexural compression 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 accordance 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
longi-Chapter 4 - Define a Bridge Design Request
Design Parameters 4 - 7 Table 4-1 Design Request Parameters for Concrete Box Girders
tudinal torsional rebar required
Concrete Box Flexure Concrete Box Flexure, PhiC, - Resistance Factor that multiplies both compression and tension stress limits
Concrete Box Principal See the Box Stress design parameter specifications
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 Cell Concrete Box Stress Factor Compression Limit -
Multi-plier on f to calculate the compression stress limit c
Multi-Cell Concrete Box Stress Factor Tension Limit Units - Mul-tiplier on sqrt( f ) to calculate the tension stress limit, given in c the units specified
Multi-Cell Concrete Box 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
Multi-Cell Concrete Box
Shear Multi-Cell Concrete Box Shear, PhiC, - Resistance Factor that mul-tiplies both compression and tension stress limits Multi-Cell Concrete Box Shear, PhiC, Lightweight Resistance
Fac-tor that multiplies nominal shear resistance to obtain facFac-tored 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 reinforce-ment - 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; De-fault 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 – 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. Cur-rently 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
4 - 8 Design Parameters
Table 4-2 Design Request Parameters for Multi-Cell Concrete Box
Multi-Cell Concrete Box
Flexure Multi-Cell Concrete Box Flexure, PhiC, - Resistance Factor that multiplies both compression and tension stress limits
Table 4-3 Design Request Parameters for Precast I or U Beams
AASHTO
Precast Comp Stress Precast Comp Stress, PhiC, - Resistance Factor that multiplies both compression and tension stress limits
Precast Comp Stress Factor Compression Limit - Multiplier on fc to calculate the compression stress limit
Precast Comp Stress Factor Tension Limit Units - Multiplier on sqrt(fc) to calculate the tension stress limit, given in the units
specified
Precast Comp Stress Factor Tension Limit - The tension limit fac-tor may be specified using either MPa or ksi units for fc and the resulting tension limit
Precast Comp Shear PhiC, - Resistance Factor that multiplies both compression and tension stress limits
PhiC, Lightweight Resistance Factor that multiplies nominal shear resistance to obtain factored resistance for light-weight concrete Negative limit on strain in nonprestressed longitudinal
reinforcement – 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 reinforce-ment - 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 de-termine the required area of transverse rebar in the girder A previously defined rebar material that will be used to determine
the required area of longitudinal rebar in the girder
Precast Comp Flexure Precast Comp Flexure, PhiC, - Resistance Factor that multiplies both compression and tension stress limits
Chapter 4 - Define a Bridge Design Request
Design Parameters 4 - 9 Table 4-4 Design Request Parameters for Steel I-Beam
AASHTO LRFD 2007
Steel I-Beam Strength Positive Yield Moment, My. Yield moment of composite section in positive flexure determined by the program in accordance with section D6.2.2 of the code and user-defined input: Mdnc and Mdc,
the factored permanent load applied before the concrete deck has hardened or is made composite, and the remainder of the fac-tored permanent load (applied to the composite section), respec-tively.
Composite Sections in Negative Flexure. The negative My is cal-culated based on the Mdnc and Mdc demands specified by the user.
Plastic Moment of Composite Section in Positive Flexure. Positive plastic moment, Mp, calculated as the moment of the plastic
forces about the plastic neutral axis.
Plastic Moment of Composite Section in Negative Flexure. Nega-tive plastic moment, Mp, calculated as the moment of the plastic
forces about the plastic neutral axis.
Hybrid Factor Rh for Sections in Positive Flexure. Taken as 1.0 for
rolled shapes, homogenous built-up sections and built-up sec-tions with a higher strength steel in the web than in both flanges. Web Load-Shedding Factor Rb for Section in Positive Flexure.
Taken as equal to 1.0 for composite sections in positive flexure. Web Load-Shedding Factor Rb for Section in Negative Flexure.
Taken as less than or equal to 1.0 for composite sections in nega-tive flexure.
User-defined combinations based on LRFD strength combina-tions. All combos are enveloped and used to calculate D/C ratios. Flange stress, fbu without consideration of flange lateral bending.
If staged construction analysis is not used, fbu is calculated by the
program using the demand moment on the noncomposite sec-tion MNC, the demand moment on the long-term composite
sec-tion MLTC, and the demand moment on the short-term composite
section, MSTC. If staged construction analysis is considered, stresses
on each flange are read directly from the section cut results. Composite Section in Positive Flexure – Compact. Nominal
flex-ural resistance of the section, Dp.
Composite Section in Positive Flexure – Non-Compact. Nominal flexural resistance of the top compression flange and the bottom tension flange used in evaluating the demand over capacity ratio. Local buckling resistance of the compression flange Fnc(FLB) as
specified in Article 6.10.8.2.2.
Local buckling resistance of the compression flange MncFLB as
specified in Article A6.3.2.
Lateral torsional buckling resistance of the compression flange MncLTB as specified in Article A6.3.3.
4 - 10 Demand Sets
Table 4-4 Design Request Parameters for Steel I-Beam
AASHTO LRFD 2007
The nominal flexural resistance of the bottom compression flange is taken as the smaller of the local buckling resistance and the lat-eral torsional buckling resistance.
Nominal shear resistance of unstiffened webs, Vn.
Nominal shear resistance of stiffened interior web panels Nominal shear resistance of web end panels
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.
Stress Design AASHTO-STD-2002 5 - 1
Chapter 5
Design Concrete Box Girder Bridges
This chapter describes the algorithms applied in accordance with the AASHTO STD-2002, LRFD 07 code for design and stress check of the superstructure of a concrete box type bridge deck section.
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 slab.
With respect to shear and torsion check, in accordance with Article 5.8.6 of the code, torsion is considered.
5.1 Stress Design AASHTO-STD-2002
5.1.1 Capacity Parameters
PhiC – Resistance Factor; Default Value = 1.0, Typical value(s): 1.0
5 - 2 Stress Design AASHTO-STD-2002
FactorCompLim – f multiplier; Default Value = 0.4; Typical value(s): 0.4 to c
0.6. The f is multiplied by the FactorCompLim to obtain the compression c
limit.
FactorTensLim – f c multiplier; Default Value = 0.19 (ksi) 0.5(MPa);
Typical value(s): 0 to 0.24 (ksi) 0 to 0.63 (MPa)
The f is multiplied by the FactorTensLim to obtain the tension limit. c
5.1.2 Demand Parameters
FactorCompLim – percentage of the basic unit stress for compression service
design; Default value = 1.0; Typical values 1.0 to 1.5
The demand compressive stresses are divided by the FactorCompLim factor. This way the controlling stress can be selected and compared against one com-pression limit.
FactorTensLim – percentage of the basic unit stress for tension service design;
Default value = 1.0; Typical values 1.0 to 1.5
The demand tensile stresses are divided by the FactorCompLim factor. This way the controlling stress can be selected and compared against one tension limit.
5.1.3 Algorithm
The stresses are evaluated at three points at the top fiber and three points at the bottom fiber. The location of the points are extreme left, Bridge Layout Line and extreme right. The stresses assume linear distribution and take into account axial (P) and both bending moments (M2 and M3).
The stresses are evaluated for each demand set. If the demand set contains live load, the program positions the load to capture extreme stress at each of the evaluation points.
The stresses are divided by the appropriate demand parameter. Then extremes are found for each point and the controlling demand set name is recorded. The stress limits are evaluated by applying the Capacity Parameters (see Sec-tion 5.1.1).
Chapter 5 - Design Concrete Box Girder Bridges
Stress Design AASHTO-LRFD-2007 5 - 3
5.2 Stress Design AASHTO-LRFD-2007
5.2.1 Capacity Parameters
PhiC – Resistance Factor; Default Value = 1.0, Typical value(s): 1.0
The compression and tension limits are multiplied by the C factor
FactorCompLim – f multiplier; Default Value = 0.4; Typical value(s): 0.4 to c
0.6. The f is multiplied by the FactorCompLim to obtain compression limit. c
FactorTensLim – f multiplier; Default Value = 0.19 (ksi) 0.5(MPa); c
Typical value(s): 0 to 0.24 (ksi) 0 to 0.63 (MPa)
The f is multiplied by the FactorTensLim to obtain tension limit c
5.2.2 Algorithm
The stresses are evaluated at three points at the top fiber and three points at the bottom fiber. The location of the points are extreme left, Bridge Layout Line and extreme right. The stresses assume linear distribution and take into account axial (P) and both bending moments (M2 and M3).
The stresses are evaluated for each demand set. 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 re-corded.
The stress limits are evaluated by applying the Capacity Parameters (see Sec-tion 5.2.1).
5.2.3 Stress Design Example
Cross Section: AASHTO Box Beam, Type BIII-48 as shown in Figure 5-1 Concrete unit weight, wc = 0.150 kcf
5 - 4 Stress Design AASHTO-LRFD-2007
Design span = 95.0 ft
Prestressing strands: ½ in. dia., seven wire, low relaxation Area of one strand = 0.153 in2
Ultimate strength fpu = 270.0 ksi Yield strength fpy = 0.9 ksi
fpu = 243 ksi
Modulus of elasticity, Ep = 28 500 ksi
Chapter 5 - Design Concrete Box Girder Bridges
Stress Design AASHTO-LRFD-2007 5 - 5
Figure 5-2 Reinforcement, LRFD 2007 Stress Design AASHTO Box Beam, Type BIII-48
Reinforcing bars:
yield strength, fy = 60.0 ksi
Section Properties
A = area of cross-section of beam = 826 in2
h = overall depth of precast beam = 39 in
I = moment of inertia about centroid of the beam = 170812 in4
yb,yt = distance from centroid to the extreme
bottom (top) fiber of the beam = 19.5 in Demand forces from Dead and PT (COMB1) at station 570:
P = 856.51 kip M3 = 897.599 kip-in Top fiber stress =
3 top top 856 51 897 599 19 5 0 9344 ksi 826 170812 P M . . y . . A I
5 - 6 Flexure Design AASHTO-LRFD-2007
Bottom fiber stress =
3 top bot 856 51 897 599 19 5 1 139 ksi 826 170812 P M . . y . . A I
Stresses reported by CSiBridge:
top fiber stress envelope = 0.9345 ksi bottom fiber stress envelope = 1.13945 ksi
5.3 Flexure Design AASHTO-LRFD-2007
5.3.1 Capacity Parameters
PhiC – Resistance Factor; Default Value = 1.0, Typical value(s): 1.0
The nominal flexural capacity is multiplied by the resistance factor to obtain factored resistance.
5.3.2 Variables
Resistance factor for flexure
Mn Nominal flexural resistance
Mr Factored flexural resistance
tslabeq Equivalent thickness of slab
bslab Effective flange width = horizontal width of slab, measured from out to out
bwebeq Equivalent thickness of all webs in section
Aslab Area of slab
APT Area of PT in tension zone
yPT Distance from extreme compression fiber to the centroid of the prestressing tendons
fpu Specified tensile strength of prestressing steel (area weighted average of all tendons in tensile zone)
Chapter 5 - Design Concrete Box Girder Bridges
Flexure Design AASHTO-LRFD-2007 5 - 7
fpy Yield tensile strength of prestressing steel (area weighted average of all tendons in tensile zone)
fps Average stress in prestressing steel (eq. 5.7.3.1.1-1)
k PT material constant (eq. 5.7.3.1.1-2)
1
Stress block factor is as specified in Section 5.7.2.2.
5.3.3 Design Process
The derivation of the moment resistance of the section is based on approximate stress distribution specified in Article 5.7.2.2. The natural relationship between concrete stress and strain is considered satisfied by an equivalent rectangular concrete compressive stress block of 0.85 f over a zone bounded by the c
edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = β1c from the extreme compression fiber. The distance c is
measured perpendicular to the neutral axis. The factor β1 is taken as 0.85 for concrete strengths not exceeding 4.0 ksi. For concrete strengths exceeding 4.0 ksi, β1 is reduced at a rate of 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi, except that β1 is not to be taken to be less than 0.65.
The flexural resistance is determined in accordance with Paragraph 5.7.3.2. The resistance is evaluated only for bending about horizontal axis 3. Separate capacity is calculated for positive and negative moment. The capacity is based only on bonded tendons defined in the Bridge Object. Mild steel reinforcement is not considered. If there is no prestressing in the tension zone of the section, the capacity is reported as zero. It is assumed that all defined tendons in a sec-tion, stressed or not, have fpe (effective stress after loses) larger than 0.5 fpu (specified tensile strength). If a certain tendon should not be considered for the flexural capacity calculation, its area must be set to zero.
The section properties are calculated for the section before skew, grade, and superelevation are applied. This is consistent with the demands being reported in the section local axis. It is assumed that the effective width of the flange (slab) in compression is equal to the width of the slab.
