Bridge Superstructure Design

Transcription

1 Bridge Superstructure Design AASHTO 2014

2 CSiBridge Bridge Superstructure Design AASHTO 2014 ISO BRG102816M8 Rev. 0 Proudly developed in the United States of America October 2016

3 Copyright Copyright Computers & Structures, Inc., All rights reserved. The CSI Logo and CSiBridge are registered trademarks of Computers & Structures, Inc. Watch & Learn TM 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. 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. info@csiamerica.com (for general information) support@csiamerica.com (for technical support)

4 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.

5 Contents Bridge Superstructure Design 1 Introduction 1.1 Organization Recommended Reading/Practice Define Loads and Load Combinations 2.1 Load Pattern Types Design Load Combinations AASHTO LRFD Code AASHTO LRFD Code with Caltrans Amendments AASHTO LRFD Code with PennDOT Amendments Default Load Combinations 2-9 i

6 CSiBridge Superstructure Design 3 Live Load Distribution 3.1 Methods for Determining Live Load Distribution Determine Live Load Distribution Factors Apply LLD Factors User Specified Calculated by CSiBridge in Accordance with AASHTO LFRD Forces Read Directly from Girders Uniformly Distribution to Girders Generate Virtual Combinations Stress Check Shear or Moment Check Read Forces/Stresses Directly from Girders Stress Check Shear or Moment Check LLD Factor Design Example Using Method Define a Bridge Design Request 4.1 Name and Bridge Object Check Type Station Range Design Parameters Demand Sets Live Load Distribution Factors 4-18 ii

7 Contents 5 Design Concrete Box Girder Bridges 5.1 Stress Design AASHTO LFRD Capacity Parameters Algorithm Stress Design Example Flexure Design AASHTO LRFD Capacity Parameters Variables Design Process Algorithm Flexure Design Example Shear Design AASHTO LRFD Capacity Parameters Variables Design Process Algorithm Shear Design Example Principal Stress Design, AASHTO LRFD Capacity Parameters Demand Parameters Design Multi-Cell Concrete Box Bridges using AMA 6.1 Stress Design Shear Design Variables Design Process Algorithms Flexure Design Variables Design Process Algorithms 6-12 iii

8 CSiBridge Superstructure Design 7 Design Precast Concrete Girder Bridges 7.1 Stress Design Shear Design Variables Design Process Algorithms Shear Design Example Flexure Design Variables Design Process Algorithms Flexure Capacity Design Example Design Steel I-Beam Bridge with Composite Slab 8.1 Section Properties Yield Moments Plastic Moments Section Classification and Factors Demand Sets Demand Flange Stresses f bu and f f Demand Flange Lateral Bending Stress f Depth of the Web in Compression Moment Gradient Modifier C b Strength Design Request Flexure Shear Service Design Request Web Fatigue Design Request Web Fatigue 8-28 iv

9 Contents Flange Fatigue Constructability Design Request Staged (Steel I Comp Construct Stgd) Non-staged (Steel I Comp Construct Non-staged) Slab Status vs Unbraced Length Flexure Shear Section Optimization PennDOT Amendments for DM Design Steel U-Tub Bridge with Composite Slab 9.1 Section Properties Yield Moments Plastic Moments Section Classification and Factors Demand Sets Demand Flange Stresses fbu and ff Demand Flange Lateral Bending Stress f Depth of the Web in Compression Strength Design Request Flexure Shear Service Design Request Web Fatigue Design Request Constructability Design Request Staged (Steel-U Comp Construct Stgd) Non-staged (Steel-U Comp Construct NonStgd) Slab Status vs Unbraced Length 9-22 v

10 CSiBridge Superstructure Design Flexure Shear Section Optimization Run a Bridge Design Request 10.1 Description of Example Model Design Preferences Load Combinations Bridge Design Request Start Design/Check of the Bridge Display Bridge Design Results Bibliography 11.1 Display Results as a Plot Additional Display Examples Display Data Tables Advanced Report Writer Verification vi

11 Chapter 1 Introduction As the ultimate versatile, integrated tool for modeling, analysis, and design of bridge structures, CSiBridge can apply appropriate code-specific design processes to concrete box girder bridge design, design when the superstructure includes Precast Concrete Box bridges with a composite slab and steel I-beam or U-tub bridges with composite slabs. The ease with which these tasks can be accomplished makes CSiBridge the most productive bridge design package in the industry. Design using CSiBridge is based on load patterns, load cases, load combinations 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 design in accordance with the available codes when modeling concrete box girder 1-1

12 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 request 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., loading combinations). Chapter 5 identifies code-specific algorithms used by CSiBridge in completing concrete box girder bridges. Chapter 6 provides codespecific algorithms used by CSiBridge in completing concrete box and multicell 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 optimize a steel U-beam bridge with composite slab. Chapter 10 describes how to run a Design Request using an example that applies the AASHTO LRFD code, and Chapter 11 describes design output for the example in Chapter 10, which can be presented graphically as plots, in data tables, and in reports generated using the Advanced Report Writer feature. 1.2 Recommended Reading/Practice It is strongly recommended that you read this manual and review any applicable Watch & Learn Series tutorials, which are found on our web site, 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

13 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 superstructure. The user may define the load combinations manually or have CSiBridge automatically generate the code generated load combinations. The appropriate design code may be selected using the Design/Rating > Superstructure Design > Preference command. When the code generated load combinations are going to be used, it is important for users to define the load pattern type in accordance with the applicable code. The load pattern type can be defined using the Loads > Load Patterns command. The user options for defining the load pattern types are summarized in the Tables 2-1 and 2-2 for the AASHTO LRFD code. 2.1 Load Pattern Types Tables 2-1 and 2-2 show the permanent and transient load pattern types that can be defined in CSiBridge. The tables also show the AASHTO abbreviation and the load pattern descriptions. Users may choose any name to identify a load pattern type. Load Pattern Types 2-1

14 CSiBridge Bridge Superstructure Design Table 2-1 PERMANENT Load Pattern Types Used in the AASHTO-LRFD Code CSiBridge Load Pattern Type AASHTO Reference Description of Load Pattern Creep CR Force effects due to creep Downdrag DD Downdrag force Dead, Dead Manufacture, Water DL DC Dead load of structural components and nonstructural attachments Wearing Surface DW Superimposed dead load of wearing surfaces and utilities Hor Eearth Pr, Hydrostatic, Passive Earth Pr, Active Earth Pr EH Horizontal earth pressures Locked In EL Misc. locked-in force effects resulting from the construction process Earth Surchr ES Earth surcharge loads Ver Earth Pr EV Vertical earth pressure Prestress, Hyperstatic PS Hyperstatic forces from post-tensioning Shrinkage SH Force effects due to shrinkage Table 2-2 TRANSIENT Load Pattern Types Used in the AASHTO LRFD Design Code CSiBridge Load Pattern Type AASHTO Reference Description of Load Pattern Braking BR Vehicle braking force Centrifugal CE Vehicular centrifugal loads Vehicle Collision CT Vehicular collision force Vessel Collision CV Vessel collision force Quake EQ Earthquake Friction FR Friction effects Ice IC Ice loads Impact IM Vehicle Dynamic Load Allowance Vehicle Live LL Vehicular live load Permit Veh Live LL-P Permit Vehicular live load Vehicle Fatigue LL-F Fatigue Vehicular live load Vehicle Deflection LL-D Deflection Vehicular live load 2-2 Load Pattern Types

15 Chapter 2 - Define Loads and Load Combinations Table 2-2 TRANSIENT Load Pattern Types Used in the AASHTO LRFD Design Code CSiBridge Load Pattern Type AASHTO Reference LL Surchr LS Live load surcharge PedestrianLL PL Pedestrian live load Description of Load Pattern Settlement SE Force effects due settlement Temp Grad TG Temperature gradient loads Temperature TU Uniform temperature effects Water Pr, Stream Flow Bouyancy WA Water load and stream pressure Wind - Live Load WL Wind on live load Wind WS Wind loads on structure 2-3

16 CSiBridge Bridge Superstructure Design 2.2 Design Load Combinations AASHTO LRFD Code The code generated design load combinations make use of the load pattern types noted in Tables 2-1 and 2-2. Table 2-3 shows the load factors and combinations that are required in accordance with the AASHTO LRFD code. Tables 2-4 and 2-5 shows the maximum and minimum factors for the permanent loads in accordance with the AASHTO LRFD code. Two combinations for each permanent load pattern are required because of the maximum and minimum factors. When the default load combinations are used, CSiBridge automatically creates both load combinations (one for the maximum and one for the minimum factor), and then automatically creates a third combination that represents an enveloped combination of the max/min combos AASHTO LRFD Code with Caltrans Amendments Table 2-6 shows the load factors and combinations that are required in accordance with the AASHTO LRFD code with Caltrans amendments AASHTO LRFD Code with PennDOT Amendments Table 2-7 and 2-8 show the load factors and live load vehicles for steel and concrete girder bridges, respectively, that are required in accordance with the AASHTO LRFD code with PennDOT amendments. 2-4 Design Load Combinations

17 Chapter 2 - Define Loads and Load Combinations Table 2-3 Load Combinations and Load Factors Used in the AASHTO LRFD Code Load Combo Limit State DC DD DW EH EV ES EL PS CR SH LL IM CE BR PL LS WA WS WL FR TU TU SE EQ IC CT CV Str I γ P / γ TG γ SE Str II γ P / γ TG γ SE Str III γ P / γ TG γ SE Str IV γ P / Str V γ P / γ TG γ SE Ext Ev I γ P γ EQ Ext Ev II γ P Serv I / 1.20 Serv II / 1.20 Serv III / 1.20 Serv IV / 1.20 γ TG γ SE γ TG γ SE Fatigue I LL, IM & CE Only Fatigue II LL, IM & CE Only Design Load Combinations 2-5

18 CSiBridge Bridge Superstructure Design Table 2-4 Load Factors for Permanent Loads, Type of Load DC: Components and Attachments DC: Strength IV only DD: Downdrag Piles, α Tomlinson Method Piles, λ Method Drilled Shafts, O Neill and Reese (1999) Method γ P, AASHTO LRFD Code Load Factor Maximum Minimum DW: Wearing Surfaces and Utilities EH: Horizontal Earth Pressure Active At-Rest AEP for Anchored Walls EL: Locked in Construction Stresses EV: Vertical Earth Pressure Overall Stability Retaining Walls and Abutments Rigid Buried Structure Rigid Frames Flexible Buried Structures other than Metal Box Culverts Flexible Metal Box Culverts ES: Earth Surcharge N/A N/A Table 2-5 Load Factors for Permanent Loads due to Superimposed Deformations, AASHTO LRFD Code γ P, Superstructures, Segmental Bridge Component PS CR, SH Concrete Substructures supporting Segmental Superstructures 1.0 See Table 2-5, DC Concrete Superstructures, non-segmental Substructures supporting non-segmental Superstructures Using Ig Using Ieffective Steel Substructures Design Load Combinations

19 Chapter 2 - Define Loads and Load Combinations Table 2-6 Load Combinations and Load Factors Used in the AASHTO LRFD Code with Caltrans Amendments Load Combo Limit State DC DD DW EH EV ES EL PS CR SH LL IM CE BR PL LS LL-P IM CE WA WS WL FR TU TU SE EQ IC CT CV Str I γ P / γ TG γ SE Str II γ P / γ TG γ SE Str III γ P / γ TG γ SE Str IV γ P / Str V γ P / γ TG γ SE Ext Ev I 1.00 γ EQ Ext Ev II Serv I / γ TG γ SE Serv II / Serv III / γ TG γ SE Serv IV / Fatigue I LL, IM & CE Only Fatigue II LL-P, IM & CE Only Design Load Combinations 2-7

20 CSiBridge Bridge Superstructure Design Table 2-7 Load factors and Live Load Vehicles for Steel Girder Bridge Used in the AASHTO LRFD Code with PennDOT Amendments Load Combination Limit State DC DW LL IM CE BR LS PL WS Design LL Vehicle (Load Type) Str I 1.25/ / PHL-93 (LL) Str IP 1.25/ / PHL-93 (LL) Str IA 1.25/ / PHL-93 (LL) Str II 1.25/ / P-82 (LL-P) Str III 1.25/ / Str IV / Str V 1.25/ / PHL-93 (LL) Serv II PHL-93 (LL) Serv IIA PHL-93 (LL) Serv IIB P-82 (LL-P) Fatigue I (infinite) LL, IM & CE Only Fatigue II (finite) LL, IM & CE Only DEFL LL, IM CE & BR Only HS20-30(LL-F) HS20-30(LL-F) PenDOT Defl Trk (LL-D) Const/ Uncured Slab / User Defined (LL) 2-8 Design Load Combinations

21 Chapter 2 - Define Loads and Load Combinations Table 2-8 Load factors and Live Load Vehicles for Prestressed Concrete Girder Bridge Used in the AASHTO LRFD Code with PennDOT Amendments Load Combination Limit State DC DW LL IM CE BR LS PL CR SH Design LL Vehicle (Load Type) Str I 1.25/ / PHL-93 (LL) Str IP 1.25/ / PHL-93 (LL) Str IA 1.25/ / PHL-93 (LL) Str II 1.25/ / P-82 (LL-P) Serv I PHL-93 (LL) Serv I with PL PHL-93 (LL) Serv III PHL-93 (LL) Serv III with PL PHL-93 (LL) Serv IIIA Controlling PHL-93 (LL) or P-82 (LL-P) Serv IIIB Controlling PHL-93 (LL) or P-82 (LL-P) Fatigue I (infinite) LL, IM & CE Only DEFL LL, IM CE & BR Only HS20-30(LL-F) PenDOT Defl Trk (LL-D) 2.3 Default Load Combinations Default design load combinations can be activated using the Design/Rating > Load Combinations > Add Default command. Users can set the load combinations by selecting the Bridge Design option, and then choose the amendments from the dropdown box if needed. Users may select the desired limit states and load cases using the Code Generated Load Combinations for Bridge Design form. The forms shown in Figure 2-1 to Figure 2-3 illustrate the options when the AASHTO LRFD code with or without amendments has been selected for design. Default Load Combinations 2-9

22 CSiBridge Bridge Superstructure Design Figure 2-1 Code-Generated Load Combinations for Bridge Design Form AASHTO LRFD 2-10 Default Load Combinations

23 Chapter 2 - Define Loads and Load Combinations Figure 2-2 Code-Generated Load Combinations for Bridge Design Form AASHTO LRFD with PennDOT Amendments for Steel Girders Default Load Combinations 2-11

24 CSiBridge Bridge Superstructure Design Figure 2-3 Code-Generated Load Combinations for Bridge Design Form AASHTO LRFD with PennDOT Amendments for Concrete Girders After the desired limit states and load cases have been selected, CSiBridge will generate all of the code-required load combinations. These can be viewed using the Home > Display > Show Tables command or by using the Show/Modify button on the Define Combinations form, which is shown in Figure Default Load Combinations

25 Chapter 2 - Define Loads and Load Combinations Figure 2-2 Define Load Combinations Form AASHTO LRFD The load combinations denoted as Str-I1, Str-I2, and so forth refer to Strength I load combinations. The load case StrIGroup1 is the name given to enveloped load combination of all of the Strength I combinations. Enveloped load combinations will allow for some efficiency later when the bridge design requests are defined (see Chapter 4). Default Load Combinations 2-13

26 Chapter 3 Live Load Distribution This chapter describes the algorithms used by CSiBridge to determine the live load distribution factors used to assign live load demands to individual girders. An explanation is given with respect to how the distribution factors are applied in a shear, stress, and moment check. The live load distribution factors derived using the code-based Method 2 described in Section 3.1 of this manual are applicable only to superstructures of the following types: precast I- or U-girders with composite slabs, steel I-girders with composite slabs, and multi-cell concrete box girders. These deck section types may also have the live loads distributed based on Methods 1, 3 or 4 described in Section 3.1 of this manual. Legend: Girder = beam + tributary area of composite slab Section Cut = all girders present in the cross-section at the cut location LLD = Live Load Distribution 3.1 Methods for Determining Live Load Distribution CSiBridge gives the user a choice of four methods to address distribution of live load to individual girders. Method 1 The LLD factors are specified directly by the user. 3-1

27 CSiBridge Bridge Superstructure Design Method 2 CSiBridge calculates the LLD factors by following procedures outlined in AASHTO LRFD Section Method 3 CSiBridge reads the calculated live load demands directly from individual girders (available only for Area models). Method 4 CSiBridge distributes the live load uniformly to all girders. It is important to note that to obtain relevant results, the definition of a Moving Load case must be adjusted depending on which method is selected. When the LLD factors are user specified or specified in accordance with the code (Method 1 or 2), only one lane with a MultiLane Scale Factor = 1 should be loaded into a Moving Load cases included in the demand set combinations. When CSiBridge reads the LLD factors directly from individual girders (Method 3, applicable to area and solid models only) or when CSiBridge applies the LLD factors uniformly (Method 4), multiple traffic lanes with relevant Multilane Scale Factors should be loaded in accordance with code requirements. 3.2 Determine Live Load Distribution Factors At every section cut, the following geometric information is evaluated to determine the LLD factors. span length the length of span for which moment or shear is being calculated the number of girders girder designation the first and last girder are designated as exterior girders and the other girders are classified as interior girders roadway width measured as the distance between curbs/barriers; medians are ignored 3-2 Determine Live Load Distribution Factors

28 Chapter 3 - Live Load Distribution overhang consists of the horizontal distance from the centerline of the exterior web of the left exterior beam at deck level to the interior edge of the curb or traffic barrier the beams includes the area, moment of inertia, torsion constant, center of gravity the thickness of the composite slab t1 and the thickness of concrete slab haunch t2 the tributary area of the composite slab which is bounded at the interior girder by the midway distances to neighboring girders and at the exterior girder; includes the entire overhang on one side, and is bounded by the midway distances to neighboring girder on the other side Young s modulus for both the slab and the beams angle of skew support. CSiBridge then evaluates the longitudinal stiffness parameter, Kg, in accordance with AASHTO LRFD (eq ). 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 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; in accordance with code; directly from individual girders; or uniformly distributed onto all girders. Apply LLD Factors 3-3

29 CSiBridge Bridge Superstructure Design 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 Calculated by CSiBridge in Accordance with AASHTO LRFD When this method is selected, CSiBridge considers the data input by the user for truck wheel spacing, minimum distance from wheel to curb/barrier and multiple presence factor for one loaded lane. Depending on the section type, CSiBridge validates several section parameters against requirements specified in the code (AASHTO LRFD Tables b- 1, d-1, a-1 and b-1). When any of the parameter values are outside the range required by the code, the section cut is excluded from the Design Request. At every section cut, CSiBridge then evaluates the live load distribution factors for moment and shear for exterior and interior girders using formulas specified in the code (AASHTO LRFD Tables b-1, d-1, a-1 and b-1). After evaluation, the LLD factor values are assigned to individual girders based on their designation (exterior, interior). The same value equal to the average of the LLD factors calculated for the left and right girders is assigned to both exterior girders. Similarly, all interior girders use the same LLD factors equal to the average of the LLD factors of all of the individual interior girders Forces Read Directly from Girders When this method is selected, CSiBridge sets the live load distribution factor for all girders to Uniformly Distributed to Girders When this method is selected, the live load distribution factor is equal to 1/n where n is the number of girders in the section. All girders have identical LLD 3-4 Apply LLD Factors

30 Chapter 3 - Live Load Distribution factors disregarding their designation (exterior, interior) and demand type (shear, moment). 3.4 Generate Virtual Combinations When the method for determining the live load distribution factors is userspecified, code-specified, or uniformly distributed (Methods 1, 2 or 4), CSiBridge 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 combinations are deleted. The process is repeated for all section cuts selected for design. Four virtual COMBO cases are generated for each COMBO that the user has specified in the Design Request (see Chapter 4). The program analyzes the design type of each load case present in the user specified COMBO and multiplies 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 (exterior 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 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 calculates the stresses on a beam by integrating axial and M3 moment demands on all the beams in the entire section cut and dividing the demands by the number of girders. Similarly, P and M3 forces in the composite slab are integrated and stresses are calculated in the individual tributary areas of the slab by dividing the total slab demand by the number of girders. Generate Virtual Combinations 3-5

31 CSiBridge Bridge Superstructure Design 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 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 individual girders based on their designation. (Forces from two virtual Combinations one for shear and one for moment generated for exterior beam are assigned 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) 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 gravity of the slab tributary area Shear or Moment Check At the Section Cut being analyzed, the girder forces are read from CSiBridge for every COMBO specified in the Design Request. CSiBridge calculates the demands on a girder by integrating axial, M3 and M2 moment demands on the girder at the center of gravity of the girder. 3-6 Read Forces/Stresses Directly from Girders

32 Chapter 3 - Live Load Distribution 3.6 LLD Factor Design Example Using Method 2 The AASHTO LRFD Specifications allow the use of advanced methods of analysis to determine the live load distribution factors. However, for typical bridges, the specifications list equations to calculate the distribution factors for different types of bridge superstructures. The types of superstructures covered by these equations are described in AASHTO LRFD Table From this table, bridges with concrete decks supported on precast concrete I or bulbtee girders are designated as cross-section K. Other tables in AASHTO LRFD list the distribution factors for interior and exterior girders including cross-section K. The distribution factor equations are largely based on work conducted in the NCHRP Project and have been verified to give accurate results compared 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 computations 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 development of the equation. When any of the parameters exceeds the listed value in the range of applicability column, CSiBridge reports the incompliance and excludes the section from design. AASHTO LRFD Article d of the specifications states: In beam-slab bridge cross-sections with diaphragms or cross-frames, the distribution factor for the exterior beam shall not be taken less than that which would be obtained by assuming that the cross-section deflects and rotates as a rigid cross-section. This provision was added to the specifications because the original study that developed the distribution factor equations did not consider intermediate diaphragms. 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 jurisdictions use different types and numbers of intermediate diaphragms. Depending on the number and stiffness of the intermediate diaphragms, the provisions of LLD Factor Design Example Using Method 2 3-7

33 CSiBridge Bridge Superstructure Design AASHTO LRFD d may not be applicable. If the user specifies option Yes in the Diaphragms Present option the program follows the procedure outlined in the provision AASHTO LRFD d. For this example, one deep reinforced concrete diaphragm is located at the midspan of each span. The stiffness of the diaphragm was deemed sufficient to force the cross-section to act as a rigid section; therefore, the provisions of AASHTO LRFD S d apply. Figure 3-1 General Dimensions Required information: AASHTO Type I-Beam (28/72) Noncomposite beam area, A g = 1,085 in 2 Noncomposite beam moment of inertia, I g = 733,320 in 4 Deck slab thickness, t s = 8 in. Span length, L = 110 ft. Girder spacing, S = 9 ft.-8 in. Modulus of elasticity of the beam, E B = 4,696 ksi Modulus of elasticity of the deck, E D = 3,834 ksi C.G. to top of the basic beam = in. C.G. to bottom of the basic beam = in. 1. Calculate n, the modular ratio between the beam and the deck. 3-8 LLD Factor Design Example Using Method 2

34 Chapter 3 - Live Load Distribution n = EB E D (AASHTO ) = = Calculate e g, the distance between the center of gravity of the noncomposite beam and the deck. Ignore the thickness of the haunch in determining e g e g = NAYT + t s 2 = = in. 3. Calculate K g, the longitudinal stiffness parameter. 2 K g = n( I Ae g ) + ( ) = ( ) = in 4. Interior girder. Calculate the moment distribution factor for an interior beam with two or more design lanes loaded using AASHTO LRFD Table S b D M = ( ) ( ) ( ) S 9.5 S L K 12.0Lt g ( ) ( ) ( )( ) s { } 0.1 = = lane (eq. 1) 5. In accordance with AASHTO LRFD e, a skew correction factor for moment may be applied for bridge skews greater than 30 degrees. The bridge in this example is skewed 20 degrees, and therefore, no skew correction factor for moment is allowed. Calculate the moment distribution factor for an interior beam with one design lane loaded using AASHTO LRFD Table b D M = ( ) ( ) ( ) S 14 S L K 12.0Lt g = ( ) ( ) ( )( ) s { } = lane (eq. 2) LLD Factor Design Example Using Method 2 3-9

35 CSiBridge Bridge Superstructure Design 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 determine the factor used for the fatigue limit state. 6. Skew correction factor for shear. In accordance with AASHTO LRFD c, 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 AASHTO LRFD Table c-1. 3 S C = ( ) Lt K tanθ s 3 = ( 110)( 8) tan 20 = g ( ) Calculate the shear distribution factor for an interior beam with two or more design lanes loaded using AASHTO LRFD Table S a-1. D V = ( ) ( ) S 12 S 35 = ( ) ( ) 2 = lane Apply the skew correction factor: D V = 1.047( 0.929) = lane (eq. 4) 8. Calculate the shear distribution factor for an interior beam with one design lane loaded using AASHTO LRFD Table S a-1. D V = ( S 25.0) = ( ) 3-10 LLD Factor Design Example Using Method 2

36 Chapter 3 - Live Load Distribution = lane Apply the skew correction factor: D V = ( ) = 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 and lane. Therefore, the moment distribution factor is lane. From (4) and (5), the service and strength limit state shear distribution factor for the interior girder is equal to the larger of and lane. Therefore, the shear distribution factor is lane. 10. Exterior girder 11. Calculate the moment distribution factor for an exterior beam with two or more design lanes using AASHTO LRFD Table d-1. D M = e DVinterior e = de 9.1 where de is the distance from the centerline of the exterior girder to the inside face of the curb or barrier. e = /9.1 = 0.97 D M = 0.97(0.796) = lane (eq. (7) 12. Calculate the moment distribution factor for an exterior beam with one design lane using the lever rule in accordance with AASHTO LRFD Table d-1. LLD Factor Design Example Using Method

37 CSiBridge Bridge Superstructure Design Figure 3-2 Lever Rule [ ] D M = ( ) = wheels 2 = lane (eq. 8) Notice that this value does not include the multiple presence factor, therefore, it is adequate for use with the fatigue limit state. For service and strength limit states, the multiple presence factor for a single lane loaded needs to be included. D M = 0.672( 1.2 ) = lane (eq. 9) (Strength and Service) 13. Calculate the shear distribution factor for an exterior beam with two or more design lanes loaded using AASHTO LRFD Table b-1. D V = e DVinterior 3-12 LLD Factor Design Example Using Method 2

38 Chapter 3 - Live Load Distribution where: e = de 10 = = D V = 0.783( ) = lane (eq. 10) 14. Calculate the shear distribution factor for an exterior beam with one design lane loaded using the lever rule in accordance with AASHTO LRFD Table b-1. This value will be the same as the moment distribution factor with the skew correction factor applied. D V = ( ) = lane (eq. 12) (Strength and Service) Notice that AASHTO LRFD d includes additional requirements for the calculation of the distribution factors for exterior girders when the girders are connected with relatively stiff cross-frames that force the cross-section to act as a rigid section. As indicated in the introduction, these provisions are applied to this example; the calculations are shown below. 15. Additional check for rigidly connected girders (AASHTO LRFD d) The multiple presence factor, m, is applied to the reaction of the exterior beam (AASHTO LRFD Table ) m 1 = 1.20 m 2 = 1.00 m 3 = R = N N + X ( e) x ( d-1) where: L b ext LLD Factor Design Example Using Method

39 CSiBridge Bridge Superstructure Design R = reaction on exterior beam in terms of lanes N L = number of loaded lanes under consideration e x = eccentricity of a design truck or a design land load from the center of gravity of the pattern of girders (ft.) = horizontal distance from the center of gravity of the pattern of girders to each girder (ft.) X ext = horizontal distance from the center of gravity of the pattern to the exterior girder (ft.) See Figure 1 for dimensions. One lane loaded (only the leftmost lane applied): ( ) R = ( 21) 2 ( ) + ( 14.52) + ( ) = = (Fatigue) Add the multiple presence factor of 1.2 for a single lane: R = ( ) = (Strength) Two lanes loaded: R = ( 21+ 9) 2 ( ) + ( 14.52) + ( ) = = ( ) Add the multiple presence factor of 1.0 for two lanes loaded: R = ( ) = (Strength) 3-14 LLD Factor Design Example Using Method 2

40 Chapter 3 - Live Load Distribution Three lanes loaded: R = ( ) ( ) 2 ( ) + ( 14.52) + ( ) = = Add the multiple presence factor of 0.85 for three or more lanes loaded: R = ( ) = (Strength) These values do not control over the distribution factors summarized in Design Step From (7) and (9), the service and strength limit state moment distribution factor for the exterior girder is equal to the larger of and lane. Therefore, the moment distribution factor is lane. From (10) and (12), the service and strength limit state shear distribution factor for the exterior girder is equal to the larger of and lane. Therefore, the shear distribution factor is lane. Table 3-1 Summary of Service and Strength Limit State Distribution Factors -- AASHTO LRFD Load Case Moment interior beams Moment exterior beams Shear interior beams Shear exterior beams Multiple lanes loaded Distribution factors from Tables in Single lane loaded Additional check for rigidly connected girders Multiple lanes loaded NA NA Single lane loaded NA NA Design Value Value reported by CSiBridge LLD Factor Design Example Using Method

41 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, precast 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., parameters that may be used to overwrite the default values automatically set by the program) and demand sets (i.e., the load combination[s] to be considered). Multiple Bridge Design Requests may be defined for the same bridge object. Before defining a design request, the applicable code should be specified using the Design/Rating > Superstructure > Preferences command. Currently, the AASHTO STD 2002, AASHTO LRFD 2007, AASHTO LRFD 2012, CAN/CSA S6, EN 1992, and Indian IRC codes are available for the design of a concrete box girder; the AASHTO 2007 LRFD, AASHTO LRFD 2012, AASHTO LRFD 2014, CAN/CSA S6, EN 1992, and Indian IRC codes are available for the design of a Precast I or U Beam with Composite Slab; the AASHTO LFRD 2007, AASHTO LRFD 2012, AASHTO LRFD 2014, CAN/CSA S6, and EN are available for Steel I-Beam with Composite Slab superstructures; and the AASHTO LRFD 2012 and AASHTO LRFD 2014 are available for a U tub bridge with a composite slab. Name and Bridge Object 4-1

42 CSiBridge Bridge Superstructure Design 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

43 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

44 CSiBridge Bridge Superstructure Design 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 available from the Bridge Object drop-down list. 4.2 Check Type The Check Type refers to the type of design to be performed and the available options depend on the type of bridge deck being modeled. For a Concrete Box Girder bridge, CSiBridge provides the following check type options: AASHTO STD 2002 Concrete Box Stress AASHTO LRFD Concrete Box Stress Concrete Box Flexure Concrete Box Shear and Torsion Concrete Box Principal CAN/CSA S6, and EN and IRC: 112 Concrete Box Stress Concrete Box Flexure Concrete Box Shear For Multi-Cell Concrete Box Girder bridge, CSiBridge provides the following check type options: 4-4 Name and Bridge Object

45 Chapter 4 - Define a Bridge Design Request AASHTO LRFD, CAN/CSA S6, EN , and IRC: 112 Concrete Box Stress Concrete Box Flexure Concrete Box Shear For bridge models with precast I or U Beams with Composite Slabs, CSiBridge provides three check type options, as follows: AASHTO LRFD, CAN/CSA S6, EN , and IRC: 112 Precast Comp Stress Precast Comp Shear Precast Comp Flexure For bridge models with steel I-beam with composite slab superstructures, CSiBridge provides the following check type option: AASHTO LRFD Steel Comp Strength Steel Comp Service Steel Comp Fatigue Steel Comp Constructability Staged Steel Comp Constructability NonStaged EN :2005 Steel Comp Ultimate Steel Comp Service Stresses Steel Comp Service Rebar Steel Comp Constructability Staged Check Type 4-5

46 CSiBridge Bridge Superstructure Design Steel Comp Constructability NonStaged For bridge models with steel U-tub with composite slab superstructures, CSiBridge provides the following check type option: AASHTO LRFD Steel Comp Strength Steel Comp Service Steel Comp Fatigue Steel Comp Constructability Staged 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 determines if the superstructure forces are to be considered before or at a station point. The user may choose the location type as before the point, after the point, or both. 4.4 Design Parameters Design parameters are overwrites that can be used to change the default values set automatically by the program. The parameters are specific to each code, 4-6 Station Range

47 Chapter 4 - Define a Bridge Design Request deck type, and check type. Figure 4-4 shows the Superstructure Design Request Parameters form. Figure 4-3 Superstructure Design Request Parameters form Table 4-1 shows the parameters for concrete box girder bridges. Table 4-2 shows the parameters for multi-cell concrete box bridges. Table 4-3 shows the parameters applicable when the superstructure has a deck that includes precast I or U girders with composite slabs. Table 4-4 shows the parameters applicable when the superstructure has a deck that includes steel I-beams. Table 4-1 Design Request Parameters for Concrete Box Girders AASHTO STD 2002 Concrete Box Stress Resistance Factor - multiplies both compression and tension stress limits Multiplier on f c to calculate the compression stress limit Multiplier on sqrt( f c ) 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 f c and the resulting tension limit Design Parameters 4-7

48 CSiBridge Bridge Superstructure Design Table 4-1 Design Request Parameters for Concrete Box Girders AASHTO LRFD Concrete Box Stress Concrete Box Shear Concrete Box Flexure 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 c ) 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 f c and the resulting tension limit 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. Specifies 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 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 longitudinal torsional rebar required Concrete Box Flexure, PhiC, - Resistance Factor that multiplies 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 f c 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 f c and the resulting tension limit Concrete Box Shear Phi Concrete ϕc -- Resistance factor for concrete (see CSA 4-8 Design Parameters

49 Chapter 4 - Define a Bridge Design Request Table 4-1 Design Request Parameters for Concrete Box Girders Clause 8.4.6) Concrete Box Flexure Phi PT ϕp -- Resistance factor for tendons (see CSA Clause 8.4.6) Cracking Strength Factor Multiplies sqrt( f c cracking strength ) to obtain EpsilonX Negative Limit -- Longitudinal negative strain limit (see Clause ) EpsilonX Positive Limit -- Longitudinal positive strain limit (see Clause ) 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 reinforcement Bottom Slab rebar cover Distance from the outside face of the bottoms lab to the centerline of the exterior closed transverse 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 Concrete Box Shear Compression limit Multiplier on fc k to calculate the compression stress limit Tension limit Multiplier on fc k to calculate the tension stress limit 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. Design Parameters 4-9

50 CSiBridge Bridge Superstructure Design Table 4-1 Design Request Parameters for Concrete Box Girders The value must be between 21.8 degrees and 45 degrees. Concrete Box Flexure Factor for PT Duct Diameter Factor that multiplies posttensioning 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 transmission length of the post tensioning used in shear resistance 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 section to get the lower limit of the inner lever arm z of the section. 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. Type of Section Type of section for shear design. Determining Factor Nu1 Method that will be used to calculate 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 longitudinal 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 posttensioning. Multiplies fpk to obtain the stress in the tendons after losses. Typical value between 0.4 and Design Parameters

51 Chapter 4 - Define a Bridge Design Request Table 4-2 Design Request Parameters for Multi-Cell Concrete Box AASHTO LRFD Multi-Cell Concrete Box Stress Multi-Cell Concrete Box Shear Multi-Cell Concrete Box Flexure 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 f c to calculate the compression stress limit Multi-Cell Concrete Box Stress Factor Tension Limit Units - Multiplier on sqrt ( f c ) to calculate the tension stress limit, given in 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, PhiC, - Resistance Factor that multiplies both compression and tension stress limits Multi-Cell Concrete Box Shear, 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 ; Default Value = -0.4x10-3, Typical value(s): 0 to -0.4x10-3 Positive limit on strain in nonprestressed longitudinal reinforcement - in accordance with section ; Default Value = 6.0x10-3, Typical value(s): 6.0x10-3 PhiC for Nu - Resistance Factor used in equation ; Default Value = 1.0, Typical value(s): 0.75 to 1.0 Phif for Mu - Resistance Factor used in equation ; 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 or Vci Vcw method in accordance with 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 determine the required area of longitudinal rebar in the girder Multi-Cell Concrete Box Flexure, PhiC, - Resistance Factor that multiplies both compression and tension stress limits CAN/CSA S6 Design Parameters 4-11

52 CSiBridge Bridge Superstructure Design Table 4-2 Design Request Parameters for Multi-Cell Concrete Box Multi-Cell Concrete Multi-Cell Concrete Box Stress Factor Compression Limit - Box Stress Multiplier on f c to calculate the compression stress limit Multi-Cell Concrete Box Shear Multi-Cell Concrete Box Flexure Eurocode EN 1992 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 Highway Class The highway class shall be determined in accordance with CSA Clause , Table 1.1 for the average daily traffic and average daily truck traffic volumes for which the structure is designed 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) Cracking Strength Factor -- Multiplies sqrt( f c ) to obtain cracking strength EpsilonX Negative Limit -- Longitudinal negative strain limit (see Clause ) EpsilonX Positive Limit -- Longitudinal positive strain limit (see Clause ) Shear Rebar Material A previously defined rebar material 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 Highway Class The highway class shall be determined in accordance with CSA Clause , Table 1.1 for the average daily traffic and average daily truck traffic volumes for which the structure is designed 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) Multi-Cell Concrete Box Stress Compression limit Multiplier on fc k to calculate the compression stress limit 4-12 Design Parameters

53 Chapter 4 - Define a Bridge Design Request Table 4-2 Design Request Parameters for Multi-Cell Concrete Box Multi-Cell Concrete Box Shear Tension limit Multiplier on fc k to calculate the tension stress limit 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 posttensioning 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 transmission length of the post tensioning used in shear resistance 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 section to get the lower limit of the inner lever arm z of the section. 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. Type of Section Type of section for shear design. Determining Factor Nu1 Method that will be used to calculate 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 longitudinal rebar in the girder. Design Parameters 4-13

54 CSiBridge Bridge Superstructure Design Table 4-2 Design Request Parameters for Multi-Cell Concrete Box Multi-Cell Concrete Gamma c for Concrete Partial safety factor for concrete. Box Flexure 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 posttensioning. Multiplies fpk to obtain the stress in the tendons after losses. Typical value between 0.4 and 0.9. Table 4-3 Design Request Parameters for Precast I or U Beams AASHTO LRFD Precast Comp Stress Precast Comp Shear Precast Comp Stress, PhiC, - Resistance Factor that multiplies 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 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 ; Default Value = -0.4x10-3, Typical value(s): 0 to -0.4x Design Parameters

55 Chapter 4 - Define a Bridge Design Request Table 4-3 Design Request Parameters for Precast I or U Beams Precast Comp Flexure CAN/CSA S6 Precast Comp Stress Precast Comp Shear Positive limit on strain in nonprestressed longitudinal reinforcement - in accordance with section ; Default Value = 6.0x10-3, Typical value(s): 6.0x10-3 PhiC for Nu - Resistance Factor used in equation ; Default Value = 1.0, Typical value(s): 0.75 to 1.0 Phif for Mu - Resistance Factor used in equation ; 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 or Vci Vcw method in accordance with 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 determine the required area of longitudinal rebar in the girder Precast Comp Flexure, PhiC, - Resistance Factor that multiplies 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 - The tension limit factor may be specified using either MPa or ksi units for f c and the resulting tension limit Highway Class The highway class shall be determined in accordance with CSA Clause , Table 1.1 for the average daily traffic and average daily truck traffic volumes for which the structure is designed 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) Cracking Strength Factor -- Multiplies sqrt( f c ) to obtain cracking strength EpsilonX Negative Limit -- Longitudinal negative strain limit (see Clause ) EpsilonX Positive Limit -- Longitudinal positive strain limit (see Clause ) Shear Rebar Material A previously defined rebar material label that will be used to determine the required area of transverse rebar in the girder. Design Parameters 4-15

56 CSiBridge Bridge Superstructure Design Table 4-3 Design Request Parameters for Precast I or U Beams Precast Comp Flexure Eurocode EN 1992 Precast Comp Stress Precast Comp Shear Longitudinal Rebar Material A previously defined rebar material that will be used to determine the required area of longitudinal rebar n the girder Highway Class The highway class shall be determined in accordance with CSA Clause , Table 1.1 for the average daily traffic and average daily truck traffic volumes for which the structure is designed 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) Compression limit Multiplier on fc k to calculate the compression stress limit Tension limit Multiplier on fc k to calculate the tension stress limit 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 transmission length of the post tensioning used in shear resistance 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 section to get the lower limit of the inner lever arm z of the section. 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. Type of Section Type of section for shear design. Determining Factor Nu1 Method that will be used to calculate the η1 factor. Factor Nu1 η1 factor 4-16 Design Parameters

57 Chapter 4 - Define a Bridge Design Request Table 4-3 Design Request Parameters for Precast I or U Beams Precast Comp Flexure 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 longitudinal 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 posttensioning. Multiplies fpk to obtain the stress in the tendons after losses. Typical value between 0.4 and 0.9. Table 4-4 Design Request Parameters for Steel I-Beam AASHTO LRFD Steel I-Beam - Resistance factor Phi for flexure Strength Resistance factor Phi for shear Do webs have longitudinal stiffeners? Use Stage Analysis load case to determine stresses on composite section? Multiplies short term modular ratio (Es/Ec) to obtain long-term modular ratio Use AASHTO, Appendix A to determine resistance in negative moment regions? Steel I Beam Comp - Service Use Stage Analysis load case to determine stresses on composite section? Shored Construction? Does concrete slab resist tension? Multiplies short term modular ratio (Es/Ec) to obtain long-term modular ratio Design Parameters 4-17

58 CSiBridge Bridge Superstructure Design Table 4-4 Design Request Parameters for Steel I-Beam Steel-I Comp - There are no user defined design request parameters for Fatigue fatigue Steel I Comp Resistance factor Phi for flexure Construct Stgd Resistance factor Phi for shear Resistance factor Phi for Concrete in Tension Do webs have longitudinal stiffeners? Steel I Comp Construct Non Stgd Concrete modulus of rupture factor in accordance with AASHTO LRFD Section , 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 Resistance factor Phi for flexure Resistance factor Phi for shear Resistance factor Phi for Concrete in Tension Do webs have longitudinal stiffeners? Concrete modulus of rupture factor in accordance with AASHTO LRFD Section , 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 considered 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 Demand Sets

59 Chapter 5 Design Concrete Box Girder Bridges This chapter describes the algorithms applied in accordance with the AASHTO LRFD 2014 (AASHTO LRFD) for design and stress check of the superstructure of a concrete box type bridge deck section. When interim revisions of the codes are published by the relevant authorities, and (when applicable) they are subsequently incorporated into CSiBridge, the program gives the user an option to select what type of interims shall be used for the design. The interims can be selected by clicking on the Code Preferences button. In CSiBridge, when distributing loads for concrete box design, the section is always treated as one beam; all load demands (permanent and transient) are distributed evenly to the webs for stress and flexure and proportionally to the slope of the web for shear. Torsion effects are always considered and assigned to the outer webs and the top and bottom slabs. With respect to shear and torsion check, in accordance with AASHTO Article 5.8.6, torsion is considered. The user has an option to select No Interims or YYYY Interims on the Bridge Design Preferences form. The form can be opened by clicking the Code Preferences button. 5-1

60 CSiBridge Bridge Superstructure Design The revisions published in the 2015 interims were incorporated into the Flexure Design. 5.1 Stress Design AASHTO LRFD Capacity Parameters PhiC Resistance Factor; Default Value = 1.0, Typical value: 1.0 The compression and tension limits are multiplied by the φ C factor FactorCompLim f c multiplier; Default Value = 0.4; Typical values: 0.4 to 0.6. The f c is multiplied by the FactorCompLim to obtain the compression limit. FactorTensLim f c multiplier; Default Values = 0.19 (ksi), 0.5(MPa); Typical values: 0 to 0.24 (ksi), 0 to 0.63 (MPa). The FactorTensLim to obtain the tension limit. f c is multiplied by the Algorithm The stresses are evaluated at three points at the top fiber and three points at the bottom fiber: extreme left, Bridge Layout Line, and extreme right. The stresses assume linear distribution and take into account axial (P) and both bending moments (M2 and M3). The stresses are evaluated for each demand set (Chapter 4). If the demand set contains live load, the program positions the load to capture extreme stress at each of the evaluation points. Extremes are found for each point and the controlling demand set name is recorded. The stress limits are evaluated by applying the Capacity Parameters (see Section 5.2.1). 5-2 Stress Design AASHTO LRFD

61 Chapter 5 - Design Concrete Box Girder Bridges Stress Design Example Cross Section: AASHTO Box Beam, Type BIII-48 as shown in Figure 5-1 Figure 5-1 AASHTO LRFD Stress Design, AASHTO Box Beam, Type BIII- 48 Concrete unit weight, w c = kcf Concrete strength at 28 days, f c = 5.0 ksi Design span = 95.0 ft Prestressing strands: ½ in. dia., seven wire, low relaxation Area of one strand = in 2 Ultimate strength f pu = ksi Yield strength f py = 0.9 ksi f pu = 243 ksi Modulus of elasticity, E p = ksi Stress Design AASHTO LRFD 5-3

62 CSiBridge Bridge Superstructure Design Figure 5-2 Reinforcement, AASHTO LRFD Stress Design AASHTO Box Beam, Type BIII-48 Reinforcing bars: yield strength, f y = 60.0 ksi Section Properties A = area of cross-section of beam = 826 in 2 h = overall depth of precast beam = 39 in I = moment of inertia about centroid of the beam = in 4 y b,y t = 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 = kip M3 = kip-in Top fiber stress = P M σ top = y top = 19.5 = ksi A I Stress Design AASHTO LRFD

63 Chapter 5 - Design Concrete Box Girder Bridges Bottom fiber stress = P M σ bot = + y bot = = 1.139ksi A I Stresses reported by CSiBridge: top fiber stress envelope = ksi bottom fiber stress envelope = ksi 5.2 Flexure Design AASHTO LRFD Capacity Parameters PhiC Resistance Factor; Default Value = 1.0, Typical value: 1.0 The nominal flexural capacity is multiplied by the resistance factor to obtain factored resistance Variables A PS Area of PT in the tension zone A S A slab b slab b webeq d P d S Area of reinforcement in the tension zone Area of the slab Effective flange width = horizontal width of the slab, measured from out to out Equivalent thickness of all webs in the section Distance from the extreme compression fiber to the centroid of the prestressing tendons Distance from the extreme compression fiber to the centroid of rebar in the tension zone f ps Average stress in prestressing steel (AASHTO LRFD eq ) f pu Specified tensile strength of prestressing steel (area weighted average of all tendons in the tensile zone) Flexure Design AASHTO LRFD 5-5

64 CSiBridge Bridge Superstructure Design f py f y Yield tensile strength of prestressing steel (area weighted average of all tendons in the tensile zone) Yield strength of rebar k PT material constant (AASHTO LRFD eq ) M n M r t slabeq αα 1 Nominal flexural resistance Factored flexural resistance Equivalent thickness of the slab Stress block factor, as specified in AASHTO LRFD 2015 Interim Section β 1 Stress block factor, as specified in AASHTO LRFD Section φ Resistance factor for flexure Design Process The derivation of the moment resistance of the section is based on the approximate stress distribution specified in AASHTO LRFD Article The natural relationship between concrete stress and strain is considered satisfied by an equivalent rectangular concrete compressive stress block of αα 1 ff cc over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = β 1c from the extreme compression fiber. If the AASHTO LRFD 2015 interim is selected the factor αα 1 is taken as 0.85 for specified compressive strengths not exceeding 10.0 ksi. For specified concrete compressive strengths exceeding 10.0ksi, αα 1 is reduced at rate of 0.02 for each 1.0ksi of strength in excess of 10.0ksi, except that αα 1 is not taken less than For AASHTO LRFD no interim the αα 1 is always taken as 0.85 independent of concrete compressive strength. The factor The distance c is measured perpendicular to the neutral axis. The factor β 1 is taken as 0.85 for concrete strengths not exceeding 4.0 ksi. For concrete strengths exceeding 4.0 ksi, β 1 is reduced at a rate of 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi, except that β 1 is not to be taken to be less than Flexure Design AASHTO LRFD

65 Chapter 5 - Design Concrete Box Girder Bridges The flexural resistance is determined in accordance with AASHTO LRFD Paragraph The resistance is evaluated for bending about horizontal axis 3 only. Separate capacity is calculated for positive and negative moment. The capacity is based on bonded tendons and mild steel located in the tension zone as defined in the Bridge Object. Tendons and mild steel reinforcement located in the compression zone are not considered. It is assumed that all defined tendons in a section, stressed or not, have f pe (effective stress after loses) larger than 0.5 f pu (specified tensile strength). If a certain tendon should not be 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 have been applied. This is consistent with the demands being reported in the section local axis. It is assumed that the effective width of the flange (slab) in compression is equal to the width of the slab Algorithm At each section: All section properties and demands are converted from CSiBridge model units to N, mm. The equivalent slab thickness is evaluated based on the slab area and slab width, assuming a rectangular shape. t slabeq = A b slab slab The equivalent web thickness is evaluated as the summation of all web horizontal thicknesses. b webeq nweb = b 1 web The αα 1 stress block factor is evaluated in accordance with AASHTO LRFD based on section f c For AASHTO LRFD 2015 Interim Flexure Design AASHTO LRFD 5-7

66 CSiBridge Bridge Superstructure Design iiii ff cc > 10.0kkkkkk, ttheeee αα 1 = mmmmmm 0.85 ff cc ; else αα 1 = 0.85 For AASHTO LRFD No Interim αα 1 = 0.85 The β 1 stress block factor is evaluated in accordance with AASHTO LRFD based on section f c f c 28 If f c > 28 MPa, then β 1 = max ; 0.65 ; 7 else β 1 = The tendon and rebar location, area, and material are read. Only bonded tendons are processed; unbonded tendons are ignored. Tendons and rebar are split into two groups depending on which sign of moment they resist negative or positive. A tendon or rebar is considered to resist a positive moment when it is located outside of the top fiber compression stress block and is considered to resist a negative moment when it is located outside of the bottom fiber compression stress block. The compression stress block extends over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = β 1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis. For each tendon group, an area weighted average of the following values is determined: sum of the tendon areas, A PS distance from the extreme compression fiber to the centroid of prestressing tendons, d P specified tensile strength of prestressing steel, f pu constant k (AASHTO LRFD eq ) 5-8 Flexure Design AASHTO LRFD

67 Chapter 5 - Design Concrete Box Girder Bridges For each rebar group, the following values are determined: sum of the tension rebar areas, A s distance from the extreme compression fiber to the centroid of the tension rebar, d s The distance c between the neutral axis and the compressive face is evaluated in accordance with (AASHTO LRFD eq ). APS fpu + Af s s c = f α β + pu 1 f c 1bslab kaps d p The distance c is compared against requirement of Section to verify if stress in mild reinforcement f s can be taken as equal to f y. The limit on ratio c/d s is calculated depending on what kind of code and its interim are specified in the Bridge Design Preferences form as shown in the table below: Code AASHTO LRFD 2012 No Interims AASHTO LRFD 2012 with 2013 Interims or later cc dd ss εε cccc where the compression control strain limit εε cccc is per AASHTO LRFD 2013 Interims table C When the limit is not satisfied the stress in mild reinforcement f s is reduced to satisfy the requirement of Section The distance c is compared to the equivalent slab thickness to determine if the section is a T-section or rectangular section. If cβ 1 > tslabeq, the section is a T-section. Flexure Design AASHTO LRFD 5-9

68 CSiBridge Bridge Superstructure Design If the section is a T-section, the distance c is recalculated in accordance with (AASHTO LRFD eq ). ( ) A f + Af α f b b t c = f α β + PS PU s s 1 c slab webeq slabeq pu 1 f c 1bwebeq kaps y pt Average stress in prestressing steel f ps is calculated in accordance with (AASHTO LRFD eq ). c fps = fpu 1 k d p Nominal flexural resistance M n is calculated in accordance with (AASHTO LRFD eq ). If the section is a T-section, cβ cβ cβ t M A f d A f d f ( b b ) t slabeq n = PS PS p + S s s +α1 c slab webeq slabeq ; else cβ1 cβ1 Mn = APS fps dp + AS fs d s. 2 2 Factored flexural resistance is obtained by multiplying M n by φ. M r = φm n Extreme moment M3 demands are found from the specified demand sets and the controlling demand set name is recorded Flexure Design Example Cross Section: AASHTO Box Beam, Type BIII-48, as shown in Figure 5-3. Concrete unit weight, w c = kcf Concrete strength at 28 days, f = 5.0 ksi (~ MPa) Design span = 95.0 ft c 5-10 Flexure Design AASHTO LRFD

69 Chapter 5 - Design Concrete Box Girder Bridges Prestressing strands: ½ in. dia., seven wire, low relaxation Area of one strand = in 2 Ultimate strength f pu = ksi Yield strength f py = 0.9 ksi f pu = 243 ksi Modulus of elasticity, E p = ksi Reinforcing bar yield strength, f y = 60.0 ksi Figure 5-3 LRFD Flexure Design Cross-Section, AASHTO Box Beam, Type BIII-48 Flexure Design AASHTO LRFD 5-11

70 CSiBridge Bridge Superstructure Design Figure 5-4 Reinforcement, AASHTO LRFD Flexure Design Cross-Section, AASHTO Box Beam, Type BIII-48 Section Properties A = area of cross-section of beam = 826 in 2 h = overall depth of precast beam = 39 in I = moment of inertia about centroid of the beam = in 4 y b, y t = 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 = kip M3 = kip-in The equivalent slab thickness is evaluated based on the slab area and slab width, assuming a rectangular shape. t A slab slabeq = = = bslab in Value reported by CSiBridge = 5.5 in The equivalent web thickness is evaluated as the summation of all web horizontal thicknesses Flexure Design AASHTO LRFD

71 Chapter 5 - Design Concrete Box Girder Bridges b webeq nweb = b = = 10 in 1 web Value reported by CSiBridge = 10.0 in Tendons are split into two groups depending on which sign of moment they resist negative or positive. A tendon is considered to resist a positive moment when it is located outside of the top fiber compression stress block and is considered to resist a negative moment when it is located outside of the bottom fiber compression stress block. The compression stress block extends over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = β 1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis. For each tendon group, an area weighted average of the following values is determined: 2 sum of the tendon areas, A ( ) PTbottom = = in Value reported by CSiBridge = in 2 distance from the center of gravity of the tendons to the extreme compression fiber, y PT bottom = 39 = in Value reported by CSiBridge = = in specified tensile strength of prestressing steel, f pu = 270 kip Value reported by CSiBridge = 270 kip constant k (AASHTO LRFD eq ) fpy 243 k = = = 0.28 fpu 270 Value reported by CSiBridge = 0.28 The β 1 stress block factor is evaluated in accordance with AASHTO LRFD based on section f c. Flexure Design AASHTO LRFD 5-13

72 CSiBridge Bridge Superstructure Design If f c > 28 MPa, then f c 28 β 1 = max ; = max ;0.65 = Value calculated by CSiBridge = (not reported) The distance c between the neutral axis and the compressive face is evaluated in accordance with (AASHTO LRFD eq ). c = 0.85 A PT f pu pu f β c 1bslab + kapt y pt f = = 6.91in Value calculated by CSiBridge = in (not reported) The distance c is compared to the equivalent slab thickness to determine if the section is a T-section or a rectangular section. If cβ 1 > tslabeq = 5.56 in > 5.5in, the section is a T-section. Value reported by CSiBridge, section = T-section If the section is a T-section, the distance c is recalculated in accordance with (AASHTO LRFD eq ). APT fpu 0.85 f c( bslab bwebeq ) tslabeq c = = f 0.85 pu f β c 1bwebeq + kapt y pt (48 10) Value reported by CSiBridge = in = in Average stress in prestressing steel f ps is calculated in accordance with (AASHTO LRFD eq ) Flexure Design AASHTO LRFD

73 Chapter 5 - Design Concrete Box Girder Bridges c fps = fpu 1 k ksi y = = pt Value reported by CSiBridge = ksi Nominal flexural resistance M n is calculated in accordance with (AASHTO LRFD ). If the section is a T-section, then cβ1 cβ t 1 slabeq Mn = APT fps ypt f c ( bslab bwebeq ) tslabeq = ( 48 10) = kip-in Value calculated by CSiBridge = kip-in (not reported) Factored flexural resistance is obtained by multiplying M n by φ. M r =φ M = = kip-in n Value reported by CSiBridge = kip-in 5.3 Shear Design AASHTO LRFD Capacity Parameters PhiC Resistance Factor; Default Value = 0.9, Typical value: 0.7 to 0.9. The nominal shear capacity of normal weight concrete sections is multiplied by the resistance factor to obtain factored resistance. PhiC (Lightweight) Resistance Factor for light-weight concrete; Default Value = 0.7, Typical values: 0.7 to 0.9. The nominal shear capacity of light-weight concrete sections is multiplied by the resistance factor to obtain factored resistance. Shear Design AASHTO LRFD 5-15

74 CSiBridge Bridge Superstructure Design Include Resal (haunched girder) Shear Effect Typical value: Yes. Specifies 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. Shear Rebar Material A previously defined rebar material label that will be used to determine the area of shear rebar required. Longitudinal Torsional Rebar Material A previously defined rebar material label that will be used to determine the required area of longitudinal torsional rebar Variables A Gross area of the section A O A l A vsweb A vtweb b b v b e d v Area enclosed by the shear flow path, including the area of holes, if any Area of longitudinal torsion reinforcement Area of shear reinforcement in web per unit length Area of transverse torsion reinforcement in web per unit length Minimum horizontal gross width of the web (not adjusted for ducts) Minimum effective horizontal width of the web adjusted for the presence of ducts Minimum effective normal width of the shear flow path adjusted to account for the presence of ducts Effective vertical height of the section = max(0.8 h, distance from the extreme compression fiber to the center of gravity of the tensile PT) CG top, CG bot Distance from the center of gravity of the section to the top and bottom fiber h p h Vertical height of the section Perimeter of the polygon defined by the centroids of the longitudinal chords of the space truss resisting torsion 5-16 Shear Design AASHTO LRFD

75 Chapter 5 - Design Concrete Box Girder Bridges P V 2, M 3, T u, u u u Factored demand forces and moments per section t Minimum normal gross width of the web (not adjusted for ducts) = bcos α ( ) web t v Minimum effective normal width of the web = b cos( α ) v web α web φ κ web λ Web angle of inclination from the vertical Resistance factor for shear Distribution factor for the web Normal or light-weight concrete factor Design Process The shear resistance is determined in accordance with AASHTO LRFD Paragraph (Shear and Torsion for Segmental Box Girder Bridges). The procedure is not applicable to discontinuity regions and applies only to sections where it is reasonable to assume that plane sections remain plane after loading. The user should select for design only those sections that comply with the preceding assumptions by defining appropriate station ranges in the Bridge Design Request (see Chapter 4). If the option to consider real effects is activated, the component of the inclined flexural compression or tension in the direction of the demand shear in variable depth members is considered when determining the design section shear force (AASHTO LRFD Paragraph ). The section design shear force is distributed into individual webs assuming that the vertical shear that is carried by a web decreases with increased inclination of the web from vertical. Section torsion moments are assigned to external webs and slabs. The rebar area and ratio are calculated using measurements normal to the web. Thus, vertical shear forces are divided by cos(alpha_web). The rebar area calculated is the actual, normal cross-section of the bars. The rebar ratio is calculated using the normal width of the web, t web = b web cos(alpha_web). Shear Design AASHTO LRFD 5-17

76 CSiBridge Bridge Superstructure Design The effects of ducts in members are considered in accordance with paragraph of the code. In determining the web or flange effective thickness, b e, one-half of the diameter of the ducts is subtracted. 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 or flange, and the minimum controlling effective web and flange thicknesses are evaluated. The tendon duct is considered as having effect on the web or flange effective thickness even if only part of the duct is within the element boundaries. In such cases, the entire one-half of the tendon duct diameter is subtracted from the element thickness. If several tendon ducts overlap in one flange or web (when projected on the horizontal axis for flange, or when projected on vertical axis for the web), the diameters of ducts are added for the sake of evaluation of the effective thickness. In the web, the effective web thickness is calculated at the top and bottom of each duct; in the flange, the effective thickness is evaluated at the left and right sides of the duct. The Shear and Torsion Design is completed first on a per web basis. Rebar needed for individual webs is then summed and reported for the entire section. The D/C ratio is calculated for each web. Then the shear area of all webs is summed and the entire section D/C is calculated. Therefore, the controlling section D/C does not necessarily match the controlling web D/C (in other words, other webs can make up the capacity for a weak web) Algorithm All section properties and demands are converted from CSiBridge model units to N, mm. If the option to consider resal effects is activated, the component of the inclined flexural compression or tension in the direction of the demand shear in variable depth members is evaluated as follows: Inclination angles of the top and bottom slabs are determined slabtop2 slabtop1 slabtop arctan y y α = Stat2 Stat Shear Design AASHTO LRFD

77 Chapter 5 - Design Concrete Box Girder Bridges slabbot2 slabbot1 slabbot arctan y y α = Stat2 Stat1 where slabtop2 slabtop1 y, y vertical coordinate of the center of gravity of the top slab at stations 1 and 2. The y origin is assumed to be at the top of the section and the + direction is up. Stat1, Stat 2 stations of adjacent sections. When the section being analyzed is Before, the current section station is Stat 2; when the section being analyzed is After, the current section station is Stat 1. Therefore, the statement Stat1 < Stat2 is always valid. The magnitudes of normal forces in slabs are determined as follows: P = A P M d u u3 slabtop slabtop slabtop A I3 P = A P M + d u u3 slabbot slabbot slabbot A I3 where dslabtop, d slabbot are distances from the center of gravity of the section to the center of gravity of the slab (positive). The magnitudes of vertical components of slab normal forces are determined as follows: P = P tanα resaltop slabtop slabtop P = P tanα resalbot slabbot slabbot On the basis of the location and inclination of each web, the per-web demand values are evaluated. Location Shear and Torsion Check Outer Web Inner Web Vuweb Tuweb Vuweb Tuweb abs( Vu 2 + Presaltop + Presalbot ) κ cosαweb Abs(Tu) abs( Vu 2 + Presaltop + Presalbot ) κ cosαweb 0 Shear Design AASHTO LRFD 5-19

78 CSiBridge Bridge Superstructure Design where κ web 1 ( αweb ) cos ( α ) cos = nweb web Evaluate effective thicknesses: Evaluate d v b v b e t v If b v 0, then D WebPassFlag = 2, = 0; Avsweb = 0; Avtweb = 0; Avsflag = 2; Avtflag = 2 C proceed to report web results If b e < 0, then SectionPassFlag = 2. Evaluate design f c : f min( f, 8.3 MPa) c Evaluate the stress variable K: c Calculate the extreme fiber stress: P A M3 CG I33 P A M3 CG I33 σ bot = + bot top top σ = σ ( ) tens = max σtop, σ bot If σ tens > 0.5 f, then K = 1; else c P K = 1 + A, f c where K < 2. Evaluate V c per web (shear capacity of concrete): Vcweb = Kλ f cbd v v. (AASHTO LRFD ) Evaluate V s per web (shear force that is left to be carried by rebar): V V φv φ uweb cweb sweb = Shear Design AASHTO LRFD

79 Chapter 5 - Design Concrete Box Girder Bridges If V sweb < 0, then A web = 0; vs else A V = sweb vsweb. fd y v Verify the minimum reinforcement requirement: If A web < 0.35t f (AASHTO LRFD eq ), then vs vs y A web = 0.35t f and A swebflag = 0; else A vswebflag = 1. Evaluate the nominal capacities: V = A fd sweb vsweb y v V = V + V nweb cweb sweb Evaluate the shear D/C for the web: Vuweb D φ = C bd f sweb v v c y. Evaluate T cr (AASHTO LRFD eq ): T = 0.166K f 2 Ab. cr c 0 e Evaluate torsion rebar: 1 If Tuweb < φ Tcr, then: 3 A vtflag = 0 A vtweb = 0 A = 0 l Shear Design AASHTO LRFD 5-21

80 CSiBridge Bridge Superstructure Design Torsion Effects Flag = 0; else: A vtflag = 1 A vtweb T = φa f uweb 0 2 y Tuweb ph Al = φa 2 f 0 ylong Torsion Effects Flag = 1. Evaluate the combined shear and torsion D/C for the web: Vuweb Tuweb + D φbd v v φ2ab 0 e =. C tweb 1.25 f Evaluate the controlling D/C for the web: c If D D > C C sweb tweb, then Ratio Flag = 0; else Ratio Flag = 1 D D D = max,. C C sweb C tweb D If > 1, then Web Pass Flag = 1; C else Web Pass Flag = 0. Assign web rebar flags where the rebar flag convention is: 5-22 Shear Design AASHTO LRFD

81 Chapter 5 - Design Concrete Box Girder Bridges Flag = 0 rebar governed by minimum code requirement Flag = 1 rebar governed by demand Flag = 2 rebar not calculated since the web b v< 0 Flag = 3 rebar not calculated since the web is not part of the shear flow path for torsion Evaluate entire section values: V V V csection ssection nsection A A A vssection vtsection lsection = V = Vs = Vn = A = A = A l cweb web web vsweb vtweb Evaluate entire section D/C: nweb uweb t 1 v φbd v v nweb t 1 v D = C ssection f c V. This is equivalent to: V u nweb td 1 v v D φ = C f and ssection c Vu Tu + nweb td 2 0 e 1 v v φ Ab D φ =. C tsection 1.25 f Evaluate controlling D/C for section: c Shear Design AASHTO LRFD 5-23

82 CSiBridge Bridge Superstructure Design If D D > C C ssection tsection, then Ratio Flag = 0 else Ratio Flag = 1 D D D = max,. C C ssection C tsection D If > 1, then Section Pass Flag = 1; C else Section Pass Flag = 0. Assign section design flags where flag convention is: Flag = 0 Section Passed all code checks Flag = 1 Section D/C > 1 Flag = 2 Section b e < 0 (section invalid) Shear Design Example Cross Section: AASHTO Box Beam, Type BIII-48, as shown in Figure 5-5. Figure 5-5 Shear Design Example, AASHTO Box Beam, Type BIII Shear Design AASHTO LRFD

83 Chapter 5 - Design Concrete Box Girder Bridges φ = 0.9 Concrete unit weight, w c = kcf λ = 1.0 Concrete strength at 28 days, f c = 5.0 ksi (~ MPa) Design span = 95.0 ft Prestressing strands: ½ in. dia., seven wire, low relaxation Area of one strand = in 2 Ultimate strength f pu = ksi Yield strength f py = 0.9 f pu = 243 ksi Modulus of elasticity, E p = ksi Reinforcing bars: yield strength, f y = 60.0 ksi (~ MPa) Section Properties A = area of cross-section of beam = 826 in 2 (~ mm 2 ) h = overall depth of precast beam = 39 in (~990.6 mm) I = moment of inertia about centroid of the beam = in 4 (~ mm 4 ) y b,y t = distance from centroid to the extreme bottom (top) fiber of the beam = 19.5 in (~495.3 mm) A slabtop= A slabbot = = 264 in 2 (~ mm 2 ) A o = (48 5) (39 5.5) = in 2 (~ mm 2 ) P h = 2 ( ) = 153 in (~ mm) Demand forces from Dead and PT (COMB1) at station 114 before: P = 800 kip (~ 3560 E+03 N) M3 = 7541 kip-in (~ 852 E+06 Nmm) V2 = 33 kip (~ E+03 N) T = 4560 kip-in (515.2 E+06 Nmm) Shear Design AASHTO LRFD 5-25

84 CSiBridge Bridge Superstructure Design Figure 5-6 Shear Design Example Reinforcement AASHTO Box Beam, Type BIII-48 All section properties and demands are converted from CSiBridge model units to N, mm. On the basis of the location and inclination of each web, the per-web demand values are evaluated. Location Shear and Torsion Check Outer Web Inner Web Vuweb Tuweb Vuweb Tuweb abs( Vu 2 + Presaltop + Presalbot ) κ = cosαweb abs(148.3e ) N cos = Abs(Tu)=515.2E+06 N/A 0 N/A where ( αweb ) ( α ) web nweb 2 1 web 1 ( ) ( ) cos cos 0 κ = = = 0.5 cos cos 0 Evaluate the effective shear flow path thicknesses: 5-26 Shear Design AASHTO LRFD

85 Chapter 5 - Design Concrete Box Girder Bridges b = min( t, t, t, t ) e firstweb lastweb topslabv botslabv = min(127,127,139.7,139.7) = 127mm Evaluate the effective web width and normal thickness: Since the web is vertical, b v = t v = 127 mm. Evaluate the effective depth: Since M3 < 0 then d = max(0.8 hy, + y ) v bot PTtop = max( , ) = 914.4mm Evaluate design f c : ( c ) ( ) f = min f,8.3mpa = min ,8.3MPa = c Evaluate stress variable K: Calculate the extreme fiber stress P M3 3560E E + 06 σ bot = + CG bot = = MPa. A I P M3 3560E E + 06 σ top = CG top = = 0.745MPa A I σ tens = max( σtop, σ bot ) = max( 12.61, 0.745) = 0.745MPa If σ tens > 0.5 f, then K = 1 false; c else P 3560E + 03 K = 1+ A = = f c where K < 2; therefore K = 2. Evaluate V c per web (shear capacity of concrete; AASHTO LRFD ): Shear Design AASHTO LRFD 5-27

86 CSiBridge Bridge Superstructure Design Vcweb = Kλ f cbd v v = = N. Evaluate V s per web (shear force that is left to be carried by the rebar): V V φv φ 0.9 uweb cweb sweb = = = If V sweb < 0, then A vsweb = 0 true; N. else A V sweb vsweb =. fd y v Verify minimum reinforcement requirement: If A web < 0.35t f (AASHTO LRFD eq ), then true A vs y vsweb = 0.35t fy = = mm / mm and A swebflag = 0; else A vswebflag = 1. Evaluate the nominal capacities: Vsweb = Avsweb fd y v = = 40645N Vnweb = Vcweb + Vsweb = = N Evaluate the shear D/C for the web: Vuweb D φ 0.9 = = = C bd f sweb v v c Evaluate T cr (AASHTO LRFD eq ): T = 0.166K f 2Ab = cr c 0 e = Nmm Evaluate the torsion rebar: 5-28 Shear Design AASHTO LRFD

87 Chapter 5 - Design Concrete Box Girder Bridges 1 1 If Tuweb < φ Tcr => 515.2E6 < E6 false, then: 3 3 A vtflag = 1 A A T 515.2E6 uweb vtweb = φ A0 2 f = y = T p 515.2E uweb h l = = = φ A0 2 fylong Torsion Effects Flag = mm / mm 2893mm Evaluate the combined shear and torsion D/C for the web: Vuweb Tuweb E6 + D φbd v v φ2ab 0 e = = C tweb 1.25 f = Evaluate the controlling D/C for the web: c 2 2 If D D > C C sweb tweb, then Ratio Flag = 0 false; else Ratio Flag =1 true D D D = max, = max( , 0.427) = C C sweb C tweb D If > 1, then Web Pass Flag =1 true; C else Web Pass Flag = 0. Assign web rebar flags where rebar flag convention is: Shear Design AASHTO LRFD 5-29

88 CSiBridge Bridge Superstructure Design Flag = 0 rebar governed by minimum code requirement Flag = 1 rebar governed by demand => true Flag = 2 rebar not calculated since web b v< 0 Flag = 3 rebar not calculated since the web is not part of the shear flow path for torsion. Evaluate the entire section values: V section = V web = = N c c Vssection = Vsweb = = N Vnsection = Vnweb = = N Avssection = Avsweb = = mm / mm A section = A web = = mm / mm A vt lsection vt = A = 2893mm Evaluate entire section D/C: l D = C ssection f 2 nweb uweb t 1 v φbd v v nweb t 1 v. This is equivalent to: c V V 148.3E3 u nweb 2 td 1 v v 1 D φ = = = C ssection f and c Shear Design AASHTO LRFD

89 Chapter 5 - Design Concrete Box Girder Bridges Vu Tu + nweb td 2 0 e 1 v v φ Ab D φ = C tsection 1.25 f c 148.3E E = = Evaluate the controlling D/C for the section: If D D > C C ssection tsection, then Ratio Flag = 0 false; else Ratio Flag = 1 true D D D = max, = max( ,0.427) = C C ssection C tsection D If > 1, then SectionPassFlag = 1 true; C else Section Pass Flag = 0. Assign the section design flags where the flag convention is: Flag = 0 Section Passed all code checks true Flag = 1 Section D/C >1 Flag = 2 Section b e < 0 (section invalid) 5.4 Principal Stress Design, AASHTO LRFD Capacity Parameters PhiC Resistance Factor; Default Value = 1.0, Typical value: 1.0. Principal Stress Design, AASHTO LRFD 5-31

90 CSiBridge Bridge Superstructure Design The compression and tension limits are multiplied by the φ C factor. FactorCompLim f c multiplier; Default Value = 0.4; Typical values: 0.4 to 0.6. The f c is multiplied by the FactorCompLim to obtain the compression limit. FactorTensLim f c multiplier; Default Values = 0.19 (ksi), 0.5(MPa); Typical values: 0 to 0.24 (ksi), 0 to 0.63 (MPa). The FactorTensLim to obtain tension limit. f c is multiplied by the 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 compression limit. FactorTensLim Percentage of the basic unit stress for tension service design; Default value = 1.0; Typical values 1.0 to 1.5. The demand tensile stresses are divided by the FactorCompLim factor. This way the controlling stress can be selected and compared against one tension limit Principal Stress Design, AASHTO LRFD

91 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 concrete box design and uses the Approximate Method of Analysis, as described in the AASHTO LRFD 2014 (AASHTO LRFD) 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 Preferences button. For MulticellConcBox design in CSiBridge, each web and its tributary slabs are designed separately. Moments and shears due to live load are distributed to individual webs in accordance with the factors specified in AASHTO LRFD Articles and of the code. To control if the section is designed as a whole-width structure in accordance with AASHTO LRFD Article of the code, select Yes for the Diaphragms Present option. When CSiBridge calculates the Live Load Distribution (LLD) factors, the section and span qualification criteria stated in AASHTO LRFD are verified and non-compliant sections are not designed. Stress Design 6-1

92 CSiBridge Bridge Superstructure Design With respect to shear and torsion check, in accordance with AASHTO LRFD Article of the code, torsion is ignored. The user has an option to select No Interims or YYYY Interims on the Bridge Design Preferences form. The form can be opened by clicking the Code Preferences button. The revisions published in the 2015 interims were incorporated into the Flexure Design. 6.1 Stress Design The following parameters are considered during stress design: PhiC Resistance Factor; Default Value = 1.0, Typical value: 1.0. The compression and tension limits are multiplied by the φ C factor. FactorCompLim f c multiplier; Default Value = 0.4; Typical values: 0.4 to 0.6. The f c is multiplied by the FactorCompLim to obtain compression limit. f' c multiplier; Default Value = 0.19 (ksi), 0.5(MPa); Typi- FactorTensLim cal values: 0 to 0.24 (ksi), 0 to 0.63 (MPa). The tortenslim to obtain tension limit. f' c is multiplied by the Fac- 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 centerline web and the right corner of the relevant slab tributary area. The location is labeled in the output plots and tables. See Chapter 9, Section Concrete strength are evaluated using the FactorCompLim - f' c multiplier. f c is read at every point, and compression and tension limits f c multiplier and FactorTensLim - The stresses assume linear distribution and take into account axial (P) and either both bending moments (M2 and M3) or only P and M3, depending on which method for determining LLD factors have been specified in the Design Request (see Chapters 3 and 4). 6-2 Stress Design

93 Chapter 6 - Design Multi-Cell Concrete Box Bridges using AMA The stresses are evaluated for each demand set (Chapter 4). Extremes are found for each point and the controlling demand set name is recorded. The stress limits are evaluated by applying the preceding parameters. 6.2 Shear Design The following parameters are considered during shear design: PhiC Resistance Factor; Default Value = 0.9, Typical values: 0.7 to 0.9. The nominal shear capacity of normal weight concrete sections is multiplied by the resistance factor to obtain factored resistance. PhiC (Lightweight) Resistance Factor for light-weight concrete; Default Value = 0.7, Typical values: 0.7 to 0.9. The nominal shear capacity of light-weight concrete sections is multiplied by the resistance factor to obtain factored resistance. Check Sub Type Typical value: MCFT. Specifies which method for shear design will be used: either Modified Compression Field Theory (MCFT) in accordance with AASHTO LRFD Section ; or the Vci/Vcw method in accordance with AASHTO LRFD Section Currently only the MCFT option is available. Negative limit on strain in nonprestressed longitudinal reinforcement in accordance with AASHTO LRFD Section ; Default Value = 0.4x10 3, Typical value(s): 0 to 0.4x10 3. Positive limit on strain in nonprestressed longitudinal reinforcement in accordance with AASHTO LRFD Section ; Default Value = 6.0x10 3, Typical value: 6.0x10 3. PhiC for N u Resistance Factor used in AASHTO LRFD Equation ; Default Value = 1.0, Typical values: 0.75 to 1.0. Phif for M u Resistance Factor used in AASHTO LRFD Equation ; Default Value = 0.9, Typical values: 0.9 to 1.0. Shear Rebar Material A previously defined rebar material label that will be used to determine the required area of transverse rebar in the girder. Shear Design 6-3

94 CSiBridge Bridge Superstructure Design Longitudinal Rebar Material A previously defined rebar material label that will be used to determine the required area of longitudinal rebar in the girder Variables A c Area of concrete on the flexural tension side of the member A ps Area of prestressing steel on the flexural tension side of the member A vl A VS Area of nonprestressed steel on the flexural tension side of the member at the section under consideration Area of transverse shear reinforcement per unit length A VS min Minimum area of transverse shear reinforcement per unit length in accordance with AASHTO LRFD Equation a b b v Depth of equivalent stress block in accordance with AASHTO LRFD Section Varies for positive and negative moment. Minimum web width Effective web width adjusted for presence of prestressing ducts in accordance with AASHTO LRFD Section d girder Depth of the girder d PTbot Distance from the top of the top slab to the center of gravity of the tendons in the bottom of the precast beam d v Effective shear depth in accordance with AASHTO LRFD E c Young s modulus of concrete E p Prestressing steel Young s modulus E s Reinforcement Young s modulus f pu Specified tensile strength of the prestressing steel 6-4 Shear Design

95 Chapter 6 - Design Multi-Cell Concrete Box Bridges using AMA M u N u V p V u V 2 c Factored moment at the section Applied factored axial force, taken as positive if tensile Component in the direction of the applied shear of the effective prestressing force; if V p has the same sign as V u, the component is resisting the applied shear. Factored shear demand per girder excluding force in tendons Shear in the Section Cut excluding the force in tendons V 2Tot Shear in the Section Cut including the force in tendons ε s Strain in nonprestressed longitudinal tension reinforcement (AASH- TO LRFD eq ) εslimitpos, εs LimitNeg = Max and min value of strain in nonprestressed longitudinal tension reinforcement as specified in the Design Request ϕ V ϕ P ϕ F Resistance factor for shear Resistance factor for axial load Resistance factor for moment Design Process The shear resistance is determined in accordance with AASHTO LRFD paragraph (derived from Modified Compression Field Theory). The procedure assumes that the concrete shear stresses are distributed uniformly over an area b v wide and d v deep, that the direction of principal compressive stresses (defined by angle θ and shown as D) remains constant over d v, and that the shear strength of the section can be determined by considering the biaxial stress conditions at just one location in the web. For design, the user should select only those sections that comply with these assumptions by defining appropriate station ranges in the Design Request (see Chapter 4). Shear Design 6-5

96 CSiBridge Bridge Superstructure Design The effective web width is taken as the minimum web width, measured parallel to the neutral axis, between the resultants of the tensile and compressive forces as a result of flexure. In determining the effective web width at a particular level, one-quarter the diameter of grouted ducts at that level is subtracted from the web width. All defined tendons in a section, stressed or not, are assumed to be grouted. Each tendon at a section is checked for presence in the web, and the minimum controlling effective web thicknesses are evaluated. The tendon duct is considered to have an effect on the web effective thickness even if only part of the duct is within the web boundaries. In such cases, the entire one-quarter of the tendon duct diameter is subtracted from the element thickness. If several tendon ducts overlap in one web (when projected on the vertical axis), the diameters of the ducts are added for the sake of evaluation of the effective thickness. The effective web thickness is calculated at the top and bottom of each duct. Shear design is completed on a per-web basis. Please refer to Chapter 3 for a description of the live load distribution to individual girders 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 COMBO Max, Min and ABS and the controlling StepType is reported. 6-6 Shear Design

97 Chapter 6 - Design Multi-Cell Concrete Box Bridges using AMA In cases where the demand moment Mu < Vu Vp d, v two new force demand u u p v sets are generated where M pos = V V d pos and Muneg = Vu Vp dvneg. The acronyms -CodeMinMuPos and -CodeMinMuNeg are added to the end of the StepType name. The signs of the P and V2 are preserved. The component in the direction of the applied shear of the effective prestressing force, positive if resisting the applied shear, is evaluated: V p V V = n 2c 2Tot girders The depth of the equivalent stress block a for both positive and negative moment is evaluated in accordance with AASHTO LRFD Equation Effective shear depth is evaluated. If M u > 0, then dv = ( dgirder dptbot dptbot a) If M u < 0, then max 0.72, 0.9, 0.5. dv = max 0.72 dgirder,0.9 ( dgirder 0.5 dcompslab ),( dgirder 0.5 dcompslab ) 0.5 a. The demand/capacity ratio (D/C) is calculated based on the maximum permissible shear capacity at a section in accordance with AASHTO LRFD Section Vu Vp D φv = C 0.25 f ' b d c v (AASHTO LRFD ) Evaluate the numerator and denominator of (AASHTO LRFD eq ). Mu ε numerator = N + V V A 0.7 f d s u u p ps pu V ε = E A + E A sdenominator p ps s vl Adjust denominator values as follows. Shear Design 6-7

98 CSiBridge Bridge Superstructure Design If ε sdenominator = 0 and ε snumerator > 0, then ε s = ε slimitpos and A vl = ε snumerator ε s E A E s p ps. If ε snumerator <0, then ε = E A + E A + E A sdenominator p ps s vl c c Evaluate (eq ). ε snumerator ε s = ε sdenominator Check if axial tension is large enough to crack the flexural compression face of the section. Nu If > f' c, A girder then ε = 2 ε. s s Check against the limit on the strain in nonprestressed longitudinal tension reinforcement specified in the Design Request, and if necessary, recalculate how much longitudinal rebar is needed to reach the EpsSpos tension limit. ε s = max( εs, ε slimitneg ) and ε s = εs ε slimitpos min(, ) Evaluate the angle θ of inclination of diagonal compressive stresses as determined in AASHTO LRFD Article εs 45 (AASHTO LRFD ) Evaluate the factor indicating the ability of diagonally cracked concrete to transmit tension and shear, as specified in AASHTO LRFD Article β= (AASHTO LRFD ) ε s Evaluate the nominal shear resistance provided by tensile stresses in the concrete (AASHTO LRFD eq ). V = β λ f ' b d c c v 6-8 Shear Design

99 Chapter 6 - Design Multi-Cell Concrete Box Bridges using AMA Evaluate how much shear demand is left to be carried by rebar. V V = V V u S p c ϕs If V < 0, then A = 0; else S VS Vs A VS = 1. fy dv tanθ (AASHTO LRFD eq ) Check against minimum transverse shear reinforcement λ f ' If Vu > 0.5 φ s Vc + Vp, then c b AVSmin = in accord- f ance with (AASHTO LRFD eq ); else A VS min = 0. If V S < 0, then AVS = AVSmin; else A VS = max(a VSmin,A VS ). Recalculate V s in accordance with (AASHTO LRFD eq ). 1 VS = AVS fy dv. tanθ Evaluate the longitudinal rebar on the flexure tension side in accordance with (AASHTO LRFD eq ). V U u VP 0.5 min VS, MU NU φs φ 1 SLreq = p ps dv φf φp tanθ fy A E A A max( A, A ) VL = VL SLreq Assign longitudinal rebar to the top or bottom side of the girder based on the moment sign. If M U < 0, then A = A and A BeamBotFlange = 0, VLCompSlabU VL else A = and A BeamBotFlange = A. VLCompSlabU 0 VL VL VL y V Shear Design 6-9

100 CSiBridge Bridge Superstructure Design 6.3 Flexure Design The following parameter is used in the design of flexure: PhiC Resistance Factor; Default Value = 1.0, Typical value(s): 1.0. The nominal flexural capacity is multiplied by the resistance factor to obtain factored resistance Variables A PS A S Area of the PT in the tension zone Area of reinforcement in the tension zone A slab Tributary area of the slab a Depth of the equivalent stress block in accordance with AASHTO LRFD b slab Effective flange width = horizontal width of the slab tributary area, measured from out to out b webeq Thickness of the beam web d P d S Distance from the extreme compression fiber to the centroid of the prestressing tendons in the tension zone Distance from the extreme compression fiber to the centroid of the rebar in the tension zone f ps Average stress in prestressing steel (AASHTO LRFD eq ) f pu Specified tensile strength of prestressing steel (area weighted average of all tendons in the tensile zone) f py Yield tensile strength of prestressing steel (area weighted average of all tendons are in the tensile zone) f y Yield strength of rebar 6-10 Flexure Design

101 Chapter 6 - Design Multi-Cell Concrete Box Bridges using AMA k PT material constant (AASHTO LRFD eq ) M n M r Nominal flexural resistance Factored flexural resistance t slabeq Thickness of the composite slab αα 1 Stress block factor, as specified in AASHTO LRFD 2015 Interim Section β 1 Stress block factor, as specified in AASHTO LRFD Section φ Resistance factor for flexure Design Process The derivation of the moment resistance of the section is based on the approximate stress distribution specified in AASHTO LRFD Article The natural relationship between concrete stress and strain is considered satisfied by an equivalent rectangular concrete compressive stress block of αα 1 ff cc over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = β 1c from the extreme compression fiber. If the AASHTO LRFD 2015 interim is selected the factor αα 1 is taken as 0.85 for specified compressive strengths not exceeding 10.0 ksi. For specified concrete compressive strengths exceeding 10.0ksi, αα 1 is reduced at rate of 0.02 for each 1.0ksi of strength in excess of 10.0ksi, except that αα 1 is not taken less than For AASHTO LRFD no interim the αα 1 is always taken as 0.85 independent of concrete compressive strength. The distance c is measured perpendicular to the neutral axis. The factor β 1 is taken as 0.85 for concrete strengths not exceeding 4.0 ksi. For concrete strengths exceeding 4.0 ksi, β 1 is reduced at a rate of 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi, except that β 1 is not to be taken to be less than The flexural resistance is determined in accordance with AASHTO LRFD Paragraph 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 Flexure Design 6-11

102 CSiBridge Bridge Superstructure Design the compression zone are not considered. It is assumed that all defined tendons in a section, stressed or not, have f pe (effective stress after loses) larger than 0.5 f pu (specified tensile strength). If a certain tendon should not be 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 have been applied. This is consistent with the demands being reported in the section local axis. It is assumed that the effective width of the flange (slab) in compression is equal to the width of the slab Algorithms At each section: All section properties and demands are converted from CSiBridge model units to N, mm. The equivalent slab thickness is evaluated based on the tributary slab area and the slab width assuming a rectangular shape. t slabeq = A b slab slab The αα 1 stress block factor is evaluated in accordance with AASHTO LRFD based on section f c For AASHTO LRFD 2015 Interim iiii ff cc > 10.0kkkkkk, ttheeee αα 1 = mmmmmm 0.85 ff cc ; else αα 1 = 0.85 For AASHTO LRFD No Interim αα 1 = Flexure Design

103 Chapter 6 - Design Multi-Cell Concrete Box Bridges using AMA β 1 stress block factor is evaluated in accordance with AASHTO LRFD based on section f c. If f c > 28 MPa, then β 1 f c 28 = max ; 0.65 ; 7 else β 1 = The tendon and rebar location, area, and material are read. Only bonded tendons are processed; unbonded tendons are ignored. Tendons and rebar are split into two groups depending on the sign of moment they resist negative or positive. A tendon or rebar is considered to resist a positive moment when it is located outside of the top fiber compression stress block and is considered to resist a negative moment when it is located outside of the bottom fiber compression stress block. The compression stress block extends over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = β 1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis. For each tendon group, an area weighted average of the following values is determined: sum of the tendon areas, A PS center of gravity of the tendons, d P specified tensile strength of prestressing steel f pu constant k (AASHTO LRFD eq ) k = f f py pu For each rebar group, the following values are determined: sum of tension rebar areas, A s distance from the extreme compression fiber to the centroid of the tension rebar, d s Flexure Design 6-13

104 CSiBridge Bridge Superstructure Design Positive moment resistance first it is assumed that the equivalent compression stress block is within the top slab. Distance c between the neutral axis and the compressive face is calculated in accordance with (AASHTO LRFD eq ) APS fpu + Af s s c = f α β + pu 1 f c 1bslab kaps d p The distance c is compared against requirement of Section to verify if stress in mild reinforcement f s can be taken as equal to f y. The limit on ratio c/d s is calculated depending on what kind of code and its interim are specified in the Bridge Design Preferences form as shown in the table below: Code AASHTO LRFD 2012 No Interims AASHTO LRFD 2012 with 2013 Interims or later cc dd ss εε cccc where the compression control strain limit εε cccc is per AASHTO LRFD 2013 Interims table C When the limit is not satisfied the stress in mild reinforcement f s is reduced to satisfy the requirement of Section The distance c is compared to the equivalent slab thickness to determine if the section is a T-section or rectangular section. cβ > t the section is a T-section. If 1 slabeq, If the section is a T-section, the distance c is recalculated in accordance with (AASHTO LRFD eq ). ( ) A f + Af α f b b t c = f α β + PS PU s s 1 c slab webeq slabeq pu 1 f c 1bwebeq kaps y pt 6-14 Flexure Design

105 Chapter 6 - Design Multi-Cell Concrete Box Bridges using AMA Average stress in prestressing steel f ps is calculated in accordance with (AASHTO LRFD eq ). c fps = fpu 1 k d p Nominal flexural resistance M n is calculated in accordance with (AASHTO LRFD eq ). If the section is a T-section, then cβ cβ cβ t M A f d A f d f ( b b ) t slabeq n = PS PS p + S s s +α1 c slab webeq slabeq ; else cβ1 cβ1 Mn = APS fps dp + AS fs ds. 2 2 Factored flexural resistance is obtained by multiplying M n by φ. M r = ϕ M n Extreme moment M3 demands are found from the specified demand sets and the controlling demand set name is recorded. The process for evaluating negative moment resistance is analogous. Flexure Design 6-15

106 Chapter 7 Design Precast Concrete Girder Bridges This chapter describes the algorithms used by CSiBridge for design and stress check when the superstructure has a deck that includes precast I or U girders with composite slabs in accordance with the AASHTO LRFD 2014 (AASHTO LRFD) 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 Preferences button. The user has an option to select No Interims or YYYY Interims on the Bridge Design Preferences form. The form can be opened by clicking the Code Preferences button. The revisions published in the 2015 interims were incorporated into the Flexure Design. 7.1 Stress Design The following parameters are considered during stress design: Stress Design 7-1

107 CSiBridge Bridge Superstructure Design PhiC Resistance Factor; Default Value = 1.0, Typical value: 1.0. The compression and tension limits are multiplied by the φ C factor. FactorCompLim f c multiplier; Default Value = 0.4; Typical values: 0.4 to 0.6. The f c is multiplied by the FactorCompLim to obtain compression limit. FactorTensLim f'c multiplier; Default Value = 0.19 (ksi), 0.5(MPa); Typical values: 0 to 0.24 (ksi), 0 to 0.63 (MPa). The FactorTensLim to obtain tension limit. f'c is multiplied by the The stresses are evaluated at three points at the top fiber of the composite slab: the left corner, the centerline beam and the right corner of the composite slab tributary area. The locations of stress output points at the slab bottom fiber and the beam top and bottom fibers depend on the type of precast beam present in the section cut. The locations are labeled in the output plots and tables. f c is read at every point and compression and tension limits Concrete strength are evaluated using the FactorCompLim f'c multiplier. f c multiplier and FactorTensLim The stresses assume linear distribution and take into account axial (P) and either both bending moments (M2 and M3) or only P and M3, depending on which method for determining the LLD factor has been specified in the Design Request (see Chapters 3 and 4). The stresses are evaluated for each demand set (Chapter 4). Extremes are found for each point and the controlling demand set name is recorded. The stress limits are evaluated by applying the preceding Parameters. 7.2 Shear Design The following parameters are considered during shear design: PhiC Resistance Factor; Default Value = 0.9, Typical values: 0.7 to 0.9. The nominal shear capacity of normal weight concrete sections is multiplied by the resistance factor to obtain factored resistance. 7-2 Shear Design

108 Chapter 7 - Design Precast Concrete Girder Bridges PhiC (Lightweight) Resistance Factor for light-weight concrete; Default Value = 0.7, Typical values: 0.7 to 0.9. The nominal shear capacity of light-weight concrete sections is multiplied by the resistance factor to obtain factored resistance. Check Sub Type Typical value: MCFT. Specifies which method for shear design will be used: Modified Compression Field Theory (MCFT) in accordance with AASHTO LRFD section ; or the Vci/Vcw method in accordance with AASHTO LRFD section Currently, only the MCFT option is available. Negative limit on strain in nonprestressed longitudinal reinforcement in accordance with AASHTO LRFD section ; Default Value = 0.4x10-3, Typical value(s): 0 to 0.4x10-3. Positive limit on strain in nonprestressed longitudinal reinforcement in accordance with AASHTO LRFD section ; Default Value = 6.0x10-3, Typical value(s): 6.0x10-3. PhiC for N u Resistance Factor used in equation of the code; Default Value = 1.0, Typical values: 0.75 to 1.0. Phif for M u Resistance Factor used in AASHTO LRFD equation ; Default Value = 0.9, Typical values: 0.9 to 1.0. Shear Rebar Material A previously defined rebar material label that will be used to determine the required area of transverse rebar in the girder. Longitudinal Rebar Material A previously defined rebar material label that will be used to determine the required area of longitudinal rebar in the girder Variables a Depth of the equivalent stress block in accordance with AASHTO LRFD section Varies for positive and negative moment. A c A ps A VS Area of concrete on the flexural tension side of the member Area of prestressing steel on the flexural tension side of the member Area of transverse shear reinforcement per unit length Shear Design 7-3

109 CSiBridge Bridge Superstructure Design A VSmin A vl b d v d girder Minimum area of transverse shear reinforcement per unit length in accordance with (AASHTO LRFD eq ) Area of nonprestressed steel on the flexural tension side of the member at the section under consideration Minimum web width of the beam Effective shear depth in accordance with AASHTO LRFD section Depth of the girder d compslab Depth of the composite slab (includes concrete haunch t2) d PTBot E c E p E s f pu M u N u V 2c V 2tot V p V u ε s Distance from the top of the composite slab to the center of gravity of the tendons in the bottom of the precast beam Young s modulus of concrete Prestressing steel Young s modulus Reinforcement Young s modulus Specified tensile strength of prestressing steel Factored moment at the section Applied factored axial force, taken as positive if tensile Shear in Section Cut, excluding the force in the tendons Shear in Section Cut, including the force in the tendons Component in the direction of the applied shear of the effective prestressing force; if V p has the same sign as V u, the component is resisting the applied shear. Factored shear demand per girder, excluding the force in the tendons Strain in nonprestressed longitudinal tension reinforcement (AASH- TO LRFD eq ) 7-4 Shear Design

110 Chapter 7 - Design Precast Concrete Girder Bridges ε slimitpos, ε slimitneg = Max and min value of strain in nonprestressed longitudinal tension reinforcement as specified in the Design Request φ V φ P φ F Resistance factor for shear Resistance factor for axial load Resistance factor for moment Design Process The shear resistance is determined in accordance with AASHTO LRFD paragraph (derived from Modified Compression Field Theory). The procedure assumes that the concrete shear stresses are distributed uniformly over an area b v wide and d v deep, that the direction of principal compressive stresses (defined by angle θ and shown as D) remains constant over d v, and that the shear strength of the section can be determined by considering the biaxial stress conditions at just one location in the web. The user should select for design only those sections that comply with these assumptions by defining appropriate station ranges in the Design Request (see Chapter 4). It is assumed that the precast beams are pre-tensioned, and therefore, no ducts are present in webs. The effective web width is taken as the minimum web width, measured parallel to the neutral axis, between the resultants of the tensile and compressive forces as a result of flexure. Shear design is completed on a per-girder basis. Please refer to Chapter 3 for a description of the live load distribution to individual girders Algorithms All section properties and demands are converted from CSiBridge model units to N, mm. For every COMBO specified in the Design Request that contains envelopes, two new force demand sets are generated. The new force demand sets are built up from the maximum tension values of P and the maximum and minimum values of V2 and minimum values of M3 of the two StepTypes (Max and Min) present in the envelope COMBO case. The StepType of these new Shear Design 7-5

111 CSiBridge Bridge Superstructure Design force demand sets are named MaxM3MinV2 and MinM3MaxV2, respectively. The signs of all force components are preserved. The two new cases are added to comply with 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 four StepTypes in the COMBO Max, Min, MaxM3MinV2, and MinM3MaxV2 and the controlling StepType is reported. In cases where the demand moment Mu < Vu Vp d, v two new force demand sets are generated where Mupos = Vu Vp dvpos and Muneg = Vu Vp dvnneg. The acronyms -CodeMinMuPos and -CodeMinMuNeg are added to the end of the StepType name. The signs of the P and V2 are preserved. The component in the direction of the applied shear of the effective prestressing force, positive if resisting the applied shear, is evaluated: V p V V = n 2c 2tot girders Depth of equivalent stress block a for both positive and negative moment is evaluated in accordance with (AASHTO LRFD eq ). Effective shear depth is evaluated. If M u > 0, then dv = ( dgirder dptbot dptbot a) If M u < 0, then max 0.72,0.9, 0.5. ( ) ( ) dv = max 0.72 dgirder,0.9 dgirder 0.5 dcompslab, dgirder 0.5 dcompslab 0.5 a. M V V d, then ( ) If < u u p v M = V V d. u u p v The demand/capacity (D/C) ratio is calculated based on the maximum permissible shear capacity at a section in accordance with AASHTO LRFD Vu Vp D φv = C 0.25 f ' b d c v (AASHTO LRFD ) 7-6 Shear Design

112 Chapter 7 - Design Precast Concrete Girder Bridges Evaluate the numerator and denominator of (AASHTO LRFD eq ): Mu ε numerator = N + V V A 0.7 f d s u u p ps pu V ε = E A + E A sdenominator p ps s vl Adjust denominator values as follows If ε sdenominator = 0 and ε snumerator > 0, then ε s =ε slimitpos and ε snumerator Ep Aps ε s A vl =. E s If ε snumerator < 0, then ε sdenominator = Ep Aps + Es Avl + Ec Ac. Evaluate (AASHTO LRFD eq ): ε snumerator ε s = ε sdenominator Check if axial tension is large enough to crack the flexural compression face of the section. Nu If > f' c, A girder then ε = 2 ε. s s Check against the limit on the strain in nonprestressed longitudinal tension reinforcement specified in the Design Request, and if necessary, recalculate how much longitudinal rebar is needed to reach the EpsSpos tension limit. ( LimitNeg ) ε = max ε, ε and ε = min ( ε, ε ) s s s s s slimitpos Evaluate the angle θ of inclination of diagonal compressive stresses as determined in AASHTO LRFD Article εs 45 (AASHTO LRFD ) Shear Design 7-7

113 CSiBridge Bridge Superstructure Design Evaluate the factor indicating the ability of diagonally cracked concrete to transmit tension and shear, as specified in AASHTO LRFD Article β= (AASHTO LRFD ) ε s Evaluate nominal shear resistance provided by tensile stresses in the concrete AASHTO LRFD eq V = β λ f ' b d c c v Evaluate how much shear demand is left to be carried by rebar. V V = V V u S p c ϕs If V < 0, then A = 0, S VS Vs else AVS =. 1 fy dv tanθ (AASHTO LRFD eq ) Check against minimum transverse shear reinforcement λ f ' c b If Vu > 0.5 φ s Vc + Vp, then AVSmin = in accordance with (AASHTO LRFD eq ); else A VS min = fy 0. If V S < 0, then AVS = AVSmin, else AVS = max( AVSmin, AVS ). Recalculate V s in accordance with (AASHTO LRFD eq ). 1 VS = AVS fy dv tanθ Evaluate longitudinal rebar on flexure tension side in accordance with (AASHTO LRFD eq ). 7-8 Shear Design

114 Chapter 7 - Design Precast Concrete Girder Bridges V U u VP 0.5 min VS, MU NU φs φ 1 SLreq = p ps dv φf φp tanθ fy A E A A = max( A, A ) VL VL SLreq Assign longitudinal rebar to the top or bottom side of the girder based on moment sign. If M < 0, then AVLCompSlabU = AVL and A VLBeamBotFlange = 0; U else A VLCompSlabU = 0 and AVLBeamBotFlange = A VL. V Shear Design Example The girder spacing is 9'-8". The girder type is AASHTO Type VI Girders, 72- inch-deep, 42-inch-wide top flange and 28-inch-wide bottom flange (AASHTO 28/72 Girders). The concrete deck is 8 inches thick, with the haunch thickness assumed = 0. Figure 7-1 Shear design example deck section Materials Concrete strength Prestressed girders 28-day strength, f c = 6 ksi, Girder final elastic modulus, E c = 4,415 ksi Deck slab: 4.0 ksi, Deck slab elastic modulus, E s = 3,834 ksi Shear Design 7-9

115 CSiBridge Bridge Superstructure Design Reinforcing steel Yield strength, f y = 60 ksi Figure 7-2 Shear design example beam section Prestressing strands 0.5-inch-diameter low relaxation strands Grade 270 Strand area, A ps = in 2 Steel yield strength, f py = 243 ksi Steel ultimate strength, f pu = 270 ksi Prestressing steel modulus, E p = 28,500 ksi Basic beam section properties Depth = 72 in. Thickness of web = 8 in. Area, A g = 1,085 in Shear Design

116 Chapter 7 - Design Precast Concrete Girder Bridges A c = Area of concrete on the flexural tension side of the member (bordered at mid depth of the beam + slab height) = 551 in 2 Moment of inertia, Ig = 733,320 in 4 N.A. to top, y t = in. N.A. to bottom, y b = in. P/S force eccentricity e = in. In accordance with AASHTO LRFD , the effective flange width of the concrete deck slab is taken as the tributary width. For the interior beam, the b slab = 9'-8" = 116 in. Demands at interior girder Section 2 = station 10, after girder Section 2, V u = kip; M u = 3678 kip-ft The component in the direction of the applied shear of the effective prestressing force, positive if resisting the applied shear, is evaluated: V p V V = n 2c 2tot girders V p = 0 since no inclined tendons are present. Depth of equivalent stress block a for both positive and negative moment is evaluated in accordance with (AASHTO LRFD eq ). Effective shear depth is evaluated: Since M u > 0, then (for calculation of the depth of the compression block, refer to the Flexure example in Section 7.3 of this manual) ( girder bot bot ) ( ) d = max 0.72 d, 0.9 d, d 0.5 a v PT PT = max ", ", 75" d = max 57. 6", 67. 5", " = " v ( ) Value reported by CSiBridge = 72.74" Check if Mu < Vu Vp dv M = = > ( ) u 3, ,136 kip-in = 23,204 kip-in Shear Design 7-11

117 CSiBridge Bridge Superstructure Design D/C is calculated based on the maximum permissible shear capacity at a section in accordance with AASHTO LRFD Vu 319 Vp 0 D φv 0.9 = = = C 0.25 f ' b d c Value reported by CSiBridge = v Evaluate the numerator and denominator of (AASHTO LRFD eq ) Mu ε snumerator = Nu + Vu Vp Aps 0.7 fpu dv = = kip ε sdenominator = Ep Aps + Es Avl = ksi 6.73 in = kip Adjust denominator values as follows If ε sdenominator = 0 and ε snumerator > 0, then ε s =ε slimitpos and εsnumerator Ep Aps εs Avl = is not applicable. E s If ε snumerator < 0, then ε sdenominator = Ep Aps + Es Avl + Ec Ac = = kip Evaluate (AASHTO LRFD eq ) ε snumerator ε s = = = εsdenominator E-4 Value reported by CSiBridge = 1.318E-4 Check if axial tension is large enough to crack the flexural compression face of the section Shear Design

118 Chapter 7 - Design Precast Concrete Girder Bridges If N A u girder > 0.52 f ', then ε = 2 ε ; this is not applicable since N u = 0. c s s Check against the limit on strain in nonprestressed longitudinal tension reinforcement as specified in the Design Request, and recalculate A vl. ( ) ( ) ε = max ε, ε = max 1.318E-4, 1.318E-4 4 = 1.318E-4 s s slimitpos Evaluate angle θ of inclination of diagonal compressive stresses as determined in AASHTO LRFD Article θ= εs 45 θ= E-4 = 28.5deg Value reported by CSiBridge = 28.5 deg Evaluate factor indicating ability of diagonally cracked concrete to transmit tension and shear as specified in AASHTO LRFD Article β= ε = s E-4 = Value reported by CSiBridge = Evaluate nominal shear resistance provided by tensile stresses in the concrete (AASHTO LRFD eq ). V = β λ f ' b d c c v = = kip Value reported by CSiBridge = kip Evaluate how much shear demand is left to be carried by rebar: Vu 319 VS = Vp Vc = = kip φ 0.9 s Value reported by CSiBridge = kip If V S < 0, then A VS = 0; else Shear Design 7-13

119 CSiBridge Bridge Superstructure Design A VS Vs = = = 1.43E-2in /in 1 1 fy dv tan θ tan 28.5 (AASHTO LRFD eq ) Check against minimum transverse shear reinforcement. If V > 0.5 φ V + V > kip > = kip is true, A VS min u s c p λ f ' c b = = = in /in f 60 If V < 0, then A A min; S VS y = else A ( A A ) Value reported by CSiBridge = 1.43E-2in 2 /in VS (AASHTO LRFD eq ) = max, = 1.43E-2in /2 VS VS min VS Recalculate V s in accordance with (AASHTO LRFD eq ). 1 1 VS = AVS fy dv = = kip tan θ tan 28.5 Value reported by CSiBridge = kip Evaluate longitudinal rebar on flexure tension side in accordance with AASHTO LRFD eq : V U u VP 0.5 min VS, MU NU φs φs 1 SLreq = p ps dv φf φp tan θ fy A E A = = in tan Value reported by CSiBridge = 0.00 in 2 no additional longitudinal rebar is required in the beam bottom flange. V Flexure Design The following parameter is used in the design of flexure: 7-14 Flexure Design

120 Chapter 7 - Design Precast Concrete Girder Bridges PhiC Resistance Factor; Default Value = 1.0, Typical value: 1.0. The nominal flexural capacity is multiplied by the resistance factor to obtain factored resistance Variables A PS Area of PT in the tension zone A S A slab a b slab b webeq d P d S Area of reinforcement in the tension zone Tributary area of the slab Depth of the equivalent stress block in accordance with AASHTO LRFD Effective flange width = horizontal width of slab tributary area, measured from out to out Thickness of the beam web Distance from the extreme compression fiber to the centroid of the prestressing tendons in the tension zone Distance from the extreme compression fiber to the centroid of the rebar in the tension zone f ps Average stress in prestressing steel (AASHTO LRFD eq ) f pu f py f y Specified tensile strength of prestressing steel (area weighted average of all tendons in the tensile zone) Yield tensile strength of prestressing steel (area weighted average of all tendons in the tensile zone) Yield strength of rebar k PT material constant (AASHTO LRFD eq ) M n M r Nominal flexural resistance Factored flexural resistance Flexure Design 7-15

121 CSiBridge Bridge Superstructure Design t slabeq αα 1 Thickness of the composite slab Stress block factor, as specified in AASHTO LRFD 2015 Interim Section β 1 Stress block factor, as specified in AASHTO LRFD Section φ Resistance factor for flexure Design Process The derivation of the moment resistance of the section is based on the approximate stress distribution specified in AASHTO LRFD Article The natural relationship between concrete stress and strain is considered satisfied by an equivalent rectangular concrete compressive stress block of αα 1 ff cc over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = β 1c from the extreme compression fiber. If the AASHTO LRFD 2015 interim is selected the factor αα 1 is taken as 0.85 for specified compressive strengths not exceeding 10.0 ksi. For specified concrete compressive strengths exceeding 10.0ksi, αα 1 is reduced at rate of 0.02 for each 1.0ksi of strength in excess of 10.0ksi, except that αα 1 is not taken less than For AASHTO LRFD no interim the αα 1 is always taken as 0.85 independent of concrete compressive strength. The distance c is measured perpendicular to the neutral axis. The factor β 1 is taken as 0.85 for concrete strengths not exceeding 4.0 ksi. For concrete strengths exceeding 4.0 ksi, β 1 is reduced at a rate of 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi, except that β 1 is not to be taken to be less than The flexural resistance is determined in accordance with AASHTO LRFD paragraph 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 compression zone are not considered. It is assumed that all defined tendons in a section, stressed or not, have f pe (effective stress after loses) larger than 0.5 f pu (specified tensile strength). If a certain tendon should not be considered for the flexural capacity calculation, its area must be set to zero Flexure Design

122 Chapter 7 - Design Precast Concrete Girder Bridges 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 Algorithms At each section: All section properties and demands are converted from CSiBridge model units to N, mm. The αα 1 stress block factor is evaluated in accordance with AASHTO LRFD based on section f c For AASHTO LRFD 2015 Interim iiii ff cc > 10.0kkkkkk, ttheeee αα 1 = mmmmmm 0.85 ff cc ; else αα 1 = 0.85 For AASHTO LRFD No Interim αα 1 = 0.85 The β 1 stress block factor is evaluated in accordance with AASHTO LRFD based on section f c. f c 28 If f c > 28 MPa, then β 1 = max ; 0.65 ; 7 else β 1 = The tendon and rebar location, area and material are read. Only bonded tendons are processed; unbonded tendons are ignored. Tendons and rebar are split into two groups depending on what sign of moment they resist negative or positive. A tendon or rebar is considered to resist a positive moment when it is located outside of the top fiber compression stress block, and it is considered to resist a negative moment when it is located outside of the bottom fiber compression stress block. The compression Flexure Design 7-17

123 CSiBridge Bridge Superstructure Design stress block extends over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = β 1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis. For each tendon group, an area weighted average of the following values is determined: sum of the tendon areas, A PS center of gravity of the tendons, d P specified tensile strength of prestressing steel f pu constant k (eq ) k = f f py pu For each rebar group the following values are determined: sum of tension rebar areas, A s distance from the extreme compression fiber to the centroid of the tension rebar, d s Positive moment resistance First it is assumed that the equivalent compression stress block is within the top slab. Distance c between the neutral axis and the compressive face is calculated in accordance with (AASHTO LRFD eq ) APS fpu + Af s s c = f α β + pu 1 f c 1bslab kaps d p The distance c is compared against requirement of Section to verify if stress in mild reinforcement f s can be taken as equal to f y. The limit on ratio c/d s is calculated depending on what kind of code and its interim are specified in the Bridge Design Preferences form as shown in the table below: Code AASHTO LRFD 2012 AASHTO LRFD 2012 with 2013 Interims or 7-18 Flexure Design

124 Chapter 7 - Design Precast Concrete Girder Bridges No Interims later Ratio limit cc dd ss εε cccc where the compression control strain limit εε cccc is per AASHTO LRFD 2013 Interims table C When the limit is not satisfied the stress in mild reinforcement f s is reduced to satisfy the requirement of Section The distance c is compared to the slab thickness. If the distance to the neutral axis c is larger than the composite slab thickness, the distance c is re-evaluated. For this calculation, the beam flange width and area are converted to their equivalents in slab concrete by multiplying the beam flange width by the modular ratio between the precast girder concrete and the slab concrete. The web width in the equation for c is substituted for the effective converted girder flange width. The distance c is recalculated in accordance with (AASHTO LRFD eq ). ( ) A f + Af α f b b t c = f α β + PS PU s s 1 c slab webeq slabeq pu 1 f c 1bwebeq kaps y pt If the calculated value of c exceeds the sum of the deck thickness and the equivalent precast girder flange thickness, the program assumes the neutral axis is below the flange of the precast girder and recalculates c. The term 1 ff cc (bb bb ww ) in the calculation is broken into two terms, one refers to the contribution of the deck to the composite section flange and the second refers to the contribution of the precast girder flange to the composite girder flange. Average stress in prestressing steel f ps is calculated in accordance with AASHTO LRFD c fps = fpu 1 k d p Nominal flexural resistance M n is calculated in accordance with AASHTO LRFD If the section is a T-section, then Flexure Design 7-19

125 CSiBridge Bridge Superstructure Design M A f cβ cβ cβ t d A f d f ( b b ) t else cβ1 cβ1 Mn = APS fps dp + AS fs ds 2 2 Factored flexural resistance is obtained by multiplying M n by φ slabeq n = PS PS p + S s s +α1 c slab webeq slabeq ; M r = ϕ M n Extreme moment M3 demands are found from the specified demand sets and the controlling demand set name is recorded. The process for evaluating negative moment resistance is analogous, except that calculation of positive moment resistance is not applicable Flexure Capacity Design Example Figure 7-3 Flexure capacity design example deck section Girder spacing: 9'-8" Girder type: AASHTO Type VI Girders, 72 inches deep, 42-inch-wide top flange, and 28-inch-wide bottom flange (AASHTO 28/72 Girders) Concrete deck: 8 inches thick, haunch thickness assumed = Flexure Design

126 Chapter 7 - Design Precast Concrete Girder Bridges Figure 7-4 Flexure capacity design example beam section Materials Concrete strength Prestressed girders 28-day strength, f c = 6 ksi, Girder final elastic modulus, Ec = 4,696 ksi Deck slab = 4.0 ksi, Deck slab elastic modulus, Es = 3,834 ksi Reinforcing steel yield strength, fy = 60 ksi Prestressing strands 0.5-inch-diameter low relaxation strands Grade 270 Strand area, Aps = in 2 Flexure Design 7-21

127 CSiBridge Bridge Superstructure Design Steel yield strength, fpy = 243 ksi Steel ultimate strength, fpu = 270 ksi Prestressing steel modulus, Ep = 28,500 ksi Basic beam section properties Depth = 72 in. Thickness of web = 8 in. Area, Ag = 1,085 in 2 Moment of inertia, Ig = 733,320 in 4 N.A. to top, yt = in. N.A. to bottom, yb = in. P/S force eccentricity e = in. In accordance with AASHTO LRFD paragraph , the effective flange width of the concrete deck slab is taken as the tributary width. For the interior beam, the b slab = 9'-8" = 116 in. Tendons are split into two groups depending on which sign of moment they resist negative or positive. A tendon is considered to resist a positive moment when it is located outside of the top fiber compression stress block and is considered to resist a negative moment when it is located outside of the bottom fiber compression stress block. The compression stress block extends over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = β 1c from the extreme compression fiber. The distance c is measured perpendicular to the neutral axis. For each tendon group, an area weighted average of the following values is determined: sum of tendon areas 2 A PTbottom = = in Value reported by CSiBridge = in 2 distance from center of gravity of tendons to extreme compression fiber y PT ( ) bottom = = 75 in specified tensile strength of prestressing steel f pu = 270 kip Value reported by CSiBridge = 270 kip 7-22 Flexure Design

128 Chapter 7 - Design Precast Concrete Girder Bridges constant k (AASHTO LRFD eq ) fpy 243 k = = = 0.28 fpu 270 Value reported by CSiBridge = 0.28 β 1 stress block factor is evaluated in accordance with AASHTO LRFD based on the composite slab f c β 1 shall be taken as 0.85 for concrete strength not exceeding 4.0 ksi. If f c > 4 ksi, then β 1 shall be reduced at a rate of 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi. Since f c = 4 ksi, β 1 = Value calculated by CSiBridge = 0.85 (not reported) The distance c between neutral axis and the compressive face is evaluated in accordance with AASHTO LRFD APTbottom fpu c = f 0.85 f c β 1 bslab + k APTbottom y PTbottom * 270 = = in Value calculated by CSiBridge = in The distance c is compared to the composite slab thickness to determine if the c needs to be re-evaluated to include the precast beam flange in the equivalent compression block. Since c = in < 8 in, the c is valid. Average stress in prestressing steel f ps is calculated in accordance with AASHTO LRFD c fps = f pu 1 k ksi y = = PTbottom 75 Value reported by CSiBridge = ksi Nominal flexural resistance M n is calculated in accordance with AASHTO LRFD pu Flexure Design 7-23

129 CSiBridge Bridge Superstructure Design Since the section is rectangular, cβ Mn = APTbottom fps yptbottom = = = kip-ft Value calculated by CSiBridge = kip-ft (not reported) Factored flexural resistance is obtained by multiplying M n by φ. M r =φ M = = kip-ft n Value reported by CSiBridge = kip-ft ( kip-in) 7-24 Flexure Design

130 Chapter 8 Design Steel I-Beam Bridge with Composite Slab This chapter describes the algorithms CSiBridge applies when designing steel I-beam with composite slab superstructures in accordance with, the AASHTO LRFD 2014 (AASHTO LRFD). 8.1 Section Properties Yield Moments Composite Section in Positive Flexure The positive yield moment, M y, is determined by the program in accordance with AASHTO LRFD Section D6.2.2 using the following user-defined input, which is part of the Design Request (see Chapter 4 for more information about Design Request). M dnc = The user specifies in the Design Request the name of the combo that represents the moment caused by the factored permanent load applied before the concrete deck has hardened or is made composite. M dc = The user specifies in the Design Request the name of the combo that represents the moment caused by the remainder of the factored permanent load (applied to the composite section). The program solves for M AD from the following equation, 8-1

131 CSiBridge Bridge Superstructure Design F yt M M M S S S dnc dc AD = + + (AASHTO LRFD D ) NC LT ST and then calculates yield moment based on the following equation where My = Mdnc + Mdc + MAD (AASHTO LRFD D ) S NC = Noncomposite section modulus (in. 3 ) S LT = Long-term composite section modulus (in. 3 ) S ST = Short-term composite section modulus (in. 3 ) M y is taken as the lesser value calculated for the compression flange, M yc, or the tension flange, M yt. The positive M y is calculated only once based on M dnc and M dc demands specified by the user in the Design Request. It should be noted that the M y calculated in the procedure described here is used by the program only to determine M npos for a compact section in positive bending in a continuous span, where the nominal flexural resistance may be controlled by M y in accordance with (AASHTO LRFD eq ). M 1.3RM n h y 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, S ST and S LT are the same value. Also, M yt is taken with respect to either the tension flange or the longitudinal reinforcement, whichever yields first. The negative M y is calculated only once based on the M dnc and M dc demands specified by the user in the Design Request. It should be noted that the M y calculated in the procedure described here is used by the program solely to determine the limiting slenderness ratio for a compact web corresponding to 2D cp /t w in (AASHTO LRFD eq. A ). 8-2 Section Properties

132 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab E Fyc Dcp λ pw( D ) = λ cp 2 rw M D p c RM h y (AASHTO LRFD A ) and web plastification factors in (AASHTO LRFD eqs. A and A ). R pc RM λ λ ( ) h yc w pw D M c p Mp = 1 1 λ λ ( ) Mp rw pw Dc Myc Myc (AASHTO LRFD A ) R pt RM λ λ ( ) h yt w pw D M c p Mp = 1 1 λ λ ( ) Mp rw pw Dc Myt Myt (AASHTO LRFD A ) Plastic Moments Composite Section in Positive Flexure The positive plastic moment, M p, is calculated as the moment of the plastic forces about the plastic neutral axis. Plastic forces in the steel portions of a cross-section are calculated using the yield strengths of the flanges, the web, and reinforcing steel, as appropriate. Plastic forces in the concrete portions of the cross-section that are in compression are based on a rectangular stress block with the magnitude of the compressive stress equal to 0.85 f c. Concrete in tension is neglected. The position of the plastic neutral axis is determined by the equilibrium condition that there is no net axial force. In calculating M p for positive moment, the contribution of the rebar in the deck is ignored. The plastic moment of a composite section in positive flexure is determined by: Calculating the element forces and using them to determine if the plastic neutral axis is in the web, top flange, or concrete deck Calculating the location of the plastic neutral axis within the element determined in the first step Section Properties 8-3

133 CSiBridge Bridge Superstructure Design Calculating Mp. Equations for the various potential locations of the plastic neutral axis (PNA) are given in Table 8-1. Table 8-1 Calculation of PNA and Mp for Sections in Positive Flexure Case PNA Condition Y and Mp I In Web D P t Pc Ps Prt Prb Y = Pt + Pw Pw P 2 w = 2 M + p Y D Y + Pd s s + Prt drt + Prbd rb + Pd c c + Pd t t 2D Pc + Ps + Prb + Pn ( ) [ ] II In Top Flange t c Pw + Pt Ps Prt Prb Y = Pc Pt + Pw + Pc P 2 c = 2 M + p Y tc Y + Pd s s + Pd n n + Prbd rb + Pw dw + Pd t t 2t Ps + Prb + Pn ( ) [ ] c III Concrete Deck Below Prb Pt + Pw + Pc c rb Ps + Prb + Pn t2 P c + Pw + Pt Prt Prb Y = ( ts ) Ps 2 Y P s Mp = + Prtdrt + Prbd rb + Pd c c + Pw dw + Pd t t 2ts [ ] IV Concrete Deck at Prb Pt + Pw + Pc + Prb crb ts Y = c rb 2 Y P Ps + Pn s Mp = + [ Prtdrt + Pd c c + Pw dw + Pd t t ] 2ts V Concrete Deck Above Prb and Below Prt Pt + Pw + Pc + Prb crt Ps + Pn ts Y ( t ) P + P + P + P P rb c w t rt = s P s M P d P d Pd P d Pd 2 Y Ps p = + rt rt + rb rb + c c + w w + t t 2ts [ ] VI Concrete Deck at Prt Pt + Pw + Pc + Prb + Pn crt ts Y = c rt 2 Y P Ps s Mp = + [ Prbdrb + Pd c c + Pw dw + Pd t t ] 2ts 8-4 Section Properties

134 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab Table 8-1 Calculation of PNA and Mp for Sections in Positive Flexure Case PNA Condition Y and Mp VII Concrete Deck Above Prt Pt + Pw + Pc + Prb + Prt < crt Ps ts Y ( t ) P + P + P + P + P rb c w t rt = s P s M P d P d Pd P d Pd 2 Y Ps p = + rt rt + rb rb + c c + w w + t t 2ts [ ] Next the section is checked for ductility requirement in accordance with equation In checking the ductility per , the depth of the haunch is neglected. D p 0.42D t where D p is the distance from the top of the concrete deck to the neutral axis of the composite section at the plastic moment, and D t is the total depth of the composite section. At the section where the ductility requirement is not satisfied, the plastic moment of a composite section in positive flexure is set to zero. t c t s D b s b c t w A rt A rb P rt P P s rb P c P w Y PNA C rb PNA Y C rt Y PNA t t b t P t CASE I CASE II CASES III-VII Figure 8-1 Plastic Neutral Axis Cases -- Positive Flexure Section Properties 8-5

135 CSiBridge Bridge Superstructure Design Composite Section in Negative Flexure The plastic moment of a composite section in negative flexure is calculated by an analogous procedure. Equations for the two cases most likely to occur in practice are given in Table 8-2. The plastic moment of a noncomposite section is calculated by eliminating the terms pertaining to the concrete deck and longitudinal reinforcement from the equations in Tables 8-1 and 8-2 for composite sections. Table 8-2 Calculation of PNA and Mp for Sections in Negative Flexure Case PNA Condition Y and Mp I In Web Pc + Pw Pt + Prb + Pn D Pc Pt Prt Prb Y = P w P M = Y + D Y + P d + P d + Pd + Pd 2D 2 ( ) [ ] w 2 p n n rb rb t t l l II In Top Flange Pc + Pw + Pt Prb + Pn tl Pw Pc Prt Prb Y = P t P M = Y + t Y + Pd + P d + P d + Pd 2 ( ) [ ] t 2 p l n n rb rb w w c c 2t l A rt A rb P rt t s P rb t t D b c t w P t P w Y PNA PNA Y t c P c b c CASE V CASE I CASE II Figure 8-2 Plastic Neutral Axis Cases -- Negative Flexure 8-6 Section Properties

136 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab in which P rt = F yrt A rt P s = 0.85 f c b st s P rb = F yrb A rb P c = F ycb ct c P w = F yw Dt w P t = F yt b tt t In the equations for M p given in Tables 8-1 and 8-2, d is the distance from an element force to the plastic neutral axis. Element forces act at (a) mid-thickness for the flanges and the concrete deck, (b) mid-depth of the web, and (c) center of reinforcement. All element forces, dimensions, and distances are taken as positive. The conditions are checked in the order listed in Tables 8-1 and Section Classification and Factors Compact or Non-Compact Positive Flexure The program determines if the section can be qualified as compact based on the following criteria: the specified minimum yield strengths of the flanges do not exceed 70.0 ksi, the web satisfies the requirement of AASHTO LRFD Article ( ), D 150 t w the section satisfies the web slenderness limit, 2D t w cp E (AASHTO LRFD ) F yc The program does not verify if the composite section is kinked (chorded) continuous or horizontally curved. Section Properties 8-7

137 CSiBridge Bridge Superstructure Design Design in Accordance with Appendix A The program determines if a section qualifies to be designed using Appendix A of the AASHTO LRFD Edition based on the following criteria: the Design Request Parameter Use Appendix A? is set to Yes (see Chapter 4 for more information about setting parameters in the Design Request), the specified minimum yield strengths of the flanges do not exceed 70.0 ksi, the web satisfies the noncompact slenderness limit, 2D t w c E < 5.7 (AASHTO LRFD ) F yc the flanges satisfy the following ratio, I I yc yt 0.3. (AASHTO LRFD ) The program does not verify if the composite section is kinked (chorded) continuous or horizontally curved Hybrid Factor Rh Composite Section Positive Flexure For rolled shapes, homogenous built-up sections, and built-up sections with a higher-strength steel in the web than in both flanges, R h is taken as 1.0. Otherwise the hybrid factor is taken as: where 3 ( ) 12 +β 3ρ ρ R h = (AASHTO LRFD ) β ρ=the smaller of F f and 1.0 yw n β= 2 Dt n w A fn (AASHTO LRFD ) A fn = bottom flange area 8-8 Section Properties

138 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab D n = the distance from the elastic neutral axis of the cross-section to the inside face of bottom flange F n = f y of the bottom flange Hybrid Factor Rh Composite Section Negative Flexure For rolled shapes, homogenous built-up sections, and built-up sections with a higher-strength steel in the web than in both flanges, R h is taken as 1.0. Otherwise the hybrid factor is taken as: where 3 ( ) 12 +β 3ρ ρ R h = (AASHTO LRFD ) β β= 2 Dt n w A fn (AASHTO LRFD ) ρ=the smaller of F f and 1.0 yw n A fn = Flange area on the side of the neutral axis corresponding to D n. If the top flange controls, then the area of longitudinal rebar in the slab is included in calculating A fn. D n = The larger of the distances from the elastic neutral axis of the cross-section to the inside face of either flange. For sections where the neutral axis is at the mid-depth of the web, this distance is from the neutral axis to the inside face of the flange on the side of the neutral axis where yielding occurs first. F n = f y of the controlling flange. When the top flange controls, then F n is equal to the largest of the minimum specified yield strengths of the top flange or the longitudinal rebar in the slab Hybrid Factor Rh Non Composite Section For rolled shapes, homogenous built-up sections, and built-up sections with a higher-strength steel in the web than in both flanges, R h is taken as 1.0. Otherwise the hybrid factor is taken as: Section Properties 8-9

139 CSiBridge Bridge Superstructure Design where 3 ( ) 12 +β 3ρ ρ R h = (AASHTO LRFD ) β ρ=the smaller of F f and 1.0 yw n β= 2 Dt n w A fn (AASHTO LRFD ) A fn = Flange area on the side of the neutral axis corresponding to D n. D n = The larger of the distances from the elastic neutral axis of the cross-section to the inside face of either flange. For sections where the neutral axis is at the mid-depth of the web, this distance is from the neutral axis to the inside face of the flange on the side of the neutral axis where yielding occurs first. F n = f y of the controlling flange Web Load-Shedding Factor Rb When checking constructability in accordance with the provisions of AASHTO LRFD Article or for composite sections in positive flexure, the R b factor is taken as equal to 1.0. For composite sections in negative flexure, the R b factor is taken as: where R b awc 2Dc = 1 λrw a wc t + w (AASHTO LRFD ) λ =5.7 rw E F yc (AASHTO LRFD ) a wc 2Dt c w = (AASHTO LRFD ) b t fc fc 8-10 Section Properties

140 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab When the user specifies the Design Request parameter Do webs have longitudinal stiffeners? as yes, the R b factor is set to 1.0 (see Chapter 4 for more information about specifying Design Request parameters) Unbraced Length Lb and Section Transitions The program assumes that the top flange is continuously braced for all Design Requests, except for Constructability. For more information about flange lateral bracing in a Constructability Design Request, see Section 8.6 of this manual. The unbraced length L b for the bottom flange is equal to the distance between the nearest downstation and upstation qualifying cross diaphragms or span support as defined in the Bridge Object. Some of the diaphragm types available in CSiBridge may not necessarily provide restraint to the bottom flange. The program assumes that the following diaphragm qualifies as providing lateral restraint to the bottom flange: single beam, all types of chords and braces except V braces without bottom beams. For unbraced lengths where the member is nonprismatic, the lateral torsional buckling resistance of the compression flange at each section within the unbraced length is taken as the smallest resistance within the unbraced length under consideration and the moment gradient modifier Cb is taken as 1.0. For unbraced lengths containing a transition to a smaller section at a distance less than or equal to 20% of the unbraced length from a brace point, the lateral torsional buckling resistance is determined assuming the transition to the smaller section does not exist provided that the lateral moment of inertia of the flange of the smaller section is equal to or larger than 0.5 times the corresponding value in the larger section. The algorithm does not distinguish at which brace point the moment demand is smaller and applies the exception at both brace points. It is the responsibility of the user to pay special attention to the section transition within the 20% of the unbraced length from the brace point and to follow the guidelines in AASHTO LRFD C For this algorithm to be effective, it is necessary to have bridge section cuts at each nonprismatic girder-section transition. This can be assured by using the local section cuts feature when updating the linked model to create additional local section cuts for each girder of steel I-girder bridge sections. Such girderonly section cuts will be created at changes in the steel I-girder section, at stag- Section Properties 8-11

141 CSiBridge Bridge Superstructure Design gered diaphragms (cross frames), and at splice locations wherever a full-width section cut does not exist. 8.2 Demand Sets Demand Set combos (at least one is required) are user-defined combinations based on LRFD combinations (see Chapter 4 for more information about 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 program assumes that the effects of the staging of loads applied to non-composite versus composite sections, as well as the concrete slab material time dependent properties, were captured by using the Nonlinear Staged Construction load case available in CSiBridge. Note that the Design Request for staged constructability check (Steel-I Comp Construct Stgd) allows only Nonlinear Staged Construction load cases to be used as Demand Sets. If Use Stage Analysis? = No, the program decomposes load cases present in every demand set combo to three Bridge Design Action categories: noncomposite, 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 dropdown list; under the heading Bridge Design Action, select the User Defined option and select a value from the list. The assigned Bridge Designed Action values are handled by the program in the following manner: Table 8-3 Bridge Design Action Bridge Design Action Value Specified by the User Non-Composite Long-Term Composite Bridge Design Action Category Used in the Design Algorithm Non-Composite Long-Term Composite 8-12 Demand Sets

142 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab Short-Term Composite Staged Other Short-Term Composite Non-Composite Non-Composite Demand Flange Stresses fbu and ff Evaluation of the flange stress, f bu, calculated without consideration of flange lateral bending is dependent on setting the Design Request parameter Use Stage Analysis? If the Use Stage Analysis? = No, then f bu P M M M = A S S S NC LTC STC comp steel LTC STC where M NC is the demand moment on the non-composite section, M LTC is the demand moment on the long-term composite section, and M STC is the demand moment on the short-term composite section. The short-term section modulus for positive moment is calculated by transforming the concrete deck using the steel-to-concrete modular ratio. The modular ratio (n) is calculated as a decimal number expressed as n=e s/e c and used without rounding. The long-term section modulus for positive moment is calculated using a modular ratio factored by n, where n is specified in the Design Parameter as the Modular ratio long-term multiplier. The effect of compression reinforcement is ignored. For negative moment, the concrete deck is assumed cracked and is not included in the section modulus calculations while tension reinforcement is accounted for. If Use Stage Analysis? = Yes, then the f bu stresses on each flange are read directly from the section cut results. The program assumes that the effects of the staging of loads applied to non-composite versus composite sections, as well as the concrete slab material time dependent properties, were captured by using the Nonlinear Staged Construction load case available in CSiBridge. In the Strength Design Check, the program verifies the sign of the stress in the composite slab, and if stress is positive (tension), the program assumes that the entire section cut demand moment is carried by the steel section only. This is to reflect the fact that the concrete in the composite slab is cracked and does not Demand Sets 8-13

143 CSiBridge Bridge Superstructure Design contribute to the resistance of the section. Flange stress f f, used in the Service Design Check, is evaluated in the same manner as stress f bu, with one exception. When the Steel Service Design Request parameter Does concrete slab resist tension? is set to Yes, the program uses section properties based on a transformed section that assumes the concrete slab to be fully effective in both tension and compression. In the Constructability checks, the program proceeds based on the status of the concrete slab. When no slab is present or the slab is non-composite, the f bu stresses on each flange are read directly from the section cut results. When the slab status is composite, the program verifies the sign of the stress in the 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 Demand Flange Lateral Bending Stress f l The flange lateral bending stress f l is evaluated only when all of the following conditions are met: Steel Girders has been selected for the deck section type (Components > Superstructure Item > Deck Sections command) and the Girder Modeling In Area Object Models Model Girders Using Area Objects option is set to Yes on the Define Bridge Section Data Steel Girder form. The bridge object is modeled using Area Objects. This option can be set using the Bridge > Update command to display the Update Bridge Structural Model form; then select the Update as Area Object Model option. Set the Live Load Distribution to Girders method to Use Forces Directly from CSiBridge on the Bridge Design Request Superstructure {Code} form, which displays when the Design/Rating > Superstructure Design > Design Requests command is used (see Chapter 3 for more information about Live Load Distribution). Since there is no live load used in the Constructability design, request this setting does not apply in that case. In all other cases, the flange lateral bending stress is set to zero. The f l stresses on each flange are read directly from the section cut results Demand Sets

144 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab Depth of the Web in Compression For composite sections in positive flexure, the depth of the web in compression is computed using the following equation: fc Dc = d tfc 0 fc f + t (AASHTO LRFD D6.3-1) where Figure 8-3 Web in Compression Positive Flexure f c = Sum of the compression-flange stresses caused by the different loads, i.e., DC1, the permanent load acting on the noncomposite section; DC2, the permanent load acting on the long-term composite section; DW, the wearing surface load; and LL+IM; acting on their respective sections. f c is taken as negative when the stress is in compression. Flange lateral bending is disregarded in this calculation. f t = Sum of the tension-flange stresses caused by the different loads. Flange lateral bending is disregarded in this calculation. For composite sections in negative flexure, D c is computed for the section consisting of the steel girder plus the longitudinal reinforcement, with the exception of the following. For composite sections in negative flexure at the Service Design Check Request where the concrete deck is considered effective in tension for computing flexural stresses on the composite section (Design Parameter Does concrete slab resist tension? = Yes), D c is computed from AASHTO LRFD Eq. D For this case, the stresses f c and f t are switched, the signs shown in the stress diagram are reversed, t fc is the thickness of the bottom flange, and D c instead extends from the neutral axis down to the top of the bottom flange. Demand Sets 8-15

145 CSiBridge Bridge Superstructure Design Moment Gradient Modifier Cb When the design request parameter Method for determining moment gradient factor C b is set to Program Determined, then for each demand set the stresses defined in AASHTO LRFD section f mid, f 0,f 1 and f 2 at the unbraced segment are determined by interpolation of demands at nearest section cuts. The designer should be aware that live load moments at neighboring section cuts within the unbraced segment are not necessarily controlled by the same load pattern and as a result the moment gradient calculation may be impacted. The moment gradient modifier C b is then calculated as: 8.3 Strength Design Request Flexure The Strength Design Check calculates at every section cut positive flexural capacity, negative flexural capacity, and shear capacity. It then compares the capacities against the envelope of demands specified in the Design Request Positive Flexure Compact The nominal flexural resistance of the section is evaluated as follows: If D p 0.1 D t, then M n = M p; otherwise M n D p = Mp Dt (AASHTO LRFD ) In a continuous span, the nominal flexural resistance of the section is determined as 8-16 Strength Design Request

146 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab M n 1.3R hm y where R h is a hybrid factor for the section in positive flexure. The demand over capacity ratio is evaluated as 1 Mu + fs 1 xt DoverC max 3 f l =, f Mn 0.6 F φ yf Positive Flexure Non-Compact Nominal flexural resistance of the top compression flange is taken as: F nc = R br hf yc (AASHTO LRFD ) Nominal flexural resistance of the bottom tension flange is taken as: F nt = R hf yt (AASHTO LRFD ) The demand over capacity ratio is evaluated as 1 fbu + f1 DoverC max 3 fbu f l =,, f Fnt f Fnc 0.6 F φ φ yf Negative Flexure in Accordance with Article The local buckling resistance of the compression flange F nc(flb) as specified in AASHTO LRFD Article is taken as: If λ f λ pf, then F nc = R br hf yc. ( ) Otherwise F Fyr λf λpf = 1 1 RRF RF h yc λrf λpf nc b h yc ( ) in which Strength Design Request 8-17

147 CSiBridge Bridge Superstructure Design bfc λ f = 2 t fc ( ) E λ pf = 0.38 ( ) F yc E λ rf = 0.56 ( ) F yr F yr = Compression-flange stress at the onset of nominal yielding within the cross-section, including residual stress effects, but not including compression-flange lateral bending, taken as the smaller of 0.7F yc and F yw, but not less than 0.5 F yc. The lateral torsional buckling resistance of the compression flange F nc(ltb) as specified in AASHTO LRFD Article ( ) is taken as follows: If L b L p, then F nc = R br hf yc. ( ) If L p < L b L r, then Fyr Lb Lp F = C 1 1 RRF RRF RF h yc Lr Lp nc b b h yc b h yc ( ) If L b > L r, then F nc = F cr R br hf yc ( ) in which E Lb = unbraced length, Lp = 1.0 rt, Lr = π rt F yc E F yr C b = moment gradient modifier F cr 2 CR b bπ E = 2 Lb r t ( ) 8-18 Strength Design Request

148 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab r t = b fc 1 Dt bfct c w fc ( ) The nominal flexural resistance of the bottom compression flange is taken as the smaller of the local buckling resistance and the lateral torsional buckling resistance: Fnc = min Fnc( FLB), Fnc( LTB) The nominal flexural resistance of the top tension flange is taken as: φ f RF h yf ( ) The demand over capacity ratio is evaluated as 1 f + f f f DoverC max,, 0.6 bu 1 3 bu 1 = φf Fm φf RF h yf F yc Negative Flexure in Accordance with Appendix A6 Sections that satisfy the following requirement qualify as compact web sections: 2D t w cp λ pw( Dcp ) (AASHTO LRFD A ) where E Fyc Dcp λ pw( Dcp ) = 2 M D p c RM h y (AASHTO LRFD A ) E λ rw = 5.7 (AASHTO LRFD A ) F yc Strength Design Request 8-19

149 CSiBridge Bridge Superstructure Design D c D cp = depth of the web in compression in the elastic range = depth of the web in compression at the plastic moment Then web plastification factors are determined as R pc M p = (AASHTO LRFD A ) M yc R pt M p = (AASHTO LRFD A ) M yt Sections that do not satisfy the requirement for compact web sections, but for which the web slenderness satisfies the following requirement: where λ <λ (AASHTO LRFD A ) w rw 2D c λ w = (AASHTO LRFD A ) t w E λ rw = 5.7 (AASHTO LRFD A ) F yc The web plastification factors are taken as: R pc RM h yc λw λpw( Dc ) Mp Mp = 1 1 Mp tw pw( Dc ) λ λ Myc Myc (AASHTO LRFD A ) R pt RM h yt λw λpw( Dc ) Mp Mp = 1 1 Mp rw pw( Dc ) λ λ Myt Myt (AASHTO LRFD A ) where 8-20 Strength Design Request

150 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab Dc λ pw( Dc) =λpw( Dcp) λ D cp rw (AASHTO LRFD A ) The local buckling resistance of the compression flange M ncflb as specified in AASHTO LRFD Article A6.3.2 is taken as: If λf λ pf, then Mnc = RpcMyc (AASHTO LRFD A ) Fyr Sxc λf λpf Otherwise Mnc = 1 1 RpcMyc RpcMyc λrf λpf (AASHTO LRFD A ) in which bfc λ f = (AASHTO LRFD A ) 2t fc E λ pf = 0.38 (AASHTO LRFD A ) F yc Ekc λ rf = 0.95 (AASHTO LRFD A ) F yr For built-up sections, k c = 4 D (AASHTO LRFD A ) t w For rolled shapes (eframeproptype =SECTION_I as defined in API function SapObject.SapModel.PropFrame.GetNameList; PropType argument) k c = 0.76 The lateral torsional buckling resistance of the compression flange M ncltb as specified in AASHTO LRFD Article A6.3.3 is taken as M nc = R pcm yc: If L L, then M = R M. (AASHTO LRFD A ) b p If L < L L, then p b r nc pc yc Strength Design Request 8-21

151 CSiBridge Bridge Superstructure Design Fyr Sxc Lb Lp Mnc = Cb 1 1 RpcMyc RpcMyc RpcMyc Lr Lp (AASHTO LRFD A ) If Lb > Lr, then Mnc = Fcr Sxc RpcMyc (AASHTO LRFD A ) in which L b = L p unbraced length, E = 1.0rt (AASHTO LRFD A ) F yc E J Fyr Sxch Lr = 1.95rt F S h E J yr xc 2 (AASHTO LRFD A ) C b = moment gradient modifier 2 Cbπ E J 2 Fcr = ( L ) 2 b rt (AASHTO LRFD A ) S h ( L r ) b t xc 3 3 fc ft fc ft ft ft 3 Dt b t w t b t t J = bfc 3 bft (AASHTO LRFD A ) r t = b fc 1 Dt b t c w fc fc (AASHTO LRFD A ) The nominal flexural resistance of the bottom compression flange is taken as the smaller of the local buckling resistance and the lateral torsional buckling resistance: Mnc = min Mnc( FLB), Mnc( LTB) 8-22 Strength Design Request

152 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab The nominal flexural resistance of the top tension flange is taken as: φ f Rpt Myt The demand over capacity ratio is evaluated as 1 Mu + f S M f DoverC max,, xc 3 u 1 = φf Mnc φf Rpt Myt F yc Net Section Fracture All tension flanges are checked for net section fracture per AASHTO LRFD section The net area of the tension flange is evaluated as follows: AA nn = rr ssssss AA gg Where r spl is a ratio defined by the user in the Splice definition (Bridge > Span Items > Optimize > Splices) command and A g is the gross flange area. The demand over capacity ratio is calculated as follows: DDDDDDDDDDDD = ff bbbb mmmmmm ff yy ;0.84 AA nn AAgg ff uu (AASHTO LRFD ) Shear Connectors The program calculates the total nominal shear force P nom as specified in AASHTO LRFD Article The user can use the P nom value to determine the minimum number of shear connectors n as defined in AASHTO LRFD eq where PP nnnnnn = PP 2 2 tt + FF rrrrrr PP tt = PP pp + PP nn PP pp = min (0.85ff cc bb sssssssstt ssssssss ; ff yyyy DDtt ww + ff yyyy bb ffff tt ffff + ff yyyy bb ffff tt ffff ) PP nn = min (0.45ff cc bb sssssssstt ssssssss ; ff yyyy DDtt ww + ff yyyy bb ffff tt ffff + ff yyyy bb ffff tt ffff ) FF rrrrrr = PP tt LL aaaaaah RR (AASHTO LRFD to 9) Strength Design Request 8-23

153 CSiBridge Bridge Superstructure Design Shear L arch is calculated as 50% of girder span length and R is the radius of the girder. When processing the Design Request from the Design module, the program assumes that there are no vertical stiffeners present and classifies all web panels as unstiffened. If the shear capacity calculated based on this classification is not sufficient to resist the demand specified in the Design Request, the program recommends minimum stiffener spacing to achieve a Demand over Capacity ratio equal to 1. The recommended stiffener spacing is reported in the result table under the column heading d0req. In the Optimization form (Design/Rating > Superstructure Design > Optimize command), the user can specify stiffeners locations and the program recalculates the shear resistance. In that case the program classifies the web panels as interior or exterior and stiffened or unstiffened based on criteria specified in AASHTO LRFD section e. 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 Nominal Resistance of Unstiffened Webs The nominal shear resistance of unstiffened webs is taken as: V n in which V = CV (AASHTO LRFD ) p = 0.58F Dt (AASHTO LRFD ) p yw w C = the ratio of the shear-buckling resistance to the shear yield strength that is determined as follows: D Ek If 1.12, then C = 1.0. t F w yw (AASHTO LRFD ) 8-24 Strength Design Request

154 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab Ek D Ek If 1.12 < 1.40, then F t F yw w yw 1.12 C = D t w Ek. F yw (AASHTO LRFD ) D Ek 1.57 Ek If > 1.40, then C =, 2 tw F yw D F yw t w (AASHTO LRFD ) 5 in which k = dc D (AASHTO LRFD ) Nominal Resistance of Stiffened Interior Web Panels The nominal shear resistance of an interior web panel and with the section at the section cut proportioned such that: 2Dt w ( bfctfc + bfttft ) 2.5 (AASHTO LRFD ) is taken as 0.87( 1 C) Vn = Vp C+ 2 do 1+ D (AASHTO LRFD ) in which V = 0.58F Dt (AASHTO LRFD ) p yw w where d o = transverse stiffener spacing. Otherwise, the nominal shear resistance is taken as follows: Strength Design Request 8-25

155 CSiBridge Bridge Superstructure Design Vn = Vp C+ 0.87( 1 C) 2 do d o 1+ + D D (AASHTO LRFD ) Nominal Resistance of End Panels The nominal shear resistance of a web end panel is taken as: in which V n = V cr = CV p (AASHTO LRFD ) V = 0.58 F Dt. (AASHTO LRFD ) p yw w The demand over capacity ratio is evaluated as Vu DoverC =. φ V 8.4 Service Design Request v n The Service Design Check calculates at every section cut stresses f f at the top steel flange of the composite section and the bottom steel flange of the composite section and compares them against limits specified in AASHTO LRFD Section For the top steel flange of composite sections: f f DoverC =. (AASHTO LRFD ) RF h For the bottom steel flange of composite sections: yf fl f f + DoverC = 2. (AASHTO LRFD ) RF h For both steel flanges of noncomposite sections: yf 8-26 Service Design Request

156 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab fl f f + DoverC = 2. (AASHTO LRFD ) RF h yf The flange stresses are derived in the same way as f bu stress demands (see Section of this manual). The user has an option to specify if the concrete slab resists tension or not by setting the Does concrete slab resist tension? Design Request parameter. It is the responsibility of the user to verify if the slab qualifies, in accordance with Does concrete slab resist tension? Section , to resist tension. For compact composite sections in positive flexure used in shored construction, the longitudinal compressive stress in the concrete deck, determined as specified in AASHTO LRFD Article d, is checked against 0.6 f c. DoverC = f deck/0.6 f c Except for composite sections in positive flexure in which the web satisfies the requirement of AASHTO LRFD Article , all section cuts are checked against the following requirement: where: fc DoverC = (AASHTO LRFD ) F crw f c = Compression-flange stress at the section under consideration due to demand loads calculated without consideration of flange lateral bending. F crw = Nominal bend-buckling resistance for webs without longitudinal stiffeners determined as specified in AASHTO LRFD Article F crw 09. Ek = 2 D t w (AASHTO LRFD ) but not to exceed the smaller of R hf yc and F yw/0.7. In which k = bend buckling coefficient Service Design Request 8-27

157 CSiBridge Bridge Superstructure Design where 9 k = (AASHTO LRFD ) ( D D) 2 c D c = Depth of the web in compression in the elastic range determined as specified in AASHTO LRFD Article D When both edges of the web are in compression, k is taken as 7.2. The highest Demand over Capacity ratio together with controlling equation is reported for each section cut. 8.5 Fatigue Design Request Web Fatigue Web Fatigue Design Request is used to calculate the Demand over Capacity ratio as defined in AASHTO LRFD Section Special Fatigue Requirement for Webs. The requirement is applicable to interior panels of webs with transverse stiffeners. When processing the Design Request from the Design module, the program assumes that there are no vertical stiffeners present and classifies all web panels as unstiffened. Therefore, when the Design Request is completed from the Design module, the Design Result Status table shows the message text No stiffeners defined use optimization form to define stiffeners. In the Optimization form (Design/Rating > Superstructure Design > Optimize command), the user can specify stiffener locations, and then the program can recalculate the Web Fatigue Request. In that case the program classifies the web panels as interior or exterior and stiffened or unstiffened based on criteria specified in AASHTO LRFD Section 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. where DoverC = Vu Vcr (AASHTO LRFD ) 8-28 Fatigue Design Request

158 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab V u = Shear in the web at the section under consideration due to demand specified in the Design Request demand set combos. If the live load distribution to girders method Use Factor Specified by Design Code is selected in the Design Request, the program adjusts for the multiple presence factor to account for the fact that fatigue load occupies only one lane (AASHTO LRFD Section b) and multiple presence factors shall not be applied when checking for the fatigue limit state (AASHTO LRFD Section ). V cr = Shear-buckling resistance determined from AASHTO LRFD eq (see Section of this manual) Flange Fatigue For every demand set the top and bottom flange tensile stress range due to vertical bending and bottom flange tensile stress range due to lateral bending are calculated at every section cut. The tensile stress ranges can be used by the user to verify AASHTO LRFD load induced fatigue criteria specified in article The flange stresses are derived in the same way as f bu stress demands (see Section of this manual). The tensile stress range for a particular demand set is calculated as delta between maximum tensile stress and minimum tensile stress. If the minimum stress is compressive and the maximum stress is tensile the stress range is set equal to the maximum stress, if both maximum and minimum stresses are compressive the stress range is set equal to zero. If demand set does not contain an envelope of values the stress range is also set to zero. 8.6 Constructability Design Request Staged (Steel-I Comp Construct Stgd) This request enables the user to verify the superstructure during construction using a Nonlinear Staged Construction load case. The use of nonlinear staged analysis allows the user to define multiple snapshots of the structure during construction where parts of the bridge deck may be at various completion stages. The user can control which stages the program will include in the calculations of controlling demand over capacity ratios. Constructability Design Request 8-29

159 CSiBridge Bridge Superstructure Design For each section cut specified in the Design Request, the constructability design check loops through the Nonlinear Staged Construction load case output steps that correspond to Output Labels specified in the Demand Set. At each step the program determines the status of the concrete slab at the girder section cut. The slab status can be non present, present non-composite, or composite. The Staged Constructability Design Check accepts Area Object models. The Staged Constructability Design Check cannot be run on Solid or Spine models 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 Structural Model Options available in the Update Bridge Structural Model form (Bridge > Update > Structural Model Options option) Slab Status vs. Unbraced Length On the basis of the slab status, the program calculates corresponding positive flexural capacity, negative flexural capacity, and shear capacity. Next the program compares the capacities against demands specified in the Demand Set by calculating the Demand over Capacity ratio. The controlling Demand Set and Output Label on a girder basis are reported for every section cut. When the slab status is composite, the program assumes that the top flange is continuously braced. When slab status in not present or non-composite, the program treats both flanges as discretely braced. It should be noted that the program does not verify the presence of diaphragms at a particular output step. It assumes that anytime a steel beam is activated at a given section cut that the unbraced length L b for the bottom flange is equal to the distance between the nearest downstation and the upstation qualifying cross diaphragms or span ends as defined in the Bridge Object. The program assumes the same L b for the top flange. In other words the unbraced length L b is based on the cross diaphragms 8-30 Constructability Design Request

160 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab Flexure that qualify as providing restraint to the bottom flange. Some of the diaphragm types available in CSiBridge may not necessarily provide restraint to the top flange. It is the user s responsibility to provide top flange temporary bracing at the diaphragm locations before slabs acting compositely Positive Flexure Non Composite The Demand over Capacity ratio is evaluated as: 1 fbucomp fltop D fbucomp + f + ltop 3 fbucomp fbutens + f lbot = max,,, C f RF h yctop f Fnc top f Fcrwtop f RF φ φ φ φ h ytbot where F nctop is the nominal flexural resistance of the discretely braced top flange determined as specified in AASHTO LRFD Article (also see Section of this manual) and F crwtop is the nominal bend buckling resistance for webs specified in AASHTO LRFD Article for webs without longitudinal stiffeners. F crw 09. Ek = 2 D t w (AASHTO LRFD ) but not to exceed the smaller of R hf yc and F yw /0.7 where 9 k = Dc D 2 When both edges of the web are in compression, k = Positive Flexure Composite The demand over capacity ratio is evaluated as: Constructability Design Request 8-31

161 CSiBridge Bridge Superstructure Design fbucomp fbucomp fbutens + flbot DC= max,, φf RF h yctop φf Fcrwtop φf RF h ytbot where F crwtop is nominal bend-buckling resistance for webs specified in AASHTO LRFD Article for webs without longitudinal stiffeners (also see Section of this manual) Negative Flexure Non Composite The Demand over Capacity ratio is evaluated as: 1 f bucomp lbot bucomp + f f + f lbot 3 fbucomp fbutens + f ltop DC= max,,, f RF h ycbot f Fnc bot f Fcrwbot f RF φ φ φ φ h yttop where F ncbot is the nominal flexural resistance of the discretely braced bottom flange determined as specified in AASHTO LRFD Article (also see Section of this manual) and F crwbot is nominal bend-buckling resistance for webs specified in AASHTO LRFD Article for webs without longitudinal stiffeners (also see Section of this manual) Negative Flexure Composite The demand over capacity ratio is evaluated as: 1 f + comp + bot comp bot comp tens deck = max, bu l bu f f f l 3 fbu fbu f DC,,, φ φ φ φ φ f RF h ycbot f Fnc bot f Fcrwbot f RF h yttop t fr where F ncbot is the nominal flexural resistance of the discretely braced bottom flange determined as specified in AASHTO LRFD Article (also see Section of this manual), F crwbot is the nominal bend buckling resistance for webs specified in AASHTO LRFD Article for webs without longitudinal stiffeners (also see Section of this manual), and f deck is the demand tensile stress in the deck and f r is the modulus of rupture of concrete as determined in AASHTO LRFD Article Constructability Design Request

162 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab Shear When processing the Design Request from the Design module, the program assumes that there are no vertical stiffeners present and classifies all web panels as unstiffened. If the shear capacity calculated based on this classification is not sufficient to resist the demand specified in the Design Request and the controlling D over C ratio is occurring at a step when the slab status is composite, the program recommends minimum stiffener spacing to achieve a Demand over Capacity ratio equal to 1. The recommended stiffener spacing is reported in the result table under the column heading d0req. In the Optimization form (Design/Rating > Superstructure Design > Optimize command), the user can specify stiffener locations and then the program can recalculate the shear resistance. In that case the program classifies the web panels as interior or exterior and stiffened or unstiffened based on criteria specified in Section of the code. It should be noted that stiffeners are not modeled in the Bridge Object and therefore adding/modifying stiffeners does not affect the magnitude of the demands. Adding stiffeners also does not increase capacity of sections cuts where the concrete slab status is other than composite Non Composite Sections The nominal shear resistance of a web end panel is taken as: in which Vn = Vcr = CVP (AASHTO LRFD ) V = 0.58 F Dt. (AASHTO LRFD ) p yw w The Demand over Capacity ratio is evaluated as Vu DoverC = φ V Composite Section v n Nominal Resistance of Unstiffened Webs The nominal shear resistance of unstiffened webs is taken as: Constructability Design Request 8-33

163 CSiBridge Bridge Superstructure Design V n in which V = CV (AASHTO LRFD ) p = 0.58F Dt (AASHTO LRFD ) p yw w C = the ratio of the shear-buckling resistance to the shear yield strength that is determined as follows: D Ek If 1.12, then C = 1.0. (AASHTO LRFD ) t F w yw Ek D Ek If 1.12 < 1.40, then F t F yw w yw 1.12 C = D t w Ek. F yw AASHTO LRFD ( ) D Ek 1.57 Ek If > 1.40, then C =, 2 tw F yw D F yw t w AASHTO LRFD ( ) 5 in which k = dc D (AASHTO LRFD ) Nominal Resistance of Stiffened Interior Web Panels The nominal shear resistance of an interior web panel, with the section at the section cut proportioned such that 2Dt w ( bfctfc + bfttft ) 2.5, (AASHTO LRFD ) is taken as 8-34 Constructability Design Request

164 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab 0.87( 1 C) Vn = Vp C+ 2 do 1+ D (AASHTO LRFD ) in which V = 0.58F Dt (AASHTO LRFD ) p yw w where d o = transverse stiffener spacing. Otherwise, the nominal shear resistance is taken as follows: Vn = Vp C+ 0.87( 1 C) 2 do d o 1+ + D D (AASHTO LRFD ) Nominal Resistance of End Panels The nominal shear resistance of a web end panel is taken as: in which Vn = Vcr = CVP (AASHTO LRFD ) V = 0.58 F Dt. (AASHTO LRFD ) p yw w The demand over capacity ratio is evaluated as Vu DoverC = φ V 8.7 Section Optimization v n 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 Section Optimization 8-35

165 CSiBridge Bridge Superstructure Design process the demands are not recalculated and are based on the current CSiBridge analysis results. The Optimization form allows simultaneous display of three versions of section sizes and associated resistance results. The section plate size versions are As Analyzed, As Designed, and Current. The section plots use distinct colors for each version black for As Analyzed, blue for As Designed, and red for Current. When the Optimization form is initially opened, all three versions are identical and equal to As Analyzed. Two graphs are available to display various forces, moments, stresses, and 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 are plotted as solid lines and the As Designed series as dashed lines. To modify steel plate sizes or vertical stiffeners, a new form can be displayed by clicking on the Modify Section button. After the section modification is completed, the Current version is shown in red in the elevation and cross section views. After the resistance has been recalculated successfully by clicking the Recalculate Resistance button, the Current version is designated to 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. 8.8 PennDOT Amendments for DM-4 When setting the bridge superstructure design code preferences for the AASH- TO LFRD 2014 code (all interims), an option called Design Amendments is available which can be set to None or PennDOT. This is done using command Design/Rating > Superstructure Design > Code Preferences PennDOT Amendments for DM-4

166 Chapter 8 - Design Steel I-Beam Bridge with Composite Slab With this option is set to PennDOT, several changes are made to the design procedure to account for the following requirements of the Pennsylvania Department of Transportation (PennDOT) Design Manual, Part 4, April 2015 Edition (DM-4): 1. When live-load distribution factors (LLDF) are used, these are calculated taking into account the provisions of DM-4 Section The provisions of DM-4 Section P regarding web bendbuckling nominal flexural resistance are incorporated. The depth of web in compression is calculated assuming that no longitudinal stiffeners are present. The stresses from dead and construction loads are derived from demands Mdnc and Mdc specified in the design request. 3. The provisions of DM-4 Section regarding end panels are incorporated. The effect of longitudinal stiffeners is not considered. It should be noted that the design procedure does not check for the presence of splices in panels when verifying if a section can be classified as compact. You should not use the design results for any panels containing splices that have been classified as compact. The DM-4 Section requirement to ignore haunches when computing flexural stiffness and resistance of beams while taking into account the haunch dead weight can be approximately satisfied by specifying haunch thickness in the bridge-section definition equal to the maximum flange thickness. The weight of the remaining haunch can be applied as a superimposed line load on top the girders. If you choose instead to include the full haunch thickness in the model, the difference in results tends to be small unless the haunch is deep. Prior to running the superstructure design, the analysis should be include the appropriate PennDOT vehicles as needed for live load. A PennDOT vehicle library is provided in addition to the regular AASHTO vehicles. Use the command Loads > Vehicles, and click the lower right arrow icon to show the Define Vehicles form. Then use the Import button to locate the vehicles under Unites States > PennDOT. Once imported, these vehicles can be modified, if necessary. Appropriate load combinations should be created prior to running the superstructure design. Use the command Design/Rating > Load Combinations > Add PennDOT Amendments for DM

167 CSiBridge Bridge Superstructure Design Defaults. Select Bridge Design, and set Amendment to PennDOT Steel Girder. See section AASHTO LRFD Code with PennDOT Amendments in this manual for more information PennDOT Amendments for DM-4

168 Chapter 9 Design Steel U-Tub Bridge with Composite Slab This chapter describes the algorithms CSiBridge applies when designing steel U-tub with composite slab superstructures in accordance with the AASHTO LRFD 2014 (AASHTO LRFD). 9.1 Section Properties Yield Moments Composite Section in Positive Flexure The positive yield moment, M y, is determined by the program in accordance with section D6.2.2 of the code using the following user-defined input, which is part of the Design Request (see Chapter 4 for more information about Design Request). M dnc = The user specifies in the Design Request the name of the combo that represents the moment caused by the factored permanent load applied before the concrete deck has hardened or is made composite. M dc = The user specifies in the Design Request the name of the combo that represents the moment caused by the remainder of the factored permanent load (applied to the composite section). The program solves for M AD from the following equation, 9-1

169 CSiBridge Bridge Superstructure Design F yt M M M S S S dnc dc AD = + + (D ) NC LT ST and then calculates yield moment based on the following equation where My = Mdnc + Mdc + MAD (D ) S NC = Noncomposite section modulus (in. 3 ) S LT = Long-term composite section modulus (in. 3 ) S ST = Short-term composite section modulus (in. 3 ) M y is taken as the lesser value calculated for the compression flange, M yc, or the tension flange, M yt. The positive M y is calculated only once based on M dnc and M dc demands specified by the user in the Design Request. It should be noted that the M y calculated in the procedure described here is used by the program only to determine M npos for compact sections in positive bending in a continuous span, where the nominal flexural resistance may be controlled by M y in accordance with (eq ). M 1.3RM n h y 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, S ST and S LT are the same value. Also, M yt is taken with respect to either the tension flange or the longitudinal reinforcement, whichever yields first. The negative M y is calculated only once based on the M dnc and M dc demands specified by the user in the Design Request Plastic Moments Composite Section in Positive Flexure The positive plastic moment, M p, is calculated as the moment of the plastic forces about the plastic neutral axis. Plastic forces in the steel portions of a 9-2 Section Properties

170 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab cross-section are calculated using the yield strengths of the flanges, the web, and reinforcing steel, as appropriate. Plastic forces in the concrete portions of the cross-section that are in compression are based on a rectangular stress block with the magnitude of the compressive stress equal to 0.85 f c. Concrete in tension is neglected. The position of the plastic neutral axis is determined by the equilibrium condition, where there is no net axial force. In calculating M p for positive moment, the contribution of the rebar in the deck is ignored. The plastic moment of a composite section in positive flexure is determined by: Calculating the effective width of bottom flange per Calculating the element forces and using them to determine if the plastic neutral axis is in the web, top flange, or concrete deck; Calculating the location of the plastic neutral axis within the element determined in the first step; and Calculating M p. Equations for the various potential locations of the plastic neutral axis (PNA) are given in Table 9-1. Table 9-1 Calculation of PNA and M p for Sections in Positive Flexure Case PNA Condition Y and Mp I In Web D Pt Pc Ps Prt P rb Y = w Pt + Pw Pc + Ps + Prb + P P 2 w 2 Mp = Y D Y + + Pd s s + Prt drt + Prbd rb + Pd c c + Pd t t 2D Pn ( ) [ ] II In Top Flanges Pt + Pw + Pc Ps + Prb + Pn t c Pw + Pt Ps Prt P rb Y = Pc P M = Y + t Y + Pd + Pd + P d + P d + Pd 2 ( ) [ ] c 2 p c s s n n rb rb w w t t 2t c Section Properties 9-3

171 CSiBridge Bridge Superstructure Design Table 9-1 Calculation of PNA and M p for Sections in Positive Flexure Case PNA Condition Y and Mp III Concrete Deck Below Prb c rb Pt + Pw + Pc t 2 Ps + Prb + Pn Y ( t ) P + P + P P P c w t rt rb = s Ps M P d P d Pd P d Pd 2 Y Ps p = + rt rt + rb rb + c c + w w + t t 2ts [ ] IV Concrete Deck at Prb c Pt + Pw + Pc + Prb t rb s Ps + Pn Y = c rb M P d Pd P d Pd 2 Y Ps p = + rt rt + c c + w w + t t 2ts [ ] V Concrete Deck Above Prb and Below Prt c Pt + Pw + Pc + Prb t rt s Ps + Pn Y ( t ) P + P + P + P P rb c w t rt = s P s M P d P d Pd P d Pd 2 Y Ps p = + rt rt + rb rb + c c + w w + t t 2ts [ ] VI Concrete Deck at Prt c Pt + Pw + Pc + Prb + Pn t rt s Ps Y = c rt M P d Pd P d Pd 2 Y Ps p = + rb rb + c c + w w + t t 2ts [ ] VII Concrete Deck Above Prt c Pt + Pw + Pc + Prb + Prt < t rt s Ps Y ( t ) P + P + P + P + P rb c w t rt = s P s M P d P d Pd P d Pd 2 Y Ps p = + rt rt + rb rb + c c + w w + t t 2ts [ ] 9-4 Section Properties

172 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab A rt A rb P rt P P s rb P c P w Y PNA C rb PNA Y C rt Y PNA P t CASE I CASE II CASES III - VII Figure 9-1 Plastic Neutral Axis Cases Positive Flexure P rt = F yrt A rt P s = 0.85 f c b st s P rb = F yrb A rb P c = 2 F ycb ct c P w = (2 F yw Dt w)/cos α web P t = F yt b tt t where b t is effective width of bottom flange per Next the section is checked for ductility requirement in accordance with equation In checking the ductility per , the depth of the haunch is neglected. where, D p 0.42D t D p is the distance from the top of the concrete deck to the neutral axis of the composite section at the plastic moment. D t is the total depth of the composite section. At the section where the ductility requirement is not satisfied, the plastic moment of a composite section in positive flexure is set to zero 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 Section Properties 9-5

173 CSiBridge Bridge Superstructure Design practice are given in Table 9-2. The plastic moment of a noncomposite section is calculated by eliminating the terms pertaining to the concrete deck and longitudinal reinforcement from the equations for composite sections. Table 9-2 Calculation of PNA and M p for Sections in Negative Flexure Case PNA Condition Y and Mp I In Web Pc + Pw Pt + Prb + Pn D Pc Pt Prt Prb Y = P w P M = Y + D Y + P d + P d + Pd + Pd 2D 2 ( ) [ ] w 2 p n n rb rb t t l l II In Top Flange Pc + Pw + Pt Prb + Pn tl Pw Pc Prt Prb Y = P t P M = Y + t Y + Pd + P d + P d + Pd 2 ( ) [ ] t 2 p l n n rb rb w w c c 2t l A rt A rb P rt P rb P t P w Y PNA PNA Y P c CASE I CASE II Figure 9-2 Plastic Neutral Axis Cases Negative Flexure P rt = F yrt A rt P s = 0 P rb = F yrb A rb P c = F ycb ct c where b c is effective width of bottom flange per Section Properties

174 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab P w = (2F yw Dt w)/cos α web P t = 2F yt b tt t In the equations for M p, 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 Section Classification and Factors Compact or Non-Compact - Positive Flexure The program determines if the section can be qualified as compact based on the following criteria: the bridge is not horizontally curved the specified minimum yield strengths of the flanges do not exceed 70.0 ksi, the web satisfies the requirement of Article ( ), D 150 t w the section satisfies requirements of the box flange is fully effective as specified in the section satisfies web slenderness limit 2D t w cp E ( ) F yc The user can control in the design request parameters how the program shall determine if the bridge is straight or horizontally. If the Determined by program option is selected the algorithm checks for radius of the layout line at every valid section cut. If the radius is a definite number the bridge is classified as horizontally curved. Section Properties 9-7

175 CSiBridge Bridge Superstructure Design Hybrid Factor Rh Positive Flexure For homogenous built-up sections, and built-up sections with a higher-strength steel in the web than in both flanges, R h is taken as 1.0. Otherwise the hybrid factor is taken as: R h where 3 ( ) 12 + β 3ρ ρ = β 2Dt n w fn ( ) β = ( ) A ρ = the smaller of F f and 1.0 yw A fn = bottom flange area. n D n = the larger of the distances from the elastic neutral axis of the crosssection to the inside face of either flange. For sections where the neutral axis is at the mid-depth of the web, D n is the distance from the neutral axis to the inside face of the flange on the side of the neutral axis where yielding occurs first. F n = f y of the bottom flange Web Load-Shedding Factor Rb Positive Flexure For composite sections in positive flexure, the R b factor is taken as equal to Web Load-Shedding Factor Rb Negative Flexure For composite sections in negative flexure, the R b factor is taken as: R b awc 2Dc = 1 λrw a wc t + w ( ) where E λ rw = 5.7 ( ) F yc 9-8 Section Properties

176 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab a wc 2Dt = c w ( ) b t fc fc When the user specifies the design request parameter Do webs have longitudinal stiffeners? as yes, the R b factor is set to 1.0 (see Chapter 4 for more information about specifying Design Request parameters). 9.2 Demand Sets Demand Set combos (at least one required) are user-defined combination based on LRFD combinations (see Chapter 4 for more information about specifying Demand Sets). The demands from all specified demand combos are enveloped and used to calculate D/C ratios. The way the demands are used depends on if the parameter "Use Stage Analysis? is set to Yes or No. If Yes, the program reads the stresses on beams and slabs directly from the section cut results. The program assumes that the effects of the staging of loads applied to non-composite versus composite section and the concrete slab material time dependent properties were captured by using the nonlinear stage analysis 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: noncomposite, composite long term, and composite short term. The program uses the load case Bridge Design Action parameter to assign the load cases to the appropriate categories. A default Bridge Design Action parameter is assigned to a load case based on its Design Type. However, the parameter can be overwritten: click the Analysis > Load Cases > {Type} > New command to display the Load Case Data {Type} form; click the Design button next to the Load case type drop down list, under the heading Bridge Design Action select the User Defined option and select a value from the list. The assigned Bridge Designed Action values are handled by the program in the following manner: Table 9-3 Bridge Design Action Bridge Design Action Value specified by the user Non-Composite Bridge Design Action Category used in the design algorithm Non-Composite Demand Sets 9-9

177 CSiBridge Bridge Superstructure Design Table 9-3 Bridge Design Action Bridge Design Action Value specified by the user Long-Term Composite Short-Term Composite Staged Other Bridge Design Action Category used in the design algorithm Long-Term Composite Short-Term Composite Non-Composite Non-Composite Demand Flange Stresses fbu and ff Evaluation of the flange stress, f bu, calculated without consideration of flange lateral bending is dependent on setting the Use Stage Analysis? design request parameter. If the Use Stage Analysis? = No, then f bu P M M M = A S S S NC LTC STC comp steel LTC STC where, M NC is the demand moment on the noncomposite section. M LTC is the demand moment on the long-term composite section. M STC is the demand moment on the short-term composite section. The short term section modulus for positive moment is calculated by transforming the concrete deck using steel to concrete modular ratio. The modular ratio (n) is calculated as a decimal number expressed as n=e s/e c and used without rounding. The long term section modulus for positive moment is using a modular ratio factored by n, where n is specified in the Modular ratio long term multiplier Design Parameter. The effect of compression reinforcement is ignored. For negative moment, the concrete deck is assumed cracked and is not included in the section modulus calculations, whereas tension reinforcement is taken into account Demand Sets

178 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab The effective width of bottom flange per is used to calculate the stresses. However, when design request parameter Use Stage Analysis? = Yes, then the f bu stresses on both top and bottom flanges are read directly from the section cut results. In that case the stresses are calculated based on gross section; the use of effective section properties cannot be accommodated with this option. Therefore, if the section bottom flange does not satisfy criteria of as being fully effective, the design parameter "Use Stage Analysis? should be set to No. When Use Stage Analysis? = Yes, the program assumes that the effects of the staging of loads applied to non-composite versus composite sections and the concrete slab material time dependent properties were captured by using the Nonlinear Staged Construction load case available in CSiBridge. The Modular ratio long-term multiplier. is not used in this case. The program verifies the sign of the stress in the composite slab, and if stress is positive (tension), the program assumes that the entire section cut demand moment is carried by the steel section only. This is to reflect the fact that the concrete in the composite slab is cracked and does not contribute to the resistance of the section. Flange stress f f used in the Service design check is evaluated in the same manner as the stress f bu, with one exception. When the Design Parameter Does concrete slab resist tension? in the Steel Service Design request is set to Yes, the program uses section properties based on a transformed section assuming the concrete slab to be fully effective in both tension and compression Demand Flange Lateral Bending Stress f l The top flange lateral bending stress f l is evaluated only for constructability design check when slab status is non-composite and when all of the following conditions are met: Steel Girders has been selected for the deck section type (Components > Superstructure Item > Deck Sections command) and the Girder Modeling In Area Object Models Model Girders Using Area Objects option is set to Yes on the Define Bridge Section Data Steel Girder form. Demand Sets 9-11

179 CSiBridge Bridge Superstructure Design The bridge object is modeled using Area Objects. This option can be set using the Bridge > Update command to display the Update Bridge Structural Model form; then select the Update as Area Object Model option. In all other cases, the top flange lateral bending stress is set to zero. The f l stresses on each top flange are read directly from the section cut results and the maximum absolute value stress from the two top flanges is reported Depth of the Web in Compression For composite sections in positive flexure, the depth of web in compression is computed using the following equation: fc Dc = d tfc 0 fc f + t (D ) Figure 9-3 Web in Compression Positive Flexure where, f c = sum of the compression-flange stresses caused by the different loads, i.e., D C1, the permanent load acting on the noncomposite section; D C2, the permanent load acting on the long-term composite section; D W, the wearing surface load; and LL+IM acting on their respective sections. f c is taken as negative when the stress is in compression. Flange lateral bending is disregarded in this calculation Demand Sets

180 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab f t = the sum of the tension-flange stresses caused by the different loads. Flange lateral bending is disregarded in this calculation. For composite sections in negative flexure, D C is computed for the section consisting of the steel U-tub plus the longitudinal reinforcement, with the exception of the following. For composite sections in negative flexure at the Service Design Check Request where the concrete deck is considered effective in tension for computing flexural stresses on the composite section (Design Parameter Does concrete slab resist tension? = Yes), D C is computed from (eq. D ). For this case, the stresses f c and f t are switched, the signs shown in the stress diagram are reversed, t fc is the thickness of the bottom flange, and D C instead extends from the neutral axis down to the top of the bottom flange. 9.3 Strength Design Request Flexure The strength design check calculates at every section cut positive flexural capacity, negative flexural capacity, and shear capacity. It then compares the capacities against the envelope of demands specified in the design request Positive Flexure Compact The nominal flexural resistance of the section is evaluated as follows: If D p 0.1 D t, then M n = M p, otherwise M n D p = Mp Dt ( ) In a continuous span the nominal flexural resistance of the section is determined as M n 1.3R hm y where R h is a hybrid factor for the section in positive flexure. The demand over capacity ratio is evaluated as MM uu DDDDDDDDDDDD = ff MM nn Strength Design Request 9-13

181 CSiBridge Bridge Superstructure Design Positive Flexure Non-Compact Nominal flexural resistance of the top compression flanges is taken as: F nc = R br hf yc ( ) Nominal flexural resistance of the bottom tension flange is taken as: Where Where ff vv = F nt = R hf ytδ ( ) TT 2AA 0 tt ffff = 1 3 ff 2 vv FF yyyy is St. Venant torsional shear stress in the flange due to the factored loads and A 0 is enclosed area within the box section The demand over capacity ratio is evaluated as Negative Flexure DDDDDDDDDDDD = mmmmmm ff bbbbbbbbbbbb ff FF nnnn, ff bbbbbbbbbbbb ff FF nnnn Nominal flexural resistance of continuously braced top flange in tension is taken as: F nt = R hf yt ( ) Nominal flexural resistance of the bottom unstiffened compression flange is taken as: FF nnnn = FF cccc 1 ff vv φφ vv FF cccc 2 ( ) In which: FF cccc = nominal axial compression buckling resistance of the flange under compression alone calculated as follows: 9-14 Strength Design Request

182 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab If λλ ff λλ pp, then: FF cccc = RR bb RR h FF yyyy Δ ( ) If λλ pp λλ ff λλ rr, then: FF cccc = RR bb RR h FF yyyy Δ Δ Δ 0.3 λ f λ p ( ) R h λ r λ p If λλ ff λλ rr, then: FF cccc = 0.9EERR bbkk λλ ff 2 ( ) FF cccc = nominal shear buckling resistance of the flange under shear alone calculated as follows: If λλ ff 1.12 EEkk ss FF yyyy, then: FF cccc = 0.58FF yyyy ( ) If 1.12 EEkk ss FF yyyy < λλ ff 1.40 EEkk ss FF yyyy, then: FF cccc = 0.65 FF yyyy EEkk ss λλ ff ( ) If λλ ff > 1.40 EEkk ss FF yyyy, then: FF cccc = 0.9EEkk ss λλ ff 2 ( ) λλ ff = slenderness ratio for the compression flange = bb ffff tt ffff ( ) λλ pp = 0.57 EEEE FF yyyy Δ ( ) Strength Design Request 9-15

183 CSiBridge Bridge Superstructure Design λλ rr = 0.95 EEEE FF yyyy ( ) Δ = 1 3 ff 2 vv FF yyyy ( ) ff vv = St. Venant torsional shear stress in the flange due to the factored loads at the section under consideration (ksi) = TT 2AA 0 tt ffff ( ) Shear FF yyyy = smaller of the compression-flange stress at the onset of nominal yielding, with consideration of residual stress effects, or the specified minimum yield strength of the web (ksi) = (Δ 0.3)FF yyyy ( ) k = plate-buckling coefficient for uniform normal stress = 4.0 k s = plate-buckling coefficient for shear stress = 5.34 The demand over capacity ratio is evaluated as DDDDDDDDDDDD = mmmmmm ff bbbbbbbbbbbb ff FF nnnn, ff bbbbbbbbbbbb ff FF nnnn When processing the design request from the Design module, the program assumes that no vertical stiffeners are present and classifies all web panels as unstiffened. If the shear capacity calculated based on this classification is not sufficient to resist the demand specified in the design request, the program recommends minimum stiffener spacing to achieve a demand over capacity ratio equal to 1. The recommended stiffener spacing is reported in the result table under the column heading d0req Strength Design Request

184 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab In the Optimization form (Design/Rating > Superstructure Design > Optimize command), the user can specify stiffener locations and the program recalculates the shear resistance. In that case the program classifies the web panels as interior or exterior and stiffened or unstiffened based on criteria specified in Section of the code. It should be noted that stiffeners are not modeled in the Bridge Object and therefore adding/modifying stiffeners does not affect the magnitude of the demands Nominal Resistance of Unstiffened Webs In the following equations D is taken as depth of the web plate measured along the slope and each web demand over capacity ratio is calculated based on shear due to factored loads taken as VV uu VV uuuu = cos αα wwwwww Where V u is vertical shear due to the factored loads on one inclined web and α web is the angle of inclination of the web plate to the vertical. The V ui value is reported in the result tables. The nominal shear resistance of unstiffened webs is taken as: V n in which V = CV ( ) p = 0.58F Dt ( ) p yw w C = the ratio of the shear-buckling resistance to the shear yield strength that is determined as follows: D Ek If 1.12, then C = 1.0. ( ) t F w yw Ek D Ek If 1.12 < 1.40, then F t F yw w yw 1.12 Ek C =. ( ) D Fyw t w Strength Design Request 9-17

185 CSiBridge Bridge Superstructure Design D Ek 1.57 Ek If > 1.40, then C =, 2 tw F yw D F yw t w 5 in which k = dc D ( ) ( ) Nominal Resistance of Stiffened Interior Web Panels The nominal shear resistance of an interior web panel and with the section at the section cut proportioned such that 2Dt w ( bfctfc + bfttft ) 2.5 ( ) is taken as 0.87( 1 C) Vn = Vp C+ 2 do 1+ D ( ) in which V = 0.58F Dt ( ) p yw w where d o = transverse stiffener spacing. Otherwise, the nominal shear resistance is taken as follows: Vn = Vp C+ 0.87( 1 C) 2 do d o 1+ + D D ( ) Nominal Resistance of End Panels The nominal shear resistance of a web end panel is taken as: Vn = Vcr = CVp ( ) 9-18 Strength Design Request

186 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab in which V = 0.58 F Dt. ( ) p yw w Torsion Effects For all single box sections, horizontally curved section, and multiple box sections in bridges not satisfying the requirements of Article , or with bottom flange that is not fully effective according to the provisions of Article V ui is taken as the sum of the flexural and St. Venant torsional shears. The St. Venant torsional shear is calculated as: VV tttttt = ff vv AA wwwwww wwheeeeee ff vv = TT 2AA 0 tt ww The demand over capacity ratio is evaluated as DDDDDDDDDDDD = VV uuuu vv VV nn 9.4 Service Design Request The service design check calculates at every section cut stresses f f at top steel flange of composite section, bottom steel flange of composite section and compares them against limits specified in Section of the code. For the top and bottom steel flange of composite sections: DDDDDDDDDDDD = ff ff 0.95RR h FF yyyy ( ) The flange stresses are derived in the same way as f bu stress demands (see Section 9.2 of this manual). The user has an option to specify whether concrete slab resists tension or not by setting the design request parameter Does concrete slab resist tension?. It is the responsibility of the user to verify if the slab qualifies per Section of the code to resist tension. Service Design Request 9-19

187 CSiBridge Bridge Superstructure Design For compact composite sections in positive flexure utilized in shored construction, the longitudinal compressive stress in the concrete deck, determined as specified in Article d, is checked against 0.6f c. DoverC = f deck/0.6f c Except for composite sections in positive flexure in which the web satisfies the requirement of Article , all section cuts are shall checked against the following requirement: where: DoverC = ff cc ff cccccc ( ) f c - compression-flange stress at the section under consideration due to demand loads calculated without consideration of flange lateral bending F crw - nominal bend-buckling resistance for webs without longitudinal stiffeners determined as specified in Article FF cccccc = 0.9EEEE ( ) DD ttww 2 but not to exceed the smaller of R hf yc and F yw/0.7. In which k=bend buckling coefficient kk = 9 ( ) DD cc DD 2 where D c= depth of the web in compression in the elastic range determined as specified in Article D6.3.1 of the code. When both edges of the web are in compression, k is taken as 7.2. The highest demand over capacity ratio together with controlling equation is reported for each section cut. 9.5 Web Fatigue Design Request Web Fatigue Design Request is used to calculate the demand over capacity ratio as defined in Section of the code Special Fatigue Requirement for 9-20 Web Fatigue Design Request

188 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab Webs. The requirement is applicable to interior panels of webs with transverse stiffeners. When processing the design request from the Design module, the program assumes that there are no vertical stiffeners present and classifies all web panels as unstiffened. Therefore when the design request is completed from the Design module the Design Result Status table shows message text No stiffeners defined use optimization form to define stiffeners. In the Optimization form (Design/Rating > Superstructure Design > Optimize command), the user can specify stiffeners locations and the program recalculates the Web Fatigue Request. In that case the program classifies the web panels as interior or exterior and stiffened or unstiffened based on criteria specified in Section of the code. It should be noted that stiffeners are not modeled in the Bridge Object and therefore adding/modifying stiffeners does not affect the magnitude of the demands. In the following equations D is taken as depth of the web plate measured along the slope and each web demand over capacity ratio is calculated based on shear due to factored loads taken as VV uu VV uuuu = cos αα wwwwww Where V u is vertical shear due to the factored loads on one inclined web and α web is the angle of inclination of the web plate to the vertical. The V ui value is reported in the result tables. For all single box sections, horizontally curved section, and multiple box sections in bridges not satisfying the requirements of Article , or with bottom flange that is not fully effective according to the provisions of Article V ui is taken as the sum of the flexural and St. Venant torsional shears. The St. Venant torsional shear is calculated as: VV tttttt = ff vv AA wwwwww wwheeeeee ff vv = TT 2AA 0 tt ww If live load distribution to girders method Use Factor Specified by Design Code is selected in the design request the program adjusts for the multiple presence factor to account for the fact that fatigue load occupies only one lane Web Fatigue Design Request 9-21

189 CSiBridge Bridge Superstructure Design (code Section b) and multiple presence factors shall not be applied when checking for fatigue limit state (code Section ). V cr = shear-buckling resistance determined from eq (see Section of this manual) DoverC=V ui/v cr ( ) 9.6 Constructability Design Request Staged (Steel-U Comp Construct Stgd) This request enables the user to verify the superstructure during construction by utilizing the Nonlinear Staged Construction load case. The use of nonlinear staged analysis allows the user to define multiple snapshots of the structure during construction where parts of the bridge deck may be at various completion stages. The user has a control of which stages the program will include in the calculations of controlling demand over capacity ratios. For each section cut specified in the design request the constructability design check loops through the Nonlinear Staged Construction load case output steps that correspond to Output Labels specified in the Demand Set. At each step the program determines the status of the concrete slab at the girder section cut. The slab status can be non-composite or composite. The Staged Constructability design check accepts the following Bridge Object Structural Model Options: - Area Object Model - Solid Object Model The Staged Constructability design check cannot be run on Spine models Non-staged (Steel-U Comp Construct NonStgd) This request enables the user to verify demand over capacity ratios during construction without the need to define and analyze 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 Constructability Design Request

190 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab The Non-Staged Constructability design check accepts all Bridge Object Structural Model Options available in Update Bridge Structural Model form. (Bridge > Update > Structural Model Options option) Slab Status vs Unbraced Length Flexure Based on the slab status the program calculates corresponding positive flexural capacity, negative flexural capacity, and shear capacity. Next the program compares the capacities against demands specified in the Demand Set by calculating the demand over capacity ratio. The controlling Demand Set and Output Label on girder basis are reported for every section cut. When slab status is composite the program assumes that both top and bottom flanges are continuously braced. When slab status in not present or noncomposite the program treats both top flanges as discretely braced. It should be noted that the program does not verify presence of diaphragms at a particular output step. It assumes that anytime a steel beam is activated at a given section cut that the unbraced length L b for the top flanges is equal to distance between the nearest downstation and upstation qualifying cross diaphragms or span ends as defined in the Bridge Object. In other words the unbraced length L b is based on the cross diaphragms that qualify as providing restraint to the bottom flange. Some of the diaphragm types available in CSiBridge may not necessarily provide restraint to the top flanges. It is the user responsibility to provide top flanges temporary bracing at the diaphragm locations prior to the slab acting compositely Positive Flexure Non Composite The local buckling resistance of the top compression flange F nc(flb) as specified in Article is taken as: If λ f λ pf, then F nc = R br hf yc. ( ) Otherwise F Fyr λf λpf = 1 1 RRF RF h yc λrf λpf nc b h yc ( ) in which Constructability Design Request 9-23

191 CSiBridge Bridge Superstructure Design bfc λ f = ( ) 2t fc E λ pf = 0.38 ( ) F yc E λ rf = 0.56 ( ) F yr F yr = compression-flange stress at the onset of nominal yielding within the cross-section, including residual stress effects, but not including compression-flange lateral bending, taken as the smaller of 0.7F yc and F yw, but not less than 0.5 F yc The lateral torsional buckling resistance of the top compression flange F nc(ltb) as specified in Article ( ) is taken as follows: If L b L p, then F nc = R br hf yc. ( ) If L p < L b L r, then Fyr Lb Lp Fnc = Cb 1 1 RRF b h yc RRF b h yc. RF h yc Lr Lp ( ) If L b > L r, then F nc = F cr R br hf yc. ( ) in which E Lb = unbraced length, Lp = 1.0 rt, Lr = πrt F yc E F yr C b = 1 (moment gradient modifier) F cr 2 CR b bπ E = 2 Lb r t ( ) 9-24 Constructability Design Request

192 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab r t = b fc 1 Dt bfct c w fc ( ) The nominal flexural resistance of the top compression flange is taken as the smaller of the local buckling resistance and the lateral torsional buckling resistance: Fnc = min Fnc( FLB), Fnc( LTB) Nominal flexural resistance of the bottom tension flange is taken as: Where Where ff vv = F nt = R hf ytδ ( ) = 1 3 ff 2 vv FF yyyy TT 2AA 0 tt ffff is St. Venant torsional shear stress in the flange due to the factored loads and A 0 is enclosed area within the box section The demand over capacity ratio is evaluated as DD/CC = max ff bbbbbbbbbbbb + ff llllllll, ff 1 bbbbbbbbbbbb + 3 ff llllllll ff bbbbbbbbbbbb ff llllllll ff bbbbbbbbbbbb,,, φφ ff RR h FF yyyyyyyyyy φφ ff FF nnnnnnnnnn φφ ff FF cccccccccccc 0.6 FF yyyyyyyy φφ ff RR h FF nnnnnnnnnn Where F crwtop is nominal bend bucking resistance for webs specified in AASHTO LRFD Article for webs without longitudinal stiffeners. FF cccccc = 0.9EEEE DD ttww 2 ( ) but not to exceed the smaller of R hf yc and F yw /0.7 where kk = 9 DD cc DD 2. When both edges of the web are in compression then k=7.2 Constructability Design Request 9-25

193 CSiBridge Bridge Superstructure Design Positive Flexure Composite Nominal flexural resistance of the top compression flanges is taken as: Where Where ff vv = F nctop= R hf ycδ ( ) TT 2AA 0 tt ffff = 1 3 ff 2 vv FF yyyy is St. Venant torsional shear stress in the flange due to the factored loads and A 0 is enclosed area within the box section Nominal flexural resistance of the bottom tension flange is taken as: Where Where ff vv = F ntbot = R hf ytδ ( ) TT 2AA 0 tt ffff = 1 3 ff 2 vv FF yyyy is St. Venant torsional shear stress in the flange due to the factored loads and A 0 is enclosed area within the box section The demand over capacity ratio is evaluated as: ff bbbbbbbbbbbb DD/CC = max ff bbbbbbbbbbbb, φφ ff FF nnnnnnnnnn φφ ff FF nnnnnnnnnn Negative Flexure Non Composite The demand over capacity ratio is evaluated as: ff llllllll DD/CC = max ff bbbbbbbbbbbb, ff bbbbbbbbbbbb + ff llllllll, φφ ff FF nnnnnnnnnn φφ ff RR h FF yyyyyyyyyy 0.6 FF yyyyyyyy 9-26 Constructability Design Request

194 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab Where F nctbot is nominal flexural resistance of the continuously braced unstiffened bottom flange determined as specified in AASHTO LRFD Article (also see Section of this manual) Negative Flexure Composite The demand over capacity ratio is evaluated as: ff bbbbbbbbbbbb DDDDDDDDDDDD = mmmmmm ff bbbbcccccccc, ff FF nnnnnnnnnn ff RR h FF yyyyyyyyyy ΔΔ, ff dddddddd φφ tt ff rr Where F nctbot is nominal flexural resistance of the continuously braced unstiffened bottom flange determined as specified in AASHTO LRFD Article (also see Section of this manual), and Where ff vv = Shear TT 2AA 0 tt ffff = 1 3 ff 2 vv FF yyyy is St. Venant torsional shear stress in the flange due to the factored loads and A 0 is enclosed area within the box section and f deck is demand tensile stress in the deck and f r is modulus of rupture of concrete as determined in AASHTO LRFD Article When processing the design request from the Design module, the program assumes that there are no vertical stiffeners present and classifies all web panels as unstiffened. If the shear capacity calculated based on this classification is not sufficient to resist the demand specified in the design request and the controlling demand over capacity ratio is occurring at step when the slab status is composite, the program recommends minimum stiffener spacing to achieve a demand over apacity ratio equal to 1. The recommended stiffener spacing is reported in the result table under the column heading d0req. In the Optimization form (Design/Rating > Superstructure Design > Optimize command), the user can specify stiffeners locations and the program recalculates the shear resistance. In that case the program classifies the web panels as interior or exterior and stiffened or unstiffened based on criteria specified in Section of the code. It should be noted that stiffeners are not mod- Constructability Design Request 9-27

195 CSiBridge Bridge Superstructure Design eled in the Bridge Object and therefore adding/modifying stiffeners does not affect the magnitude of the demands. Adding stiffeners also does not increase capacity of sections cuts where concrete slab status is other then composite. In the following equations D is taken as depth of the web plate measured along the slope and each web demand over capacity ratio is calculated based on shear due to factored loads taken as VV uu VV uuuu = cos αα wwwwww Where V u is vertical shear due to the factored loads on one inclined web and α web is the angle of inclination of the web plate to the vertical. The V ui value is reported in the result tables Torsion Effects For all single box sections, horizontally curved section, and multiple box sections in bridges not satisfying the requirements of Article , or with bottom flange that is not fully effective according to the provisions of Article V ui is taken as the sum of the flexural and St. Venant torsional shears. The St. Venant torsional shear is calculated as: VV tttttt = ff vv AA wwwwww wwheeeeee ff vv = TT 2AA 0 tt ww Non Composite Sections The nominal shear resistance of a web end panel is taken as: in which VV nn = VV cccc = CCCC pp ( ) V = 0.58 F Dt. ( ) p yw w The demand over capacity ratio is evaluated as Vu DoverC = φ V v n 9-28 Constructability Design Request

196 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab Composite Sections Nominal Resistance of Unstiffened Webs The nominal shear resistance of unstiffened webs is taken as: V n in which V = CV ( ) p = 0.58F Dt ( ) p yw w C = the ratio of the shear-buckling resistance to the shear yield strength that is determined as follows: D Ek If 1.12, then C = 1.0. ( ) t F w yw Ek D Ek If 1.12 < 1.40, then F t F yw w yw 1.12 Ek C =. ( ) D Fyw t w D Ek 1.57 Ek If > 1.40, then C =, 2 tw F yw D F yw t w 5 in which k = dc D ( ) ( ) Nominal Resistance of Stiffened Interior Web Panels The nominal shear resistance of an interior web panel and with the section at the section cut proportioned such that: 2Dt w ( bfctfc + bfttft ) 2.5 ( ) is taken as Constructability Design Request 9-29

197 CSiBridge Bridge Superstructure Design 0.87( 1 C) Vn = Vp C+ 2 do 1+ D ( ) in which V = 0.58F Dt ( ) p yw w where d o = transverse stiffener spacing. Otherwise, the nominal shear resistance is taken as follows: Vn = Vp C+ 0.87( 1 C) 2 do d o 1+ + D D ( ) Nominal Resistance of End Panels The nominal shear resistance of a web end panel is taken as: VV nn = VV cccc = CCVV pp ( ) in which V = 0.58 F Dt. ( ) p yw w The demand over capacity ratio is evaluated as Vu DoverC = φ V 9.7 Section Optimization v n After at least one Steel Design Request has been successfully processed, CSiBridge enables the user to open a Steel Section Optimization module. The Optimization module allows interactive modification of certain steel plate sizes, materials, and definition of vertical stiffeners along each girder and span. The U tub section plate parameters that are available for modification are: 9-30 Section Optimization

198 Chapter 9 - Design Steel U-Tub Bridge with Composite Slab Top flange thickness, width and material Webs thickness, material Bottom flange thickness, material The program recalculates resistance on the fly based on the modified section without the need to unlock the model and rerun the analysis. It should be noted that in the optimization process the demands are not recalculated and are based on the current CSiBridge analysis results. The Optimization form allows simultaneous display of three versions of section sizes and associated resistance results. The section plate size versions are As Analyzed, As Designed, and Current. The section plots use distinct colors for each version black for As Analyzed, blue for As Designed, and red for Current. When the Optimization form is initially opened, all three versions are identical and equal to As Analyzed. Two graphs are available to display various forces, moments, stresses, and 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 are plotted as solid lines and the As Designed series as dashed lines. To modify steel plate sizes or vertical stiffeners, a new form can be displayed by clicking on the Modify Section button. After the section modification is completed, the Current version is shown in red in the elevation and cross section views. After the resistance has been recalculated successfully by clicking the Recalculate Resistance button, the Current version is designated to 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. Section Optimization 9-31

199 CSiBridge Bridge Superstructure Design 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 Section Optimization

200 Chapter 10 Run a Bridge Design Request This chapter identifies the steps involved in running a Bridge Design Request. (Chapter 4 explains how to define the Request.) Running the Request applies the following to the specified Bridge Object: Program defaults in accordance with the selected code the Preferences Type of design to be performed the check type (Section 4.2.1) Portion of the bridge to be designed the station ranges (Section 4.1.3) Overwrites of the Preferences the Design Request parameters (Section 4.1.4) Load combinations the 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 It is assumed that the user is familiar with the steps that are necessary to create a CSiBridge model of a concrete box girder bridge. If additional assistance is needed to create the model, a 30-minute Watch and Learn video entitled, Bridge Bridge Information Modeler is available at the CSI website 10-1

201 CSiBridge Bridge Superstructure Design The tutorial video guides the user through the creation of the bridge model referenced in this chapter. Figure D view of example concrete box girder bridge model 10.1 Description of Example Model The example bridge is a two-span prestressed concrete box girder bridge with the following features: Abutments: The abutments are skewed by 15 degrees and connected to the bottom of the box girder only. Prestress: The concrete box girder bridge is prestressed with four 10-in 2 tendons (one in each girder) and a jacking force of 2160 kips per tendon. Bents: The one interior bent has three 5-foot-square columns. Deck: The concrete box girder has a nominal depth of 5 feet. The deck has a parabolic variation in depth from 5 feet at the abutments to a maximum of 10 feet at the interior bent support. Spans: The two spans are each approximately 100 feet long. Figure 10-2 Elevation view of example bridge 10-2 Description of Example Model

202 Chapter 10 - Run a Bridge Design Request 10.2 Design Preferences Figure 10-3 Plan view of the example bridge Use the Design/Rating > Superstructure Design > Preferences command to select the AASHTO LRFD 2007 design code. The Bridge Design Preferences form shown in Figure 10-4 displays Load Combinations Figure 10-4 Bridge Design Preferences form 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 Combinations for Bridge Design form shown in Figure 10-5 displays. The form is used Design Preferences 10-3

203 CSiBridge Bridge Superstructure Design to specify the desired limit states. Only the Strength II limit state was selected for this example. Normally, several limit states would be selected. Figure 10-5 Code-Generated Load Combinations for Bridge Design form The defined load combinations for this example are shown in Figure Figure 10-6 Define Load Combinations form 10-4 Load Combinations

204 Chapter 10 - Run a Bridge Design Request The Str-II1, Str-II2 and StrIIGroup1 designations for the load combinations are specified by the program and indicate that the limit state for the combinations is Strength Level II Bridge Design Request After the Design/Rating > Superstructure Design > Design Request command has been used, the Bridge Design Request form shown in Figure 10-7 displays. Figure 10-7 Define Load Combinations form The name given to this example Design Request is FLEX_1, the Check Type is for Concrete Box Flexure and the Demand Set, DSet1, specifies the combination as StrII (Strength Level II). Bridge Design Request 10-5

205 CSiBridge Bridge Superstructure Design 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 Start Design/Check of the Bridge After an analysis has been run, the bridge model is ready for a design/check. Use the Design/Rating > Superstructure Design > Run Super command to start the design process. Select the design to be run using the Perform Bridge Design form shown in Figure 10-8: Figure 10-8 Perform Bridge Design - Superstructure The user may select the desired Design Request(s) and click on the Design Now button. A plot of the bridge model, similar to that shown in Figure 10-9, will display. If several Design Requests have been run, the individual Design Requests can be selected from the Design Check options drop-down list. This plot is described further in Chapter 11. Figure 10-9 Plot of flexure check results 10-6 Start Design/Check of the Bridge

206 Chapter 11 Display Bridge Design Results Bridge design results can be displayed on screen and as printed output. The on-screen display can depict the bridge response graphically as a plot or in data tables. The Advanced Report Writer can be used to create the printed output, which can include the graphical display as well as the database tables. This chapter displays the results for the example used in Chapter 10. The model is a concrete box girder bridge and the code applied is AASHTO LRFD Creation of the model is shown in a 30-minute Watch and Learn video on the CSI website, 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 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 enveloped and shown in the blue region, and the negative capacity moments are shown with a brown line. If the demand moments do not exceed the capacity moments, the superstructure may be deemed adequate in response to the flexure Design Request. Move the mouse pointer onto the demand or capacity plot to view the values for each nodal point. Move the pointer to the capacity moment Display Results as a Plot 11-1

207 CSiBridge Bridge Superstructure Design at station 1200 and kip-in is shown. A verification calculation that shows agreement with this CSiBridge result is provided in Section Figure 11-1 Plot of flexure check results for the example bridge design model Additional Display Examples Use the Home > Display > Show Bridge Forces/Stresses command to select, on the example form shown in Figure 11-2, the location along the top or bottom portions of a beam or slab for which stresses are to be displayed. Figures 11-3 through 11-9 illustrate the left, middle, and right portions as they apply to Multicell Concrete Box Sections. Location 1, as an example, refers to the top left selection option while location 5 would refer to the bottom center selection option. Locations 1, 2, and 3 refer to the top left, top center, and top right selection option while locations 4, 5, and 6 refer to the bottom left, bottom center, and bottom right selection options Display Results as a Plot

208 Chapter 11 - Display Bridge Design Results Figure 11-2 Select the location on the beam or slab for which results are to be displayed Top slab cut line 4 Bottom slab cut line 5 6 Centerline of the web Centerline of the web Figure 11-3 Bridge Concrete Box Deck Section - External Girders Vertical Display Results as a Plot 11-3

209 CSiBridge Bridge Superstructure Design Top slab cut Bottom slab cut line Centerline of the web Centerline of the web Figure 11-4 Bridge Concrete Box Deck Section - External Girders Sloped Top slab cut Bottom slab cut line Centerline of the web Centerline of the web Figure 11-5 Bridge Concrete Box Deck Section - External Girders Clipped 11-4 Display Results as a Plot

210 Chapter 11 - Display Bridge Design Results Top slab cut Bottom slab cut line Centerline of the web Centerline of the web Figure 11-6 Bridge Concrete Box Deck Section - External Girders and Radius Top slab cut line Bottom slab cut line 4, Centerline of the web Centerline of the web Centerline of the web Figure 11-7 Bridge Concrete Box Deck Section - External Girders Sloped Max Display Results as a Plot 11-5

211 CSiBridge Bridge Superstructure Design Top slab cut line Bottom slab cut line Centerline of the web Centerline of the web Figure 11-8 Bridge Concrete Box Deck Section - Advanced Top slab cut line Bottom slab cut line Centerline of the web Figure 11-9 Bridge Concrete Box Deck Section - AASHTO - PCI - ASBI Standard 11-6 Display Results as a Plot

212 Chapter 11 - Display Bridge Design Results 11.2 Display Data Tables To view design results on screen in tables, click the Home > Display > Show Tables command, which will display the Choose Tables for Display form shown in Figure Use the options on that form to select which data results are to be viewed. Multiple selection may be made. Figure 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 will display. Note the drop-down list in the upper right-hand corner of the table. That drop-down list will include the various data tables that match the selections made on the Choose Tables for Display form. Select from that list to change to a different database table. Display Data Tables 11-7

213 CSiBridge Bridge Superstructure Design Figure 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 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 command is executed, a form similar to that shown in Figure displays Advanced Report Writer

214 Chapter 11 - Display Bridge Design Results Figure 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 Click the appropriate button (e.g., Find existing 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. Advanced Report Writer 11-9

215 CSiBridge Bridge Superstructure Design Figure 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 various 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 shows an example of the printed output generated by the Report Writer Advanced Report Writer

216 Chapter 11 - Display Bridge Design Results 11.4 Verification Figure An example of the printed output As a verification check of the design results, the output at station 1200 is examined. The following output for negative bending has been pulled from the ConBoxFlexure data table, a portion of which is shown in Figure 11-10: Demand moment, DemandMax (kip-in) = Resisting moment, ResistingNeg (kip-in) = Total area of prestressing steel, AreaPTTop (in 2 ) = 20.0 Top k factor, kfactortop = Neutral axis depth, c, CDistForNeg (in) = Effective stress in prestressing, f ps, EqFpsForNeg (kip/in 2 ) = A hand calculation that verifies the results follows: For top k factor, from (eq ), f PY k = = = f PU 270 (Results match) Verification 11-11