Innovative Bridge Designs for Rapid Renewal Toolkit (2012)

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119 B ABC SAMPLE DESIGN CALCULATIONS

120 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT APPENDIX B ABC SAMPLE DESIGN CALCULATIONS Three design examples are presented in this appendix, as follows:  Sample Calculation 1: Decked Steel Girder Design for ABC  Sample Calculation 2: Decked Precast Prestressed Concrete Girder Design for ABC  Sample Calculation 3: Precast Pier Design for ABC The design examples illustrate the design steps involved in the ABC design process as given in the breakdown below. The ABC design philosophy and design criteria have been described. Annotations have been used for the purpose of providing explanation of the design steps. LRFD code references have also been included to guide the reader. Sample Calculation 1: Decked Steel Girder Design for ABC B-3 General: 1. Introduction 2. Design Philosophy 3. Design Criteria 4. Material Properties 5. Load Combinations Girder Design: 6. Beam Section Properties 7. Permanent Loads 8. Precast Lifting Weight 9. Live Load Distribution Factors 10. Load Results 11. Flexural Strength 12. Flexural Strength Checks 13. Flexural Service Checks 14. Shear Strength 15. Fatigue Limit States 16. Bearing Stiffeners 17. Shear Connectors Deck Design: 18. Slab Properties 19. Permanent Loads 20. Live Loads 21. Load Results 22. Flexural Strength Capacity Check 23. Longitudinal Deck Reinforcing Design 24. Design Checks 25. Deck Overhang Design Continuity Design: 26. Compression Splice 27. Closure Pour Design

121 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Sample Calculation 2: Decked Precast Prestressed Concrete girder Design for ABC B-44 General: 1. Introduction 2. Design Philosophy 3. Design Criteria Girder Design: 4. Beam Section 5. Material Properties 6. Permanent Loads 7. Precast Lifting Weight 8. Live Load 9. Prestress Properties 10. Prestress Losses 11. Concrete Stresses 12. Flexural Strength 13. Shear Strength 14. Splitting Resistance 15. Camber and Deflections 16. Negative Moment Flexural Strength Sample Calculation 3a: Precast Pier Design for ABC (70’ Span Straddle Bent) B-80 1. Bent Cap Loading 2. Bent Cap Flexural Design 3. Bent Cap Shear and Torsion Design 4. Column / Drilled Shaft Loading and Design 5. Precast Component Design Sample Calculation 3b: Precast Pier Design for ABC (70’ Span Conventional Pier) B-115 1. Bent Cap Loading 2. Bent Cap Flexural Design 3. Bent Cap Shear and Torsion Design 4. Column / Drilled Shaft Loading and Design 5. Precast Component Design

122 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ABC SAMPLE CALCULATION – 1 Decked Steel Girder Design for ABC

123 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT CONCRETE DECKED STEEL GIRDER DESIGN FOR ABC This document shows the procedure for the design of a steel girder bridge with precast deck element for use in a rapid bridge replacement design in Accelerated Bridge Construction (ABC). This sample calculation is intended as an informational tool for the practicing bridge engineer. These calculations illustrate the procedure followed to develop a similar design but shall not be considered fully exhaustive. This sample calculation is based on the AASHTO LRFD Bridge Design Specifications (Fifth Edition with 2010 interims). References to the AASHTO LRFD Bridge Design Specifications are included throughout the design example. AASHTO references are presented in a dedicated column in the right margin of each page, immediately adjacent to the corresponding design procedure. An analysis of the superstructure was performed using structural modeling software. The design moments, shears, and reactions used in the design example are taken from the output, but their computation is not shown in the design example. BRIDGE GEOMETRY: Design member parameters: Deck Width: wdeck 47ft 2in C. to C. Piers: Length 70ft Roadway Width: wroadway 44ft C. to C. Bearings Lspan 67ft 10in Skew Angle: Skew 0deg Bridge Length: Ltotal 3 Length 210 ft Deck Thickness td 10.5in Stringer W30x99 Haunch Thickness th 2in Stringer Weight ws1 99plf Haunch Width wh 10.5in Stringer Length Lstr Length 6 in 69.5 ft Girder Spacing spacingint 3ft 11in Average spacing of adjacent beams. This value is used so that effective deck width is not overestimated. spacingext 4ft

124 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT TABLE OF CONTENTS: General: 1. Introduction 2. Design Philosophy 3. Design Criteria 4. Material Properties 5. Load Combinations Girder Design: 6. Beam Section Properties 7. Permanent Loads 8. Precast Lifting Weight 9. Live Load Distribution Factors 10. Load Results 11. Flexural Strength 12. Flexural Strength Checks 13. Flexural Service Checks 14. Shear Strength 15. Fatigue Limit States 16. Bearing Stiffeners 17. Shear Connectors Deck Design: 18. Slab Properties 19. Permanent Loads 20. Live Loads 21. Load Results 22. Flexural Strength Capacity Check 23. Longitudinal Deck Reinforcing Design 24. Design Checks 25. Deck Overhang Design Continuity Design: 26. Compression Splice 27. Closure Pour Design

125 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 1. INTRODUCTION The design of this superstructure system follows AASHTO LRFD and is based on a bridge of three even spans, with no skew. The bridge has two 14-foot lanes and two 8-foot shoulders, for a total roadway width of 44' from curb to curb. The out-to-out width of the bridge is 47'-2". The bridge deck is precast reinforced concrete with overhangs at the outermost girders. The longitudinal girders are placed as simply supported modules, and made continuous with connection plates and cast-in-place deck joints. The design of the continuity at the deck joint is addressed in final sections of this example. The cross-section consists of six modules. The interior modules are identical and consist of two steel girders and a 7'-10" precast composite deck slab. Exterior modules include two steel girders and a 7'-11" precast composite deck slab, with F-shape barriers. Grade 50 steel is used throughout, and the deck concrete has a compressive strength of 5,000 psi. The closure pour joints between the modules use Ultra High Performance Concrete with a strength of 21,000 psi. The following sections detail the design of the steel girders, including constructability checks, fatigue design for infinite fatigue lift (unless otherwise noted), and bearing stiffener design. The diaphragms are not designed in detail. A brief deck design is also included, with focus on the necessary checks for this type of modular superstructure. Tips for reading this Design Example: This calculation was prepared with Mathcad version 14. Mathcad is a computational aide for the practicing engineer. It allows for repetitive calculations in a clear, understandable and presentable fashion. Other computational aides may be used in lieu of Mathcad. Mathcad is not a design software. Mathcad executes user mathematical and simple logic commands. Example 1: User inputs are noted with dark shaded boxes. Shading of boxes allows the user to easily find the location of a desired variable. Given that equations are written in mathcad in the same fashion as they are on paper, except that they are interactive, shading input cells allows the user to quicly locate inputs amongst other data on screen. Units are user inputs. Height of Structure: Hstructure 25ft Example 2: Equations are typed directly into the workspace. Mathcad then reads the operators and executes the calculations. Panels are 2.5' Npanels Hstructure 2.5ft  Npanels 10 Example 3: If Statements are an important operator that allow for the user to dictate a future value with given parameters. They are marked by a solid bar and operate with the use of program specific logic commands.

126 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Operator offers discount per volume of panels Discount .75 Npanels 6if .55 Npanels 10if 1 otherwise  Discount 0.6 Example 4: True or False Verification Statements are an important operator that allow for the user to verify a system criteria that has been manually input. They are marked by lighter shading to make a distinction between the user inputs. True or false statements check a single or pairs of variables and return a Zero or One. Owner to proceed if discounts on retail below 60% Discount .55 1 2. DESIGN PHILOSOPHY The geometry of this superstructure uses modules consisting of two rolled steel girders supporting a segment of bridge deck cast along the girder lengths. It is assumed that the initial condition for the girders is simply supported under the weight of the cast deck. Each girder is assumed to carry half the weight of the precast deck. After the deck and girders are made composite, the barrier is added to the exterior modules. The barrier dead load is assumed to be evenly distributed between the two modules. Under the additional barrier dead load, the girders are again assumed to be simply supported. During transport, it is assumed that 28-day concrete strength has been reached in the deck and the deck is fully composite with the girders. The self-weight of the module during lifting and placement is assumed as evenly distributed to four pick points (two per girder). The modules are placed such that there is a bearing on each end and are again simply supported. The continuous span configuration, which includes two bearings per pier on either side of the UHPC joints, is analyzed for positive and negative bending and shear (using simple or refined methods). The negative bending moment above the pier is used to find the force couple for continuity design, between the compression plates at the bottom of the girders and the closure joint in the deck. The deck design utilizes the equivalent strip method. 3. DESIGN CRITERIA The first step for any bridge design is to establish the design criteria. The following is a summary of the primary design criteria for this design example: Governing Specifications: AASTHO LRFD Bridge Desing Specifications (5th Edition with 2010 interims) Design Methodology: Load and Resistance Factor Design (LRFD) Live Load Requirements: HL-93 S S3.6 Section Constraints: Wmod.max 200 kip Upper limit on the weight of the modules, based on common lifting and transport capabilities without significantly increasing time and/or cost due to unconventional equipment or permits

127 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 4. MATERIAL PROPERTIES Structural Steel Yield Strength: Fy 50ksi STable 6.4.1-1 Structural Steel Tensile Strength: Fu 65ksi STable 6.4.1-1 Concrete 28-day Compressive Strength: fc 5ksi fc_uhpc 21ksi S5.4.2.1 Reinforcement Strength: Fs 60ksi S5.4.3 & S6.10.3.7 Steel Density: ws 490pcf STable 3.5.1-1 Concrete Density: wc 150pcf STable 3.5.1-1 Modulus of Elasticity - Steel: Es 29000ksi Modulus of Elasticity - Concrete: Ec 33000 wc 1000pcf   1.5  fc ksi 4286.8 ksi Modular Ratio: n ceil Es Ec   7 Future Wearing Surface Density: Wfws 140pcf STable 3.5.1-1 Future Wearing Surface Thickness: tfws 2.5in (Assumed) 5. LOAD COMBINATIONS The following load combinations will be used in this design example, in accordance with Table 3.4.1-1. Strength I = 1.25DC + 1.5DW + 1.75(LL+IM), where IM = 33% Strength III = 1.25DC + 1.5DW + 1.40WS Strength V = 1.25DC + 1.5DW + 1.35(LL+IM) + 0.40WS + 1.0WL, where IM = 33% Service I = 1.0DC + 1.0DW + 1.0(LL+IM) + 0.3WS + 1.0WL, where IM = 33% Service II = 1.0DC + 1.0DW + 1.3(LL+IM), where IM = 33% Fatigue I = 1.5(LL+IM), where IM = 15% 6. BEAM SECTION Determine Beam Section Properties: btfx ttfGirder W30x99 Top Flange btf 10.45in ttf 0.67in Bottom Flange bbf 10.45in tbf 0.67in Dw x twWeb Dw 28.31in tw 0.52in Girder Depth dgird 29.7in bbfx tbf Check Flange Proportion Requeirements Met: S 6.10.2.2

128 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT btf 2 ttf 12.0 1 bbf 2 tbf 12.0 1 btf Dw 6  1 bbf Dw 6  1 ttf 1.1 tw 1 tbf 1.1 tw 1 0.1 tbf 3 bbf 12 ttf 3 btf 12  10 1 tbf bbf 12 ttf btf 12 0.3 1 Properties for use when analyzing under beam self weight (steel only): Atf btf ttf Abf bbf tbf Aw Dw tw Asteel Abf Atf Aw Asteel 28.7 in2 Total steel area. Steel centroid from top. ysteel Atf ttf 2  Abf tbf 2 Dw ttf   Aw Dw 2 ttf   Asteel  ysteel 14.8 in Calculate Iz: Moment of inertia about Z axis. Izsteel tw Dw 3 12 btf ttf 3 12  bbf tbf 3 12  Aw Dw 2 ttf ysteel   2  Atf ysteel ttf 2   2  Abf Dw tbf 2  ttf ysteel   2  Calculate Iy: Iysteel Dw tw 3 ttf btf3 tbf bbf3 12  Moment of inertia about Y axis. Calculate Ix: Moment of inertia about X axis. Ixsteel 1 3 btf ttf 3 bbf tbf3 Dw tw3  Izsteel 3923.795 in 4 Iysteel 127.762 in4 Ixsteel 3.4 in4 Asteel 28.7 in2

129 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Composite Section Properties (Uncracked Section - used for barrier dead load and live load positive bending): Determine composite slab and reinforcing properties Slab thickness assumes some sacrificial thickness; use: tslab 8in Dt tslab ttf Dw tbf  37.6 in Total section depth beff spacingint beff 47 in Effective width. S 4.6.2.6.1 LRFD Transformed slab width as steel.btr beff n  Transformed slab moment of inertia about z axis as steel.Izslab btr tslab 3 12  Aslab btr tslab Transformed slab area as steel. Slab reinforcement: (Use #5 @ 8" top, and #6 @ 8" bottom; additional bar for continuous segments of #6 @ 12") Typical Cross Section Cross Section Over Support Art 0.465 in2 ft beff 1.8 in2 Arb 0.66 in2 ft beff 2.6 in2 Artadd 0.44 in2 ft  beff 1.7 in2 Ar Art Arb 4.4 in2 Arneg Ar Artadd 6.1 in2 crt 2.5in 0.625in 5 16  in 3.4 in crb tslab 1.75in 6 16  in 5.9 in ref from top of slab cr Art crt Arb crb  Ar 4.9 in crneg Art crt Arb crb Artadd crt  Arneg 4.5 in

130 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Find composite section centroid: Ax Asteel Ar n 1( ) n  Aslab yslab tslab 2  Centroid of steel from top of slab.yst Atf ttf 2 tslab   Abf tbf 2 Dw ttf tslab   Aw Dw 2 ttf tslab   Asteel  Centroid of transformed composite section from top of slab.yc yst Asteel cr Ar n 1( ) n  Aslab yslab Ax  yc 10.3 in Calculate Transformed Iz for composite section: Transformed moment of inertia about the z axis.Iz Izsteel Asteel yst yc 2 Izslab Aslab yslab yc 2 Ar n 1( ) n cr yc 2 Calculate Transformed Iy for composite section: ttr tslab n  Transformed slab thickness. Iyslab ttr beff 3 12  Transformed moment of inertia about y axis of slab. Transformed moment of inertia about the y axis (ignoring reinforcement). Iy Iysteel Iyslab Calculate Transformed Ix for composite section: Transformed moment of inertia about the x axis.Ix 1 3 btf ttf 3 bbf tbf3 Dw tw3 btr tslab3  Results: Ax 86.2 in 2 Iy 10015.7 in4 Iz 10959.8 in4 Ix 1149.3 in4 Composite Section Properties (Uncracked Section - used for live load negative bending): Find composite section area and centroid: Axneg Asteel Arneg n 1( ) n  Aslab Centroid of transformed composite section from top of slab.ycneg ysteel Asteel crneg Arneg n 1( ) n  Aslab yslab Axneg  ycneg 7.6 in Calculate Transformed Izneg for composite negative moment section: Transformed moment of inertia about the z axis. Izneg Izsteel Asteel ysteel ycneg 2 Izslab Aslab yslab ycneg 2 Arneg n 1( )n crneg ycneg  2 Izneg 6457.4 in 4

131 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Composite Section Properties (Cracked Section - used for live load negative bending): Find cracked section area and centroid: Acr Asteel Arneg 34.9 in2 ycr Asteel ysteel Arneg crneg  Acr 13 in ycrb tslab ttf Dw tbf ycr 24.6 in Find cracked section moments of inertia and section moduli: Izcr Izsteel Asteel ysteel ycr 2 Ar cr ycr 2 Izcr 4310.8 in4 Iycr Iysteel Iycr 127.8 in4 Ixcr 1 3 btf ttf 3 bbf ttf3 Dw tw3  Ixcr 3.4 in4 dtopcr ycr crt dtopcr 9.6 in dbotcr tslab ttf Dw tbf ycr dbotcr 24.6 in Stopcr Izcr dtopcr  Stopcr 450.7 in3 Sbotcr Izcr dbotcr  Sbotcr 174.9 in3 7. PERMANENT LOADS Phase 1: Steel girders are simply supported, and support their self-weight plus the weight of the slab. Steel girders in each module for this example are separated by three diaphragms - one at each bearing location, and one at midspan. Other module span configurations may require an increase or decrease in the number of diaphragms. Wdeck_int wc spacingint td Wdeck_int 514.1 plf Wdeck_ext wc spacingext td Wdeck_ext 525 plf Whaunch wc wh th Whaunch 21.9 plf Wstringer ws1 Wstringer 99 plf Diaphragms: MC18x42.7 Thickness Conn. Plate tconn 5 8 in Diaphragm Weight ws2 42.7plf Width Conn. Plate wconn 5in Diaphragm Length Ldiaph 4ft 2.5in Height Conn. Plate hconn 28.5in Wdiaphragm ws2 Ldiaph 2  Wdiaphragm 89.8 lbf Wconn 2 ws tconn wconn hconn Wconn 50.5 lbf WDCpoint Wdiaphragm Wconn  1.05 WDCpoint 147.4 lbf Equivalent distributed load from DC point loads: wDCpt_equiv 3 WDCpoint Lstr 6.4 plf Interior Uniform Dead Load, Phase 1: WDCuniform1_int Wdeck_int Whaunch Wstringer wDCpt_equiv 641.3 plf Exterior Uniform Dead Load, Phase 1: WDCuniform1_ext Wdeck_ext Whaunch Wstringer wDCpt_equiv 652.2 plf

132 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Moments due to Phase 1 DL: MDC1_int x( ) WDCuniform1_int x 2 Lstr x  MDC1_ext x( ) WDCuniform1_ext x2 Lstr x  Shear due to Phase 1 DL: VDC1_int x( ) WDCuniform1_int Lstr 2 x  VDC1_ext x( ) WDCuniform1_ext Lstr 2 x  Phase 2: Steel girders are simply supported and composite with the deck slab, and support their self-weight plus the weight of the slab in addition to barriers on exterior modules. Barriers are assumed to be evenly distributed between the two exterior module girders. Barrier Area Abarrier 2.89ft 2 Barrier Weight Wbarrier wc Abarrier  2  Wbarrier 216.8 plf Interior Dead Load, Phase 2: WDCuniform_int WDCuniform1_int 641.3 plf Exterior Dead Load, Phase 2: WDCuniform_ext WDCuniform1_ext Wbarrier 869 plf Moments due to Phase 2 DL: MDC2_int x( ) WDCuniform_int x 2 Lstr x  MDC2_ext x( ) WDCuniform_ext x2 Lstr x  Shear due to Phase 2 DL: VDC2_int x( ) WDCuniform_int Lstr 2 x  VDC2_ext x( ) WDCuniform_ext Lstr 2 x  Phase 3: Girders are composite and have been made continuous. Utilities and future wearing surface are applied. Unit Weight Overlay wws 30psf Wws_int wws spacingint Wws_int 117.5 plf Wws_ext wws spacingext 1 ft 7in  Wws_ext 72.5 plf Unit Weight Utilities Wu 15plf WDWuniform_int Wws_int Wu WDWuniform_int 132.5 plf WDWuniform_ext Wws_ext Wu WDWuniform_ext 87.5 plf Moments due to DW: MDW_int x( ) WDWuniform_int x 2 Lstr x  MDW_ext x( ) WDWuniform_ext x2 Lstr x  Shears due to DW: VDW_int x( ) WDWuniform_int Lstr 2 x  VDW_ext x( ) WDWuniform_ext Lstr 2 x 

133 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 8. PRECAST LIFTING WEIGHTS AND FORCES This section addresses the construction loads for lifting the module into place. The module is lifted from four points, at some distance, Dlift from each end of each girder. Distance from end of lifting point: Dlift 8.75ft Assume weight uniformly distributed along girder, with 30% Dynamic Dead Load Allowance: Dynamic Dead Load Allowance: DLIM 30% Interior Module: Total Interior Module Weight: Wint Lstr WDCuniform_int 3 WDCpoint  2 1 DLIM( ) 117 kip Vertical force at lifting point: Flift_int Wint 4 29.3 kip Equivalent distributed load: wint_IM Wint 2 Lstr  842 plf Min (Neg.) Moment during lifting: Mlift_neg_max_int wint_IM Dlift 2  2  Mlift_neg_max_int 32.2 kip ft Max (Pos.) Moment during lifting: Mlift_pos_max_int 0 wint_IM Lstr 2 Dlift 2 8 Mlift_neg_max_int 0if wint_IM Lstr 2 Dlift 2 8 Mlift_neg_max_int  Mlift_pos_max_int 252.4 kip ft Exterior Module: Total Exterior Module Weight: Wext Lstr WDCuniform_ext 3 WDCpoint Wbarrier Lstr  2 1 DLIM( ) 197.3 kip Vertical force at lifting point: Flift_ext Wext 4 49.3 kip Equivalent distributed load: wext_IM Wext 2 Lstr 1419.7 plf Min (Neg.) Moment during lifting: Mlift_neg_max_ext wext_IM Dlift 2 2  Mlift_neg_max_ext 54.3 kip ft Max (Pos.) Moment during lifting: Mlift_pos_max_ext 0 wext_IM Lstr 2 Dlift 2 8 Mlift_neg_max_ext 0if wext_IM Lstr 2 Dlift 2 8 Mlift_neg_max_ext  Mlift_pos_max_ext 425.5 kip ft Max Shear during lifting: Vlift max wext_IM Dlift Flift_ext wext_IM Dlift  36.9 kip

134 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 9. LIVE LOAD DISTRIBUTION FACTORS These factors represent the distribution of live load from the deck to the girders in accordance with AASHTO Section 4, and assumes the deck is fully continuous across the joints. Girder Section Modulus: Izsteel 3923.8 in 4 Girder Area: Asteel 28.7 in 2 Girder Depth: dgird 29.7 in Distance between centroid of deck and centroid of beam: eg td 2 th dgird 2  22.1 in Modular Ratio: n 7 Multiple Presence Factors: MP1 1.2 MP2 1.0 S3.6.1.1.2-1 Interior Stringers for Moment: S4.6.2.2.1-1 One Lane Loaded: Kg n Izsteel Asteel eg 2  125670.9 in4 gint_1m 0.06 spacingint 14ft   0.4 spacingint Lspan   0.3  Kg Lspan td 3     0.1      0.269 Two Lanes Loaded: gint_2m 0.075 spacingint 9.5ft   0.6 spacingint Lspan   0.2  Kg Lspan td 3     0.1      0.347 Governing Factor: gint_m max gint_1m gint_2m  0.347 Interior Stringers for Shear: One Lane Loaded: gint_1v 0.36 spacingint 25ft   0.517 Two Lanes Loaded: gint_2v 0.2 spacingint 12ft  spacingint 35ft   2      0.514 Governing Factor: gint_v max gint_1v gint_2v  0.517 Exterior Stringers for Moment: One Lane Loaded: Use Lever Rule. Wheel is 2' from barrier; barrier is 2" beyond exterior stringer. de 2in Lspa 4.5ft r Lspa de 2ft 2.7 ft gext_1m MP1 0.5r Lspa  0.356 Two Lanes Loaded: e2m 0.77 de 9.1ft  0.7883 gext_2m e2m gint_2m 0.273 Governing Factor: gext_m max gext_1m gext_2m  0.356 Exterior Stringers for Shear: One Lane Loaded: Use Lever Rule. gext_1v gext_1m 0.356

135 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Two Lanes Loaded: e2v 0.6 de 10ft  0.62 gext_2v e2v gint_2v 0.317 Governing Factor: gext_v max gext_1v gext_2v  0.356 FACTOR TO USE FOR SHEAR: gv max gint_v gext_v  0.517 FACTOR TO USE FOR MOMENT: gm max gint_m gext_m  0.356 10. LOAD RESULTS Case 1: Dead Load on Steel Only (calculated in Section 7). Negative moments are zero and are not considered. Because the girder is simply supported, the maximum moment is at x = Lstr/2 and the maximum shear is at x = 0. Interior Girder MDC1int MDC1_int Lstr 2   387.2 kip ft MDW1int 0 kip ft MLL1int 0kip ft VDC1int VDC1_int 0( ) 22.3 kip VDW1int 0 kip VLL1int 0 kip Exterior Girder MDC1ext MDC1_ext Lstr 2   393.8 kip ft MDW1ext 0 kip ft MLL1ext 0 kip ft VDC1ext VDC1_ext 0( ) 22.7 kip VDW1ext 0 kip VLL1ext 0 kip ft Load Cases: M1_STR_I max 1.25 MDC1int 1.5 MDW1int 1.75 MLL1int 1.25 MDC1ext 1.5 MDW1ext 1.75 MLL1ext  492.3 kip ft V1_STR_I max 1.25 VDC1int 1.5 VDW1int 1.75 VLL1int 1.25 VDC1ext 1.5 VDW1ext 1.75 VLL1ext  28.3 kip Case 2: Dead Load on Composite Section (calculated in Section 7). Negative moments are zero and are not considered. Again, the maximum moment occur at x = Lstr/2 and the maximum shear is at x = 0. Interior Girder MDC2int MDC2_int Lstr 2   387.2 kip ft MDW2int 0 kip ft MLL2int 0 kip ft VDC2int VDC2_int 0( ) 22.3 kip VDW2int 0 kip VLL2int 0 kip Exterior Girder MDC2ext MDC2_ext Lstr 2   524.7 kip ft MDW2ext 0 kip ft MLL2ext 0 kip ft VDC2ext VDC2_ext 0( ) 30.2 kip VDW2ext 0 kip VLL2ext 0 kip Load Cases: M2_STR_I max 1.25 MDC2int 1.5 MDW2int 1.75 MLL2int 1.25 MDC2ext 1.5 MDW2ext 1.75 MLL2ext  655.8 kip ft V2_STR_I max 1.25 VDC2int 1.5 VDW2int 1.75 VLL2int 1.25 VDC2ext 1.5 VDW2ext 1.75 VLL2ext  37.7 kip Case 3: Composite girders are lifted into place from lifting points located distance Dlift from the girder edges. Maximum moments and shears were calculated in Section 8. Interior Girder MDC3int Mlift_pos_max_int 252.4 kip ft MDW3int 0 kip ft MLL3int 0 kip ft MDC3int_neg Mlift_neg_max_int 32.2 kip ft MDW3int_neg 0 kip ft MLL3int_neg 0 kip ft VDC3int Vlift 36.9 kip VDW3int 0 kip VLL3int 0 kip Exterior Girder MDC3ext Mlift_pos_max_ext 425.5 kip ft MDW3ext 0 kip ft MLL3ext 0 kip ft MDC3ext_neg Mlift_neg_max_ext 54.3 kip ft MDW3ext_neg 0 kip ft MLL3ext_neg 0 kip ft VDC3ext Vlift 36.9 kip VDW3ext 0 kip VLL3ext 0 kip Load Cases: M3_STR_I max 1.5 MDC3int 1.5 MDW3int 1.5 MDC3ext 1.5 MDW3ext  638.3 kip ft M3_STR_I_neg max 1.5 MDC3int_neg 1.5 MDW3int_neg 1.5 MDC3ext_neg 1.5 MDW3ext_neg  81.5 kip ft

136 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT V3_STR_I max 1.5 VDC3int 1.5 VDW3int 1.5 VDC3ext 1.5 VDW3ext  55.4 kip Case 4: Composite girders made continuous. Utilities and future wearing surface are applied, and live load. Maximum moment and shear results are from a finite element analysis not included in this design example. The live load value includes the lane fraction calculated in Section 9, and impact. Governing Loads: MDC4 440 kip ft MDW4 43.3 kip ft MLL4 590.3 kip ft MWS4 0kip ft MW4 0kip ft MDC4neg 328.9 kip ft MDW4neg 32.3 kip ft MLL4neg 314.4 kip ft MWS4neg 0 kip ft MWL4neg 0 kip ft Vu 145.3kip Load Cases: M4_STR_I 1.25 MDC4 1.5 MDW4 1.75 MLL4 1648 kip ft M4_STR_I_neg 1.25 MDC4neg 1.5 MDW4neg 1.75 MLL4neg 1009.8 kip ft M4_STR_III 1.25 MDC4 1.5 MDW4 1.4 MWS4 614.9 kip ft M4_STR_III_neg 1.25 MDC4neg 1.5 MDW4neg 1.4 MWS4 459.6 kip ft M4_STR_V 1.25 MDC4 1.5 MDW4 1.35 MLL4 0.4 MWS4 1.0 MW4 1411.9 kip ft M4_STR_V_neg 1.25 MDC4neg 1.5 MDW4neg 1.35 MLL4neg 0.4 MWS4neg 1.0 MWL4neg 884 kip ft M4_SRV_I 1.0 MDC4 1.0 MDW4 1.0 MLL4 0.3 MWS4 1.0 MW4 1073.6 kip ft M4_SRV_I_neg 1.0 MDC4neg 1.0 MDW4neg 1.0 MLL4neg 0.3 MWS4neg 1.0 MWL4neg 675.6 kip ft M4_SRV_II 1.0 MDC4 1.0 MDW4 1.3 MLL4 1250.7 kip ft M4_SRV_II_neg 1.0 MDC4neg 1.0 MDW4neg 1.3 MLL4neg 769.9 kip ft

137 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 11. FLEXURAL STRENGTH The flexural resistance shall be determined as specified in LRFD Design Article 6.10.6.2. Determine Stringer Plastic Moment Capacity First. LFRD Appendix D6 Plastic Moment Find location of PNA: Forces: Prt Art Fs 109.3 kip Ps 0.85 fc beff tslab 1598 kip Pw Fy Dw tw 736.1 kip Prb Arb Fs 155.1 kip Pc Fy btf ttf 350.1 kip Pt Fy bbf tbf 350.1 kip PNApos "case 1" Pt Pw  Pc Ps Prt Prb if "case 2" Pt Pw Pc  Ps Prt Prb  if "case 3" Pt Pw Pc  crbtslab Ps Prt Prb     if "case 4" Pt Pw Pc Prb  crbtslab Ps Prt     if "case 5" Pt Pw Pc Prb  crttslab Ps Prt     if "case 6" Pt Pw Pc Prb Prt  crttslab Ps   if "case 7" Pt Pw Pc Prb Prt  crttslab Ps   if otherwise otherwise otherwise otherwise otherwise otherwise  PNApos "case 4" PNAneg "case 1" Pc Pw  Pt Prt Prb if "case 2" Pt Pw Pc  Prt Prb  if otherwise  PNAneg "case 1" Calculate Y, Dp, and Mp: D Dw ts tslab th 0 Crt crt Crb crb Case I : Plastic Nuetral Axis in the Steel Web Y1 D 2 Pt Pc Ps Prt Prb Pw 1   DP1 ts th ttf Y1

138 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT MP1 Pw 2D Y1 2 D Y1 2  Ps Y1 ts2 ttf th   Prt ts Crt ttf Y1 th  Prb ts Crb ttf Y1 th  Pc Y1 ttf 2   Pt D Y1 tbf 2            Y1neg D 2   1 Pc Pt Prt Prb  Pw    Dp1neg ts th ttf Y1neg DCP1neg D 2 Pw   Pt Pw Prb Prt Pc  Mp1neg Pw 2 D   Y1neg 2 Dw Y1neg 2  Prt ts Crt ttf Y1neg th  Prb ts Crb ttf Y1neg th  Pt D Y1neg tbf 2   Pc Y1neg ttf 2            Case II: Plastic Nuetral Axis in the Steel Top Flange Y2 ttf 2 Pw Pt Ps Prt Prb Pc 1   DP2 ts th Y2 MP2 Pc 2ttf Y2 2 ttf Y2 2  Ps Y2 ts2 th   Prt ts Crt th Y2  Prb ts Crb th Y2  Pw D 2 ttf Y2  Pt D Y2 tbf 2  ttf            Y2neg ttf 2   1 Pw Pc Prt Prb  Pt    DP2neg ts th Y2neg DCP2neg D Mp2neg Pt 2 ttf   Y2neg 2 ttf Y2neg 2  Prt ts Crt th Y2neg  Prb ts Crb th Y2neg  Pw ttf Y2neg D 2   Pc ts th Y2neg ttf 2        Case III: Plastic Nuetral Axis in the Concrete Deck Below the Bottom Reinforcing Y3 ts Pc Pw Pt Prt Prb Ps    DP3 Y3 MP3 Ps 2ts Y3 2  Prt Y3 Crt  Prb Crb Y3  Pc ttf2 ts th Y3   Pw D 2 ttf th ts Y3  Pt D tbf 2  ttf ts th Y3            Case IV: Plastic Nuetral Axis in the Concrete Deck in the bottom reinforcing layer Y4 Crb DP4 Y4 MP4 Ps 2ts Y4 2  Prt Y4 Crt  Pc ttf2 th ts Y4   Pw D 2 ttf th ts Y4  Pt D tbf 2  ttf th ts Y4           

139 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Case V: Plastic Nuetral Axis in the Concrete Deck between top and bot reinforcing layers Y5 ts Prb Pc Pw Pt Prt Ps    DP5 Y5 MP5 Ps 2ts Y5 2  Prt Y5 Crt  Prb ts Crb  Y5  Pc ttf2 ts th Y5   Pw D 2 ttf th ts Y5  Pt D tbf 2  ttf ts th Y5            Ypos Y1 PNApos "case 1"=if Y2 PNApos "case 2"=if Y3 PNApos "case 3"=if Y4 PNApos "case 4"=if Y5 PNApos "case 5"=if  DPpos DP1 PNApos "case 1"=if DP2 PNApos "case 2"=if DP3 PNApos "case 3"=if DP4 PNApos "case 4"=if DP5 PNApos "case 5"=if  MPpos MP1 PNApos "case 1"=if MP2 PNApos "case 2"=if MP3 PNApos "case 3"=if MP4 PNApos "case 4"=if MP5 PNApos "case 5"=if  Ypos 5.9 in DPpos 5.9 in MPpos 2338.1 kip ft Dp = distance from the top of slab of composite section to the neutral axis at the plastic moment (neglect positive moment reinforcement in the slab). Yneg Y1neg PNAneg "case 1"=if Y2neg PNAneg "case 2"=if  DPneg Dp1neg PNAneg "case 1"=if DP2neg PNAneg "case 2"=if  MPneg Mp1neg PNAneg "case 1"=if Mp2neg PNAneg "case 2"=if  Yneg 9.1 in DPneg 17.7 in MPneg 19430.1 kip in Depth of web in compression at the plastic moment [D6.3.2]: At bbf tbf Ac btf ttf Dcppos D 2 Fy At Fy Ac 0.85 fc Aslab Fs Ar Fy Aw 1   Dcppos 0in( ) PNApos "case 1"if 0in( ) Dcppos 0 if Dcppos PNApos "case 1"=if  Dcpneg DCP1neg PNAneg "case 1"=if DCP2neg PNAneg "case 2"=if  Dcpneg 19.2 in Dcppos 0 in Positive Flexural Compression Check: From LRFD Article 6.10.2 Check for compactness: Web Proportions: Web slenderness Limit: Dw tw 150 1 2 Dcppos tw  3.76 Es Fy  1 S 6.10.6.2.2 Therefore Section is considered compact and shall satisfy the requirements of Article 6.10.7.1. Mn MPpos DPpos 0.1 Dtif MPpos 1.07 0.7 DPpos Dt    otherwise  Mn 2246.4 kip ft

140 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Negative Moment Capacity Check (Appendix A6): Web Slenderness: Dt 37.6 in Dcneg Dt ycr tbf 24 in 2 Dcneg tw 5.7 Es Fy  1 S Appendix A6 (for skew less than 20 deg). Moment ignoring concrete: Myt Fy Sbotcr 8745.1 kip in Myc Fs Stopcr 27039.2 kip in My min Myc Myt  8745.1 kip in Web Compactness: Check for Permanent Deformations (6.10.4.2): Dn max tslab ttf Dw yc yc tslab ttf  26.7 in Gov if yc tslab ttf yc crt Dn  6.9 in fn M4_SRV_II_neg Gov Iz  5.8 ksi Steel stress on side of Dn ρ min 1.0 Fy fn   1 β 2 Dn tw Atf  4 Rh 12 β 3ρ ρ3   12 2 β( ) 1 λrw 5.7 Es Fy  λPWdcp min λrw Dcpneg Dcneg  Es Fy 0.54 MPneg Rh My  0.09  2            19.6 2 Dcpneg tw  λPWdcp 0 Web Plastification: Rpc MPneg Myc 0.7 Rpt MPneg Myt 2.2 Flexure Factor: ϕf 1.0 Tensile Limit: Mr_neg_t ϕf Rpt Myt 1619.2 kip ft Compressive Limit: Local Buckling Resistance: λf bbf 2 tbf 7.8 λrf 0.95 0.76 Es Fy  19.9 λpf 0.38 Es Fy  9.2 Fyresid max min 0.7 Fy Rh Fy Stopcr Sbotcr  Fy   0.5 Fy   35.0 ksi MncLB Rpc Myc  λf λpfif Rpc Myc 1 1 Fyresid Stopcr Rpc Myc   λf λpf λrf λpf       otherwise  MncLB 1619.2 kip ft

141 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Lateral Torsional Buckling Resistance: Lb Lstr  2 3 11.6 ft Inflection point assumed to be at 1/6 span rt bbf 12 1 1 3 Dcneg tw bbf tbf    2.4 in Lp 1.0 rt Es Fy  57.6 in h D tbf 29 in Cb 1.0 Jb D tw 3 3 bbf tbf 3 3 1 0.63 tbf bbf    btf ttf 3 3 1 0.63 ttf btf    3.3 in4 Lr 1.95 rt Es Fyresid  Jb Sbotcr h  1 1 6.76 Fyresid Es Sbotcr h Jb   2  240 in Fcr Cb π2 Es Lb rt   2 1 0.078 Jb Sbotcr h  Lb rt   2  91.7 ksi MncLTB Rpc Myc  Lb Lpif min Cb 1 1 Fyresid Sbotcr Rpc Myc   Lb Lp  Lr Lp     Rpc Myc Rpc Myc   Lp Lb Lrif min Fcr Sbotcr Rpc Myc  Lb Lrif  MncLTB 1124.2 kip ft Mr_neg_c ϕf min MncLB MncLTB  1124.2 kip ft Governing negative moment capacity: Mr_neg min Mr_neg_t Mr_neg_c  1124.2 kip ft 12. FLEXURAL STRENGTH CHECKS Phase 1: First, check the stress due to the dead load on the steel section only. (LRFD 6.10.3 - Constructability Requirements Reduction factor for construction ϕconst 0.9 Load Combination for construction 1.25 MDC Max Moment applied, Phase 1: (at midspan) Mint_P1 1.25 MDC1_int Lstr 2   484 kip ft Interior( ) Mext_P1 1.25 MDC1_ext Lstr 2   492.3 kip ft Exterior( ) Maximum Stress, Phase 1: fint_P1 Mint_P1 ysteel Izsteel 21.9 ksi Interior( ) fext_P1 Mext_P1 ysteel Izsteel 22.3 ksi Exterior( ) Stress limits: fP1_max ϕconst Fy

142 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT fint_P1 fP1_max 1 fext_P1 fP1_max 1 Phase 2: Second, check the stress due to dead load on the composite section (with barriers added) Reduction factor for construction ϕconst 0.9 Load Combination for construction 1.25 MDC Max Moment applied, Phase 2: (at midspan) M2_STR_I 655.8 kip ft Capacity for positive flexure: Mn 2246.4 kip ft Check Moment: M2_STR_I ϕconst Mn 1 Phase 3: Next, check the flexural stress on the stringer during transport and picking, to ensure no cracking. Reduction factor for construction ϕconst 0.9 Load Combination for construction 1.5 MDC when dynamic construction loads are involved (Section 10). Loads and stresses on stringer during transport and picking: M3_STR_I_neg 81.5 kip ft Concrete rupture stress fr 0.24 fc ksi 0.5 ksi Concrete stress during construction not to exceed: fcmax ϕconst fr 0.5 ksi fcconst M3_STR_I_neg yc Iz n 0.1 ksi fcconst fcmax 1 Phase 4: Check flexural capacity under dead load and live load for fully installed continuous composite girders. Strength I Load Combination ϕf 1.0 M4_STR_I 1648 kip ft M4_STR_I_neg 1009.8 kip ft M4_STR_I ϕf Mn 1 M4_STR_I_neg Mr_neg 1 Strength III Load Combination M4_STR_III 614.9 kip ft M4_STR_III_neg 459.6 kip ft M4_STR_III ϕf Mn 1 M4_STR_III_neg Mr_neg 1 Strength V Load Combination M4_STR_V 1411.9 kip ft M4_STR_V_neg 884 kip ft M4_STR_V ϕf Mn 1 M4_STR_V_neg Mr_neg 1 13. FLEXURAL SERVICE CHECKS Check service load combinations for the fully continuous beam with live load (Phase 4): under Service II for stress limits - M4_SRV_II 1250.7 kip ft M4_SRV_II_neg 769.9 kip ft under Service I for cracking - M4_SRV_I_neg 675.6 kip ft Ignore positive moment for Service I as there is no tension in the concrete in this case.

143 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Service Load Stress Limits: Top Flange: ftfmax 0.95 Rh Fy 47.5 ksi Bottom Flange: fbfmax ftfmax 47.5 ksi Concrete (Negative bending only): fr 0.5 ksi Service Load Stresses, Positive Moment: Top Flange: fSRVII_tf M4_SRV_II yc tslab  Iz  3.2 ksi fSRVII_tf ftfmax 1 Bottom Flange: fbfs2 M4_SRV_II tslab ttf Dw tbf yc  Iz  37.4 ksi fl 0 fbfs2 fl 2  fbfmax 1 Service Load Stresses, Negative Moment: Top (Concrete): fcon.neg M4_SRV_I_neg ycneg n Izneg 1.4 ksi Using Service I Loading fcon.neg fr 0 Bottom Flange: fbfs2.neg M4_SRV_I_neg tslab ttf Dw tbf ycneg  Izneg 37.8 ksi fbfs2.neg fbfmax 1 Check LL Deflection: ΔDT 1.104 in from independent Analysis - includes 100% design truck (w/impact), or 25% design truck (w/impact) + 100% lane load DFδ 3 12 0.3 Deflection distribution factor = (no. lanes)/(no. stringers) Lstr ΔDT DFδ 3021.7 Equivalent X, where L/X = Deflection*Distribution Factor Lstr ΔDT DFδ 800 1

144 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 14. SHEAR STRENGTH Shear Capacity based on AASHTO LRFD 6.10.9 Nominal resistance of unstiffened web: Fy 50.0 ksi Dw 28.3 in tw 0.5 in ϕv 1.0 k 5 Vp 0.58 Fy Dw tw 426.9 kip C1 1.0 Dw tw 1.12 Es k Fy if 1.57 Dw tw   2 Es k Fy         Dw tw 1.40 Es k Fy if 1.12 Dw tw Es k Fy      otherwise  C1 1 Vn C1 Vp 426.9 kip Vu ϕv Vn 1 15. FATIGUE LIMIT STATES: Fatigue check shall follow LRFD Article 6.10.5. Moments used for fatigue calculations were found using an outside finite element analysis program. First check Fatigue I (infinite life); then find maximum single lane ADTT for Fatigue II if needed. Fatigue Stress Limits: ΔFTH_1 16 ksi Category B: non-coated weathering steel ΔFTH_2 12 ksi Category C': Base metal at toe of transverse stiffener fillet welds ΔFTH_3 10 ksi Category C: Base metal at shear connectors Fatigue Moment Ranges at Detail Locations (from analysis): MFAT_B 301 kip ft MFAT_CP 285.7 kip ft MFAT_C 207.1kip ft nfat 2 Lstr 40 ftif 1.0 otherwise γFATI 1.5 γFATII 0.75 Constants to use for detail checks: ADTTSL_INF_B 860 AFAT_B 120 108 ADTTSL_INF_CP 660 AFAT_CP 44 108 ADTTSL_INF_C 1290 AFAT_C 44 108 Category B Check: Stress at Bottom Flange, Fatigue I fFATI_B γFATI MFAT_B tslab ttf Dw tbf yc  Iz 13.5 ksi fFATI_B ΔFTH_1 1 fFATII_B γFATII γFATI fFATI_B 6.8 ksi

145 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ADTTSL_B_MAX ADTTSL_INF_B nfat fFATI_B ΔFTH_1if AFAT_B ksi 3 365 75 nfat fFATII_B3 otherwise  ADTTSL_B_MAX 860 Category C' Check: Stress at base of transverse stiffener (top of bottom flange) fFATI_CP γFATI MFAT_CP tslab ttf Dw yc  Iz  12.5 ksi fFATI_CP ΔFTH_2 0 fFATII_CP γFATII γFATI fFATI_CP 6.3 ksi ADTTSL_CP_MAX ADTTSL_INF_CP nfat fFATI_CP ΔFTH_2if AFAT_CP ksi 3 365 75 nfat fFATII_CP3 otherwise  ADTTSL_CP_MAX 656 Category C Check: Stress at base of shear connectors (top of top flange) fFATI_C γFATI MFAT_C yc tslab  Iz  0.8 ksi fFATI_C ΔFTH_3 1 fFATII_C γFATII γFATI fFATI_C 0.4 ksi ADTTSL_C_MAX ADTTSL_INF_C nfat fFATI_C ΔFTH_3if AFAT_C ksi 3 365 75 nfat fFATII_C3 otherwise  ADTTSL_C_MAX 1290 FATIGUE CHECK: ADTTSL_MAX min ADTTSL_B_MAX ADTTSL_CP_MAX ADTTSL_C_MAX  Ensure that single lane ADTT is less than ADTTSL_MAX 656 If not, then the beam requires redesign.

146 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 16. BEARING STIFFENERS bp x tpUsing LRFD Article 6.10.11 for stiffeners: tp 5 8 in bp 5in ϕb 1.0 tp_weld 516  in 9tw x tw 9tw x tw *Check min weld size Projecting Width Slenderness Check: bp 0.48tp Es Fy  1 bp x tp Stiffener Bearing Resistance: Apn 2 bp tp_weld  tp Apn 5.9 in2 Rsb_n 1.4 Apn Fy Rsb_n 410.2 kip Rsb_r ϕb Rsb_n Rsb_r 410.2 kip RDC 26.721kip RDW 2.62kip RLL 53.943kip ϕDC_STR_I 1.25 ϕDW_STR_I 1.5 ϕLL_STR_I 1.75 Ru ϕDC_STR_I RDC ϕDW_STR_I RDW ϕLL_STR_I RLL Ru 131.7 kip Ru Rsb_r 1 Weld Check: throat tp_weld 2 2  throat 0.2 in Lweld Dw 2 3 in Lweld 22.3 in Aeff_weld throat Lweld Aeff_weld 4.9 in2 Fexx 70ksi ϕe2 0.8 Rr_weld 0.6 ϕe2 Fexx Rr_weld 33.6 ksi Ru_weld Ru 4 Aeff_weld  Ru_weld 6.7 ksi Ru_weld Ru_weld 1 Axial Resistance of Bearing Stiffeners: ϕc 0.9 Aeff 2 9 tw tp  tw 2 bp tp Aeff 11.4 in2 Leff 0.75 Dw Leff 21.2 in Ixp 2 9 tw tw3 12 tp 2 bp tw 3 12  Ixp 60.7 in4 Iyp tw tp 2 9 tw 3 12 2bp tp 3 12  Iyp 43.3 in4 rp min Ixp Iyp  Aeff  rp 1.9 in Q 1 for bearing stiffeners Kp 0.75 Po Q Fy Aeff 572.1 kip

147 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Pe π2Es Aeff Kp Leff rp   2 48919.6 kip Pn 0.658 Po Pe         Po Pe Po   0.44if 0.877 Pe otherwise  Pn 569.3 kip Pr ϕc Pn Pr 512.4 kip Ru Pr 1 17. SHEAR CONNECTORS: Shear Connector design to follow LRFD 6.10.10. Stud Properties: ds 7 8 in Diameter hs 6in Height of Stud hs ds 4 1 cs tslab hs cs 2in 1 ss 3.5in Spacing ss 4ds 1 ns 3 Studs per row btf ss ns 1  ds  2 1.0in 1 Asc π ds 2   2  Asc 0.6 in2 Fu 60ksi Fatigue Resistance: Zr 5.5 ds 2 kip in2  Zr 4.2 kip Qslab Aslab yc yslab  Qslab 338.9 in3 Vf 47.0kip Vfat Vf Qslab Iz 1.5 kip in  ps ns Zr Vfat 8.7 in 6 ds ps 24in 1 Strength Resistance: ϕsc 0.85 fc 5 ksi Ec 33000 0.15 1.5 fc ksi 4286.8 ksi Qn min 0.5 Asc fc Ec Asc Fu  Qn 36.1 kip Qr ϕsc Qn Qr 30.7 kip Psimple min 0.85 fc beff ts Fy Asteel  Psimple 1436.2 kip Pcont Psimple min 0.45 fc beff ts Fy Asteel  Pcont 2282.2 kip nlines Pcont Qr ns  nlines 24.8

148 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Find required stud spacing along the girder (varies as applied shear varies) i 0 23 x 0.00 1.414 4.947 8.480 12.013 15.546 19.079 22.612 26.145 29.678 33.210 33.917 34.624 36.037 36.743 40.276 43.809 47.342 50.875 54.408 57.941 61.474 65.007 67.833                                                               ft Vfi 61.5 59.2 56.8 54.4 52.0 49.5 47.1 44.7 42.7 40.6 40.6 40.6 40.6 40.6 40.6 42.3 44.2 46.6 49.1 51.5 53.9 56.3 58.7 61.5                                                               kip Vfati Vfi Qslab Iz 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1.9 1.8 1.8 1.7 1.6 1.5 1.5 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 ... kip in  Pmax ns Zr Vfati 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6.6 6.9 7.2 7.5 7.9 8.3 8.7 9.1 9.6 10.1 10.1 10.1 10.1 10.1 10.1 ... in min Pmax  6.6 in max Pmax  10.1 in 18. SLAB PROPERTIES This section details the geometric and material properties of the deck. Because the equivalent strip method is used in accordance with AASHTO LRFD Section 4, different loads are used for positive and negative bending. Unit Weight Concrete wc 150 pcf Deck Thickness for Design tdeck 8.0in tdeck 7in 1 Deck Thickness for Loads td 10.5 in Rebar yield strength Fs 60 ksi Strength of concrete fc 5 ksi Concrete clear cover Bottom Top cb 1.0in cb 1.0in 1 ct 2.5in ct 2.5in 1

149 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Transverse reinforcement Bottom Reinforcing ϕtb 68 in ϕtt 5 8 inTop Reinforcing Bottom Spacing stb 8in Top Spacing stt 8in stb 1.5ϕtb 1.5in 1 stt 1.5ϕtt 1.5in 1 stb 1.5 tdeck 18in 1 stt 1.5 tdeck 18in 1 Astb 12in stb π ϕtb 2   2  0.7 in2 Astt 12in stt π ϕtt 2   2  0.5 in2 Design depth of Bar dtb tdeck cb ϕtb 2   6.6 in dtt tdeck ct ϕtt 2   5.2 in Girder Spacing spacingint_max 4ft 6in spacingext 4 ft Equivalent Strip, +M wposM 26 6.6 spacingint_max ft   in wposM 55.7 in Equivalent Strip, -M wnegM 48 3.0 spacingint_max ft   in wnegM 61.5 in Once the strip widths are determined, the dead loads can be calculated. 19. PERMANENT LOADS This section calculates the dead loads on the slab. These are used later for analysis to determine the design moments. Weight of deck, +M wdeck_pos wc td wposM wdeck_pos 609.2 plf Weight of deck, -M wdeck_neg wc td wnegM wdeck_neg 672.7 plf Unit weight of barrier wb 433.5plf Barrier point load, +M Pb_pos wb wposM Pb_pos 2.01 kip Barrier point load, -M Pb_neg wb wnegM Pb_neg 2.22 kip 20. LIVE LOADS This section calculates the live loads on the slab. These loads are analyzed in a separate program with the permanent loads to determine the design moments. Truck wheel load Pwheel 16kip Impact Factor IM 1.33 Multiple presence factors MP1 1.2 MP2 1.0 MP3 0.85 Wheel Loads P1 IM MP1 Pwheel P2 IM MP2 Pwheel P3 IM MP3 Pwheel P1 25.54 kip P2 21.3 kip P3 18.09 kip 21. LOAD RESULTS A separate finite element analysis program was used to analyze the deck as an 11-span continuous beam with cantilevered overhangs on either end, with supports stationed at girder locations. The dead and live loads were applied separately. The results are represented here as input values, highlighted.

150 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Design Moments Mpos 38.9kip ft Mpos_dist Mpos wposM  Mpos_dist 8.38 kip ft ft  Mneg 21.0 kip ft Mneg_dist Mneg wnegM  Mneg_dist 4.1 kip ft ft  22. FLEXURAL STRENGTH CAPACITY CHECK: Consider a 1'-0" strip: ϕb 0.9 b 12in β1 0.85 fc 4ksiif 0.85 0.05 fc ksi 4  otherwise  β1 0.8 Bottom: Top: ctb Astb Fs 0.85 fc β1 b 1 in ctt Astt Fs 0.85 fc β1 b 0.7 in atb β1 ctb 0.8 in att β1 ctt 0.5 in Mntb Astb Fs b dtb atb 2   20.7 kip ft ft  Mntt Astt Fs ft dtt att 2   11.3 kip ft ft  Mrtb ϕb Mntb 18.6 kip ftft Mrtt ϕb Mntt 10.2 kip ft ft  Mrtb Mpos_dist 1 Mrtt Mneg_dist 1 23. LONGITUDINAL DECK REINFORCEMENT DESIGN: Longitudinal reinforcement ϕlb 58 in slb 12in ϕlt 5 8 in slt 12in Aslb 12in slb π ϕlb 2   2  0.3 in2 Aslt 12in slt π ϕlt 2   2 0.3 in2 Distribution Reinforcement (AASHTO 9.7.3.2) A%dist min 220 spacingint_max ft 67      100 67 % Adist A%dist Astb  0.4 in2 Aslb Aslt Adist 1

151 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 24. DESIGN CHECKS This section will conduct design checks on the reinforcing according to various sections in AASHTO LRFD. CHECK MINIMUM REINFORCEMENT (AASHTO LRFD 5.7.3.3.2): Modulus of Rupture fr 0.37 fc ksi 0.8 ksi Ec 4286.8 ksi Es 29000 ksi Section Modulus Snc b tdeck 2 6 128 in3 Adeck tdeck b 96 in2 ybar_tb Adeck tdeck 2  n 1( ) Astb dtb Adeck n 1( ) Astb 4.1 in ybar_tt Adeck tdeck 2  n 1( ) Astt dtt Adeck n 1( ) Astt 4 in Itb b tdeck 3 12 Adeck tdeck 2 ybar_tb   2  n 1( ) Astb dtb ybar_tb 2 538.3 in4 Itt b tdeck 3 12 Adeck tdeck 2 ybar_tt   2  n 1( ) Astt dtt ybar_tt 2 515.8 in4 Sc_tb Itb tdeck ybar_tb 138.2 in3 Sc_tt Itt tdeck ybar_tt 130 in3 Unfactored Dead Load Mdnc_pos_t 1.25 kip ft ft  Mdnc_neg_t 0.542 kip ft ft 

152 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT S 5.7.3.3.2 Cracking Moment Mcr_tb max Sc_tb fr ft Mdnc_pos_t Sc_tb Snc 1   Sc_tb fr ft   9.5 kip ft ft  Mcr_tt max Sc_tt fr ft Mdnc_neg_t Sc_tt Snc 1   Sc_tt fr ft   9 kip ft ft  Minimum Factored Flexural Resistance Mr_min_tb min 1.2 Mcr_tb 1.33 Mpos_dist  11.1 kip ftft Mrtb Mr_min_tb 1 Mr_min_tt min 1.2 Mcr_tt 1.33 Mneg_dist  5.4 kip ftft Mrtt Mr_min_tt 1 CHECK CRACK CONTROL (AASHTO LRFD 5.7.3.4): γeb 1.0 γet 0.75 MSL_pos 29.64kip ft MSL_neg 29.64kip ft MSL_pos_dist MSL_pos wposM 6.4 kip ft ft  MSL_neg_dist MSL_neg wnegM 5.8 kip ft ft  fssb MSL_pos_dist b n Itb dtb ybar_tb 2.5 ksi fsst MSL_neg_dist b n Itt dtt ybar_tt 1.1 ksi dcb cb ϕtb 2  1.4 in dct ct ϕtt 2  2.8 in βsb 1 dcb 0.7 tdeck dcb  1.3 βst 1 dct 0.7 tdeck dct  1.8 sb 700 γeb kip βsb fssb in 2 dcb 212.2 in st 700 γet kip βst fsst in 2 dct 266.5 in stb sb 1 stt st 1 SHRINKAGE AND TEMPERATURE REINFORCING (AASHTO LRFD 5.10.8): Ast 1.30 b tdeck 2 b tdeck  Fs kip in  0.11in2 1.30 b tdeck 2 b tdeck  Fs kip in  0.60in2if 0.11in2 1.30 b tdeck 2 b tdeck  Fs kip in  0.11in2if 0.60in2 1.30 b tdeck 2 b tdeck  Fs kip in  0.60in2if 0.1 in2 Astb Ast 1 Astt Ast 1 Aslb Ast 1 Aslt Ast 1 SHEAR RESISTANCE (AASHTO LRFD 5.8.3.3): ϕ 0.9 β 2 θ 45deg b 1 ft

153 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT dv_tb max 0.72 tdeck dtb atb 2  0.9 dtb   6.2 in dv_tt max 0.72 tdeck dtt att 2  0.9 dtt   5.8 in dv min dv_tb dv_tt  5.8 in Vc 0.0316 β fc ksi b dv 9.8 kip Vs 0kip Shear capacity of reinforcing steel Vps 0kip Shear capacity of prestressing steel Vns min Vc Vs Vps 0.25 fc b dv Vps  9.8 kip Vr ϕ Vns 8.8 kip Total factored resistance Vus 8.38kip Total factored load Vr Vus 1 DEVELOPMENT AND SPLICE LENGTHS (AASHTO LRFD 5.11): Development and splice length design follows standard calculations in AASHTO LRFD 5.11, or as dictated by the State DOT Design Manual. 25. DECK OVERHANG DESIGN (AASHTO LRFD A.13.4): Deck Properties: Deck Overhang Length Lo 1ft 9in Parapet Properties: Note: Parapet properties are per unit length. Compression reinforcement is ignored. Cross Sectional Area Ap 2.84ft 2 Height of Parapet Hpar 2ft 10in Parapet Weight Wpar wc Ap 426 plf Width at base wbase 1ft 5in Average width of wall wwall 13in 9.5in 2 11.3 in Height of top portion of parapet h1 2ft Width at top of parapet width1 9.5 in 9.5 in Height of middle portion of parapet h2 7in Width at middle transition of parapet width2 12 in 12 in

154 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Height of lower portion of parapet h3 3in Width at base of parapet width3 1ft 5 in 17 in b1 width1 b2 width2 width1 b3 width3 width2 Parapet Center of Gravity CGp h1 h2 h3  b1 2 2  1 2 h1 b2 b1 b2 3   h2 h3  b2 b3  b1 b2 b32   1 2 h2 b3 b1 b2 2b3 3    h1 h2 h3  b1 12 h1 b2 h2 h3  b2 b3  1 2 h2 b3 6.3 in Parapet Reinforcement Vertically Aligned Bars in Wall Horizontal Bars Rebar spacing: spa 12in npl 5 Rebar Diameter: ϕpa 58 in ϕpl 5 8 in Rebar Area: Ast_p π ϕpa 2   2  b spa  0.3 in2 Asl_p π ϕpl 2   2  0.3 in2 Cover: cst 3in csl 2in ϕpa 2.6 in Effective Depth: dst wbase cst ϕpa 2  13.7 in dsl wwall csl ϕpl 2  8.3 in Parapet Moment Resistance About Horizontal Axis: ϕext 1.0 S 5.7.3.1.2-4 S 5.7.3.2.3 Depth of Equivalent Stress Block: ah Ast_p Fs 0.85 fc b 0.4 in Moment Capacity of Upper Segment of Barrier (about longitudinal axis): Average width of section w1 width1 width2 2 10.7 in Cover cst1 2in dh1 w1 cst1 ϕpa 2  8.4 inDepth Factored Moment Resistance ϕMnh1 ϕext Ast_p Fs dh1 ah 2   b 12.7 kip ft ft  Moment Capacity of Middle Segment of Barrier (about longitudinal axis): Average width of section w2 width2 width3 2 14.5 in Cover cst2 3in dh2 w2 cst2 ϕpa 2  11.2 inDepth Factored Moment Resistance ϕMnh2 ϕext Ast_p Fs dh2 ah 2   b 16.9 kip ft ft 

155 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Parapet Base Moment Resistance (about longitudinal axis): development in tension cst3 3in coverbase_vert cst3 ϕpa 2  3.3 in minc_ta 1.5 cst3 3 ϕpa spa ϕpa 6 ϕpaif 1.2 otherwise 1.2 mdec_ta 0.8 spa 6inif 1.0 otherwise 0.8 ldb_ta max 1.25in Ast_p Fs kip  fc ksi 0.4 ϕpa Fs ksi          ϕpa 118 inif 2.70in Fs ksi  fc ksi ϕpa 148 in=if 3.50in Fs ksi  fc ksi ϕpa 188 in=if  ldt_ta ldb_ta minc_ta mdec_ta 14.4 in hooked bar developed in tension lhb_ta 38 ϕpa fc ksi 10.6 in minc 1.2 ldh_ta max 6in 8 ϕpa minc lhb_ta  12.7 in lap splice in tension llst_ta max 12in 1.3 ldt_ta  18.7 in benefit ldt_ta ldh_ta 1.7 in ldev_a 7 13 16  in Fdev benefit ldev_a ldt_ta 0.7 Fd 0.75 Distance from NA to Compressive Face ct_b Fd Ast_p Fs 0.85 fc β1 b 0.3 in S 5.7.3.1.2-4 Depth of Equivalent Stress Block at β1 ct_b 0.3 in S 5.7.3.2.3 Nominal Moment Resistance Mnt Fd Ast_p Fs dst at 2   15.6 kip ft S 5.7.3.2.2-1 Factored Moment Resistance Mcb ϕext Mnt ft  15.6 kip ft ft  S 5.7.3.2 Average Moment Capacity of Barrier (about longitudinal axis):

156 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Factored Moment Resistance about Horizontal Axis Mc ϕMnh1 h1 ϕMnh2 h2 Mcb h3 h1 h2 h3 13.8 kip ft ft  Parapet Moment Resistance (about vertical axis): Height of Transverse Reinforcement in Parapet y1 5in Width of Parapet at Transverse Reinforcement x1 width3 y1 h3  b3 h2  15.6 in y2 11.5in x2 b1 b2 y2 h3 h2  b2 h1  11.8 in y3 18in x3 b1 b2 y3 h3 h2  b2 h1  11.2 in y4 24.5in x4 b1 b2 y4 h3 h2  b2 h1  10.5 in y5 31in x5 b1 b2 y5 h3 h2  b2 h1  9.8 in Depth of Equivalent Stress Block a npl Asl_p Fs 0.85 fc Hpar 0.6 in Concrete Cover in Parapet coverr 2in coverrear coverr ϕpa ϕpl 2  2.9 in coverbase cst3 ϕpa ϕpl 2  3.9 in coverf 2in coverfront 2in ϕpa ϕpl 2  covert x5 2 4.9 in covertop covert 4.9 in Design depth d1i x1 coverbase 11.6 in d1o x1 coverrear 12.6 in d2i x2 coverfront 8.9 in d2o x2 coverrear 8.9 in d3i x3 coverfront 8.2 in d3o x3 coverrear 8.2 in d4i x4 coverfront 7.6 in d4o x4 coverrear 7.6 in d5i x5 covertop 4.9 in d5o x5 covertop 4.9 in Nominal Moment Resistance - Tension on Inside Face ϕMn1i ϕext Asl_p Fs d1i a2   208.3 kip in ϕMn2i ϕext Asl_p Fs d2i a2   158.1 kip in ϕMn3i ϕext Asl_p Fs d3i a2   145.6 kip in ϕMn4i ϕext Asl_p Fs d4i a2   133.2 kip in ϕMn5i ϕext Asl_p Fs d5i a2   84.5 kip in Mwi ϕMn1i ϕMn2i ϕMn3i ϕMn4i ϕMn5i 60.8 kip ft Nominal Moment Resistance - Tension on Outside Face ϕMn1o ϕext Asl_p Fs d1o a2   18.9 kip ft ϕMn2o ϕext Asl_p Fs d2o a2   13.2 kip ft ϕMn3o ϕext Asl_p Fs d3o a2   12.1 kip ft

157 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ϕMn4o ϕext Asl_p Fs d4o a2   11.1 kip ft ϕMn5o ϕext Asl_p Fs d5o a2   7 kip ft Mwo ϕMn1o ϕMn2o ϕMn3o ϕMn4o ϕMn5o 62.3 kip ft Vertical Nominal Moment Resistance of Parapet Mw 2 Mwi Mwo 3 61.3 kip ft Parapet Design Factors: Crash Level CL "TL-4" Transverse Design Force Ft 13.5kip CL "TL-1"=if 27.0kip CL "TL-2"=if 54.0kip CL "TL-3"=if 54.0kip CL "TL-4"=if 124.0kip CL "TL-5"=if 175.0kip otherwise 54 kip Lt 4.0ft CL "TL-1"=if 4.0ft CL "TL-2"=if 4.0ft CL "TL-3"=if 3.5ft CL "TL-4"=if 8.0ft CL "TL-5"=if 8.0ft otherwise 3.5 ft Longitudinal Design Force Fl 4.5kip CL "TL-1"=if 9.0kip CL "TL-2"=if 18.0kip CL "TL-3"=if 18.0kip CL "TL-4"=if 41.0kip CL "TL-5"=if 58.0kip otherwise 18 kip Ll 4.0ft CL "TL-1"=if 4.0ft CL "TL-2"=if 4.0ft CL "TL-3"=if 3.5ft CL "TL-4"=if 8.0ft CL "TL-5"=if 8.0ft otherwise 3.5 ft Vertical Design Force (Down) Fv 4.5kip CL "TL-1"=if 4.5kip CL "TL-2"=if 4.5kip CL "TL-3"=if 18.0kip CL "TL-4"=if 80.0kip CL "TL-5"=if 80.0kip otherwise 18 kip Lv 18.0ft CL "TL-1"=if 18.0ft CL "TL-2"=if 18.0ft CL "TL-3"=if 18.0ft CL "TL-4"=if 40.0ft CL "TL-5"=if 40.0ft otherwise 18 ft Critical Length of Yield Line Failure Pattern: Mb 0kip ft Lc Lt 2 Lt 2   2 8 Hpar Mb Mw  Mc  11.9 ft S A13.3.1-2 Rw 2 2 Lc Lt 8 Mb 8 Mw Mc Lc 2 Hpar       116.2 kip S A13.3.1-1 T Rw b Lc 2 Hpar 6.6 kip S A13.4.2-1

158 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT The parapet design must consider three design cases. Design Case 1 is for longitudinal and transverse collision loads under Extreme Event Load Combination II. Design Case 2 represents vertical collision loads under Extreme Event Load Combination II; however, this case does not govern for decks with concrete parapets or barriers. Design Case 3 is for dead and live load under Strength Load Combination I; however, the parapet will not carry wheel loads and therefore this case does not govern. Design Case 1 is the only case that requires a check. Design Case 1: Longitudinal and Transverse Collision Loads, Extreme Event Load Combination II DC - 1A: Inside face of parapet S A13.4.1 S Table 3.4.1-1ϕext 1 γDC 1.0 γDW 1.0 γLL 0.5 llip 2in wbase 17 in Adeck_1A tdeck llip wbase  152 in2 Ap 2.8 ft2 Wdeck_1A wc Adeck_1A 0.2 klf Wpar 0.4 klf MDCdeck_1A γDC Wdeck_1A llip wbase 2  0.1 kip ft ft  MDCpar_1A γDC Wpar llip CGp  0.3 kip ftft Mtotal_1A Mcb MDCdeck_1A MDCpar_1A 16 kip ft ft  ϕtt_add 58 in stt_add 8in Astt_p 12in stt π ϕtt 2   2  12in stt_add π ϕtt_add 2   2  0.9 in2 dtt_add tdeck ct ϕtt_add 2   5.2 in ctt_p Astt_p Fs 0.85 fc β1 b 1.4 in att_p β1 ctt_p 1.1 in Mntt_p Astt_p Fs ft dtt_add att_p 2   21.4 kip ft ft  Mrtt_p ϕb Mntt_p 19.2 kip ftft Mrtt_p Mtotal_1A 1 AsT Astt Astb 1.1 in2 ϕPn ϕext AsT Fs 67.4 kip ϕPn T 1 Mu_1A Mrtt_p 1 T ϕPn    17.4 kip ft ft  Mu_1A Mtotal_1A 1 DC - 1B: Design Section in Overhang Notes: Distribution length is assumed to increase based on a 30 degree angle from the face of parapet. Moment of collision loads is distributed over the length Lc + 30 degree spread from face of parapet to location of overhang design section. Axial force of collision loads is distributed over the length Lc + 2Hpar + 30 degree spread from face of parapet to location of overhang design section. Future wearing surface is neglected as contribution is negligible. Adeck_1B tdeck Lo 168 in2 Ap 2.8 ft2

159 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Wdeck_1B wc Adeck_1B 0.2 klf Wpar 0.4 klf MDCdeck_1B γDC Wdeck_1B Lo 2  0.2 kip ft ft  MDCpar_1B γDC Wpar Lo llip CGp  0.5 kip ftft Lspread_B Lo llip width3 2 in spread 30deg wspread_B Lspread_B tan spread( ) 1.2 in Mcb_1B Mcb Lc Lc 2 wspread_B 15.3 kip ft ft  Mtotal_1B Mcb_1B MDCdeck_1B MDCpar_1B 15.9 kip ft ft  Mrtt_p 19.2 kip ft ft  Mrtt_p Mtotal_1B 1 ϕPn 67.4 kip Pu T Lc 2 Hpar  Lc 2 Hpar 2 wspread_B 6.5 kip ϕPn Pu 1 Mu_1B Mrtt_p 1 Pu ϕPn    17.4 kip ft ft  Mu_1B Mtotal_1B 1 DC - 1C: Design Section in First Span Assumptions: Moment of collision loads is distributed over the length Lc + 30 degree spread from face of parapet to location of overhang design section. Axial force of collision loads is distributed over the length Lc + 2Hpar + 30 degree spread from face of parapet to location of overhang design section. Future wearing surface is neglected as contribution is negligible. Mpar_G1 MDCpar_1B 0.5 kip ft ft  Mpar_G2 0.137 kip ft ft  (From model output) M1 Mcb 15.6 kip ft ft  M2 M1 Mpar_G2 Mpar_G1  4.7 kip ft ft  bf 10.5in Mc_M2M1 M1 1 4 bf M1 M2  spacingint_max  14.6 kip ft ft  Lspread_C Lo llip wbase bf 4  4.6 in wspread_C Lspread_C tan spread( ) 2.7 in Mcb_1C Mc_M2M1 Lc Lc 2 wspread_C 14.1 kip ft ft 

160 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Mtotal_1C Mcb_1C MDCdeck_1B MDCpar_1B 14.7 kip ft ft  Mrtt_p 19.2 kip ft ft  Mrtt_p Mtotal_1C 1 ϕPn 67.4 kip PuC T Lc 2 Hpar  Lc 2 Hpar 2 wspread_C 6.4 kip ϕPn PuC 1 Mu_1C Mrtt_p 1 Pu ϕPn    17.4 kip ft ft  Mu_1B Mtotal_1B 1 Compute Overhang Reinforcement Cut-off Length Requirement Maximum crash load moment at theoretical cut-ff point: Mc_max Mrtt 10.2 kip ft ft  LMc_max M2 Mrtt M2 M1 spacingint_max 3.3 ft Lspread_D Lo llip wbase LMc_max 41.6 in wspread_D Lspread_D tan spread( ) 24 in Mcb_max Mc_max Lc Lc 2 wspread_D 7.6 kip ft ft  extension max dtt_add 12 ϕtt_add 0.0625 spacingint_max  7.5 in cutt_off LMc_max extension 47.1 in Att_add π ϕtt_add 2   2  0.3 in2 mthick_tt_add 1.4 tdeck ct 12inif 1.0 otherwise 1 mepoxy_tt_add 1.5 ct 3 ϕtt_add stt_add 2 ϕtt_add 6 ϕtt_addif 1.2 otherwise 1.5 minc_tt_add min mthick_tt_add mepoxy_tt_add 1.7  1.5 mdec_tt_add 0.8 stt_add 2 6inif 1.0 otherwise 1

161 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ldb_tt_add max 1.25in Att_add Fs kip  fc ksi 0.4 ϕtt_add Fs ksi          ϕtt_add 118 inif 2.70in Fs ksi  fc ksi ϕtt_add 148 in=if 3.50in Fs ksi  fc ksi ϕtt_add 188 in=if  ldb_tt_add 15 in ldt_tt_add ldb_tt_add minc_tt_add mdec_tt_add 22.5 in Cuttoffpoint LMc_max ldt_tt_add spacingint_max 8.1 in extension past second interior girder Check for Cracking in Overhang under Service Limit State: Does not govern - no live load on overhang. 25. COMPRESSION SPLICE: See sheet S7 for drawing. Ensure compression splice and connection can handle the compressive force in the force couple due to the negative moment over the pier. Live load negative moment over pier: MLLPier 541.8 kip ft Factored LL moment: MUPier 1.75 MLLPier 948.1 kip ft The compression splice is comprised of a splice plate on the underside of the bottom flange, and built-up angles on either side of the web, connecting to the bottom flange as well. Calculate Bottom Flange Stress: Composite moment of inertia: Iz 10959.8 in 4 Distance to center of bottom flange from composite section centroid: ybf tbf 2 Dw ttf tslab yc 27 in Stress in bottom flange: fbf MUPier ybf Iz  28 ksi Calculate Bottom Flange Force: Design Stress: Fbf max fbf Fy 2 0.75 Fy   39 ksi Effective Flange Area: Aef bbf tbf 7 in2 Force in Flange: Cnf Fbf Aef 273.2 kip Calculate Bottom Flange Stress, Ignoring Concrete: Moment of inertia: Izsteel 3923.8 in 4 Distance to center of bottom flange: ybfsteel tbf 2 Dw ttf ysteel 14.5 in

162 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Stress in bottom flange: fbfsteel MUPier ybfsteel Izsteel  42 ksi Bottom Flange Force for design: Design Stress: Fcf max fbfsteel Fy 2 0.75 Fy   46 ksi Design Force: Cn max Fbf Fcf  Aef 322.1 kip Compression Splice Plate Dimensions: Bottom Splice Plate: bbsp bbf 10.4 in tbsp 0.75in Absp bbsp tbsp 7.8 in2 Built-Up Angle Splice Plate Horizontal Leg: basph 4.25in tasph 0.75in Aasph 2 basph tasph 6.4 in 2 Built-Up Angle Splice Plate Vertical Leg: baspv 7.75in taspv 0.75in Aaspv 2 baspv taspv 11.6 in 2 Total Area: Acsp Absp Aasph Aaspv 25.8 in2 Average Stress: fcs Cn Acsp 12.5 ksi Proportion Load into each plate based on area: Cbsp Cn Absp Acsp 97.7 kip Casph Cn Aasph Acsp 79.5 kip Caspv Cn Aaspv Acsp 144.9 kip Check Plates Compression Capacity: Bottom Splice Plate: kcps 0.75 for bolted connection lcps 9in rbsp min bbsp tbsp 3 12 tbsp bbsp 3 12      Absp 0.2 in Pebsp π2 Es Absp kcps lcps rbsp   2 2307.9 kip Qbsp 1.0 bbsp tbsp 0.45 Es Fy if 1.34 0.76 bbsp tbsp    Fy Es   0.45 Es Fy  bbsp tbsp  0.91 Es Fy if 0.53 Es Fy bbsp tbsp   2  otherwise 0.9 Pobsp Qbsp Fy Absp 352.8 kip

163 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Pnbsp 0.658 Pobsp Pebsp         Pobsp     Pebsp Pobsp 0.44if 0.877 Pebsp  otherwise 330.9 kip Pnbsp_allow 0.9 Pnbsp 297.8 kip Check "NG" Cbsp Pnbsp_allowif "OK" Pnbsp_allow Cbspif "OK" Horizontal Angle Leg: kcps 0.75 for bolted connection lcps 9 in rasph min basph tasph 3 12 tasph basph 3 12      Aasph 0.153 in Peasph π2 Es Aasph kcps lcps rasph   2 938.6 kip Qasph 1.0 basph tasph 0.45 Es Fy if 1.34 0.76 basph tasph    Fy Es   0.45 Es Fy  basph tasph  0.91 Es Fy if 0.53 Es Fy basph tasph   2  otherwise 1 Poasph Qasph Fy Aasph 318.7 kip Pnasph 0.658 Poasph Peasph         Poasph     Peasph Poasph 0.44if 0.877 Peasph  otherwise 276.5 kip Pnasph_allow 0.9 Pnasph 248.9 kip Check2 "NG" Casph Pnasph_allowif "OK" Pnasph_allow Casphif "OK" Vertical Angle Leg: kcps 0.75 for bolted connection lcps 9 in raspv min baspv taspv 3 12 taspv baspv 3 12      Aaspv 0.153 in Peaspv π2 Es Aaspv kcps lcps raspv   2 1711.6 kip

164 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Qaspv 1.0 baspv taspv 0.45 Es Fy if 1.34 0.76 baspv taspv    Fy Es   0.45 Es Fy  baspv taspv  0.91 Es Fy if 0.53 Es Fy baspv taspv   2  otherwise 1 Poaspv Qaspv Fy Aaspv 581.2 kip Pnaspv 0.658 Poaspv Peaspv         Poaspv     Peaspv Poaspv 0.44if 0.877 Peaspv  otherwise 504.2 kip Pnaspv_allow 0.9 Pnaspv 453.8 kip Check3 "NG" Caspv Pnaspv_allowif "OK" Pnaspv_allow Caspvif "OK" Additional Checks: Design Bolted Connections of the splice plates to the girders, checking for shear, bearing, and slip critical connections. 26. CLOSURE POUR DESIGN: See sheet S2 for drawing of closure pour. Check the closure pour according to the negative bending capacity of the section. Use the minimum reinforcing properties for design, to be conservative. Asteel 28.7 in 2 Art 1.8 in2 Arb 2.6 in2 cgsteel tslab ysteel 22.8 in cgrt 3in 1.5 5 8 in 3.9 in cgrb tslab 1in 1.5 5 8  in  6.1 in Overall CG: Aneg Asteel Art Arb 33.1 in2 cgneg Asteel cgsteel Art cgrt Arb cgrb Aneg 20.5 in Moment of Inertia: Izstl 3990in 4 Ineg Izstl Asteel cgsteel cgneg 2 Art cgrt cgneg 2 Arb cgrb cgneg 2 5183.7 in4 Section Moduli: Stop_neg Ineg cgneg cgrt 313.4 in3 rneg Ineg Aneg 12.5 in Sbot_neg Ineg tslab ttf Dw tbf cgneg  301.9 in 3 Concrete Properties: fc 5 ksi Steel Properties: Fy 50 ksi Lbneg 13.42ft Ec 4286.8 ksi Es 29000 ksi

165 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Fyr 0.7 Fy 35 ksi Negative Flexural Capacity: Slenderness ratio for compressive flange: λfneg bbf 2 tbf 7.8 Limiting ratio for compactness: λpfneg 0.38 Es Fy  9.2 Limiting ratio for noncompact λrfneg 0.56 Es Fyr  16.1 Hybrid Factor: Rh 1 Dcneg2 Dw 2 14.2 in awc 2 Dcneg2 tw bbf tbf 2.1 Rb 1.0 2 Dcneg2 tw  5.7 Es Fy if min 1.0 1 awc 1200 300 awc 2 Dcneg2 tw  5.7 Es Fy     otherwise  Rb 1 Flange compression resistance: Fnc1 Rb Rh Fy λfneg λpfnegif 1 1 Fyr Rh Fy   λfneg λpfneg  λrfneg λpfneg    Rb Rh Fy   otherwise  Fnc1 50 ksi Lateral Torsional Buckling Resistance: rtneg bbf 12 1 Dcneg2 tw 3 bbf tbf    2.6 in Lpneg 1.0 rtneg Es Fy  62.5 in Lrneg π rtneg Es Fyr  234.7 in Cb 1 Fnc2 Rb Rh Fy Lbneg Lpnegif min Cb 1 1 Fyr Rh Fy   Lbneg Lpneg  Lrneg Lpneg     Rb Rh Fy Rb Rh Fy    Fnc2 41.4 ksi Compressive Resistance: Fnc min Fnc1 Fnc2  41.4 ksi Tensile Flexural Resistance: Fnt Rh Fy 50 ksi For Strength

166 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Fnt_Serv 0.95 Rh Fy 47.5 ksi For Service Ultimate Moment Resistance: Mn_neg min Fnt Stop_neg Fnc Sbot_neg  1042 kip ft MUPier 948.1 kip ft from external FE analysis Check4 Mn_neg MUPier 1 For additional design, one may calculate the force couple at the section over the pier to find the force in the UHPC closure joint. This force can be used to design any additional reinforcement used in the joint.

167 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ABC SAMPLE CALCULATION – 2 Decked Precast Prestressed Concrete girder Design for ABC

168 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT   DECKED PRECAST PRESTRESSED CONCRETE GIRDER DESIGN FOR ABC Unit Definition: kcf kip ft 3 This example is for the design of a superstructure system that can be used for rapid bridge replacement in an Accelerated Bridge Construction (ABC) application. The following calculations are intended to provide the designer guidance in developing a similar design with regard to design considerationS characteristic of this type of construction, and they shall not be considered fully exhaustive. Overall Width, W Roadway Width, WrBarrier Width, Wb Joint Width, Wj Slope, CS Beam Spacing, SS Wj 2 TYPICAL SECTION THROUGH SPAN Lend Design Span Length, L Girder Length, Lg GIRDER ELEVATION Bridge Geometry: L 70 ft Lend 2 ft skew 0 deg W 47.167 ft Wb 1.5 ft Smax 8 ft Wj 0.5 ft Ng ceil W Wj Smax   6 Minimum number of girders in cross-section S W Wj Ng 7.945 ft Girder spacing

169 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ORDER OF CALCULATIONS Introduction1. Design Philosophy2. Design Criteria3. Beam Section4. Material Properties5. Permanent Loads6. Precast Lifting Weight7. Live Load8. Prestress Properties9. Prestress Losses10. Concrete Stresses11. Flexural Strength12. Shear Strength13. Splitting Resistance14. Camber and Deflections15. Negative Moment Flexural Strength16. 1. INTRODUCTION The superstructure system considered here consists of precast prestressed concrete girders with a top flange width nominally equal to the beam spacing, such that the top flange will serve as the riding surface once closure joints between the girders are poured. The intended use of these girders is to facilitate rapid bridge construction by providing a precast deck on the girder, thereby eliminating the need for a cast-in-place deck in the field. Concepts used in this example are taken from previous and on-going research, the focus of which is overcoming issues detracting from the benefits of decked precast beams and promoting widespread acceptance by transportation agencies and the construction industry. The cross-section is adapted from the optimized girder sections recommended by NCHRP Project No. 12-69, Design and Construction Guidelines for Long-Span Decked Precast, Prestressed Concrete Girder Bridges. The section considered here has an additional 3" added to the top flange to accommodate the joint continuity detail utilized in this project. The girder design does not include the option to re-deck because the final re-decked system, without additional prestressing, is generally expected to have a shorter span length capability, effectively under-utilizing the initial precast section. Sacrifical wearing thickness, use of stainles steel rebars and the application of a future membrane and wearing surface can mitigate the need to replace the deck, so these characteristics are included in lieu of "re-deckability". The bridge used in this example represents a typical design problem. The calculations are equally as applicable to a single-span or multiple-span bridge because beam design moments are not reduced for continuity in multiple-span bridges at intermediate support. Design of the continuity details is not addressed in this example. The cross-section consists of a two-lane roadway with normal crown, bordered by standard barrier wall along each fascia. The structural system is made up of uniformly spaced decked precast prestressed concrete girders set normal to the cross-slope to allow for a uniform top flange and to simplify bearing details. The girder flanges are 9" at the tips, emulating an 8" slab with an allowance (1/2") for wear and an additional allowance (1/2") for grinding for smoothness and profile adjustment. The intent of this example is the illustrate aspects of design unique to decked precast prestressed girders used in an ABC application. Prestress forces and concrete stresses at the service limit states due to the uncommon cross-section, unusually high self-weight, and unconventional sequence of load application are of particular concern, and appropriate detailed calculations are included. Flexure and shear at the strength limit state are not anticipated to differ significantly from a conventional prestressed beam design. With the exception of computing flexural resistance at midspan, flexure and shear are omitted from this example for brevity. Omission of these checks does not indicate they are not necessary, nor does it relieve the designer of the responsibility to satisfy any and all design requirements, as specified by AASHTO and the Owner.

170 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 2. DESIGN PHILOSOPHY Geometry of the section is selected based on availability of standard formwork across many geographic regions, as evidenced by sections commonly used by many state transporation agencies. Depth variations are limited to constant-thickness region of the web, maintaining the shapes of the top flange and bottom bulb. Concrete strengths can vary widely, and strengths ranging from below 6 ksi to over 10 ksi are common. For the purposes of these calculations, concrete with a 28-day minimum compressive strength of 8 ksi is used. Because this beam is unable to take advantage of the benefits of composite behavior due to its casting sequence, and because allowable tension in the bottom of the beam at the service limit state is limited (discussed in Section 4), end region stresses are expected to be critical. Therefore, minimum concrete strength at release is required to be 80 percent of the 28-day compressive strength of the concrete, increasing the allowable stresses at the top and bottom of the section. The prestressing steel can also be optimized to minimize the stresses in the end region, as discussed below. Prestressing steel is arranged in a draped, or harped, pattern in order to maximize its effectiveness at midspan while minimizing its eccentricity at the ends of the beam where the concrete is easily overstressed because there is little positive dead load moment to offset the negative prestress moment. Effectiveness of the strand group is optimized at midspan by bundling the harped strands between hold-down points, maximizing the eccentricity of the strand group. The number and deflection angle of the harped strands is constrained by an upper limit on the hold-down force required for a single strand and for a single hold-down device, i.e., the entire group of strands. For longer spans, concrete stresses in the end regions at release will be excessive, and debonding without harped strands is not likely to reduce stresses to within allowable limits. Therefore, since harped strands will be required, this method of stress relief will be used exclusively without debonding. Temporary strands are not considered. 3. DESIGN CRITERIA In addition to the provisions of AASHTO, several criteria have been selected to govern the design of these beams, based on past and current practice, as well as research related to decked precast sections and accelerated bridge construction. The following is a summary of limiting design values for which the beams are proportioned, and they are categorized as section constraints, prestress limits, and concrete limits: Section Constraints: Wpc.max 200 kip Upper limit on the weight of the entire precast element, based on common lifting and transport capabilities without significantly increasing time and/or cost due to unconventional equipment or permits Smax 8 ft Upper limit on girder spacing and, therefore, girder flange width (defined on first page) Prestress Limits: Fhd.single 4 kip Maximum hold-down force for a single strand Fhd.group 48 kip Maximum hold-down force for the group of harped strands Stress limits in the prestressing steel immediately prior to prestress and at the service limit state after all losses are as prescribed by AASHTO LRFD.

171 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 3. DESIGN CRITERIA (cont'd) Concrete Limits: Allowable concrete stresses are generally in line with AASHTO LRFD requirements, with one exception. Allowable tension in the bottom of the section at final, Service III, is limited to 0 ksi, based on the research of NCHRP Project No. 12-69. Imposing this limitation precludes the need to evaluate the flexural effects on the girder section arising from forces applied to correct differential camber between adjacent beams. The reliability of this approach is enhanced without the need for additional calculations by specifying a differential camber tolerance equally as, or more stringent than, the tolerance assumed in the subject project. For the purposes of this example, the differential camber tolerance is assumed be at least as stringent. ft.all.ser 0 ksi Allowable bottom fiber tension at the Service III Limit State, when camber leveling forces are to be neglected, regardless of exposure As previously mentioned, release concrete strength is specified as 80 percent of the minimum 28-day compressive strength to maximize allowable stresses in the end region of beam at release. fc.rel f( ) 0.80 f Minimum strength of concrete at release At the intermediate erection stage, stresses in the beam due to various lifting and transportation support conditions need to be considered. Using AASHTO LRFD Table 5.9.4.2.1-1, allowable compression during handling can be limited to 60% of the concrete strength. This provision is not explicitly applicable to this case, however, it does apply to handling stresses in prestressed piling and is more appropriate than the more restrictive sustained permanent load limit of 45% due to anticipated dynamic dead load effects. For allowable tension, a "no cracking" approach is considerd due to reduced lateral stability after cracking. Therefore, allowable tension is limited to the modulus of rupture, further modified by an appropriate factor of safety. Both allowable values are based on the concrete strength at the time of lifting and transportation. At this stage, assuming the beams will be lifted sometime after release and before the final strength is attained, allowable stresses are based on the average of the release strength and the specified 28-day strength, i.e., 90% of the specified strength. DIM 30% Dynamic dead load allowance fc.erec f( ) 0.90 f Assumed attained concrete strength during lifting and transportation FSc 1.5 Factor of safety against cracking during lifting transportation ft.erec f( ) 0.24 f ksi FSc  Allowable tension in concrete during lifting and transportation to avoid cracking

172 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT b1 b2 b3 bn+1 bn bn-1 bn-2 dn dn-1 dn-2 d1 d2 TYPICAL GIRDER SECTION COMPRISED   OF n TRAPEZOIDAL REGIONS  y x 4. BEAM SECTION Use trapezoidal areas to define the cross-section. The flange width is defined as the beam spacing less the width of the longitudinal closure joint to reflect pre-erection conditions. Live load can be conservatively applied to this section, as well. h 42 in Beam section depth tflange 9 in Flange thickness at tip tsac 1 in Total sacrificial depth for grinding and wear b1 26 in b2 26 in d1 7 in b2 26 in b3 6 in d2 3 in b3 6 in b4 6 in b4 6 in b5 10 in d4 2 in b5 10 in b6 49 in d5 3 in b6 49 in b7 S Wj d6 0 in b7 89.334 in b8 S Wj d7 tflange tsac d3 h tsac d d3 18 in Gross Section Properties bf 89.334 in Precast girder flange width Ag 1157.172 in 2 Cross-sectional area (does not include sacrifical thickness) Ixg 203462 in 4 Moment of inertia (does not include sacrificial thickness) ytg 12.649 in ybg 28.351 in Top and bottom fiber distances from neutal axis (positive up) Stg 16085.5 in 3 Sbg 7176.5 in3 Top and bottom section moduli Iyg 493395 in 4 Weak-axis moment of inertia 50 40 30 20 10 0 10 20 30 40 502 3.75 9.5 15.25 21 26.75 32.5 38.25 44 GIRDER SECTION PLOT (N.T.S.)

173 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 5. MATERIAL PROPERTIES Concrete: fc 8 ksi Minimum 28-day compressive strength of concrete fci fc.rel fc  6.4 ksi Minimum strength of concrete at release γc .150 kcf Unit weight of concrete K1 1.0 Correction factor for standard aggregate (5.4.2.4) Eci 33000 K1 γc kcf   1.5  fci ksi 4850 ksi Modulus of elasticity at release (5.4.2.4-1) Ec 33000 K1 γc kcf   1.5  fc ksi 5422 ksi Modulus of elasticity (5.4.2.4-1) fr.cm 0.37 fc ksi 1.047 ksi Modulus of rupture for cracking moment (5.4.2.6) fr.cd 0.24 fc ksi 0.679 ksi Modulus of rupture for camber and deflection (5.4.2.6) H 70 Relative humidity (5.4.2.3) Prestressing Steel: fpu 270 ksi Ultimate tensile strength fpy 0.9 fpu 243 ksi Yield strength, low-relaxation strand (Table 5.4.4.1-1) fpbt.max 0.75 fpu 202.5 ksi Maximum stress in steel immediately prior to transfer fpe.max 0.80 fpy 194.4 ksi Maximum stress in steel after all losses Ep 28500 ksi Modulus of elasticity (5.4.4.2) dps 0.5 in Strand diameter Ap 0.153 in 2 Strand area Nps.max 40 Maximum number of strands in section npi Ep Eci 5.9 Modular ratio at release np Ep Ec 5.3 Modular ratio Mild Steel: fy 60 ksi Specified minimum yield strength Es 29000 ksi Modulus of elasticity (5.4.3.2)

174 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 6. PERMANENT LOADS Permanent loads to be considered in the design of this girder are self-weight, diaphragms, barrier, and future wearing surface. The barrier can be cast with the beam, superimposed on the exterior girder only in the field, or superimposed on the bridge after the closure joints have attained sufficient strength. Distribution of the barrier weight to the girders should accurately reflect the stage at which it was installed. In this example, the barrier is assumed to be cast on the exterior girder in the casting yard, after release of prestress, but prior to shipping. This concept increases the dead load to be supported by the exterior girder while eliminating a time-consuming task to be completed in the field. BeamLoc 1 Location of beam within the cross-section (0 - Interior, 1 - Exterior) Load at Release: γc.DL .155 kcf Concrete density used for weight calculations Ag.DL Ag tsac S Wj  1246.506 in2 Area used for weight calculations, including sacrificial thickness wg Ag.DL γc.DL 1.342 klf Uniform load due to self-weight, including sacrificial thickness Lg L 2 Lend 74 ft Span length at release Mgr x( ) wg x 2 Lg x  Moment due to beam self-weight (supported at ends) Vgr x( ) wg Lg 2 x  Shear due to beam self-weight (supported at ends) Load at Erection: Mg x( ) wg x 2 L x( ) Moment due to beam self-weight Vg x( ) wg L 2 x  Shear due to beam self-weight wbar 0.430 klf Uniform load due to barrier weight, exterior beams only wbar if BeamLoc 1= wbar 0  0.43 klf Redfine to 0 if interior beam (BeamLoc = 0) Mbar x( ) wbar x 2 L x( ) Moment due to beam self-weight Vbar x( ) wbar L 2 x  Shear due to beam self-weight

175 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 6. PERMANENT LOADS (cont'd) Load at Service: pfws 25 psf Assumed weight of future wearing surface wfws pfws S 0.199 klf Uniform load due to future wearing surface Mfws x( ) wfws x 2 L x( ) Moment due to future wearing surface Vfws x( ) wfws L 2 x  Shear due to future wearing surface wj Wj d7 γc.DL 0.052 klf Uniform load due to weight of longitudinal closure joint Mj x( ) wj x 2 L x( ) Moment due to longitudinal closure joint Vj x( ) wj L 2 x  Shear due to longitudinal closure joint

176 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 7. PRECAST LIFTING WEIGHT Precast Superstructure Wg wg wbar  Lg 131.1 kip Precast girder, including barrier if necessary Substructure Precast with Superstructure Lcorb 1 ft Length of approach slab corbel Bcorb bf bf 89.334 in Width of corbel cast with girder Dcorb 1.5 ft Average depth of corbel Vcorb Lcorb Bcorb Dcorb 11.17 ft3 Volume of corbel Lia 2.167 ft Length of integral abutment Lgia 1.167 ft Length of girder embedded in integral abutment Bia S Wj 7.444 ft Width of integral abutment cast with girder Dia h 4 in 46 in Depth of integral abutment Via Vcorb Lia Bia Dia Ag tflange bf  Lgia  70.14 ft3 Volume of integral abutment cast with girder Wia Via γc 11 kip Weight of integral abutment cast with girder Lsa 2.167 ft Length of semi-integral abutment Lgsa 4 in Length of girder embedded in semi-integral abutment Bsa S Wj 7.444 ft Width of semi-integral abutment cast with girder Dsa h 16 in 58 in Depth of semi-integral abutment Vsa Vcorb Lsa Bsa Dsa Ag tflange bf  Lgsa  88.32 ft3 Volume of semi-integral abutment cast with girder Wsa Vsa γc 13 kip Weight of semi-integral abutment cast with girder

177 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Semi-Integral Abutment Backwall Integral Abutment Backwall

178 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 8. LIVE LOAD Vehicular loading conforms to the HL-93 design load prescribed by AASHTO. If project-specific erection schemes require the bridge to support construction loads at any stage of erection, these loads should be considered as a separate load case and applied to the beam section at an appropriate attained age of the concrete. Longitudinal joint is designed and detailed for a full moment connection. Therefore, the beams are considered "sufficiently connected to act as a unit" and distribution factors are computed for cross-section type "j", as defined in AASHTO 4.6.2.2. For purposes of computing the longitudinal stiffness parameter, the constant-depth region of the top flange is treated as the slab and the remaining area of the beam section is considered the non-composite beam. Distribution Factors for Moment: From Table 4.6.2.2.2b-1 for moment in interior girders, Ibb 59851 in 4 Moment of inertia of section below the top flange Abb 442.5 in 2 Area of beam section below the top flange eg h tsac ts 2   ybb 22.617 in Distance between c.g.'s of beam and flange Kg 1.0 Ibb Abb eg 2  286209 in4 Longitudinal stiffness parameter (Eqn. 4.6.2.2.1-1) Verify this girder design is within the range of applicability for Table 4.6.2.2.2b-1. CheckMint if S 16 ft( ) S 3.5 ft( ) ts 4.5 in  ts 12.0 in  L 20 ft( ) L 240 ft( ) "OK" "No Good"  CheckMint if CheckMint "OK"=( ) Ng 4  Kg 10000 in4  Kg 7000000 in4  "OK" "No Good"  CheckMint "OK" gmint1 0.06 S 14 ft   0.4 S L   0.3  Kg L ts 3     0.1  0.458 Single loaded lane gmint2 0.075 S 9.5 ft   0.6 S L   0.2  Kg L ts 3     0.1  0.633 Two or more loaded lanes gmint max gmint1 gmint2  0.633 Distribution factor for moment at interior beams

179 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 8. LIVE LOAD (cont'd) From Table 4.6.2.2.2d-1 for moment in exterior girders, de S 2 Wb 29.667 in CheckMext if de 1 ft  de 5.5 ft  Ng 4  "OK" "No Good"  "OK" For a single loaded lane, use the Lever Rule. gmext1 S 0.5 bf Wb 5 ft  S 0.65 Single loaded lane em 0.77 de 9.1 ft 1.042 gmext2 em gmint 0.659 Two or more loaded lanes gmext max gmext1 gmext2  0.659 Distribution factor for moment at exterior beams Distribution Factors for Shear: From Table 4.6.2.2.3a-1 for shear in interior girders, Verify this girder design is within the range of applicability for Table 4.6.2.2.3a-1. CheckVint if S 16 ft( ) S 3.5 ft( ) ts 4.5 in  ts 12.0in  L 20 ft( ) L 240 ft( ) "OK" "No Good"  CheckVint if CheckMint "OK"=( ) Ng 4  "OK" "No Good"  CheckVint "OK" gvint1 0.36 S 25 ft   0.678 Single loaded lane gvint2 0.2 S 12 ft   S 35 ft   2.0  0.811 Two or more loaded lanes gvint max gvint1 gvint2  0.811 Distribution factor for shear at interior beams

180 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 8. LIVE LOAD (cont'd) From Table 4.6.2.2.3b-1 for shear in exterior girders, For a single loaded lane, use the Lever Rule. CheckVext if de 1 ft  de 5.5 ft  Ng 4  "OK" "No Good"  "OK" g1 S 0.5 bf Wb 5 ft  S 0.65 Single loaded lane (same as for moment) ev 0.6 de 10 ft 0.847 g2 ev gvint 0.687 Two or more loaded lanes gvext max g1 g2  0.687 Distribution factor for shear at exterior beams From Table 4.6.2.2.3c-1 for skewed bridges, θ skew 0 deg CheckSkew if θ 60 deg( ) 3.5 ft S 16 ft( ) 20 ft L 240 ft( ) Ng 4  "OK" "No Good"  "OK" cskew 1.0 0.20 L ts 3 Kg     0.3  tan θ( ) 1.00 Correction factor for skew

181 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 8. LIVE LOAD (cont'd) Design Live Load Moment at Midspan: wlane 0.64 klf Design lane load Ptruck 32 kip Design truck axle load IM 33% Dynamic load allowance (truck only) Mlane x( ) wlane x 2 L x( ) Design lane load moment Influence coefficient for truck moment calculationδ x( ) x L x 2 L  Mtruck x( ) Ptruck δ x( ) max 9 x L x( ) 14 ft 3 x L( )4 x L x( ) 9 L x( ) 84 ft 4 L x( )   Design truck moment MHL93 x( ) Mlane x( ) 1 IM( ) Mtruck x( ) HL93 design live load moment per lane Mll.i x( ) MHL93 x( ) gmint Design live load moment at interior beam Mll.e x( ) MHL93 x( ) gmext Design live load moment at exterior beam Mll x( ) if BeamLoc 1= Mll.e x( ) Mll.i x( )  Design live load moment Design Live Load Shear: Vlane x( ) wlane L 2 x  Design lane load shear Vtruck x( ) Ptruck 9 L 9 x 84 ft 4 L   Design truck shear VHL93 x( ) Vlane x( ) 1 IM( ) Vtruck x( ) HL93 design live load shear Vll.i x( ) VHL93 x( ) gvint Design live load shear at interior beam Vll.e x( ) VHL93 x( ) gvext Design live load shear at exterior beam Vll x( ) if BeamLoc 1= Vll.e x( ) Vll.i x( )  Design live load shear

182 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 9. PRESTRESS PROPERTIES Because allowable tension at the service limit state is reduced to account for camber leveling forces, the prestress force required at midspan is expected to be excessive in the ends at release without measures to reduce the prestress moment. Estimate losses and prestress eccentricity at midspan to select a trial prestress force that results in a bottom fiber tension stress less than allowable. Compute instantaneous losses in the prestressing steel and check release stresses at the end of the beam. Once end stresses are satisfied, estimate total loss of prestress. As long as computed losses do not differ significantly from the assumed values, the prestress layout should be adequate. Concrete stresses at all limit states are evaluated in Section 9. yp.est 5 in Assumed distance from bottom of beam to centroid of prestress at midspan ycgp.est ybg yp.est 23.35 in Eccentricity of prestress from neutral axis, based on assumed location Δfp.est 25% Estimate of total prestress losses at the service limit state Compute bottom fiber service stresses at midspan using gross section properties. X L 2  Distance from support Mdl.ser Mg X( ) Mfws X( ) Mj X( ) Mbar X( ) 1238 kip ft Total dead load moment fb.serIII Mdl.ser 0.8 Mll X( ) Sbg 3.567 ksi Total bottom fiber service stress fpj fpbt.max 202.5 ksi Prestress jacking force fpe.est fpj 1 Δfp.est  151.9 ksi Estimate of effective prestress force Aps.est Ag fb.serIII ft.all.ser fpe.est   1 Ag ycgp.est Sbg   5.703 in2 Estimated minimum area of prestressing steel Nps.est ceil Aps.est Ap   38 Estimated number of strands required Nps 38 Number of strands used ( Nps.max 40 ) This number is used to lay out the strand pattern and compute an actual location and eccentricity of the strand group, after which, the required area is computed again. If the location estimate was accurate, the recomputed number of strands should not differ from the number defined here. If the estimate was low, consider increasing the number of strands. It should be noted that the number of strands determined in this section is based on assumed prestressed losses and gross section properties and may not accurately reflect the final number of strands required to satisfy design requirements. Concrete stresses are evaluated in Section 10. Strand pattern geometry calculations assume a vertical spacing of 2" between straight strands, as well as harped strands at the ends of the beam. Harped strands are bundled at midpsan,where the centroid of these strands is 5" from the bottom

183 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 9. PRESTRESS PROPERTIES (cont'd) Nh 2 Nps 12if 4 12 Nps 24if 6 24 Nps 30if 6 Nps 30  Nps 30if  Nh 14 Assumes all flange rows are filled prior to filling rows in web above the flange, which maximized efficiency. Use override below to shift strands from flange to web if needed to satisfy end stresses. Additional harped strands in web (strands to be moved from flange to web)Nh.add 16 16 strands or half of total strands maximum harped in webNh min Nh Nh.add 16 2 floor Nps 4     Nh 16 yh 1 in 2 in( ) 1 0.5 Nh 1 2   yh 10 in Centroid of harped strands from bottom, equallyspaced yhb 5 in Centroid of harped strands from bottom, bundled Ns Nps Nh Ns 22 Number of straight strands in flange ys 1 in 2 in Ns 10if 4 in( ) Ns 20 in Ns 10 Ns 20if 6 in( ) Ns 60 in Ns 20 Ns 24if 3.5 in otherwise  ys 4.273 in Centroid of straight strands from bottom yp Ns ys Nh yhb Ns Nh 4.579 in Centroid of prestress from bottom at midspan ycgp ybg yp 23.77 in Eccentricity of prestress from neutral axis Aps.req Ag fb.serIII ft.all.ser fpe.est   1 Ag ycgp Sbg   5.623 in2 Estimated minimum area of prestressing steel Nps.req ceil Aps.req Ap   37 Estimated number of strands required CheckNps if Nps Nps.max  Nps.req Nps  "OK" "No Good"  "OK" Aps.h Nh Ap 2.448 in2 Area of prestress in web (harped) Aps.s Ns Ap 3.366 in2 Area of prestress in flange (straight)

184 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Aps Aps.h Aps.s 5.814 in2 Total area of prestress 9. PRESTRESS PROPERTIES (cont'd) Compute transformed section properties based on prestress layout. Transformed Section Properties Initial Transformed Section (release): Final Transformed Section (service): Ati 1185.5 in 2 Atf 1181.9 in2 Ixti 219101 in 4 Ixtf 217153 in4 ytti 13.217 in Stti 16577 in3 yttf 13.146 in Sttf 16518 in3 ycgpi 23.204 in Scgpi 9442 in3 ycgpf 23.275 in Scgpf 9330 in3 ybti 27.783 in Sbti 7886 in3 ybtf 27.854 in Sbtf 7796 in3 Determine initial prestress force after instantaneous loss due to elastic shortening. Use transformed properties to compute stress in the concrete at the level of prestress. Pj fpj Aps 1177.3 kip Jacking force in prestress, prior to losses Stress in concrete at the level of prestress after instantaneous lossesfcgpi Pj 1 Ati ycgpi Scgpi    Mgr Lg 2   Scgpi  2.719 ksi Prestress loss due to elastic shortening (5.9.5.2.3a-1)ΔfpES npi fcgpi 15.978 ksi fpi fpj ΔfpES 186.522 ksi Initial prestress after instantaneous losses Pi fpi Aps 1084.4 kip Initial prestress force Determine deflection of harped strands required to satisfy allowable stresses at the end of the beam at release. fc.all.rel 0.6 fci 3.84 ksi Allowable compression before losses (5.9.4.1.1) ft.all.rel max 0.0948 fci ksi 0.2 ksi  0.200 ksi Allowable tension before losses (Table 5.9.4.1.2-1) Lt 60 dps 2.5 ft Transfer length (AASHTO 5.11.4.1) ycgp.t ft.all.rel Mgr Lt  Stti  Pi 1 Ati        Stti 18.367 in Prestress eccentricity required for tension

185 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ycgp.b fc.all.rel Mgr Lt  Sbti  Pi 1 Ati        Sbti 22.6 in Prestress eccentricity required for compression 9. PRESTRESS PROPERTIES (cont'd) ycgp.req max ycgp.t ycgp.b  18.367 in Required prestress eccentricity at end of beam Minimum distance to harped prestress centroid from bottom of beam at centerline of bearingyh.brg.req ycgp.req ybti  Ns Nh  ys Ns Nh 16.488 in Minimum distance between uppermost strand and top of beamytop.min 18 in αhd 0.4 Hold-down point, fraction of the design span length Maximum slope of an individual strand to limit hold-down force to 4 kips/strandslopemax if dps 0.6 in= 1 12  1 8   0.125 Set centroid of harped strands as high as possible to minimize release and handling stressesyh.brg h ytop.min 0.5 Nh 1 2   2 in( ) 17 in yh.brg min yh.brg yhb slopemax αhd L  17 in Verify that slope requirement is satisfied at uppermost strand CheckEndPrestress if yh.brg yh.brg.req "OK" "Verify release stresses."  "OK" yp.brg Ns ys Nh yh.brg Ns Nh 9.632 in Centroid of prestress from bottom at bearing slopecgp yp.brg yp αhd L 0.015 Slope of prestress centroid within the harping length ypx x( ) yp slopecgp Lend αhd L x  x Lend αhd Lif yp otherwise  Distance to center of prestress from the bottom of the beam at any position

186 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 10. PRESTRESS LOSSES As with any prestressed concrete design, total prestress loss can be considered as the sum of instantaneous (short-term) and time-dependent (long-term) losses. For pretensioned girders, the instantaneous loss consists of elastic shortening of the beam upon release of the prestress force. The time-dependendent losses consist of creep and shrinkage of beam concrete, creep and shrinkage of deck concrete, and relaxation of the prestressing steel. These long-term effects in the girder are further subdivided into two stages to represent a significant event in the construction of the bridge: time between transfer of the prestress force and placement of the deck, and the period of time between placement of the deck and final service. For the specific case of a decked beam, computation of long-term losses is somewhat simplified because the cross-section does not change between these two stages and the term related to shrinkage of the deck concrete is eliminated since the deck is cast monolithically with the beam. There will be no gains or losses in the steel associated with deck placement after transfer. AASHTO provides two procedures for estimating time-dependent losses: Approximate Estimate (5.9.5.3)1. Refined Estimate (5.9.5.4)2. The approximate method is intended for systems with composite decks and is based upon assumptions related to timing of load application, the cross-section to which load is applied (non-composite or composite), and ratios of dead load and live load to total load. The conditions under which these beams are to be fabricated, erected, and loaded differ from the conditions assumed in development of the approximate method. Therefore, the refined method is used to estimate time-dependent losses in the prestressing steel. Time-dependent loss equations of 5.9.5.4 include age-adjusted transformed section factors to permit loss computations using gross section properties. Assumed time sequence in the life of the girder for loss calculations: ti 1 Time (days) between casting and release of prestress tb 20 Time (days) to barrier casting (exterior girder only) td 30 Time (days) to erection of precast section, closure joint pour tf 20000 Time (days) to end of service life Terms and equations used in the loss calculations: Prestressing steel factor for low-relaxation strands (C5.9.5.4.2c)KL 45 VS Ag Peri 4.023 in Volume-to-surface ratio of the precast section ks max 1.45 0.13 VS in  1.0  1.00 Factor for volume-to-surface ratio (5.4.2.3.2-2) khc 1.56 0.008 H 1.00 Humidity factor for creep (5.4.2.3.2-3) khs 2.00 0.014 H 1.02 Humidity factor for shrinkage (5.4.2.3.3-2) kf 5 1 fci ksi  0.676 Factor for effect of concrete strength (5.4.2.3.2-4)

187 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 10. PRESTRESS LOSSES (cont'd) ktd t( ) t 61 4 fci ksi  t  Time development factor (5.4.2.3.2-5) ψ t tinit  1.9 ks khc kf ktd t( ) tinit  0.118 Creep coefficient (5.4.2.3.2-1) εsh t( ) ks khs kf ktd t( ) 0.48 10 3  Concrete shrinkage strain (5.4.2.3.3-1) Time from Transfer to Erection: Eccentricity of prestress force with respect to the neutral axis of the gross non-composite beam, positive below the beam neutral axisepg yp ybg  23.772 in Stress in the concrete at the center prestress immediately after transferfcgp Pi 1 Ag epg 2 Ixg       Mg L 2   Ixg yp ybg  2.797 ksi fpt max fpi 0.55 fpy  186.522 ksi Stress in strands immediately after transfer (5.9.5.4.2c-1) ψbid ψ td ti  0.589 Creep coefficient at erection due to loading at transfer ψbif ψ tf ti  1.282 Creep coefficient at final due to loading at transfer εbid εsh td ti  1.490 10 4 Concrete shrinkage between transfer and erection Kid 1 1 npi Aps Ag  1 Ag epg 2 Ixg       1 0.7 ψbif  0.809 Age-adjusted transformed section coefficient (5.9.5.4.2a-2) ΔfpSR εbid Ep Kid 3.435 ksi Loss due to beam shrinkage (5.9.5.4.2a-1) ΔfpCR npi fcgp ψbid Kid 7.831 ksi Loss due to creep (5.9.5.4.2b-1) ΔfpR1 fpt KL log 24 td  log 24 ti  fpt fpy 0.55    1 3 ΔfpSR ΔfpCR  fpt    Kid 1.237 ksi Loss due to relaxation (C5.9.5.4.2c-1 Δfpid ΔfpSR ΔfpCR ΔfpR1 12.502 ksi

188 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 10. PRESTRESS LOSSES (cont'd) Time from Erection to Final: epc epg 23.772 in Eccentricity of prestress force does not change Ac Ag Ic Ixg Section properties remain unchanged Change in concrete stress at center of prestress due to initial time-dependent losses and superimposed dead load. Deck weight is not included for this design. Δfcd Mfws L 2   Mj L 2   Scgpf Δfpid np  2.182 ksi ψbdf ψ tf td  0.858 Creep coefficient at final due to loading at erection εbif εsh tf ti  3.302 10 4 Concrete shrinkage between transfer and final εbdf εbif εbid 1.813 10 4 Concrete shrinkage between erection and final Kdf 1 1 npi Aps Ac  1 Ac epc 2 Ic       1 0.7 ψbif  0.809 Age-adjusted transformed section coefficient remains unchanged ΔfpSD εbdf Ep Kdf 4.179 ksi Loss due to beam shrinkage ΔfpCD npi fcgp ψbif ψbid  Kdf np Δfcd ψbdf Kdf 17.168 ksi Loss due to creep ΔfpR2 ΔfpR1 1.237 ksi Loss due to relaxation ΔfpSS 0 Loss due to deck shrinkage Δfpdf ΔfpSD ΔfpCD ΔfpR2 ΔfpSS 22.584 ksi Prestress Loss Summary ΔfpES 15.978 ksi ΔfpES fpj 7.9 % ΔfpLT Δfpid Δfpdf 35.087 ksi ΔfpLT fpj 17.3 % ΔfpTotal ΔfpES ΔfpLT 51.065 ksi ΔfpTotal fpj 25.2 % Δfp.est 25 % fpe fpj ΔfpTotal 151.4 ksi Final effective prestress CheckFinalPrestress if fpe fpe.max "OK" "No Good"  "OK"

189 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 11. CONCRETE STRESSES Stresses in the concrete section at release, during handling, and at final service are computed and checked against allowable values appropriate for the stage being considered. Concrete Stresses at Release Stresses at release are computed using the overall beam length as the span because the beam will be supported at its ends in the casting bed after the prestress force is transfered. Define locations for which stresses are to be calculated: xr Lg 0 min Lt Lg Lend Lg   max Lt Lg Lend Lg   0.1 0.2 0.3 αhd 0.5  T  ir 1 last xr  Functions for computing beam stresses: ftop.r x( ) min x Lt 1  Pi 1 Ati ybti ypx x( ) Stti    Mgr x( ) Stti  Top fiber stress at release fbot.r x( ) min x Lt 1  Pi 1 Ati ybti ypx x( ) Sbti    Mgr x( ) Sbti  Bottom fiber stress at release 0 4 8 12 16 20 24 28 32 36 40 1 0 1 2 3 4 Stresses in Concrete at Release (Half Beam) Distance along Beam (ft) St re ss (k si ) ftop.r x( ) ksi fbot.r x( ) ksi fc.all.rel ksi ft.all.rel ksi 0 x ft

190 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 11. CONCRETE STRESSES (cont'd) Compare beam stresses to allowable stresses. ft.all.rel 0.2 ksi Allowable tension at release fc.all.rel 3.84 ksi Allowable compression at release TopRelir ftop.r xrir  TopRelT 0.000 0.148 0.192 0.097 0.002 0.047 0.040 0.062( ) ksi CheckTopRel if max TopRel( ) fc.all.rel  min TopRel( ) ft.all.rel  "OK" "No Good"  "OK" BotRelir fbot.r xrir  BotRelT 0.000 2.582 3.241 3.042 2.834 2.738 2.754 2.708( ) ksi CheckBotRel if max BotRel( ) fc.all.rel  min BotRel( ) ft.all.rel  "OK" "No Good"  "OK" Concrete Stresses During Lifting and Transportation Stresses in the beam during lifting and transportation may govern over final service limit state stresses due to different support locations, dynamic effects of dead load during shipment and placement, and lateral bending stresses due to rolling during lifting or superelevation of the roadway during shipping. Assume end diaphragms on both ends of the beam. For prestressing effects, compute the effective prestress force using only the losses occuring between transfer and erection (i.e., the ∆fpid). a h 3.5 ft Maximum distance to lift point from bearing line a' a Lend 5.5 ft Distance to lift point from end of beam Pdia max Wia Wsa  13.2 kip Approximate abutment weight Pm Pj 1 ΔfpES Δfpid  fpj    1011.7 kip Effective prestress during lifting and shipping Define locations for which stresses are to be calculated: xe Lg 0 min Lt Lg Lend Lg   max Lt Lg Lend Lg   a' Lg αhd 0.5  T  ie 1 last xe  Compute moment in the girder during lifting with supports at the lift points. Mlift x( ) wg wbar  x2 2 Pdia x     x a'if Mgr x( ) Mgr a'( ) wg wbar  a'( )2 2  Pdia a'     otherwise 

191 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 11. CONCRETE STRESSES (cont'd) Functions for computing beam stresses: ftop.lift x( ) min x Lt 1  Pm 1 Atf ybtf ypx x( ) Sttf    Mlift x( ) Sttf  Top fiber stress during lifting Top fiber stress during lifting, impact increasing dead loadftop.DIM.inc x( ) min x Lt 1  Pm 1 Atf ybtf ypx x( ) Sttf    Mlift x( ) Sttf 1 DIM( ) Top fiber stress during lifting, impact decreasing dead loadftop.DIM.dec x( ) min x Lt 1  Pm 1 Atf ybtf ypx x( ) Sttf    Mlift x( ) Sttf 1 DIM( ) TopLift1ie ftop.lift xeie  TopLift1T 0.000 0.230 0.294 0.371 0.181 0.158( ) ksi TopLift2ie ftop.DIM.inc xeie  TopLift2T 0.000 0.236 0.302 0.393 0.065 0.035( ) ksi TopLift3ie ftop.DIM.dec xeie  TopLift3T 0.000 0.223 0.285 0.349 0.296 0.282( ) ksi fbot.lift x( ) min x Lt 1  Pm 1 Atf ybtf ypx x( ) Sbtf    Mlift x( ) Sbtf  Bottom fiber stress during lifting Bottom fiber stress during lifting, impact increasing dead loadfbot.DIM.inc x( ) min x Lt 1  Pm 1 Atf ybtf ypx x( ) Sbtf    Mlift x( ) Sbtf 1 DIM( ) Bottom fiber stress during lifting, impact decreasing dead loadfbot.DIM.dec x( ) min x Lt 1  Pm 1 Atf ybtf ypx x( ) Sbtf    Mlift x( ) Sbtf 1 DIM( ) BotLift1ie fbot.lift xeie  BotLift1T 0.000 2.623 3.292 3.456 3.052 3.005( ) ksi BotLift2ie fbot.DIM.inc xeie  BotLift2T 0.000 2.637 3.310 3.502 2.808 2.744( ) ksi BotLift3ie fbot.DIM.dec xeie  BotLift3T 0.000 2.609 3.274 3.410 3.297 3.267( ) ksi Allowable stresses during handling: fcm fc.erec fc  7.2 ksi Assumed concrete strength when handling operations begin fc.all.erec 0.6 fcm 4.32 ksi Allowable compression during lifting and shipping ft.all.erec ft.erec fcm  0.429 ksi Allowable tension during lifting and shipping

192 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 11. CONCRETE STRESSES (cont'd) 0 4 8 12 16 20 24 28 32 36 40 0 2 4 Stresses in Concrete During Lifting (Half Beam) Distance along Beam (ft) St re ss (k si ) ftop.lift x( ) ksi ftop.DIM.inc x( ) ksi ftop.DIM.dec x( ) ksi fbot.lift x( ) ksi fbot.DIM.inc x( ) ksi fbot.DIM.dec x( ) ksi fc.all.erec ksi ft.all.erec ksi 0 x ft Compare beam stresses to allowable stresses. TopLiftMaxie max TopLift1ie TopLift2ie TopLift3ie  TopLiftMaxT 0 0.223 0.285 0.349 0.065 0.035( ) ks TopLiftMinie min TopLift1ie TopLift2ie TopLift3ie  TopLiftMinT 0 0.236 0.302 0.393 0.296 0.282( ) ks CheckTopLift if max TopLiftMax( ) fc.all.erec  min TopLiftMin( ) ft.all.erec  "OK" "No Good"  "OK" BotLiftMaxie max BotLift1ie BotLift2ie BotLift3ie  BotLiftMaxT 0 2.637 3.31 3.502 3.297 3.267( ) ksi BotLiftMinie min BotLift1ie BotLift2ie BotLift3ie  BotLiftMinT 0 2.609 3.274 3.41 2.808 2.744( ) ksi CheckBotLift if max BotLiftMax( ) fc.all.erec  min BotLiftMin( ) ft.all.erec  "OK" "No Good"  "OK"

193 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 11. CONCRETE STRESSES (cont'd) Concrete Stresses at Final Stresses at final are also computed using the design span length. Top flange compression and bottom flange tension are evaluated at the Service I and Service III limit states, respectively. fc.all.ser1 0.4 fc 3.2 ksi Allowable compression due to effective prestress and dead load (Table 5.9.4.2.1-1) Allowable compression due to effective prestress, permanent load, and transient loads, as well as stresses during shipping and handling (Table 5.9.4.2.1-1)fc.all.ser2 0.6 fc 4.8 ksi ft.all.ser 0 ksi Allowable tension (computed previously) Pe fpe Aps 880.4 kip Effective prestress after all losses Compute stresses at midspan and compare to allowable values. ftop.ser1 x( ) min Lend x Lt 1  Pe 1 Atf ybtf ypx x( ) Sttf    Mg x Lend  Stti  Mbar x( ) Mfws x( ) Mj x( ) Sttf  ftop.ser2 x( ) min Lend x Lt 1  Pe 1 Atf ybtf ypx x( ) Sttf    Mg x Lend  Stti  Mbar x( ) Mfws x( ) Mj x( ) Mll x( ) Sttf  fbot.ser x( ) min Lend x Lt 1  Pe 1 Atf ybtf ypx x( ) Sbtf    Mg x Lend  Sbti  Mbar x( ) Mfws x( ) Mj x( ) 0.8 Mll x( ) Sbtf  0 4 8 12 16 20 24 28 32 36 40 0 2 4 6 Stresses in Concrete at Service (Half Beam) Distance along Beam (ft) St re ss (k si ) ftop.ser1 x( ) ksi ftop.ser2 x( ) ksi fbot.ser x( ) ksi ft.all.ser ksi fc.all.ser1 ksi fc.all.ser2 ksi x ft

194 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 11. CONCRETE STRESSES (cont'd) Compare beam stresses to allowable stresses. xs L Lt L 0.1 0.15 0.2 0.25 0.3 0.35 αhd 0.45 0.5  T  is 1 last xs  TopSer1is ftop.ser1 xsis  TopSer1T 0.046 0.101 0.195 0.272 0.330 0.370 0.393 0.397 0.398 0.400( ) ksi TopSer2is ftop.ser2 xsis  TopSer2T 0.075 0.415 0.636 0.820 0.966 1.074 1.148 1.191 1.211 1.212( ) ksi CheckCompSerI if max TopSer1( ) fc.all.ser1  max TopSer2( ) fc.all.ser2  "OK" "No Good"  "OK" BotSeris fbot.ser xsis  BotSerT 2.218 1.581 1.168 0.825 0.554 0.355 0.221 0.146 0.112 0.109( ) ksi CheckTenSerIII if min BotSer( ) ft.all.ser "OK" "No Good"  "OK" 12. FLEXURAL STRENGTH Verify flexural resistance at the Strength Limit State. Compute the factored moment at midspan due to the Strength I load combination, then compare it to the factored resistance calculated in accordance with AASHTO LRFD 5.7.3. MDC x( ) Mg x( ) Mbar x( ) Mj x( ) Self weight of components MDW x( ) Mfws x( ) Weight of future wearing surface MLL x( ) Mll x( ) Live load MStrI x( ) 1.25 MDC x( ) 1.5 MDW x( ) 1.75 MLL x( ) Factored design moment For minimum reinforcement check, per 5.7.3.3.2 fcpe Pe 1 Ag ycgp Sbg    3.677 ksi Concrete compression at extreme fiber due to effective prestress Mcr fr.cm fcpe  Sbg 2825 kip ft Cracking moment (5.7.3.3.2-1) Mu x( ) max MStrI x( ) min 1.33 MStrI x( ) 1.2 Mcr   Design moment

195 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 12. FLEXURAL STRENGTH (cont'd) Compute factored flexural resistance. β1 max 0.65 0.85 0.05 fc ksi 4    0.65 Stress block factor (5.7.2.2) k 2 1.04 fpy fpu    0.28 Tendon type factor (5.7.3.1.1-2) Distance from compression fiber to prestress centroiddp x( ) h ypx x Lend  dp X( ) 37.421 in hf d7 8 in Structural flange thickness btaper b6 b5 2 19.5 in Average width of taper at bottom of flange htaper d5 3 in Depth of taper at bottom of flange a x( ) Aps fpu 0.85 fc bf k β1 Aps fpu dp x( )     a X( ) 2.509 in Depth of equivalent stress block for rectangular section c x( ) a x( ) β1 c X( ) 3.861 in Neutral axis location CheckTC if c X( ) dp X( ) .003 .003 .005   "OK" "NG"   "OK" Tension-controlled section check (midspan) Resistance factor for prestressed concrete (5.5.4.2)φf min 1.0 max 0.75 0.583 0.25 dp X( ) c X( ) 1      1.00 fps fpu 1 k c X( ) dp X( )    262.2 ksi Average stress in the prestressing steel (5.7.3.1.1-1) Ld 1.6 ksi fps 2 3 fpe  dps 10.75 ft Bonded strand devlepment length (5.11.4.2-1) fpx x( ) fpe x Lend  Lt x Lt Lendif fpe x Lend  Lt Ld Lt fps fpe  Lt Lend x Ld Lendif fps otherwise  Stress in prestressing steel along the length for bonded strand (5.11.4.2) Mr x( ) φf Aps fpx x( ) dp x( ) a x( )2     Flexure resistance along the length

196 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 12. FLEXURAL STRENGTH (cont'd) xmom L 0.01 Lt Lend L Ld Lend L αhd 0.5  T  imom 1 last xmom  Mrximom Mr xmomimom  Muximom Mu xmomimom  DCmom Mux Mrx  max DCmom  0.769 Demand-Capacity ratio for moment CheckMom if max DCmom  1.0 "OK" "No Good"  "OK" Flexure resistance check 0 4 8 12 16 20 24 28 32 36 40 0 1000 2000 3000 4000 Design Moment and Flexure Resistance (Half Beam) Distance along Beam (ft) M om en t ( ki p· ft) MStrI x( ) kip ft 1.2 Mcr kip ft 1.33 MStrI x( ) kip ft Mu x( ) kip ft Mr x( ) kip ft x ft

197 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 13. SHEAR STRENGTH Shear Resistance Compute the factored shear at the critical shear section and at tenth points along the span due to the Strength I load combination, then compare it to the factored resistance calculated in accordance with AASHTO LRFD 5.8. VDC x( ) Vg x( ) Vbar x( ) Vj x( ) Self weight of components VDW x( ) Vfws x( ) Weight of future wearing surface VLL x( ) Vll x( ) Live load Vu x( ) 1.25 VDC x( ) 1.5 VDW x( ) 1.75 VLL x( ) Factored design shear Resistance factor for shear in normal weight concrete (AASHTO LRFD 5.5.4.2)φv 0.90 dend h ypx Lend  32.368 in Depth to steel centroid at bearing dv min 0.9 dend 0.72 h  29.132 in Effective shear depth lower limit at end Vp x( ) Pe slopecgp x Lend Lt  x Lt Lendif Pe slopecgp Lt Lend x αhd Lif 0 otherwise  Vertical component of effective prestress force bv b3 6 in Web thickness Shear stress on concrete (5.8.2.9-1) vu x( ) Vu x( ) φv Vp x( ) φv bv dv Mushr x( ) max MStrI x( ) Vu x( ) Vp x( ) dv  Factored moment for shear Stress in prestressing steel due to locked-in strain after casting concretefpo 0.7 fpu 189 ksi Steel strain at the centroid of the prestressing steelεs x( ) max 0.4 10 3 Mu x( ) dv Vu x( ) Vp x( ) Aps fpo Ep Aps         β x( ) 4.8 1 750 εs x( ) Shear resistance parameter θ x( ) 29 3500 εs x( )  deg Principal compressive stress angle Vc x( ) 0.0316 ksi β x( ) fc ksi  bv dv Concrete contribution to total shear resistance

198 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 13. SHEAR STRENGTH (cont'd) α 90 deg Angle of inclination of transverse reinforcement Transverse reinforcement area and spacing providedAv 1.02 0.62 0.62 0.62 0.31( ) T in2 sv 3 6 6 12 12( )T in xv 0 0.25 h 1.5 h 0.3 L 0.5 L 0.6 L( )T xvT 0 0.875 5.25 21 35 42( ) ft Avs x( ) out Avi svi  xvi x xvi 1if i 1 last Av for out  . Vs x( ) Avs x( ) fy dv cot θ x( )( ) cot α( )( ) sin α( ) Steel contribution to total shear resistance Vr x( ) φv Vc x( ) Vs x( ) Vp x( )  Factored shear resistance xshr outi i 0.5 L 100  i 1 100for out  ishr 1 last xshr  Vuxishr Vu xshrishr  Vrxishr Vr xshrishr  DCshr Vux Vrx  max DCshr  0.787 CheckShear if max DCshr  1.0 "OK" "No Good"  "OK" Shear resistance check 0 4 8 12 16 20 24 28 32 36 40 0 100 200 300 400 Design Shear and Resistance (Half Beam) Distance along Beam (ft) Sh ea r ( ki ps ) Vu x( ) kip Vr x( ) kip x ft

199 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 13. SHEAR STRENGTH (cont'd) Longitudinal Reinforcement Al.req x( ) a1 MStrI x( ) φf fpx x( ) dp x( ) a x( )2    a2 Vu x( ) φv 0.5 Vs x( ) Vp x( )   cot θ x( )( ) fpx x( )  a3 Mushr x( ) dv φf Vu x( ) φv Vp x( ) 0.5 Vs x( )   cot θ x( )( ) fpx x( )  min a1 a2( ) x dv 5 inif min a1 a3( ) otherwise  Longitudinal reinforcement required for shear (5.8.3.5) As.add 0.40 in 2 Ld.add 18.67 ft Additional longitudinal steel and developed length from end of beam Al.prov x( ) if x Ld.add Lend As.add 0  Ap Ns x LendLd x Ld Lendif Ap Ns Ld Lend x yh.brg 0.5 h slopecgp 0.5 Nh 1 2   2 in( ) cot slopecgp if Ap Nh Ns  otherwise  0 4 8 12 16 20 24 28 32 36 40 0 2 4 6 Longitudinal Reinforcement Required and Provided (Half Beam) Distance along Beam (ft) St ee l A re a (in 2) Al.req x( ) in2 Al.prov x( ) in2 x ft Al.reqishr Al.req xshrishr  Al.provishr Al.prov xshrishr  DClong Al.req Al.prov  max DClong  0.93 CheckLong if max DClong  1.0 "OK" "No Good"  "OK" Longitudinal reinforcement check

200 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 14. SPLITTING RESISTANCE Splitting Resistance Checking splitting resistance provided by first zone of transverse reinforcement defined in the previous section for shear design. As Av1 xv2  sv1 3.57 in2 fs 20 ksi Limiting stress in steel for crack control (5.10.10.1) Pr fs As 71.4 kip Splitting resistance provided (5.10.10.1-1) Pr.min 0.04 Pj 47.1 kip Minimum splitting resistance required CheckSplit if Pr Pr.min "OK" "No Good"  "OK" Splitting resistance check 15. CAMBER AND DEFLECTIONS Δps Pi Eci Ixg ycgp Lg 2 8 ybg yp.brg  αhd L Lend 2 6      2.131 in Deflection due to prestress at release Δgr 5384 wg Lg 4 Eci Ixg  0.917 in Deflection due to self-weight at release Δbar 5384 wbar Lg 4 Ec Ixg  0.263 in Deflection due to barrier weight 2Δj 5384 wj L 4 Ec Ixg  if BeamLoc 0= 1 0.5( ) 0.013 in Deflection due to longitudinal joint Δfws 5384 wfws L 4 Ec Ixg  if BeamLoc 0= 1 S Wb S   0.079 in Deflection due to future wearing surface tbar 20 Age at which barrier is assumed to be cast T ti 7 14 21 28 60 120 240 ∞ T Concrete ages at which camber is computed

201 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 15. CAMBER AND DEFLECTIONS (cont'd) Δcr1 t( ) ψ t ti ti  Δgr Δps  Δcr2 t( ) ψ t ti ti  ψ tbar ti ti   Δgr Δps  ψ t tbar tbar  Δbar Δcr3 t( ) ψ t ti ti  ψ td ti ti   Δgr Δps  ψ t tbar tbar  ψ td tbar tbar   Δbar ψ t td td  Δj   Δcr t( ) Δcr1 t( ) t tbarif Δcr1 tbar  Δcr2 t( ) tbar t tdif Δcr1 tbar  Δcr2 td  Δcr3 t( ) t tdif  Defl t( ) Δgr Δps  Δcr1 t( ) t tbarif Δgr Δps  Δcr1 tbar  Δbar Δcr2 t( ) tbar t tdif Δgr Δps  Δcr1 tbar  Δbar Δcr2 td  Δj Δcr3 t( ) t tdif  C outj Defl Tj  j 1 last T( )for out  CT 1.213 1.439 1.632 1.506 1.581 1.78 1.955 2.081 2.247( ) in 0 20 40 60 0 1 2 3 60-Day Deflection at Midspan Age of Concrete (days) D ef le ct io n (in ) Δcr t( ) in Defl t( ) in t 0 500 1000 1500 2000 0 1 2 3 Long-term Deflection at Midspan Age of Concrete (days) D ef le ct io n (in ) Δcr t( ) in Defl t( ) in t

202 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 16. NEGATIVE MOMENT FLEXURAL STRENGTH Compute the factored moment to be resisted across the interior pier and determine the required reinforcing steel to be fully developed in the top flange. Negative Live Load Moment Compute the negative moment over the interior support due to the design live load load, in accordance with AASHTO LRFD 3.6.1.3.1. Live Load Truck and Truck Train Moment Calculations Maximum negative moment due to a single truckmin Mtruck  889 kip ft Maximum negative moment due to two trucks in a single lanemin Mtrain  1650 kip ft Negative moment due to lane load on adjacent spansMneg.lane wlane L2 2 1568 kip ft Mneg.truck Mneg.lane 1 IM( ) min Mtruck  2750 kip ft Live load negative moment for single truck Live load negative moment for two trucks in a single laneMneg.train 0.9 Mneg.lane 1 IM( ) min Mtrain   3387 kip ft Design negative live load moment, per design laneMHL93.neg min Mneg.truck Mneg.train  3387 kip ft Design negative live load moment at interior beamMll.neg.i MHL93.neg gmint 2144 kip ft Design negative live load moment at exterior beamMll.neg.e MHL93.neg gmext 2233 kip ft MLL.neg if BeamLoc 1= Mll.neg.e Mll.neg.i  2233 kip ft Design negative live load moment Factored Negative Design Moment Dead load applied to the continuity section at interior supports is limited to the future overlay. Superimposed dead load resisted by continuity sectionMDW.neg wfws L2 2 487 kip ft Mu.neg.StrI 1.5 MDW.neg 1.75 MLL.neg 4638 kip ft Strength Limit State Mu.neg.StrI 1.0 MDW.neg 1.0 MLL.neg 2720 kip ft Service Limit State

203 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 16. NEGATIVE MOMENT FLEXURAL STRENGTH (cont'd) Reinforcing Steel Requirement in the Top Flange for Strength Reduction factor for strength in tension- controlled reinforced concrete (5.5.4.2)φf 0.90 bc b1 26 in Width of compression block at bottom flange Distance to centroid of negative moment steel, taken at mid-depth of top flangednms h tsac 0.5 tflange tsac  37 in Factored load, in terms of stress in concrete at depth of steel, for computing steel requirement Ru Mu.neg.StrI φf bc dnms2 1.019 ksi m fy 0.85 fc 8.824 Steel-to-concrete strength ratio ρreq 1m 1 1 2 m Ru fy    0.0185 Required negative moment steel ratio Anms.req ρreq bc dnms 17.787 in2 Required negative moment steel in top flange Full-length longitudinal reinforcement to be made continuous across jointAs.long.t 2.0 in 2 As.long.b 2.0 in2 Additional negative moment reinforcing bar areaAbar 0.44 in 2 Additional reinforcement area required in the top mat (2/3 of total)Anms.t 2 3 Anms.req As.long.t 9.858 in2 nbar.t ceil Anms.t Abar   23 Additional bars required in the top mat Additional reinforcement area required in the bottom matAnms.b 1 3 Anms.req As.long.b 3.929 in2 nbar.b ceil Anms.b Abar   9 Additional bars required in the top mat sbar.top S Wj 6 in nbar.t 1 3.788 in Spacing of bars in top mat As.nms nbar.t nbar.b  Abar As.long.t As.long.b 18.08 in2 Total reinforcing steel provided over pier a As.nms fy 0.85 fc bc 6.136 in Depth of compression block Mr.neg φf As.nms fy dnms a2   2761 kip ft Factored flexural resistance at interior pier DCneg.mom Mu.neg.StrI Mr.neg 0.985 CheckNegMom if DCneg.mom 1.0 "OK" "No Good"  "OK" Negative flexure resistance check

204 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ABC SAMPLE CALCULATION – 3a Precast Pier Design for ABC (70’ Span Straddle Bent)

205 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT PRECAST PIER DESIGN FOR ABC (70' SPAN STRADDLE BENT) Nomenclature FNofBm Total Number of Beams in Forward Span= BNofBm Total Number of Beams in Backward Span= FSpan Forward Span Length= BSpan Backward Span Length= FDeckW Out to Out Forward Span Deck Width= BDeckW Out to Out Backward Span Deck Width= FBmAg Forward Span Beam X Sectional Area= BBmAg Backward Span Beam X Sectional Area= FBmFlange Forward Span Beam Top Flange Width= BBmFlange Backward Span Beam Top Flange Width= FHaunch Forward Span Haunch Thickness= BHaunch Backward Span Haunch Thickness= FBmD Forward Span Beam Depth or Height= BBmD Backward Span Beam Depth or Height= FBmIg Forward Span Beam Moment of Inertia= BBmIg Backward Span Beam Moment of Inertia= yFt Forward Span Beam Top Distance from cg= yBt Backward Span Beam Top Distance from cg= NofCol Number of Columns per Bents=SlabTh Slab Thickness= NofDs Number of Drilled Shaft per Bents=RailWt Railing Weight= wCol Width of Column Section=RailH Railing Height= bCol Breadth of Column Section=RailW Rail Base Width= DsDia Drilled Shaft Diameter=LeftOH Left Overhang Distance= HCol Height of Column=RightOH Right Overhang Distance= wEarWall Width of Ear Wall=DeckW Out to Out Deck Width at Bent= hEarWall Height of Ear Wall=RoadW Roadway Width= tEarWall Thickness of Ear Wall=BrgTh Bearing Pad Thickness Bearing Seat Thickness= tSWalk Thickness of Side Walk=NofLane Number of Lanes= bSWalk Breadth of Side Walk=wCap Cap Width= BmMat Beam Material either Steel or Concrete=hCap Cap Depth= hbS Bottom Solid Height at Foam=CapL Cap Length= htS Top Solid Height at Foam=wFoam Width of Foam for Blockout= γst Unit Weight of Steel=hFoam heigth of Foam for Blockout= γc wc Unit Weight of Concrete=LFoam Length fo Foam for Blockout=

206 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT SlabDCInt Dead Load for Slab per Interior Beam= SlabDCExt Dead Load for Slab per Exterior Beam= BeamDC Self Weight of Beam= HaunchDC Dead Load of Haunch Concrete per Beam= RailDC Weight of Rail per Beam= FSuperDCInt Half of Forward Span Super Structure Dead Load Component per Interior Beam= FSuperDCExt Half of Forward Span Super Structure Dead Load Component per Exterior Beam= FSuperDW Half of Forward Span Overlay Dead Load Component per Beam= BSuperDCInt Half of Backward Span Super Structure Dead Load Component per Interior Beam= BSuperDCExt Half of Backward Span Super Structure Dead Load Component per Exterior Beam= BSuperDW Half of Backward Span Overlay Dead Load Component per Beam= TorsionDCInt DeadLoad Torsion in a Cap due to difference in Forward and Backward span length per Interior Beam= TorsionDCExt DeadLoad Torsion in a Cap due to difference in Forward and Backward span length per Exterior Beam= TorsionDW DW Torsion in a Cap due to difference in Forward and Backward span length per Beam= DiapWt Weight of Diaphragm= tBrgSeat Thickness of Bearing Seat= bBrgSeat Breadth of Bearing Seat=

207 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Note: Use of Light-Weight-Concrete (LWC) may be considered to reduce the weight of the pier cap instead of styrofoam blockouts.

208 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT FORWARD SPAN PARAMETER INPUT: FNofBm 12 FSpan 70 ft FDeckW 283 6 ft FBmAg 29.1 in2 FBmFlange 10.5 in yFt 14.85 inFHaunch 0 in FBmD 29.7 in FBmIg 3990 in4 BACKWARD SPAN PARAMETER INPUT: BNofBm 12 BSpan 70 ft BDeckW 283 6 ft BBmAg 29.1 in2 BBmFlange 10.5 in yBt 14.85 inBHaunch 0 in BBmD 29.7 in BBmIg 3990 in4 COMMON BRIDGE PARAMETER INPUT: Intermediate Bent between Forward and Backward span Parameters SlabTh 9 in Overlay 25 psf θ 0 deg DeckOH 1.75 ft BrgTh 3.5 in RailWt 0.43 klf RailW 19 in RailH 34.0 in tBrgSeat 0 in bBrgSeat 0 ft DeckW 283 6 ft NofLane 3 m 0.85 wc 0.150 kcf f'c 5 ksi Cap( ) wCap 4.5 ft hCap 5 ft CapL 47 ft NofDs 2 DsDia 6 ft wCol 4 ft bCol 4 ft NofCol 2 HCol 22.00 ft f'cs 4 ksi Slab( ) γc 0.150 kcf ebrg 13 in NofBm 12 Sta 0.25 ftincr DiapWt 0.2 kip wEarWall 0 ft hEarWall 0 ft tEarWall 0 in IM 0.33 BmMat Steel LFoam 35 ft wFoam 14 in hFoam 31 in hbS 15 in (Bottom Solid Depth of Section) Es 29000 ksi γst 490 pcf steel( ) Modulus of elasticity of Concrete: E fc  33000 wc 1.5 fc ksi (AASHTO LRFD EQ 5.4.2.4-1 for K1 = 1) Eslab E f'cs  Eslab 3834.254 ksi Ecap E f'c  Ecap 4286.826 ksi Modulus of Beam or Girder: Input Beam Material, BmMat = Steel or Concrete Ebeam if BmMat Steel= Es E f'c   Ebeam 29000 ksi

209 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 1. BENT CAP LOADING DEAD LOAD FROM SUPERSTRUCTURE: The permanent dead load components (DC) consist of slab, rail, sidewalk, haunch weight and beam self weight. Slab dead weight components will be distributed to each beam by slab tributary width between beams. Interior Beam tributary width (IntBmTriW) is taken as the average of consecutive beam spacing for a particular interior beam. Exterior Beam tributary width (ExtBmTriW) is taken as half of beam spacing plus the overhang distance. Rail, sidewalk dead load components and future wearing surface weight components (DW) can be distributed evenly among each beam. Half of DC and DW components from forward span and backward span comprise the total superstructure load or dead load reaction per beam on the pier cap or the bent cap. FORWARD SPAN SUPERSTRUCTURE DEAD LOAD: consists of 12 W30x99 Beams 12 beams were spaced 4.5' and 3'-4" alternately in forward span. For beam spacing see Typical Section Details sheet FBmSpa1 4.5 ft FBmSpa2 10 3 ft FIntBmTriW FBmSpa1 2 FBmSpa2 2  FIntBmTriW 3.917 ft FExtBmTriW FBmSpa1 2 DeckOH FExtBmTriW 4 ft RoadW 0.25 FDeckW 3 DeckW( ) 2 RailW RoadW 44 ft SlabDCInt γc FIntBmTriW SlabTh FSpan2   SlabDCInt 15.422 kip beam  SlabDCExt γc FExtBmTriW SlabTh FSpan2   SlabDCExt 15.75 kip beam  BeamDC γst FBmAg FSpan2   BeamDC 3.466 kip beam  HaunchDC γc FHaunch FBmFlange FSpan2   HaunchDC 0 kip beam  NOTE: Permanent loads such as the weight of the Rail (Barrier), Future wearing surface may be distributed uniformly among all beams if following conditions are met. Apply for live load distribution factors too. AASHTO LRFD 4.6.2.2.1 1. Width of deck is constant 2. Number of Beams >= 4 beams 3. Beams are parallel and have approximately same stiffness 4. The Roadway part of the overhang, de<= 3ft 5. Curvature in plan is < 4o 6. Bridge cross-section is consistent with one of the x-section shown in AASHTO LRFD TABLE 4.6.2.2.1-1 RailDC 2 RailWt FNofBm FSpan 2   RailDC 2.508 kip beam  OverlayDW RoadW Overlay FNofBm FSpan 2   OverlayDW 3.208 kip beam 

210 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Forward Span Superstructure DC & DW per Interior and Exterior Beam: FSuperDCInt RailDC BeamDC SlabDCInt HaunchDC DiapWt FSuperDCInt 21.596 kip beam  FSuperDCExt RailDC BeamDC SlabDCExt HaunchDC 0.5 DiapWt FSuperDCExt 21.824 kip beam  FSuperDW OverlayDW FSuperDW 3.208 kip beam  BACKWARD SPAN SUPERSTRUCTURE DEAD LOAD: consists of 12 W30x99 beams 12 beams were spaced 4.5' and 3'-4" alternately in backward span. For beam spacing see Typical Section Details sheet BBmSpa1 4.5 ft BBmSpa2 10 3 ft BIntBmTriW BBmSpa1 2 BBmSpa2 2  BIntBmTriW 3.917 ft BExtBmTriW BBmSpa1 2 DeckOH BExtBmTriW 4 ft RoadW 0.25 BDeckW 3 DeckW( ) 2 RailW RoadW 44 ft SlabDCInt γc BIntBmTriW SlabTh BSpan2   SlabDCInt 15.422 kip beam  SlabDCExt γc BExtBmTriW SlabTh BSpan2   SlabDCExt 15.75 kip beam  BeamDC γst BBmAg BSpan2   BeamDC 3.466 kip beam  HaunchDC γc BHaunch BBmFlange BSpan2   HaunchDC 0 kip beam  RailDC 2 RailWt BNofBm BSpan 2   RailDC 2.508 kip beam  OverlayDW RoadW Overlay BNofBm BSpan 2   OverlayDW 3.208 kip beam  Total Backward Span Superstructure DC & DW per Interior and Exterior Beam: BSuperDCInt RailDC BeamDC SlabDCInt HaunchDC DiapWt BSuperDCInt 21.596 kip beam  BSuperDCExt RailDC BeamDC SlabDCExt HaunchDC 0.5 DiapWt BSuperDCExt 21.824 kip beam  BSuperDW OverlayDW BSuperDW 3.208 kip beam 

211 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Total Superstructure DC & DW per Beam on Bent Cap: SuperDCInt FSuperDCInt BSuperDCInt SuperDCInt 43.192 kip beam  SuperDCExt FSuperDCExt BSuperDCExt SuperDCExt 43.648 kip beam  SuperDW FSuperDW BSuperDW SuperDW 6.417 kip beam  TorsionDCInt max FSuperDCInt BSuperDCInt  min FSuperDCInt BSuperDCInt   ebrg TorsionDCInt 0 kftbeam TorsionDCExt max FSuperDCExt BSuperDCExt  min FSuperDCExt BSuperDCExt   ebrg TorsionDCExt 0 kftbeam TorsionDW max FSuperDW BSuperDW( ) min FSuperDW BSuperDW( )( ) ebrg TorsionDW 0 kft beam  CAP, EAR WALL & BEARING SEAT WEIGHT: The Bent cap has two sections along the length. One is a solid rectangular section 6ft from the both ends. The middle section is made hollow by placing foam blockouts in two sides of mid section as can be seen in the typical section and pier elevation figure. CapDC1 is the weight of the solid section and CapDC2 is the weight of the hollow section. CapDC1 wCap hCap γc Applicable for 0 ft CapL 6 ft( ) 41 ft CapL 47 ft( ) CapDC1 3.375 kipft CapDC2 wCap hCap 2 wFoam hFoam( ) γc Applicable for 6 ft CapL 41 ft( ) CapDC2 2.471 kipft EarWallDC wEarWall hEarWall tEarWall( ) γc EarWallDC 0 kip BrgSeatDC tBrgSeat bBrgSeat wCap( ) γc BrgSeatDC 0 kipbeam Distribution Factor RESULTS OF DISTRIBUTION FACTORS: Forward Span Distribution Factors: DFMFmax 0.391 (Distribution Factor for Moment) DFSFmax 0.558 (Distribution Factor for Shear) Backward Span Distribution Factors: DFMBmax 0.391 (Distribution Factor for Moment) DFSBmax 0.558 (Distribution Factor for Shear)

212 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT LIVE LOAD FOR SIMPLY SUPPORTED BRIDGE: HL-93 Loading: According to AASHTO LRFD 3.6.1.2.1, HL-93 consists of Design Truck + Design Lane Load or Design Tandem + Design Lane Load. Design Truck rather than Design Tandem + Design Lane Load controls the maximum Live Load Reactions at an interior bent for a span longer than 26'. For maximum reaction, place middle axle (P2 = 32 kip) of design truck over the support at a bent between the forward and the backward span and place rear axle (P3 = 32 kip) 14' away from P2 on the longer span while placing P1 14' away from P1 on either spans yielding maximum value. P1 Front Axle of Design Truck= P2 Middle Axle of Design Truck= P3 Rear Axle of Design Truck= Design Truck Axle Load: P1 8 kip P2 32 kip P3 32 kip AASHTO LRFD 3.6.1.2.2( ) TruckT P1 P2 P3 Design Lane Load: wlane 0.64 klf AASHTO LRFD 3.6.1.2.4( ) LongSpan max FSpan BSpan( ) ShortSpan min FSpan BSpan( ) Llong LongSpan Lshort ShortSpan Lane Load Reaction Lane wlane Llong Lshort 2   Lane 44.8 kip lane  Truck Load Reaction Truck P2 P3 Llong 14ft  Llong  P1 max Llong 28ft  Llong Lshort 14ft  Lshort      Truck 64 kip lane  Maximum Live Load Reaction with Impact (LLRxn) over support on Bent: The Dynamic Load Allowance or Impact Factor, IM 0.33 AASHTO LRFD Table 3.6.2.1 1( ) LLRxn Lane Truck 1 IM( ) LLRxn 129.92 kip lane  Live Load Model for Cap Loading Program: AASHTO LRFD Recommended Live Load Model For Cap Loading Program: Live Load reaction on the pier cap using distribution factors are not sufficient to design bent cap for moment and shear. Therefore, the reaction from live load is uniformly distributed to over a 10' width (which becomes W) and the reaction from the truck is applied as two concentrated loads (P and P) 6' apart. The loads act within a 12' wide traffic lane. The reaction W and the truck move across the width of the traffic lane. However, neither of the P loads can be placed closer than 2' from the edge of the traffic lane. One lane, two lanes, three lanes and so forth loaded traffic can be moved across the width of the roadway to create maximum load effects. Load on one rear wheel out of rear axle of the truck with Impact: P 0.5 P3  1 IM( ) P 21.28 kip The Design Lane Load Width Transversely in a Lane wlaneTransW 10 ft AASHTO LRFD Article 3.6.1.2.1 The uniform load portion of the Live Load, kip/station for Cap Loading Program: W LLRxn 2 P( ) Sta wlaneTransW  W 2.184 kip incr 

213 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT LOADS generated above will be placed into a CAP LOADING PROGRAM to obtain moment and shear values for Bent Cap. Torsion on Bent Cap per Beam and per Drilled Shaft: Torsional load about center line of bent cap occurs due to horizontal loads acting on the superstructure perpendicular to the bent length or along the bridge length. Braking force, Centrifugal force, WS on superstructure, and WL cause torsion on bent. In addition, torque about center line of bent cap for the dead load reaction on beam brg location occurs due to differences in forward and backward span length and eccentricity between center line of bent cap and brg location. Torsion can be neglected if Tu<0.25Tcr (AASHTO LRFD 5.8.2.1) The maximum torsional effects on the pier cap will be obtained from RISA frame analysis under loading as stated in AASHTO LRFD SECTION 3 for different load combinations using AASHTO LRFD Table 3.4.1-1

214 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 2. BENT CAP FLEXURAL DESIGN FLEXURAL DESIGN OF BENT CAP: h( ) b( ) f'c 5.0 ksi fy 60 ksi Es 29000 ksi ϕm 0.9 ϕv 0.9 ϕn 1 γc 0.150 kcf bcover 2 in tcover 2 in h 5 ft b 4.5 ft Ec Ecap n round Es Ec 0     (AASHTO LRFD 5.7.1) n 7 EIcap1 Ec b h3  12  Applicable for 0 CapL 6 41 CapL 47 EIcap1 2.894 10 7 kip ft2 ycg2 wCap hCap hCap 2  2 wFoam hFoam( ) hFoam 2 hbS  wCap hCap 2 wFoam hFoam( ) (ycg of from Bottom of Cap Section) ycg2 29.817 in Icap2 wCap hCap3 12 wCap hCap hCap 2 ycg2  2  2 wFoam hFoam 3 12 wFoam hFoam hFoam 2 hbS ycg2  2     Icap2 902191.259 in 4 EIcap2 Ec Icap2 Applicable for 6 CapL 41 EIcap2 2.686 10 7 kip ft2 OUTPUT of BENT CAP LOADING PROGRAM: The maximum load effects from different applicable limit states: DEAD LOAD MdlPos 3309.6 kft MdlNeg 30.1 kft SERVICE I MsPos 5377.1 kft MsNeg 45.1 kft

215 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT STRENGTH I MuPos 7830.6 kft MuNeg 64.6 kft FLEXURE DESIGN: AASHTO LRFD 5.7.3.3.2 MINIMUM FLEXURAL REINFORCEMENT Factored Flexural Resistance, Mr, must be greater than or equal to the lesser of 1.2Mcr or 1.33 Mu. Applicable to both positive and negative moment. Modulus of rupture fr 0.37 f'c ksi (AASHTO LRFD EQ 5.4.2.6) fr 0.827 ksi S Icap2 ycg2  (Bottom Section Modulus for Positive Moment) S 30257.581 in3 Cracking moment Mcr S fr (AASHTO LRFD EQ 5.7.3.3.2-1) Mcr 2086.122 kip ft Mcr1 1.2 Mcr Mcr1 2503.346 kip ft Mcr2 1.33 max MuPos MuNeg  Mcr2 10414.698 kip ft Mcr_min min Mcr1 Mcr2  Therefore Mr must be greater than Mcr_min 2503.346 kip ft Moment Capacity Design (Positive Moment, Bottom Bars B) AASHTO LRFD 5.7.3.2 Bottom Steel arrangement for the Cap: Input no. of total rebar in a row from bottom of cap up to 12 rows (in unnecessary rows input zero) Np 9 9 9 0 0 0 0 0 0 0 0 0( ) Input area of rebar corresponding to above rows from bottom of cap, not applicable for mixed rebar in a single row Abp 1.56 1.56 1.56 0 0 0 0 0 0 0 0 0( ) in 2 Input center to center vertical distance between each rebar row starting from bottom of cap clp 3.5 4 4 0 0 0 0 0 0 0 0 0( ) in dc Calc for Pos Moment nsPos 3 (No. of Bottom or Positive Steel Layers) Distance from centroid of positive rebar to extreme bottom tension fiber (dcPos): dcPos Ayp0 0  in dcPos 7.5 in Effective depth from centroid of bottom rebar to extreme compression fiber (dPos): dPos h dcPos dPos 52.5 in

216 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Compression Block depth under ultimate load AASHTO LRFD 5.7.2.2 β1 min 0.85 max 0.65 0.85 0.05ksi f'c 4 ksi    β1 0.8 The Amount of Bottom or Positive Steel As Required, AsReq 0.85 f'c b dPos fy     1 1 2 MuPos 0.85 ϕm f'c b dPos2       AsReq 36.454 in 2 The Amount of Positive As Provided, NofBarsPos Np NofBarsPos 27 AsPos Ayp0 1  in2 AsPos 42.12 in2 htS h hFoam hbS (Top solid depth) htS 14 in Compression depth under ultimate load cPos AsPos fy 0.85 f'c β1 b  (AASHTO LRFD EQ 5.7.3.1.1-4) cPos 13.765 in aPos β1 cPos aPos htS OK  (AASHTO LRFD 5.7.3.2.2) aPos 11.012 in Nominal flexural resistance: MnPos AsPos fy dPos aPos 2   (AASHTO LRFD EQ 5.7.3.2.2-1) MnPos 9896.961 kip ft Tension controlled resistance factor for flexure ϕmPos min 0.65 0.15 dPos cPos 1     0.9     (AASHTO LRFD EQ 5.5.4.2.1-2) ϕmPos 0.9 or simply use, ϕm 0.9 (AASHTO LRFD 5.5.4.2) MrPos ϕmPos MnPos (AASHTO LRFD EQ 5.7.3.2.1-1) MrPos 8907.265 kip ft MuPos 7830.6 kip ft MinReinChkPos if MrPos Mcr_min  "OK" "NG"  MinReinChkPos "OK"

217 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT UltimateMomChkPos if MrPos MuPos  "OK" "NG"  UltimateMomChkPos "OK" Moment Capacity Design (Negative Moment, Top Bars A) AASHTO LRFD 5.7.3.2 Top Steel arrangement for the Cap: Input no. of total rebar in a row from top of cap up to 12 rows (in unnecessary rows input zero) Nn 6 6 0 0 0 0 0 0 0 0 0 0( ) Input area of rebar corresponding to above rows from top of cap, not applicable for mixed rebar in a single row Abn 0.6 1.27 0 0 0 0 0 0 0 0 0 0( ) in 2 Input center to center vertical distance between each rebar row starting from top of cap cln 3.5 4 0 0 0 0 0 0 0 0 0 0( ) in dc Calc for Neg. Moment nsNeg 2 (No. of Negative or Top Steel Layers) Distance from centroid of negative rebar to top extreme tension fiber (dcNeg): dcNeg Ayn0 0  in dcNeg 6.217 in Effective depth from centroid of top rebar to extreme compression fiber (dNeg): dNeg h dcNeg dNeg 53.783 in The Amount of Negative As Required, AsReq 0.85 f'c b dNeg fy     1 1 2 MuNeg 0.85 ϕm f'c b dNeg2       AsReq 0.267 in 2 The Amount of Negative As Provided, NofBarsNeg Nn NofBarsNeg 12 AsNeg Ayn0 1  in2 AsNeg 11.22 in2 Compression depth under ultimate load cNeg AsNeg fy 0.85 f'c β1 b  cNeg 3.667 in aNeg β1 cNeg aNeg 2.933 in Thus, nominal flexural resistance:

218 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT MnNeg AsNeg fy dNeg aNeg 2   MnNeg 2934.97 kip ft Factored flexural resistance MrNeg ϕm MnNeg MrNeg 2641.473 kip ft MuNeg 64.6 kip ft MinReinChkNeg if MrNeg Mcr_min  "OK" "NG"  MinReinChkNeg "OK" UltimateMomChkNeg if MrNeg MuNeg  "OK" "NG"  UltimateMomChkNeg "OK" Control of Cracking at Service Limit State AASHTO LRFD 5.7.3.4 exposure_cond 1 (for exposure condition, input Class 1 = 1 and Class 2 = 2) γe if exposure_cond 1= 1 0.75( ) (Exposure condition factor) γe 1 sidecTop sidecBot  5.625 4.75( ) in (Input side cover for Top and Bottom Rebars) Positive Moment (Bottom Bars B) To find Smax: S is spacing of first layer of rebar closest to tension face n round Es Ec 0     (modular ratio) n 7 ρPos AsPos b dPos  ρPos 0.0149 kPos ρPos n 1 2 1 ρPos n kPos 0.364(Applicable for Solid Rectangular Section) kdP kPos dPos Location of NA from Top of Cap for Pos Moment kdP 19.098 in StressBlockPos if kdP htS "T-Section" "Rec-Section"  StressBlockPos "T-Section" Comression Force Tension Force= OR Moment of Comression Area Moment of Tension Area about NA= b kdPos 2 2 wFoam kdPos hStop 2 2 n AsPos dPos kdPos = b 2 wFoam( ) kdPos 2 2 n AsPos 4 wFoam hStop  kdPos  2 wFoam hStop2 n AsPos dPos  0=

219 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT kdPos 2 n AsPos 4 wFoam htS  2 n AsPos 4 wFoam htS 2 4 b 2 wFoam( ) 2 wFoam htS 2 n AsPos dPos   2 b 2 wFoam( ) kdPos 19.405 in Location of NA from Top of Cap Location of Resultant Compression force from NA for Positive Moment: xPos b kdPos 2 3  2 3 wFoam kdPos htS 2 1 htSkdPos      1 2 b kdPos wFoam kdPos htS  1 htSkdPos       xPos 13.328 in jdPos dPos kdPos xPos jdPos 46.423 in Tensile Stress at Service Limit State fssPos MsPos AsPos jdPos  fssPos 33 ksi dc1Pos clp0 0 (Distance of bottom first row rebar closest to tension face) dc1Pos 3.5 in βsPos 1 dc1Pos 0.7 h dc1Pos  βsPos 1.088 smaxPos 700 kip in γe βsPos fssPos 2 dc1Pos AASHTO LRFD EQ (5.7.3.4-1) smaxPos 12.488 in sActualPos b 2 sidecBot Np0 0 1 (Equal horizontal spacing of bottom first rebar row closest to tension face) sActualPos 5.563 in Actual Max Spacing Provided in Bottom first row closest to Tension Face, saPosProvided 7 in sActualPos max saPosProvided sActualPos  sActualPos 7 in SpacingCheckPos if smaxPos sActualPos  "OK" "NG"  SpacingCheckPos "OK"

220 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Negative Moment (Top Bars A) ρNeg AsNeg b dNeg  ρNeg 3.863 10 3 kNeg ρNeg n 1 2 1 ρNeg n (Applicable for Solid Rectangular Section) kNeg 0.207 kdN kNeg dNeg Location of NA from Bottom of Cap for Neg Moment kdN 11.138 in StressBlockNeg if kdN hbS "T-Section" "Rec-Section"  StressBlockNeg "Rec-Section" jNeg 1 kNeg 3  jNeg 0.931 fssNeg MsNeg AsNeg jNeg dNeg  fssNeg 0.963 ksi dc1Neg cln0 0 (Distance of top first row rebar closest to tension face) dc1Neg 3.5 in βsNeg 1 dc1Neg 0.7 h dc1Neg  βsNeg 1.088 smaxNeg 700 kip in γe βsNeg fssNeg 2 dc1Neg smaxNeg 660.561 in sActualNeg b 2 sidecTop Nn0 0 1 (Equal horizontal spacing of top first rebar row closest to tension face) sActualNeg 8.55 in Actual Max Spacing Provided in Top first row closest to Tension Face, saNegProvided 11.125 in sActualNeg max saNegProvided sActualNeg  sActualNeg 11.125 in SpacingCheckNeg if smaxNeg sActualNeg  "OK" "NG"  SpacingCheckNeg "OK" SUMMARY OF FLEXURE DESIGN:

221 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Bottom Rebar or B Bars: use 27~#11 bars @ 9 bars in each row of 3 rows Top Rebar or A Bars: use 6~#7 bars and 6~#10 bars in first and 2nd row from top SKIN REINFORCEMENT (BARS T) AASHTO LRFD 5.7.3.4 SkBarNo 8 (Size of a skin bar) Area of a skin bar, AskBar 0.79 in 2 dcTop cln dcTop 7.5 in dcBot clp dcBot 11.5 in Effective Depth from centroid of ExtremeTension Steel to Extreme compression Fiber (dl): dl max h clp0 0 h cln0 0  dl 56.5 in Effective Depth from centroid of Tension Steel to Extreme compression Fiber (de): de max dPos dNeg  de 53.783 in As min AsNeg AsPos  min. of negative and positive reinforcement As 11.22 in2 dskin h dcTop dcBot  dskin 41 in Skin Reinforcement Requirement: AASHTO LRFD EQ 5.7.3.4-2 AskReq if dl 3ft min 0.012 in ft  dl 30 in  dskin As Aps4   0in 2  AskReq 1.087 in 2 NoAskbar1 R AskReq AskBar      NoAskbar1 2 per Side Maximum Spacing of Skin Reinforcement: SskMax min de 6 12 in  AASHTO LRFD 5.7.3.4 SskMax 8.964 in NoAskbar2 if dl 3ft R dskin SskMax 1     1     NoAskbar2 4 per Side NofSideBarsreq max NoAskbar1 NoAskbar2  NofSideBarsreq 4 SskRequired dskin 1 NofSideBarsreq  SskRequired 8.2 in

222 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT NofSideBars 5 (No. of Side Bars Provided) SskProvided dskin 1 NofSideBars SskProvided 6.833 in SskChk if SskProvided SskMax "OK" "N.G."  SskChk "OK" Therefore Use: NofSideBars 5 and Size SkBarNo 8 3. BENT CAP SHEAR AND TORSION DESIGN SHEAR DESIGN OF CAP: Effective Shear Depth, dv max de a 2  0.9 de 0.72 h                 = (AASHTO LRFD 5.8.2.9) dv Distance between the resultants of tensile and compressive Force= ds Effective depth from cg of the nonprestressed tensile steel to extreme compression fiber= dp Effective depth from cg of the prestressed tendon to extreme compression fiber= de Effective depth from centroid of the tensile force to extreme compression fiber at critical shear Location= θ Angle of inclination diagonal compressive stress= Ao Area enclosed by shear flow path including area of holes therein= Ac Area of concrete on flexural tension side of member shown in AASHTO LRFD Figure 5.8.3.4.2 1= Aoh Area enclosed by centerline of exterior closed transverse torsion reinforcement including area of holes therein= Total Pos Flexural Steel Area, As AsPos As 42.12 in 2 Nominal Flexure, Mn MnPos Mn 9896.961 kft Stress block Depth, a aPos a 11.012 in Effective Depth, de dPos de 52.5 in Effective web Width at critical Location, bv b bv 4.5 ft Input initial  θ 35 deg cotθ cot θ( ) Shear Resistance Factor, ϕv 0.9 Cap Depth & Width, h 60 in b 54 in

223 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Moment Arm, de a 2   46.994 in 0.9 de 47.25 in 0.72 h 43.2 in Effective Shear Depth at Critical Location, dv max de a 2  0.9 de 0.72 h                  (AASHTO LRFD 5.8.2.9) dv 47.25 in hh h tcover bcover (Height of shear reinforcement) hh 56 in bh b 2 bcover (Width of shear reinforcement) bh 50 in ph 2 hh bh  (Perimeter of shear reinforcement) ph 212 in Aoh hh  bh  (Area enclosed by the shear reinforcement) Aoh 2800 in2 Ao 0.85 Aoh (AASHTO LRFD C5.8.2.1) Ao 2380 in 2 Ac 0.5 b h AASHTO LRFD FIGURE 5.8.3.4.2 1( ) Ac 1620 in 2 Yield strength & Modulus of Elasticity of Steel Reinforcement: fy Es  60 29000( ) ksi AASHTO LRFD 5.4.3.1 5.4.3.2( ) Input Mu, Tu, Vu, Nu for the critical section to be investigated: (Loads from Bent Cap & RISA Analysis) Mu Tu  1314.8 964.6( ) kft Vu Nu  665.4 0( ) kip M'u max Mu Vu Vp dv  AASHTO LRFD B5.2 M'u 2620.013 kip ft V'u Vu 2 0.9 ph Tu 2 Ao     2  (Equivalent shear) AASHTO LRFD EQ (5.8.2.1-6) for solid section V'u 811.194 kip Assuming atleast minimum transverse reinforcement is provided (Always provide min. transverse reinf.) εx M'u dv     0.5 Nu 0.5 V'u Vp  cotθ Aps fpo 2 Es As Ep Aps = (Strain from Appendix B5) AASHTO LRFD EQ (B5.2-1)

224 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT vu Vu ϕv Vp  ϕv bv dv  (Shear Stress) AASHTO LRFD EQ (5.8.2.9-1) vu 0.29 ksi r max 0.075 vu f'c      (Shear stress ratio) r 0.075 Determining Beta & Theta After Interpolating the value of Θ Β( ) Θ 30.773 deg Β 2.572 Nominal Shear Resistance by Concrete, Vc 0.0316 Β f'c ksi bv dv AASHTO LRFD EQ (5.8.3.3-3) Vc 463.7 kip Vu 665.4 kip 0.5 ϕv Vc Vp  208.673 kip REGION REQUIRING TRANSVERSE REINFORCEMENT: AASHTO LRFD 5.8.2.4 Vu 0.5 ϕv Vc Vp  AASHTO LRFD EQ (5.8.2.4-1) check if Vu 0.5 ϕv Vc Vp  "Provide Shear Reinf" "No reinf."  check "Provide Shear Reinf" Vn min Vc Vs Vp 0.25 f'c bv dv Vp         = (Nominal Shear Resistance) AASHTO LRFD EQ 5.8.3.3 1 2( ) Vs Av fy dv cotθ cotα( ) sinα S = (Shear Resistance of Steel) AASHTO LRFD EQ 5.8.3.3 4( ) Vs Av fy dv cotθ S = Shear Resistance of Steel when α 90 deg=( ) AASHTO LRFD EQ (C5.8.3.3-1) Sv 6 in (Input Stirrup Spacing) Vp 0 kip Vu Vc  665.4 463.718( ) kip fy 60 ksi dv 47.25 in Θ 30.773 deg (Derive from AASHTO LRFD EQ 5.8.3.3-1, C5.8.3.3-1 and Vn >= Vu)Av_req Vu ϕv Vc Vp     Sv fy dv cotΘ      Av_req 0.3474 in 2 Torsional Steel:

225 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT At Tu 2 ϕv Ao fy cotΘ Sv (Derive from AASHTO LRFD EQ 5.8.3.6.2-1 and Tn >= Tu) At 0.161 in 2 Avt_req Av_req 2 At Shear Torsion( ) Avt_req 0.669 in 2 Avt 4 0.44 in 2  (Use 2 #6 double leg Stirrup at Sv c/c,) Provided, Avt 1.76 in2 Avt_check if Avt Avt_req "OK" "NG"  Avt_check "OK" AASHTO LRFD Article 5.8.2.7Maximum Spacing Check: Vu 665.4 kip 0.125 f'c bv dv 1594.69 kip Svmax if Vu 0.125 f'c bv dv min 0.8 dv 24 in  min 0.4 dv 12 in   Svmax 24 in Svmax_check if Sv Svmax "OK" "use lower spacing"  Svmax_check "OK" Av Avt At (Shear Reinf. without Torsion Reinf.) Av 1.599 in 2 Vs Av fy dv cotΘ Sv  Vs 1268.855 kip AASHTO LRFD Article 5.8.2.5Minimum Transverse Reinforcement Check: bv 54 in Avmin 0.0316 f'c ksi bv Sv fy  AASHTO LRFD EQ 5.8.2.5 1( ) Avmin 0.382 in 2 Avmin_check if Avt Avmin "OK" "NG"  Avmin_check "OK" Maximum Nominal Shear: To ensure that the concrete in the web of beam will not crush prior to yield of shear reinforcement, LRFD Specification has given an upper limit of 0.25 f'c bv dv Vp 3189.375 kip Vc Vs Vp 1732.573 kip Vn min Vc Vs Vp 0.25 f'c bv dv Vp          AASHTO LRFD EQ 5.8.3.3 1 2( ) Vn 1732.573 kip ϕv Vn 1559.316 kip Vu 665.4 kip ϕVn_check if ϕv Vn Vu "OK" "NG"  ϕVn_check "OK" Torsional Resistance,

226 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Tn 2 Ao 0.5 Avt  fy cotΘ Sv  AASHTO LRFD EQ 5.8.3.6.2 1( ) ϕv Tn 5275.8 kip ft Longitudinal Reinforcement Requirements including Torsion: AASHTO LRFD 5.8.3.6.3 AASHTO LRFD EQ 5.8.3.6.3 1( ) Applicable for solid section with Torsion Aps fps As fy M'u ϕm dv     0.5 Nu ϕn  cotΘ Vuϕv Vp 0.5 V's     2 0.45 ph Tu 2 ϕv Ao     2  ϕm ϕv ϕn  0.9 0.9 1( ) As fy Aps fps 2527.2 kip M'u 2620.013 kip ft Vu 665.4 kip Nu 0 kip Vs 1268.855 kip Tu 964.6 kip ft ph 212 in Vp 0 kip As 42.12 in 2 V's min Vu ϕv Vs      AASHTO LRFD 5.8.3.5 V's 739.333 kip F M'u ϕm dv     0.5 Nu ϕn  cotΘ Vuϕv Vp 0.5 V's     2 0.45 Tu ph 2 ϕv Ao     2  F 1496.141 kip Fcheck if Aps fps As fy F "OK" "NG"  AASHTO LRFD EQ 5.8.3.6.3 1( ) Fcheck "OK"

227 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 4. COLUMN/DRILLED SHAFT LOADING AND DESIGN Superstructure to substructure force: AASHTO LRFD SECTION 3 LOADS and LOAD COMBINATIONS Subscript: X = Parallel to the Bent cap Length and Z = Perpendicular to the bent Cap Length th 2 in (Haunch Thickness) Beam Depth, BmH FBmD ColH HCol 0 ft (Column height + 0 ft Column Capital) TribuLength FSpan BSpan 2  Scour Depth: hscour 0 ft Scour to Fixity Depth: hscf min 3 DsDia 10 ft( ) Total Drilled Shaft height: DsH hscour hscf DsH 10 ft ho BrgTh BmH th SlabTh (Top of cap to top of slab height) ho 3.683 ft h6 ho 6ft (Top of cap to top of slab height + 6 ft) h6 9.683 ft hsup BmH th SlabTh RailH (Height of Superstructure) hsup 6.225 ft h1 DsH ColH hCap 2  (Height of Cap cg from Fixity of Dshaft) h1 34.5 ft h2 DsH ColH hCap h6 h2 46.683 ft h3 DsH ColH hCap BrgTh hsup 2  h3 40.404 ft Tributary area for Superstructure, Asuper hsup( ) TribuLength( ) Asuper 435.75 ft 2

228 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT LIVE LOAD REACTIONS: LL Live load Reaction LL on cap can be taken only the vertical Rxn occurs when HL93 is on both the forward and backward span or when HL93 Loading is on one span only which causes torsion too. To maximize the torsion, LL only acts on the longer span between forward and backward span. For maximum reaction, place rear axle (P3 = 32 kip) over the support at bent while the design truck traveling along the span. Maximum Forward Span Design Truck (FTruck) & Lane Load Reaction (FLane): FTruck P3 P2 FSpan 14 ft( ) FSpan   P1 FSpan 28ft( ) FSpan  FTruck 62.4 kip FLane wlane FSpan 2   FLane 22.4 kip lane  Forward Span Live Load Reactions with Impact (FLLRxn): FLLRxn FLane FTruck 1 IM( ) FLLRxn 105.392 kip lane  Maximum Backward Span Design Truck (BTruck) & Lane Load Reaction (BLane): BTruck P3 P2 BSpan 14 ft( ) BSpan   P1 BSpan 28ft( ) BSpan  BTruck 62.4 kip BLane wlane BSpan 2   BLane 22.4 kip lane  Backward Span Live Load Reactions with Impact (BLLRxn): BLLRxn BLane BTruck 1 IM( ) BLLRxn 105.392 kip lane  Live Load Reactions per Beam with Impact (BmLLRxn) using Distribution Factors: BmLLRxn LLRxn( ) max DFSFmax DFSBmax  Max reaction when mid axle on support( ) BmLLRxn 72.556 kipbeam FBmLLRxn FLLRxn( ) DFSFmax Only Forward Span is Loaded( ) FBmLLRxn 58.858 kip beam  BBmLLRxn BLLRxn( ) DFSBmax Only Backward Span is Loaded( ) BBmLLRxn 58.858 kip beam  Torsion due to the eccentricity from CL of Bearing to CL of Bent when only Longer Span is loaded with HL-93 Loading TorsionLL max FBmLLRxn BBmLLRxn( ) ebrg TorsionLL 63.763 kip ft beam  Live Load Reactions per Beam without Impact (BmLLRxnn) using Distribution Factors: BmLLRxnn Lane Truck( ) max DFSFmax DFSBmax  BmLLRxnn 60.761 kipbeam FBmLLRxnn FLane FTruck( ) DFSFmax  FBmLLRxnn 47.358 kipbeam BBmLLRxnn BLane BTruck( ) DFSBmax  BBmLLRxnn 47.358 kipbeam Torsion due to the eccentricity of CL of Bearing and CL of Bent without Impact

229 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT TorsionLLn max FBmLLRxnn BBmLLRxnn  ebrg TorsionLLn 51.305 kftbeam CENTRIFUGAL FORCE: CF (AASHTO LRFD 3.6.3) Skew Angle of Bridge, θ 0 deg Design Speed v 45 mph f g( ) 4 3 32.2 ft sec2   Degree of Curve, ϕc 0.00001 deg (Input 4o curve or 0.00001o for 0o curve) Radius of Curvature, Rc 360 deg( ) 100 ft 2 π ϕc  Rc 572957795.131 ft Rc ∞ ft=  Centri. Force Factor, C f v2 Rc g  AASHTO LRFD EQ 3.6.3 1( ) C 0 Pcf C TruckT NofLane( ) m( ) Pcf 0 kip Centrifugal force parallel to bent (X-direction) CFX Pcf cos θ( ) NofBm   CFX 0 kip beam  Centrifugal force normal to bent (Z-direction) CFZ Pcf sin θ( ) NofBm   CFZ 0 kip beam  Moments at cg of the Bent Cap due to Centrifugal Force MCF_X CFZ h6 hCap 2   MCF_X 0 kft beam  MCF_Z CFX h6 hCap 2   MCF_Z 0 kft beam  BRAKING FORCE: BR (AASHTO LRFD 3.6.4) The braking force shall be taken as maximum of 5% of the Resultant Truck plus lane load OR 5% of the Design Tandem plus Lane Load or 25% of the design truck. Pbr1 5% Lane TruckT( ) NofLane( ) m( ) Truck Lane( ) Pbr1 14.892 kip Pbr2 5% Lane 50 kip( ) NofLane( ) m( ) Tandem Lane( ) Pbr2 12.087 kip Pbr3 25% TruckT( ) NofLane( ) m( ) DesignTruck( ) Pbr3 kip Pbr max Pbr1 Pbr2 Pbr3  Pbr 45.9 kip Braking force parallel to bent (X-direction) BRX Pbr sin θ( ) NofBm  BRX 0 kip beam 

230 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Braking force normal to bent (Z-direction) BRZ Pbr cos θ( ) NofBm  BRZ 3.825 kip beam  Moments at cg of the Bent Cap due to Braking Force MBR_X BRZ h6 hCap 2   MBR_X 46.601 kft beam  MBR_Z BRX h6 hCap 2   MBR_Z 0 kft beam  WATER LOADS: WA (AASHTO LRFD 3.7) Note : To be applied only on bridge components below design high water surface. Substructure: V 0 ft sec  (Design Stream Velocity) Specific Weight, γwater 62.4 pcf Longitudinal Stream Pressure: AASHTO LRFD 3.7.3.1 AASHTO LRFD Table 3.7.3.1-1 for Drag Coefficient, CD semicircular-nosed pier 0.7 square-ended pier 1.4 debries lodged against the pier 1.4 wedged-nosed pier with nose angle 90 deg or less 0.8 Columns and Drilled Shafts: Longitudinal Drag Force Coefficient for Column, CD_col 1.4 Longitudinal Drag Force Coefficient for Drilled Shaft, CD_ds 0.7 pT CD V2 2 g γwater= (Longitudinal stream pressure) AASHTO LRFD EQ (C3.7.3.1-1) pT_col CD_col V2 2 g γwater pT_col 0 ksf pT_ds CD_ds V2 2 g γwater pT_ds 0 ksf Lateral Stream Pressure: AASHTO LRFD 3.7.3.2

231 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT AASHTO LRFD Table 3.7.3.2-1 for Lateral Drag Coefficient, CL Angle,, between direction of flowr and longitudina axis of the pie 0deg 0 5deg 0.5 10deg 0.7 20deg 0.9 >30deg 1 CL Lateral Drag Force Coefficient, CL 0.0 Lateral stream pressure, pL CL V2 2 g γwater pL 0 ksf Bent Cap: Longitudinal stream pressure CL 1.4 pTcap CL V2 2 g γwater pTcap 0 ksf WA on Columns Water force on column parallel to bent (X-direction) WAcol_X wCol pT_col WAcol_X 0 kip ft  If angle between direction of flow and longitudinal axis of pile = 0 then apply load at one exterior column only otherwise apply it on all columns. WA at all columns will be distributed uniformly rather than triangular distribution on Column Height. Water force on column normal to bent (Z-direction) WAcol_Z bCol pL WAcol_Z 0 kip ft  WA on Drilled Shafts Water force on drilled shaft parallel to bent (X-direction) WAdshaft_X DsDia pT_ds WAdshaft_X 0 kip ft  Water force on drilled shaft normal to bent (Z-direction) WAdshaft_Z DsDia pL WAdshaft_Z 0 kip ft  WA on Bent Cap (input as a punctual load) Water force on bent cap parallel to bent (X-direction) WAcap_X wCap hCap pTcap  (If design HW is below cap then input zero) WAcap_X 0 kip Water force on bent cap normal to bent (Z-direction) WAcap_Z hCap pL (If design HW is below cap then input zero) WAcap_Z 0 kip ft  WIND ON SUPERSTRUCTURE: WS (AASHTO LRFD 3.8.1.2.2) Note : Wind Loads to be applied only on bridge exposed components above water surface

232 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT AASHTO LRFD Table 3.8.1.2.2-1 specifies the wind load components for various angles of attack. In order to simplify the analysis, this calculation considers as default values those for girders which generate the maximum effect on structure. The results can be considered as conservative. For a superstructure other than a girder type and/or for a more detailed analysis, use the proper values as specified in the above mentioned table. AASHTO LRFD table 3.8.1.2.2-1 (modified) If the bridge is approximately 30’ high and local wind velocities are known to be less than 100 mph, wind load for this bridge should be from AASHTO LRFD TABLE 3.8.2.2-1. Otherwise use AASHTO LRFD EQ 3.8.1.2.1-1 as mentioned above. ptsup 0.05ksf Normal to superstructure (conservative suggested value 0.050 ksf) plsup 0.012ksf Along Superstructure (conservative suggested value 0.019 ksf) WSchk if ptsup hsup 0.3 klf "OK" "N.G."  WSchk "OK" WsupLong plsup hsup TribuLength NofBm  WsupLong 0.436 kip beam  WsupTrans ptsup hsup TribuLength NofBm  WsupTrans 1.816 kip beam  Wind force on superstructure parallel to bent (X-direction) WSsuper_X WsupLong sin θ( ) WsupTrans cos θ( ) WSsuper_X 1.816 kipbeam Wind force on superstructure normal to bent (Z-direction) WSsuper_Z WsupLong cos θ( ) WsupTrans sin θ( ) WSsuper_Z 0.436 kipbeam Moments at cg of the Bent Cap due to Wind load on superstructure Msuper_X WSsuper_Z hCap 2 BrgTh hsup 2   Msuper_X 2.573 kft beam  Msuper_Z WSsuper_X hCap 2 BrgTh hsup 2   Msuper_Z 10.72 kft beam  WIND ON SUBSTRUCTURE: WS (AASHTO LRFD 3.8.1.2.3) Base Wind pressure, psub 0.04 ksf will be applied on exposed substructure both transverse & longitudinal direction Wind on Columns Wind force on columns parallel to bent (X-direction)

233 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT WScol_X psub bCol cos θ( ) wCol sin θ( )( )  WScol_X 0.16 kip ft  Apply WS loads at all columns even with zero degree attack angle. Wind force on columns normal to bent (Z-direction) WScol_Z psub bCol sin θ( ) wCol cos θ( )( )  WScol_Z 0.16 kip ft  Wind on Bent Cap & Ear Wall WSew_X psub hEarWall wEarWall sin θ( ) wCap cos θ( )( ) WSew_X 0 kip WSew_Z psub hEarWall wEarWall cos θ( ) wCap sin θ( )( ) WSew_Z 0 kip Wind force on bent cap parallel to bent (X-direction) WScap_X psub hCap CapL sin θ( ) wCap cos θ( )( )  WSew_X (punctual load) WScap_X 0.9 kip Wind force on bent cap normal to bent (Z-direction) WScap_Z psub hCap CapL cos θ( ) wCap sin θ( )( )  WSew_Z CapL  WScap_Z 0.2 kip ft  WIND ON VEHICLES: WL (AASHTO LRFD 3.8.1.3) AASHTO LRFD Table 3.8.1.3-1 specifies the wind on live load components for various angles of attack. In order to simplify the analysis, this calculation considers as default values the maximum wind components as defined in the above mentioned table. The results can be considered conservative. For a more detailed analysis, use the proper skew angle according to the table. AASHTO LRFD table 3.8.1.3-1 (suggested value 0.1 kip/ft) pWLt 0.1 kip ft  (suggested value 0.038 kip/ft) pWLl 0.04 kip ft  WLPar pWLl TribuLength NofBm  WLPar 0.233 kip beam  WLNor pWLt TribuLength NofBm  WLNor 0.583 kip beam  Wind force on live load parallel to bent (X-direction)

234 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT WLX WLNor cos θ( ) WLPar sin θ( ) WLX 0.583 kipbeam Wind force on live load normal to bent (Z-direction) WLZ WLNor sin θ( ) WLPar cos θ( ) WLZ 0.233 kipbeam Moments at cg of the Bent Cap due to Wind load on Live Load MWL_X WLZ h6 hCap 2   MWL_X 2.843 kft beam  MWL_Z WLX h6 hCap 2   MWL_Z 7.107 kft beam  Vertical Wind Pressure: (AASHTO LRFD 3.8.2) DeckWidth FDeckW Bridge deck width including parapet and sidewalk Puplift 0.02ksf( ) DeckWidth TribuLength (Acts upword Y-direction) Puplift 66.033 kip Applied at the windward quarter-point of the deck width. Note: Applied only for Strength III and for Service IV for minimum permanent loads only. (AASHTO LRFD table 3.4,1-2, factors for permanent loads) Load Combinations: using AASHTO LRFD Table 3.4.1-1 STRENGTH_I 1.25 DC 1.5 DW 1.75 LL BR CF( ) 1.0 WA= STRENGTH_IA 0.9 DC 0.65 DW 1.75 LL BR CF( ) 1.0 WA= STRENGTH_III 1.25 DC 1.5 DW 1.4 WS 1.0 WA 1.4 Puplift= STRENGTH_IIIA 0.9 DC 0.65 DW 1.4 WS 1.0 WA 1.4 Puplift= STRENGTH_V 1.25 DC 1.5 DW 1.35 LL BR CF( ) 0.4 WS 1.0 WA 1.0 WL= STRENGTH_VA 0.9 DC 0.65 DW 1.35 LL BR CF( ) 0.4 WS 1.0 WA 1.0 WL= SERVICE_I 1.0 DC 1.0 DW 1.0 LLno_Impact BR CF  0.3 WS 1.0 WA 1.0 WL= All these loadings as computed above such as DC, DW, LL, WL, WA, WS etc. are placed on the bent frame composed of bent cap and columns and drilled shafts. The frame is analyzed in RISA using load combinations as stated above. Output Loadings for various load combinations for column and drilled shaft are used to run PCA Column program to design the columns. It is found that 4'X4' Column with 20~#11 bars is sufficient for the loadings. Drilled shaft or other foundation shall be designed for appropriate loads. Total Vertical Foundation Load at Service I Limit State: Forward Span Superstructure DC (FFDC) & DW (FFDW):

235 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT FFDC FNofBm 2( ) FSuperDCInt 2 FSuperDCExt FFDC 259.607 kip FFDW FNofBm( ) FSuperDW FFDW 38.5 kip Backward Span Superstructure DC (FBDC) & DW (FBDW): FBDC BNofBm 2( ) BSuperDCInt 2 BSuperDCExt FBDC 259.607 kip FBDW BNofBm( ) BSuperDW FBDW 38.5 kip Total Cap Dead Load Weight (TCapDC): CapDC CapDC1 CapL LFoam( ) CapDC2 LFoam CapDC 126.979 kip TCapDC CapDC NofBm( ) BrgSeatDC( ) EarWallDC TCapDC 126.979 kip Total DL on columns including Cap weight (FDC): FDL FFDC FFDW  FBDC FBDW  TCapDC FDL 723.194 kip Column & Drilled Shaft Self Weight: DSahft Length, DsHt 0 ft if Rounded Col, ColDia 0 ft ColDC if ColDia 0ft π 4 ColDia( )2 HCol( ) γc wCol bCol HCol γc  Column Wt, ColDC 52.8 kip DsDC π 4 DsDia( )2 DsHt( ) γc Dr Shaft Wt, DsDC 0 kip Total Dead Load on Drilled Shaft (DL_on_DShaft): DL_on_DShaft FDL NofCol( ) ColDC( ) NofDs( ) DsDC( ) DL_on_DShaft 828.794 kip Live Load on Drilled Shaft: m 0.85 (Multiple Presence Factors for 3 Lanes) AASHTO LRFD Table 3.6.1.1.2 1( RLL Lane Truck( ) NofLane( ) m( ) (Total LIVE LOAD without Impact) RLL 277.44 kip Total Load, DL+LL per Drilled Shaft of Intermediate Bent: Load_on_DShaft DL_on_DShaft RLL NofDs  Load_on_DShaft 276.6 ton

236 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 5. PRECAST COMPONENT DESIGN Precast Cap Construction and Handling: w1 b h γc applicable for 0 ft Lcap 6 ft w1 3.375 klf (Cap selfweight) w2 b h 2 wFoam hFoam( ) γc applicable for 6 ft Lcap 41 ft w2 2.471 klf (Cap selfweight) w3 b h γc applicable for 41 ft Lcap 47 ft w3 3.375 klf (Cap selfweight) l1 6 ft l2 35 ft l3 6 ft Lcap l1 l2 l3 (Total Cap Length) Lcap 47 ft Due to the location of girder bolts, pickup points at 8' from both ends. Indeed, we can model cap lifting points as simply supported beam under self weight supported at 8' and 39' respectively from very end.   l2 = 35 ft l1 = 6 ft  l3 = 6 ft lc = 8 ftlb = 31 ft la = 8 ft  la 8 ft lb 31 ft lc 8ft Construction factor: λcons 1.25 λcons 1.25 Maximum Positive Moment (MmaxP) & Negative Moment (MmaxN): Rxn 0.5 w1 l1 w2 l2 w3 l3  Rxn 63.49 kip MmaxP Rxn lb 2  w1 l1 l1 2 la l1 lb 2   w2 2 la l1 lb 2   2  MmaxP 190.617 kft MmaxN w1 l1 l1 2 la l1   w2 2 la l1 2 MmaxN 106.192 kft Factored Maximum Positive Moment (MuP) & Negative Moment (MuN): MuP λcons MmaxP (Positive Moment at the middle of the cap) MuP 238.271 kft MuN λcons MmaxN (Negative Moment at the support point) MuN 132.74 kft Maximum Positive Stress (ftP) & Negative Stress (ftN):

237 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ftP MuP h ycg2  Icap2  ftP 95.657 psi ftN MuN ycg2 Icap2  ftN 52.644 psi Modulus of Rupture: According PCI hand book 6th edition modulus of rupture, fr = 7.5\/f'c is divided by a safety factor 1.5 in order to design a member without cracking f'c 5 ksi (Compressive Strength of Concrete) Unit weight factor, λ 1 fr 5 λ f'c psi (PCI EQ 5.3.3.2) fr 353.553 psi fr_check if fr ftP  fr ftN  "OK" "N.G."  fr_check "OK" Precast Column Construction and Handling: wCol 4 ft (Column width) Column breadth, bCol 4 ft wcol wCol bCol γc (Column self weight) wcol 2.4 klf Due to the location of girder bolts on column, pickup points at 3' from both ends. Indeed, we can model column lifting points as simply supported beam under self weight supported at 3' and 19' respectively from very end.   w  = 2.4 klf lc = 3 ft lb = 16 ftla = 3 ft  la 3 ft lb 16 ft lc 3 ft Maximum Positive Moment (MmaxP) & Negative Moment (MmaxN): MmaxP wcol HCol 2 HCol 4 la  MmaxP 66 kft MmaxN wcol la 2 2  MmaxN 10.8 kft Factored Maximum Positive Moment (MuP) & Negative Moment (MuN): MuP λcons MmaxP MuP 82.5 kft MuN λcons MmaxN MuN 13.5 kft

238 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Scol wCol bCol2 6  (Column Section Modulus) Scol 18432 in 3 Maximum Positive Stress (ftP) & Negative Stress (ftN): ftP MuP Scol  ftP 53.711 psi ftN MuN Scol  ftN 8.789 psi Modulus of Rupture: According PCI hand book 6th edition modulus of rupture, fr = 7.5\/f'c is divided by a safety factor 1.5 in order to design a member without cracking f'c 5 ksi (Compressive Strength of Concrete) Unit weight factor, λ 1 fr 5 λ f'c psi (PCI EQ 5.3.3.2) fr 353.553 psi fr_check if fr ftP  fr ftN  "OK" "N.G."  fr_check "OK" DEVELOPMENT LENGTH: AASHTO LRFD 5.11 Ab 1.56 in 2 (Area of Bar) db 1.41 in (Diameter of Bar) f'c 5 ksi Modification Factor: According to AASHTO LRFD 5.11.2.1.2, the basic development length, ldb is required to multiply by the modification factor to obtain the development length ld for tension or compression. λmod 1.0 Basic Tension Development: AASHTO LRFD 5.11.2.1 for bars upto #11 ldb max 1.25 Ab in   fy f'c ksi  0.4 db fy ksi  12 in    (AASHTO LRFD 5.11.2.1.1) ldb 52.324 in ld λmod  ldb ld 4.36 ft Basic Compression Development: AASHTO LRFD 5.11.2.2 ldb max 0.63 db fy f'c ksi 0.3 db fy ksi  8 in    AASHTO LRFD EQ 5.11.2.2.1 1 2( ) ldb 25.38 in ld λmod  ldb ld 2.115 ft

239 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ABC SAMPLE CALCULATION – 3b Precast Pier Design for ABC (70’ Conventional Pier)

240 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT PRECAST PIER DESIGN FOR ABC (70' SPAN CONVENTIONAL PIER) Nomenclature kip 1000 lb * plf lb ft klf kip ft  ksi kip in2  psi lb in2  kcf kip ft3  ksf kip ft2  pcf lb ft3  incr 1 kft kip ft beam 1psf lb ft2  wingwall 1 lane 1 SlabTh = Thickness of Slab, in BmWt = Weight of Beam per unit length, klf BmSpa = Spacing of beams, ft Haunch = Haunch thickness, in wcap = Width of Abutment/Bent Cap, ft hcap = Depth of Abutment/Bent Cap, ft Railwt =Weight of rail per unit length, klf Ohang = Length of overhang from centreline of the edge beam, ft BmH = height of beam, in BmFlange = Top flange Width of the Beam, in NofCol = Number of Columns per bent DsH = length of Drilled shaft from pt. of fixity to col base, ft DsDia= Shaft diameter, ft ColH = ht of column, ft V= Stream flo velocity, ft/sec Ncomp =Normal wind load component, kip/ft Pcomp= Parallel wind load component, kip/ft BrWidth = Overall Bridge width, ft CapL = Length of Bent cap, ft h’= superstructure depth below surface of water, ft LatLoad = Wind pressure normal to superstructure, ksf LongLoad= wind pressure parallel to superstructure, ksf Steel 1 Concrete 2 Nomenclature FNofBm Total Number of Beams in Forward Span= BNofBm Total Number of Beams in Backward Span= FSpan Forward Span Length= BSpan Backward Span Length= FDeckW Out to Out Forward Span Deck Width= BDeckW Out to Out Backward Span Deck Width= FBmAg Forward Span Beam X Sectional Area= BBmAg Backward Span Beam X Sectional Area= FBmFlange Forward Span Beam Top Flange Width= BBmFlange Backward Span Beam Top Flange Width= FHaunch Forward Span Haunch Thickness= BHaunch Backward Span Haunch Thickness= FBmD Forward Span Beam Depth or Height= BBmD Backward Span Beam Depth or Height= FBmIg Forward Span Beam Moment of Inertia= BBmIg Backward Span Beam Moment of Inertia=

241 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT yFt Forward Span Beam Top Distance from cg= yBt Backward Span Beam Top Distance from cg= NofCol Number of Columns per Bent=SlabTh Slab Thickness= NofDs Number of Drilled Shaft per Bent=RailWt Railing Weight= wCol Width of Column Section=RailH Railing Height= bCol Breadth of Column Section=RailW Rail Base Width= DsDia Drilled Shaft Diameter=DeckOH Deck Overhang Distance= HCol Height of Column=DeckW Out to Out Deck Width at Bent= wEarWall Width of Ear Wall=RoadW Roadway Width= hEarWall Height of Ear Wall=BrgTh Bearing Pad Thickness Bearing Seat Thickness= tEarWall Thickness of Ear Wall=NofLane Number of Lanes= tSWalk Thickness of Side Walk=wCap Cap Width= bSWalk Breadth of Side Walk=hCap Cap Depth= CapL Cap Length= BmMat Beam Material either Steel or Concrete= γc Unit Weight of Concrete= DiapWt Weight of Diaphragm= wc Unit Weight of Concrete= γst Unit Weight of Steel= SlabDCInt Dead Load for Slab per Interior Beam= SlabDCExt Dead Load for Slab per Exterior Beam= BeamDC Self Weight of Beam= HaunchDC Dead Load of Haunch Concrete per Beam= RailDC Weight of Rail per Beam= FSuperDCInt Half of Forward Span Super Structure Dead Load Component per Interior Beam= FSuperDCExt Half of Forward Span Super Structure Dead Load Component per Exterior Beam= FSuperDW Half of Forward Span Overlay Dead Load Component per Beam= BSuperDCInt Half of Backward Span Super Structure Dead Load Component per Interior Beam= BSuperDCExt Half of Backward Span Super Structure Dead Load Component per Exterior Beam= BSuperDW Half of Backward Span Overlay Dead Load Component per Beam= TorsionDCInt DeadLoad Torsion in a Cap due to difference in Forward and Backward span length per Interior Beam= TorsionDCExt DeadLoad Torsion in a Cap due to difference in Forward and Backward span length per Exterior Beam= TorsionDW DW Torsion in a Cap due to difference in Forward and Backward span length per Beam=

242 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT tBrgSeat Thickness of Bearing Seat= bBrgSeat Breadth of Bearing Seat=

243 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Note: Use of Light Weight Concrete (LWC) may be considered to reduce the weight of the pier cap instead of using styrofoam blockouts.

244 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT FORWARD SPAN PARAMETER INPUT: FNofBm 12 FSpan 70 ft FDeckW 283 6 ft FBmAg 29.1 in2 FBmFlange 10.5 in yFt 14.85 inFHaunch 0 in FBmD 29.7 in FBmIg 3990 in4 BACKWARD SPAN PARAMETER INPUT: BNofBm 12 BSpan 70 ft BDeckW 283 6 ft BBmAg 29.1 in2 BBmFlange 10.5 in yBt 14.85 inBHaunch 0 in BBmD 29.7 in BBmIg 3990 in4 COMMON BRIDGE PARAMETER INPUT: Bent in Question Parameters SlabTh 9 in Overlay 25 psf θ 0 deg DeckOH 1.75 ft BrgTh 3.5 in RailWt 0.43 klf RailW 19 in RailH 34.0 in tBrgSeat 0 in bBrgSeat 0 ft DeckW 283 6 ft NofLane 3 m 0.85 wc 0.150 kcf f'c 5 ksi Cap( ) wCap 4.0 ft hCap 4.0 ft CapL 47 ft NofDs 2 DsDia 5 ft wCol 3.5 ft bCol 3.5 ft NofCol 2 HCol 22.00 ft f'cs 4 ksi Slab( ) γc 0.150 kcf ebrg 13 in NofBm 12 Sta 0.25 ftincr DiapWt 0.2 kip wEarWall 0 ft hEarWall 0 ft tEarWall 0 in IM 0.33 BmMat Steel Es 29000 ksi γst 490 pcf steel( ) Modulus of elasticity of Concrete: E fc  33000 wc 1.5 fc ksi (AASHTO LRFD EQ 5.4.2.4-1 for K1 = 1) Eslab E f'cs  Eslab 3834.254 ksi Ecap E f'c  Ecap 4286.826 ksi Modulus of Beam or Girder: Input Beam Material, BmMat = Steel or Concrete Ebeam if BmMat Steel= Es E f'c   Ebeam 29000 ksi

245 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 1. BENT CAP LOADING DEAD LOAD FROM SUPERSTRUCTURE: The permanent dead load components (DC) consist of slab, rail, sidewalk, haunch weight and beam self weight. Slab Dead weight components will be distributed to each beam by slab tributary width between beams. Interior Beam tributary width (IntBmTriW) is taken as the average of consecutive beam spacing for a particular interior beam. Exterior Beam tributary width (ExtBmTriW) is taken as half of beam spacing plus the overhang distance. Rail, sidewalk dead load components and future wearing surface weight components (DW) can be distributed evenly among each beam. Half of DC and DW components from forward span and backward span comprise the total superstructure load or dead load reaction per beam on the pier cap or the bent cap. FORWARD SPAN SUPERSTRUCTURE DEAD LOAD: consists of 12 W30x99 Beams 12 beams were spaced 4.5' and 3'-4" alternately in forward span. For beam spacing see Typical Section Details sheet FBmSpa1 4.5 ft FBmSpa2 10 3 ft FIntBmTriW FBmSpa1 2 FBmSpa2 2  FIntBmTriW 3.917 ft FExtBmTriW FBmSpa1 2 DeckOH FExtBmTriW 4 ft RoadW 0.25 FDeckW 3 DeckW( ) 2 RailW RoadW 44 ft SlabDCInt γc FIntBmTriW SlabTh FSpan2   SlabDCInt 15.422 kip beam  SlabDCExt γc FExtBmTriW SlabTh FSpan2   SlabDCExt 15.75 kip beam  BeamDC γst FBmAg FSpan2   BeamDC 3.466 kip beam  HaunchDC γc FHaunch FBmFlange FSpan2   HaunchDC 0 kip beam  NOTE: Permanent loads such as the weight of the Rail (Barrier), Future wearing surface may be distributed uniformly among all beams if following conditions are met. Apply for live load distribution factors too. AASHTO LRFD 4.6.2.2.1 1. Width of deck is constant 2. Number of Beams >= 4 beams 3. Beams are parallel and have approximately same stiffness 4. The Roadway part of the overhang, de<= 3ft 5. Curvature in plan is < 4o 6. Bridge cross-section is consistent with one of the x-section shown in AASHTO LRFD TABLE 4.6.2.2.1-1 RailDC 2 RailWt FNofBm FSpan 2   RailDC 2.508 kip beam 

246 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT OverlayDW RoadW Overlay FNofBm FSpan 2   OverlayDW 3.208 kip beam  Forward Span Superstructure DC & DW per Interior and Exterior Beam: FSuperDCInt RailDC BeamDC SlabDCInt HaunchDC DiapWt FSuperDCInt 21.596 kip beam  FSuperDCExt RailDC BeamDC SlabDCExt HaunchDC 0.5 DiapWt FSuperDCExt 21.824 kip beam  FSuperDW OverlayDW FSuperDW 3.208 kip beam  BACKWARD SPAN SUPERSTRUCTURE DEAD LOAD: consists of 12 W30x99 beams 12 beams were spaced 4.5' and 3'-4" alternately in Backward span. For beam spacing see Typical Section Details sheet BBmSpa1 4.5 ft BBmSpa2 10 3 ft BIntBmTriW BBmSpa1 2 BBmSpa2 2  BIntBmTriW 3.917 ft BExtBmTriW BBmSpa1 2 DeckOH BExtBmTriW 4 ft RoadW 0.25 BDeckW 3 DeckW( ) 2 RailW RoadW 44 ft SlabDCInt γc BIntBmTriW SlabTh BSpan2   SlabDCInt 15.422 kip beam  SlabDCExt γc BExtBmTriW SlabTh BSpan2   SlabDCExt 15.75 kip beam  BeamDC γst BBmAg BSpan2   BeamDC 3.466 kip beam  HaunchDC γc BHaunch BBmFlange BSpan2   HaunchDC 0 kip beam  RailDC 2 RailWt BNofBm BSpan 2   RailDC 2.508 kip beam  OverlayDW RoadW Overlay BNofBm BSpan 2   OverlayDW 3.208 kip beam  Total Backward Span Superstructure DC & DW per Interior and Exterior Beam: BSuperDCInt RailDC BeamDC SlabDCInt HaunchDC DiapWt BSuperDCInt 21.596 kip beam  BSuperDCExt RailDC BeamDC SlabDCExt HaunchDC 0.5 DiapWt BSuperDCExt 21.824 kip beam 

247 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT BSuperDW OverlayDW BSuperDW 3.208 kip beam  Total Superstructure DC & DW Reactions per Beam on Bent Cap: SuperDCInt FSuperDCInt BSuperDCInt SuperDCInt 43.192 kip beam  SuperDCExt FSuperDCExt BSuperDCExt SuperDCExt 43.648 kip beam  SuperDW FSuperDW BSuperDW SuperDW 6.417 kip beam  TorsionDCInt max FSuperDCInt BSuperDCInt  min FSuperDCInt BSuperDCInt   ebrg TorsionDCInt 0 kftbeam TorsionDCExt max FSuperDCExt BSuperDCExt  min FSuperDCExt BSuperDCExt   ebrg TorsionDCExt 0 kftbeam TorsionDW max FSuperDW BSuperDW( ) min FSuperDW BSuperDW( )( ) ebrg TorsionDW 0 kft beam  CAP, EAR WALL & BEARING SEAT WEIGHT: The bent cap has only one solid section along the length. The solid rectangular section of 4'X4' can be seen in typical section and pier elevation figure. CapDC is the weight of the section of the bent or pier cap. CapDC wCap hCap γc CapDC 2.4 klf CapDCsta wCap hCap γc  Sta( ) CapDCsta 0.6 kipincr EarWallDC wEarWall hEarWall tEarWall( ) γc EarWallDC 0 kip BrgSeatDC tBrgSeat bBrgSeat wCap( ) γc BrgSeatDC 0 kipbeam EIcap Ecap wCap hCap3 12   EIcap 1.317 10 7 kip ft2 Distribution Factor RESULTS OF DISTRIBUTION FACTORS: Forward Span Distribution Factors: DFMFmax 0.391 (Distribution Factor for Moment) DFSFmax 0.558 (Distribution Factor for Shear) Backward Span Distribution Factors:

248 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT DFMBmax 0.391 (Distribution Factor for Moment) DFSBmax 0.558 (Distribution Factor for Shear) LIVE LOAD FOR SIMPLY SUPPORTED BRIDGE: HL-93 Loading: According to AASHTO LRFD 3.6.1.2.1 HL-93, consists of Design Truck + Design Lane Load or Design Tandem + Design Lane Load. Design Truck rather than Design Tandem + Design Lane Load controls the maximum Live Load Reactions at an interior bent for a span longer than 26'. For maximum reaction, place middle axle (P2 = 32 kip) of design truck over the support at a bent between the forward and the backward span and place rear axle (P3 = 32 kip) 14' away from P2 on the longer span while placing P1 14' away from P1 on either spans yielding maximum value. P1 Front Axle of Design Truck= P2 Middle Axle of Design Truck= P3 Rear Axle of Design Truck= Design Truck Axle Load: P1 8 kip P2 32 kip P3 32 kip AASHTO LRFD 3.6.1.2.2( ) TruckT P1 P2 P3 Design Lane Load: wlane 0.64 klf AASHTO LRFD 3.6.1.2.4( ) Longer Span Length, Llong max FSpan BSpan( ) Shorter Span Length, Lshort min FSpan BSpan( ) Lane Load Reaction: Lane wlane Llong Lshort 2   Lane 44.8 kip lane  Truck Load Reaction: Truck P2 P3 Llong 14ft  Llong  P1 max Llong 28ft  Llong Lshort 14ft  Lshort      Truck 64 kip lane  Maximum Live Load Reaction with Impact (LLRxn) over support on Bent: The Dynamic Load Allowance or Impact Factor, IM 0.33 AASHTO LRFD Table 3.6.2.1 1( ) LLRxn Lane Truck 1 IM( ) LLRxn 129.92 kip lane  Live Load Model for Cap Loading Program: AASHTO LRFD Recommended Live Load Model For Cap Loading Program: Live Load reaction on the pier cap using distribution factors are not sufficient to design bent cap for moment and shear. Therefore, the reaction from live load is uniformly distributed to over a 10' width (which becomes W) and the reaction from the truck is applied as two concentrated loads (P and P) 6' apart. The loads act within a 12' wide traffic lane. The reaction W and the truck move across the width of the traffic lane. However, neither of the P loads can be placed closer than 2' from the edge of the traffic lane. One lane, two lane, three lane and so forth loaded traffic can be moved across the width of the roadway to create maximum load effects. Load on one rear wheel out of rear axle of the truck with Impact: P 0.5 P3  1 IM( ) P 21.28 kip The Design Lane Load Width Transversely in a Lane wlaneTransW 10 ft AASHTO LRFD Article 3.6.1.2.1 The uniform load portion of the Live Load, kip/station for Cap Loading Program:

249 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT W LLRxn 2 P( ) Sta wlaneTransW  W 2.184 kip incr  LOADS generated above will be placed into a CAP LOADING PROGRAM to obtain moment and shear values for Bent Cap design. Torsion on Bent Cap per Beam and per Drilled Shaft: Torsional load about center line of bent cap occurs due to horizontal loads acting on the superstructure perpendicular to the bent length or along the bridge length. Braking force, Centrifugal force, WS on superstructure, and WL cause torsion on bent. In addition, torque about center line of bent cap for the dead load reaction on beam brg location occurs due to differences in forward and backward span length and eccentricity between center line of bent cap and brg location. Torsion can be neglected if Tu<0.25Tcr (AASHTO LRFD 5.8.2.1) The maximum torsional effects on the pier cap will be obtained from RISA frame analysis under loading as stated in AASHTO LRFD SECTION 3 for different load combinations using AASHTO LRFD Table 3.4.1-1

250 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 2. BENT CAP FLEXURAL DESIGN FLEXURAL DESIGN OF BENT CAP: h( ) b( ) f'c 5.0 ksi fy 60 ksi Es 29000 ksi ϕm 0.9 ϕv 0.9 ϕn 1 γc 0.150 kcf bcover 2.5 in tcover 2.5 in h 4.0 ft b 4.0 ft Ec Ecap OUTPUT of BENT CAP LOADING PROGRAM: The maximum load effects from different applicable limit states: DEAD LOAD MdlPos 627.2 kft MdlNeg 783.4 kft SERVICE I MsPos 1462.5 kft MsNeg 1297.7 kft STRENGTH I MuPos 1900.5 kft MuNeg 2262.8 kft

251 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT FLEXURE DESIGN: Minimum Flexural Reinforcement AASHTO LRFD 5.7.3.3.2 Factored Flexural Resistance, Mr, must be greater than or equal to the lesser of 1.2Mcr or 1.33 Mu. Applicable to both positive and negative moment. Modulus of rupture fr 0.37 f'c ksi (AASHTO LRFD EQ 5.4.2.6) fr 0.827 ksi S b h2 6  (Section Modulus) S 18432 in3

252 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Cracking moment Mcr S fr (AASHTO LRFD EQ 5.7.3.3.2-1) Mcr 1270.802 kip ft Mcr1 1.2 Mcr Mcr1 1524.963 kip ft Mcr2 1.33 max MuPos MuNeg  Mcr2 3009.524 kip ft Mcr_min min Mcr1 Mcr2  Therefore Mr must be greater than Mcr_min 1524.963 kip ft Moment Capacity Design (Positive Moment, Bottom Bars B) AASHTO LRFD 5.7.3.2 Bottom Steel arrangement for the Cap: Input no. of total rebar in a row from bottom of cap up to 12 rows (in unnecessary rows input zero) Np 5 5 0 0 0 0 0 0 0 0 0 0( ) Input area of rebar corresponding to above rows from bottom of cap, not applicable for mixed rebar in a single row Abp 1.56 1.56 0 0 0 0 0 0 0 0 0 0( ) in 2 Input center to center vertical distance between each rebar row starting from bottom of cap clp 3.5 4 0 0 0 0 0 0 0 0 0 0( ) in dc Calc for Pos Moment nsPos 2 (No. of Bottom or Positive Steel Layers) Distance from centroid of positive rebar to extreme bottom tension fiber (dcPos): dcPos Ayp0 0  in dcPos 5.5 in Effective depth from centroid of bottom rebar to extreme compression fiber (dPos): dPos h dcPos dPos 42.5 in Compression Block depth under ultimate load AASHTO LRFD 5.7.2.2 β1 min 0.85 max 0.65 0.85 0.05ksi f'c 4 ksi    β1 0.8 The Amount of Bottom or Positive Steel As Required, b 48 in AsReq 0.85 f'c b dPos fy     1 1 2 MuPos 0.85 ϕm f'c b dPos2       AsReq 10.305 in 2 The Amount of Positive As Provided,

253 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT NofBarsPos Np NofBarsPos 10 AsPos Ayp0 1  in2 AsPos 15.6 in2 Compression depth under ultimate load cPos AsPos fy 0.85 f'c β1 b  (AASHTO LRFD EQ 5.7.3.1.1-4) cPos 5.735 in aPos β1 cPos (AASHTO LRFD 5.7.3.2.2) aPos 4.588 in Nominal flexural resistance: MnPos AsPos fy dPos aPos 2   (AASHTO LRFD EQ 5.7.3.2.2-1) MnPos 3136.059 kip ft Tension controlled resistance factor for flexure ϕmPos min 0.65 0.15 dPos cPos 1     0.9     (AASHTO LRFD EQ 5.5.4.2.1-2) ϕmPos 0.9 or simply use, ϕm 0.9 (AASHTO LRFD 5.5.4.2) MrPos ϕmPos MnPos (AASHTO LRFD EQ 5.7.3.2.1-1) MrPos 2822.453 kip ft MinReinChkPos if MrPos Mcr_min  "OK" "NG"  MinReinChkPos "OK" UltimateMomChkPos if MrPos MuPos  "OK" "NG"  UltimateMomChkPos "OK" Moment Capacity Design (Negative Moment, Top Bars A) AASHTO LRFD 5.7.3.2 Top Steel arrangement for the Cap: Input no. of total rebar in a row from top of cap up to 12 rows (in unnecessary rows input zero) Nn 8 0 0 0 0 0 0 0 0 0 0 0( ) Input area of rebar corresponding to above rows from top of cap, not applicable for mixed rebar in a single row Abn 1.56 0 0 0 0 0 0 0 0 0 0 0( ) in 2 Input center to center vertical distance between each rebar row starting from top of cap cln 3.5 0 0 0 0 0 0 0 0 0 0 0( ) in dc Calc for Neg. Moment

254 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT nsNeg 1 (No. of Negative or Top Steel Layers) Distance from centroid of negative rebar to top extreme tension fiber (dcNeg): dcNeg Ayn0 0  in dcNeg 3.5 in Effective depth from centroid of top rebar to extreme compression fiber (dNeg): dNeg h dcNeg dNeg 44.5 in The Amount of Negative As Required, AsReq 0.85 f'c b dNeg fy     1 1 2 MuNeg 0.85 ϕm f'c b dNeg2       AsReq 11.757 in 2 The Amount of Negative As Provided, NofBarsNeg Nn NofBarsNeg 8 AsNeg Ayn0 1  in2 AsNeg 12.48 in2 Compression depth under ultimate load cNeg AsNeg fy 0.85 f'c β1 b  cNeg 4.588 in aNeg β1 cNeg aNeg 3.671 in Thus, nominal flexural resistance: MnNeg AsNeg fy dNeg aNeg 2   MnNeg 2662.278 kip ft MrNeg ϕm MnNeg (Factored flexural resistance) MrNeg 2396.05 kip ft MinReinChkNeg if MrNeg Mcr_min  "OK" "NG"  MinReinChkNeg "OK" UltimateMomChkNeg if MrNeg MuNeg  "OK" "NG"  UltimateMomChkNeg "OK" Control of Cracking at Service Limit State AASHTO LRFD 5.7.3.4 exposure_cond 1 (for exposure condition, input Class 1 = 1 and Class 2 = 2) γe if exposure_cond 1= 1 0.75( ) (Exposure condition factor) γe 1 sidecTop sidecBot  4.75 4.75( ) in (Input side cover for Top and Bottom Rebars) Positive Moment (Bottom Bars B) To find Smax: S is spacing of first layer of rebar closest to tension face

255 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT n round Es Ec 0     (modular ratio) (AASHTO LRFD 5.7.1) n 7 ρPos AsPos b dPos  ρPos 0.0076 kPos ρPos n 1 2 1 ρPos n (Applicable for Solid Rectangular Section) kPos 0.278 jPos 1 kPos 3  jPos 0.907 fssPos MsPos AsPos jPos dPos  fssPos 29.174 ksi(Tensile Stress at Service Limit State) dc1Pos clp0 0 (Distance of bottom first row rebar closest to tension face) dc1Pos 3.5 in βsPos 1 dc1Pos 0.7 h dc1Pos  βsPos 1.112 smaxPos 700 kip in γe βsPos fssPos 2 dc1Pos AASHTO LRFD EQ (5.7.3.4-1) smaxPos 14.57 in sActualPos b 2 sidecBot Np0 0 1 (Equal horizontal spacing of Bottom first Rebar row closest to Tension Face) sActualPos 9.625 in Actual Max Spacing in Bottom first Layer, saPosProvided 7 in sActualPos max saPosProvided sActualPos  sActualPos 9.625 in SpacingCheckPos if smaxPos sActualPos  "OK" "NG"  SpacingCheckPos "OK" Negative Moment (Top Bars A) ρNeg AsNeg b dNeg  ρNeg 0.006 kNeg ρNeg n 1 2 1 ρNeg n (Applicable for Solid Rectangular Section) kNeg 0.248 jNeg 1 kNeg 3  jNeg 0.917

256 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT fssNeg MsNeg AsNeg jNeg dNeg  fssNeg 30.567 ksi dc1Neg cln0 0 (Distance of Top first layer rebar closest to tension face) dc1Neg 3.5 in βsNeg 1 dc1Neg 0.7 h dc1Neg  βsNeg 1.112 smaxNeg 700 kip in γe βsNeg fssNeg 2 dc1Neg smaxNeg 13.587 in sActualNeg b 2 sidecTop Nn0 0 1 (Equal horizontal spacing of top first Rebar row closest to Tension Face) sActualNeg 5.5 in Actual Max Spacing Provided in Top first row closest to Tension Face, saNegProvided 11.125 in sActualNeg max saNegProvided sActualNeg  sActualNeg 11.125 in SpacingCheckNeg if smaxNeg sActualNeg  "OK" "NG"  SpacingCheckNeg "OK" SUMMARY OF FLEXURE DESIGN: Bottom Rebar or B Bars: use 10~#11 bars @ 5 bars in each row of 2 rows Top Rebar or A Bars: use 8~#11 bars @ 8 bars in top row SKIN REINFORCEMENT (BARS T) AASHTO LRFD 5.7.3.4 SkBarNo 5 (Size of a skin bar) Area of a skin bar, AskBar 0.31 in 2 dcTop cln dcTop 3.5 in dcBot clp dcBot 7.5 in Effective Depth from centroid of Extreme Tension Steel to Extreme compression Fiber (dl): dl max h clp0 0 h cln0 0  dl 44.5 in Effective Depth from centroid of Tension Steel to Extreme compression Fiber (de):

257 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT de max dPos dNeg  de 44.5 in As min AsNeg AsPos  min. of negative and positive reinforcement As 12.48 in2 dskin h dcTop dcBot  dskin 37 in Skin Reinforcement Requirement: AASHTO LRFD EQ 5.7.3.4-2 AskReq if dl 3ft min 0.012 in ft  dl 30 in  dskin As Aps4   0in 2  AskReq 0.537 in 2 NoAskbar1 R AskReq AskBar      NoAskbar1 2 per Side Maximum Spacing of Skin Reinforcement: SskMax min de 6 12 in  AASHTO LRFD 5.7.3.4 SskMax 7.417 in NoAskbar2 if dl 3ft R dskin SskMax 1     1     NoAskbar2 4 per Side NofSideBarsreq max NoAskbar1 NoAskbar2  NofSideBarsreq 4 SskRequired dskin 1 NofSideBarsreq  SskRequired 7.4 in NofSideBars 4 (No. of Side Bars Provided) SskProvided dskin 1 NofSideBars SskProvided 7.4 in SskChk if SskProvided SskMax "OK" "N.G."  SskChk "OK" Therefore Use: NofSideBars 4 and Size SkBarNo 5

258 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 3. BENT CAP SHEAR AND TORSION DESIGN SHEAR DESIGN OF CAP: Effective Shear Depth, dv max de a 2  0.9 de 0.72 h                 = (AASHTO LRFD 5.8.2.9) dv Distance between the resultants of tensile and compressive Force= ds Effective depth from cg of the nonprestressed tensile steel to extreme compression fiber= dp Effective depth from cg of the prestressed tendon to extreme compression fiber= de Effective depth from centroid of the tensile force to extreme compression fiber at critical shear Location= θ Angle of inclination diagonal compressive stress= Ao Area enclosed by shear flow path including area of holes therein= Ac Area of concrete on flexural tension side of member shown in AASHTO LRFD Figure 5.8.3.4.2 1= Aoh Area enclosed by centerline of exterior closed transverse torsion reinforcement including area of holes therein= Total Flexural Steel Area, As AsNeg As 12.48 in 2 Nominal Flexure, Mn MnNeg Mn 2662.278 kft Stress block Depth, a aNeg a 3.671 in Effective Depth, de dNeg de 44.5 in Effective web Width at critical Location, bv b bv 4 ft Input initial  θ 35 deg cotθ cot θ( ) Shear Resistance Factor, ϕv 0.9

259 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Cap Depth & Width, h 48 in b 48 in Moment Arm, de a 2   42.665 in 0.9 de 40.05 in 0.72 h 34.56 in Effective Shear Depth at Critical Location, dv max de a 2  0.9 de 0.72 h                  (AASHTO LRFD 5.8.2.9) dv 42.665 in hh h tcover bcover (Height of shear reinforcement) hh 43 in bh b 2 bcover (Width of shear reinforcement) bh 43 in ph 2 hh bh  (Perimeter of shear reinforcement) ph 172 in Aoh hh  bh  (Area enclosed by the shear reinforcement) Aoh 1849 in2 Ao 0.85 Aoh (AASHTO LRFD C5.8.2.1) Ao 1571.65 in 2 Ac 0.5 b h AASHTO LRFD FIGURE 5.8.3.4.2 1( ) Ac 1152 in 2 Yield strength & Modulus of Elasticity of Steel Reinforcement: fy Es  60 29000( ) ksi AASHTO LRFD 5.4.3.1 5.4.3.2( ) Input Mu, Tu, Vu, Nu for the critical section to be investigated: (Loads from Bent Cap & RISA Analysis) Mu Tu  1398.6 570.2( ) kft Vu Nu  463.4 0( ) kip M'u max Mu Vu Vp dv  AASHTO LRFD B5.2 M'u 1647.569 kip ft V'u Vu 2 0.9 ph Tu 2 Ao     2  (Equivalent shear) AASHTO LRFD EQ (5.8.2.1-6) for solid section V'u 572.966 kip Assuming atleast minimum transverse reinforcement is provided (Always provide min. transverse reinf.) εx M'u dv     0.5 Nu 0.5 V'u Vp  cotθ Aps fpo 2 Es As Ep Aps = (Strain from Appendix B5) AASHTO LRFD EQ (B5.2-1)

260 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT vu Vu ϕv Vp  ϕv bv dv  (Shear Stress) AASHTO LRFD EQ (5.8.2.9-1) vu 0.251 ksi r max 0.075 vu f'c      (Shear stress ratio) r 0.075 Determining Beta & Theta After Interpolating the value of Θ Β( ) Θ 36.4 deg Β 2.23 Nominal Shear Resistance by Concrete, Vc 0.0316 Β f'c ksi bv dv AASHTO LRFD EQ (5.8.3.3-3) Vc 322.7 kip Vu 463.4 kip 0.5 ϕv Vc Vp  145.211 kip REGION REQUIRING TRANSVERSE REINFORCEMENT: AASHTO LRFD 5.8.2.4 Vu 0.5 ϕv Vc Vp  AASHTO LRFD EQ (5.8.2.4-1) check if Vu 0.5 ϕv Vc Vp  "Provide Shear Reinf" "No reinf."  check "Provide Shear Reinf" Vn min Vc Vs Vp 0.25 f'c bv dv Vp         = (Nominal Shear Resistance) AASHTO LRFD EQ 5.8.3.3 1 2( ) Vs Av fy dv cotθ cotα( ) sinα S = (Shear Resistance of Steel) AASHTO LRFD EQ 5.8.3.3 4( ) Vs Av fy dv cotθ S = Shear Resistance of Steel when α 90 deg=( ) AASHTO LRFD EQ (C5.8.3.3-1) Sv 9 in (Input Stirrup Spacing) Vp 0 kip Vu Vc  463.4 322.691( ) kip fy 60 ksi dv 42.665 in Θ 36.4 deg (Derive from AASHTO LRFD EQ 5.8.3.3-1, C5.8.3.3-1 and Vn >= Vu)Av_req Vu ϕv Vc Vp     Sv fy dv cotΘ      Av_req 0.4982 in 2 Torsional Steel:

261 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT At Tu 2 ϕv Ao fy cotΘ Sv (Derive from AASHTO LRFD EQ 5.8.3.6.2-1 and Tn >= Tu) At 0.267 in 2 Avt_req Av_req 2 At Shear Torsion( ) Avt_req 1.033 in 2 Avt 4 0.44 in 2  (Use 2 #6 double leg Stirrup at Sv c/c,) Provided, Avt 1.76 in2 Avt_check if Avt Avt_req "OK" "NG"  Avt_check "OK" Maximum Spacing Check: AASHTO LRFD Article 5.8.2.7 Vu 463.4 kip 0.125 f'c bv dv 1279.94 kip Svmax if Vu 0.125 f'c bv dv min 0.8 dv 24 in  min 0.4 dv 12 in   Svmax 24 in Svmax_check if Sv Svmax "OK" "use lower spacing"  Svmax_check "OK" Av Avt At (Shear Reinf. without Torsion Reinf.) Av 1.493 in 2 Vs Av fy dv cotΘ Sv  Vs 575.804 kip Minimum Transverse Reinforce Check: AASHTO LRFD Article 5.8.2.5 bv 48 in Avmin 0.0316 f'c ksi bv Sv fy  AASHTO LRFD EQ 5.8.2.5 1( ) Avmin 0.509 in 2 Avmin_check if Avt Avmin "OK" "NG"  Avmin_check "OK" Maximum Nominal Shear: To ensure that the concrete in the web of beam will not crush prior to yield of shear reinforcement, LRFD Specification has given an upper limit of 0.25 f'c bv dv Vp 2559.882 kip Vc Vs Vp 898.495 kip Vn min Vc Vs Vp 0.25 f'c bv dv Vp          AASHTO LRFD EQ 5.8.3.3 1 2( ) Vn 898.495 kip ϕv Vn 808.645 kip Vu 463.4 kip ϕVn_check if ϕv Vn Vu "OK" "NG"  ϕVn_check "OK" Torsional Resistance,

262 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Tn 2 Ao 0.5 Avt  fy cotΘ Sv  AASHTO LRFD EQ 5.8.3.6.2 1( ) ϕv Tn 1875.9 kip ft Longitudinal Reinforcement Requirements including Torsion: AASHTO LRFD 5.8.3.6.3 AASHTO LRFD EQ 5.8.3.6.3 1( ) Applicable for solid section with Torsion Aps fps As fy M'u ϕm dv     0.5 Nu ϕn  cotΘ Vuϕv Vp 0.5 V's     2 0.45 ph Tu 2 ϕv Ao     2  ϕm ϕv ϕn  0.9 0.9 1( ) As fy Aps fps 748.8 kip M'u 1647.569 kip ft Vu 463.4 kip Nu 0 kip Vs 575.804 kip Tu 570.2 kip ft ph 172 in Vp 0 kip As 12.48 in 2 V's min Vu ϕv Vs      AASHTO LRFD 5.8.3.5 V's 514.889 kip F M'u ϕm dv     0.5 Nu ϕn  cotΘ Vuϕv Vp 0.5 V's     2 0.45 Tu ph 2 ϕv Ao     2  F 946.64 kip Fcheck if Aps fps As fy F "OK" "N.G."  AASHTO LRFD EQ 5.8.3.6.3 1( ) Fcheck "N.G." N.B.-The longitudinal reinforcement check can be ignored for typical multi-column pier cap. This check must be considered for straddle pier cap with no overhangs. Refer to AASHTO LRFD 5.8.3.5 for further information.

263 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT 4. COLUMN/DRILLED SHAFT LOADING AND DESIGN Superstructure to substructure force: AASHTO LRFD SECTION 3 LOADS and LOAD COMBINATIONS Subscript: X = Parallel to the Bent cap Length and Z = Perpendicular to the bent Cap Length th 2.5 in (Haunch Thickness) Beam Depth, BmH FBmD ColH HCol 0 ft (Column height + 0 ft Column Capital) TribuLength FSpan BSpan 2  Scour Depth: hscour 0 ft Scour to Fixity Depth: hscf min 3 DsDia 10 ft( ) Total Drilled Shaft height: DsH hscour hscf DsH 10 ft ho BrgTh BmH th SlabTh (Top of cap to top of slab height) ho 3.725 ft h6 ho 6ft (Top of cap to top of slab height + 6 ft) h6 9.725 ft

264 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT hsup BmH th SlabTh RailH (Height of Superstructure) hsup 6.267 ft h1 DsH ColH hCap 2  (Height of Cap cg from Fixity of Dshaft) h1 34 ft h2 DsH ColH hCap h6 h2 45.725 ft h3 DsH ColH hCap BrgTh hsup 2  h3 39.425 ft Tributary area for Superstructure, Asuper hsup( ) TribuLength( ) Asuper 438.667 ft 2 LIVE LOAD REACTIONS: LL Live load Reaction LL on cap can be taken only the vertical Rxn occurs when HL93 is on both the forward and backward span or when HL93 Loading is on one span only which causes torsion too. To maximize the torsion, LL only acts on the longer span between forward and backward span. For maximum reaction, place rear axle (P3 = 32 kip) over the support at bent while the design truck traveling along the span. Maximum Forward Span Design Truck (FTruck) & Lane Load Reaction (FLane): FTruck P3 P2 FSpan 14 ft( ) FSpan   P1 FSpan 28ft( ) FSpan  FTruck 62.4 kip FLane wlane FSpan 2   FLane 22.4 kip lane  Forward Span Live Load Reactions with Impact (FLLRxn): FLLRxn FLane FTruck 1 IM( ) FLLRxn 105.392 kip lane  Maximum Backward Span Design Truck (BTruck) & Lane Load Reaction (BLane): BTruck P3 P2 BSpan 14 ft( ) BSpan   P1 BSpan 28ft( ) BSpan  BTruck 62.4 kip BLane wlane BSpan 2   BLane 22.4 kip lane  Backward Span Live Load Reactions with Impact (BLLRxn): BLLRxn BLane BTruck 1 IM( ) BLLRxn 105.392 kip lane  Live Load Reactions per Beam with Impact (BmLLRxn) using Distribution Factors: BmLLRxn LLRxn( ) max DFSFmax DFSBmax  Max reaction when mid axle on support( ) BmLLRxn 72.556 kipbeam FBmLLRxn FLLRxn( ) DFSFmax Only Forward Span is Loaded( ) FBmLLRxn 58.858 kip beam  BBmLLRxn BLLRxn( ) DFSBmax Only Backward Span is Loaded( ) BBmLLRxn 58.858 kip beam  Torsion due to the eccentricity from CL of Bearing to CL of Bent when only Longer Span is loaded with HL-93 Loading

265 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT TorsionLL max FBmLLRxn BBmLLRxn( ) ebrg TorsionLL 63.763 kip ft beam  Live Load Reactions per Beam without Impact (BmLLRxnn) using Distribution Factors: BmLLRxnn Lane Truck( ) max DFSFmax DFSBmax  BmLLRxnn 60.761 kipbeam FBmLLRxnn FLane FTruck( ) DFSFmax  FBmLLRxnn 47.358 kipbeam BBmLLRxnn BLane BTruck( ) DFSBmax  BBmLLRxnn 47.358 kipbeam Torsion due to the eccentricity of CL of Bearing and CL of Bent without Impact TorsionLLn max FBmLLRxnn BBmLLRxnn  ebrg TorsionLLn 51.305 kftbeam CENTRIFUGAL FORCE: CF (AASHTO LRFD 3.6.3) Skew Angle of Bridge, θ 0 deg Design Speed v 45 mph f g( ) 4 3 32.2 ft sec2   Degree of Curve, ϕc 0.00001 deg (Input 4o curve or 0.00001o for 0o curve) Radius of Curvature, Rc 360 deg( ) 100 ft 2 π ϕc  Rc 572957795.131 ft Rc ∞=  Centri. Force Factor, C f v2 Rc g  AASHTO LRFD EQ 3.6.3 1( ) C 0 Pcf C TruckT NofLane( ) m( ) Pcf 0 kip Centrifugal force parallel to bent (X-direction) CFX Pcf cos θ( ) NofBm   CFX 0 kip beam  Centrifugal force normal to bent (Z-direction) CFZ Pcf sin θ( ) NofBm   CFZ 0 kip beam  Moments at cg of the Bent Cap due to Centrifugal Force MCF_X CFZ h6 hCap 2   MCF_X 0 kft beam  MCF_Z CFX h6 hCap 2   MCF_Z 0 kft beam  BRAKING FORCE: BR (AASHTO LRFD 3.6.4) The braking force shall be taken as maximum of 5% of the Resultant Truck plus lane load OR 5% of the Design Tandem plus Lane Load or 25% of the design truck. Pbr1 5% Lane TruckT( ) NofLane( ) m( ) Truck Lane( ) Pbr1 14.892 kip

266 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Pbr2 5% Lane 50 kip( ) NofLane( ) m( ) Tandem Lane( ) Pbr2 12.087 kip Pbr3 25% TruckT( ) NofLane( ) m( ) DesignTruck( ) Pbr3 45.9 kip Pbr max Pbr1 Pbr2 Pbr3  Pbr 45.9 kip Braking force parallel to bent (X-direction) BRX Pbr sin θ( ) NofBm  BRX 0 kip beam  Braking force normal to bent (Z-direction) BRZ Pbr cos θ( ) NofBm  BRZ 3.825 kip beam  Moments at cg of the Bent Cap due to Braking Force MBR_X BRZ h6 hCap 2   MBR_X 44.848 kft beam  MBR_Z BRX h6 hCap 2   MBR_Z 0 kft beam  WATER LOADS: WA (AASHTO LRFD 3.7) Note : To be applied only on bridge components below design high water surface. Substructure: V 0 ft sec  (Design Stream Velocity) Specific Weight, γwater 62.4 pcf Longitudinal Stream Pressure: AASHTO LRFD 3.7.3.1 AASHTO LRFD Table 3.7.3.1-1 for Drag Coefficient, CD semicircular-nosed pier 0.7 square-ended pier 1.4 debries lodged against the pier 1.4 wedged-nosed pier with nose angle 90 deg or less 0.8 Columns and Drilled Shafts: Longitudinal Drag Force Coefficient for Column, CD_col 1.4 Longitudinal Drag Force Coefficient for Drilled Shaft, CD_ds 0.7 pT CD V2 2 g γwater= (Longitudinal stream pressure) AASHTO LRFD EQ (C3.7.3.1-1) pT_col CD_col V2 2 g γwater pT_col 0 ksf

267 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT pT_ds CD_ds V2 2 g γwater pT_ds 0 ksf Lateral Stream Pressure: AASHTO LRFD 3.7.3.2 AASHTO LRFD Table 3.7.3.2-1 for Lateral Drag Coefficient, CL Angle,, between direction of flowr and longitudina axis of the pie 0deg 0 5deg 0.5 10deg 0.7 20deg 0.9 >30deg 1 CL Lateral Drag Force Coefficient, CL 0.0 Lateral stream pressure, pL CL V2 2 g γwater pL 0 ksf Bent Cap: Longitudinal stream pressure CL 1.4 pTcap CL V2 2 g γwater pTcap 0 ksf WA on Columns Water force on column parallel to bent (X-direction) WAcol_X wCol pT_col WAcol_X 0 kip ft  If angle between direction of flow and longitudinal axis of pile = 0 then apply load at one exterior column only otherwise apply it on all columns. WA at all columns will be distributed uniformly rather than triangular distribution on column height. Water force on column normal to bent (Z-direction) WAcol_Z bCol pL WAcol_Z 0 kip ft  WA on Drilled Shafts Water force on drilled shaft parallel to bent (X-direction) WAdshaft_X DsDia pT_ds WAdshaft_X 0 kip ft  Water force on drilled shaft normal to bent (Z-direction) WAdshaft_Z DsDia pL WAdshaft_Z 0 kip ft  WA on Bent Cap (input as a punctual load) Water force on bent cap parallel to bent (X-direction) WAcap_X wCap hCap pTcap  (If design HW is below cap then input zero) WAcap_X 0 kip Water force on bent cap normal to bent (Z-direction)

268 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT WAcap_Z hCap pL (If design HW is below cap then input zero) WAcap_Z 0 kip ft  WIND ON SUPERSTRUCTURE: WS (AASHTO LRFD 3.8.1.2.2) Note : Wind Loads to be applied only on bridge exposed components above water surface AASHTO LRFD Table 3.8.1.2.2-1 specifies the wind load components for various angles of attack. In order to simplify the analysis, this calculation considers as default values those for girders which generate the maximum effect on structure. The results can be considered as conservative. For a superstructure other than a girder type and/or for a more detailed analysis, use the proper values as specified in the above mentioned table. AASHTO LRFD table 3.8.1.2.2-1 (modified) If the bridge is approximately 30’ high and local wind velocities are known to be less than 100 mph, wind load for this bridge should be from AASHTO LRFD TABLE 3.8.2.2-1. Otherwise use AASHTO LRFD EQ 3.8.1.2.1-1 as mentioned above. ptsup 0.05ksf Normal to superstructure (conservative suggested value 0.050 ksf) plsup 0.012ksf Along Superstructure (conservative suggested value 0.019 ksf) WSchk if ptsup hsup 0.3 klf "OK" "N.G."  WSchk "OK" WsupLong plsup hsup TribuLength NofBm  WsupLong 0.439 kip beam  WsupTrans ptsup hsup TribuLength NofBm  WsupTrans 1.828 kip beam  Wind force on superstructure parallel to bent (X-direction) WSsuper_X WsupLong sin θ( ) WsupTrans cos θ( ) WSsuper_X 1.828 kipbeam Wind force on superstructure normal to bent (Z-direction) WSsuper_Z WsupLong cos θ( ) WsupTrans sin θ( ) WSsuper_Z 0.439 kipbeam Moments at cg of the Bent Cap due to Wind load on superstructure Msuper_X WSsuper_Z hCap 2 BrgTh hsup 2   Msuper_X 2.38 kft beam 

269 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Msuper_Z WSsuper_X hCap 2 BrgTh hsup 2   Msuper_Z 9.916 kft beam  WIND ON SUBSTRUCTURE: WS (AASHTO LRFD 3.8.1.2.3) Base Wind pressure, psub 0.04 ksf will be applied on exposed substructure both transverse & longitudinal direction Wind on Columns Wind force on columns parallel to bent (X-direction) WScol_X psub bCol cos θ( ) wCol sin θ( )( )  WScol_X 0.14 kip ft  Apply WS loads at all columns even with zero degree attack angle. Wind force on columns normal to bent (Z-direction) WScol_Z psub bCol sin θ( ) wCol cos θ( )( )  WScol_Z 0.14 kip ft  Wind on Bent Cap & Ear Wall WSew_X psub hEarWall wEarWall sin θ( ) wCap cos θ( )( ) WSew_X 0 kip WSew_Z psub hEarWall wEarWall cos θ( ) wCap sin θ( )( ) WSew_Z 0 kip Wind force on bent cap parallel to bent (X-direction) WScap_X psub hCap CapL sin θ( ) wCap cos θ( )( )  WSew_X (punctual load) WScap_X 0.64 kip Wind force on bent cap normal to bent (Z-direction) WScap_Z psub hCap CapL cos θ( ) wCap sin θ( )( )  WSew_Z CapL  WScap_Z 0.16 kip ft  WIND ON VEHICLES: WL (AASHTO LRFD 3.8.1.3) AASHTO LRFD Table 3.8.1.3-1 specifies the wind on live load components for various angles of attack. In order to simplify the analysis, this calculation considers as default values the maximum wind components as defined in the above mentioned table. The results can be considered conservative. For a more detailed analysis, use the proper skew angle according to the table. AASHTO LRFD table 3.8.1.3-1 (suggested value 0.1 kip/ft) pWLt 0.1 kip ft  (suggested value 0.038 kip/ft) pWLl 0.04 kip ft 

270 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT WLPar pWLl TribuLength NofBm  WLPar 0.233 kip beam  WLNor pWLt TribuLength NofBm  WLNor 0.583 kip beam  Wind force on live load parallel to bent (X-direction) WLX WLNor cos θ( ) WLPar sin θ( ) WLX 0.583 kipbeam Wind force on live load normal to bent (Z-direction) WLZ WLNor sin θ( ) WLPar cos θ( ) WLZ 0.233 kipbeam Moments at cg of the Bent Cap due to Wind load on Live Load MWL_X WLZ h6 hCap 2   MWL_X 2.736 kft beam  MWL_Z WLX h6 hCap 2   MWL_Z 6.84 kft beam  Vertical Wind Pressure: (AASHTO LRFD 3.8.2) DeckWidth FDeckW Bridge deck width including parapet and sidewalk Puplift 0.02ksf( ) DeckWidth TribuLength (Acts upword Y-direction) Puplift 66.033 kip Applied at the windward quarter-point of the deck width. Note: Applied only for Strength III and for Service IV limit states only when the direction of wind is perpendicular to the longitudinal axis of the bridge. (AASHTO LRFD table 3.4,1-2, factors for permanent loads) Load Combinations: using AASHTO LRFD Table 3.4.1-1 STRENGTH_I 1.25 DC 1.5 DW 1.75 LL BR CF( ) 1.0 WA= STRENGTH_IA 0.9 DC 0.65 DW 1.75 LL BR CF( ) 1.0 WA= STRENGTH_III 1.25 DC 1.5 DW 1.4 WS 1.0 WA 1.4 Puplift= STRENGTH_IIIA 0.9 DC 0.65 DW 1.4 WS 1.0 WA 1.4 Puplift= STRENGTH_V 1.25 DC 1.5 DW 1.35 LL BR CF( ) 0.4 WS 1.0 WA 1.0 WL= STRENGTH_VA 0.9 DC 0.65 DW 1.35 LL BR CF( ) 0.4 WS 1.0 WA 1.0 WL= SERVICE_I 1.0 DC 1.0 DW 1.0 LLno_Impact BR CF  0.3 WS 1.0 WA 1.0 WL=

271 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT All these loadings as computed above such as DC, DW, LL, WL, WA, WS etc. are placed on the bent frame composed of bent cap and columns and drilled shafts. The frame is analyzed in RISA using load combinations as stated above. Output Loadings for various load combinations for column and drilled shaft are used to run PCA Column program to design the columns. It is found that 3'-6"X3'-6" Column with 12~#11 bars is sufficient for the loadings. Drilled shaft and other foundation shall be designed for appropriate loads. Total Vertical Foundation Load at Service I Limit State: Forward Span Superstructure DC (FFDC) & DW (FFDW): FFDC FNofBm 2( ) FSuperDCInt 2 FSuperDCExt FFDC 259.607 kip FFDW FNofBm( ) FSuperDW FFDW 38.5 kip Backward Span Superstructure DC (FBDC) & DW (FBDW): FBDC BNofBm 2( ) BSuperDCInt 2 BSuperDCExt FBDC 259.607 kip FBDW BNofBm( ) BSuperDW FBDW 38.5 kip Total Cap Dead Load Weight (TCapDC): TCapDC CapDC( ) CapL( ) NofBm( ) BrgSeatDC( ) EarWallDC TCapDC 112.8 kip Total DL on columns including Cap weight (FDC): FDL FFDC FFDW  FBDC FBDW  TCapDC FDL 709.015 kip Column & Drilled Shaft Self Weight: DSahft Length, DsHt 0 ft if Rounded Col, ColDia 0 ft ColDC if ColDia 0ft π 4 ColDia( )2 HCol( ) γc wCol bCol HCol γc  Column Wt, ColDC 40.425 kip DsDC π 4 DsDia( )2 DsHt( ) γc Dr Shaft Wt, DsDC 0 kip Total Dead Load on Drilled Shaft (DL_on_DShaft): DL_on_DShaft FDL NofCol( ) ColDC( ) NofDs( ) DsDC( ) DL_on_DShaft 789.865 kip Live Load on Drilled Shaft: m 0.85 (Multile Presence Factors for 3 Lanes) AASHTO LRFD Table 3.6.1.1.2 1( ) RLL Lane Truck( ) NofLane( ) m( ) (Total LLRxn without Impact) RLL 277.44 kip Total Load, DL+LL per Drilled Shaft of Intermediate Bent:

272 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT Load_on_DShaft DL_on_DShaft RLL NofDs  Load_on_DShaft 266.8 ton 5. PRECAST COMPONENT DESIGN Precast Cap Construction and Handling: w b h γc (Cap selfweight) w 2.4 klf Due to the location of girder bolts on cap, pickup points at 8' from both ends. Indeed, we can model cap lifting points as simply supported beam under self weight supported at 8' and 39' respectively from very end.   w = 2.4 klf lc = 8 ft lb = 31 ftla = 8 ft  la 8 ft lb 31 ft lc 8ft Construction factor: λcons 1.25 λcons 1.25 Maximum Positive Moment (MmaxP) & Negative Moment (MmaxN): MmaxP w CapL 2 CapL 4 la  MmaxP 211.5 kft MmaxN w la 2 2  MmaxN 76.8 kft Factored Maximum Positive Moment (MuP) & Negative Moment (MuN):

273 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT MuP λcons MmaxP MuP 264.375 kft MuN λcons MmaxN MuN 96 kft S b h2 6  (Cap Section Modulus) S 18432 in3 Maximum Positive Stress (ftP) & Negative Stress (ftN): ftP MuP S  ftP 172.119 psi ftN MuN S  ftN 62.5 psi Modulus of Rupture: According PCI hand book 6th edition modulus of rupture, fr = 7.5\/f'c is divided by a safety factor 1.5 in order to design a member without cracking f'c 5 ksi (Compressive Strength of Concrete) Unit weight factor, λ 1 fr 5 λ f'c psi (PCI EQ 5.3.3.2) fr 353.553 psi fr_check if fr ftP  fr ftN  "OK" "N.G."  fr_check "OK" Precast Column Construction and Handling: wCol 3.5 ft (Column width) Column breadth, bCol 3.5 ft wcol wCol bCol γc (Column self weight) wcol 1.837 klf Due to the location of girder bolts on column, pickup points at 3' from both ends. Indeed, we can model column lifting points as simply supported beam under self weight supported at 3' and 19' respectively from very end.   w  = 1.837 klf lc = 3 ftlb = 16 ft la = 3 ft  la 3 ft lb 16 ft lc 3 ft Maximum Positive Moment (MmaxP) & Negative Moment (MmaxN):

274 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT MmaxP wcol HCol 2 HCol 4 la  MmaxP 50.531 kft MmaxN wcol la 2 2  MmaxN 8.269 kft Factored Maximum Positive Moment (MuP) & Negative Moment (MuN): MuP λcons MmaxP MuP 63.164 kft MuN λcons MmaxN MuN 10.336 kft Scol wCol bCol2 6  (Column Section Modulus) Scol 12348 in 3 Maximum Positive Stress (ftP) & Negative Stress (ftN): ftP MuP Scol  ftP 61.384 psi ftN MuN Scol  ftN 10.045 psi Modulus of Rupture: According PCI hand book 6th edition modulus of rupture, fr = 7.5\/f'c is divided by a safety factor 1.5 in order to design a member without cracking f'c 5 ksi (Compressive Strength of Concrete) Unit weight factor, λ 1 fr 5 λ f'c psi (PCI EQ 5.3.3.2) fr 353.553 psi fr_check if fr ftP  fr ftN  "OK" "N.G."  fr_check "OK" DEVELOPMENT LENGTH: AASHTO LRFD 5.11 Ab 1.56 in 2 (Area of Bar) db 1.41 in (Diameter of Bar) f'c 5 ksi Modification Factor: According to AASHTO LRFD 5.11.2.1.2, the basic development length, ldb is required to multiply by the modification factor to obtain the development length ld for tension or compression. λmod 1.0 Basic Tension Development: AASHTO LRFD 5.11.2.1 for bars upto #11

275 INNOVATIVE BRIDGE DESIGNS FOR RAPID RENEWAL: ABC TOOLKIT ldb max 1.25 Ab in   fy f'c ksi  0.4 db fy ksi  12 in    (AASHTO LRFD 5.11.2.1.1) ldb 52.324 in ld λmod  ldb ld 4.36 ft Basic Compression Development: AASHTO LRFD 5.11.2.2 ldb max 0.63 db fy f'c ksi 0.3 db fy ksi  8 in    AASHTO LRFD EQ 5.11.2.2.1 1 2( ) ldb 25.38 in ld λmod  ldb ld 2.115 ft