How To Design A Long Bridge

Transcription

1 LRFD Design Example #1: Prestressed Precast Concrete Beam Bridge Design Click here for Table of Contents

2 LRFD DESIGN EXAMPLE: PRESTRESSED PRECAST CONCRETE BEAM BRIDGE DESIGN Table of Contents Cover Section 1: Project Information 1.01 About this Design Example 1.0 General Notes 1.03 Design Parameters Section : Superstructure Design.01 Dead Loads.0 Live Load Distribution Factors.03 Live Load Analysis.04 Prestressed Beam Design - Part I.05 Prestressed Beam Design - Part II.06 Traditional Deck Design.07 Deck Overhang Design.08 Creep and Shrinkage Parameters.09 Expansion Joint Design.10 Composite Neoprene Bearing Pad Design.11 Beam Stability Section 3: Substructure Design 3.01 Dead Loads 3.0 Pier Cap Live Load Analysis 3.03 Pier Cap Design Loads 3.04 Pier Cap Design 3.05 Pier Column Design Loads 3.06 Pier Column Design 3.07 Pier Foundation Design Loads 3.08 Pier Pile Vertical Load Design 3.09 Pier Footing Design 3.10 End Bent Live Load Analysis 3.11 End Bent Design Loads 3.1 End Bent Cap Design (similar to Section 3.04) 3.13 End Bent Foundation Design Loads 3.14 End Bent Pile Vertical Load Design (similar to Section 3.08) 3.15 End Bent Backwall Design LRFD Design Example Table of Contents i

3 SUPERSTRUCTURE DESIGN About this Design Example Description This document provides guidance for the design of a precast, prestressed beam bridge utilizing the AASHTO LRFD Bridge Design Specifications. The example includes the following component designs: Traditional deck design Prestressed beam design Composite Neoprene bearing pad design Multi-column pier design End bent design The following assumptions have been incorporated in the example: Two simple 90'-0" each, 0 degree skew. Minor horizontal curvature Multi-column pier on prestressed concrete piles. No phased construction. Two traffic railing barriers and one median barrier. No sidewalks. Permit vehicles are not considered. Design for jacking is not considered. Load rating is not addressed. No utilities on the bridge. For purposes of wind load calculation, the bridge is located in an area with a basic wind speed of 150 mph. Since this example is presented in a Mathcad document, a user can alter assumptions, constants, or equations to create a customized application. PROJECT INFORMATION 1.01 About this Design Example 1

4 Standards The example utilizes the following design standards: Florida Department of Transportation Standard Specifications for Road and Bridge Construction (010 edition) and applicable modifications. AASHTO LRFD Bridge Design Specifications, 5th Edition, 010. Florida Department of Transportation Structures Design Guidelines, January 011 Edition. Florida Department of Transportation Structures Detailing Manual, January 011 Edition. Florida Department of Transportation Design Standards, 010 Interim Edition. Acknowlegements The Tampa office of HDR Engineering, Inc. prepared this document for the Florida Department of Transportation. The Structures Design Office of the Florida Department of Transportation updated the example in 011. Notice The materials in this document are only for general information purposes. This document is not a substitute for competent professional assistance. Anyone using this material does so at his or her own risk and assumes any resulting liability. PROJECT INFORMATION 1.01 About this Design Example

5 PROJECT INFORMATION General Notes Design Method... Load and Resistance Factor Design (LRFD) except that the Prestressed Beams and Prestressed Piles have been designed for Service Load. Earthquake... No seismic analysis required (SDG.3.1). Must meet minimum support length requirement (LRFD ). Concrete... Class Minimum 8-day Compressive Strength (psi) Location II f`c = 3400 Traffic Barriers II (Bridge Deck) f`c = 4500 CIP Bridge Deck IV f`c = 5500 CIP Substructure V (Special) f`c = 6000 Concrete Piling VI f`c = 8500 Prestressed Beams Environment... The superstructure is classified as slightly aggressive. The substructure is classfied as moderately aggressive. Reinforcing Steel... ASTM A615, Grade 60 Concrete Cover... Superstructure Top deck surfaces.5" (Long bridge) All other surfaces " Substructure External surfaces not in contact with water 3" External surfaces cast against earth 4" Prestressed Piling 3" Top of Girder Pedestals " Concrete cover does not include reinforcement placement or fabrication tolerances, unless shown as "minimum cover". See FDOT Standard Specifications for allowable reinforcement placement tolerances. Assumed Loads... Item Load Live Load HL-93 Traffic Railing (plf) 40 Wearing Surface (psf) 0 Utilities (plf) 0 Stay-In-Place Metal Forms (psf) 0 Median Traffic Railing (plf) 485 Bridge Deck Sacrificial Thickness (in) 0.5 Dimensions... All dimensions are in feet or inches, except as noted. PROJECT INFORMATION 1.0 General Notes 3

6 PROJECT INFORMATION Design Parameters Description This section provides the design input parameters necessary for the superstructure and substructure design. Page Contents 5 A. General Criteria A1. Bridge Geometry A. Number of Lanes A3. Concrete, Reinforcing and Prestressing Steel Properties 9 B. LRFD Criteria B1. Dynamic Load Allowance [LRFD 3.6.] B. Resistance Factors [LRFD ] B3. Limit States [LRFD 1.3.] 1 C. Florida DOT Criteria C1. Chapter 1 - General requirements C. Chapter - Loads and Load Factors C3. Chapter 4 - Superstructure Concrete C4. Chapter 6 - Superstructure Components C5. Miscellaneous 1 D. Substructure D1. End Bent Geometry D. Pier Geometry D3. Footing Geometry D4. Pile Geometry D5. Approach Slab Geometry D6. Soil Properties PROJECT INFORMATION 1.03 Design Parameters 4

7 A. General Criteria This section provides the general layout and input parameters for the bridge example. A1. Bridge Geometry Horizontal Profile A slight horizontal curvature is shown in the plan view. This curvature is used to illustrate centrifugal forces in the substructure design. For all other component designs, the horizontal curvature will be taken as zero. PROJECT INFORMATION 1.03 Design Parameters 5

8 In addition, the bridge is also on a skew which is defined as Skew 0deg Vertical Profile PROJECT INFORMATION 1.03 Design Parameters 6

9 Overall bridge length... L bridge 180ft Bridge design span length... L span 90ft Beam grade... Beam Grade.15% Height of superstructure... z sup 0.5ft Height of substructure... z sub 8.5ft Typical Cross-secton Superstructure Beam Type... BeamType "FIB-36" Number of beams... N beams 9 Beam Spacing... BeamSpacing 10ft Deck overhang at End Bent and Pier... Overhang 4ft 6.5in 4.54 ft Average buildup... h buildup 1in PROJECT INFORMATION 1.03 Design Parameters 7

10 A. Number of Lanes Design Lanes [LRFD ] Current lane configurations show two striped lanes per roadway with a traffic median barrier separating the roadways. Using the roadway clear width between barriers, Rdwy width, the number of design traffic lanes per roadway, N lanes, can be calculated as: Roadway clear width... Rdwy width 4ft Number of design traffic lanes Rdwy width per roadway... N lanes floor 3 1ft Substructure Design In order to maximize the design loads of the substructure components, e.g. pier cap negative moment, pier columns, footing loads, etc., HL-93 vehicle loads were placed on the deck. In some cases, the placement of the loads ignored the location of the median traffic barrier. This assumption is considered to be conservative. Braking forces The bridge is NOT expected to become one-directional in the future. Future widening is expected to occur to the outside if additional capacity is needed. Therefore, for braking force calculations, N lanes 3. The designer utilized engineering judgement to ignore the location of the median barrier for live load placement for the substructure design and NOT ignore the median barrier for braking forces. The designer feels that the probability exists that the combination of lanes loaded on either side of the median barrier exists. However, this same approach was not used for the braking forces since these loaded lanes at either side of the median traffic barrier will NOT be braking in the same direction. A3. Concrete, Reinforcing and Prestressing Steel Properties Unit weight of concrete... γ conc 150pcf Modulus of elasticity for reinforcing steel... E s 9000ksi Ultimate tensile strength for prestressing tendon... f pu 70ksi Modulus of elasticity for prestressing tendon... E p 8500ksi PROJECT INFORMATION 1.03 Design Parameters 8

11 B. LRFD Criteria The bridge components are designed in accordance with the following LRFD design criteria: B1. Dynamic Load Allowance [LRFD 3.6.] An impact factor will be applied to the static load of the design truck or tandem, except for centrifugal and braking forces. Impact factor for fatigue and 15 fracture limit states... IM fatigue Impact factor for all other limit 33 states... IM B. Resistance Factors [LRFD ] Flexure and tension of reinforced concrete... ϕ 0.9 Flexure and tension of prestressed concrete... ϕ' 1.00 Shear and torsion of normal weight concrete... ϕ v 0.90 B3. Limit States [LRFD 1.3.] The LRFD defines a limit state as a condition beyond which the bridge or component ceases to satisfy the provisions for which it was designed. There are four limit states prescribed by LRFD. These are as follows: STRENGTH LIMIT STATES Load combinations which ensure that strength and stability, both local and global, are provided to resist the specified statistically significant load combinations that a bridge is expected to experience in its design life. Extensive distress and structural damage may occur under strength limit state, but overall structural integrity is expected to be maintained. EXTREME EVENT LIMIT STATES Load combinations which ensure the structural survival of a bridge during a major earthquake or flood, or when collided by a vessel, vehicle, or ice flow, possibly under scoured conditions. Extreme event limit states are considered to be unique occurrences whose return period may be significantly greater than the design life of the bridge. SERVICE LIMIT STATES Load combinations which place restrictions on stress, deformation, and crack width under regular service conditions. FATIGUE LIMIT STATES Load combinations which place restrictions on stress range as a result of a single design truck occurring at the number of expected stress range cycles. It is intended to limit crack growth under repetitive loads to prevent fracture during the design life of the bridge. PROJECT INFORMATION 1.03 Design Parameters 9

12 Table Load Combinations and Load Factors Revisions to LRFD Table above per SDG: 1. SDG.1.1 states: In LRFD Table , under Load Combination: LL, IM, etc., Limit State: Extreme Event I, use γ eq Per SDG.4.1B: PROJECT INFORMATION 1.03 Design Parameters 10

13 Table Load factors for permanent loads, γ p The load factor for wind in Strength Load Combination III in construction is 1.5 [LRFD ]. PROJECT INFORMATION 1.03 Design Parameters 11

14 C. FDOT Criteria C1. Chapter 1 - General Requirements General [SDG 1.1] The design life for bridge structures is 75 years. Criteria for Deflection and Span-to-Depth Ratios [SDG 1.] Per SDG 1., either LRFD or should be met. Based on the superstructure depth; is not met, so should be met. The deflection limit is span/800 for vehicular load and span/300 on cantilever arms. Environmental Classifications [SDG 1.3] The environment can be classified as either "Slightly", "Moderately" or "Extremely" aggressive. Per 1.0 General Notes: Environmental classification for superstructure... Environment super "Slightly" Environmental classification for substructure... Environment sub "Moderately" Concrete and Environment [SDG 1.4] The concrete cover for each bridge component is based on either the environmental classification or the length of bridge [SDG 1.4]. Concrete cover for the deck.. cover deck in if L bridge 100ft.5in [SDG 4..1].5in otherwise Concrete cover for substructure not in contact with water... cover sub 4in if Environment sub = "Extremely" 3in 3in otherwise Concrete cover for substructure cast against earth or in contact with water... cover sub.earth 4.5in if Environment sub = "Extremely" 4in 4in otherwise PROJECT INFORMATION 1.03 Design Parameters 1

15 Minimum 8-day compressive strength of concrete components... Class Location Correction factor for Florida lime rock coarse aggregate... K II (Bridge Deck) CIP Bridge Deck Approach Slabs f c.slab 4.5ksi IV CIP Substructure f c.sub 5.5ksi V (Special) Concrete Piling f c.pile 6.0ksi VI Prestressed Beams f c.beam 8.5ksi Unit Weight of Florida lime rock concrete (kcf)... w c.limerock.145 kip ft 3 Modulus of elasticity for 1.5 w c.limerock slab... E c.slab 33000K 1 kip ft 3 f c.slab ksi 3479ksi Modulus of elasticity for 1.5 w c.limerock beam... E c.beam 33000K 1 kip ft 3 Modulus of elasticity for 1.5 w c.limerock substructure... E c.sub 33000K 1 kip ft 3 Modulus of elasticity for 1.5 w c.limerock piles... E c.pile 33000K 1 kip ft 3 C. Chapter - Loads and Load Factors Dead loads [SDG.] f c.beam ksi f c.sub ksi f c.pile ksi 4781ksi 3846ksi 4017ksi Weight of future wearing surface... ρ fws 15psf if L bridge 100ft 0psf [SDG 4..1] 0psf otherwise Weight of sacrificial milling surface, using t mill 0.5in.... ρ mill t mill γ conc 6.5psf [SDG 4...A] PROJECT INFORMATION 1.03 Design Parameters 13

16 Table. 1 Miscellaneous Dead Loads ITEM UNIT LOAD General Concrete, Counterweight (Plain) Lb/cf 145 Concrete, Structural Lb/cf 150 Future Wearing Surface Lb/sf 15 1 Soil; Compacted Lb/cf 115 Stay in Place Metal Forms Lb/sf 0 Traffic Railings 3" F Shape (Index 40) Lb/ft 40 Median, 3" F Shape (Index 41) Lb/ft 485 4" Vertical Shape (Index 4) Lb/ft 590 3" Vertical Shape (Index 43) Lb/ft 385 4" F Shape (Index 45) Lb/ft 65 Corral Shape (Index 44) Lb/ft 460 Thrie Beam Retrofit (Index 471, 475 & 476) Lb/ft 40 Thrie Beam Retrofit (Index 47, 473 & 474) Lb/ft 30 Vertical Face Retrofit with 8" curb height (Index ) Lb/ft 70 Traffic Railing/Sound Barrier (8' 0") (Index 510) Lb/ft 1010 Prestressed Beams 3 Florida I 36 Beam (Index 0036) Lb/ft Future Wearing Surface allowance applies only to minor widenings of existing bridges originally designed for a Future Wearing Surface, regardless of length (see SDG 7. Widening Classifications and Definitions) or new short bridges (see SDG 4. Bridge Length Definitions).. Unit load of metal forms and concrete required to fill the form flutes. Apply load over the projected plan area of the metal forms. 3. Weight of buildup concrete for camber and cross slope not included. Weight of traffic railing barrier... w barrier.ea 40plf Weight of traffic railing median barrier... w median.bar 485plf Weight of compacted soil... γ soil 115pcf Weight of stay-in-place metal forms... ρ forms 0psf PROJECT INFORMATION 1.03 Design Parameters 14

17 Barrier / Railing Distribution for Beam-Slab Bridges [SDG.8 & LRFD ] Dead load of barriers applied to the exterior and interior w barrier.ea beams... w barrier N beams 0.093klf For purposes of this design example, all barriers will be equally distributed amongst all the beams comprising the superstructure. Include the dead load of the traffic barriers on the design w median.bar load of the exterior beams... w barrier.exterior w barrier N beams 0.147klf Include the dead load of the traffic barriers on the design w median.bar load of the interior beams... w barrier.interior w barrier N beams 0.147klf Seismic Provisions [SDG.3 & LRFD & ] Seismic provisions for minimum bridge support length only. Wind Loads [SDG.4] Basic wind speed (mph)... V 150 Height, superstructure... z sup 0.5 ft Height, substructure... z sub 8.5 ft Gust effect factor... G 0.85 Pressure coefficient, superstructure... C p.sup 1.1 Pressure coefficient, substructure... C p.sub 1.6 Velocity pressure exposure.105 z sup coefficient, superstructure... K z.sup max ft PROJECT INFORMATION 1.03 Design Parameters 15

18 Velocity pressure exposure.105 z sub coefficient, substructure... K z.sub max ft Wind pressure, superstructure, Strength III, Service IV... P z.sup.striii.serviv K z.sup V GC p.sup Wind pressure, superstructure, Strength V, Service I... P z.sup.strv.servi K z.sup 70 GC p.sup Wind pressure, substructure, Strength III, Service IV... P z.sub.striii.serviv K z.sub V GC p.sub Wind pressure, substructure, Strength V, Service I... P z.sub.strv.servi K z.sub 70 GC p.sub C3. Chapter 4 - Superstructure Concrete General [SDG 4.1] Yield strength of reinforcing steel... f y 60ksi Note: Epoxy coated reinforcing not allowed on FDOT projects. Deck Slabs [SDG 4.] Bridge length definition... BridgeType "Short" if L bridge 100ft "Long" "Long" otherwise Thickness of sacrificial milling surface... t mill 0in if L bridge 100ft 0.5in otherwise 0.5in Deck thickness... t slab 8.0in PROJECT INFORMATION 1.03 Design Parameters 16

19 Deck Slab Design [SDG 4..4] The empirical design method is not permitted per SDG 4..4.A. Therefore, the traditional design method will be used. The minimum transverse top slab reinforcing at the median barrier and overhang may be determined using the table in SDG 4..4.B because a minimum 8" slab depth and less than 6' overhang is provided. A minimum area of steel of 0.40 in per foot should be provided in the top of the deck slab at the median barrier, and 0.80 in per foot should be provided at the F-shape barrier. Pretensioned Beams [SDG 4.3] (Note: Compression = +, Tension = -) Minimum compressive concrete strength at release is the greater of 4.0 ksi or 0.6 f c ksi f ci.beam.min max 4ksi0.6f c.beam Maximum compressive concrete strength at release is the lesser of 6.0 ksi or 0.8 f c... 6ksi f ci.beam.max min 0.8f c.beam 6.0ksi Any value between the minimum and maximum may be selected for the design. Compressive concrete strength at release... f ci.beam 6ksi Corresponding modulus of 1.5 w c.limerock elasticity... E ci.beam 33000K 1 kip ft 3 f ci.beam ksi 4017ksi Limits for tension in top of beam at release (straight strand only) [SDG C] Outer 15 percent of design beam... f top.outer15 1 f ci.beam psi 930psi Center 70 percent of design beam [LRFD ] f top.center70 min 0.ksi f ci.beam ksi psi PROJECT INFORMATION 1.03 Design Parameters 17

20 Time-dependent variables for creep and shrinkage calculations Relative humidity... H 75 Age (days) of concrete when load is applied... T 0 1 Age (days) of concrete when section becomes composite... T 1 10 Age (days) of concrete used to determine long term losses... T C4. Chapter 6 - Superstructure Components Temperature Movement [SDG 6.3] The temperature values for "Concrete Only" in the preceding table apply to this example. Temperature mean... t mean 70 F Temperature high... t high 105 F Temperature low... t low 35 F Temperature rise... Δt rise t high t mean 35 F Temperature fall... Δt fall t mean t low 35 F Coefficient of thermal expansion [LRFD 5.4..] for normal weight concrete... α t F PROJECT INFORMATION 1.03 Design Parameters 18

21 Expansion Joints [SDG 6.4] For new construction, use only the joint types listed in the preceding table. A typical joint for most prestressed beam bridges is the poured joint with backer rod [DS Index 1110]. Maximum joint width... W max 3in Proposed joint width at 70 o F... W 1in Minimum joint width... W min 0.5W Movement [6.4.] For prestressed concrete structures, the movement is based on the greater of the following combinations: Movement from the combination of temperature fall, creep, and shrinkage... Δx fall = Δx temperature.fall (Note: A temperature rise with creep Δx and shrinkage is not investigated since creep.shrinkage they have opposite effects). Temperature Load Factor γ TU 1. Movement from factored effects of temperature... Δx rise = γ TU Δx temperature.rise Δx fall = γ TU Δx temperature.fall (Note: For concrete structures, the temperature rise and fall ranges are the same. PROJECT INFORMATION 1.03 Design Parameters 19

22 C5. Miscellaneous Beam Parameters Distance from centerline pier to centerline bearing... Distance from centerline end bent (FFBW) to centerline bearing... K1 K 11in 16in (Note: Sometimes the K value at the end bent and pier may differ. Distance from end of beam to centerline of bearing... J 8in Beam length... L beam L span ( K1 J) ( K J) ft Beam design length... L design L span K1 K ft PROJECT INFORMATION 1.03 Design Parameters 0

23 D. Substructure D1. End Bent Geometry (Note: End bent back wall not shown) Depth of end bent cap... h EB.5ft Width of end bent cap... b EB 3.5ft Length of end bent cap... L EB 88ft Height of back wall... h BW 3.6ft Back wall design width... L BW 1ft Thickness of back wall... t BW 1in D. Pier Geometry Depth of pier cap... h Cap 4.5ft Column diameter... b Col 4.0ft Width of pier cap... b Cap 4.5ft Number of columns... n Col 4 Length of pier cap... L Cap 88ft Surcharge on top of footing... h Surcharge.0ft Height of pier column... h Col 14.0ft PROJECT INFORMATION 1.03 Design Parameters 1

24 D3. Footing Geometry Depth of footing... h Ftg 4.0ft Width of footing... b Ftg 7.5ft Length of footing... L Ftg 7.5ft D4. Pile Geometry Pile Embedment Depth... Pile embed 1in Pile Size... Pile size 18in D5. Approach Slab Geometry Approach slab thickness... t ApprSlab 13.75in Approach slab length... L ApprSlab 3ft D6. Soil Properties (Note: The min. approach slab dimension due to the 30ft skew is ft ). cos( Skew) Unit weight of soil... γ soil 115pcf Defined Units PROJECT INFORMATION 1.03 Design Parameters

25 SUPERSTRUCTURE DESIGN Dead Loads Reference Reference:C:\Users\st986ch\AAAdata\LRFD PS Beam Design Example\103DesignPar.xmcd(R) Description This section provides the dead loads for design of the bridge components. Page Contents 4 A. Non-Composite Section Properties A1. Summary of the properties for the selected beam type A. Effective Flange Width [LRFD ] 6 B. Composite Section Properties B1. Interior beams B. Exterior beams B3. Summary of Properties 9 C. Dead Loads C1. Interior Beams C. Exterior Beams C3. Summary Superstructure Design.01 Dead Loads 3

26 A. Non-Composite Section Properties A1. Summary of Properties for the Selected Beam Type BeamTypeTog BeamType PCBeams NON-COMPOSITE PROPERTIES FIB-36 FIB-45 FIB-54 FIB-63 FIB-7 FIB-78 Moment of Inertia [in 4 ] I Section Area [in ] A b ytop [in] y top ybot [in] y bot De pth [in] h Top flange width [in] b tf Top flange depth [in] h tf Width of web [in] b web Bottom flange width [in] b Bottom flange depth [in] h bf Bottom flange taper [in] E output( beampropstype) beamprops 1 if type = "FIB-36" beamprops if type = "FIB-45" beamprops 3 if type = "FIB-54" beamprops 4 if type = "FIB-63" beamprops 5 if type = "FIB-7" beamprops 6 if type = "FIB-78" beamprops 0 00 otherwise Superstructure Design.01 Dead Loads 4

27 FIB in FIB in FIB in FIB in Beamtype FIB36 if BeamType = "FIB-36" FIB45 if BeamType = "FIB-45" FIB54 if BeamType = "FIB-54" FIB63 if BeamType = "FIB-63" FIB7 if BeamType = "FIB-7" FIB78 if BeamType = "FIB-78" I nc A nc output( PCBeamsBeamTypeTog) in 4 0 output( PCBeamsBeamTypeTog) in yt nc output( PCBeamsBeamTypeTog) in output( PCBeamsBeamTypeTog) yb nc h nc output( PCBeamsBeamTypeTog) in 3 output( PCBeamsBeamTypeTog) in b tf h tf output( PCBeamsBeamTypeTog) in 5 output( PCBeamsBeamTypeTog) in b w b bf output( PCBeamsBeamTypeTog) in 7 output( PCBeamsBeamTypeTog) in 8 h bf output( PCBeamsBeamTypeTog) in 9 Jx output( PCBeamsBeamTypeTog) in 4 11 Superstructure Design.01 Dead Loads 5

28 The non-composite beam properties are given and can be obtained from the FDOT Instructions for Design Standards, Index 0010 Series. NON-COMPOSITE PROPERTIES FIB-36 Moment of Inertia [in 4 ] I nc Section Area [in ] A nc 807 ytop [in] yt nc ybot [in] yb nc De pth [in] h nc 36 Top flange width [in] b tf 48 Top flange depth [in] h tf 3.5 Width of web [in] b w 7 Bottom flange width [in] b bf 38 Bottom flange depth [in] h bf 7 Bottom flange taper [in] E 15.5 Section Modulus top [in 3 ] S tnc 6537 Section Modulus bottom [in 3 ] S bnc BeamType "FIB-36" A. Effective Flange Width [LRFD ] Interior beams The effective flange width: b eff.interior BeamSpacing 10 ft Exterior beams For exterior beams, the effective flange width: BeamSpacing b eff.exterior = Overhang Δw where: Cross-sectional area of the barrier... A b.77ft Δw A b t slab.078 ft BeamSpacing Effective flange width: b eff.exterior Overhang Δw ft Superstructure Design.01 Dead Loads 6

29 Transformed Properties To develop composite section properties, the effective flange width of the slab should be transformed to the concrete properties of the beam. E c.slab n 0.78 Modular ratio between the deck and beam. E c.beam Transformed slab width for interior beams b tr.interior n b eff.interior in Transformed slab width for exterior beams b tr.exterior n b eff.exterior in Superstructure Design.01 Dead Loads 7

30 B. Composite Section Properties B1. Interior beams Height of the composite section... h h nc h buildup t slab 45in Area of the composite section... A slab b tr.interior t slab 698.5in A fillet b tf h buildup 48in A Interior A nc A fillet A slab in Distance from centroid of beam to extreme fiber in tension y b h buildup A nc yb nc A fillet h nc A slab h nc h buildup A Interior t slab 8.1in Distance from centroid of beam to extreme fiber in compression... y t h y b 16.9in Moment of Inertia... 1 I slab 1 b tr.interior t 3 t slab slab A slab h y b in 4 I fillet 3 b tf h buildup 1 I Interior I nc A nc y b yb nc h buildup A fillet h nc y b 3368in 4 I slab I fillet in 4 I Interior Section Modulus (top, top of beam, bottom)... S t 1319in 3 y t S tb I Interior h nc y b 45695in 3 S b I Interior 1787in 3 y b Superstructure Design.01 Dead Loads 8

31 B. Exterior beams Calculations are similar to interior beams. Height of the composite section... h h nc h buildup t slab 45in Area of the composite section... A slab b tr.exterior t slab in A fillet b tf h buildup 48in A Exterior A nc A fillet A slab in Distance from centroid of beam to extreme fiber in tension y' b h buildup A nc yb nc A fillet h nc A slab h nc h buildup A Exterior t slab 9.00in Distance from centroid of beam to extreme fiber in compression... y' t h y' b in Moment of Inertia... 1 I slab 1 b tr.exterior t 3 t slab slab A slab h y' b 11157in 4 I fillet 3 b tf h buildup 1 I Exterior I nc A nc y' b yb nc h buildup A fillet h nc y' b 70in 4 I slab I fillet in 4 I Exterior Section Modulus (top, top of beam, bottom)... S t 361.in 3 y' t S tb I Exterior h nc y' b in 3 S b I Exterior in 3 y' b Superstructure Design.01 Dead Loads 9

32 B3. Summary of Properties COMPOSITE SECTION PROPERTIES INTERIOR EXTERIOR Effective slab width [in] b eff.interior/exterior Transformed slab width [in] b tr.interior/exterior Height of composite section [in] h Effective slab area [in ] A slab Area of composite section [in ] A Interior/Exterior Neutral axis to bottom fiber [in] y b Neutral axis to top fiber [in] y t Inertia of composite section [in 4 ] I Interior/Exterior Section modulus top of slab [in 3 ] S t Section modulus top of beam [in 3 ] S tb Section modulus bottom of beam [in 3 ] S b Superstructure Design.01 Dead Loads 30

33 C. Dead Loads Calculate the moments and shears as a function of "x", where "x" represents any point along the length of the beam from 0 feet to L design. The values for the moment and shear at key design check points are given... where Support 0ft ShearChk 3.ft Debond1 Debond 10ft 0ft {Check beam for debonding, if not debonding, enter 0 ft.) (Check beam for debonding, if not debonding, enter 0 ft.) Midspan 0.5L design ft For convenience in Mathcad, place these points in a matrix... C1. Interior Beams Support ShearChk 0 3. x Debond1 10 ft pt 0 4 Debond 0 Midspan Design Moments and Shears for DC Dead Loads Weight of beam w BeamInt A nc γ conc 0.841klf Moment - self-weight of beam at Release.. Moment - self-weight of beam... Shear - self-weight of beam... M RelBeamInt ( x) M BeamInt ( x) V BeamInt ( x) w BeamInt L beam x w BeamInt L design x w BeamInt L design w BeamInt x w BeamInt x w BeamInt x Weight of deck slab, includes haunch and milling surface w SlabInt t slab t mill BeamSpacing h buildup b tf γ conc 1.11klf Moment - self-weight of deck slab, includes haunch and milling surface... M SlabInt ( x) w SlabInt L design x w SlabInt x Shear - self-weight of deck slab, includes haunch and milling surface... V SlabInt ( x) w SlabInt L design w SlabInt x Superstructure Design.01 Dead Loads 31

34 Weight of stay-in-place forms w FormsInt BeamSpacing b tf ρ forms 0.1klf Moment - stay-in-place forms... Shear - stay-in-place forms.... M FormsInt ( x) V FormsInt ( x) w FormsInt L design x w FormsInt L design w FormsInt x w FormsInt x Weight of traffic railing barriers w barrier.interior 0.147klf Moment - traffic railing barriers... Shear - traffic railing barriers... M TrbInt ( x) V TrbInt ( x) w barrier.interior L design x w barrier.interior L design w barrier.interior x w barrier.interior x DC Load total w DC.BeamInt w BeamInt w SlabInt w FormsInt w barrier.interior.klf DC Load Moment M DC.BeamInt ( x) M BeamInt ( x) M SlabInt ( x) M FormsInt ( x) M TrbInt ( x) DC Load Shear V DC.BeamInt ( x) V BeamInt ( x) V SlabInt ( x) V FormsInt ( x) V TrbInt ( x) DC Load Rotation L design 3 w DC.BeamInt w barrier.interior θ DC.BeamInt 4E c.beam I nc 3 w barrier.interior L design 4E c.beam I Interior 0.81deg Design Moments and Shears for DW Dead Loads Weight of future wearing surface w FwsInt BeamSpacingρ fws 0klf Moment - weight of future wearing surface... M FwsInt ( x) w FwsInt L design x w FwsInt x Superstructure Design.01 Dead Loads 3