Computer Aided Bridge Engineering (Detail Design of Pre-Stressed Concrete I-Girder / Box-Girder Bridges)

Contents
Preface
	The Design in AASHTO LRFD Standard
Introduction
Acknowledgements
List of Abbreviations
Chapter 1
The Aim of This Work
	1.1. The Design in AASHTO LRFD Standard
	1.2. The Design in British Standard Eurocodes
	1.3. The Design in IRC Standard
	References
Chapter 2
Grillage Model Analysis of Bridge Deck  and Girder by microSAP
	Abstract
	2.1. General
	2.2. Overview of Deck-Girder Grillage Model
		2.2.1. Geometry
		2.2.2. Member Section Properties
		2.2.3. Cantilever Footpaths
		2.2.4. Bearing Support
		2.2.5. Loading
		2.2.6. Dead Loading
		2.2.7. Live Loading
		2.2.8. Results
	2.3. Grillage Modeling of Slab-on-Girders Bridge
	2.4. Grillage Modeling of Box-Girder Bridge
	2.5. Evaluation of Equivalent Elastic Properties
		2.5.1. Flexural Moment of Inertia, ‘I’
		2.5.2. Torsional Inertia, ‘J’
	2.6. Application of Loads, Analysis,  Force Responses and Interpretations
		2.6.1. Dead Load
		2.6.2. Live Load
		2.6.3. Impact Load
		2.6.4. Panels in the Grillage Model
		2.6.5. Transfer of Loads to the Nodes
			2.6.5.1. Transfer of Dead Loads
			2.6.5.2. Transfer of Live Loads
				Footpath Live Load
				Vehicular Live Load
					Case I: Equivalent Vertical Nodal Load
					Case II: Equivalent Vertical Nodal Load and Moments
		2.6.6. Forces Developed in a Rectangular Panel (Normal & Skew Bridges)
		2.6.7. Forces Developed in a Triangular Panel (Skew Bridges)
		2.6.8. Forces Developed in a Parallelogram Panel (Skew Bridges)
		2.6.9. Grillage Analysis and Force Responses
			2.6.9.1. Analysis of Grillage Model
				Step 1: Formulation of Stiffness Matrix
				Step 2: Formulation of Load Vectors
				Step 3: Identification of Support Conditions
				Step 4: Solution of Simultaneous Equations
				Step 5: Determination of Nodal and Member Deformations and Forces
			2.6.9.2. Force Responses
		2.6.10. Interpretation of Results of Grillage Analysis
		2.6.11. Grillage Model and Analysis for Slab Bridges
		2.6.12. Grillage Model and Analysis for Bridge Decks with Slab-on-Girders
		2.6.13. Grillage Model and Analysis for Box-Girder or Cellular Bridges
	2.7. The Analysis Data  for the Deck-Girder Grillage Model
		2.7.1. Title of the Analysis Data
		2.7.2. Units for Linear Measurements and Loads of the Analysis Data
		2.7.3. Joint Coordinates of Grillage Model
		2.7.4. Elements/Members Connectivity of Grillage Model
		2.7.5. Section Properties of the Beam Elements/Members
		2.7.6. Material Properties of the Beam Elements/Members
		2.7.7. Support at the Nodes/Joints of the Beam Elements/Members
		2.7.8. Applied Loads on the Beam Elements/Members
			2.7.8.1. Dead Loads and Super Imposed Dead Loads
			2.7.8.2. AASHTO-LRFD Class Live Loads
		2.7.9. Analysis Specifications
	2.8. Computer Applications for the Analysis  of PSC I-Girder Bridge Grillage Model  with AASHTO LRFD Live Load
	References
Chapter 3
Design of PSC I-Girder Bridge  Deck-Girder Superstructure  in AASHTO-LRFD
	Abstract
	3.1. General
		3.1.1. Service Limit State Design (3.5.5)
		3.1.2. Strength Limit State Design  (3.5.6.1 Flexural Strength Design Check)
		3.1.3. Shear Strength Design Check (3.5.6.2)
		3.1.4. Longitudinal Design (3.6.1 Design Methodology)
		3.1.5. Tendon Layout and Envelope (3.6.2)
	3.2. Design of RCC Deck Slab
		3.2.1. AASHTO-LRFD Design Step 4.1 Deck Slab Design
		3.2.2. AASHTO-LRFD Design Step 4.2 Deck Thickness
		3.2.3. AASHTO-LRFD Design Step 4.3 Overhang Thickness
		3.2.4. AASHTO-LRFD Design Step 4.4 Concrete Parapet
		3.2.5. AASHTO-LRFD Design Step 4.5 Equivalent Strip Method (S4.6.2)
		3.2.6. AASHTO-LRFD Design Step 4.5.1 Design Dead Load Moments
		3.2.7. AASHTO-LRFD Design Step 4.6 Distance from the Center  of the Girder to the Design Section for Negative Moment
		3.2.8. AASHTO-LRFD Design Step 4.7 Determining Live Load Effects
		3.2.9. AASHTO-LRFD Design Step 4.8 Design  for Positive Moment in the Deck
			3.2.9.1. Factored loads
				Live Load
				Dead Load + Live Load Design Factored Positive Moment  (Strength I Limit State)
				Check Maximum and Minimum Reinforcement
				Stresses under Service Loads (S5.7.1)
		3.2.10. AASHTO-LRFD Design Step 4.9 Design  for Negative Moment at Interior Girders
			3.2.10.1. Live Load
			3.2.10.2. Dead Load
		3.2.11. AASHTO-LRFD Design Step 4.10 Design of the Overhang
			3.2.11.1. Assumed Loads
				Design Case 1: Check Overhang for Horizontal Vehicular Collision Load (SA13.4.1, Case 1)
			3.2.11.2. At Design Section in the Overhang  (Section B-B in Figure 3.7, 4-7 AASHTO)
			3.2.11.3. Check Dead Load + Collision Moments at Design Section in First Span (Section C-C in Figure 3.7)
				Design Case 2: Vertical Collision Force (SA13.4.1, Case 2)
				Design Case 3: Check DL + LL (SA13.4.1, Case 3)
			3.2.11.4. Design Section in the Overhang (Section B-B in Figure 3.7)
			3.2.11.5. Check Dead Load + Live Load Moments at Design Section in First Span (Section C-C in Figure 3.7)
		3.2.12. AASHTO-LRFD Design Step 4.11 Detailing  of Overhang Reinforcement
		3.2.13. AASHTO-LRFD Design Step 4.12 Longitudinal Reinforcement
			3.2.13.1. Top Longitudinal Reinforcement
			3.2.13.2. Design Step 4.13. Deck Top Longitudinal Reinforcement in the Girder Negative Moment Region
			3.2.13.3. Design Step 4.14. Check Shrinkage and Temperature Reinforcement according to S5.10.8
	3.3. Design of PSC I-Girder
		3.3.1. AASHTO-LRFD Design Step 5.1 -  Live Load Distribution Factors (S 4.6.2.2)
			3.3.1.1. AASHTO-LRFD Design Step 5.1.1
			3.3.1.2. AASHTO-LRFD Design Step 5.1.2
			3.3.1.3. AASHTO-LRFD Design Step 5.1.3
			3.3.1.4. AASHTO-LRFD Design Step 5.1.4: Interior Girder
			3.3.1.5. AASHTO-LRFD Design Step 5.1.5
			3.3.1.6. AASHTO-LRFD Design Step 5.1.6:  Skew Correction Factor for Shear
			3.3.1.7. AASHTO-LRFD Design Step 5.1.7
			3.3.1.8. AASHTO-LRFD Design Step 5.1.8
			3.3.1.9. AASHTO-LRFD Design Step 5.1.9
			3.3.1.10. AASHTO-LRFD Design Step 5.1.10: Exterior Girder
			3.3.1.11. AASHTO-LRFD Design Step 5.1.11
			3.3.1.12. AASHTO-LRFD Design Step 5.1.12
			3.3.1.13. AASHTO-LRFD Design Step 5.1.13
			3.3.1.14. AASHTO-LRFD Design Step 5.1.14
			3.3.1.15. AASHTO-LRFD Design Step 5.1.15:  Additional Check for Rigidly Connected Girders (S 4.6.2.2.2d)
			3.2.1.16. AASHTO-LRFD Design Step 5.1.16
		3.3.2. AASHTO-LRFD Design Step 5.2 - Dead Load Calculation
			3.3.2.1. Interior Girder
			3.3.2.2. Exterior Girder
			3.3.2.3. Haunch Weight
			3.3.2.4. Concrete Diaphragm Weight
			3.3.2.5. Parapet Weight
			3.3.2.6. Future Wearing Surface
		3.3.3. AASHTO-LRFD Design Step 5.3 -  Un-Factored and Factored Load Effects
			3.3.3.1. AASHTO-LRFD Design Step 5.3.1 Summary of Loads
			3.3.3.2. AASHTO-LRFD Design Step 5.3.2 Analysis of Creep and Shrinkage Effects
				AASHTO-LRFD Design Step5.3.2.1 Creep Effects
				AASHTO-LRFD Design Step 5.3.2.2 Shrinkage Effects
					Calculations of Creep and Shrinkage Effects
				AASHTO-LRFD Design Step 5.3.2.3 Effect of Beam Age at the Time of the Continuity Connection Application
		3.3.4. AASHTO-LRFD Design Step 5.4 - Loss of Pre-Stress (S 5.9.5)
			3.3.4.1. Design Step 5.4.1 General
			3.3.4.2. AASHTO-LRFD Design Step 5.4.2 Calculate the Initial Stress in the Tendons Immediately Prior to Transfer (S5.9.3)
			3.3.4.3. AASHTO-LRFD Design Step 5.4.3 Determine  the Instantaneous Losses (S5.9.5.2)
			3.3.4.4. AASHTO-LRFD Design Step 5.4.4 Calculate  the Pre-Stressing Stress Immediately after Transfer
			3.2.4.5. AASHTO-LRFD Design Step 5.4.5 Calculate  the Pre-Stressing Force at Transfer
			3.3.4.6. AASHTO-LRFD Design Step 5.4.6 Time-Dependent Losses after Transfer, Refined Method (S5.9.5.4)
				AASHTO-LRFD Design Step 5.4.6.1 Creep Coefficients (S5.4.2.3.2)
				AASHTO-LRFD Design Step 5.4.6.2 Shrinkage Strain (S5.4.2.3.3)
				AASHTO-LRFD Design Step 5.4.6.3 Shrinkage Losses  (S5.9.5.4.2a, S5.9.5.4.3a, and S5.9.5.4.3d)
				AASHTO-LRFD Design Step 5.4.6.4 Creep Losses (S5.9.5.4.2b and S5.9.5.4.3b)
				AASHTO-LRFD Design Step 5.4.6.5 Relaxation Losses  (S5.9.5.4.2c and S5.9.5.4.3c)
			3.3.4.7. AASHTO-LRFD Design Step 5.4.7 Calculate  Total Time Dependent Loss after Transfer
			3.3.4.8. AASHTO-LRFD Design Step 5.4.8 Calculate the Final  Effective Pre-Stress Responses
			3.3.4.9. AASHTO-LRFD Design Step 5.4.9 Calculate Jacking Stress, fpj
		3.3.5. AASHTO-LRFD Design Step 5.5 - Stress in Pre-Stressing Strands
			3.3.5.1. Design Step 5.5.1 Stress in Pre-Stressing Strands  at Nominal Flexural Resistance
			3.3.5.2. Design Step 5.5.2 Transfer and Development Length
			3.3.5.3. Design Step 5.5.3 Variation in Stress in Pre-Stressing Steel  along the Length of the Girders
			3.3.5.4. Design Step 5.5.4 Sample Strand Stress Calculations
				Pre-Stress Force at Centerline of End Bearing after Losses  under Service or Strength
				Pre-Stress Force at a Section 11 ft. from the Centerline of End Bearing after Losses under Service Conditions
				Strands Maximum Resistance at Nominal Flexural Capacity at a Section 7.0 ft. from the Centerline of End Bearing
				Strands Maximum Resistance at Nominal Flexural Capacity at a Section 22 ft. from Centerline of End Bearing
		3.3.6. AASHTO-LRFD Design Step 5.6 - Flexure Design
			3.3.6.1. AASHTO-LRFD Design Step 5.6.1 Flexural Stress at Transfer
				AASHTO-LRFD Design Step 5.6.1.1
					Stress Limits at Transfer
				AASHTO-LRFD Design Step 5.6.1.2 Stress Calculations at Transfer
					Sample Calculations for Flexural Stresses at Transfer
					Sample Calculations at 1 ft. – 9 in. from CL of Bearing (2 ft. – 6 in. from Girder End)
			3.3.6.2. AASHTO-LRFD Design Step 5.6.2 Final Flexural Stress  under Service Limit State
				AASHTO-LRFD Design Step 5.6.2.1
					Stress Limits
				AASHTO-LRFD Design Step 5.6.2.2
					Sample Calculations at 11 ft. From the CL of Bearing  (11 ft. – 9 in. From Girder End)
					Stresses at Service Limit State for Sections in the Negative Moment Region
					Compressive Forces in the Concrete
					Check Force Equilibrium
					Check Moment Equilibrium
			3.3.6.3. AASHTO-LRFD Design Step 5.6.3 Longitudinal Steel  at Top of Girder
			3.3.6.4. AASHTO-LRFD Design Step 5.6.4 Flexural Resistance  at the Strength Limit State in Positive Moment Region (S5.7.3.1)
				Sample Calculations at Mid-Span
				AASHTO-LRFD Design Step 5.6.4.1
					Check if Section Is Tension-Controlled
				AASHTO-LRFD Design Step 5.6.4.2
					Check Minimum Required Reinforcement (S5.7.3.3.2)
			3.3.6.5. AASHTO-LRFD Design Step 5.6.5 Continuity Connection at Intermediate Support
				AASHTO-LRFD Design Step 5.6.5.1
					Negative Moment Connection at the Strength Limit State
				AASHTO-LRFD Design Step 5.6.5.2
					Positive Moment Connection
			3.3.6.6. AASHTO-LRFD Design Step 5.6.6 Fatigue in Pre-Stressed Steel (S5.5.3)
			3.3.6.7. AASHTO-LRFD Design Step 5.6.7 Camber (S5.7.3.6)
				AASHTO-LRFD Design Step 5.6.7.1
					Camber to Determine Bridge Seat Elevations
				AASHTO-LRFD Design Step 5.6.7.2
					Haunch Thickness
				AASHTO-LRFD Design Step 5.6.7.3
					Camber to Determine Probable Sag in Bridge
			3.3.6.8. AASHTO-LRFD Design Step 5.6.8 Optional Live Load Deflection Check
		3.3.7. AASHTO-LRFD Design Step 5.7 - Shear Design (S 5.8)
			3.3.7.1. AASHTO-LRFD Design Step 5.7.1 Critical Section for Shear near the End Support
			3.3.7.2. AASHTO-LRFD Design Step 5.7.2 Shear Analysis for a Section in the Positive Moment Region. Sample Calculations
				Design Step 5.7.2 Shear Analysis for a Section  in the Positive Moment Region. Sample Calculations
					AASHTO-LRFD Design Step 5.7.2.1
				AASHTO-LRFD Design Step 5.7.2.2
					Minimum Required Transverse Reinforcement
				AASHTO-LRFD Design Step 5.7.2.3
					Maximum Spacing for Transverse Reinforcement
				AASHTO-LRFD Design Step 5.7.2.4
					Shear Strength
			3.3.7.3. AASHTO-LRFD Design Step 5.7.3 Shear Analysis  for Sections in the Negative Moment Region
				AASHTO-LRFD Design Step 5.7.3.1
				AASHTO-LRFD Design Step 5.7.3.2
					Determine the Effective Depth for Shear, dv
				AASHTO-LRFD Design Step 5.7.3.3
					Shear Stress on Concrete
				AASHTO-LRFD Design Step 5.7.3.4
					Minimum Required Transverse Reinforcement
				AASHTO-LRFD Design Step 5.7.3.5
					Maximum Spacing for Transverse Reinforcement
				AASHTO-LRFD Design Step 5.7.3.6
					Shear Resistance
			3.3.7.4. AASHTO-LRFD Design Step 5.7.4 Factored Splitting Resistance (S5.10.10.1)
			3.3.7.5. AASHTO-LRFD Design Step 5.7.5 Confinement Reinforcement (S5.10.10.2)
			3.3.7.6. Design Step 5.7.6 Force in the Longitudinal Reinforcement Including  the Effect of the Applied Shear (S5.8.3.5)
			3.3.7.7. AASHTO-LRFD Design Step 5.7.7 Horizontal Shear between the Beam and Slab
	3.4. Computer Applications for the Design  of PSC I-Girder Bridge Superstructure  in AASHTO LRFD
	References
Chapter 4
Design of Bridge Abutments
	Abstract
	4.1. General
		4.1.1. Integral Abutment Design in AASHTO-LRFD Design Step 7.1
			4.1.1.1. General Considerations and Common Practices
			4.1.1.2. Design Criteria
			4.1.1.3. Bridge Length Limits
			4.1.1.4. Soil Conditions
			4.1.1.5. Skew Angle
			4.1.1.6. Horizontal Alignment and Bridge Plan Geometry
			4.1.1.7. Vertical Grade
			4.1.1.8. Girder Types, Maximum Depth and Placement
			4.1.1.9. Type and Orientation of Piles
			4.1.1.10. Consideration of Dynamic Load Allowance in Pile Design
			4.1.1.11. Construction Sequence
			4.1.1.12. Negative Moment Connection between the Integral Abutment  and the Superstructure
			4.1.1.13. Wing Walls
			4.1.1.14. Approach Slab
			4.1.1.15. Expansion Joints
			4.1.1.16. Bearing Pads
			4.1.1.17. AASHTO-LRFD Design Step 7.1.1 - Gravity Loads
			4.1.1.18. AASHTO-LRFD Design Step 7.1.2 - Pile Cap Design
			4.1.1.19. AASHTO-LRFD Design Step 7.1.3 Design of Piles
				General Pile Design
			4.1.1.20. AASHTO-LRFD Design Step 7.1.3.1 Pile Compressive Resistance
				Pile Compressive Resistance (S6.15 and S6.9.2)
			4.1.1.21. AASHTO-LRFD Design Step 7.1.3.2 Determine of Number of Piles
				Determine the Number of Piles Required
			4.1.1.22. AASHTO-LRFD Design Step 7.1.3.3 Pile Spacing
				Pile Spacing
			4.1.1.23. AASHTO-LRFD Design Step 7.1.4 Back-Wall Design
				Case A
					Flexural Design for CASE A
					Shear Design for Case A
				Case B
					Flexural Design for CASE B
					Shear Design for CASE B
			4.1.1.24. AASHTO-LRFD Design Step 7.1.5 Wing Wall Design
				Load Case 1
				Load Case 2
	4.2. Computer Applications for the Design  of Bridge Abutment in AASHTO LRFD
	References
Chapter 5
Design of Bridge Piers
	Abstract
	5.1. General
	5.2. Pier Design in AASHTO-LRFD
		5.2.1. AASHTO-LRFD Design Step 7.2 Intermediate Pier Design
			5.2.1.1. Dead Load
			5.2.1.2. Live Load Transmitted from the Superstructure to the Substructure
			5.2.1.3. Load Combinations
			5.2.1.4. Temperature and Shrinkage Forces
			5.2.1.5. Torsion
			5.2.1.6. Superstructure Dead Load
				Pier Cap Un-Factored Dead Load
				Single Column Un-Factored Dead Load
				Single Footing Un-Factored Dead Load
				Live Load from the Superstructure
				Braking Force (BR) (S3.6.4)
				Wind Load on Superstructure (S3.8.1.2)
				Wind Load Transverse to the Superstructure
				Wind Load along Axes of Superstructure  (Longitudinal Direction)
				Resultant Wind Load along Axes of Pier
				Wind Load on Substructure (S3.8.1.2.3)
				Wind on Live Load (S3.8.1.3)
				Temperature Force (S3.12.2)
				Shrinkage (S3.12.4)
				Load Combinations
		5.2.2. AASHTO-LRFD Design Step 7.2.2 Pier Cap Design
		5.2.3. AASHTO-LRFD Design Step 7.2.2.1 -  Pier Cap Flexural Resistance (S5.7.3.2)
			5.2.3.1. Pier Cap Flexural Resistance (S5.7.3.2)
		5.2.4. AASHTO-LRFD Design Step 7.2.2.2 -  Maximum Positive Moment and Reinforcement
			5.2.4.1. Maximum Positive Moment
			5.2.4.2. Check Positive Moment Resistance (Bottom Steel)
				Limits for Reinforcement (S5.7.3.3)
				Check the Minimum Reinforcement Requirements (S5.7.3.3.2)
		5.2.5. AASHTO-LRFD Design Step 7.2.2.3 -  Maximum Negative Moment and Reinforcement
			5.2.5.1. Maximum Negative Moment
			5.2.5.2. Check Negative Moment Resistance (Top Steel)
			5.2.5.3. Limits for Reinforcement (S5.7.3.3)
			5.2.5.4. Check Minimum Reinforcement (S5.7.3.3.2)
			5.2.5.5. Check the Service Load Applied Steel Stress, fs, Actual
		5.2.6. AASHTO-LRFD Design Step 7.2.2.4  Check Minimum Temperature and Shrinkage Steel
		5.2.7. AASHTO-LRFD Design Step 7.2.2.5 - Skin Reinforcement
			5.2.7.1. Skin Reinforcement (S5.7.3.4)
		5.2.8. AASHTO-LRFD Design Step 7.2.2.6 - Maximum Shear
			5.2.8.1. Maximum Shear
			5.2.8.2. Check the Minimum Transverse Reinforcement (S5.8.2.5)
			5.2.8.3. Check the Maximum Spacing of the Transverse Reinforcement (S5.8.2.7)
		5.2.9. AASHTO-LRFD Design Step 7.2.3 - Column Design
			5.2.9.1. Required Information
			5.2.9.2. Applied Moments and Shears
			5.2.9.3. Maximum Shear Occurs on Column 1 at 0.0 ft. from the Bottom (Top Face of Footing)
			5.2.9.4. Check Limits for Reinforcement in Compression Members (S5.7.4.2)
			5.2.9.5. Strength Reduction Factor, ϕ, to Be Applied to the Nominal Axial Resistance (S5.5.4.2)
		5.2.10. AASHTO-LRFD Design Step 7.2.3.1
			5.2.10.1. Slenderness Effects
			5.2.10.2. Slenderness Ratio in the Plane of the Bent
			5.2.10.3. Slenderness Ratio out of the Plane of the Bent
			5.2.10.4. Moment Magnification in the Bent
		5.2.11. AASHTO-LRFD Design Step 7.2.3.2 -  Transverse Reinforcement for Compression Members
			5.2.11.1. Transverse Reinforcement for Compression Members (S5.10.6)
		5.2.12. AASHTO-LRFD Design Step 7.2.4 Footing Design
			5.2.12.1. Required Information:
			5.2.12.2. Location of Critical Sections
			5.2.12.3. Determine the Critical Faces along the y-Axis for Moment
			5.2.12.4. Determine the Critical Faces along the x-Axis for Moment
			5.2.12.5. Design Factored Loads at the Critical Section
			5.2.12.6. Sample Calculations for the Critical Footing under the Critical Case of Loading
			5.2.12.7. Moment
			5.2.12.8. Shear
		5.2.13. AASHTO-LRFD Design Step 7.2.4.1 Flexural Resistance (S5.7.3.2)
		5.2.14. AASHTO-LRFD Design Step 7.2.4.2 Limits  for Reinforcement (S5.7.3.3)
			5.2.14.1. Check Maximum Reinforcement (S5.7.3.3.1)
			5.2.14.2. Check the Moment Resistance for Moment at the Critical Transverse Face
		5.2.15. AASHTO-LRFD Design Step 7.2.4.3 Control  of Cracking by Distribution of Reinforcement (S5.7.3.4)
			5.2.15.1. Check Distribution about Footing Length, L
			5.2.15.2. Check Actual Steel Stress, fs, Actual
			5.2.15.3. Check Distribution about Footing Width, W
		5.2.16. AASHTO-LRFD Design Step 7.2.4.4 Shear Analysis
			5.2.16.1. Check Design Shear Strength (S5.8.3.3)
			5.2.16.2. Determine the Location of the Critical Face  along the y-Axis
			5.2.16.3. Determine the Location of the Critical Face  along the x-Axis
			5.2.16.4. Determine One-Way Shear Capacity for Longitudinal Face (S5.8.3.3)
			5.2.16.5. Determine Two-Way (Punching) Shear Capacity at the Column (S5.13.3.6.3)
		5.2.17. AASHTO-LRFD Design Step 7.2.4.5 Foundation Soil Bearing Resistance at the Strength Limit State (S10.6.3)
			5.2.17.1. Foundation Assumptions
			5.2.17.2. Footing Effective Dimensions
			5.2.17.3. Resistance Factor
	5.3. Computer Applications  for the Design of Bridge Piers in AASHTO LRFD
	References
Chapter 6
Design of Pre-Stressed  Post Tension Box-Girder Bridge Superstructures in AASHTO-LRFD
	Abstract
	6.1. General
	6.2. Basic Concepts of Post Tension
	6.3. Material Properties
	6.4. Design of Pre-Stressed Post Tension  Box-Girder Bridge
		6.4.1. Service Limit State Design (3.5.5)
		6.4.2. Strength Limit State Design (3.5.6.1 Flexural Strength Design Check)
		6.4.3. Shear Strength Design Check (3.5.6.2)
		6.4.4. Longitudinal Design (3.6.1 Design Methodology)
		6.4.5. Tendon Layout and Envelope (3.6.2)
		6.4.6. Design of Top RCC Deck Slab
			6.4.6.1. 2-Span Cast-in-Place Post-Tensioned Concrete Box Girder Bridge [CIPPTCBGB] Design
			6.4.6.2. AASHTO LRFD [Table 2.5.2.6.3-1] Minimum Requirements
				AASHTO LRFD Cl. [9.7.1.1] [BDG]
				AASHTO LRFD Cl. [5.14.1.5.1b] [BDG]
				AASHTO LRFD Cl. [C5.14.1.5.1c] [BDG]
				Concrete Deck Slab Minimum Requirements
			6.4.6.3. AASHTO Cl. [5.4.3.1] and [5.4.3.2] Reinforcing Steel
			6.4.6.4. AASHTO LRFD [Table 5.4.4.1-1] and [5.4.4.2] Pre-Stressing STRAND
			6.4.6.5. AASHTO LRFD Cl. [5.4.2.1] [BDG] Concrete
				Superstructure Column & Drilled Shaft
					AASHTO LRFD [Table 3.5.1-1]
					AASHTO LRFD Cl. [C3.5.1]
					AASHTO LRFD Cl. [C5.4.2.4]
					AASHTO LRFD Cl. [5.7.1]
					AASHTO LRFD Cl. [5.7.2.2]
			6.4.6.6. AASHTO LRFD Cl. [5.4.2.6] Modulus of Rupture
				Service Level Cracking
				Minimum Reinforcing
			6.4.6.7. AASHTO LRFD Cl. [1.3.2] Limit States
			6.4.6.8. AASHTO LRFD Cl. [1.3.3] Ductility
			6.4.6.9. AASHTO LRFD Cl. [3.4.1] [BDG] Redundancy
			6.4.6.10. AASHTO LRFD Cl. [1.3.4] and [1.3.5]  Operational Importance
				AASHTO LRFD Cl. [3.4.1] [BDG]
			6.4.6.11. Deck Design [BDG]
			6.4.6.12. AASHTO LRFD Cl. [9.7.2.3] Effective Length [BDG]
			6.4.6.13. AASHTO LRFD Cl. [9.6.1] Method of Analysis [BDG]
			6.4.6.14. AASHTO LRFD Cl. [A4.1] Live Loads
				Positive Moment Design
			6.4.6.15. AASHTO LRFD Cl. [9.5.2] Service I Limit State [BDG]
			6.4.6.16. AASHTO Cl. [9.5.2] Allowable Stress [BDG]
			6.4.6.17. Control of Cracking
				AASHTO Cl. [5.7.3.4]
				AASHTO Cl. [5.7.3.4-1]
			6.4.6.18. AASHTO LRFD [Table 3.4.1-1] Strength I Limit State
			6.4.6.19. AASHTO LRFD [5.7.3] and [5.7.3.2.2-1] Flexural Resistance
				AASHTO LRFD [5.7.3.1.1-4]
				AASHTO LRFD [5.7.3.2.3]
				AASHTO Cl. [5.5.4.2.1]
			6.4.6.20. AASHTO Cl. [5.7.3.3.1] Maximum Reinforcing
			6.4.6.21. AASHTO Cl. [5.7.3.3.2] Minimum Reinforcing
			6.4.6.22. AASHTO Cl. [9.5.3] & [5.5.3.1] Fatigue Limit State
			6.4.6.23. AASHTO Cl. [9.7.3.2] Distribution Reinforcement
			6.4.6.24. AASHTO Cl. [9.7.1.3] Skewed Decks [BPG]
			6.4.6.25. Negative Moment Design
			6.4.6.26. Service Limit State
				AASHTO LRFD [9.5.2] [BDG] & [Table 3.4.1-1]
			6.4.6.27. Allowable Stress
				AASHTO Cl. [9.5.2] [BDG]
			6.4.6.28. Control of Cracking
				AASHTO Cl. [5.7.3.4]
				AASHTO Cl. [5.7.3.4-1]
			6.4.6.29. AASHTO Cl. [3.4.1] Strength I Limit State
			6.4.6.30. AASHTO Cl. [5.7.3] Flexural Resistance
				AASHTO Cl. [5.7.3]
				AASHTO Cl. [5.7.3.1.1-4]
				AASHTO Cl. [5.7.3.2.3]
				AASHTO Cl.[5.5.4.2.1]
			6.4.6.31. AASHTO Cl. [5.7.3.3.2] Minimum Reinforcing
			6.4.6.32. AASHTO Cl. [9.5.3] & [5.5.3.1] Fatigue Limit State
			6.4.6.33. AASHTO Cl. [C4.6.2.1.6] Shear
			6.4.6.34. Overhang Design
				AASHTO Cl. [Appendix A13] and AASHTO Cl. [Article A13.4.1]
					Design Case 1
				AASHTO Cl. [A13.3.1-1]
				AASHTO Cl. [A13.3.1-2]
				AASHTO Cl. [Section 9] [BDG]
					Barrier Connection to Deck
					Flexure
			6.4.6.35. Shear
			6.4.6.36. Moment at Face of Barrier
				AASHTO Cl. [3.5.1] [BDG]
				[Appendix A 13] AASHTO Cl. [A13.4.1]
				Extreme Event II
				AASHTO LRFD [Table 3.4.1-1]
			6.4.6.37. Simplified Method
			6.4.6.38. Development Length AASHTO Cl. [5.11.2]
				AASHTO Cl. [5.11.2.1.1]
				Exterior Support, Location 2, Figure 6.8
				Dimensions
				Moment at Exterior Support
					DC Loads
					DW Loads
					Extreme Event II AASHTO Cl. [A13.4.1][3.4.1]
				Interior Support Location 3 Figure 6.7
					Design Case 1
					Dimensions
					Moment at Interior Support
					Extreme Event II AASHTO Cl. [A13.4.1] and [3.4.1]
					Extreme Event II AASHTO Cl. [A13.4.1] and [3.4.1] Design Case 2: Vertical forces specified in AASHTO Cl. [A13.2] and Extreme Event in  Limit State AASHTO Cl. [A13.4.1]
				AASHTO Cl. [A13.2-1]
				Flexural Resistance AASHTO Cl. [5.7.3.2]
				AASHTO Cl. [5.7.3.1.1-4]
				AASHTO Cl. [C 5.5.4.2.1]
				AASHTO Cl. [1.3.2.1]
				LL Distribution AASHTO Cl. [BDG]
				AASHTO LRFD [Table 4.6.2.1.3-1]
				AASHTO LRFDIM [3.6.2]
				Multiple Presence Factor AASHTO Cl. [3.6.1.1.2-1]
					Strength Limit State. Design Case 3: The loads specified in [3.6.1] that occupy the overhang Strength and Service Limit State Design Case 3
				Service I Limit State AASHTO Cl.[3.4.1]
			6.4.1.39. Allowable Stress [BDG]
			6.4.1.40. Control of Cracking
			6.4.1.41. Temperature and Shrinkage Reinforcing AASHTO Cl. [5.10.8]
				AASHTO Cl. [5.10.8-1]
				AASHTO Cl. [5.10.8-2]
					Top Slab
					Bottom Slab
			6.4.1.42. Superstructure Design - Section Properties
				AASHTO LRFD [10.7.4.2]
				Dead Load AASHTO Cl. [3.5.1]
				Live Load AASHTO Cl. [3.6]
			6.4.1.43. Pre-Stress Secondary Moment
			6.4.1.44. Live Load Distribution
				AASHTO Cl. [4.6.2.2.1]
				AASHTO Cl. [4.6.2.2.2b-1]
			6.4.1.45. Skew Reduction
			6.4.1.46. Dynamic Load Allowance
				AASHTO Cl. [3.6.2.1-1]
				AASHTO Cl. [C5.7.1]
				AASHTO LRFD [Table 3.4.1-1]
		6.4.2. Pre-Stress Design
			6.4.2.1. Step 1 – Assume Cable Path
			6.4.2.2. Step 2 – Verify Cable Path AASHTO Cl. [C5.9.1.6]
			6.4.2.3. Step 3 – Calculate Friction Losses AASHTO Cl. [5.9.5] [BDG]
				AASHTO Cl. [5.9.5.2.2b-1]
					0.6 Span 2
					End Seat Loss 92.09 ft (See Step 4)
					Span 2
					0.4 Span 1
					Non-Jacking End
			6.4.2.4. Step 4 – Calculate Anchor Set Losses
				0.6 Span 2
			6.4.2.5. Step 5 – Calculate Pre-Stress Losses
				Elastic Shortening AASHTO Cl. [C 5.9.5.2.3b-1]
				Pre-Stress Loss
					0.6 Span 2
				Elastic Shortening
				AASHTO Cl. [5.9.5.2.3b-1]
				Time-Dependent Losses AASHTO Cl. [5.9.5] [BDG]
				Shrinkage AASHTO Cl. [5.9.5.] [BDG]
				Creep AASHTO Cl. [5.9.5] [BDG]
				Relaxation AASHTO Cl. [5.9.5] [BDG]
				Total Losses
				Pre-Stress Loss
					0.4 Span 1
				Elastic Shortening
				Shrinkage
				Creep
				Relaxation
				Pre-Stress Loss, Pier Span 2, and Elastic Shortening
				Shrinkage
				Creep
				Relaxation
			6.4.2.6. Step 6 –Check Allowable Stress in Strands
			6.4.2.7. Step 7 – Verify Initial Concrete Strength
				AASHTO Cl. [5.9.4.1.1]
					0.6 Span 2
					0.4 Span 1
					Pier Span 2
					Jacking End
			6.4.2.8. Step 8 – Temporary Tension at Ends AASHTO Cl. [5.9.4.1.2]
			6.4.2.9. Step 9 – Determine Final Concrete Strength AASHTO Cl. [5.9.4.2.1]
				0.6 Span 2
					AASHTO Cl. [5.7.4.7.2c-1]
					AASHTO Cl. [5.7.4.7.1]
				0.4 Span 1
					Case I – Permanent Loads Plus Effective Pre-Stress
					Case II – One-Half the Case I Loads Plus LL + IM
					Case III – Effective Pre-Stress, Permanent Loads and Transient Loads
				Pier Span 2
					Case I – Permanent Loads Plus Effective Pre-Stress
					Case II – One-Half the Case I Loads Plus LL + IM
					Case III – Effective Pre-Stress, Permanent Loads and Transient Loads
			6.4.2.10. Step 10 – Determine Final Concrete Tension [BPG]
				Bottom Fiber at 0.6 Span 2
				Bottom Fiber at 0.4 Span 1
				Top Fiber at Pier Span 2
				[BPG]
				Fatigue Limit State AASHTO Cl. [5.5.3.1]
			6.4.2.11. Step 11 – Flexural Resistance
				0.6 Span 2
					AASHTO Cl. [5.7.3.1.1-1]
					AASHTO Cl. [5.7.3.1.1-2]
					AASHTO Cl. [5.7.3.1.1-4]
					AASHTO Cl. [5.7.3.2.3]
					AASHTO Cl. [5.7.3.2.2-1]
					AASHTO Cl. [5.5.4.2] [BDG]
					Maximum Reinforcing AASHTO Cl. [5.7.3.3.1]
					Minimum Reinforcing AASHTO Cl. [5.7.3.3.2]
					AASHTO Cl. [5.7.3.3.2-1]
			Flexural Resistance
				0.4 Span 1
					AASHTO Cl. [5.7.3.1-1]
					AASHTO Cl. [5.7.3.1.1-4]
					AASHTO Cl. [5.7.3.2.2-1]
					[BDG]
					Maximum Reinforcing AASHTO Cl. [5.7.3.3.1]
					Minimum Reinforcing AASHTO Cl. [5.7.3.3.2]
					AASHTO Cl. [5.7.3.3.2-1]
					Flexural Resistance AASHTO Cl. [5.7.3]
				Pier Span 2
					AASHTO Cl. [5.7.3.1.1-1]
					AASHTO Cl. [5.7.3.1.1-4]
					AASHTO Cl. [5.7.3.1.1-3]
					AASHTO Cl. [5.7.3.2.3]
					AASHTO Cl. [5.7.3.2.2-1]
					[BDG]
					Minimum Reinforcing AASHTO Cl. [5.7.3.3.2]
					AASHTO Cl. [5.7.3.3.2-1]
					AASHTO Cl. [5.7.3.1.1-3]
					[BDG]
			6.4.2.12. Step 12 – Shear Design (LRFD Method) AASHTO Cl. [5.8]
				AASHTO Cl. [5.8.3.2] dv [5.8.2.9] Critical Section
				Step 1  – Determine Shear
					Live Load Distribution AASHTO Cl. [4.6.2.2.1]
					AASHTO LRFD [Table 4.6.2.2.3a-1]
					Skew Effect AASHTO LRFD [Table 4.6.2.2.3c-1]
				Step 2  – Determine Analysis Model
					Sectional Model AASHTO Cl. [5.8.3]
				Step 3  – Shear Depth, dv
					AASHTO Cl. [5.7.3.1.1-3]
					AASHTO Cl. [5.7.3.2.3]
					AASHTO Cl. [5.7.3.1.1-1]
				Step 4  – Calculate, Vp
				Step 5  – Check Shear Width, bv
					AASHTO Cl. [5.8.3.3-2]
				Step 6  – Evaluate Shear Stress
					AASHTO Cl. [5.8.2.9-1]
				Step 7  – Estimate Crack Angle θ
				Step 8  – Calculate Strain, εx
					AASHTO Cl. [5.8.3.4.2-3]
					AASHTO Cl. [5.8.3.4.2-1]
				Step 9  - Calculate Concrete Shear Strength, Vc
					AASHTO Cl. [5.8.3.3-3]
				Step 10  - Determine Required Vertical Reinforcement, Vs
					AASHTO Cl. [5.8.3.3-2]
					AASHTO Cl. [5.8.3.3-1]
				Step 11  - Longitudinal Reinforcement
					[BDG]
		6.4.3. Computer Applications for the Design of PSC Box-Girder Bridge Superstructure in AASHTO LRFD
	References
Conclusion
About the Author
Index
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