Design Example Precast Balanced Cantilever Bridge Design Using AASHTO LRFD Bridge Design Specifications Prepared by Teddy S. Theryo, PE Major Bridge Service Center Prepared for American Segmental Bridge Institute January, 2005 NOTICE OF DISCLAIMER This document is a draft effort at developing a design example of a precast balanced cantilever bridge design based on the third edition of the AASHTO LRFD Bridge Design Specifications, 2004. In its current form, it is not intended to represent a definitive reference for the design of either a segmental bridge or for the application of the LRFD Specifications to segmental bridge design. Additionally, the design steps shown in this example problem do not represent all of the steps that are required for the complete design of a segmental box girder bridge. TABLE OF CONTENTS 1. Introduction..................................................................................................................1-1 2. Design Criteria............................................................................................................2-1 3. Span Configuration and Typical Sections.......................................................3-1 4. Erection Scheme........................................................................................................4-1 5. Deck Design 5.1 Introduction...............................................................................................................5-1 5.2 Design Approach......................................................................................................5-1 5.3 Live Load Analysis...................................................................................................5-4 5.4 Post-Tensioning Tendon Layout............................................................................5-15 5.5 Summary of Design Forces...................................................................................5-17 5.6 Service Limit State Design.....................................................................................5-17 5.7 Ultimate Flexural Strength Check..........................................................................5-20 5.8 Ultimate Shear Strength Check.............................................................................5-20 6. Longitudinal Design 6.1 Design Methodology................................................................................................6-1 6.2 Tendon Layout/Envelope.........................................................................................6-2 6.3 LRFD Live Load.......................................................................................................6-7 6.4 Shear Lag Effect....................................................................................................6-14 6.5 Temperature Load..................................................................................................6-19 6.6 Time Dependent Effect..........................................................................................6-24 6.7 Secondary Forces..................................................................................................6-27 6.8 Summary of Design Forces...................................................................................6-31 6.9 Service Limit State Design.....................................................................................6-39 6.10 Principal Tension Stress Check.............................................................................6-52 6.11 Flexural Strength Check.........................................................................................6-56 6.12 Shear and Torsion Design.....................................................................................6-59 7. Construction Stage Analysis 7.1 Stability during Construction....................................................................................7-1 7.2 Erection Tendons...................................................................................................7-10 8. Detailing 8.1 Combined Transverse Bending and Longitudinal Design.......................................8-1 8.2 Shear Key Design....................................................................................................8-1 9. Discussion and Recommendations for Improvement 9.1 Discussion................................................................................................................9-1 9.2 Longitudinal Design..................................................................................................9-1 9.3 Transverse Design...................................................................................................9-2 10. Acknowledgment.....................................................................................................10-1 11. Reference .................................................................................................................11-1 LRFD Design Example Precast Balanced Cantilever 1-1 1. INTRODUCTION The AASHTO-PCI-ASBI Joint Committee was formed in Chicago, Illinois in October, 1994. The main goal of the committee was to develop a set of standard box sections for precast segmental grade separation bridges which would cover bridges of short to medium span ranges (approximately 200’-0” maximum span). The present practice in the industry shows that only sufficiently large projects can be competitively built using the precast segmental erection method due to the high cost of setting up a casting yard which is generally used only for one particular project. However, by using standardized cross sections, it is expected that precasters in the concrete industry could afford to build their own casting cells due to potential for repetitive work from contractors. In addition, the standard cross sections would be useful for structural engineers as an initial section for conceptual design and preliminary design stages. Development of a family of standardized segmental box girder sections in metric units was completed and published by PCI / ASBI in 1998. The next step of the Committee’s work is to evaluate the proposed standard sections through the creation of design examples. Three separate design examples were created: span-by-span erection with all external tendons, span- by-span erection with both external and internal tendons, and balanced cantilever erection. In additional to design issues, detailing will be discussed. The design examples will be done in accordance with the current AASHTO LRFD Bridge Design Specifications, Third Edition, 2004. This design example has been extensively used over the years in the annual ASBI “Design and Construction of Segmental Concrete Bridges” Seminar since its publication in 1996. The following design report will cover only precast segmental balanced cantilever construction. The design example is a five-span precast segmental bridge with three 200’-0” interior spans and two 150’-0” end spans. The bridge will be supported on bearings, all of which are sliding bearings except for fixed bearings at Pier 4. The width of the bridge deck is 43’-0” which will accommodate two lanes of traffic plus inside and outside shoulders of an interstate ramp. The Type 2700-2 AASHTO-PCI-ASBI Standard Section was selected for this design example. The section depth is 9’-0” with a maximum span-to-depth ratio of 22. This report will also make a brief comparative study between AASHTO LRFD and LFD Design Specifications Load Combinations, including shear design. The longitudinal analysis of the bridge will be performed using the Proprietary TANGO Program which enables the effects of stage-by-stage construction and time dependent analysis to be considered in the design. The transverse design will be accomplished with the aid of Proprietary GT-STRUDL and BDAC Programs. LRFD Design Example Precast Balanced Cantilever 2-1 2. DESIGN CRITERIA The following criteria will be used for this design example: A. Specifications, Codes, and Standards: AASHTO LRFD Bridge Design Specifications, Third Edition 2004 B. Design Loadings: 1. Load Modifier: A load modifier of 1.0 will be used for all limit states based on redundant members with the possibility of non-ductile components and connections, assuming an operational importance factor of 1.0 for all components. 2. Dead Load: Unit Weight of Reinforced Concrete (DC): 0.150 KCF (23.5 KN/m3) Unit Weight of Post-Tensioned Concrete (DC): 0.155 KCF (24.3 KN/m3) Wearing Surface (DW): 0.015 KSF (0.72 KN/m2) Traffic Barriers (DC): 0.421 KLF (6.14 KN/m each) Weight of Blisters (DC): 1 KIP each (4.4 KN each) 3. Live Load: Vehicle: HL-93 (3 design lanes) using multiple presence factors and dynamic load allowance, as appropriate. 4. Wind Loads: Design in accordance with LRFD Article 3.8. 5. Thermal Forces: Seasonal Variation: Mean Temperature: 70o F (21oC) Thermal Coefficient: 6.5 x 10-6 o F (10.8 x 10-6 per oC) Temperature Rise: 30o F (17o C) Temperature Fall: 45o F (25o C) Differential Temperature: Longitudinal: Non-linear temperature gradient as per LRFD Article 3.12.3 using a plain concrete surface for Solar Radiation Zone 3. Transverse: Reversible linear gradient of 10o F (6o C) between inside and outside of box girders. 6. Creep and Shrinkage: Strains calculated in accordance with CEB-FIP 1990 Model Code for superstructures. 7. Earthquake: Seismic Zone 1 Acceleration Coefficient: 0.06 Soil Type II 8. Construction Loads: LRFD Design Example Precast Balanced Cantilever Construction 2-2 Construction loads are in accordance with LRFD Article 5.14.2.3. using the appropriate construction load combinations and allowable stresses. Load factor for temperature gradient during construction γ = 0.0. TG C. MATERIALS: 1. Concrete: 28 day Cylinder Compressive Strength: 6.0 KSI (42 Mpa) Modulus of Elasticity: 4933 KSI (34,000 Mpa) Allowable Stresses: As per LRFD Article 5.9.4. Superstructure concrete cover for main reinforcing, plastic (PE) ducts, and hardware: Top riding surface 2 Inches (50 mm) Exterior and interior 2 Inches (50 mm) Concrete cover to plastic ducts shall not be less than one-half the diameter of the duct. 2. Reinforcing Steel: Yield Strength: 60 KSI (400 Mpa) Modulus of Elasticity: 29,000 KSI (200,000 Mpa) 3. Prestressing Steel: Strand tendons shall consist of low-relaxation steel. Material Properties: Ultimate Tensile Strength (f ): 270 KSI (1860 Mpa) pu Yield Strength (fpy): 243 KSI (1674 Mpa) Apparent Modulus of Elasticity: 28,500 KSI (197,000 Mpa) Friction Coefficient: 0.23 per RAD Wobble Coefficient: 0.00020 per ft (0.00066 per m) Anchor Set: 3/8 “ (10 mm) Allowable Stresses: Jacking Force: 0.80 f pu At anchorages After Anchoring 0.70 f pu At other locations After Anchoring 0.74 f pu At Service Limit State After Losses 0.80 f py Bar tendons shall consist of high strength threaded bars. Material Properties: Ultimate Tensile Strength (f ): 150 KSI (1035 Mpa) pu Yield Strength (f ): 120 KSI (828 Mpa) py Modulus of Elasticity: 30,000 KSI (207,000 Mpa) Friction Coefficient: 0.30 per RAD Wobble Coefficient: 0.00020 per ft (0.00066 per m) Anchor Set: 0.0625 inches (1.6 mm) Allowable Stresses: Permanent Bars: Jacking Force: 0.75 f pu At Anchorages After Anchoring: 0.66 f pu At Service Limit State After Losses: 0.80 f py Temporary Bars for Reuse: LRFD Design Example Precast Balanced Cantilever Construction 2-3 Jacking Force 0.50 f pu D. Design Method: All applicable limit states (Strength, Extreme Event, Service, and Fatigue) will be satisfied in accordance with the LRFD Specifications. LRFD Design Example Precast Balanced Cantilever Construction 3-1 3. SPAN CONFIGURATION AND TYPICAL SECTIONS The structure is a five-span bridge with span configuration of 150’, 200’, 200’, 200’, 150’, producing a total length of 900 feet. The bridge carries two 12’-0” lanes of traffic in one direction with a left shoulder width of 6’-0” and a right shoulder width of 10’-0”. Expansion bearings are placed at all piers except Pier 4 which is fixed. The typical section selected is the AASHTO-PCI-ASBI Segmental Box Girder Standard Type 2700-2, a single-cell concrete box girder with 43’-0” wide deck and 9’-0” in depth. Cantilevered overhangs are 10’-4.5” each. Minimum top slab thickness is 9”. The thickness of the bottom slab is 18” for three segments on both sides of each pier and 9” thick elsewhere. The thickness of the webs is 16”, which are sloped at 2.5:1. The top slab can accommodate 12 tendons in each half of the box girder, for a total of 24 tendons in the top slab. The bottom slab can accommodate 6 tendons in each half of the box, for a total of 12 tendons in the bottom slab. Additional tendons may still be accommodated either in the top or bottom slab. When dealing with development of a cross-section, it is important to investigate the efficiency of the proposed cross-section. The section efficiency of the AASHTO-PCI-ASBI 2700-2 section can be computed using Guyon’s formula: I ρ= c A y y c t b where, I = Moment of inertia of the section c A = Area of the section c y = Distance from the top fiber to the center of gravity of the section t y = Distance from the bottom fiber to the center of gravity of the section b The efficiency of the cross-section, ρ, is 0.6 which is considered to be high. For the sake of comparison, the flat slab is the most inefficient section with a ρ value of 0.33. This design example utilizes a 12’-0” typical segment length, resulting in a maximum segment weight of 72.5 tons for the thin bottom slab segment and 80 tons for the thick bottom slab segment. LRFD Design Example Precast Balanced Cantilever Construction 3-2 LRFD Design Example Precast Balanced Cantilever Construction