Contenido Computational Analysis and Design of Bridge Structures

Gain Confidence in Modeling Techniques Used for Complicated Bridge Structures

Bridge structures vary considerably in form, size, complexity, and importance. The methods for their computational analysis and design range from approximate to refined analyses, and rapidly improving computer technology has made the more refined and complex methods of analyses more commonplace. The key methods of analysis and related modeling techniques are set out, mainly for highway bridges, but also with some information on railway bridges. Special topics such as strut-and-tie modeling, linear and nonlinear buckling analysis, redundancy analysis, integral bridges, dynamic/earthquake analysis, and bridge geometry are also covered. The material is largely code independent. The book is written for students, especially at MSc level, and for practicing professionals in bridge design offices and bridge design authorities worldwide.

Effectively Analyze Structures Using Simple Mathematical Models
 
Divided into three parts and comprised of 18 chapters, this text:
 

•Covers the methods of computational analysis and design suitable for bridge structures
•Provides information on the methods of analysis and related modeling techniques suitable for the design and evaluation of various types of bridges
•Presents material on a wide range of bridge structural types and is fairly code independent

Computational Analysis and Design of Bridge Structures covers the general aspects of bridges, bridge behavior and the modeling of bridges, and special topics on bridges. This text explores the physical meanings behind modeling, and reveals how bridge structures can be analyzed using mathematical models.

Table Contents

Preface
Acknowledgments
Authors

Part I General

1 Introduction
1.1 History of bridges
1.2 Bridge types and design process
1.3 Loads and load factors 9
1.4 Current development of analysis and design of bridges
1.5 Outlook on analysis and design of bridges

2 Approximate and refined analysis methods

2.1 Introduction
2.2 Various bridge structural forms
       2.2.1 Beam deck type
       2.2.2 Slab deck type
       2.2.3 Beam–slab deck type
       2.2.4 Cellular deck type
2.3 Approximate analysis methods
       2.3.1 Plane frame analysis method
2.4 Refined analysis methods
       2.4.1 Grillage analogy method
       2.4.2 Orthotropic plate method
       2.4.3 Articulated plate method
       2.4.4 Finite strip method
       2.4.5 Finite element method
       2.4.6 Live load influence surface
2.5 Different types of bridges with their selected mathematical modeling
      2.5.1 Beam bridge and rigid frame bridge
      2.5.2 Slab bridge
      2.5.3 Beam–slab bridge
      2.5.4 Cellular/box girder bridge
      2.5.5 Curved bridge
      2.5.6 Truss bridge
      2.5.7 Arch bridge
      2.5.8 Cable-stayed bridge
      2.5.9 Suspension bridge
 
3 Numerical methods in bridge structure analysis

3.1 Introduction
3.2 Finite element method
      3.2.1 Basics
      3.2.2 Geometric and elastic equations
      3.2.3 Displacement functions of an element
      3.2.4 Strain energy and principles of minimum potential energy and virtual works
      3.2.5 Displacement relationship processing when assembling global stiffness matrix
      3.2.6 Nonlinearities
      3.2.7 Frame element
      3.2.8 Elastic stability
      3.2.9 Applications in bridge analysis
3.3 Automatic time incremental creep analysis method
      3.3.1 Incremental equilibrium equation in creep and shrinkage analysis
      3.3.2 Calculation of equivalent loads due to incremental creep and shrinkage
      3.3.3 Automatic-determining time step
      3.3.4 A simple example of creep analysis
3.4 Influence line/surface live loading method
      3.4.1 Dynamic planning method and its application in searching extreme live loads
3.4.2 Transverse live loading
3.4.3 Influence surface loading

Part II Bridge behavior and modeling

4 Reinforced concrete bridges

4.1 Introduction
4.2 Concrete and steel material properties
       4.2.1 Unconfined and confined concrete
       4.2.2 Reinforcing steel
       4.2.3 FRC and FRP
                 4.2.3.1 Inverse analysis method
4.3 Behavior of nonskewed/skewed concrete beam–slab bridges
4.4 Principle and modeling of concrete beam–slab bridges
      4.4.1 Linear elastic modeling
      4.4.2 Nonlinear modeling
                4.4.2.1 Cracking and retention of shear stiffness
      4.4.3 FRC/FRP modeling
4.5 2D and 3D illustrated examples: Three-span continuous skewed concrete slab bridges
4.6 2D and 3D illustrated examples: RC T-beam bridge
4.7 3D illustrated examples: Skewed simple-span transversely post-tensioned adjacent precast-concrete slab bridges—Knoxville Bridge, Frederick, Maryland

5 Prestressed/post-tensioned concrete bridges

5.1 Prestressing basics
5.2 Principle and modeling of prestressing
      5.2.1 Tendon modeled as applied loading
      5.2.2 Tendon modeled as load-resisting elements
      5.2.3 2D and 3D modeling
5.3 2D illustrated example of a prototype prestressed/ post-tensioned concrete bridge in the United States
5.4 3D illustrated example of a double-cell post-tensioning concrete bridge—Verzasca 2 Bridge, Switzerland
       5.4.1 Visual Bridge design system
       5.4.2 Verzasca 2 Bridge models
                  5.4.2.1 Model 1: Continuous girder with constant cross section
                  5.4.2.2 Model 2: Continuous girder with skew supports
                  5.4.2.3 Model 3: One girder built in a single stage
                  5.4.2.4 Model 4: Girder built with actual construction stages
                  5.4.2.5 Model 5: Three girders skew supported
       5.4.3 Verzasca 2 Bridge analysis results
                  5.4.3.1 Model 1: Continuous girder with constant cross section
                  5.4.3.2 Model 2: Continuous girder with skew supports
                  5.4.3.3 Model 3: One girder built in a single stage
                  5.4.3.4 Model 4: Girder built with actual construction stages
                  5.4.3.5 Model 5: Three girders skew supported
5.5 3D illustrated example of US23043 precast prestressed concrete beam bridge—Maryland
       5.5.1 US23043 bridge models
                  5.5.1.1 Model 1: Slab modeled with plate elements
                  5.5.1.2 Model 2: Slab modeled with beam elements
       5.5.2 US23043 bridge analysis results
                  5.5.2.1 Model 1: Slab modeled with beam elements
5.6 Illustrated example of a three-span prestressed box-girder bridge
5.7 Illustrated example of long-span concrete cantilever bridges—Jiangsu, People’s Republic of China
      5.7.1 The continuous rigid frame of Sutong Bridge approach spans
      5.7.2 Results of webs’ bent-down tendons
      5.7.3 Results of two approaches on deflections

6 Curved concrete bridges

6.1 Basics of curved concrete bridges
      6.1.1 Introduction
      6.1.2 Stresses of curved concrete box under torsion
                6.1.2.1 Equations for multiple cells
                6.1.2.2 Equilibrium equations
                6.1.2.3 Compatibility equations
                6.1.2.4 Constitutive laws of materials
      6.1.3 Construction geometry control
6.2 Principle and modeling of curved concrete bridges
      6.2.1 Modeling of curved concrete bridges
      6.2.2 Modeling of material properties
      6.2.3 Modeling of live loads
      6.2.4 Modeling of lateral restraint and movement
6.3 Spine model illustrated examples of Pengpo Interchange, Henan, People’s Republic of China
6.4 Grillage model illustrated examples—FHWA Bridge No. 4
6.5 3D finite element model illustrated examples—NCHRP case study bridge

7 Straight and curved steel I-girder bridges

7.1 Behavior of steel I-girder bridges
       7.1.1 Composite bridge sections under different load levels
       7.1.2 Various stress effects
       7.1.3 Section property in the grid modeling considerations
7.2 Principle and modeling of steel I-girder bridges
       7.2.1 Analysis methods
       7.2.2 Modeling in specific regions
       7.2.3 Live load application
       7.2.4 Girder–substringer systems
       7.2.5 Steel I-girder bridge during construction
7.3 2D and 3D illustrated example of a haunched steel I-girder bridge—MD140 Bridge, Maryland
7.4 2D and 3D illustrated example of a curved steel I-girder bridge—Rock Creek Trail Pedestrian Bridge, Maryland
7.5 2D and 3D illustrated example of a skewed and kinked steel I-girder bridge with straddle bent
7.6 2D and 3D illustrated example of a global and local modeling of a simple-span steelI-girder bridge—I-270 Middlebrook Road
Bridge, Germantown, Maryland

8 Straight and curved steel box girder bridges

8.1 Behavior of steel box girder bridges
       8.1.1 Bending effects
                 8.1.1.1 Longitudinal bending
                 8.1.1.2 Bending distortion
       8.1.2 Torsional effects
                 8.1.2.1 Mixed torsion
                 8.1.2.2 Torsional distortion
       8.1.3 Plate behavior and design
8.2 Principle and modeling of steel box girder bridges
       8.2.1 2D and 3D finite element method
       8.2.2 Consideration of modeling steel box girder bridges
                 8.2.2.1 Design considerations
                 8.2.2.2 Construction
                 8.2.2.3 Description of the noncomposite  bridge models
8.3 2D and 3D illustrated examples of a straight box girder bridge
       8.3.1 Straight box shell model (M1)
       8.3.2 Straight box beam model (M3)
       8.3.3 Comparison results
8.4 2D and 3D illustrated examples of a curved box girder bridge—Metro bridge over I495, Washington, DC
       8.4.1 Curved box shell model (M2)
       8.4.2 Curved box beam model (M4)
8.5 2D and 3D illustrated examples of threespan curved box girder bridge—Estero Parkway Bridge, Lee County, Florida

9 Arch bridges

9.1 Introduction
      9.1.1 Classifications of arch bridges
9.2 Construction of arch bridges
      9.2.1 Lupu Bridge, People’s Republic of China
                9.2.1.1 Foundations
                9.2.1.2 Arch ribs
                9.2.1.3 Deck girders
      9.2.2 Yajisha Bridge, People’s Republic of China
                9.2.2.1 Cross section of the main arch
                9.2.2.2 Vertical rotation
                9.2.2.3 Horizontal rotation
9.3 Principle and analysis of arch bridges
      9.3.1 Perfect arch axis of an arch bridge
      9.3.2 Fatigue analysis and affecting factors
               9.3.2.1 Positions of hangers
               9.3.2.2 Space of hangers
               9.3.2.3 Distance between side hanger and arch springing
     9.3.3 Measuring of hanger-cable force
9.4 Modeling of arch bridges
     9.4.1 Arches
     9.4.2 Deck
     9.4.3 Hangers
     9.4.4 Stability
9.5 3D illustrated example of construction analyses—Yajisha Bridge, Guangzhou, People’s Republic of China
9.6 3D illustrated example of a proposed tied-arch bridge analyses—Linyi, People’s Republic of China
9.7 3D illustrated example of an arch bridge—Liujiang Yellow River Bridge, Zhengzhou,People’s Republic of China

10 Steel truss bridges

10.1 Introduction
10.2 Behavior of steel truss bridges
         10.2.1 Simple and continuous truss bridges
         10.2.2 Cantilevered truss bridges
         10.2.3 Truss arch bridges
10.3 Principle and modeling of steel truss bridges
10.4 3D illustrated example—Pedestrian pony truss bridge
10.5 2D illustrated example—Tydings Bridge, Maryland
         10.5.1 Thermal analysis
10.6 3D illustrated example—Francis Scott Key Bridge, Maryland
10.7 3D illustrated examples—Shang Xin Bridge, Zhejiang, People’s Republic of China

11 Cable-stayed bridges

11.1 Basics of cable-stayed bridges
11.2 Behavior of cable-stayed bridges
        11.2.1 Weakness of cable supports
        11.2.2 Ideal state
        11.2.3 Desired state
        11.2.4 Anchor of pylons
        11.2.5 Backward and forward analyses
        11.2.6 Geometric nonlinearity—P-Delta effect
        11.2.7 Geometric nonlinearity—Cable sag effect
        11.2.8 Geometric nonlinearity—Large displacements
        11.2.9 Stability
        11.2.10 Dynamic behavior
11.3 Construction control
        11.3.1 Observation errors
        11.3.2 Measurement of cable forces
        11.3.3 Construction errors
        11.3.4 General procedures of construction control
11.4 Principle and modeling of cable-stayed bridges
        11.4.1 Main girders
        11.4.2 Pylons
        11.4.3 Connections between girder and pylon
        11.4.4 Cables
11.5 Illustrated example of Sutong Bridge, Jiangsu, People’s Republic of China
11.6 Illustrated example with dynamic mode analysis of Panyu Bridge, Guangdong, People’s Republic of China
11.7 Illustrated example with dynamic mode analysis of long cables with crossties

12 Suspension bridges

12.1 Basics of suspension bridges
12.2 Construction of suspension bridges
         12.2.1 Construction of pylons and anchorages and install catwalk system
         12.2.2 Erection of main cables
         12.2.3 Erection of stiffened girder
12.3 Behavior of suspension bridges
         12.3.1 Basis of cable structures—Initial stress and large displacements
         12.3.2 Basics of suspension bridge analysis
         12.3.3 Live load analyses of a suspension bridge
         12.3.4 Determination of the initial configuration of a suspension bridge
         12.3.5 Consideration of cable tangent changes
         12.3.6 Offset of saddles and release of the deflection of pylons
         12.3.7 Low initial stress stiffness of the main cable close to pylon
12.4 Principle and modeling of suspension bridges
         12.4.1 Main cables
         12.4.2 Hangers
         12.4.3 Stiffened girder
         12.4.4 Pylons
         12.4.5 Saddles
12.5 3D illustrated example of Chesapeake Bay Suspension Bridge, Maryland

Part III  Special topics of bridges

13 Strut-and-tie modeling

13.1 Principle of strut-and-tie model
        13.1.1 Development of STM
        13.1.2 Design methodology
                    13.1.2.1 Struts
                    13.1.2.2 Ties
                    13.1.2.3 Nodes
13.2 Hand-calculation example of STM
         13.2.1 Hammerhead Pier No. 49 of Thomas Jefferson Bridge, Maryland
                     13.2.1.1 Data
                     13.2.1.2 Determination of member forces
                     13.2.1.3 Design of the tie
                     13.2.1.4 Design of the strut
         13.2.2 Representative pile-supported footing
                     13.2.2.1 Check the capacity of the ties
                     13.2.2.2 Check the capacity of struts
                     13.2.2.3 Check nodal zone stress limits
                     13.2.2.4 Check the detailing for the anchorage of the ties
13.3 2D illustrated example 1—Abutment on pile
         13.3.1 General properties
13.4 2D illustrated example 2—Walled pier
13.5 2D illustrated example 3—Crane beam
13.6 2D/3D illustrated example 4—Hammerhead Pier of Thomas Jefferson Bridge
13.7 2D illustrated example 5—Integral bent cap
13.8 Alternate compatibility STM and 2D illustrated example 6—Cracked deep bent cap

14 Stability

14.1 Basics of structural stability
14.2 Buckling
         14.2.1 Linear buckling of a steel plate
                     14.2.1.1 Formulation of plate buckling
                     14.2.1.2 Solving plate and box girder buckling problem
         14.2.2 Linear buckling of steel members
                     14.2.2.1 Buckling of steel structure members
                     14.2.2.2 Buckling analysis of a pony truss by Timoshenko’s method
                     14.2.2.3 Case study of pony truss by Timoshenko’s method
14.3 FEM approach of stability analysis
14.4 3D illustrated example with linear buckling analysisof a pony truss, Pennsylvania
14.5 3D illustrated example with linear buckling analysis of a standard simple arch rib
14.6 3D illustrated example with linear buckling analysis of a proposed tied-arch bridge—Linyi,People’s Republic of China
14.7 3D illustrated example with nonlinear stability analysis of a cable-stayed bridge, Jiangsu, People’s Republic of China

15 Redundancy analysis

15.1 Basics of bridge redundancy
15.2 Principle and modeling of bridge redundancy analysis
        15.2.1 Analysis cases
        15.2.2 Finite element modeling
15.3 3D example with redundancy analysis of a pony truss, Pennsylvania
        15.3.1 Loading cases
        15.3.2 Results
                    15.3.2.1 Extreme event III
                    15.3.2.2 Extreme event IV
15.4 3D redundancy analysis under blast loading of a PC beam bridge, Maryland
         15.4.1 Bridge model
         15.4.2 Attack scenarios
         15.4.3 Analyze structural response
15.5 3D analysis under blast loading of a steel plate girder bridge, Maryland
         15.5.1 Bridge model
         15.5.2 Attack scenarios
         15.5.3 Analyze structural response

16 Integral bridges

16.1 Basics of integral bridges
         16.1.1 Introduction
         16.1.2 Types of integral abutment
16.2 Principle and analysis of IABs
        16.2.1 Force analysis
16.3 Modeling of IABs
        16.3.1 Equivalent cantilever finite element model
        16.3.2 Soil spring finite element model
                    16.3.2.1 Soil spring and p–y curve
                    16.3.2.2 Soil behind the abutment
                    16.3.2.3 Soil around piles
        16.3.3 Soil continuum finite element model
16.4 Illustrated example of a steel girder bridge in soil spring finite element model
        16.4.1 Soil
16.5 Illustrated example of a steel girder bridge in 3D soil continuum finite element model

17 Dynamic/earthquake analysis

17.1 Basics of dynamic analysis
17.2 Principle of bridge dynamic analysis
        17.2.1 Vehicle–bridge interaction
        17.2.2 Pedestrian bridge vibrations
        17.2.3 Bridge earthquake analysis
                    17.2.3.1 Linear and nonlinear seismic analyses
                    17.2.3.2 Nonlinear time-history analysis
        17.2.5 Wind analysis
17.3 Modeling of bridge for dynamic analysis
        17.3.1 Linear elastic dynamic analysis
        17.3.2 Soil stiffness
        17.3.3 Nonlinear analysis
                    17.3.3.1 Nonlinear static—Standard pushover analysis
                    17.3.3.2 Nonlinear static alternate—Modal pushover analysis
17.4 3D illustrated example of earthquake analysis by SPA, MPA, and NL-THA—FHWA Bridge No. 4
         17.4.1 Foundation stiffness
         17.4.2 Finite element model and analyses
17.5 3D illustrated example of a high-pier bridge subjected to oblique incidence seismic waves— Pingtang bridge, People’s Republic of China

18 Bridge geometry

18.1 Introduction
18.2 Roadway curves
        18.2.1 Types of horizontal curves
        18.2.2 Types of vertical curves
        18.2.3 Types of transverse curves
        18.2.4 Superelevation and superwidening
        18.2.5 Bridge curves
18.3 Curve calculations
        18.3.1 Bridge mainline curve model
        18.3.2 Roadway transverse curve model
        18.3.3 Transitions of transverse curves
        18.3.4 Spiral calculation
        18.3.5 Vertical parabola calculation
18.4 Curve and surface tessellation
18.5 Bridge deck point calculations
18.6 Precast segmental bridge geometry control
         18.6.1 Basics
                     18.6.1.1 Long-line casting and short-line casting
                     18.6.1.2 Final curve and theoretical casting curve
                     18.6.1.3 Casting segment and match cast segment
         18.6.2 Casting and matching
         18.6.3 Control points and transformation
         18.6.4 Procedures of casting and control
         18.6.5 Error finding and correction
         18.6.6 Evolution of geometry control in precast segmental bridge
         18.6.7 Geometry transformation
                     18.6.7.1 Direction cosines
                     18.6.7.2 Direction cosines matrix of a local coordinate system
                     18.6.7.3 Transformation between two coordinate systems
                     18.6.7.4 Definition of the casting system in global system
         18.6.8 An example of short-line match casting geometry control
18.7 Trend of bridge computer modeling and visualization

References

Index