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Seismic Design Aids for Nonlinear Pushover Analysis of Reinforced Concrete and Steel Bridges

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Chapter 1 describes the evolution of seismic bridge design codes in the United States over the past 70 years and includes a comparison between force-based and displacement-based  design  approaches.  Regardless  of  the  design  approach  being used, it demonstrates the importance of using pushover analysis for seismic bridge design and retrofitting evaluation. Chapter 2 summarizes the application of pushover analysis in force-based bridge design as well as in displacement-based seismic bridge design. Other applications such as capacity/demand analysis for the evaluation of existing bridges, quantitative bridge redundancy evaluation, moment–curvature analysis, and estimation of inelastic response demand for buildings are also described in this chapter. Nonlinear  pushover  analysis  procedure  is  described  in  Chapter  3. 

 The  flowchart for structural modeling and the procedures for solutions SOL01 and SOL04 are described. Material and element libraries are provided, including 12 material and  7  element  types.  The  material  library  covers  elastic  material  and  hysteresis models  of  bilinear,  Takeda,  gap/restrainer,  hinge,  interaction  axial  load–moment, finite-segment (steel), finite-segment (reinforced concrete), FSMC, plate, point, and brace materials. The element library includes elastic three-dimensional (3D) beam, spring, inelastic 3D beam, finite-segment, plate, point, and brace elements. The nonlinear bending stiffness matrix formulations for reinforced concrete members are described in Chapter 4, including the above-mentioned FSFS, FSMC, PM, CMR, and PHL methods. Since most bridge columns in the United States are reinforced concrete columns, it is necessary to check all the possible concrete column failure modes in the pushover analysis. Possible concrete column failure modes include 

1. Compression failure of unconfined concrete due to fracture of transverse reinforcement 

2. Compression  failure  of  confined  concrete  due  to  fracture  of  transverse reinforcement 

3. Compression failure due to buckling of the longitudinal reinforcement

 4. Longitudinal tensile fracture of reinforcing bars

 5. Low cycle fatigue of the longitudinal reinforcement

 6. Failure in the lap-splice zone

 7. Shear failure of the member that limits ductile behavior 

8. Failure of the beam–column connection joint INSTRUCT is capable of checking all the possible concrete column failure modes. The approaches used to check individual failure modes are also described in this chapter. Chapter 5 describes how to combine bending, shear, axial, and torsional stiffnesses to form the 3D element stiffness matrices for bridge columns and cap beams

The stiffness matrix formulation for other elements such as brace and plate elements  is  introduced  in  this  chapter.  Once  all  the  element  stiffness  matrices  are formulated,  a  3D  structural  system  subjected  to  both  static  and  nonlinear  pushover loadings can be analyzed. The definitions of structural joints and degrees of freedom (dofs), including free, restrained, condensed, or constrained dofs, are also described in detail. Chapter  6  contains  detailed  input  data  instructions. 

 The  modular  form  of INSTRUCT allows the addition of new materials and/or new elements into the program depending on future needs. The structural analysis adopted in the program is based on the matrix method. The system formulation in INSTRUCT has the following attributes: (1) joint-based degrees of freedom, (2) rigid body and planar constraints, (3) material and geometric stiffness matrix formulation, and (4) unbalanced load correction.

 INSTRUCT has been developed to achieve efficiency in both computation and data preparation. The output solutions include the results of joint forces and displacements, member forces and deformations, member ductility factors, and structural  displacement  capacities  corresponding  to  different  performance-based limit states.

 Chapter 7 provides 13 numerical examples to illustrate the preparation of input data and the output solutions for the bridge pushover analysis of reinforced concrete and steel bridge bents. Most examples provide a comparison between the numerical results and available experimental test results.

 Many existing steel diaphragms (cross frames) in steel or prestressed concrete girder bridges were not designed for high seismic loads, and the inelastic buckling of brace members could occur when subjected to lateral loads. For steel pile cap bents, the steel piles may develop plastic hinges and the diagonal brace members may buckle due to lateral seismic load.

 As shown in some of the examples, INSTRUCT is capable of performing pushover analysis for steel pile cap bents and steel diaphragms, with consideration of postbuckling effects of steel members. 

The majority of the mathematic derivations for the nonlinear stiffness matrices of  various  structural  elements,  nonlinear  member  cross-sectional  properties,  and different numerical analyses described in this book are included in Appendices A through E, I, and J. Although this book is mainly for readers who have fundamental earthquake engineering and structural dynamics background, Appendices F through H provide structural engineers with basic knowledge of dynamic analysis of structures, including elastic and inelastic time history analyses, damped free vibration, damped vibration with dynamic force, the development elastic and inelastic response spectra, equivalent viscous damping, and the response spectrum analysis of the multiple-degrees-of-freedom system. The  photo  shown  on  the  book  cover  is  of  the  Tanana  River  Bridge  near  Tok, Alaska, which was one of the first bridges in Alaska designed using the AASHTO Guide  Specifications  for  LRFD  Seismic  Bridge  Design (AASHTO,  2009)  and pushover analysis to ensure that the displacement capacities of individual piers are greater than the corresponding seismic displacement demands.