Investigation of the structural response of the groot Olifants River bridge to seismic excitation.

I. SINGLE-DEGREE-OF-FREEDOM SYSTEMS. 1. Equations of Motion, Problem Statement, and Solution Methods. Simple Structures. Single-Degree-of-Freedom System. Force-Displacement Relation. Damping Force. Equation of Motion: External Force. Mass-Spring-Damper System. Equation of Motion: Earthquake Excitation. Problem Statement and Element Forces. Combining Static and Dynamic Responses. Methods of Solution of the Differential Equation. Study of SDF Systems: Organization. Appendix 1: Stiffness Coefficients for a Flexural Element. 2. Free Vibration. Undamped Free Vibration. Viscously Damped Free Vibration. Energy in Free Vibration. Coulomb-Damped Free Vibration. 3. Response to Harmonic and Periodic Excitations. Viscously Damped Systems: Basic Results. Harmonic Vibration of Undamped Systems. Harmonic Vibration with Viscous Damping. Viscously Damped Systems: Applications. Response to Vibration Generator. Natural Frequency and Damping from Harmonic Tests. Force Transmission and Vibration Isolation. Response to Ground Motion and Vibration Isolation. Vibration-Measuring Instruments. Energy Dissipated in Viscous Damping. Equivalent Viscous Damping. Systems with Nonviscous Damping. Harmonic Vibration with Rate-Independent Damping. Harmonic Vibration with Coulomb Friction. Response to Periodic Excitation. Fourier Series Representation. Response to Periodic Force. Appendix 3: Four-Way Logarithmic Graph Paper. 4. Response to Arbitrary, Step, and Pulse Excitations.Response to Arbitrarily Time-Varying Forces. Response to Unit Impulse. Response to Arbitrary Force. Response to Step and Ramp Forces. Step Force. Ramp or Linearly Increasing Force. Step Force with Finite Rise Time. Response to Pulse Excitations. Solution Methods. Rectangular Pulse Force. Half-Cycle Sine Pulse Force. Symmetrical Triangular Pulse Force. Effects of Pulse Shape and Approximate Analysis for Short Pulses. Effects of Viscous Damping. Response to Ground Motion. 5. Numerical Evaluation of Dynamic Response. Time-Stepping Methods. Methods Based on Interpolation of Excitation. Central Difference Method. Newmark's Method. Stability and Computational Error. Analysis of Nonlinear Response: Central Difference Method. Analysis of Nonlinear Response: Newmark's Method. 6. Earthquake Response of Linear Systems. Earthquake Excitation. Equation of Motion. Response Quantities. Response History. Response Spectrum Concept. Deformation, Pseudo-Velocity, and Pseudo-Acceleration Response Spectra. Peak Structural Response from the Response Spectrum. Response Spectrum Characteristics. Elastic Design Spectrum. Comparison of Design ad Response Spectra. Distinction between Design and Response Spectra. Velocity and Acceleration Response Spectra. Appendix 6: El Centro, 1940 Ground Motion. 7. Earthquake Response of Inelastic Systems. Force-Deformation Relations. Normalized Yield Strength, Yield Strength Reduction Factor, and Ductility Factor. Equation of Motion and Controlling Parameters. Effects of Yielding. Response Spectrum for Yield Deformation and Yield Strength. Yield Strength and Deformation from the Response Spectrum. Yield Strength-Ductility Relation. Relative Effects of Yielding and Damping. Dissipated Energy. Energy Dissipation Devices. Inelastic Design Spectrum. Applications of the Design Spectrum. Comparison of Design and Response Spectra. 8. Generalized Single-Degree-of-Freedom Systems. Generalized SDF Systems. Rigid-Body Assemblages. Systems with Distributed Mass and Elasticity. Lumped-Mass System: Shear Building. Natural Vibration Frequency by Rayleigh's Method. Selection of Shape Function. Appendix 8: Inertia Forces for Rigid Bodies. II. MULTI-DEGREE-OF-FREEDOM SYSTEMS. 9. Equations of Motion, Problem Statement, and Solution Methods. Simple System: Two-Story Shear Building. General Approach for Linear Systems. Static Condensation. Planar or Symmetric-Plan Systems: Ground Motion. Unsymmetric-Plan Building: Ground Motion. Symmetric-Plan Buildings: Torsional Excitation. Multiple Support Excitation. Inelastic Systems. Problem Statement. Element Forces. Methods for Solving the Equations of Motion: Overview. 10. Free Vibration. Natural Vibration Frequencies and Modes. Systems without Damping. Natural Vibration Frequencies and Modes. Modal and Spectral Matrices. Orthogonality of Modes. Interpretation of Modal Orthogonality. Normalization of Modes. Modal Expansion of Displacements. Free Vibration Response. Solution of Free Vibration Equations: Undamped Systems. Free Vibration of Systems with Damping. Solution of Free Vibration Equations: Classically Damped Systems. Computation of Vibration Properties. Solution Methods for the Eigenvalue Problem. Rayleigh's Quotient. Inverse Vector Iteration Method. Vector Iteration with Shifts: Preferred Procedure. Transformation of kA A = ...w2mA A to the Standard Form. 11. Damping in Structures.Experimental Data and Recommended Modal Damping Ratios. Vibration Properties of Millikan Library Building. Estimating Modal Damping Ratios. Construction of Damping Matrix. Damping Matrix. Classical Damping Matrix. Nonclassical Damping Matrix. 12. Dynamic Analysis and Response of Linear Systems.Two-Degree-of-Freedom Systems. Analysis of Two-DOF Systems without Damping. Vibration Absorber or Tuned Mass Damper. Modal Analysis. Modal Equations for Undamped Systems. Modal Equations for Damped Systems. Displacement Response. Element Forces. Modal Analysis: Summary. Modal Response Contributions. Modal Expansion of Excitation Vector p (t) = s p(T). Modal Analysis for p (t) = s p(T). Modal Contribution Factors. Modal Responses and Required Number of Modes. Special Analysis Procedures. Static Correction Method. Mode Acceleration Superposition Method. Analysis of Nonclassically Damped Systems. 13. Earthquake Analysis of Linear Systems.Response History Analysis. Modal Analysis. Multistory Buildings with Symmetric Plan. Multistory Buildings with Unsymmetric Plan. Torsional Response of Symmetric-Plan Buildings. Response Analysis for Multiple Support Excitation. Structural Idealization and Earthquake Response. Response Spectrum Analysis. Peak Response from Earthquake Response Spectrum. Multistory Buildings with Symmetric Plan. Multistory Buildings with Unsymmetric Plan. 14. Reduction of Degrees of Freedom. Kinematic Constraints. Mass Lumping in Selected DOFs. Rayleigh-Ritz Method. Selection of Ritz Vectors. Dynamic Analysis Using Ritz Vectors. 15. Numerical Evaluation of Dynamic Response. Time-Stepping Methods. Analysis of Linear Systems with Nonclassical Damping. Analysis of Nonlinear Systems. 16. Systems with Distributed Mass and Elasticity. Equation of Undamped Motion: Applied Forces. Equation of Undamped Motion: Support Excitation. Natural Vibration Frequencies and Modes. Modal Orthogonality. Modal Analysis of Forced Dynamic Response. Earthquake Response History Analysis. Earthquake Response Spectrum Analysis. Difficulty in Analyzing Practical Systems. 17. Introduction to the Finite Element Method.Rayleigh-Ritz Method. Formulation Using Conservation of Energy. Formulation Using Virtual Work. Disadvantages of Rayleigh-Ritz Method. Finite Element Method. Finite Element Approximation. Analysis Procedure. Element Degrees of Freedom and Interpolation Function. Element Stiffness Matrix. Element Mass Matrix. Element (Applied) Force Vector. Comparison of Finite Element and Exact Solutions. Dynamic Analysis of Structural Continua. III. EARTHQUAKE RESPONSE AND DESIGN OF MULTISTORY BUILDINGS. 18. Earthquake Response of Linearly Elastic Buildings. Systems Analyzed, Design Spectrum, and Response Quantities. Influence of T 1 and r on Response. Modal Contribution Factors. Influence of T 1 on Higher-Mode Response. Influence of r on Higher-Mode Response. Heightwise Variation of Higher-Mode Response. How Many Modes to Include. 19. Earthquake Response of Inelastic Buildings. Allowable Ductility and Ductility Demand. Buildings with "Weak" or "Soft" First Story. Buildings Designed for Code Force Distribution. Limited Scope. Appendix 19: Properties of Multistory Buildings. 20. Earthquake Dynamics of Base-Isolated Buildings. Isolation Systems. Base-Isolated One-Story Buildings. Effectiveness of Base Isolation. Base-Isolated Multistory Buildings. Applications of Base Isolation. 21. Structural Dynamics in Building Codes. Building Codes and Structural Dynamics. International Building Code (United States), 2000. National Building Code of Canada, 1995. Mexico Federal District Code, 1993. Eurocode 8. Structural Dynamics in Building Codes. Evaluation of Building Codes. Base Shear. Story Shears and Equivalent Static Forces. Overturning Moments. Concluding Remarks. Appendix A: Frequency Domain Method of Response Analysis.Appendix B: Notation.Appendix C: Answers to Selected Problems.Index.

Dynamics of Structures: Theory and Applications to Earthquake Engineering

Aspects relating to the shear strength of circular and rectangular columns under seismic loading are presented An examination of existing design equations reveals wide differences in predicted responses Particular emphasis is placed on models capable of representing the interaction between flexural ductility and shear strength A simple method is proposed whereby the strength enhancement provided by axial compression is separated from the concrete component of shear strength and considered to result from arch action The strength of the concrete component is reduced as flexural displacement ductility increases Prediction of shear strength from the proposed and alternative methods are compared with results from a wide range of tests of columns failing in shear The proposed method is shown to provide significantly improved correlation with experimental results Conservative modifications are made to enable the method to be used for design

Seismic Shear Strength of Reinforced Concrete Columns

Digital image correlation technique is used for measuring vertical deflections of bridge girders during a bridge load testing. A bridge is loaded by a heavy cargo truck on the bridge road. Then, the deflection distribution is measured by digital image correlation. The applicability of digital image correlation to bridge deflection measurement is investigated by comparing the results obtained by digital image correlation with those obtained by displacement transducers. The effect of random pattern on an object surface is also investigated by measuring with and without random pattern. The results show that the deflection distributions of the bridge obtained by digital image correlation agree well with those obtained by the displacement transducers when the random pattern is attached on the bridge surface. In addition, it is found that the deflections can be measured even if the artificial random pattern is not applied to the surface of the bridge girder. It is emphasized that noncontact displacement measurement is possible by simple and easy procedure with digital image correlation for the structural evaluation of infrastructures.

Bridge deflection measurement using digital image correlation

This paper presents a procedure for the evaluation of the expected seismic damage to bridges and highway systems in Memphis and Shelby County, Tenn. Data pertinent to 452 bridges and major arterial routes were collected and implemented as a geographic information system database. The bridges were classified into several bridge types using a bridge classification system modified from the NBIS/Federal Highway Administration coding guidelines. The bridge damage states considered are no/minor damage, repairable damage, and significant damage. The fragility curves corresponding to these damage states were established for various bridge types. Given an earthquake with a moment magnitude of 7.0 occurring at Marked Tree, Ark., the intensity of ground shaking and liquefaction-induced permanent ground deformation in Memphis and Shelby County were estimated, and then the expected damage to bridges and highway systems was determined. The results can be used to prioritize bridges for retrofitting, to prepare a pre-earthquake preparedness plan, to develop a postearthquake emergency response plan, and to assess the regional economic impact from the damage to highway transportation systems.

Evaluation of Seismic Damage to Memphis Bridges and Highway Systems

The paper presents the experimental and analytical modal analysis of a steel-girder arch bridge. The field test is carried out by ambient vibration testing under traffic and wind-induced excitations. Both the peak picking method in the frequency domain and the stochastic subspace identification method in the time domain are used for the output-only modal identification. A good agreement in identified frequencies has been found between the two methods. It is further demonstrated that the stochastic subspace identification method provides better mode shapes. The three-dimensional finite element models are constructed and an analytical modal analysis is then performed to generate natural frequencies and mode shapes in the three-orthogonal directions. The finite element models are validated to match the field natural frequencies and mode shapes. It is observed that the finite element Model-2 with the concrete slab provides the greater stiffness in the transverse direction of the bridge. The finite element Model-1 with the lumped masses agrees well with the field tests and can serve as a baseline model of the bridge. DOI: 10.1061/~ASCE!0733-9445~2004!130:7~1022! CE Database subject headings: Modal analysis; Model tests; Experimentation; Vibration; Bridges, steel; Bridges, arch.

Investigation of the structural response of the groot Olifants River bridge to seismic excitation.

References

Dynamics of Structures: Theory and Applications to Earthquake Engineering

Seismic Shear Strength of Reinforced Concrete Columns

Bridge deflection measurement using digital image correlation

Evaluation of Seismic Damage to Memphis Bridges and Highway Systems

Experimental and Analytical Modal Analysis of Steel Arch Bridge