Earthquake Engineering - Vol 1 | 6. Equations of Motion of SDOF System for Mass as well as Base Excitation by Abraham | Learn Smarter
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6. Equations of Motion of SDOF System for Mass as well as Base Excitation

6. Equations of Motion of SDOF System for Mass as well as Base Excitation

The chapter emphasizes the analysis of dynamic responses in Single Degree of Freedom (SDOF) systems, which are essential for understanding structural behavior during seismic events. Key concepts include equations of motion for mass and base excitation, free and forced vibrations, and the impact of damping on seismic response. The chapter also covers practical considerations in earthquake engineering and highlights the significance of using SDOF models in designing resilient structures.

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Sections

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  1. 6
    Equations Of Motion Of Sdof System For Mass As Well As Base Excitation

    This section discusses the equations of motion for single degree of freedom...

  2. 6.1
    Single Degree Of Freedom (Sdof) System – An Overview

    The Single Degree of Freedom (SDOF) System is a fundamental mechanical model...

  3. 6.2
    Free Vibration Of Undamped Sdof System

    This section discusses the free vibration of an undamped Single Degree of...

  4. 6.3
    Free Vibration Of Damped Sdof System

    This section discusses the free vibration response of a damped Single Degree...

  5. 6.4
    Forced Vibration Due To External Force (Mass Excitation)

    This section discusses the equations of motion for a Single Degree of...

  6. 6.4.1
    Equation Of Motion For External Force

    This section presents the equation of motion for an SDOF system subjected to...

  7. 6.4.2
    Response To Harmonic Loading

    This section discusses the response of a Single Degree of Freedom (SDOF)...

  8. 6.5
    Seismic Excitation As Base Motion

    This section covers the concept of seismic excitation, particularly how...

  9. 6.5.1
    Concept Of Base Excitation

    The section introduces base excitation, focusing on how ground motion...

  10. 6.6
    Derivation Of Equation Of Motion For Base Excitation

    This section covers the derivation of the equation of motion for a Single...

  11. 6.6.1
    Free Body Diagram Analysis

    This section focuses on the analysis of free body diagrams in the context of...

  12. 6.7
    Absolute Vs Relative Motion

    This section explains the distinction between absolute and relative motion...

  13. 6.8
    Solution Approaches For Base Excitation Problems

    This section discusses various solution approaches for analyzing base...

  14. 6.8.1
    Duhamel’s Integral

    Duhamel’s Integral provides a method for analyzing the response of linear...

  15. 6.8.2
    Numerical Methods

    This section covers numerical methods used to solve equations of motion in...

  16. 6.9
    Response Spectra Concept

    The Response Spectra Concept describes the peak response of a Single Degree...

  17. 6.10
    Comparison: Mass Vs Base Excitation

    This section contrasts mass and base excitation, highlighting their...

  18. 6.11
    Practical Considerations In Earthquake Engineering

    This section emphasizes the importance of accurate damping estimation,...

  19. 6.12
    Idealization Of Structures As Sdof Systems

    This section explains the idealization of complex multi-degree-of-freedom...

  20. 6.12.1
    Criteria For Idealization

    This section outlines the criteria essential for idealizing complex...

  21. 6.12.2
    Lumped Mass Idealization

    The lumped mass idealization involves concentrating mass onto specific floor...

  22. 6.12.3
    Translational Vs Rotational Sdof

    This section differentiates between translational and rotational Single...

  23. 6.13
    Effect Of Damping On Seismic Response

    Damping significantly reduces the amplitude of oscillations during seismic...

  24. 6.13.1
    Typical Damping Values

    This section outlines the typical damping ratios for various structural...

  25. 6.13.2
    Hysteretic Damping

    Hysteretic damping results from inelastic deformations in materials and is...

  26. 6.14
    Role Of Initial Conditions In Sdof Response

    This section highlights how initial conditions, specifically initial...

  27. 6.15
    Design Implications Based On Sdof Seismic Response

    This section discusses how understanding SDOF system behavior under seismic...

  28. 6.15.1
    Determination Of Design Base Shear

    The section discusses the crucial concept of determining the design base...

  29. 6.15.2
    Ductility Demand

    Ductility demand measures the extent a structure can deform without failure,...

  30. 6.16
    Influence Of Ground Motion Characteristics

    Ground motion characteristics significantly influence the equation of motion...

  31. 6.16.1
    Peak Ground Acceleration (Pga)

    Peak Ground Acceleration (PGA) is a crucial parameter in evaluating the...

  32. 6.16.2
    Duration Of Motion

    This section emphasizes the significance of motion duration on structural...

  33. 6.16.3
    Frequency Content And Resonance

    This section focuses on how the frequency content of seismic ground motion...

  34. 6.17
    Limitations Of Sdof Modeling

    SDOF models effectively simplify dynamic analysis but have significant...

  35. 6.18
    Advanced Concepts Linked To Sdof Systems

    This section covers advanced concepts related to Single Degree of Freedom...

  36. 6.18.1
    Response History Analysis

    This section discusses the response history analysis of Single Degree of...

  37. 6.18.2
    Incremental Dynamic Analysis (Ida)

    Incremental Dynamic Analysis (IDA) involves subjecting SDOF models to scaled...

  38. 6.18.3
    Base Isolation And Tuned Mass Dampers

    This section discusses base isolation systems and tuned mass dampers as...

  39. 6.19
    Application In Earthquake-Resistant Design

    This section discusses the application of Single Degree of Freedom (SDOF)...

What we have learnt

  • An SDOF system can effectively represent the dynamic behavior of structures under seismic loads.
  • Damping significantly influences the performance of a structure during an earthquake.
  • Effective seismic design incorporates understanding of both mass and base excitation.

Key Concepts

-- Single Degree of Freedom (SDOF) System
A mechanical system characterized by a single coordinate to describe motion, involving mass, spring, and damper.
-- Damping Ratio (ζ)
A dimensionless measure that describes how oscillations in a system decay after a disturbance, affecting energy dissipation.
-- Free Vibration
The oscillation of a mechanical system without external forces, described by its natural frequency.
-- Base Excitation
A condition in which the ground motion affects a structure at its base, applying forces indirectly rather than directly on the mass.

Additional Learning Materials

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