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DRPS : Course Catalogue : School of Engineering : Postgrad (School of Engineering)

Postgraduate Course: Structural Dynamics and Earthquake Engineering (PGEE11051)

Course Outline
SchoolSchool of Engineering CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityNot available to visiting students
SCQF Credits10 ECTS Credits5
SummaryStructures are often subjected to dynamic forces of one form or the other during their lifetime. This course introduces the theory of dynamic response of structures with emphasis on physical insight into the analytical procedures and with particular application to earthquake engineering. The structural dynamics component of the course includes free and forced vibration response of single and multi-degree of freedom systems. The earthquake engineering component considers seismic analysis methods, earthquake resistant design philosophy and includes elements of engineering seismology.
Course description Lectures - 2 hours per week; Tutorials - 1 hour per week

Lecture topics:

L1 Vibrations in Structures
Sources and classification of dynamic loads; basic definitions; structure idealisation.
L2 Equation of motion of SDOF Systems
Inertia, damping and elastic resistance forces on a vibrating SDOF (single degree of freedom) system; establishment of the general equation of motion for a SDOF system including situations of base excitation; deduction of the free vibration equation of motion from the general one.
L3 Free Vibration Response of SDOF Systems: 1
Characteristic equation for free vibrations; response evaluation for undamped free vibrations with examples; natural frequency and period; damped free vibrations; overdamped, critically damped and underdamped systems with examples.
L4 Free Vibration Response of SDOF Systems: 2
Different forms for expressing the response of underdamped systems; concept of damping ratio;
response of underdamped systems to initial conditions with examples; logarithmic decrement.
L5 Response of SDOF systems subjected dynamic forces
Solution of equations of motion under forced vibration - homogeneous and particular solutions; method of undetermined coefficients for evaluating the particular integral; response of an underdamped system to linearly varying forces.
L6 Response of SDOF systems to harmonic loading
Derivation of the response of a damped system subjected to harmonic excitation; special case of undamped system subjected to harmonic excitation when the exciting frequency equals the natural frequency; transient and steady state response; dynamic amplification under harmonic excitation; resonance; phase lag.
L7 Response of SDOF systems to impulsive and arbitrary loading: 1
Response of SDOF systems to step loading and load amplification; response to rectangular loading and variation of response for loads of different durations; examples; response to a triangular loading;
L8 Response of SDOF systems to impulsive and arbitrary loading: 2
Response of undamped SDOF systems to impulse loading; response of damped and undamped SDOF systems to an impulse; examples; analysis of SDOF systems under general dynamic loading - Duhamel integral; examples.
L9 MDOF systems: 1
Introduction to the analysis of simple multi-degree of freedom (MDOF) dynamic systems; equations of motion.
L10 MDOF systems: 2
Analysis of vibration frequencies with examples;
analysis of vibration modes with examples; orthogonality of vibration modes derivation and examples.
L11 MDOF systems: 3
Practical evaluation of vibration modes; description of the free vibration response of complex MDOF systems; examples; introduction to dynamic response of MDOF systems under forced vibration.
L12 Lessons from past earthquakes
Different types of damage caused by earthquakes; typical planning and design weaknesses; design details that can prevent damage to low-rise structures; non-engineered construction.
L13 Seismology
Causes of earthquakes; seismic waves; focus, magnitude and intensity; terms used in seismology; role of a seismologist and an earthquake engineer; characteristics of strong ground motions; translational and rotational components of ground motions; introduction to earthquake measuring instruments.
L14 Response spectrum: 1
Response of SDOF systems to earthquake excitation; response quantities of interest; response history. The concept of response spectrum; deformation, pseudo-velocity and pseudo-acceleration response spectra.
L15 Response spectrum: 2
Combined D-V-A spectrum; construction of response spectrum; response spectrum characteristics; elastic design spectrum; difference between response and design spectra; design spectra in codes; peak structural response from the response spectrum; examples.
L16 Earthquake response analysis: 1
Concept of mode superposition analysis; generalized mass stiffness and force; uncoupled equations of motion.
L17 Earthquake response analysis: 2
Mode superposition analysis; modal expansion of earthquake excitation vector; examples.
L18 Earthquake response analysis: 3
Response/design spectrum analysis; combination of peak modal responses; examples.
L19 Earthquake response analysis: 4
Direct integration methods of analysis; example.
L20 Earthquake codes
Earthquake design philosophy; simplified design procedures.
L21 Revision

Tutorial Topics:

- Formulating equations of motion
- Free vibration analysis of SDOF systems
- Response of SDOF systems to harmonic loadings
- Response of SDOF systems to impulsive and arbitrary loadings
- Free vibration analysis of MDOF systems
- Response spectrum and earthquake response analysis of SDOF systems
- Earthquake response analysis of MDOF systems
- Time history analysis
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Other requirements None
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  1. Derive differential equations for single degree of freedom (SDOF) systems and for multi-degree of freedom systems (MDOF) and evaluate their free vibration characteristics.
  2. Evaluate the response of SDOF and MDOF systems subjected to forced vibrations.
  3. Identify the possible causes of failure in a poorly designed structures subjected to earthquake loading.
  4. Describe basic concepts of engineering seismology.
  5. Describe the construction of response/design spectra and be able to apply these for seismic analysis.
Reading List
Anil K. Chopra - Dynamics of Structures: Theory and Application to Earthquake Engineering, Prentice Hall.

Ray W. Clough and Joseph Penzien Dynamics of Structures, McGraw Hill.

R.R. Craig - Structural Dynamics, John Wiley.

G.B. Warburton - Dynamical Behaviour of Structures, Pergamon Press.
Additional Information
Graduate Attributes and Skills Not entered
KeywordsStructural dynamics,Earthquake,seismic analysis of structures
Course organiserDr Pankaj Pankaj
Tel: (0131 6)50 5800
Course secretaryMiss Margaret Robertson
Tel: (0131 6)50 5565
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